1,1,81,0,0.0350419,"\int \log ^4(c (d+e x)) \, dx","Int[Log[c*(d + e*x)]^4,x]","\frac{(d+e x) \log ^4(c (d+e x))}{e}-\frac{4 (d+e x) \log ^3(c (d+e x))}{e}+\frac{12 (d+e x) \log ^2(c (d+e x))}{e}-\frac{24 (d+e x) \log (c (d+e x))}{e}+24 x","\frac{(d+e x) \log ^4(c (d+e x))}{e}-\frac{4 (d+e x) \log ^3(c (d+e x))}{e}+\frac{12 (d+e x) \log ^2(c (d+e x))}{e}-\frac{24 (d+e x) \log (c (d+e x))}{e}+24 x",1,"24*x - (24*(d + e*x)*Log[c*(d + e*x)])/e + (12*(d + e*x)*Log[c*(d + e*x)]^2)/e - (4*(d + e*x)*Log[c*(d + e*x)]^3)/e + ((d + e*x)*Log[c*(d + e*x)]^4)/e","A",5,3,10,0.3000,1,"{2389, 2296, 2295}"
2,1,61,0,0.0266686,"\int \log ^3(c (d+e x)) \, dx","Int[Log[c*(d + e*x)]^3,x]","\frac{(d+e x) \log ^3(c (d+e x))}{e}-\frac{3 (d+e x) \log ^2(c (d+e x))}{e}+\frac{6 (d+e x) \log (c (d+e x))}{e}-6 x","\frac{(d+e x) \log ^3(c (d+e x))}{e}-\frac{3 (d+e x) \log ^2(c (d+e x))}{e}+\frac{6 (d+e x) \log (c (d+e x))}{e}-6 x",1,"-6*x + (6*(d + e*x)*Log[c*(d + e*x)])/e - (3*(d + e*x)*Log[c*(d + e*x)]^2)/e + ((d + e*x)*Log[c*(d + e*x)]^3)/e","A",4,3,10,0.3000,1,"{2389, 2296, 2295}"
3,1,41,0,0.0184991,"\int \log ^2(c (d+e x)) \, dx","Int[Log[c*(d + e*x)]^2,x]","\frac{(d+e x) \log ^2(c (d+e x))}{e}-\frac{2 (d+e x) \log (c (d+e x))}{e}+2 x","\frac{(d+e x) \log ^2(c (d+e x))}{e}-\frac{2 (d+e x) \log (c (d+e x))}{e}+2 x",1,"2*x - (2*(d + e*x)*Log[c*(d + e*x)])/e + ((d + e*x)*Log[c*(d + e*x)]^2)/e","A",3,3,10,0.3000,1,"{2389, 2296, 2295}"
4,1,21,0,0.0080155,"\int \log (c (d+e x)) \, dx","Int[Log[c*(d + e*x)],x]","\frac{(d+e x) \log (c (d+e x))}{e}-x","\frac{(d+e x) \log (c (d+e x))}{e}-x",1,"-x + ((d + e*x)*Log[c*(d + e*x)])/e","A",2,2,8,0.2500,1,"{2389, 2295}"
5,1,15,0,0.0092104,"\int \frac{1}{\log (c (d+e x))} \, dx","Int[Log[c*(d + e*x)]^(-1),x]","\frac{\text{li}(c (d+e x))}{c e}","\frac{\text{li}(c (d+e x))}{c e}",1,"LogIntegral[c*(d + e*x)]/(c*e)","A",2,2,10,0.2000,1,"{2389, 2298}"
6,1,36,0,0.0154824,"\int \frac{1}{\log ^2(c (d+e x))} \, dx","Int[Log[c*(d + e*x)]^(-2),x]","\frac{\text{li}(c (d+e x))}{c e}-\frac{d+e x}{e \log (c (d+e x))}","\frac{\text{li}(c (d+e x))}{c e}-\frac{d+e x}{e \log (c (d+e x))}",1,"-((d + e*x)/(e*Log[c*(d + e*x)])) + LogIntegral[c*(d + e*x)]/(c*e)","A",3,3,10,0.3000,1,"{2389, 2297, 2298}"
7,1,63,0,0.024063,"\int \frac{1}{\log ^3(c (d+e x))} \, dx","Int[Log[c*(d + e*x)]^(-3),x]","\frac{\text{li}(c (d+e x))}{2 c e}-\frac{d+e x}{2 e \log ^2(c (d+e x))}-\frac{d+e x}{2 e \log (c (d+e x))}","\frac{\text{li}(c (d+e x))}{2 c e}-\frac{d+e x}{2 e \log ^2(c (d+e x))}-\frac{d+e x}{2 e \log (c (d+e x))}",1,"-(d + e*x)/(2*e*Log[c*(d + e*x)]^2) - (d + e*x)/(2*e*Log[c*(d + e*x)]) + LogIntegral[c*(d + e*x)]/(2*c*e)","A",4,3,10,0.3000,1,"{2389, 2297, 2298}"
8,1,85,0,0.032716,"\int \frac{1}{\log ^4(c (d+e x))} \, dx","Int[Log[c*(d + e*x)]^(-4),x]","\frac{\text{li}(c (d+e x))}{6 c e}-\frac{d+e x}{6 e \log ^2(c (d+e x))}-\frac{d+e x}{3 e \log ^3(c (d+e x))}-\frac{d+e x}{6 e \log (c (d+e x))}","\frac{\text{li}(c (d+e x))}{6 c e}-\frac{d+e x}{6 e \log ^2(c (d+e x))}-\frac{d+e x}{3 e \log ^3(c (d+e x))}-\frac{d+e x}{6 e \log (c (d+e x))}",1,"-(d + e*x)/(3*e*Log[c*(d + e*x)]^3) - (d + e*x)/(6*e*Log[c*(d + e*x)]^2) - (d + e*x)/(6*e*Log[c*(d + e*x)]) + LogIntegral[c*(d + e*x)]/(6*c*e)","A",5,3,10,0.3000,1,"{2389, 2297, 2298}"
9,1,98,0,0.0495554,"\int \log ^{\frac{5}{2}}(c (d+e x)) \, dx","Int[Log[c*(d + e*x)]^(5/2),x]","-\frac{15 \sqrt{\pi } \text{Erfi}\left(\sqrt{\log (c (d+e x))}\right)}{8 c e}+\frac{(d+e x) \log ^{\frac{5}{2}}(c (d+e x))}{e}-\frac{5 (d+e x) \log ^{\frac{3}{2}}(c (d+e x))}{2 e}+\frac{15 (d+e x) \sqrt{\log (c (d+e x))}}{4 e}","-\frac{15 \sqrt{\pi } \text{Erfi}\left(\sqrt{\log (c (d+e x))}\right)}{8 c e}+\frac{(d+e x) \log ^{\frac{5}{2}}(c (d+e x))}{e}-\frac{5 (d+e x) \log ^{\frac{3}{2}}(c (d+e x))}{2 e}+\frac{15 (d+e x) \sqrt{\log (c (d+e x))}}{4 e}",1,"(-15*Sqrt[Pi]*Erfi[Sqrt[Log[c*(d + e*x)]]])/(8*c*e) + (15*(d + e*x)*Sqrt[Log[c*(d + e*x)]])/(4*e) - (5*(d + e*x)*Log[c*(d + e*x)]^(3/2))/(2*e) + ((d + e*x)*Log[c*(d + e*x)]^(5/2))/e","A",7,5,12,0.4167,1,"{2389, 2296, 2299, 2180, 2204}"
10,1,74,0,0.037502,"\int \log ^{\frac{3}{2}}(c (d+e x)) \, dx","Int[Log[c*(d + e*x)]^(3/2),x]","\frac{3 \sqrt{\pi } \text{Erfi}\left(\sqrt{\log (c (d+e x))}\right)}{4 c e}+\frac{(d+e x) \log ^{\frac{3}{2}}(c (d+e x))}{e}-\frac{3 (d+e x) \sqrt{\log (c (d+e x))}}{2 e}","\frac{3 \sqrt{\pi } \text{Erfi}\left(\sqrt{\log (c (d+e x))}\right)}{4 c e}+\frac{(d+e x) \log ^{\frac{3}{2}}(c (d+e x))}{e}-\frac{3 (d+e x) \sqrt{\log (c (d+e x))}}{2 e}",1,"(3*Sqrt[Pi]*Erfi[Sqrt[Log[c*(d + e*x)]]])/(4*c*e) - (3*(d + e*x)*Sqrt[Log[c*(d + e*x)]])/(2*e) + ((d + e*x)*Log[c*(d + e*x)]^(3/2))/e","A",6,5,12,0.4167,1,"{2389, 2296, 2299, 2180, 2204}"
11,1,50,0,0.0313145,"\int \sqrt{\log (c (d+e x))} \, dx","Int[Sqrt[Log[c*(d + e*x)]],x]","\frac{(d+e x) \sqrt{\log (c (d+e x))}}{e}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\log (c (d+e x))}\right)}{2 c e}","\frac{(d+e x) \sqrt{\log (c (d+e x))}}{e}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\log (c (d+e x))}\right)}{2 c e}",1,"-(Sqrt[Pi]*Erfi[Sqrt[Log[c*(d + e*x)]]])/(2*c*e) + ((d + e*x)*Sqrt[Log[c*(d + e*x)]])/e","A",5,5,12,0.4167,1,"{2389, 2296, 2299, 2180, 2204}"
12,1,25,0,0.0219619,"\int \frac{1}{\sqrt{\log (c (d+e x))}} \, dx","Int[1/Sqrt[Log[c*(d + e*x)]],x]","\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\log (c (d+e x))}\right)}{c e}","\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\log (c (d+e x))}\right)}{c e}",1,"(Sqrt[Pi]*Erfi[Sqrt[Log[c*(d + e*x)]]])/(c*e)","A",4,4,12,0.3333,1,"{2389, 2299, 2180, 2204}"
13,1,49,0,0.0301805,"\int \frac{1}{\log ^{\frac{3}{2}}(c (d+e x))} \, dx","Int[Log[c*(d + e*x)]^(-3/2),x]","\frac{2 \sqrt{\pi } \text{Erfi}\left(\sqrt{\log (c (d+e x))}\right)}{c e}-\frac{2 (d+e x)}{e \sqrt{\log (c (d+e x))}}","\frac{2 \sqrt{\pi } \text{Erfi}\left(\sqrt{\log (c (d+e x))}\right)}{c e}-\frac{2 (d+e x)}{e \sqrt{\log (c (d+e x))}}",1,"(2*Sqrt[Pi]*Erfi[Sqrt[Log[c*(d + e*x)]]])/(c*e) - (2*(d + e*x))/(e*Sqrt[Log[c*(d + e*x)]])","A",5,5,12,0.4167,1,"{2389, 2297, 2299, 2180, 2204}"
14,1,77,0,0.038312,"\int \frac{1}{\log ^{\frac{5}{2}}(c (d+e x))} \, dx","Int[Log[c*(d + e*x)]^(-5/2),x]","\frac{4 \sqrt{\pi } \text{Erfi}\left(\sqrt{\log (c (d+e x))}\right)}{3 c e}-\frac{2 (d+e x)}{3 e \log ^{\frac{3}{2}}(c (d+e x))}-\frac{4 (d+e x)}{3 e \sqrt{\log (c (d+e x))}}","\frac{4 \sqrt{\pi } \text{Erfi}\left(\sqrt{\log (c (d+e x))}\right)}{3 c e}-\frac{2 (d+e x)}{3 e \log ^{\frac{3}{2}}(c (d+e x))}-\frac{4 (d+e x)}{3 e \sqrt{\log (c (d+e x))}}",1,"(4*Sqrt[Pi]*Erfi[Sqrt[Log[c*(d + e*x)]]])/(3*c*e) - (2*(d + e*x))/(3*e*Log[c*(d + e*x)]^(3/2)) - (4*(d + e*x))/(3*e*Sqrt[Log[c*(d + e*x)]])","A",6,5,12,0.4167,1,"{2389, 2297, 2299, 2180, 2204}"
15,1,101,0,0.0487596,"\int \frac{1}{\log ^{\frac{7}{2}}(c (d+e x))} \, dx","Int[Log[c*(d + e*x)]^(-7/2),x]","\frac{8 \sqrt{\pi } \text{Erfi}\left(\sqrt{\log (c (d+e x))}\right)}{15 c e}-\frac{4 (d+e x)}{15 e \log ^{\frac{3}{2}}(c (d+e x))}-\frac{2 (d+e x)}{5 e \log ^{\frac{5}{2}}(c (d+e x))}-\frac{8 (d+e x)}{15 e \sqrt{\log (c (d+e x))}}","\frac{8 \sqrt{\pi } \text{Erfi}\left(\sqrt{\log (c (d+e x))}\right)}{15 c e}-\frac{4 (d+e x)}{15 e \log ^{\frac{3}{2}}(c (d+e x))}-\frac{2 (d+e x)}{5 e \log ^{\frac{5}{2}}(c (d+e x))}-\frac{8 (d+e x)}{15 e \sqrt{\log (c (d+e x))}}",1,"(8*Sqrt[Pi]*Erfi[Sqrt[Log[c*(d + e*x)]]])/(15*c*e) - (2*(d + e*x))/(5*e*Log[c*(d + e*x)]^(5/2)) - (4*(d + e*x))/(15*e*Log[c*(d + e*x)]^(3/2)) - (8*(d + e*x))/(15*e*Sqrt[Log[c*(d + e*x)]])","A",7,5,12,0.4167,1,"{2389, 2297, 2299, 2180, 2204}"
16,1,45,0,0.0283106,"\int \log ^p(c (d+e x)) \, dx","Int[Log[c*(d + e*x)]^p,x]","\frac{(-\log (c (d+e x)))^{-p} \log ^p(c (d+e x)) \text{Gamma}(p+1,-\log (c (d+e x)))}{c e}","\frac{(-\log (c (d+e x)))^{-p} \log ^p(c (d+e x)) \text{Gamma}(p+1,-\log (c (d+e x)))}{c e}",1,"(Gamma[1 + p, -Log[c*(d + e*x)]]*Log[c*(d + e*x)]^p)/(c*e*(-Log[c*(d + e*x)])^p)","A",3,3,10,0.3000,1,"{2389, 2299, 2181}"
17,1,131,0,0.0738035,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^4 \, dx","Int[(a + b*Log[c*(d + e*x)^n])^4,x]","\frac{12 b^2 n^2 (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-24 a b^3 n^3 x-\frac{4 b n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^4}{e}-\frac{24 b^4 n^3 (d+e x) \log \left(c (d+e x)^n\right)}{e}+24 b^4 n^4 x","\frac{12 b^2 n^2 (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-24 a b^3 n^3 x-\frac{4 b n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^4}{e}-\frac{24 b^4 n^3 (d+e x) \log \left(c (d+e x)^n\right)}{e}+24 b^4 n^4 x",1,"-24*a*b^3*n^3*x + 24*b^4*n^4*x - (24*b^4*n^3*(d + e*x)*Log[c*(d + e*x)^n])/e + (12*b^2*n^2*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e - (4*b*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/e + ((d + e*x)*(a + b*Log[c*(d + e*x)^n])^4)/e","A",6,3,16,0.1875,1,"{2389, 2296, 2295}"
18,1,99,0,0.0532955,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \, dx","Int[(a + b*Log[c*(d + e*x)^n])^3,x]","6 a b^2 n^2 x-\frac{3 b n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}+\frac{6 b^3 n^2 (d+e x) \log \left(c (d+e x)^n\right)}{e}-6 b^3 n^3 x","6 a b^2 n^2 x-\frac{3 b n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}+\frac{6 b^3 n^2 (d+e x) \log \left(c (d+e x)^n\right)}{e}-6 b^3 n^3 x",1,"6*a*b^2*n^2*x - 6*b^3*n^3*x + (6*b^3*n^2*(d + e*x)*Log[c*(d + e*x)^n])/e - (3*b*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e + ((d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/e","A",5,3,16,0.1875,1,"{2389, 2296, 2295}"
19,1,65,0,0.0347364,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-2 a b n x-\frac{2 b^2 n (d+e x) \log \left(c (d+e x)^n\right)}{e}+2 b^2 n^2 x","\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-2 a b n x-\frac{2 b^2 n (d+e x) \log \left(c (d+e x)^n\right)}{e}+2 b^2 n^2 x",1,"-2*a*b*n*x + 2*b^2*n^2*x - (2*b^2*n*(d + e*x)*Log[c*(d + e*x)^n])/e + ((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e","A",4,3,16,0.1875,1,"{2389, 2296, 2295}"
20,1,29,0,0.0145399,"\int \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Int[a + b*Log[c*(d + e*x)^n],x]","a x+\frac{b (d+e x) \log \left(c (d+e x)^n\right)}{e}-b n x","a x+\frac{b (d+e x) \log \left(c (d+e x)^n\right)}{e}-b n x",1,"a*x - b*n*x + (b*(d + e*x)*Log[c*(d + e*x)^n])/e","A",3,2,14,0.1429,1,"{2389, 2295}"
21,1,63,0,0.0549784,"\int \frac{1}{a+b \log \left(c (d+e x)^n\right)} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(-1),x]","\frac{e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b e n}","\frac{e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b e n}",1,"((d + e*x)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)])/(b*e*E^(a/(b*n))*n*(c*(d + e*x)^n)^n^(-1))","A",3,3,16,0.1875,1,"{2389, 2300, 2178}"
22,1,96,0,0.0613845,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(-2),x]","\frac{e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b^2 e n^2}-\frac{d+e x}{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}","\frac{e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b^2 e n^2}-\frac{d+e x}{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}",1,"((d + e*x)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)])/(b^2*e*E^(a/(b*n))*n^2*(c*(d + e*x)^n)^n^(-1)) - (d + e*x)/(b*e*n*(a + b*Log[c*(d + e*x)^n]))","A",4,4,16,0.2500,1,"{2389, 2297, 2300, 2178}"
23,1,135,0,0.0812606,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^3} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(-3),x]","\frac{e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{2 b^3 e n^3}-\frac{d+e x}{2 b^2 e n^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}-\frac{d+e x}{2 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^2}","\frac{e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{2 b^3 e n^3}-\frac{d+e x}{2 b^2 e n^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}-\frac{d+e x}{2 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^2}",1,"((d + e*x)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)])/(2*b^3*e*E^(a/(b*n))*n^3*(c*(d + e*x)^n)^n^(-1)) - (d + e*x)/(2*b*e*n*(a + b*Log[c*(d + e*x)^n])^2) - (d + e*x)/(2*b^2*e*n^2*(a + b*Log[c*(d + e*x)^n]))","A",5,4,16,0.2500,1,"{2389, 2297, 2300, 2178}"
24,1,179,0,0.1476192,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(5/2),x]","-\frac{15 \sqrt{\pi } b^{5/2} n^{5/2} e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{8 e}+\frac{15 b^2 n^2 (d+e x) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{4 e}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{e}-\frac{5 b n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{2 e}","-\frac{15 \sqrt{\pi } b^{5/2} n^{5/2} e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{8 e}+\frac{15 b^2 n^2 (d+e x) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{4 e}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{e}-\frac{5 b n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{2 e}",1,"(-15*b^(5/2)*n^(5/2)*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(8*e*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + (15*b^2*n^2*(d + e*x)*Sqrt[a + b*Log[c*(d + e*x)^n]])/(4*e) - (5*b*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^(3/2))/(2*e) + ((d + e*x)*(a + b*Log[c*(d + e*x)^n])^(5/2))/e","A",7,5,18,0.2778,1,"{2389, 2296, 2300, 2180, 2204}"
25,1,143,0,0.1069016,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(3/2),x]","\frac{3 \sqrt{\pi } b^{3/2} n^{3/2} e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{4 e}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{e}-\frac{3 b n (d+e x) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{2 e}","\frac{3 \sqrt{\pi } b^{3/2} n^{3/2} e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{4 e}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{e}-\frac{3 b n (d+e x) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{2 e}",1,"(3*b^(3/2)*n^(3/2)*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(4*e*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) - (3*b*n*(d + e*x)*Sqrt[a + b*Log[c*(d + e*x)^n]])/(2*e) + ((d + e*x)*(a + b*Log[c*(d + e*x)^n])^(3/2))/e","A",6,5,18,0.2778,1,"{2389, 2296, 2300, 2180, 2204}"
26,1,111,0,0.0912926,"\int \sqrt{a+b \log \left(c (d+e x)^n\right)} \, dx","Int[Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\frac{(d+e x) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{e}-\frac{\sqrt{\pi } \sqrt{b} \sqrt{n} e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{2 e}","\frac{(d+e x) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{e}-\frac{\sqrt{\pi } \sqrt{b} \sqrt{n} e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{2 e}",1,"-(Sqrt[b]*Sqrt[n]*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(2*e*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + ((d + e*x)*Sqrt[a + b*Log[c*(d + e*x)^n]])/e","A",5,5,18,0.2778,1,"{2389, 2296, 2300, 2180, 2204}"
27,1,80,0,0.0734574,"\int \frac{1}{\sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Int[1/Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\frac{\sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e \sqrt{n}}","\frac{\sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e \sqrt{n}}",1,"(Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(Sqrt[b]*e*E^(a/(b*n))*Sqrt[n]*(c*(d + e*x)^n)^n^(-1))","A",4,4,18,0.2222,1,"{2389, 2300, 2180, 2204}"
28,1,116,0,0.1010955,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(-3/2),x]","\frac{2 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e n^{3/2}}-\frac{2 (d+e x)}{b e n \sqrt{a+b \log \left(c (d+e x)^n\right)}}","\frac{2 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e n^{3/2}}-\frac{2 (d+e x)}{b e n \sqrt{a+b \log \left(c (d+e x)^n\right)}}",1,"(2*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(b^(3/2)*e*E^(a/(b*n))*n^(3/2)*(c*(d + e*x)^n)^n^(-1)) - (2*(d + e*x))/(b*e*n*Sqrt[a + b*Log[c*(d + e*x)^n]])","A",5,5,18,0.2778,1,"{2389, 2297, 2300, 2180, 2204}"
29,1,156,0,0.1199513,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(-5/2),x]","\frac{4 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{3 b^{5/2} e n^{5/2}}-\frac{4 (d+e x)}{3 b^2 e n^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{2 (d+e x)}{3 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}","\frac{4 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{3 b^{5/2} e n^{5/2}}-\frac{4 (d+e x)}{3 b^2 e n^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{2 (d+e x)}{3 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}",1,"(4*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(3*b^(5/2)*e*E^(a/(b*n))*n^(5/2)*(c*(d + e*x)^n)^n^(-1)) - (2*(d + e*x))/(3*b*e*n*(a + b*Log[c*(d + e*x)^n])^(3/2)) - (4*(d + e*x))/(3*b^2*e*n^2*Sqrt[a + b*Log[c*(d + e*x)^n]])","A",6,5,18,0.2778,1,"{2389, 2297, 2300, 2180, 2204}"
30,1,192,0,0.1486314,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{7/2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(-7/2),x]","\frac{8 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{15 b^{7/2} e n^{7/2}}-\frac{8 (d+e x)}{15 b^3 e n^3 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{4 (d+e x)}{15 b^2 e n^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}-\frac{2 (d+e x)}{5 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}","\frac{8 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{15 b^{7/2} e n^{7/2}}-\frac{8 (d+e x)}{15 b^3 e n^3 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{4 (d+e x)}{15 b^2 e n^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}-\frac{2 (d+e x)}{5 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}",1,"(8*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(15*b^(7/2)*e*E^(a/(b*n))*n^(7/2)*(c*(d + e*x)^n)^n^(-1)) - (2*(d + e*x))/(5*b*e*n*(a + b*Log[c*(d + e*x)^n])^(5/2)) - (4*(d + e*x))/(15*b^2*e*n^2*(a + b*Log[c*(d + e*x)^n])^(3/2)) - (8*(d + e*x))/(15*b^3*e*n^3*Sqrt[a + b*Log[c*(d + e*x)^n]])","A",7,5,18,0.2778,1,"{2389, 2297, 2300, 2180, 2204}"
31,1,103,0,0.058868,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^p \, dx","Int[(a + b*Log[c*(d + e*x)^n])^p,x]","\frac{e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^p \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{e}","\frac{e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^p \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{e}",1,"((d + e*x)*Gamma[1 + p, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*(a + b*Log[c*(d + e*x)^n])^p)/(e*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^p)","A",3,3,16,0.1875,1,"{2389, 2300, 2181}"
32,1,88,0,0.0675028,"\int \left(a+b \log \left(c \sqrt{d+e x}\right)\right)^p \, dx","Int[(a + b*Log[c*Sqrt[d + e*x]])^p,x]","\frac{2^{-p} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \sqrt{d+e x}\right)\right)^p \left(-\frac{a+b \log \left(c \sqrt{d+e x}\right)}{b}\right)^{-p} \text{Gamma}\left(p+1,-\frac{2 \left(a+b \log \left(c \sqrt{d+e x}\right)\right)}{b}\right)}{c^2 e}","\frac{2^{-p} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \sqrt{d+e x}\right)\right)^p \left(-\frac{a+b \log \left(c \sqrt{d+e x}\right)}{b}\right)^{-p} \text{Gamma}\left(p+1,-\frac{2 \left(a+b \log \left(c \sqrt{d+e x}\right)\right)}{b}\right)}{c^2 e}",1,"(Gamma[1 + p, (-2*(a + b*Log[c*Sqrt[d + e*x]]))/b]*(a + b*Log[c*Sqrt[d + e*x]])^p)/(2^p*c^2*e*E^((2*a)/b)*(-((a + b*Log[c*Sqrt[d + e*x]])/b))^p)","A",3,3,18,0.1667,1,"{2389, 2299, 2181}"
33,1,20,0,0.0467459,"\int \frac{(e+f x)^{-1+p}}{\log \left(d (e+f x)^p\right)} \, dx","Int[(e + f*x)^(-1 + p)/Log[d*(e + f*x)^p],x]","\frac{\text{li}\left(d (e+f x)^p\right)}{d f p}","\frac{\text{li}\left(d (e+f x)^p\right)}{d f p}",1,"LogIntegral[d*(e + f*x)^p]/(d*f*p)","A",3,3,22,0.1364,1,"{2390, 2307, 2298}"
34,1,42,0,0.0760003,"\int \frac{(e g+f g x)^{-1+p}}{\log \left(d (e+f x)^p\right)} \, dx","Int[(e*g + f*g*x)^(-1 + p)/Log[d*(e + f*x)^p],x]","\frac{(e+f x)^{1-p} (g (e+f x))^{p-1} \text{li}\left(d (e+f x)^p\right)}{d f p}","\frac{(e+f x)^{1-p} (g (e+f x))^{p-1} \text{li}\left(d (e+f x)^p\right)}{d f p}",1,"((e + f*x)^(1 - p)*(g*(e + f*x))^(-1 + p)*LogIntegral[d*(e + f*x)^p])/(d*f*p)","A",4,4,25,0.1600,1,"{2390, 2308, 2307, 2298}"
35,1,178,0,0.1004705,"\int (f+g x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Int[(f + g*x)^4*(a + b*Log[c*(d + e*x)^n]),x]","\frac{(f+g x)^5 \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 g}-\frac{b n x (e f-d g)^4}{5 e^4}-\frac{b n (f+g x)^2 (e f-d g)^3}{10 e^3 g}-\frac{b n (f+g x)^3 (e f-d g)^2}{15 e^2 g}-\frac{b n (e f-d g)^5 \log (d+e x)}{5 e^5 g}-\frac{b n (f+g x)^4 (e f-d g)}{20 e g}-\frac{b n (f+g x)^5}{25 g}","\frac{(f+g x)^5 \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 g}-\frac{b n x (e f-d g)^4}{5 e^4}-\frac{b n (f+g x)^2 (e f-d g)^3}{10 e^3 g}-\frac{b n (f+g x)^3 (e f-d g)^2}{15 e^2 g}-\frac{b n (e f-d g)^5 \log (d+e x)}{5 e^5 g}-\frac{b n (f+g x)^4 (e f-d g)}{20 e g}-\frac{b n (f+g x)^5}{25 g}",1,"-(b*(e*f - d*g)^4*n*x)/(5*e^4) - (b*(e*f - d*g)^3*n*(f + g*x)^2)/(10*e^3*g) - (b*(e*f - d*g)^2*n*(f + g*x)^3)/(15*e^2*g) - (b*(e*f - d*g)*n*(f + g*x)^4)/(20*e*g) - (b*n*(f + g*x)^5)/(25*g) - (b*(e*f - d*g)^5*n*Log[d + e*x])/(5*e^5*g) + ((f + g*x)^5*(a + b*Log[c*(d + e*x)^n]))/(5*g)","A",3,2,22,0.09091,1,"{2395, 43}"
36,1,149,0,0.0696452,"\int (f+g x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Int[(f + g*x)^3*(a + b*Log[c*(d + e*x)^n]),x]","\frac{(f+g x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 g}-\frac{b n x (e f-d g)^3}{4 e^3}-\frac{b n (f+g x)^2 (e f-d g)^2}{8 e^2 g}-\frac{b n (e f-d g)^4 \log (d+e x)}{4 e^4 g}-\frac{b n (f+g x)^3 (e f-d g)}{12 e g}-\frac{b n (f+g x)^4}{16 g}","\frac{(f+g x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 g}-\frac{b n x (e f-d g)^3}{4 e^3}-\frac{b n (f+g x)^2 (e f-d g)^2}{8 e^2 g}-\frac{b n (e f-d g)^4 \log (d+e x)}{4 e^4 g}-\frac{b n (f+g x)^3 (e f-d g)}{12 e g}-\frac{b n (f+g x)^4}{16 g}",1,"-(b*(e*f - d*g)^3*n*x)/(4*e^3) - (b*(e*f - d*g)^2*n*(f + g*x)^2)/(8*e^2*g) - (b*(e*f - d*g)*n*(f + g*x)^3)/(12*e*g) - (b*n*(f + g*x)^4)/(16*g) - (b*(e*f - d*g)^4*n*Log[d + e*x])/(4*e^4*g) + ((f + g*x)^4*(a + b*Log[c*(d + e*x)^n]))/(4*g)","A",3,2,22,0.09091,1,"{2395, 43}"
37,1,120,0,0.0544044,"\int (f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Int[(f + g*x)^2*(a + b*Log[c*(d + e*x)^n]),x]","\frac{(f+g x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g}-\frac{b n x (e f-d g)^2}{3 e^2}-\frac{b n (e f-d g)^3 \log (d+e x)}{3 e^3 g}-\frac{b n (f+g x)^2 (e f-d g)}{6 e g}-\frac{b n (f+g x)^3}{9 g}","\frac{(f+g x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g}-\frac{b n x (e f-d g)^2}{3 e^2}-\frac{b n (e f-d g)^3 \log (d+e x)}{3 e^3 g}-\frac{b n (f+g x)^2 (e f-d g)}{6 e g}-\frac{b n (f+g x)^3}{9 g}",1,"-(b*(e*f - d*g)^2*n*x)/(3*e^2) - (b*(e*f - d*g)*n*(f + g*x)^2)/(6*e*g) - (b*n*(f + g*x)^3)/(9*g) - (b*(e*f - d*g)^3*n*Log[d + e*x])/(3*e^3*g) + ((f + g*x)^3*(a + b*Log[c*(d + e*x)^n]))/(3*g)","A",3,2,22,0.09091,1,"{2395, 43}"
38,1,91,0,0.036921,"\int (f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Int[(f + g*x)*(a + b*Log[c*(d + e*x)^n]),x]","\frac{(f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g}-\frac{b n (e f-d g)^2 \log (d+e x)}{2 e^2 g}-\frac{b n x (e f-d g)}{2 e}-\frac{b n (f+g x)^2}{4 g}","\frac{(f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g}-\frac{b n (e f-d g)^2 \log (d+e x)}{2 e^2 g}-\frac{b n x (e f-d g)}{2 e}-\frac{b n (f+g x)^2}{4 g}",1,"-(b*(e*f - d*g)*n*x)/(2*e) - (b*n*(f + g*x)^2)/(4*g) - (b*(e*f - d*g)^2*n*Log[d + e*x])/(2*e^2*g) + ((f + g*x)^2*(a + b*Log[c*(d + e*x)^n]))/(2*g)","A",3,2,20,0.1000,1,"{2395, 43}"
39,1,29,0,0.0158583,"\int \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Int[a + b*Log[c*(d + e*x)^n],x]","a x+\frac{b (d+e x) \log \left(c (d+e x)^n\right)}{e}-b n x","a x+\frac{b (d+e x) \log \left(c (d+e x)^n\right)}{e}-b n x",1,"a*x - b*n*x + (b*(d + e*x)*Log[c*(d + e*x)^n])/e","A",3,2,14,0.1429,1,"{2389, 2295}"
40,1,63,0,0.0521351,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{f+g x} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(f + g*x),x]","\frac{b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}","\frac{b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}",1,"((a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/g + (b*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g","A",3,3,22,0.1364,1,"{2394, 2393, 2391}"
41,1,74,0,0.0316396,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(f + g*x)^2,x]","-\frac{a+b \log \left(c (d+e x)^n\right)}{g (f+g x)}+\frac{b e n \log (d+e x)}{g (e f-d g)}-\frac{b e n \log (f+g x)}{g (e f-d g)}","-\frac{a+b \log \left(c (d+e x)^n\right)}{g (f+g x)}+\frac{b e n \log (d+e x)}{g (e f-d g)}-\frac{b e n \log (f+g x)}{g (e f-d g)}",1,"(b*e*n*Log[d + e*x])/(g*(e*f - d*g)) - (a + b*Log[c*(d + e*x)^n])/(g*(f + g*x)) - (b*e*n*Log[f + g*x])/(g*(e*f - d*g))","A",4,3,22,0.1364,1,"{2395, 36, 31}"
42,1,112,0,0.0622702,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x)^3} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(f + g*x)^3,x]","-\frac{a+b \log \left(c (d+e x)^n\right)}{2 g (f+g x)^2}+\frac{b e^2 n \log (d+e x)}{2 g (e f-d g)^2}-\frac{b e^2 n \log (f+g x)}{2 g (e f-d g)^2}+\frac{b e n}{2 g (f+g x) (e f-d g)}","-\frac{a+b \log \left(c (d+e x)^n\right)}{2 g (f+g x)^2}+\frac{b e^2 n \log (d+e x)}{2 g (e f-d g)^2}-\frac{b e^2 n \log (f+g x)}{2 g (e f-d g)^2}+\frac{b e n}{2 g (f+g x) (e f-d g)}",1,"(b*e*n)/(2*g*(e*f - d*g)*(f + g*x)) + (b*e^2*n*Log[d + e*x])/(2*g*(e*f - d*g)^2) - (a + b*Log[c*(d + e*x)^n])/(2*g*(f + g*x)^2) - (b*e^2*n*Log[f + g*x])/(2*g*(e*f - d*g)^2)","A",3,2,22,0.09091,1,"{2395, 44}"
43,1,141,0,0.0821917,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x)^4} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(f + g*x)^4,x]","-\frac{a+b \log \left(c (d+e x)^n\right)}{3 g (f+g x)^3}+\frac{b e^2 n}{3 g (f+g x) (e f-d g)^2}+\frac{b e^3 n \log (d+e x)}{3 g (e f-d g)^3}-\frac{b e^3 n \log (f+g x)}{3 g (e f-d g)^3}+\frac{b e n}{6 g (f+g x)^2 (e f-d g)}","-\frac{a+b \log \left(c (d+e x)^n\right)}{3 g (f+g x)^3}+\frac{b e^2 n}{3 g (f+g x) (e f-d g)^2}+\frac{b e^3 n \log (d+e x)}{3 g (e f-d g)^3}-\frac{b e^3 n \log (f+g x)}{3 g (e f-d g)^3}+\frac{b e n}{6 g (f+g x)^2 (e f-d g)}",1,"(b*e*n)/(6*g*(e*f - d*g)*(f + g*x)^2) + (b*e^2*n)/(3*g*(e*f - d*g)^2*(f + g*x)) + (b*e^3*n*Log[d + e*x])/(3*g*(e*f - d*g)^3) - (a + b*Log[c*(d + e*x)^n])/(3*g*(f + g*x)^3) - (b*e^3*n*Log[f + g*x])/(3*g*(e*f - d*g)^3)","A",3,2,22,0.09091,1,"{2395, 44}"
44,1,301,0,0.5353766,"\int (f+g x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Int[(f + g*x)^3*(a + b*Log[c*(d + e*x)^n])^2,x]","-\frac{b n \left(\frac{36 g^2 (d+e x)^2 (e f-d g)^2}{e^4}+\frac{16 g^3 (d+e x)^3 (e f-d g)}{e^4}+\frac{48 g (d+e x) (e f-d g)^3}{e^4}+\frac{12 (e f-d g)^4 \log (d+e x)}{e^4}+\frac{3 g^4 (d+e x)^4}{e^4}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{24 g}+\frac{(f+g x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 g}+\frac{2 b^2 g^2 n^2 (d+e x)^3 (e f-d g)}{9 e^4}+\frac{2 b^2 n^2 x (e f-d g)^3}{e^3}+\frac{3 b^2 g n^2 (d+e x)^2 (e f-d g)^2}{4 e^4}+\frac{b^2 n^2 (e f-d g)^4 \log ^2(d+e x)}{4 e^4 g}+\frac{b^2 g^3 n^2 (d+e x)^4}{32 e^4}","-\frac{2 b g^2 n (d+e x)^3 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 e^4}-\frac{b n (e f-d g)^4 \log (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^4 g}-\frac{2 b n (d+e x) (e f-d g)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^4}-\frac{3 b g n (d+e x)^2 (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^4}-\frac{b g^3 n (d+e x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{8 e^4}+\frac{(f+g x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 g}+\frac{2 b^2 g^2 n^2 (d+e x)^3 (e f-d g)}{9 e^4}+\frac{2 b^2 n^2 x (e f-d g)^3}{e^3}+\frac{3 b^2 g n^2 (d+e x)^2 (e f-d g)^2}{4 e^4}+\frac{b^2 n^2 (e f-d g)^4 \log ^2(d+e x)}{4 e^4 g}+\frac{b^2 g^3 n^2 (d+e x)^4}{32 e^4}",1,"(2*b^2*(e*f - d*g)^3*n^2*x)/e^3 + (3*b^2*g*(e*f - d*g)^2*n^2*(d + e*x)^2)/(4*e^4) + (2*b^2*g^2*(e*f - d*g)*n^2*(d + e*x)^3)/(9*e^4) + (b^2*g^3*n^2*(d + e*x)^4)/(32*e^4) + (b^2*(e*f - d*g)^4*n^2*Log[d + e*x]^2)/(4*e^4*g) - (b*n*((48*g*(e*f - d*g)^3*(d + e*x))/e^4 + (36*g^2*(e*f - d*g)^2*(d + e*x)^2)/e^4 + (16*g^3*(e*f - d*g)*(d + e*x)^3)/e^4 + (3*g^4*(d + e*x)^4)/e^4 + (12*(e*f - d*g)^4*Log[d + e*x])/e^4)*(a + b*Log[c*(d + e*x)^n]))/(24*g) + ((f + g*x)^4*(a + b*Log[c*(d + e*x)^n])^2)/(4*g)","A",6,6,24,0.2500,1,"{2398, 2411, 43, 2334, 12, 2301}"
45,1,243,0,0.4125807,"\int (f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Int[(f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^2,x]","-\frac{b n \left(\frac{9 g^2 (d+e x)^2 (e f-d g)}{e^3}+\frac{18 g (d+e x) (e f-d g)^2}{e^3}+\frac{6 (e f-d g)^3 \log (d+e x)}{e^3}+\frac{2 g^3 (d+e x)^3}{e^3}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{9 g}+\frac{(f+g x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 g}+\frac{2 b^2 n^2 x (e f-d g)^2}{e^2}+\frac{b^2 g n^2 (d+e x)^2 (e f-d g)}{2 e^3}+\frac{b^2 n^2 (e f-d g)^3 \log ^2(d+e x)}{3 e^3 g}+\frac{2 b^2 g^2 n^2 (d+e x)^3}{27 e^3}","-\frac{2 b n (e f-d g)^3 \log (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 e^3 g}-\frac{2 b n (d+e x) (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^3}-\frac{b g n (d+e x)^2 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^3}-\frac{2 b g^2 n (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{9 e^3}+\frac{(f+g x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 g}+\frac{2 b^2 n^2 x (e f-d g)^2}{e^2}+\frac{b^2 g n^2 (d+e x)^2 (e f-d g)}{2 e^3}+\frac{b^2 n^2 (e f-d g)^3 \log ^2(d+e x)}{3 e^3 g}+\frac{2 b^2 g^2 n^2 (d+e x)^3}{27 e^3}",1,"(2*b^2*(e*f - d*g)^2*n^2*x)/e^2 + (b^2*g*(e*f - d*g)*n^2*(d + e*x)^2)/(2*e^3) + (2*b^2*g^2*n^2*(d + e*x)^3)/(27*e^3) + (b^2*(e*f - d*g)^3*n^2*Log[d + e*x]^2)/(3*e^3*g) - (b*n*((18*g*(e*f - d*g)^2*(d + e*x))/e^3 + (9*g^2*(e*f - d*g)*(d + e*x)^2)/e^3 + (2*g^3*(d + e*x)^3)/e^3 + (6*(e*f - d*g)^3*Log[d + e*x])/e^3)*(a + b*Log[c*(d + e*x)^n]))/(9*g) + ((f + g*x)^3*(a + b*Log[c*(d + e*x)^n])^2)/(3*g)","A",8,7,24,0.2917,1,"{2398, 2411, 43, 2334, 12, 14, 2301}"
46,1,186,0,0.1636942,"\int (f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Int[(f + g*x)*(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{(d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2}-\frac{b g n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^2}+\frac{g (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2}-\frac{2 a b n x (e f-d g)}{e}-\frac{2 b^2 n (d+e x) (e f-d g) \log \left(c (d+e x)^n\right)}{e^2}+\frac{b^2 g n^2 (d+e x)^2}{4 e^2}+\frac{2 b^2 n^2 x (e f-d g)}{e}","\frac{(d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2}-\frac{b g n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^2}+\frac{g (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2}-\frac{2 a b n x (e f-d g)}{e}-\frac{2 b^2 n (d+e x) (e f-d g) \log \left(c (d+e x)^n\right)}{e^2}+\frac{b^2 g n^2 (d+e x)^2}{4 e^2}+\frac{2 b^2 n^2 x (e f-d g)}{e}",1,"(-2*a*b*(e*f - d*g)*n*x)/e + (2*b^2*(e*f - d*g)*n^2*x)/e + (b^2*g*n^2*(d + e*x)^2)/(4*e^2) - (2*b^2*(e*f - d*g)*n*(d + e*x)*Log[c*(d + e*x)^n])/e^2 - (b*g*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(2*e^2) + ((e*f - d*g)*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e^2 + (g*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(2*e^2)","A",9,7,22,0.3182,1,"{2401, 2389, 2296, 2295, 2390, 2305, 2304}"
47,1,65,0,0.0386196,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-2 a b n x-\frac{2 b^2 n (d+e x) \log \left(c (d+e x)^n\right)}{e}+2 b^2 n^2 x","\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-2 a b n x-\frac{2 b^2 n (d+e x) \log \left(c (d+e x)^n\right)}{e}+2 b^2 n^2 x",1,"-2*a*b*n*x + 2*b^2*n^2*x - (2*b^2*n*(d + e*x)*Log[c*(d + e*x)^n])/e + ((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e","A",4,3,16,0.1875,1,"{2389, 2296, 2295}"
48,1,111,0,0.113655,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x),x]","\frac{2 b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{g}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g}","\frac{2 b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{g}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g}",1,"((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(f + g*x))/(e*f - d*g)])/g + (2*b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g - (2*b^2*n^2*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/g","A",4,4,24,0.1667,1,"{2396, 2433, 2374, 6589}"
49,1,132,0,0.0883066,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x)^2,x]","-\frac{2 b^2 e n^2 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g (e f-d g)}-\frac{2 b e n \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x) (e f-d g)}","-\frac{2 b^2 e n^2 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g (e f-d g)}-\frac{2 b e n \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x) (e f-d g)}",1,"((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/((e*f - d*g)*(f + g*x)) - (2*b*e*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/(g*(e*f - d*g)) - (2*b^2*e*n^2*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/(g*(e*f - d*g))","A",4,4,24,0.1667,1,"{2397, 2394, 2393, 2391}"
50,1,233,0,0.3854804,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x)^3} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x)^3,x]","-\frac{b^2 e^2 n^2 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g (e f-d g)^2}+\frac{e^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g (e f-d g)^2}-\frac{b e^2 n \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)^2}-\frac{b e n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(f+g x) (e f-d g)^2}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g (f+g x)^2}+\frac{b^2 e^2 n^2 \log (f+g x)}{g (e f-d g)^2}","\frac{b^2 e^2 n^2 \text{PolyLog}\left(2,-\frac{e f-d g}{g (d+e x)}\right)}{g (e f-d g)^2}-\frac{b e^2 n \log \left(\frac{e f-d g}{g (d+e x)}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)^2}-\frac{b e n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(f+g x) (e f-d g)^2}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g (f+g x)^2}+\frac{b^2 e^2 n^2 \log (f+g x)}{g (e f-d g)^2}",1,"-((b*e*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n]))/((e*f - d*g)^2*(f + g*x))) + (e^2*(a + b*Log[c*(d + e*x)^n])^2)/(2*g*(e*f - d*g)^2) - (a + b*Log[c*(d + e*x)^n])^2/(2*g*(f + g*x)^2) + (b^2*e^2*n^2*Log[f + g*x])/(g*(e*f - d*g)^2) - (b*e^2*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/(g*(e*f - d*g)^2) - (b^2*e^2*n^2*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/(g*(e*f - d*g)^2)","A",9,9,24,0.3750,1,"{2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31}"
51,1,347,0,0.6048547,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x)^4} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x)^4,x]","-\frac{2 b^2 e^3 n^2 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{3 g (e f-d g)^3}+\frac{e^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 g (e f-d g)^3}-\frac{2 b e^3 n \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g (e f-d g)^3}-\frac{2 b e^2 n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 (f+g x) (e f-d g)^3}+\frac{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g (f+g x)^2 (e f-d g)}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 g (f+g x)^3}-\frac{b^2 e^2 n^2}{3 g (f+g x) (e f-d g)^2}-\frac{b^2 e^3 n^2 \log (d+e x)}{3 g (e f-d g)^3}+\frac{b^2 e^3 n^2 \log (f+g x)}{g (e f-d g)^3}","\frac{2 b^2 e^3 n^2 \text{PolyLog}\left(2,-\frac{e f-d g}{g (d+e x)}\right)}{3 g (e f-d g)^3}-\frac{2 b e^3 n \log \left(\frac{e f-d g}{g (d+e x)}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g (e f-d g)^3}-\frac{2 b e^2 n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 (f+g x) (e f-d g)^3}+\frac{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g (f+g x)^2 (e f-d g)}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 g (f+g x)^3}-\frac{b^2 e^2 n^2}{3 g (f+g x) (e f-d g)^2}-\frac{b^2 e^3 n^2 \log (d+e x)}{3 g (e f-d g)^3}+\frac{b^2 e^3 n^2 \log (f+g x)}{g (e f-d g)^3}",1,"-(b^2*e^2*n^2)/(3*g*(e*f - d*g)^2*(f + g*x)) - (b^2*e^3*n^2*Log[d + e*x])/(3*g*(e*f - d*g)^3) + (b*e*n*(a + b*Log[c*(d + e*x)^n]))/(3*g*(e*f - d*g)*(f + g*x)^2) - (2*b*e^2*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n]))/(3*(e*f - d*g)^3*(f + g*x)) + (e^3*(a + b*Log[c*(d + e*x)^n])^2)/(3*g*(e*f - d*g)^3) - (a + b*Log[c*(d + e*x)^n])^2/(3*g*(f + g*x)^3) + (b^2*e^3*n^2*Log[f + g*x])/(g*(e*f - d*g)^3) - (2*b*e^3*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/(3*g*(e*f - d*g)^3) - (2*b^2*e^3*n^2*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/(3*g*(e*f - d*g)^3)","A",13,11,24,0.4583,1,"{2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
52,1,598,0,0.5520665,"\int (f+g x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \, dx","Int[(f + g*x)^3*(a + b*Log[c*(d + e*x)^n])^3,x]","\frac{2 b^2 g^2 n^2 (d+e x)^3 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 e^4}+\frac{9 b^2 g n^2 (d+e x)^2 (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 e^4}+\frac{3 b^2 g^3 n^2 (d+e x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{32 e^4}+\frac{6 a b^2 n^2 x (e f-d g)^3}{e^3}+\frac{g^2 (d+e x)^3 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e^4}-\frac{b g^2 n (d+e x)^3 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^4}+\frac{3 g (d+e x)^2 (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{2 e^4}-\frac{9 b g n (d+e x)^2 (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 e^4}+\frac{(d+e x) (e f-d g)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e^4}-\frac{3 b n (d+e x) (e f-d g)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^4}+\frac{g^3 (d+e x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{4 e^4}-\frac{3 b g^3 n (d+e x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{16 e^4}+\frac{6 b^3 n^2 (d+e x) (e f-d g)^3 \log \left(c (d+e x)^n\right)}{e^4}-\frac{2 b^3 g^2 n^3 (d+e x)^3 (e f-d g)}{9 e^4}-\frac{9 b^3 g n^3 (d+e x)^2 (e f-d g)^2}{8 e^4}-\frac{6 b^3 n^3 x (e f-d g)^3}{e^3}-\frac{3 b^3 g^3 n^3 (d+e x)^4}{128 e^4}","\frac{2 b^2 g^2 n^2 (d+e x)^3 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 e^4}+\frac{9 b^2 g n^2 (d+e x)^2 (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 e^4}+\frac{3 b^2 g^3 n^2 (d+e x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{32 e^4}+\frac{6 a b^2 n^2 x (e f-d g)^3}{e^3}+\frac{g^2 (d+e x)^3 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e^4}-\frac{b g^2 n (d+e x)^3 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^4}+\frac{3 g (d+e x)^2 (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{2 e^4}-\frac{9 b g n (d+e x)^2 (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 e^4}+\frac{(d+e x) (e f-d g)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e^4}-\frac{3 b n (d+e x) (e f-d g)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^4}+\frac{g^3 (d+e x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{4 e^4}-\frac{3 b g^3 n (d+e x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{16 e^4}+\frac{6 b^3 n^2 (d+e x) (e f-d g)^3 \log \left(c (d+e x)^n\right)}{e^4}-\frac{2 b^3 g^2 n^3 (d+e x)^3 (e f-d g)}{9 e^4}-\frac{9 b^3 g n^3 (d+e x)^2 (e f-d g)^2}{8 e^4}-\frac{6 b^3 n^3 x (e f-d g)^3}{e^3}-\frac{3 b^3 g^3 n^3 (d+e x)^4}{128 e^4}",1,"(6*a*b^2*(e*f - d*g)^3*n^2*x)/e^3 - (6*b^3*(e*f - d*g)^3*n^3*x)/e^3 - (9*b^3*g*(e*f - d*g)^2*n^3*(d + e*x)^2)/(8*e^4) - (2*b^3*g^2*(e*f - d*g)*n^3*(d + e*x)^3)/(9*e^4) - (3*b^3*g^3*n^3*(d + e*x)^4)/(128*e^4) + (6*b^3*(e*f - d*g)^3*n^2*(d + e*x)*Log[c*(d + e*x)^n])/e^4 + (9*b^2*g*(e*f - d*g)^2*n^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(4*e^4) + (2*b^2*g^2*(e*f - d*g)*n^2*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n]))/(3*e^4) + (3*b^2*g^3*n^2*(d + e*x)^4*(a + b*Log[c*(d + e*x)^n]))/(32*e^4) - (3*b*(e*f - d*g)^3*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e^4 - (9*b*g*(e*f - d*g)^2*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(4*e^4) - (b*g^2*(e*f - d*g)*n*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])^2)/e^4 - (3*b*g^3*n*(d + e*x)^4*(a + b*Log[c*(d + e*x)^n])^2)/(16*e^4) + ((e*f - d*g)^3*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/e^4 + (3*g*(e*f - d*g)^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^3)/(2*e^4) + (g^2*(e*f - d*g)*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])^3)/e^4 + (g^3*(d + e*x)^4*(a + b*Log[c*(d + e*x)^n])^3)/(4*e^4)","A",19,7,24,0.2917,1,"{2401, 2389, 2296, 2295, 2390, 2305, 2304}"
53,1,432,0,0.3844783,"\int (f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \, dx","Int[(f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^3,x]","\frac{3 b^2 g n^2 (d+e x)^2 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^3}+\frac{2 b^2 g^2 n^2 (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{9 e^3}+\frac{6 a b^2 n^2 x (e f-d g)^2}{e^2}-\frac{3 b g n (d+e x)^2 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^3}-\frac{3 b n (d+e x) (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^3}+\frac{g (d+e x)^2 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e^3}+\frac{(d+e x) (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e^3}-\frac{b g^2 n (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 e^3}+\frac{g^2 (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{3 e^3}+\frac{6 b^3 n^2 (d+e x) (e f-d g)^2 \log \left(c (d+e x)^n\right)}{e^3}-\frac{3 b^3 g n^3 (d+e x)^2 (e f-d g)}{4 e^3}-\frac{6 b^3 n^3 x (e f-d g)^2}{e^2}-\frac{2 b^3 g^2 n^3 (d+e x)^3}{27 e^3}","\frac{3 b^2 g n^2 (d+e x)^2 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^3}+\frac{2 b^2 g^2 n^2 (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{9 e^3}+\frac{6 a b^2 n^2 x (e f-d g)^2}{e^2}-\frac{3 b g n (d+e x)^2 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^3}-\frac{3 b n (d+e x) (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^3}+\frac{g (d+e x)^2 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e^3}+\frac{(d+e x) (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e^3}-\frac{b g^2 n (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 e^3}+\frac{g^2 (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{3 e^3}+\frac{6 b^3 n^2 (d+e x) (e f-d g)^2 \log \left(c (d+e x)^n\right)}{e^3}-\frac{3 b^3 g n^3 (d+e x)^2 (e f-d g)}{4 e^3}-\frac{6 b^3 n^3 x (e f-d g)^2}{e^2}-\frac{2 b^3 g^2 n^3 (d+e x)^3}{27 e^3}",1,"(6*a*b^2*(e*f - d*g)^2*n^2*x)/e^2 - (6*b^3*(e*f - d*g)^2*n^3*x)/e^2 - (3*b^3*g*(e*f - d*g)*n^3*(d + e*x)^2)/(4*e^3) - (2*b^3*g^2*n^3*(d + e*x)^3)/(27*e^3) + (6*b^3*(e*f - d*g)^2*n^2*(d + e*x)*Log[c*(d + e*x)^n])/e^3 + (3*b^2*g*(e*f - d*g)*n^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(2*e^3) + (2*b^2*g^2*n^2*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n]))/(9*e^3) - (3*b*(e*f - d*g)^2*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e^3 - (3*b*g*(e*f - d*g)*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(2*e^3) - (b*g^2*n*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])^2)/(3*e^3) + ((e*f - d*g)^2*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/e^3 + (g*(e*f - d*g)*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^3)/e^3 + (g^2*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])^3)/(3*e^3)","A",15,7,24,0.2917,1,"{2401, 2389, 2296, 2295, 2390, 2305, 2304}"
54,1,265,0,0.2187665,"\int (f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \, dx","Int[(f + g*x)*(a + b*Log[c*(d + e*x)^n])^3,x]","\frac{3 b^2 g n^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 e^2}+\frac{6 a b^2 n^2 x (e f-d g)}{e}-\frac{3 b n (d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2}+\frac{(d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e^2}-\frac{3 b g n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 e^2}+\frac{g (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{2 e^2}+\frac{6 b^3 n^2 (d+e x) (e f-d g) \log \left(c (d+e x)^n\right)}{e^2}-\frac{3 b^3 g n^3 (d+e x)^2}{8 e^2}-\frac{6 b^3 n^3 x (e f-d g)}{e}","\frac{3 b^2 g n^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 e^2}+\frac{6 a b^2 n^2 x (e f-d g)}{e}-\frac{3 b n (d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2}+\frac{(d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e^2}-\frac{3 b g n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 e^2}+\frac{g (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{2 e^2}+\frac{6 b^3 n^2 (d+e x) (e f-d g) \log \left(c (d+e x)^n\right)}{e^2}-\frac{3 b^3 g n^3 (d+e x)^2}{8 e^2}-\frac{6 b^3 n^3 x (e f-d g)}{e}",1,"(6*a*b^2*(e*f - d*g)*n^2*x)/e - (6*b^3*(e*f - d*g)*n^3*x)/e - (3*b^3*g*n^3*(d + e*x)^2)/(8*e^2) + (6*b^3*(e*f - d*g)*n^2*(d + e*x)*Log[c*(d + e*x)^n])/e^2 + (3*b^2*g*n^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(4*e^2) - (3*b*(e*f - d*g)*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e^2 - (3*b*g*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(4*e^2) + ((e*f - d*g)*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/e^2 + (g*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^3)/(2*e^2)","A",11,7,22,0.3182,1,"{2401, 2389, 2296, 2295, 2390, 2305, 2304}"
55,1,99,0,0.0524308,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \, dx","Int[(a + b*Log[c*(d + e*x)^n])^3,x]","6 a b^2 n^2 x-\frac{3 b n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}+\frac{6 b^3 n^2 (d+e x) \log \left(c (d+e x)^n\right)}{e}-6 b^3 n^3 x","6 a b^2 n^2 x-\frac{3 b n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}+\frac{6 b^3 n^2 (d+e x) \log \left(c (d+e x)^n\right)}{e}-6 b^3 n^3 x",1,"6*a*b^2*n^2*x - 6*b^3*n^3*x + (6*b^3*n^2*(d + e*x)*Log[c*(d + e*x)^n])/e - (3*b*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e + ((d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/e","A",5,3,16,0.1875,1,"{2389, 2296, 2295}"
56,1,158,0,0.1768912,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{f+g x} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^3/(f + g*x),x]","-\frac{6 b^2 n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}+\frac{3 b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g}+\frac{6 b^3 n^3 \text{PolyLog}\left(4,-\frac{g (d+e x)}{e f-d g}\right)}{g}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{g}","-\frac{6 b^2 n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}+\frac{3 b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g}+\frac{6 b^3 n^3 \text{PolyLog}\left(4,-\frac{g (d+e x)}{e f-d g}\right)}{g}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{g}",1,"((a + b*Log[c*(d + e*x)^n])^3*Log[(e*(f + g*x))/(e*f - d*g)])/g + (3*b*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g - (6*b^2*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/g + (6*b^3*n^3*PolyLog[4, -((g*(d + e*x))/(e*f - d*g))])/g","A",5,5,24,0.2083,1,"{2396, 2433, 2374, 2383, 6589}"
57,1,190,0,0.1537376,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(f+g x)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^3/(f + g*x)^2,x]","-\frac{6 b^2 e n^2 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)}+\frac{6 b^3 e n^3 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{g (e f-d g)}-\frac{3 b e n \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g (e f-d g)}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(f+g x) (e f-d g)}","-\frac{6 b^2 e n^2 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)}+\frac{6 b^3 e n^3 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{g (e f-d g)}-\frac{3 b e n \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g (e f-d g)}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(f+g x) (e f-d g)}",1,"((d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/((e*f - d*g)*(f + g*x)) - (3*b*e*n*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(f + g*x))/(e*f - d*g)])/(g*(e*f - d*g)) - (6*b^2*e*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/(g*(e*f - d*g)) + (6*b^3*e*n^3*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/(g*(e*f - d*g))","A",5,5,24,0.2083,1,"{2397, 2396, 2433, 2374, 6589}"
58,1,370,0,0.6249206,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(f+g x)^3} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^3/(f + g*x)^3,x]","-\frac{3 b^2 e^2 n^2 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)^2}+\frac{3 b^3 e^2 n^3 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g (e f-d g)^2}+\frac{3 b^3 e^2 n^3 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{g (e f-d g)^2}+\frac{3 b^2 e^2 n^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)^2}-\frac{3 b e^2 n \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g (e f-d g)^2}+\frac{e^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{2 g (e f-d g)^2}-\frac{3 b e n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 (f+g x) (e f-d g)^2}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{2 g (f+g x)^2}","\frac{3 b^2 e^2 n^2 \text{PolyLog}\left(2,-\frac{e f-d g}{g (d+e x)}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)^2}+\frac{3 b^3 e^2 n^3 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g (e f-d g)^2}+\frac{3 b^3 e^2 n^3 \text{PolyLog}\left(3,-\frac{e f-d g}{g (d+e x)}\right)}{g (e f-d g)^2}+\frac{3 b^2 e^2 n^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)^2}-\frac{3 b e^2 n \log \left(\frac{e f-d g}{g (d+e x)}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g (e f-d g)^2}-\frac{3 b e n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 (f+g x) (e f-d g)^2}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{2 g (f+g x)^2}",1,"(-3*b*e*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(2*(e*f - d*g)^2*(f + g*x)) + (e^2*(a + b*Log[c*(d + e*x)^n])^3)/(2*g*(e*f - d*g)^2) - (a + b*Log[c*(d + e*x)^n])^3/(2*g*(f + g*x)^2) + (3*b^2*e^2*n^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/(g*(e*f - d*g)^2) - (3*b*e^2*n*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(f + g*x))/(e*f - d*g)])/(2*g*(e*f - d*g)^2) + (3*b^3*e^2*n^3*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/(g*(e*f - d*g)^2) - (3*b^2*e^2*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/(g*(e*f - d*g)^2) + (3*b^3*e^2*n^3*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/(g*(e*f - d*g)^2)","A",12,11,24,0.4583,1,"{2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391}"
59,1,525,0,1.140291,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(f+g x)^4} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^3/(f + g*x)^4,x]","-\frac{2 b^2 e^3 n^2 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)^3}+\frac{3 b^3 e^3 n^3 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g (e f-d g)^3}+\frac{2 b^3 e^3 n^3 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{g (e f-d g)^3}+\frac{3 b^2 e^3 n^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)^3}+\frac{b^2 e^2 n^2 (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(f+g x) (e f-d g)^3}+\frac{e^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{3 g (e f-d g)^3}-\frac{b e^3 n \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g (e f-d g)^3}-\frac{b e^3 n \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g (e f-d g)^3}-\frac{b e^2 n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x) (e f-d g)^3}+\frac{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g (f+g x)^2 (e f-d g)}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{3 g (f+g x)^3}-\frac{b^3 e^3 n^3 \log (f+g x)}{g (e f-d g)^3}","\frac{2 b^2 e^3 n^2 \text{PolyLog}\left(2,-\frac{e f-d g}{g (d+e x)}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)^3}-\frac{b^3 e^3 n^3 \text{PolyLog}\left(2,-\frac{e f-d g}{g (d+e x)}\right)}{g (e f-d g)^3}+\frac{2 b^3 e^3 n^3 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g (e f-d g)^3}+\frac{2 b^3 e^3 n^3 \text{PolyLog}\left(3,-\frac{e f-d g}{g (d+e x)}\right)}{g (e f-d g)^3}+\frac{2 b^2 e^3 n^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)^3}+\frac{b^2 e^3 n^2 \log \left(\frac{e f-d g}{g (d+e x)}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)^3}+\frac{b^2 e^2 n^2 (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(f+g x) (e f-d g)^3}-\frac{b e^3 n \log \left(\frac{e f-d g}{g (d+e x)}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g (e f-d g)^3}-\frac{b e^2 n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x) (e f-d g)^3}+\frac{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g (f+g x)^2 (e f-d g)}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{3 g (f+g x)^3}-\frac{b^3 e^3 n^3 \log (f+g x)}{g (e f-d g)^3}",1,"(b^2*e^2*n^2*(d + e*x)*(a + b*Log[c*(d + e*x)^n]))/((e*f - d*g)^3*(f + g*x)) - (b*e^3*n*(a + b*Log[c*(d + e*x)^n])^2)/(2*g*(e*f - d*g)^3) + (b*e*n*(a + b*Log[c*(d + e*x)^n])^2)/(2*g*(e*f - d*g)*(f + g*x)^2) - (b*e^2*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/((e*f - d*g)^3*(f + g*x)) + (e^3*(a + b*Log[c*(d + e*x)^n])^3)/(3*g*(e*f - d*g)^3) - (a + b*Log[c*(d + e*x)^n])^3/(3*g*(f + g*x)^3) - (b^3*e^3*n^3*Log[f + g*x])/(g*(e*f - d*g)^3) + (3*b^2*e^3*n^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/(g*(e*f - d*g)^3) - (b*e^3*n*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(f + g*x))/(e*f - d*g)])/(g*(e*f - d*g)^3) + (3*b^3*e^3*n^3*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/(g*(e*f - d*g)^3) - (2*b^2*e^3*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/(g*(e*f - d*g)^3) + (2*b^3*e^3*n^3*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/(g*(e*f - d*g)^3)","A",21,15,24,0.6250,1,"{2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391, 2319, 2301, 2314, 31}"
60,1,340,0,0.2806018,"\int (f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^4 \, dx","Int[(f + g*x)*(a + b*Log[c*(d + e*x)^n])^4,x]","\frac{12 b^2 n^2 (d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2}-\frac{3 b^3 g n^3 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^2}+\frac{3 b^2 g n^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2}-\frac{24 a b^3 n^3 x (e f-d g)}{e}-\frac{4 b n (d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e^2}+\frac{(d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^4}{e^2}-\frac{b g n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e^2}+\frac{g (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^4}{2 e^2}-\frac{24 b^4 n^3 (d+e x) (e f-d g) \log \left(c (d+e x)^n\right)}{e^2}+\frac{3 b^4 g n^4 (d+e x)^2}{4 e^2}+\frac{24 b^4 n^4 x (e f-d g)}{e}","\frac{12 b^2 n^2 (d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2}-\frac{3 b^3 g n^3 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^2}+\frac{3 b^2 g n^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2}-\frac{24 a b^3 n^3 x (e f-d g)}{e}-\frac{4 b n (d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e^2}+\frac{(d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^4}{e^2}-\frac{b g n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e^2}+\frac{g (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^4}{2 e^2}-\frac{24 b^4 n^3 (d+e x) (e f-d g) \log \left(c (d+e x)^n\right)}{e^2}+\frac{3 b^4 g n^4 (d+e x)^2}{4 e^2}+\frac{24 b^4 n^4 x (e f-d g)}{e}",1,"(-24*a*b^3*(e*f - d*g)*n^3*x)/e + (24*b^4*(e*f - d*g)*n^4*x)/e + (3*b^4*g*n^4*(d + e*x)^2)/(4*e^2) - (24*b^4*(e*f - d*g)*n^3*(d + e*x)*Log[c*(d + e*x)^n])/e^2 - (3*b^3*g*n^3*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(2*e^2) + (12*b^2*(e*f - d*g)*n^2*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e^2 + (3*b^2*g*n^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(2*e^2) - (4*b*(e*f - d*g)*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/e^2 - (b*g*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^3)/e^2 + ((e*f - d*g)*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^4)/e^2 + (g*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^4)/(2*e^2)","A",13,7,22,0.3182,1,"{2401, 2389, 2296, 2295, 2390, 2305, 2304}"
61,1,131,0,0.0710391,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^4 \, dx","Int[(a + b*Log[c*(d + e*x)^n])^4,x]","\frac{12 b^2 n^2 (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-24 a b^3 n^3 x-\frac{4 b n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^4}{e}-\frac{24 b^4 n^3 (d+e x) \log \left(c (d+e x)^n\right)}{e}+24 b^4 n^4 x","\frac{12 b^2 n^2 (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-24 a b^3 n^3 x-\frac{4 b n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^4}{e}-\frac{24 b^4 n^3 (d+e x) \log \left(c (d+e x)^n\right)}{e}+24 b^4 n^4 x",1,"-24*a*b^3*n^3*x + 24*b^4*n^4*x - (24*b^4*n^3*(d + e*x)*Log[c*(d + e*x)^n])/e + (12*b^2*n^2*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e - (4*b*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/e + ((d + e*x)*(a + b*Log[c*(d + e*x)^n])^4)/e","A",6,3,16,0.1875,1,"{2389, 2296, 2295}"
62,1,205,0,0.2313131,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^4}{f+g x} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^4/(f + g*x),x]","\frac{24 b^3 n^3 \text{PolyLog}\left(4,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}-\frac{12 b^2 n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g}+\frac{4 b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{g}-\frac{24 b^4 n^4 \text{PolyLog}\left(5,-\frac{g (d+e x)}{e f-d g}\right)}{g}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^4}{g}","\frac{24 b^3 n^3 \text{PolyLog}\left(4,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}-\frac{12 b^2 n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g}+\frac{4 b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{g}-\frac{24 b^4 n^4 \text{PolyLog}\left(5,-\frac{g (d+e x)}{e f-d g}\right)}{g}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^4}{g}",1,"((a + b*Log[c*(d + e*x)^n])^4*Log[(e*(f + g*x))/(e*f - d*g)])/g + (4*b*n*(a + b*Log[c*(d + e*x)^n])^3*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g - (12*b^2*n^2*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/g + (24*b^3*n^3*(a + b*Log[c*(d + e*x)^n])*PolyLog[4, -((g*(d + e*x))/(e*f - d*g))])/g - (24*b^4*n^4*PolyLog[5, -((g*(d + e*x))/(e*f - d*g))])/g","A",6,5,24,0.2083,1,"{2396, 2433, 2374, 2383, 6589}"
63,1,248,0,0.2346894,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^4}{(f+g x)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^4/(f + g*x)^2,x]","\frac{24 b^3 e n^3 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)}-\frac{12 b^2 e n^2 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g (e f-d g)}-\frac{24 b^4 e n^4 \text{PolyLog}\left(4,-\frac{g (d+e x)}{e f-d g}\right)}{g (e f-d g)}-\frac{4 b e n \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{g (e f-d g)}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^4}{(f+g x) (e f-d g)}","\frac{24 b^3 e n^3 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (e f-d g)}-\frac{12 b^2 e n^2 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g (e f-d g)}-\frac{24 b^4 e n^4 \text{PolyLog}\left(4,-\frac{g (d+e x)}{e f-d g}\right)}{g (e f-d g)}-\frac{4 b e n \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{g (e f-d g)}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^4}{(f+g x) (e f-d g)}",1,"((d + e*x)*(a + b*Log[c*(d + e*x)^n])^4)/((e*f - d*g)*(f + g*x)) - (4*b*e*n*(a + b*Log[c*(d + e*x)^n])^3*Log[(e*(f + g*x))/(e*f - d*g)])/(g*(e*f - d*g)) - (12*b^2*e*n^2*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/(g*(e*f - d*g)) + (24*b^3*e*n^3*(a + b*Log[c*(d + e*x)^n])*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/(g*(e*f - d*g)) - (24*b^4*e*n^4*PolyLog[4, -((g*(d + e*x))/(e*f - d*g))])/(g*(e*f - d*g))","A",6,6,24,0.2500,1,"{2397, 2396, 2433, 2374, 2383, 6589}"
64,1,19,0,0.0058197,"\int \log (a+b x) \, dx","Int[Log[a + b*x],x]","\frac{(a+b x) \log (a+b x)}{b}-x","\frac{(a+b x) \log (a+b x)}{b}-x",1,"-x + ((a + b*x)*Log[a + b*x])/b","A",2,2,6,0.3333,1,"{2389, 2295}"
65,1,37,0,0.0143306,"\int \log ^2(a+b x) \, dx","Int[Log[a + b*x]^2,x]","\frac{(a+b x) \log ^2(a+b x)}{b}-\frac{2 (a+b x) \log (a+b x)}{b}+2 x","\frac{(a+b x) \log ^2(a+b x)}{b}-\frac{2 (a+b x) \log (a+b x)}{b}+2 x",1,"2*x - (2*(a + b*x)*Log[a + b*x])/b + ((a + b*x)*Log[a + b*x]^2)/b","A",3,3,8,0.3750,1,"{2389, 2296, 2295}"
66,1,55,0,0.0184441,"\int \log ^3(a+b x) \, dx","Int[Log[a + b*x]^3,x]","\frac{(a+b x) \log ^3(a+b x)}{b}-\frac{3 (a+b x) \log ^2(a+b x)}{b}+\frac{6 (a+b x) \log (a+b x)}{b}-6 x","\frac{(a+b x) \log ^3(a+b x)}{b}-\frac{3 (a+b x) \log ^2(a+b x)}{b}+\frac{6 (a+b x) \log (a+b x)}{b}-6 x",1,"-6*x + (6*(a + b*x)*Log[a + b*x])/b - (3*(a + b*x)*Log[a + b*x]^2)/b + ((a + b*x)*Log[a + b*x]^3)/b","A",4,3,8,0.3750,1,"{2389, 2296, 2295}"
67,1,25,0,0.0147451,"\int \log (a+b x+c x) \, dx","Int[Log[a + b*x + c*x],x]","\frac{(a+x (b+c)) \log (a+x (b+c))}{b+c}-x","\frac{(a+x (b+c)) \log (a+x (b+c))}{b+c}-x",1,"-x + ((a + (b + c)*x)*Log[a + (b + c)*x])/(b + c)","A",3,3,9,0.3333,1,"{2444, 2389, 2295}"
68,1,49,0,0.0252992,"\int \log ^2(a+b x+c x) \, dx","Int[Log[a + b*x + c*x]^2,x]","\frac{(a+x (b+c)) \log ^2(a+x (b+c))}{b+c}-\frac{2 (a+x (b+c)) \log (a+x (b+c))}{b+c}+2 x","\frac{(a+x (b+c)) \log ^2(a+x (b+c))}{b+c}-\frac{2 (a+x (b+c)) \log (a+x (b+c))}{b+c}+2 x",1,"2*x - (2*(a + (b + c)*x)*Log[a + (b + c)*x])/(b + c) + ((a + (b + c)*x)*Log[a + (b + c)*x]^2)/(b + c)","A",4,4,11,0.3636,1,"{2444, 2389, 2296, 2295}"
69,1,73,0,0.0317987,"\int \log ^3(a+b x+c x) \, dx","Int[Log[a + b*x + c*x]^3,x]","\frac{(a+x (b+c)) \log ^3(a+x (b+c))}{b+c}-\frac{3 (a+x (b+c)) \log ^2(a+x (b+c))}{b+c}+\frac{6 (a+x (b+c)) \log (a+x (b+c))}{b+c}-6 x","\frac{(a+x (b+c)) \log ^3(a+x (b+c))}{b+c}-\frac{3 (a+x (b+c)) \log ^2(a+x (b+c))}{b+c}+\frac{6 (a+x (b+c)) \log (a+x (b+c))}{b+c}-6 x",1,"-6*x + (6*(a + (b + c)*x)*Log[a + (b + c)*x])/(b + c) - (3*(a + (b + c)*x)*Log[a + (b + c)*x]^2)/(b + c) + ((a + (b + c)*x)*Log[a + (b + c)*x]^3)/(b + c)","A",5,4,11,0.3636,1,"{2444, 2389, 2296, 2295}"
70,1,24,0,0.0086375,"\int \log \left(c (d+e x)^n\right) \, dx","Int[Log[c*(d + e*x)^n],x]","\frac{(d+e x) \log \left(c (d+e x)^n\right)}{e}-n x","\frac{(d+e x) \log \left(c (d+e x)^n\right)}{e}-n x",1,"-(n*x) + ((d + e*x)*Log[c*(d + e*x)^n])/e","A",2,2,10,0.2000,1,"{2389, 2295}"
71,1,24,0,0.026475,"\int \frac{\log \left(-\frac{g (d+e x)}{e f-d g}\right)}{f+g x} \, dx","Int[Log[-((g*(d + e*x))/(e*f - d*g))]/(f + g*x),x]","-\frac{\text{PolyLog}\left(2,\frac{e (f+g x)}{e f-d g}\right)}{g}","-\frac{\text{PolyLog}\left(2,\frac{e (f+g x)}{e f-d g}\right)}{g}",1,"-(PolyLog[2, (e*(f + g*x))/(e*f - d*g)]/g)","A",2,2,27,0.07407,1,"{2393, 2391}"
72,1,15,0,0.0193654,"\int \frac{a+b \log \left(c \left(\frac{1}{c}+e x\right)\right)}{x} \, dx","Int[(a + b*Log[c*(c^(-1) + e*x)])/x,x]","a \log (x)-b \text{PolyLog}(2,-c e x)","a \log (x)-b \text{PolyLog}(2,-c e x)",1,"a*Log[x] - b*PolyLog[2, -(c*e*x)]","A",2,2,18,0.1111,1,"{2392, 2391}"
73,1,16,0,0.0152334,"\int \frac{\log (3+e x)}{x} \, dx","Int[Log[3 + e*x]/x,x]","\log (3) \log (x)-\text{PolyLog}\left(2,-\frac{e x}{3}\right)","\log (3) \log (x)-\text{PolyLog}\left(2,-\frac{e x}{3}\right)",1,"Log[3]*Log[x] - PolyLog[2, -(e*x)/3]","A",2,2,10,0.2000,1,"{2392, 2391}"
74,1,16,0,0.0149935,"\int \frac{\log (2+e x)}{x} \, dx","Int[Log[2 + e*x]/x,x]","\log (2) \log (x)-\text{PolyLog}\left(2,-\frac{e x}{2}\right)","\log (2) \log (x)-\text{PolyLog}\left(2,-\frac{e x}{2}\right)",1,"Log[2]*Log[x] - PolyLog[2, -(e*x)/2]","A",2,2,10,0.2000,1,"{2392, 2391}"
75,1,8,0,0.007346,"\int \frac{\log (1+e x)}{x} \, dx","Int[Log[1 + e*x]/x,x]","-\text{PolyLog}(2,-e x)","-\text{PolyLog}(2,-e x)",1,"-PolyLog[2, -(e*x)]","A",1,1,10,0.1000,1,"{2391}"
76,1,10,0,0.0061649,"\int \frac{\log (e x)}{x} \, dx","Int[Log[e*x]/x,x]","\frac{1}{2} \log ^2(e x)","\frac{1}{2} \log ^2(e x)",1,"Log[e*x]^2/2","A",1,1,8,0.1250,1,"{2301}"
77,1,20,0,0.0185377,"\int \frac{\log (-1+e x)}{x} \, dx","Int[Log[-1 + e*x]/x,x]","\text{PolyLog}(2,1-e x)+\log (e x) \log (e x-1)","\text{PolyLog}(2,1-e x)+\log (e x) \log (e x-1)",1,"Log[e*x]*Log[-1 + e*x] + PolyLog[2, 1 - e*x]","A",2,2,10,0.2000,1,"{2394, 2315}"
78,1,25,0,0.0197499,"\int \frac{\log (-2+e x)}{x} \, dx","Int[Log[-2 + e*x]/x,x]","\text{PolyLog}\left(2,1-\frac{e x}{2}\right)+\log \left(\frac{e x}{2}\right) \log (e x-2)","\text{PolyLog}\left(2,1-\frac{e x}{2}\right)+\log \left(\frac{e x}{2}\right) \log (e x-2)",1,"Log[(e*x)/2]*Log[-2 + e*x] + PolyLog[2, 1 - (e*x)/2]","A",2,2,10,0.2000,1,"{2394, 2315}"
79,1,21,0,0.0208121,"\int \frac{a+b \log (3+e x)}{x} \, dx","Int[(a + b*Log[3 + e*x])/x,x]","\log (x) (a+b \log (3))-b \text{PolyLog}\left(2,-\frac{e x}{3}\right)","\log (x) (a+b \log (3))-b \text{PolyLog}\left(2,-\frac{e x}{3}\right)",1,"(a + b*Log[3])*Log[x] - b*PolyLog[2, -(e*x)/3]","A",2,2,14,0.1429,1,"{2392, 2391}"
80,1,21,0,0.0214168,"\int \frac{a+b \log (2+e x)}{x} \, dx","Int[(a + b*Log[2 + e*x])/x,x]","\log (x) (a+b \log (2))-b \text{PolyLog}\left(2,-\frac{e x}{2}\right)","\log (x) (a+b \log (2))-b \text{PolyLog}\left(2,-\frac{e x}{2}\right)",1,"(a + b*Log[2])*Log[x] - b*PolyLog[2, -(e*x)/2]","A",2,2,14,0.1429,1,"{2392, 2391}"
81,1,14,0,0.0183462,"\int \frac{a+b \log (1+e x)}{x} \, dx","Int[(a + b*Log[1 + e*x])/x,x]","a \log (x)-b \text{PolyLog}(2,-e x)","a \log (x)-b \text{PolyLog}(2,-e x)",1,"a*Log[x] - b*PolyLog[2, -(e*x)]","A",2,2,14,0.1429,1,"{2392, 2391}"
82,1,17,0,0.0112685,"\int \frac{a+b \log (e x)}{x} \, dx","Int[(a + b*Log[e*x])/x,x]","\frac{(a+b \log (e x))^2}{2 b}","\frac{(a+b \log (e x))^2}{2 b}",1,"(a + b*Log[e*x])^2/(2*b)","A",1,1,12,0.08333,1,"{2301}"
83,1,26,0,0.0222327,"\int \frac{a+b \log (-1+e x)}{x} \, dx","Int[(a + b*Log[-1 + e*x])/x,x]","b \text{PolyLog}(2,1-e x)+\log (e x) (a+b \log (e x-1))","b \text{PolyLog}(2,1-e x)+\log (e x) (a+b \log (e x-1))",1,"Log[e*x]*(a + b*Log[-1 + e*x]) + b*PolyLog[2, 1 - e*x]","A",2,2,14,0.1429,1,"{2394, 2315}"
84,1,31,0,0.0227376,"\int \frac{a+b \log (-2+e x)}{x} \, dx","Int[(a + b*Log[-2 + e*x])/x,x]","b \text{PolyLog}\left(2,1-\frac{e x}{2}\right)+\log \left(\frac{e x}{2}\right) (a+b \log (e x-2))","b \text{PolyLog}\left(2,1-\frac{e x}{2}\right)+\log \left(\frac{e x}{2}\right) (a+b \log (e x-2))",1,"Log[(e*x)/2]*(a + b*Log[-2 + e*x]) + b*PolyLog[2, 1 - (e*x)/2]","A",2,2,14,0.1429,1,"{2394, 2315}"
85,1,156,0,0.1916443,"\int x^2 \log ^2\left(c (a+b x)^n\right) \, dx","Int[x^2*Log[c*(a + b*x)^n]^2,x]","-\frac{1}{9} n \left(\frac{18 a^2 (a+b x)}{b^3}-\frac{6 a^3 \log (a+b x)}{b^3}-\frac{9 a (a+b x)^2}{b^3}+\frac{2 (a+b x)^3}{b^3}\right) \log \left(c (a+b x)^n\right)+\frac{2 a^2 n^2 x}{b^2}-\frac{a^3 n^2 \log ^2(a+b x)}{3 b^3}-\frac{a n^2 (a+b x)^2}{2 b^3}+\frac{2 n^2 (a+b x)^3}{27 b^3}+\frac{1}{3} x^3 \log ^2\left(c (a+b x)^n\right)","\frac{2 a^3 n \log (a+b x) \log \left(c (a+b x)^n\right)}{3 b^3}-\frac{2 a^2 n (a+b x) \log \left(c (a+b x)^n\right)}{b^3}+\frac{2 a^2 n^2 x}{b^2}-\frac{a^3 n^2 \log ^2(a+b x)}{3 b^3}+\frac{a n (a+b x)^2 \log \left(c (a+b x)^n\right)}{b^3}-\frac{2 n (a+b x)^3 \log \left(c (a+b x)^n\right)}{9 b^3}-\frac{a n^2 (a+b x)^2}{2 b^3}+\frac{2 n^2 (a+b x)^3}{27 b^3}+\frac{1}{3} x^3 \log ^2\left(c (a+b x)^n\right)",1,"(2*a^2*n^2*x)/b^2 - (a*n^2*(a + b*x)^2)/(2*b^3) + (2*n^2*(a + b*x)^3)/(27*b^3) - (a^3*n^2*Log[a + b*x]^2)/(3*b^3) - (n*((18*a^2*(a + b*x))/b^3 - (9*a*(a + b*x)^2)/b^3 + (2*(a + b*x)^3)/b^3 - (6*a^3*Log[a + b*x])/b^3)*Log[c*(a + b*x)^n])/9 + (x^3*Log[c*(a + b*x)^n]^2)/3","A",7,7,16,0.4375,1,"{2398, 2411, 43, 2334, 12, 14, 2301}"
86,1,193,0,0.3061621,"\int \frac{\log ^2\left(c (a+b x)^n\right)}{x^4} \, dx","Int[Log[c*(a + b*x)^n]^2/x^4,x]","\frac{2 b^3 n^2 \text{PolyLog}\left(2,\frac{b x}{a}+1\right)}{3 a^3}-\frac{b^3 \log ^2\left(c (a+b x)^n\right)}{3 a^3}+\frac{2 b^3 n \log \left(-\frac{b x}{a}\right) \log \left(c (a+b x)^n\right)}{3 a^3}+\frac{2 b^2 n (a+b x) \log \left(c (a+b x)^n\right)}{3 a^3 x}-\frac{b^2 n^2}{3 a^2 x}-\frac{b^3 n^2 \log (x)}{a^3}+\frac{b^3 n^2 \log (a+b x)}{3 a^3}-\frac{\log ^2\left(c (a+b x)^n\right)}{3 x^3}-\frac{b n \log \left(c (a+b x)^n\right)}{3 a x^2}","-\frac{2 b^3 n^2 \text{PolyLog}\left(2,\frac{a}{a+b x}\right)}{3 a^3}+\frac{2 b^3 n \log \left(1-\frac{a}{a+b x}\right) \log \left(c (a+b x)^n\right)}{3 a^3}+\frac{2 b^2 n (a+b x) \log \left(c (a+b x)^n\right)}{3 a^3 x}-\frac{b^2 n^2}{3 a^2 x}-\frac{b^3 n^2 \log (x)}{a^3}+\frac{b^3 n^2 \log (a+b x)}{3 a^3}-\frac{\log ^2\left(c (a+b x)^n\right)}{3 x^3}-\frac{b n \log \left(c (a+b x)^n\right)}{3 a x^2}",1,"-(b^2*n^2)/(3*a^2*x) - (b^3*n^2*Log[x])/a^3 + (b^3*n^2*Log[a + b*x])/(3*a^3) - (b*n*Log[c*(a + b*x)^n])/(3*a*x^2) + (2*b^2*n*(a + b*x)*Log[c*(a + b*x)^n])/(3*a^3*x) + (2*b^3*n*Log[-((b*x)/a)]*Log[c*(a + b*x)^n])/(3*a^3) - (b^3*Log[c*(a + b*x)^n]^2)/(3*a^3) - Log[c*(a + b*x)^n]^2/(3*x^3) + (2*b^3*n^2*PolyLog[2, 1 + (b*x)/a])/(3*a^3)","A",13,11,16,0.6875,1,"{2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
87,1,285,0,0.2237188,"\int x^2 \log ^3\left(c (a+b x)^n\right) \, dx","Int[x^2*Log[c*(a + b*x)^n]^3,x]","\frac{6 a^2 n^2 (a+b x) \log \left(c (a+b x)^n\right)}{b^3}-\frac{3 a^2 n (a+b x) \log ^2\left(c (a+b x)^n\right)}{b^3}+\frac{a^2 (a+b x) \log ^3\left(c (a+b x)^n\right)}{b^3}-\frac{6 a^2 n^3 x}{b^2}+\frac{2 n^2 (a+b x)^3 \log \left(c (a+b x)^n\right)}{9 b^3}-\frac{3 a n^2 (a+b x)^2 \log \left(c (a+b x)^n\right)}{2 b^3}-\frac{n (a+b x)^3 \log ^2\left(c (a+b x)^n\right)}{3 b^3}+\frac{3 a n (a+b x)^2 \log ^2\left(c (a+b x)^n\right)}{2 b^3}+\frac{(a+b x)^3 \log ^3\left(c (a+b x)^n\right)}{3 b^3}-\frac{a (a+b x)^2 \log ^3\left(c (a+b x)^n\right)}{b^3}-\frac{2 n^3 (a+b x)^3}{27 b^3}+\frac{3 a n^3 (a+b x)^2}{4 b^3}","\frac{6 a^2 n^2 (a+b x) \log \left(c (a+b x)^n\right)}{b^3}-\frac{3 a^2 n (a+b x) \log ^2\left(c (a+b x)^n\right)}{b^3}+\frac{a^2 (a+b x) \log ^3\left(c (a+b x)^n\right)}{b^3}-\frac{6 a^2 n^3 x}{b^2}+\frac{2 n^2 (a+b x)^3 \log \left(c (a+b x)^n\right)}{9 b^3}-\frac{3 a n^2 (a+b x)^2 \log \left(c (a+b x)^n\right)}{2 b^3}-\frac{n (a+b x)^3 \log ^2\left(c (a+b x)^n\right)}{3 b^3}+\frac{3 a n (a+b x)^2 \log ^2\left(c (a+b x)^n\right)}{2 b^3}+\frac{(a+b x)^3 \log ^3\left(c (a+b x)^n\right)}{3 b^3}-\frac{a (a+b x)^2 \log ^3\left(c (a+b x)^n\right)}{b^3}-\frac{2 n^3 (a+b x)^3}{27 b^3}+\frac{3 a n^3 (a+b x)^2}{4 b^3}",1,"(-6*a^2*n^3*x)/b^2 + (3*a*n^3*(a + b*x)^2)/(4*b^3) - (2*n^3*(a + b*x)^3)/(27*b^3) + (6*a^2*n^2*(a + b*x)*Log[c*(a + b*x)^n])/b^3 - (3*a*n^2*(a + b*x)^2*Log[c*(a + b*x)^n])/(2*b^3) + (2*n^2*(a + b*x)^3*Log[c*(a + b*x)^n])/(9*b^3) - (3*a^2*n*(a + b*x)*Log[c*(a + b*x)^n]^2)/b^3 + (3*a*n*(a + b*x)^2*Log[c*(a + b*x)^n]^2)/(2*b^3) - (n*(a + b*x)^3*Log[c*(a + b*x)^n]^2)/(3*b^3) + (a^2*(a + b*x)*Log[c*(a + b*x)^n]^3)/b^3 - (a*(a + b*x)^2*Log[c*(a + b*x)^n]^3)/b^3 + ((a + b*x)^3*Log[c*(a + b*x)^n]^3)/(3*b^3)","A",14,7,16,0.4375,1,"{2401, 2389, 2296, 2295, 2390, 2305, 2304}"
88,1,299,0,0.4523567,"\int \frac{(f+g x)^3}{a+b \log \left(c (d+e x)^n\right)} \, dx","Int[(f + g*x)^3/(a + b*Log[c*(d + e*x)^n]),x]","\frac{3 g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 (e f-d g) \left(c (d+e x)^n\right)^{-3/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b e^4 n}+\frac{3 g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b e^4 n}+\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g)^3 \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b e^4 n}+\frac{g^3 e^{-\frac{4 a}{b n}} (d+e x)^4 \left(c (d+e x)^n\right)^{-4/n} \text{Ei}\left(\frac{4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b e^4 n}","\frac{3 g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 (e f-d g) \left(c (d+e x)^n\right)^{-3/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b e^4 n}+\frac{3 g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b e^4 n}+\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g)^3 \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b e^4 n}+\frac{g^3 e^{-\frac{4 a}{b n}} (d+e x)^4 \left(c (d+e x)^n\right)^{-4/n} \text{Ei}\left(\frac{4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b e^4 n}",1,"((e*f - d*g)^3*(d + e*x)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)])/(b*e^4*E^(a/(b*n))*n*(c*(d + e*x)^n)^n^(-1)) + (3*g*(e*f - d*g)^2*(d + e*x)^2*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)])/(b*e^4*E^((2*a)/(b*n))*n*(c*(d + e*x)^n)^(2/n)) + (3*g^2*(e*f - d*g)*(d + e*x)^3*ExpIntegralEi[(3*(a + b*Log[c*(d + e*x)^n]))/(b*n)])/(b*e^4*E^((3*a)/(b*n))*n*(c*(d + e*x)^n)^(3/n)) + (g^3*(d + e*x)^4*ExpIntegralEi[(4*(a + b*Log[c*(d + e*x)^n]))/(b*n)])/(b*e^4*E^((4*a)/(b*n))*n*(c*(d + e*x)^n)^(4/n))","A",14,6,24,0.2500,1,"{2399, 2389, 2300, 2178, 2390, 2310}"
89,1,219,0,0.2932584,"\int \frac{(f+g x)^2}{a+b \log \left(c (d+e x)^n\right)} \, dx","Int[(f + g*x)^2/(a + b*Log[c*(d + e*x)^n]),x]","\frac{2 g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b e^3 n}+\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b e^3 n}+\frac{g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b e^3 n}","\frac{2 g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b e^3 n}+\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b e^3 n}+\frac{g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b e^3 n}",1,"((e*f - d*g)^2*(d + e*x)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)])/(b*e^3*E^(a/(b*n))*n*(c*(d + e*x)^n)^n^(-1)) + (2*g*(e*f - d*g)*(d + e*x)^2*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)])/(b*e^3*E^((2*a)/(b*n))*n*(c*(d + e*x)^n)^(2/n)) + (g^2*(d + e*x)^3*ExpIntegralEi[(3*(a + b*Log[c*(d + e*x)^n]))/(b*n)])/(b*e^3*E^((3*a)/(b*n))*n*(c*(d + e*x)^n)^(3/n))","A",11,6,24,0.2500,1,"{2399, 2389, 2300, 2178, 2390, 2310}"
90,1,139,0,0.1619259,"\int \frac{f+g x}{a+b \log \left(c (d+e x)^n\right)} \, dx","Int[(f + g*x)/(a + b*Log[c*(d + e*x)^n]),x]","\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b e^2 n}+\frac{g e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b e^2 n}","\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b e^2 n}+\frac{g e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b e^2 n}",1,"((e*f - d*g)*(d + e*x)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)])/(b*e^2*E^(a/(b*n))*n*(c*(d + e*x)^n)^n^(-1)) + (g*(d + e*x)^2*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)])/(b*e^2*E^((2*a)/(b*n))*n*(c*(d + e*x)^n)^(2/n))","A",8,6,22,0.2727,1,"{2399, 2389, 2300, 2178, 2390, 2310}"
91,1,63,0,0.0463784,"\int \frac{1}{a+b \log \left(c (d+e x)^n\right)} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(-1),x]","\frac{e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b e n}","\frac{e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b e n}",1,"((d + e*x)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)])/(b*e*E^(a/(b*n))*n*(c*(d + e*x)^n)^n^(-1))","A",3,3,16,0.1875,1,"{2389, 2300, 2178}"
92,0,0,0,0.0374711,"\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","Int[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])),x]","\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)},x\right)",0,"Defer[Int][1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])), x]","A",0,0,0,0,-1,"{}"
93,0,0,0,0.0354016,"\int \frac{1}{(f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","Int[1/((f + g*x)^2*(a + b*Log[c*(d + e*x)^n])),x]","\int \frac{1}{(f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{(f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)},x\right)",0,"Defer[Int][1/((f + g*x)^2*(a + b*Log[c*(d + e*x)^n])), x]","A",0,0,0,0,-1,"{}"
94,1,339,0,0.7884037,"\int \frac{(f+g x)^3}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Int[(f + g*x)^3/(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{9 g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 (e f-d g) \left(c (d+e x)^n\right)^{-3/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b^2 e^4 n^2}+\frac{6 g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b^2 e^4 n^2}+\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g)^3 \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b^2 e^4 n^2}+\frac{4 g^3 e^{-\frac{4 a}{b n}} (d+e x)^4 \left(c (d+e x)^n\right)^{-4/n} \text{Ei}\left(\frac{4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b^2 e^4 n^2}-\frac{(d+e x) (f+g x)^3}{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}","\frac{9 g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 (e f-d g) \left(c (d+e x)^n\right)^{-3/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b^2 e^4 n^2}+\frac{6 g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b^2 e^4 n^2}+\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g)^3 \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b^2 e^4 n^2}+\frac{4 g^3 e^{-\frac{4 a}{b n}} (d+e x)^4 \left(c (d+e x)^n\right)^{-4/n} \text{Ei}\left(\frac{4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b^2 e^4 n^2}-\frac{(d+e x) (f+g x)^3}{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}",1,"((e*f - d*g)^3*(d + e*x)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)])/(b^2*e^4*E^(a/(b*n))*n^2*(c*(d + e*x)^n)^n^(-1)) + (6*g*(e*f - d*g)^2*(d + e*x)^2*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)])/(b^2*e^4*E^((2*a)/(b*n))*n^2*(c*(d + e*x)^n)^(2/n)) + (9*g^2*(e*f - d*g)*(d + e*x)^3*ExpIntegralEi[(3*(a + b*Log[c*(d + e*x)^n]))/(b*n)])/(b^2*e^4*E^((3*a)/(b*n))*n^2*(c*(d + e*x)^n)^(3/n)) + (4*g^3*(d + e*x)^4*ExpIntegralEi[(4*(a + b*Log[c*(d + e*x)^n]))/(b*n)])/(b^2*e^4*E^((4*a)/(b*n))*n^2*(c*(d + e*x)^n)^(4/n)) - ((d + e*x)*(f + g*x)^3)/(b*e*n*(a + b*Log[c*(d + e*x)^n]))","A",26,7,24,0.2917,1,"{2400, 2399, 2389, 2300, 2178, 2390, 2310}"
95,1,259,0,0.517006,"\int \frac{(f+g x)^2}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Int[(f + g*x)^2/(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{4 g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b^2 e^3 n^2}+\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b^2 e^3 n^2}+\frac{3 g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b^2 e^3 n^2}-\frac{(d+e x) (f+g x)^2}{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}","\frac{4 g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b^2 e^3 n^2}+\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b^2 e^3 n^2}+\frac{3 g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b^2 e^3 n^2}-\frac{(d+e x) (f+g x)^2}{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}",1,"((e*f - d*g)^2*(d + e*x)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)])/(b^2*e^3*E^(a/(b*n))*n^2*(c*(d + e*x)^n)^n^(-1)) + (4*g*(e*f - d*g)*(d + e*x)^2*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)])/(b^2*e^3*E^((2*a)/(b*n))*n^2*(c*(d + e*x)^n)^(2/n)) + (3*g^2*(d + e*x)^3*ExpIntegralEi[(3*(a + b*Log[c*(d + e*x)^n]))/(b*n)])/(b^2*e^3*E^((3*a)/(b*n))*n^2*(c*(d + e*x)^n)^(3/n)) - ((d + e*x)*(f + g*x)^2)/(b*e*n*(a + b*Log[c*(d + e*x)^n]))","A",20,7,24,0.2917,1,"{2400, 2399, 2389, 2300, 2178, 2390, 2310}"
96,1,177,0,0.2480994,"\int \frac{f+g x}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Int[(f + g*x)/(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b^2 e^2 n^2}+\frac{2 g e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b^2 e^2 n^2}-\frac{(d+e x) (f+g x)}{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}","\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b^2 e^2 n^2}+\frac{2 g e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b^2 e^2 n^2}-\frac{(d+e x) (f+g x)}{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}",1,"((e*f - d*g)*(d + e*x)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)])/(b^2*e^2*E^(a/(b*n))*n^2*(c*(d + e*x)^n)^n^(-1)) + (2*g*(d + e*x)^2*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)])/(b^2*e^2*E^((2*a)/(b*n))*n^2*(c*(d + e*x)^n)^(2/n)) - ((d + e*x)*(f + g*x))/(b*e*n*(a + b*Log[c*(d + e*x)^n]))","A",12,7,22,0.3182,1,"{2400, 2399, 2389, 2300, 2178, 2390, 2310}"
97,1,96,0,0.063036,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(-2),x]","\frac{e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b^2 e n^2}-\frac{d+e x}{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}","\frac{e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b^2 e n^2}-\frac{d+e x}{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}",1,"((d + e*x)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)])/(b^2*e*E^(a/(b*n))*n^2*(c*(d + e*x)^n)^n^(-1)) - (d + e*x)/(b*e*n*(a + b*Log[c*(d + e*x)^n]))","A",4,4,16,0.2500,1,"{2389, 2297, 2300, 2178}"
98,0,0,0,0.0341539,"\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Int[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^2),x]","\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2},x\right)",0,"Defer[Int][1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^2), x]","A",0,0,0,0,-1,"{}"
99,0,0,0,0.0334217,"\int \frac{1}{(f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Int[1/((f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^2),x]","\int \frac{1}{(f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2},x\right)",0,"Defer[Int][1/((f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^2), x]","A",0,0,0,0,-1,"{}"
100,1,351,0,0.8645873,"\int \frac{(f+g x)^2}{\left(a+b \log \left(c (d+e x)^n\right)\right)^3} \, dx","Int[(f + g*x)^2/(a + b*Log[c*(d + e*x)^n])^3,x]","\frac{4 g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b^3 e^3 n^3}+\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{2 b^3 e^3 n^3}+\frac{9 g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{2 b^3 e^3 n^3}+\frac{(d+e x) (f+g x) (e f-d g)}{b^2 e^2 n^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}-\frac{3 (d+e x) (f+g x)^2}{2 b^2 e n^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}-\frac{(d+e x) (f+g x)^2}{2 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^2}","\frac{4 g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b^3 e^3 n^3}+\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{2 b^3 e^3 n^3}+\frac{9 g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{2 b^3 e^3 n^3}+\frac{(d+e x) (f+g x) (e f-d g)}{b^2 e^2 n^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}-\frac{3 (d+e x) (f+g x)^2}{2 b^2 e n^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}-\frac{(d+e x) (f+g x)^2}{2 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^2}",1,"((e*f - d*g)^2*(d + e*x)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)])/(2*b^3*e^3*E^(a/(b*n))*n^3*(c*(d + e*x)^n)^n^(-1)) + (4*g*(e*f - d*g)*(d + e*x)^2*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)])/(b^3*e^3*E^((2*a)/(b*n))*n^3*(c*(d + e*x)^n)^(2/n)) + (9*g^2*(d + e*x)^3*ExpIntegralEi[(3*(a + b*Log[c*(d + e*x)^n]))/(b*n)])/(2*b^3*e^3*E^((3*a)/(b*n))*n^3*(c*(d + e*x)^n)^(3/n)) - ((d + e*x)*(f + g*x)^2)/(2*b*e*n*(a + b*Log[c*(d + e*x)^n])^2) + ((e*f - d*g)*(d + e*x)*(f + g*x))/(b^2*e^2*n^2*(a + b*Log[c*(d + e*x)^n])) - (3*(d + e*x)*(f + g*x)^2)/(2*b^2*e*n^2*(a + b*Log[c*(d + e*x)^n]))","A",33,7,24,0.2917,1,"{2400, 2399, 2389, 2300, 2178, 2390, 2310}"
101,1,261,0,0.360439,"\int \frac{f+g x}{\left(a+b \log \left(c (d+e x)^n\right)\right)^3} \, dx","Int[(f + g*x)/(a + b*Log[c*(d + e*x)^n])^3,x]","\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{2 b^3 e^2 n^3}+\frac{2 g e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b^3 e^2 n^3}+\frac{(d+e x) (e f-d g)}{2 b^2 e^2 n^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}-\frac{(d+e x) (f+g x)}{b^2 e n^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}-\frac{(d+e x) (f+g x)}{2 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^2}","\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{2 b^3 e^2 n^3}+\frac{2 g e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{b^3 e^2 n^3}+\frac{(d+e x) (e f-d g)}{2 b^2 e^2 n^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}-\frac{(d+e x) (f+g x)}{b^2 e n^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}-\frac{(d+e x) (f+g x)}{2 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^2}",1,"((e*f - d*g)*(d + e*x)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)])/(2*b^3*e^2*E^(a/(b*n))*n^3*(c*(d + e*x)^n)^n^(-1)) + (2*g*(d + e*x)^2*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)])/(b^3*e^2*E^((2*a)/(b*n))*n^3*(c*(d + e*x)^n)^(2/n)) - ((d + e*x)*(f + g*x))/(2*b*e*n*(a + b*Log[c*(d + e*x)^n])^2) + ((e*f - d*g)*(d + e*x))/(2*b^2*e^2*n^2*(a + b*Log[c*(d + e*x)^n])) - ((d + e*x)*(f + g*x))/(b^2*e*n^2*(a + b*Log[c*(d + e*x)^n]))","A",17,8,22,0.3636,1,"{2400, 2399, 2389, 2300, 2178, 2390, 2310, 2297}"
102,1,135,0,0.0803857,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^3} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(-3),x]","\frac{e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{2 b^3 e n^3}-\frac{d+e x}{2 b^2 e n^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}-\frac{d+e x}{2 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^2}","\frac{e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{2 b^3 e n^3}-\frac{d+e x}{2 b^2 e n^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}-\frac{d+e x}{2 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^2}",1,"((d + e*x)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)])/(2*b^3*e*E^(a/(b*n))*n^3*(c*(d + e*x)^n)^n^(-1)) - (d + e*x)/(2*b*e*n*(a + b*Log[c*(d + e*x)^n])^2) - (d + e*x)/(2*b^2*e*n^2*(a + b*Log[c*(d + e*x)^n]))","A",5,4,16,0.2500,1,"{2389, 2297, 2300, 2178}"
103,0,0,0,0.03413,"\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3} \, dx","Int[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^3),x]","\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3} \, dx","\text{Int}\left(\frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3},x\right)",0,"Defer[Int][1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^3), x]","A",0,0,0,0,-1,"{}"
104,0,0,0,0.0336433,"\int \frac{1}{(f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3} \, dx","Int[1/((f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^3),x]","\int \frac{1}{(f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3} \, dx","\text{Int}\left(\frac{1}{(f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3},x\right)",0,"Defer[Int][1/((f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^3), x]","A",0,0,0,0,-1,"{}"
105,1,404,0,0.7011427,"\int (f+g x)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)} \, dx","Int[(f + g*x)^2*Sqrt[a + b*Log[c*(d + e*x)^n]],x]","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} g \sqrt{n} e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{2 e^3}-\frac{\sqrt{\pi } \sqrt{b} \sqrt{n} e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{2 e^3}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} g^2 \sqrt{n} e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{6 e^3}+\frac{g (d+e x)^2 (e f-d g) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{e^3}+\frac{(d+e x) (e f-d g)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{e^3}+\frac{g^2 (d+e x)^3 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{3 e^3}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} g \sqrt{n} e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{2 e^3}-\frac{\sqrt{\pi } \sqrt{b} \sqrt{n} e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{2 e^3}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} g^2 \sqrt{n} e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{6 e^3}+\frac{g (d+e x)^2 (e f-d g) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{e^3}+\frac{(d+e x) (e f-d g)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{e^3}+\frac{g^2 (d+e x)^3 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{3 e^3}",1,"-(Sqrt[b]*(e*f - d*g)^2*Sqrt[n]*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(2*e^3*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) - (Sqrt[b]*g*(e*f - d*g)*Sqrt[n]*Sqrt[Pi/2]*(d + e*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(2*e^3*E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)) - (Sqrt[b]*g^2*Sqrt[n]*Sqrt[Pi/3]*(d + e*x)^3*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(6*e^3*E^((3*a)/(b*n))*(c*(d + e*x)^n)^(3/n)) + ((e*f - d*g)^2*(d + e*x)*Sqrt[a + b*Log[c*(d + e*x)^n]])/e^3 + (g*(e*f - d*g)*(d + e*x)^2*Sqrt[a + b*Log[c*(d + e*x)^n]])/e^3 + (g^2*(d + e*x)^3*Sqrt[a + b*Log[c*(d + e*x)^n]])/(3*e^3)","A",17,9,26,0.3462,1,"{2401, 2389, 2296, 2300, 2180, 2204, 2390, 2305, 2310}"
106,1,255,0,0.3405513,"\int (f+g x) \sqrt{a+b \log \left(c (d+e x)^n\right)} \, dx","Int[(f + g*x)*Sqrt[a + b*Log[c*(d + e*x)^n]],x]","-\frac{\sqrt{\pi } \sqrt{b} \sqrt{n} e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{2 e^2}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} g \sqrt{n} e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{4 e^2}+\frac{(d+e x) (e f-d g) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{e^2}+\frac{g (d+e x)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{2 e^2}","-\frac{\sqrt{\pi } \sqrt{b} \sqrt{n} e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{2 e^2}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} g \sqrt{n} e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{4 e^2}+\frac{(d+e x) (e f-d g) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{e^2}+\frac{g (d+e x)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{2 e^2}",1,"-(Sqrt[b]*(e*f - d*g)*Sqrt[n]*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(2*e^2*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) - (Sqrt[b]*g*Sqrt[n]*Sqrt[Pi/2]*(d + e*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(4*e^2*E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)) + ((e*f - d*g)*(d + e*x)*Sqrt[a + b*Log[c*(d + e*x)^n]])/e^2 + (g*(d + e*x)^2*Sqrt[a + b*Log[c*(d + e*x)^n]])/(2*e^2)","A",12,9,24,0.3750,1,"{2401, 2389, 2296, 2300, 2180, 2204, 2390, 2305, 2310}"
107,1,111,0,0.0866578,"\int \sqrt{a+b \log \left(c (d+e x)^n\right)} \, dx","Int[Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\frac{(d+e x) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{e}-\frac{\sqrt{\pi } \sqrt{b} \sqrt{n} e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{2 e}","\frac{(d+e x) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{e}-\frac{\sqrt{\pi } \sqrt{b} \sqrt{n} e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{2 e}",1,"-(Sqrt[b]*Sqrt[n]*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(2*e*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + ((d + e*x)*Sqrt[a + b*Log[c*(d + e*x)^n]])/e","A",5,5,18,0.2778,1,"{2389, 2296, 2300, 2180, 2204}"
108,0,0,0,0.0473416,"\int \frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{f+g x} \, dx","Int[Sqrt[a + b*Log[c*(d + e*x)^n]]/(f + g*x),x]","\int \frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{f+g x} \, dx","\text{Int}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{f+g x},x\right)",0,"Defer[Int][Sqrt[a + b*Log[c*(d + e*x)^n]]/(f + g*x), x]","A",0,0,0,0,-1,"{}"
109,0,0,0,0.102329,"\int \frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{(f+g x)^2} \, dx","Int[Sqrt[a + b*Log[c*(d + e*x)^n]]/(f + g*x)^2,x]","\int \frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{(f+g x)^2} \, dx","\frac{(d+e x) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{(f+g x) (e f-d g)}-\frac{b e n \text{Int}\left(\frac{1}{(f+g x) \sqrt{a+b \log \left(c (d+e x)^n\right)}},x\right)}{2 (e f-d g)}",0,"((d + e*x)*Sqrt[a + b*Log[c*(d + e*x)^n]])/((e*f - d*g)*(f + g*x)) - (b*e*n*Defer[Int][1/((f + g*x)*Sqrt[a + b*Log[c*(d + e*x)^n]]), x])/(2*(e*f - d*g))","A",0,0,0,0,-1,"{}"
110,0,0,0,0.2164647,"\int \frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{(f+g x)^3} \, dx","Int[Sqrt[a + b*Log[c*(d + e*x)^n]]/(f + g*x)^3,x]","\int \frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{(f+g x)^3} \, dx","\frac{b e n \text{Int}\left(\frac{1}{(d+e x) (f+g x)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}},x\right)}{4 g}-\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{2 g (f+g x)^2}",0,"-Sqrt[a + b*Log[c*(d + e*x)^n]]/(2*g*(f + g*x)^2) + (b*e*n*Defer[Int][1/((d + e*x)*(f + g*x)^2*Sqrt[a + b*Log[c*(d + e*x)^n]]), x])/(4*g)","A",0,0,0,0,-1,"{}"
111,1,526,0,0.812482,"\int (f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2} \, dx","Int[(f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^(3/2),x]","\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} g n^{3/2} e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{8 e^3}+\frac{3 \sqrt{\pi } b^{3/2} n^{3/2} e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{4 e^3}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} g^2 n^{3/2} e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{12 e^3}+\frac{g (d+e x)^2 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{e^3}+\frac{(d+e x) (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{e^3}-\frac{3 b g n (d+e x)^2 (e f-d g) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{4 e^3}-\frac{3 b n (d+e x) (e f-d g)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{2 e^3}+\frac{g^2 (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{3 e^3}-\frac{b g^2 n (d+e x)^3 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{6 e^3}","\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} g n^{3/2} e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{8 e^3}+\frac{3 \sqrt{\pi } b^{3/2} n^{3/2} e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{4 e^3}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} g^2 n^{3/2} e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{12 e^3}+\frac{g (d+e x)^2 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{e^3}+\frac{(d+e x) (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{e^3}-\frac{3 b g n (d+e x)^2 (e f-d g) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{4 e^3}-\frac{3 b n (d+e x) (e f-d g)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{2 e^3}+\frac{g^2 (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{3 e^3}-\frac{b g^2 n (d+e x)^3 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{6 e^3}",1,"(3*b^(3/2)*(e*f - d*g)^2*n^(3/2)*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(4*e^3*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + (3*b^(3/2)*g*(e*f - d*g)*n^(3/2)*Sqrt[Pi/2]*(d + e*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(8*e^3*E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)) + (b^(3/2)*g^2*n^(3/2)*Sqrt[Pi/3]*(d + e*x)^3*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(12*e^3*E^((3*a)/(b*n))*(c*(d + e*x)^n)^(3/n)) - (3*b*(e*f - d*g)^2*n*(d + e*x)*Sqrt[a + b*Log[c*(d + e*x)^n]])/(2*e^3) - (3*b*g*(e*f - d*g)*n*(d + e*x)^2*Sqrt[a + b*Log[c*(d + e*x)^n]])/(4*e^3) - (b*g^2*n*(d + e*x)^3*Sqrt[a + b*Log[c*(d + e*x)^n]])/(6*e^3) + ((e*f - d*g)^2*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^(3/2))/e^3 + (g*(e*f - d*g)*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^(3/2))/e^3 + (g^2*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])^(3/2))/(3*e^3)","A",20,9,26,0.3462,1,"{2401, 2389, 2296, 2300, 2180, 2204, 2390, 2305, 2310}"
112,1,330,0,0.42635,"\int (f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2} \, dx","Int[(f + g*x)*(a + b*Log[c*(d + e*x)^n])^(3/2),x]","\frac{3 \sqrt{\pi } b^{3/2} n^{3/2} e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{4 e^2}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} g n^{3/2} e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{16 e^2}+\frac{(d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{e^2}-\frac{3 b n (d+e x) (e f-d g) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{2 e^2}+\frac{g (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{2 e^2}-\frac{3 b g n (d+e x)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{8 e^2}","\frac{3 \sqrt{\pi } b^{3/2} n^{3/2} e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{4 e^2}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} g n^{3/2} e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{16 e^2}+\frac{(d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{e^2}-\frac{3 b n (d+e x) (e f-d g) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{2 e^2}+\frac{g (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{2 e^2}-\frac{3 b g n (d+e x)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{8 e^2}",1,"(3*b^(3/2)*(e*f - d*g)*n^(3/2)*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(4*e^2*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + (3*b^(3/2)*g*n^(3/2)*Sqrt[Pi/2]*(d + e*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(16*e^2*E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)) - (3*b*(e*f - d*g)*n*(d + e*x)*Sqrt[a + b*Log[c*(d + e*x)^n]])/(2*e^2) - (3*b*g*n*(d + e*x)^2*Sqrt[a + b*Log[c*(d + e*x)^n]])/(8*e^2) + ((e*f - d*g)*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^(3/2))/e^2 + (g*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^(3/2))/(2*e^2)","A",14,9,24,0.3750,1,"{2401, 2389, 2296, 2300, 2180, 2204, 2390, 2305, 2310}"
113,1,143,0,0.1088578,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(3/2),x]","\frac{3 \sqrt{\pi } b^{3/2} n^{3/2} e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{4 e}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{e}-\frac{3 b n (d+e x) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{2 e}","\frac{3 \sqrt{\pi } b^{3/2} n^{3/2} e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{4 e}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{e}-\frac{3 b n (d+e x) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{2 e}",1,"(3*b^(3/2)*n^(3/2)*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(4*e*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) - (3*b*n*(d + e*x)*Sqrt[a + b*Log[c*(d + e*x)^n]])/(2*e) + ((d + e*x)*(a + b*Log[c*(d + e*x)^n])^(3/2))/e","A",6,5,18,0.2778,1,"{2389, 2296, 2300, 2180, 2204}"
114,0,0,0,0.0564951,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{f+g x} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(3/2)/(f + g*x),x]","\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{f+g x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{f+g x},x\right)",0,"Defer[Int][(a + b*Log[c*(d + e*x)^n])^(3/2)/(f + g*x), x]","A",0,0,0,0,-1,"{}"
115,0,0,0,0.1056158,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{(f+g x)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(3/2)/(f + g*x)^2,x]","\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{(f+g x)^2} \, dx","\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{(f+g x) (e f-d g)}-\frac{3 b e n \text{Int}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{f+g x},x\right)}{2 (e f-d g)}",0,"((d + e*x)*(a + b*Log[c*(d + e*x)^n])^(3/2))/((e*f - d*g)*(f + g*x)) - (3*b*e*n*Defer[Int][Sqrt[a + b*Log[c*(d + e*x)^n]]/(f + g*x), x])/(2*(e*f - d*g))","A",0,0,0,0,-1,"{}"
116,0,0,0,0.207254,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{(f+g x)^3} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(3/2)/(f + g*x)^3,x]","\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{(f+g x)^3} \, dx","\frac{3 b e n \text{Int}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{(d+e x) (f+g x)^2},x\right)}{4 g}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{2 g (f+g x)^2}",0,"-(a + b*Log[c*(d + e*x)^n])^(3/2)/(2*g*(f + g*x)^2) + (3*b*e*n*Defer[Int][Sqrt[a + b*Log[c*(d + e*x)^n]]/((d + e*x)*(f + g*x)^2), x])/(4*g)","A",0,0,0,0,-1,"{}"
117,1,660,0,0.9835884,"\int (f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2} \, dx","Int[(f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^(5/2),x]","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} g n^{5/2} e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{32 e^3}-\frac{15 \sqrt{\pi } b^{5/2} n^{5/2} e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{8 e^3}-\frac{5 \sqrt{\frac{\pi }{3}} b^{5/2} g^2 n^{5/2} e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{72 e^3}+\frac{15 b^2 g n^2 (d+e x)^2 (e f-d g) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{16 e^3}+\frac{15 b^2 n^2 (d+e x) (e f-d g)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{4 e^3}+\frac{5 b^2 g^2 n^2 (d+e x)^3 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{36 e^3}+\frac{g (d+e x)^2 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{e^3}+\frac{(d+e x) (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{e^3}-\frac{5 b g n (d+e x)^2 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{4 e^3}-\frac{5 b n (d+e x) (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{2 e^3}+\frac{g^2 (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{3 e^3}-\frac{5 b g^2 n (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{18 e^3}","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} g n^{5/2} e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{32 e^3}-\frac{15 \sqrt{\pi } b^{5/2} n^{5/2} e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{8 e^3}-\frac{5 \sqrt{\frac{\pi }{3}} b^{5/2} g^2 n^{5/2} e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{72 e^3}+\frac{15 b^2 g n^2 (d+e x)^2 (e f-d g) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{16 e^3}+\frac{15 b^2 n^2 (d+e x) (e f-d g)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{4 e^3}+\frac{5 b^2 g^2 n^2 (d+e x)^3 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{36 e^3}+\frac{g (d+e x)^2 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{e^3}+\frac{(d+e x) (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{e^3}-\frac{5 b g n (d+e x)^2 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{4 e^3}-\frac{5 b n (d+e x) (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{2 e^3}+\frac{g^2 (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{3 e^3}-\frac{5 b g^2 n (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{18 e^3}",1,"(-15*b^(5/2)*(e*f - d*g)^2*n^(5/2)*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(8*e^3*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) - (15*b^(5/2)*g*(e*f - d*g)*n^(5/2)*Sqrt[Pi/2]*(d + e*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(32*e^3*E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)) - (5*b^(5/2)*g^2*n^(5/2)*Sqrt[Pi/3]*(d + e*x)^3*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(72*e^3*E^((3*a)/(b*n))*(c*(d + e*x)^n)^(3/n)) + (15*b^2*(e*f - d*g)^2*n^2*(d + e*x)*Sqrt[a + b*Log[c*(d + e*x)^n]])/(4*e^3) + (15*b^2*g*(e*f - d*g)*n^2*(d + e*x)^2*Sqrt[a + b*Log[c*(d + e*x)^n]])/(16*e^3) + (5*b^2*g^2*n^2*(d + e*x)^3*Sqrt[a + b*Log[c*(d + e*x)^n]])/(36*e^3) - (5*b*(e*f - d*g)^2*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^(3/2))/(2*e^3) - (5*b*g*(e*f - d*g)*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^(3/2))/(4*e^3) - (5*b*g^2*n*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])^(3/2))/(18*e^3) + ((e*f - d*g)^2*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^(5/2))/e^3 + (g*(e*f - d*g)*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^(5/2))/e^3 + (g^2*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])^(5/2))/(3*e^3)","A",23,9,26,0.3462,1,"{2401, 2389, 2296, 2300, 2180, 2204, 2390, 2305, 2310}"
118,1,413,0,0.5081767,"\int (f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2} \, dx","Int[(f + g*x)*(a + b*Log[c*(d + e*x)^n])^(5/2),x]","-\frac{15 \sqrt{\pi } b^{5/2} n^{5/2} e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{8 e^2}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} g n^{5/2} e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{64 e^2}+\frac{15 b^2 n^2 (d+e x) (e f-d g) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{4 e^2}+\frac{15 b^2 g n^2 (d+e x)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{32 e^2}+\frac{(d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{e^2}-\frac{5 b n (d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{2 e^2}+\frac{g (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{2 e^2}-\frac{5 b g n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{8 e^2}","-\frac{15 \sqrt{\pi } b^{5/2} n^{5/2} e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{8 e^2}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} g n^{5/2} e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{64 e^2}+\frac{15 b^2 n^2 (d+e x) (e f-d g) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{4 e^2}+\frac{15 b^2 g n^2 (d+e x)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{32 e^2}+\frac{(d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{e^2}-\frac{5 b n (d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{2 e^2}+\frac{g (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{2 e^2}-\frac{5 b g n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{8 e^2}",1,"(-15*b^(5/2)*(e*f - d*g)*n^(5/2)*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(8*e^2*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) - (15*b^(5/2)*g*n^(5/2)*Sqrt[Pi/2]*(d + e*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(64*e^2*E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)) + (15*b^2*(e*f - d*g)*n^2*(d + e*x)*Sqrt[a + b*Log[c*(d + e*x)^n]])/(4*e^2) + (15*b^2*g*n^2*(d + e*x)^2*Sqrt[a + b*Log[c*(d + e*x)^n]])/(32*e^2) - (5*b*(e*f - d*g)*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^(3/2))/(2*e^2) - (5*b*g*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^(3/2))/(8*e^2) + ((e*f - d*g)*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^(5/2))/e^2 + (g*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^(5/2))/(2*e^2)","A",16,9,24,0.3750,1,"{2401, 2389, 2296, 2300, 2180, 2204, 2390, 2305, 2310}"
119,1,179,0,0.1299802,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(5/2),x]","-\frac{15 \sqrt{\pi } b^{5/2} n^{5/2} e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{8 e}+\frac{15 b^2 n^2 (d+e x) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{4 e}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{e}-\frac{5 b n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{2 e}","-\frac{15 \sqrt{\pi } b^{5/2} n^{5/2} e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{8 e}+\frac{15 b^2 n^2 (d+e x) \sqrt{a+b \log \left(c (d+e x)^n\right)}}{4 e}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{e}-\frac{5 b n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{2 e}",1,"(-15*b^(5/2)*n^(5/2)*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(8*e*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + (15*b^2*n^2*(d + e*x)*Sqrt[a + b*Log[c*(d + e*x)^n]])/(4*e) - (5*b*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^(3/2))/(2*e) + ((d + e*x)*(a + b*Log[c*(d + e*x)^n])^(5/2))/e","A",7,5,18,0.2778,1,"{2389, 2296, 2300, 2180, 2204}"
120,0,0,0,0.0573681,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{f+g x} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(5/2)/(f + g*x),x]","\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{f+g x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{f+g x},x\right)",0,"Defer[Int][(a + b*Log[c*(d + e*x)^n])^(5/2)/(f + g*x), x]","A",0,0,0,0,-1,"{}"
121,0,0,0,0.1135019,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{(f+g x)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(5/2)/(f + g*x)^2,x]","\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{(f+g x)^2} \, dx","\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{(f+g x) (e f-d g)}-\frac{5 b e n \text{Int}\left(\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{f+g x},x\right)}{2 (e f-d g)}",0,"((d + e*x)*(a + b*Log[c*(d + e*x)^n])^(5/2))/((e*f - d*g)*(f + g*x)) - (5*b*e*n*Defer[Int][(a + b*Log[c*(d + e*x)^n])^(3/2)/(f + g*x), x])/(2*(e*f - d*g))","A",0,0,0,0,-1,"{}"
122,0,0,0,0.2348743,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{(f+g x)^3} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(5/2)/(f + g*x)^3,x]","\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{(f+g x)^3} \, dx","\frac{5 b e n \text{Int}\left(\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{(d+e x) (f+g x)^2},x\right)}{4 g}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{2 g (f+g x)^2}",0,"-(a + b*Log[c*(d + e*x)^n])^(5/2)/(2*g*(f + g*x)^2) + (5*b*e*n*Defer[Int][(a + b*Log[c*(d + e*x)^n])^(3/2)/((d + e*x)*(f + g*x)^2), x])/(4*g)","A",0,0,0,0,-1,"{}"
123,1,383,0,0.7276024,"\int \frac{(f+g x)^3}{\sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Int[(f + g*x)^3/Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\frac{\sqrt{3 \pi } g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 (e f-d g) \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e^4 \sqrt{n}}+\frac{3 \sqrt{\frac{\pi }{2}} g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e^4 \sqrt{n}}+\frac{\sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g)^3 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e^4 \sqrt{n}}+\frac{\sqrt{\pi } g^3 e^{-\frac{4 a}{b n}} (d+e x)^4 \left(c (d+e x)^n\right)^{-4/n} \text{Erfi}\left(\frac{2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{2 \sqrt{b} e^4 \sqrt{n}}","\frac{\sqrt{3 \pi } g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 (e f-d g) \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e^4 \sqrt{n}}+\frac{3 \sqrt{\frac{\pi }{2}} g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e^4 \sqrt{n}}+\frac{\sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g)^3 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e^4 \sqrt{n}}+\frac{\sqrt{\pi } g^3 e^{-\frac{4 a}{b n}} (d+e x)^4 \left(c (d+e x)^n\right)^{-4/n} \text{Erfi}\left(\frac{2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{2 \sqrt{b} e^4 \sqrt{n}}",1,"((e*f - d*g)^3*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(Sqrt[b]*e^4*E^(a/(b*n))*Sqrt[n]*(c*(d + e*x)^n)^n^(-1)) + (g^3*Sqrt[Pi]*(d + e*x)^4*Erfi[(2*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(2*Sqrt[b]*e^4*E^((4*a)/(b*n))*Sqrt[n]*(c*(d + e*x)^n)^(4/n)) + (3*g*(e*f - d*g)^2*Sqrt[Pi/2]*(d + e*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(Sqrt[b]*e^4*E^((2*a)/(b*n))*Sqrt[n]*(c*(d + e*x)^n)^(2/n)) + (g^2*(e*f - d*g)*Sqrt[3*Pi]*(d + e*x)^3*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(Sqrt[b]*e^4*E^((3*a)/(b*n))*Sqrt[n]*(c*(d + e*x)^n)^(3/n))","A",18,7,26,0.2692,1,"{2401, 2389, 2300, 2180, 2204, 2390, 2310}"
124,1,283,0,0.5157217,"\int \frac{(f+g x)^2}{\sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Int[(f + g*x)^2/Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\frac{\sqrt{2 \pi } g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e^3 \sqrt{n}}+\frac{\sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e^3 \sqrt{n}}+\frac{\sqrt{\frac{\pi }{3}} g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e^3 \sqrt{n}}","\frac{\sqrt{2 \pi } g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e^3 \sqrt{n}}+\frac{\sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e^3 \sqrt{n}}+\frac{\sqrt{\frac{\pi }{3}} g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e^3 \sqrt{n}}",1,"((e*f - d*g)^2*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(Sqrt[b]*e^3*E^(a/(b*n))*Sqrt[n]*(c*(d + e*x)^n)^n^(-1)) + (g*(e*f - d*g)*Sqrt[2*Pi]*(d + e*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(Sqrt[b]*e^3*E^((2*a)/(b*n))*Sqrt[n]*(c*(d + e*x)^n)^(2/n)) + (g^2*Sqrt[Pi/3]*(d + e*x)^3*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(Sqrt[b]*e^3*E^((3*a)/(b*n))*Sqrt[n]*(c*(d + e*x)^n)^(3/n))","A",14,7,26,0.2692,1,"{2401, 2389, 2300, 2180, 2204, 2390, 2310}"
125,1,181,0,0.2728416,"\int \frac{f+g x}{\sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Int[(f + g*x)/Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\frac{\sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e^2 \sqrt{n}}+\frac{\sqrt{\frac{\pi }{2}} g e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e^2 \sqrt{n}}","\frac{\sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e^2 \sqrt{n}}+\frac{\sqrt{\frac{\pi }{2}} g e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e^2 \sqrt{n}}",1,"((e*f - d*g)*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(Sqrt[b]*e^2*E^(a/(b*n))*Sqrt[n]*(c*(d + e*x)^n)^n^(-1)) + (g*Sqrt[Pi/2]*(d + e*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(Sqrt[b]*e^2*E^((2*a)/(b*n))*Sqrt[n]*(c*(d + e*x)^n)^(2/n))","A",10,7,24,0.2917,1,"{2401, 2389, 2300, 2180, 2204, 2390, 2310}"
126,1,80,0,0.0702715,"\int \frac{1}{\sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Int[1/Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\frac{\sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e \sqrt{n}}","\frac{\sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{\sqrt{b} e \sqrt{n}}",1,"(Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(Sqrt[b]*e*E^(a/(b*n))*Sqrt[n]*(c*(d + e*x)^n)^n^(-1))","A",4,4,18,0.2222,1,"{2389, 2300, 2180, 2204}"
127,0,0,0,0.0519149,"\int \frac{1}{(f+g x) \sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Int[1/((f + g*x)*Sqrt[a + b*Log[c*(d + e*x)^n]]),x]","\int \frac{1}{(f+g x) \sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","\text{Int}\left(\frac{1}{(f+g x) \sqrt{a+b \log \left(c (d+e x)^n\right)}},x\right)",0,"Defer[Int][1/((f + g*x)*Sqrt[a + b*Log[c*(d + e*x)^n]]), x]","A",0,0,0,0,-1,"{}"
128,1,422,0,1.3153438,"\int \frac{(f+g x)^3}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}} \, dx","Int[(f + g*x)^3/(a + b*Log[c*(d + e*x)^n])^(3/2),x]","\frac{6 \sqrt{3 \pi } g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 (e f-d g) \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^4 n^{3/2}}+\frac{6 \sqrt{2 \pi } g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^4 n^{3/2}}+\frac{2 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g)^3 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^4 n^{3/2}}+\frac{4 \sqrt{\pi } g^3 e^{-\frac{4 a}{b n}} (d+e x)^4 \left(c (d+e x)^n\right)^{-4/n} \text{Erfi}\left(\frac{2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^4 n^{3/2}}-\frac{2 (d+e x) (f+g x)^3}{b e n \sqrt{a+b \log \left(c (d+e x)^n\right)}}","\frac{6 \sqrt{3 \pi } g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 (e f-d g) \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^4 n^{3/2}}+\frac{6 \sqrt{2 \pi } g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^4 n^{3/2}}+\frac{2 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g)^3 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^4 n^{3/2}}+\frac{4 \sqrt{\pi } g^3 e^{-\frac{4 a}{b n}} (d+e x)^4 \left(c (d+e x)^n\right)^{-4/n} \text{Erfi}\left(\frac{2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^4 n^{3/2}}-\frac{2 (d+e x) (f+g x)^3}{b e n \sqrt{a+b \log \left(c (d+e x)^n\right)}}",1,"(2*(e*f - d*g)^3*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(b^(3/2)*e^4*E^(a/(b*n))*n^(3/2)*(c*(d + e*x)^n)^n^(-1)) + (4*g^3*Sqrt[Pi]*(d + e*x)^4*Erfi[(2*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(b^(3/2)*e^4*E^((4*a)/(b*n))*n^(3/2)*(c*(d + e*x)^n)^(4/n)) + (6*g*(e*f - d*g)^2*Sqrt[2*Pi]*(d + e*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(b^(3/2)*e^4*E^((2*a)/(b*n))*n^(3/2)*(c*(d + e*x)^n)^(2/n)) + (6*g^2*(e*f - d*g)*Sqrt[3*Pi]*(d + e*x)^3*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(b^(3/2)*e^4*E^((3*a)/(b*n))*n^(3/2)*(c*(d + e*x)^n)^(3/n)) - (2*(d + e*x)*(f + g*x)^3)/(b*e*n*Sqrt[a + b*Log[c*(d + e*x)^n]])","A",33,8,26,0.3077,1,"{2400, 2401, 2389, 2300, 2180, 2204, 2390, 2310}"
129,1,325,0,0.8690921,"\int \frac{(f+g x)^2}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}} \, dx","Int[(f + g*x)^2/(a + b*Log[c*(d + e*x)^n])^(3/2),x]","\frac{4 \sqrt{2 \pi } g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^3 n^{3/2}}+\frac{2 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^3 n^{3/2}}+\frac{2 \sqrt{3 \pi } g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^3 n^{3/2}}-\frac{2 (d+e x) (f+g x)^2}{b e n \sqrt{a+b \log \left(c (d+e x)^n\right)}}","\frac{4 \sqrt{2 \pi } g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^3 n^{3/2}}+\frac{2 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^3 n^{3/2}}+\frac{2 \sqrt{3 \pi } g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^3 n^{3/2}}-\frac{2 (d+e x) (f+g x)^2}{b e n \sqrt{a+b \log \left(c (d+e x)^n\right)}}",1,"(2*(e*f - d*g)^2*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(b^(3/2)*e^3*E^(a/(b*n))*n^(3/2)*(c*(d + e*x)^n)^n^(-1)) + (4*g*(e*f - d*g)*Sqrt[2*Pi]*(d + e*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(b^(3/2)*e^3*E^((2*a)/(b*n))*n^(3/2)*(c*(d + e*x)^n)^(2/n)) + (2*g^2*Sqrt[3*Pi]*(d + e*x)^3*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(b^(3/2)*e^3*E^((3*a)/(b*n))*n^(3/2)*(c*(d + e*x)^n)^(3/n)) - (2*(d + e*x)*(f + g*x)^2)/(b*e*n*Sqrt[a + b*Log[c*(d + e*x)^n]])","A",25,8,26,0.3077,1,"{2400, 2401, 2389, 2300, 2180, 2204, 2390, 2310}"
130,1,220,0,0.4027611,"\int \frac{f+g x}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}} \, dx","Int[(f + g*x)/(a + b*Log[c*(d + e*x)^n])^(3/2),x]","\frac{2 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^2 n^{3/2}}+\frac{2 \sqrt{2 \pi } g e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^2 n^{3/2}}-\frac{2 (d+e x) (f+g x)}{b e n \sqrt{a+b \log \left(c (d+e x)^n\right)}}","\frac{2 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^2 n^{3/2}}+\frac{2 \sqrt{2 \pi } g e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e^2 n^{3/2}}-\frac{2 (d+e x) (f+g x)}{b e n \sqrt{a+b \log \left(c (d+e x)^n\right)}}",1,"(2*(e*f - d*g)*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(b^(3/2)*e^2*E^(a/(b*n))*n^(3/2)*(c*(d + e*x)^n)^n^(-1)) + (2*g*Sqrt[2*Pi]*(d + e*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(b^(3/2)*e^2*E^((2*a)/(b*n))*n^(3/2)*(c*(d + e*x)^n)^(2/n)) - (2*(d + e*x)*(f + g*x))/(b*e*n*Sqrt[a + b*Log[c*(d + e*x)^n]])","A",15,8,24,0.3333,1,"{2400, 2401, 2389, 2300, 2180, 2204, 2390, 2310}"
131,1,116,0,0.0952645,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(-3/2),x]","\frac{2 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e n^{3/2}}-\frac{2 (d+e x)}{b e n \sqrt{a+b \log \left(c (d+e x)^n\right)}}","\frac{2 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{3/2} e n^{3/2}}-\frac{2 (d+e x)}{b e n \sqrt{a+b \log \left(c (d+e x)^n\right)}}",1,"(2*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(b^(3/2)*e*E^(a/(b*n))*n^(3/2)*(c*(d + e*x)^n)^n^(-1)) - (2*(d + e*x))/(b*e*n*Sqrt[a + b*Log[c*(d + e*x)^n]])","A",5,5,18,0.2778,1,"{2389, 2297, 2300, 2180, 2204}"
132,0,0,0,0.060626,"\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}} \, dx","Int[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^(3/2)),x]","\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}} \, dx","\text{Int}\left(\frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}},x\right)",0,"Defer[Int][1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^(3/2)), x]","A",0,0,0,0,-1,"{}"
133,1,520,0,2.3326321,"\int \frac{(f+g x)^3}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}} \, dx","Int[(f + g*x)^3/(a + b*Log[c*(d + e*x)^n])^(5/2),x]","\frac{12 \sqrt{3 \pi } g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 (e f-d g) \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{5/2} e^4 n^{5/2}}+\frac{8 \sqrt{2 \pi } g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{5/2} e^4 n^{5/2}}+\frac{4 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g)^3 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{3 b^{5/2} e^4 n^{5/2}}+\frac{32 \sqrt{\pi } g^3 e^{-\frac{4 a}{b n}} (d+e x)^4 \left(c (d+e x)^n\right)^{-4/n} \text{Erfi}\left(\frac{2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{3 b^{5/2} e^4 n^{5/2}}+\frac{4 (d+e x) (f+g x)^2 (e f-d g)}{b^2 e^2 n^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{16 (d+e x) (f+g x)^3}{3 b^2 e n^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{2 (d+e x) (f+g x)^3}{3 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}","\frac{12 \sqrt{3 \pi } g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 (e f-d g) \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{5/2} e^4 n^{5/2}}+\frac{8 \sqrt{2 \pi } g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{5/2} e^4 n^{5/2}}+\frac{4 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g)^3 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{3 b^{5/2} e^4 n^{5/2}}+\frac{32 \sqrt{\pi } g^3 e^{-\frac{4 a}{b n}} (d+e x)^4 \left(c (d+e x)^n\right)^{-4/n} \text{Erfi}\left(\frac{2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{3 b^{5/2} e^4 n^{5/2}}+\frac{4 (d+e x) (f+g x)^2 (e f-d g)}{b^2 e^2 n^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{16 (d+e x) (f+g x)^3}{3 b^2 e n^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{2 (d+e x) (f+g x)^3}{3 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}",1,"(4*(e*f - d*g)^3*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(3*b^(5/2)*e^4*E^(a/(b*n))*n^(5/2)*(c*(d + e*x)^n)^n^(-1)) + (32*g^3*Sqrt[Pi]*(d + e*x)^4*Erfi[(2*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(3*b^(5/2)*e^4*E^((4*a)/(b*n))*n^(5/2)*(c*(d + e*x)^n)^(4/n)) + (8*g*(e*f - d*g)^2*Sqrt[2*Pi]*(d + e*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(b^(5/2)*e^4*E^((2*a)/(b*n))*n^(5/2)*(c*(d + e*x)^n)^(2/n)) + (12*g^2*(e*f - d*g)*Sqrt[3*Pi]*(d + e*x)^3*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(b^(5/2)*e^4*E^((3*a)/(b*n))*n^(5/2)*(c*(d + e*x)^n)^(3/n)) - (2*(d + e*x)*(f + g*x)^3)/(3*b*e*n*(a + b*Log[c*(d + e*x)^n])^(3/2)) + (4*(e*f - d*g)*(d + e*x)*(f + g*x)^2)/(b^2*e^2*n^2*Sqrt[a + b*Log[c*(d + e*x)^n]]) - (16*(d + e*x)*(f + g*x)^3)/(3*b^2*e*n^2*Sqrt[a + b*Log[c*(d + e*x)^n]])","A",59,8,26,0.3077,1,"{2400, 2401, 2389, 2300, 2180, 2204, 2390, 2310}"
134,1,421,0,1.3987848,"\int \frac{(f+g x)^2}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}} \, dx","Int[(f + g*x)^2/(a + b*Log[c*(d + e*x)^n])^(5/2),x]","\frac{16 \sqrt{2 \pi } g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{3 b^{5/2} e^3 n^{5/2}}+\frac{4 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{3 b^{5/2} e^3 n^{5/2}}+\frac{4 \sqrt{3 \pi } g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{5/2} e^3 n^{5/2}}+\frac{8 (d+e x) (f+g x) (e f-d g)}{3 b^2 e^2 n^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{4 (d+e x) (f+g x)^2}{b^2 e n^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{2 (d+e x) (f+g x)^2}{3 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}","\frac{16 \sqrt{2 \pi } g e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{3 b^{5/2} e^3 n^{5/2}}+\frac{4 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{3 b^{5/2} e^3 n^{5/2}}+\frac{4 \sqrt{3 \pi } g^2 e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{b^{5/2} e^3 n^{5/2}}+\frac{8 (d+e x) (f+g x) (e f-d g)}{3 b^2 e^2 n^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{4 (d+e x) (f+g x)^2}{b^2 e n^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{2 (d+e x) (f+g x)^2}{3 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}",1,"(4*(e*f - d*g)^2*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(3*b^(5/2)*e^3*E^(a/(b*n))*n^(5/2)*(c*(d + e*x)^n)^n^(-1)) + (16*g*(e*f - d*g)*Sqrt[2*Pi]*(d + e*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(3*b^(5/2)*e^3*E^((2*a)/(b*n))*n^(5/2)*(c*(d + e*x)^n)^(2/n)) + (4*g^2*Sqrt[3*Pi]*(d + e*x)^3*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(b^(5/2)*e^3*E^((3*a)/(b*n))*n^(5/2)*(c*(d + e*x)^n)^(3/n)) - (2*(d + e*x)*(f + g*x)^2)/(3*b*e*n*(a + b*Log[c*(d + e*x)^n])^(3/2)) + (8*(e*f - d*g)*(d + e*x)*(f + g*x))/(3*b^2*e^2*n^2*Sqrt[a + b*Log[c*(d + e*x)^n]]) - (4*(d + e*x)*(f + g*x)^2)/(b^2*e*n^2*Sqrt[a + b*Log[c*(d + e*x)^n]])","A",41,8,26,0.3077,1,"{2400, 2401, 2389, 2300, 2180, 2204, 2390, 2310}"
135,1,311,0,0.5638479,"\int \frac{f+g x}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}} \, dx","Int[(f + g*x)/(a + b*Log[c*(d + e*x)^n])^(5/2),x]","\frac{4 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{3 b^{5/2} e^2 n^{5/2}}+\frac{8 \sqrt{2 \pi } g e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{3 b^{5/2} e^2 n^{5/2}}+\frac{4 (d+e x) (e f-d g)}{3 b^2 e^2 n^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{8 (d+e x) (f+g x)}{3 b^2 e n^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{2 (d+e x) (f+g x)}{3 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}","\frac{4 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{3 b^{5/2} e^2 n^{5/2}}+\frac{8 \sqrt{2 \pi } g e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{3 b^{5/2} e^2 n^{5/2}}+\frac{4 (d+e x) (e f-d g)}{3 b^2 e^2 n^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{8 (d+e x) (f+g x)}{3 b^2 e n^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{2 (d+e x) (f+g x)}{3 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}",1,"(4*(e*f - d*g)*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(3*b^(5/2)*e^2*E^(a/(b*n))*n^(5/2)*(c*(d + e*x)^n)^n^(-1)) + (8*g*Sqrt[2*Pi]*(d + e*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(3*b^(5/2)*e^2*E^((2*a)/(b*n))*n^(5/2)*(c*(d + e*x)^n)^(2/n)) - (2*(d + e*x)*(f + g*x))/(3*b*e*n*(a + b*Log[c*(d + e*x)^n])^(3/2)) + (4*(e*f - d*g)*(d + e*x))/(3*b^2*e^2*n^2*Sqrt[a + b*Log[c*(d + e*x)^n]]) - (8*(d + e*x)*(f + g*x))/(3*b^2*e*n^2*Sqrt[a + b*Log[c*(d + e*x)^n]])","A",21,9,24,0.3750,1,"{2400, 2401, 2389, 2300, 2180, 2204, 2390, 2310, 2297}"
136,1,156,0,0.1170134,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^(-5/2),x]","\frac{4 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{3 b^{5/2} e n^{5/2}}-\frac{4 (d+e x)}{3 b^2 e n^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{2 (d+e x)}{3 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}","\frac{4 \sqrt{\pi } e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)}{3 b^{5/2} e n^{5/2}}-\frac{4 (d+e x)}{3 b^2 e n^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}-\frac{2 (d+e x)}{3 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}",1,"(4*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(3*b^(5/2)*e*E^(a/(b*n))*n^(5/2)*(c*(d + e*x)^n)^n^(-1)) - (2*(d + e*x))/(3*b*e*n*(a + b*Log[c*(d + e*x)^n])^(3/2)) - (4*(d + e*x))/(3*b^2*e*n^2*Sqrt[a + b*Log[c*(d + e*x)^n]])","A",6,5,18,0.2778,1,"{2389, 2297, 2300, 2180, 2204}"
137,0,0,0,0.0587893,"\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}} \, dx","Int[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^(5/2)),x]","\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}} \, dx","\text{Int}\left(\frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}},x\right)",0,"Defer[Int][1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^(5/2)), x]","A",0,0,0,0,-1,"{}"
138,1,163,0,0.163095,"\int (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Int[(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n]),x]","\frac{2 (f+g x)^{5/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 g}-\frac{4 b n \sqrt{f+g x} (e f-d g)^2}{5 e^2 g}+\frac{4 b n (e f-d g)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{5 e^{5/2} g}-\frac{4 b n (f+g x)^{3/2} (e f-d g)}{15 e g}-\frac{4 b n (f+g x)^{5/2}}{25 g}","\frac{2 (f+g x)^{5/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 g}-\frac{4 b n \sqrt{f+g x} (e f-d g)^2}{5 e^2 g}+\frac{4 b n (e f-d g)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{5 e^{5/2} g}-\frac{4 b n (f+g x)^{3/2} (e f-d g)}{15 e g}-\frac{4 b n (f+g x)^{5/2}}{25 g}",1,"(-4*b*(e*f - d*g)^2*n*Sqrt[f + g*x])/(5*e^2*g) - (4*b*(e*f - d*g)*n*(f + g*x)^(3/2))/(15*e*g) - (4*b*n*(f + g*x)^(5/2))/(25*g) + (4*b*(e*f - d*g)^(5/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(5*e^(5/2)*g) + (2*(f + g*x)^(5/2)*(a + b*Log[c*(d + e*x)^n]))/(5*g)","A",6,4,24,0.1667,1,"{2395, 50, 63, 208}"
139,1,132,0,0.0854166,"\int \sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Int[Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n]),x]","\frac{2 (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g}+\frac{4 b n (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{3 e^{3/2} g}-\frac{4 b n \sqrt{f+g x} (e f-d g)}{3 e g}-\frac{4 b n (f+g x)^{3/2}}{9 g}","\frac{2 (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g}+\frac{4 b n (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{3 e^{3/2} g}-\frac{4 b n \sqrt{f+g x} (e f-d g)}{3 e g}-\frac{4 b n (f+g x)^{3/2}}{9 g}",1,"(-4*b*(e*f - d*g)*n*Sqrt[f + g*x])/(3*e*g) - (4*b*n*(f + g*x)^(3/2))/(9*g) + (4*b*(e*f - d*g)^(3/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(3*e^(3/2)*g) + (2*(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n]))/(3*g)","A",5,4,24,0.1667,1,"{2395, 50, 63, 208}"
140,1,97,0,0.0586838,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\sqrt{f+g x}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/Sqrt[f + g*x],x]","\frac{2 \sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}+\frac{4 b n \sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{\sqrt{e} g}-\frac{4 b n \sqrt{f+g x}}{g}","\frac{2 \sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}+\frac{4 b n \sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{\sqrt{e} g}-\frac{4 b n \sqrt{f+g x}}{g}",1,"(-4*b*n*Sqrt[f + g*x])/g + (4*b*Sqrt[e*f - d*g]*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(Sqrt[e]*g) + (2*Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n]))/g","A",4,4,24,0.1667,1,"{2395, 50, 63, 208}"
141,1,81,0,0.0532964,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x)^{3/2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(f + g*x)^(3/2),x]","-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{g \sqrt{f+g x}}-\frac{4 b \sqrt{e} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{g \sqrt{e f-d g}}","-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{g \sqrt{f+g x}}-\frac{4 b \sqrt{e} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{g \sqrt{e f-d g}}",1,"(-4*b*Sqrt[e]*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(g*Sqrt[e*f - d*g]) - (2*(a + b*Log[c*(d + e*x)^n]))/(g*Sqrt[f + g*x])","A",3,3,24,0.1250,1,"{2395, 63, 208}"
142,1,114,0,0.0815045,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x)^{5/2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(f + g*x)^(5/2),x]","-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g (f+g x)^{3/2}}-\frac{4 b e^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{3 g (e f-d g)^{3/2}}+\frac{4 b e n}{3 g \sqrt{f+g x} (e f-d g)}","-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g (f+g x)^{3/2}}-\frac{4 b e^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{3 g (e f-d g)^{3/2}}+\frac{4 b e n}{3 g \sqrt{f+g x} (e f-d g)}",1,"(4*b*e*n)/(3*g*(e*f - d*g)*Sqrt[f + g*x]) - (4*b*e^(3/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(3*g*(e*f - d*g)^(3/2)) - (2*(a + b*Log[c*(d + e*x)^n]))/(3*g*(f + g*x)^(3/2))","A",4,4,24,0.1667,1,"{2395, 51, 63, 208}"
143,1,145,0,0.1107266,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x)^{7/2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(f + g*x)^(7/2),x]","-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 g (f+g x)^{5/2}}+\frac{4 b e^2 n}{5 g \sqrt{f+g x} (e f-d g)^2}-\frac{4 b e^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{5 g (e f-d g)^{5/2}}+\frac{4 b e n}{15 g (f+g x)^{3/2} (e f-d g)}","-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 g (f+g x)^{5/2}}+\frac{4 b e^2 n}{5 g \sqrt{f+g x} (e f-d g)^2}-\frac{4 b e^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{5 g (e f-d g)^{5/2}}+\frac{4 b e n}{15 g (f+g x)^{3/2} (e f-d g)}",1,"(4*b*e*n)/(15*g*(e*f - d*g)*(f + g*x)^(3/2)) + (4*b*e^2*n)/(5*g*(e*f - d*g)^2*Sqrt[f + g*x]) - (4*b*e^(5/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(5*g*(e*f - d*g)^(5/2)) - (2*(a + b*Log[c*(d + e*x)^n]))/(5*g*(f + g*x)^(5/2))","A",5,4,24,0.1667,1,"{2395, 51, 63, 208}"
144,1,176,0,0.1442473,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x)^{9/2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(f + g*x)^(9/2),x]","-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{7 g (f+g x)^{7/2}}+\frac{4 b e^3 n}{7 g \sqrt{f+g x} (e f-d g)^3}+\frac{4 b e^2 n}{21 g (f+g x)^{3/2} (e f-d g)^2}-\frac{4 b e^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{7 g (e f-d g)^{7/2}}+\frac{4 b e n}{35 g (f+g x)^{5/2} (e f-d g)}","-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{7 g (f+g x)^{7/2}}+\frac{4 b e^3 n}{7 g \sqrt{f+g x} (e f-d g)^3}+\frac{4 b e^2 n}{21 g (f+g x)^{3/2} (e f-d g)^2}-\frac{4 b e^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{7 g (e f-d g)^{7/2}}+\frac{4 b e n}{35 g (f+g x)^{5/2} (e f-d g)}",1,"(4*b*e*n)/(35*g*(e*f - d*g)*(f + g*x)^(5/2)) + (4*b*e^2*n)/(21*g*(e*f - d*g)^2*(f + g*x)^(3/2)) + (4*b*e^3*n)/(7*g*(e*f - d*g)^3*Sqrt[f + g*x]) - (4*b*e^(7/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(7*g*(e*f - d*g)^(7/2)) - (2*(a + b*Log[c*(d + e*x)^n]))/(7*g*(f + g*x)^(7/2))","A",6,4,24,0.1667,1,"{2395, 51, 63, 208}"
145,1,590,0,2.1685869,"\int (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Int[(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{8 b^2 n^2 (e f-d g)^{5/2} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{5 e^{5/2} g}-\frac{8 b n \sqrt{f+g x} (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 e^2 g}+\frac{8 b n (e f-d g)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 e^{5/2} g}-\frac{8 b n (f+g x)^{3/2} (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)}{15 e g}+\frac{2 (f+g x)^{5/2} \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{5 g}-\frac{8 b n (f+g x)^{5/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{25 g}+\frac{368 b^2 n^2 \sqrt{f+g x} (e f-d g)^2}{75 e^2 g}-\frac{8 b^2 n^2 (e f-d g)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{5 e^{5/2} g}-\frac{368 b^2 n^2 (e f-d g)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{75 e^{5/2} g}+\frac{16 b^2 n^2 (e f-d g)^{5/2} \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{5 e^{5/2} g}+\frac{128 b^2 n^2 (f+g x)^{3/2} (e f-d g)}{225 e g}+\frac{16 b^2 n^2 (f+g x)^{5/2}}{125 g}","\frac{8 b^2 n^2 (e f-d g)^{5/2} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{5 e^{5/2} g}-\frac{8 b n \sqrt{f+g x} (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 e^2 g}+\frac{8 b n (e f-d g)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 e^{5/2} g}-\frac{8 b n (f+g x)^{3/2} (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)}{15 e g}+\frac{2 (f+g x)^{5/2} \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{5 g}-\frac{8 b n (f+g x)^{5/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{25 g}+\frac{368 b^2 n^2 \sqrt{f+g x} (e f-d g)^2}{75 e^2 g}-\frac{8 b^2 n^2 (e f-d g)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{5 e^{5/2} g}-\frac{368 b^2 n^2 (e f-d g)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{75 e^{5/2} g}+\frac{16 b^2 n^2 (e f-d g)^{5/2} \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{5 e^{5/2} g}+\frac{128 b^2 n^2 (f+g x)^{3/2} (e f-d g)}{225 e g}+\frac{16 b^2 n^2 (f+g x)^{5/2}}{125 g}",1,"(368*b^2*(e*f - d*g)^2*n^2*Sqrt[f + g*x])/(75*e^2*g) + (128*b^2*(e*f - d*g)*n^2*(f + g*x)^(3/2))/(225*e*g) + (16*b^2*n^2*(f + g*x)^(5/2))/(125*g) - (368*b^2*(e*f - d*g)^(5/2)*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(75*e^(5/2)*g) - (8*b^2*(e*f - d*g)^(5/2)*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]^2)/(5*e^(5/2)*g) - (8*b*(e*f - d*g)^2*n*Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n]))/(5*e^2*g) - (8*b*(e*f - d*g)*n*(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n]))/(15*e*g) - (8*b*n*(f + g*x)^(5/2)*(a + b*Log[c*(d + e*x)^n]))/(25*g) + (8*b*(e*f - d*g)^(5/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*(a + b*Log[c*(d + e*x)^n]))/(5*e^(5/2)*g) + (2*(f + g*x)^(5/2)*(a + b*Log[c*(d + e*x)^n])^2)/(5*g) + (16*b^2*(e*f - d*g)^(5/2)*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*Log[2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(5*e^(5/2)*g) + (8*b^2*(e*f - d*g)^(5/2)*n^2*PolyLog[2, 1 - 2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(5*e^(5/2)*g)","A",28,15,26,0.5769,1,"{2398, 2411, 2346, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 50}"
146,1,510,0,1.5005778,"\int \sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Int[Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{8 b^2 n^2 (e f-d g)^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{3 e^{3/2} g}+\frac{8 b n (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 e^{3/2} g}-\frac{8 b n (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{9 g}-\frac{8 b n \sqrt{f+g x} (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 e g}+\frac{2 (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 g}-\frac{8 b^2 n^2 (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{3 e^{3/2} g}-\frac{64 b^2 n^2 (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{9 e^{3/2} g}+\frac{16 b^2 n^2 (e f-d g)^{3/2} \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{3 e^{3/2} g}+\frac{64 b^2 n^2 \sqrt{f+g x} (e f-d g)}{9 e g}+\frac{16 b^2 n^2 (f+g x)^{3/2}}{27 g}","\frac{8 b^2 n^2 (e f-d g)^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{3 e^{3/2} g}+\frac{8 b n (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 e^{3/2} g}-\frac{8 b n (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{9 g}-\frac{8 b n \sqrt{f+g x} (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 e g}+\frac{2 (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 g}-\frac{8 b^2 n^2 (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{3 e^{3/2} g}-\frac{64 b^2 n^2 (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{9 e^{3/2} g}+\frac{16 b^2 n^2 (e f-d g)^{3/2} \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{3 e^{3/2} g}+\frac{64 b^2 n^2 \sqrt{f+g x} (e f-d g)}{9 e g}+\frac{16 b^2 n^2 (f+g x)^{3/2}}{27 g}",1,"(64*b^2*(e*f - d*g)*n^2*Sqrt[f + g*x])/(9*e*g) + (16*b^2*n^2*(f + g*x)^(3/2))/(27*g) - (64*b^2*(e*f - d*g)^(3/2)*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(9*e^(3/2)*g) - (8*b^2*(e*f - d*g)^(3/2)*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]^2)/(3*e^(3/2)*g) - (8*b*(e*f - d*g)*n*Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n]))/(3*e*g) - (8*b*n*(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n]))/(9*g) + (8*b*(e*f - d*g)^(3/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*(a + b*Log[c*(d + e*x)^n]))/(3*e^(3/2)*g) + (2*(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n])^2)/(3*g) + (16*b^2*(e*f - d*g)^(3/2)*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*Log[2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(3*e^(3/2)*g) + (8*b^2*(e*f - d*g)^(3/2)*n^2*PolyLog[2, 1 - 2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(3*e^(3/2)*g)","A",21,15,26,0.5769,1,"{2398, 2411, 2346, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 50}"
147,1,418,0,1.0672633,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{\sqrt{f+g x}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/Sqrt[f + g*x],x]","\frac{8 b^2 n^2 \sqrt{e f-d g} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{\sqrt{e} g}-\frac{8 b n \sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}+\frac{2 \sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g}+\frac{8 b n \sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{e} g}-\frac{8 b^2 n^2 \sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{\sqrt{e} g}-\frac{16 b^2 n^2 \sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{\sqrt{e} g}+\frac{16 b^2 n^2 \sqrt{e f-d g} \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{\sqrt{e} g}+\frac{16 b^2 n^2 \sqrt{f+g x}}{g}","\frac{8 b^2 n^2 \sqrt{e f-d g} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{\sqrt{e} g}-\frac{8 b n \sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}+\frac{2 \sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g}+\frac{8 b n \sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{e} g}-\frac{8 b^2 n^2 \sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{\sqrt{e} g}-\frac{16 b^2 n^2 \sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{\sqrt{e} g}+\frac{16 b^2 n^2 \sqrt{e f-d g} \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{\sqrt{e} g}+\frac{16 b^2 n^2 \sqrt{f+g x}}{g}",1,"(16*b^2*n^2*Sqrt[f + g*x])/g - (16*b^2*Sqrt[e*f - d*g]*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(Sqrt[e]*g) - (8*b^2*Sqrt[e*f - d*g]*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]^2)/(Sqrt[e]*g) - (8*b*n*Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n]))/g + (8*b*Sqrt[e*f - d*g]*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*(a + b*Log[c*(d + e*x)^n]))/(Sqrt[e]*g) + (2*Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n])^2)/g + (16*b^2*Sqrt[e*f - d*g]*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*Log[2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(Sqrt[e]*g) + (8*b^2*Sqrt[e*f - d*g]*n^2*PolyLog[2, 1 - 2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(Sqrt[e]*g)","A",15,15,26,0.5769,1,"{2398, 2411, 2346, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 50}"
148,1,312,0,0.7659237,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x)^{3/2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x)^(3/2),x]","-\frac{8 b^2 \sqrt{e} n^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{g \sqrt{e f-d g}}-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g \sqrt{f+g x}}-\frac{8 b \sqrt{e} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g \sqrt{e f-d g}}+\frac{8 b^2 \sqrt{e} n^2 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{g \sqrt{e f-d g}}-\frac{16 b^2 \sqrt{e} n^2 \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{g \sqrt{e f-d g}}","-\frac{8 b^2 \sqrt{e} n^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{g \sqrt{e f-d g}}-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g \sqrt{f+g x}}-\frac{8 b \sqrt{e} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g \sqrt{e f-d g}}+\frac{8 b^2 \sqrt{e} n^2 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{g \sqrt{e f-d g}}-\frac{16 b^2 \sqrt{e} n^2 \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{g \sqrt{e f-d g}}",1,"(8*b^2*Sqrt[e]*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]^2)/(g*Sqrt[e*f - d*g]) - (8*b*Sqrt[e]*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*(a + b*Log[c*(d + e*x)^n]))/(g*Sqrt[e*f - d*g]) - (2*(a + b*Log[c*(d + e*x)^n])^2)/(g*Sqrt[f + g*x]) - (16*b^2*Sqrt[e]*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*Log[2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(g*Sqrt[e*f - d*g]) - (8*b^2*Sqrt[e]*n^2*PolyLog[2, 1 - 2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(g*Sqrt[e*f - d*g])","A",10,12,26,0.4615,1,"{2398, 2411, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315}"
149,1,423,0,1.120816,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x)^{5/2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x)^(5/2),x]","-\frac{8 b^2 e^{3/2} n^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{3 g (e f-d g)^{3/2}}-\frac{8 b e^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g (e f-d g)^{3/2}}+\frac{8 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g \sqrt{f+g x} (e f-d g)}-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 g (f+g x)^{3/2}}+\frac{8 b^2 e^{3/2} n^2 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{3 g (e f-d g)^{3/2}}+\frac{16 b^2 e^{3/2} n^2 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{3 g (e f-d g)^{3/2}}-\frac{16 b^2 e^{3/2} n^2 \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{3 g (e f-d g)^{3/2}}","-\frac{8 b^2 e^{3/2} n^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{3 g (e f-d g)^{3/2}}-\frac{8 b e^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g (e f-d g)^{3/2}}+\frac{8 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g \sqrt{f+g x} (e f-d g)}-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 g (f+g x)^{3/2}}+\frac{8 b^2 e^{3/2} n^2 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{3 g (e f-d g)^{3/2}}+\frac{16 b^2 e^{3/2} n^2 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{3 g (e f-d g)^{3/2}}-\frac{16 b^2 e^{3/2} n^2 \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{3 g (e f-d g)^{3/2}}",1,"(16*b^2*e^(3/2)*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(3*g*(e*f - d*g)^(3/2)) + (8*b^2*e^(3/2)*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]^2)/(3*g*(e*f - d*g)^(3/2)) + (8*b*e*n*(a + b*Log[c*(d + e*x)^n]))/(3*g*(e*f - d*g)*Sqrt[f + g*x]) - (8*b*e^(3/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*(a + b*Log[c*(d + e*x)^n]))/(3*g*(e*f - d*g)^(3/2)) - (2*(a + b*Log[c*(d + e*x)^n])^2)/(3*g*(f + g*x)^(3/2)) - (16*b^2*e^(3/2)*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*Log[2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(3*g*(e*f - d*g)^(3/2)) - (8*b^2*e^(3/2)*n^2*PolyLog[2, 1 - 2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(3*g*(e*f - d*g)^(3/2))","A",14,14,26,0.5385,1,"{2398, 2411, 2347, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319}"
150,1,503,0,1.5117624,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x)^{7/2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x)^(7/2),x]","-\frac{8 b^2 e^{5/2} n^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{5 g (e f-d g)^{5/2}}+\frac{8 b e^2 n \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 g \sqrt{f+g x} (e f-d g)^2}-\frac{8 b e^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 g (e f-d g)^{5/2}}+\frac{8 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}{15 g (f+g x)^{3/2} (e f-d g)}-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{5 g (f+g x)^{5/2}}-\frac{16 b^2 e^2 n^2}{15 g \sqrt{f+g x} (e f-d g)^2}+\frac{8 b^2 e^{5/2} n^2 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{5 g (e f-d g)^{5/2}}+\frac{64 b^2 e^{5/2} n^2 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{15 g (e f-d g)^{5/2}}-\frac{16 b^2 e^{5/2} n^2 \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{5 g (e f-d g)^{5/2}}","-\frac{8 b^2 e^{5/2} n^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{5 g (e f-d g)^{5/2}}+\frac{8 b e^2 n \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 g \sqrt{f+g x} (e f-d g)^2}-\frac{8 b e^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 g (e f-d g)^{5/2}}+\frac{8 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}{15 g (f+g x)^{3/2} (e f-d g)}-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{5 g (f+g x)^{5/2}}-\frac{16 b^2 e^2 n^2}{15 g \sqrt{f+g x} (e f-d g)^2}+\frac{8 b^2 e^{5/2} n^2 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{5 g (e f-d g)^{5/2}}+\frac{64 b^2 e^{5/2} n^2 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{15 g (e f-d g)^{5/2}}-\frac{16 b^2 e^{5/2} n^2 \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{5 g (e f-d g)^{5/2}}",1,"(-16*b^2*e^2*n^2)/(15*g*(e*f - d*g)^2*Sqrt[f + g*x]) + (64*b^2*e^(5/2)*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(15*g*(e*f - d*g)^(5/2)) + (8*b^2*e^(5/2)*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]^2)/(5*g*(e*f - d*g)^(5/2)) + (8*b*e*n*(a + b*Log[c*(d + e*x)^n]))/(15*g*(e*f - d*g)*(f + g*x)^(3/2)) + (8*b*e^2*n*(a + b*Log[c*(d + e*x)^n]))/(5*g*(e*f - d*g)^2*Sqrt[f + g*x]) - (8*b*e^(5/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*(a + b*Log[c*(d + e*x)^n]))/(5*g*(e*f - d*g)^(5/2)) - (2*(a + b*Log[c*(d + e*x)^n])^2)/(5*g*(f + g*x)^(5/2)) - (16*b^2*e^(5/2)*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*Log[2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(5*g*(e*f - d*g)^(5/2)) - (8*b^2*e^(5/2)*n^2*PolyLog[2, 1 - 2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(5*g*(e*f - d*g)^(5/2))","A",19,15,26,0.5769,1,"{2398, 2411, 2347, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 51}"
151,1,583,0,1.8483941,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x)^{9/2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x)^(9/2),x]","-\frac{8 b^2 e^{7/2} n^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{7 g (e f-d g)^{7/2}}+\frac{8 b e^3 n \left(a+b \log \left(c (d+e x)^n\right)\right)}{7 g \sqrt{f+g x} (e f-d g)^3}+\frac{8 b e^2 n \left(a+b \log \left(c (d+e x)^n\right)\right)}{21 g (f+g x)^{3/2} (e f-d g)^2}-\frac{8 b e^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{7 g (e f-d g)^{7/2}}+\frac{8 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}{35 g (f+g x)^{5/2} (e f-d g)}-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{7 g (f+g x)^{7/2}}-\frac{128 b^2 e^3 n^2}{105 g \sqrt{f+g x} (e f-d g)^3}-\frac{16 b^2 e^2 n^2}{105 g (f+g x)^{3/2} (e f-d g)^2}+\frac{8 b^2 e^{7/2} n^2 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{7 g (e f-d g)^{7/2}}+\frac{368 b^2 e^{7/2} n^2 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{105 g (e f-d g)^{7/2}}-\frac{16 b^2 e^{7/2} n^2 \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{7 g (e f-d g)^{7/2}}","-\frac{8 b^2 e^{7/2} n^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{7 g (e f-d g)^{7/2}}+\frac{8 b e^3 n \left(a+b \log \left(c (d+e x)^n\right)\right)}{7 g \sqrt{f+g x} (e f-d g)^3}+\frac{8 b e^2 n \left(a+b \log \left(c (d+e x)^n\right)\right)}{21 g (f+g x)^{3/2} (e f-d g)^2}-\frac{8 b e^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{7 g (e f-d g)^{7/2}}+\frac{8 b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}{35 g (f+g x)^{5/2} (e f-d g)}-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{7 g (f+g x)^{7/2}}-\frac{128 b^2 e^3 n^2}{105 g \sqrt{f+g x} (e f-d g)^3}-\frac{16 b^2 e^2 n^2}{105 g (f+g x)^{3/2} (e f-d g)^2}+\frac{8 b^2 e^{7/2} n^2 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{7 g (e f-d g)^{7/2}}+\frac{368 b^2 e^{7/2} n^2 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{105 g (e f-d g)^{7/2}}-\frac{16 b^2 e^{7/2} n^2 \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{7 g (e f-d g)^{7/2}}",1,"(-16*b^2*e^2*n^2)/(105*g*(e*f - d*g)^2*(f + g*x)^(3/2)) - (128*b^2*e^3*n^2)/(105*g*(e*f - d*g)^3*Sqrt[f + g*x]) + (368*b^2*e^(7/2)*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(105*g*(e*f - d*g)^(7/2)) + (8*b^2*e^(7/2)*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]^2)/(7*g*(e*f - d*g)^(7/2)) + (8*b*e*n*(a + b*Log[c*(d + e*x)^n]))/(35*g*(e*f - d*g)*(f + g*x)^(5/2)) + (8*b*e^2*n*(a + b*Log[c*(d + e*x)^n]))/(21*g*(e*f - d*g)^2*(f + g*x)^(3/2)) + (8*b*e^3*n*(a + b*Log[c*(d + e*x)^n]))/(7*g*(e*f - d*g)^3*Sqrt[f + g*x]) - (8*b*e^(7/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*(a + b*Log[c*(d + e*x)^n]))/(7*g*(e*f - d*g)^(7/2)) - (2*(a + b*Log[c*(d + e*x)^n])^2)/(7*g*(f + g*x)^(7/2)) - (16*b^2*e^(7/2)*n^2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*Log[2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(7*g*(e*f - d*g)^(7/2)) - (8*b^2*e^(7/2)*n^2*PolyLog[2, 1 - 2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(7*g*(e*f - d*g)^(7/2))","A",25,15,26,0.5769,1,"{2398, 2411, 2347, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 51}"
152,0,0,0,0.0414031,"\int \frac{(f+g x)^{3/2}}{a+b \log \left(c (d+e x)^n\right)} \, dx","Int[(f + g*x)^(3/2)/(a + b*Log[c*(d + e*x)^n]),x]","\int \frac{(f+g x)^{3/2}}{a+b \log \left(c (d+e x)^n\right)} \, dx","\text{Int}\left(\frac{(f+g x)^{3/2}}{a+b \log \left(c (d+e x)^n\right)},x\right)",0,"Defer[Int][(f + g*x)^(3/2)/(a + b*Log[c*(d + e*x)^n]), x]","A",0,0,0,0,-1,"{}"
153,0,0,0,0.0375366,"\int \frac{\sqrt{f+g x}}{a+b \log \left(c (d+e x)^n\right)} \, dx","Int[Sqrt[f + g*x]/(a + b*Log[c*(d + e*x)^n]),x]","\int \frac{\sqrt{f+g x}}{a+b \log \left(c (d+e x)^n\right)} \, dx","\text{Int}\left(\frac{\sqrt{f+g x}}{a+b \log \left(c (d+e x)^n\right)},x\right)",0,"Defer[Int][Sqrt[f + g*x]/(a + b*Log[c*(d + e*x)^n]), x]","A",0,0,0,0,-1,"{}"
154,0,0,0,0.0388233,"\int \frac{1}{\sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","Int[1/(Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n])),x]","\int \frac{1}{\sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{\sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)},x\right)",0,"Defer[Int][1/(Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n])), x]","A",0,0,0,0,-1,"{}"
155,0,0,0,0.0424962,"\int \frac{1}{(f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","Int[1/((f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n])),x]","\int \frac{1}{(f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{(f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)},x\right)",0,"Defer[Int][1/((f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n])), x]","A",0,0,0,0,-1,"{}"
156,0,0,0,0.2646884,"\int \sqrt{f+g x} \sqrt{a+b \log \left(c (d+e x)^n\right)} \, dx","Int[Sqrt[f + g*x]*Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\int \sqrt{f+g x} \sqrt{a+b \log \left(c (d+e x)^n\right)} \, dx","\frac{2 (f+g x)^{3/2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{3 g}-\frac{b e n \text{Int}\left(\frac{(f+g x)^{3/2}}{(d+e x) \sqrt{a+b \log \left(c (d+e x)^n\right)}},x\right)}{3 g}",0,"(2*(f + g*x)^(3/2)*Sqrt[a + b*Log[c*(d + e*x)^n]])/(3*g) - (b*e*n*Defer[Int][(f + g*x)^(3/2)/((d + e*x)*Sqrt[a + b*Log[c*(d + e*x)^n]]), x])/(3*g)","A",0,0,0,0,-1,"{}"
157,0,0,0,0.2434622,"\int \frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{f+g x}} \, dx","Int[Sqrt[a + b*Log[c*(d + e*x)^n]]/Sqrt[f + g*x],x]","\int \frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{f+g x}} \, dx","\frac{2 \sqrt{f+g x} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{g}-\frac{b e n \text{Int}\left(\frac{\sqrt{f+g x}}{(d+e x) \sqrt{a+b \log \left(c (d+e x)^n\right)}},x\right)}{g}",0,"(2*Sqrt[f + g*x]*Sqrt[a + b*Log[c*(d + e*x)^n]])/g - (b*e*n*Defer[Int][Sqrt[f + g*x]/((d + e*x)*Sqrt[a + b*Log[c*(d + e*x)^n]]), x])/g","A",0,0,0,0,-1,"{}"
158,0,0,0,0.2566991,"\int \frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{(f+g x)^{3/2}} \, dx","Int[Sqrt[a + b*Log[c*(d + e*x)^n]]/(f + g*x)^(3/2),x]","\int \frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{(f+g x)^{3/2}} \, dx","\frac{b e n \text{Int}\left(\frac{1}{(d+e x) \sqrt{f+g x} \sqrt{a+b \log \left(c (d+e x)^n\right)}},x\right)}{g}-\frac{2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{g \sqrt{f+g x}}",0,"(-2*Sqrt[a + b*Log[c*(d + e*x)^n]])/(g*Sqrt[f + g*x]) + (b*e*n*Defer[Int][1/((d + e*x)*Sqrt[f + g*x]*Sqrt[a + b*Log[c*(d + e*x)^n]]), x])/g","A",0,0,0,0,-1,"{}"
159,0,0,0,0.0546673,"\int \frac{\sqrt{f+g x}}{\sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Int[Sqrt[f + g*x]/Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\int \frac{\sqrt{f+g x}}{\sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","\text{Int}\left(\frac{\sqrt{f+g x}}{\sqrt{a+b \log \left(c (d+e x)^n\right)}},x\right)",0,"Defer[Int][Sqrt[f + g*x]/Sqrt[a + b*Log[c*(d + e*x)^n]], x]","A",0,0,0,0,-1,"{}"
160,0,0,0,0.0556426,"\int \frac{1}{\sqrt{f+g x} \sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Int[1/(Sqrt[f + g*x]*Sqrt[a + b*Log[c*(d + e*x)^n]]),x]","\int \frac{1}{\sqrt{f+g x} \sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","\text{Int}\left(\frac{1}{\sqrt{f+g x} \sqrt{a+b \log \left(c (d+e x)^n\right)}},x\right)",0,"Defer[Int][1/(Sqrt[f + g*x]*Sqrt[a + b*Log[c*(d + e*x)^n]]), x]","A",0,0,0,0,-1,"{}"
161,0,0,0,0.0578403,"\int \frac{1}{(f+g x)^{3/2} \sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Int[1/((f + g*x)^(3/2)*Sqrt[a + b*Log[c*(d + e*x)^n]]),x]","\int \frac{1}{(f+g x)^{3/2} \sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","\text{Int}\left(\frac{1}{(f+g x)^{3/2} \sqrt{a+b \log \left(c (d+e x)^n\right)}},x\right)",0,"Defer[Int][1/((f + g*x)^(3/2)*Sqrt[a + b*Log[c*(d + e*x)^n]]), x]","A",0,0,0,0,-1,"{}"
162,1,94,0,0.0499173,"\int (f+g x)^m \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Int[(f + g*x)^m*(a + b*Log[c*(d + e*x)^n]),x]","\frac{(f+g x)^{m+1} \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (m+1)}+\frac{b e n (f+g x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{e (f+g x)}{e f-d g}\right)}{g (m+1) (m+2) (e f-d g)}","\frac{(f+g x)^{m+1} \left(a+b \log \left(c (d+e x)^n\right)\right)}{g (m+1)}+\frac{b e n (f+g x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{e (f+g x)}{e f-d g}\right)}{g (m+1) (m+2) (e f-d g)}",1,"(b*e*n*(f + g*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (e*(f + g*x))/(e*f - d*g)])/(g*(e*f - d*g)*(1 + m)*(2 + m)) + ((f + g*x)^(1 + m)*(a + b*Log[c*(d + e*x)^n]))/(g*(1 + m))","A",2,2,22,0.09091,1,"{2395, 68}"
163,0,0,0,0.0273663,"\int \frac{(f+g x)^m}{a+b \log \left(c (d+e x)^n\right)} \, dx","Int[(f + g*x)^m/(a + b*Log[c*(d + e*x)^n]),x]","\int \frac{(f+g x)^m}{a+b \log \left(c (d+e x)^n\right)} \, dx","\text{Int}\left(\frac{(f+g x)^m}{a+b \log \left(c (d+e x)^n\right)},x\right)",0,"Defer[Int][(f + g*x)^m/(a + b*Log[c*(d + e*x)^n]), x]","A",0,0,0,0,-1,"{}"
164,0,0,0,0.0268786,"\int \frac{(f+g x)^m}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Int[(f + g*x)^m/(a + b*Log[c*(d + e*x)^n])^2,x]","\int \frac{(f+g x)^m}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{(f+g x)^m}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2},x\right)",0,"Defer[Int][(f + g*x)^m/(a + b*Log[c*(d + e*x)^n])^2, x]","A",0,0,0,0,-1,"{}"
165,0,0,0,0.0530024,"\int (f+g x)^m \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2} \, dx","Int[(f + g*x)^m*(a + b*Log[c*(d + e*x)^n])^(3/2),x]","\int (f+g x)^m \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2} \, dx","\text{Int}\left((f+g x)^m \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2},x\right)",0,"Defer[Int][(f + g*x)^m*(a + b*Log[c*(d + e*x)^n])^(3/2), x]","A",0,0,0,0,-1,"{}"
166,0,0,0,0.0426145,"\int (f+g x)^m \sqrt{a+b \log \left(c (d+e x)^n\right)} \, dx","Int[(f + g*x)^m*Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\int (f+g x)^m \sqrt{a+b \log \left(c (d+e x)^n\right)} \, dx","\text{Int}\left((f+g x)^m \sqrt{a+b \log \left(c (d+e x)^n\right)},x\right)",0,"Defer[Int][(f + g*x)^m*Sqrt[a + b*Log[c*(d + e*x)^n]], x]","A",0,0,0,0,-1,"{}"
167,0,0,0,0.0458975,"\int \frac{(f+g x)^m}{\sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Int[(f + g*x)^m/Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\int \frac{(f+g x)^m}{\sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","\text{Int}\left(\frac{(f+g x)^m}{\sqrt{a+b \log \left(c (d+e x)^n\right)}},x\right)",0,"Defer[Int][(f + g*x)^m/Sqrt[a + b*Log[c*(d + e*x)^n]], x]","A",0,0,0,0,-1,"{}"
168,0,0,0,0.0542058,"\int \frac{(f+g x)^m}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}} \, dx","Int[(f + g*x)^m/(a + b*Log[c*(d + e*x)^n])^(3/2),x]","\int \frac{(f+g x)^m}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}} \, dx","\text{Int}\left(\frac{(f+g x)^m}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}},x\right)",0,"Defer[Int][(f + g*x)^m/(a + b*Log[c*(d + e*x)^n])^(3/2), x]","A",0,0,0,0,-1,"{}"
169,0,0,0,0.0262465,"\int (f+g x)^m \left(a+b \log \left(c (d+e x)^n\right)\right)^n \, dx","Int[(f + g*x)^m*(a + b*Log[c*(d + e*x)^n])^n,x]","\int (f+g x)^m \left(a+b \log \left(c (d+e x)^n\right)\right)^n \, dx","\text{Int}\left((f+g x)^m \left(a+b \log \left(c (d+e x)^n\right)\right)^n,x\right)",0,"Defer[Int][(f + g*x)^m*(a + b*Log[c*(d + e*x)^n])^n, x]","A",0,0,0,0,-1,"{}"
170,1,474,0,0.5487059,"\int (f+g x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^n \, dx","Int[(f + g*x)^3*(a + b*Log[c*(d + e*x)^n])^n,x]","\frac{g^2 3^{-n} e^{-\frac{3 a}{b n}} (d+e x)^3 (e f-d g) \left(c (d+e x)^n\right)^{-3/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{e^4}+\frac{3 g 2^{-n-1} e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g)^2 \left(c (d+e x)^n\right)^{-2/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{e^4}+\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g)^3 \left(c (d+e x)^n\right)^{-1/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{e^4}+\frac{g^3 4^{-n-1} e^{-\frac{4 a}{b n}} (d+e x)^4 \left(c (d+e x)^n\right)^{-4/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{e^4}","\frac{g^2 3^{-n} e^{-\frac{3 a}{b n}} (d+e x)^3 (e f-d g) \left(c (d+e x)^n\right)^{-3/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{e^4}+\frac{3 g 2^{-n-1} e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g)^2 \left(c (d+e x)^n\right)^{-2/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{e^4}+\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g)^3 \left(c (d+e x)^n\right)^{-1/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{e^4}+\frac{g^3 4^{-n-1} e^{-\frac{4 a}{b n}} (d+e x)^4 \left(c (d+e x)^n\right)^{-4/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{e^4}",1,"(4^(-1 - n)*g^3*(d + e*x)^4*Gamma[1 + n, (-4*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*(a + b*Log[c*(d + e*x)^n])^n)/(e^4*E^((4*a)/(b*n))*(c*(d + e*x)^n)^(4/n)*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^n) + (g^2*(e*f - d*g)*(d + e*x)^3*Gamma[1 + n, (-3*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*(a + b*Log[c*(d + e*x)^n])^n)/(3^n*e^4*E^((3*a)/(b*n))*(c*(d + e*x)^n)^(3/n)*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^n) + (3*2^(-1 - n)*g*(e*f - d*g)^2*(d + e*x)^2*Gamma[1 + n, (-2*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*(a + b*Log[c*(d + e*x)^n])^n)/(e^4*E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^n) + ((e*f - d*g)^3*(d + e*x)*Gamma[1 + n, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*(a + b*Log[c*(d + e*x)^n])^n)/(e^4*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^n)","A",14,6,24,0.2500,1,"{2401, 2389, 2300, 2181, 2390, 2310}"
171,1,348,0,0.3637631,"\int (f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^n \, dx","Int[(f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^n,x]","\frac{g 2^{-n} e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{e^3}+\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{e^3}+\frac{g^2 3^{-n-1} e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{e^3}","\frac{g 2^{-n} e^{-\frac{2 a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{-2/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{e^3}+\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g)^2 \left(c (d+e x)^n\right)^{-1/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{e^3}+\frac{g^2 3^{-n-1} e^{-\frac{3 a}{b n}} (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{e^3}",1,"(3^(-1 - n)*g^2*(d + e*x)^3*Gamma[1 + n, (-3*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*(a + b*Log[c*(d + e*x)^n])^n)/(e^3*E^((3*a)/(b*n))*(c*(d + e*x)^n)^(3/n)*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^n) + (g*(e*f - d*g)*(d + e*x)^2*Gamma[1 + n, (-2*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*(a + b*Log[c*(d + e*x)^n])^n)/(2^n*e^3*E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^n) + ((e*f - d*g)^2*(d + e*x)*Gamma[1 + n, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*(a + b*Log[c*(d + e*x)^n])^n)/(e^3*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^n)","A",11,6,24,0.2500,1,"{2401, 2389, 2300, 2181, 2390, 2310}"
172,1,225,0,0.2051885,"\int (f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^n \, dx","Int[(f + g*x)*(a + b*Log[c*(d + e*x)^n])^n,x]","\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{e^2}+\frac{g 2^{-n-1} e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{e^2}","\frac{e^{-\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{-1/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{e^2}+\frac{g 2^{-n-1} e^{-\frac{2 a}{b n}} (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)}{e^2}",1,"(2^(-1 - n)*g*(d + e*x)^2*Gamma[1 + n, (-2*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*(a + b*Log[c*(d + e*x)^n])^n)/(e^2*E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^n) + ((e*f - d*g)*(d + e*x)*Gamma[1 + n, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*(a + b*Log[c*(d + e*x)^n])^n)/(e^2*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^n)","A",8,6,22,0.2727,1,"{2401, 2389, 2300, 2181, 2390, 2310}"
173,1,103,0,0.0595006,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^n \, dx","Int[(a + b*Log[c*(d + e*x)^n])^n,x]","\frac{e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{e}","\frac{e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{e}",1,"((d + e*x)*Gamma[1 + n, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*(a + b*Log[c*(d + e*x)^n])^n)/(e*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^n)","A",3,3,16,0.1875,1,"{2389, 2300, 2181}"
174,0,0,0,0.0293431,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^n}{f+g x} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^n/(f + g*x),x]","\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^n}{f+g x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^n}{f+g x},x\right)",0,"Defer[Int][(a + b*Log[c*(d + e*x)^n])^n/(f + g*x), x]","A",0,0,0,0,-1,"{}"
175,1,260,0,0.5060147,"\int \frac{(h+i x)^4 (a+b \log (c (e+f x)))}{d e+d f x} \, dx","Int[((h + i*x)^4*(a + b*Log[c*(e + f*x)]))/(d*e + d*f*x),x]","\frac{\left(\frac{36 i^2 (e+f x)^2 (f h-e i)^2}{f^4}+\frac{16 i^3 (e+f x)^3 (f h-e i)}{f^4}+\frac{48 i (e+f x) (f h-e i)^3}{f^4}+\frac{12 (f h-e i)^4 \log (e+f x)}{f^4}+\frac{3 i^4 (e+f x)^4}{f^4}\right) (a+b \log (c (e+f x)))}{12 d f}-\frac{3 b i^2 (e+f x)^2 (f h-e i)^2}{2 d f^5}-\frac{4 b i^3 (e+f x)^3 (f h-e i)}{9 d f^5}-\frac{4 b i x (f h-e i)^3}{d f^4}-\frac{b (f h-e i)^4 \log ^2(e+f x)}{2 d f^5}-\frac{b i^4 (e+f x)^4}{16 d f^5}","\frac{3 i^2 (e+f x)^2 (f h-e i)^2 (a+b \log (c (e+f x)))}{d f^5}+\frac{4 i^3 (e+f x)^3 (f h-e i) (a+b \log (c (e+f x)))}{3 d f^5}+\frac{(f h-e i)^4 \log (e+f x) (a+b \log (c (e+f x)))}{d f^5}+\frac{4 i (e+f x) (f h-e i)^3 (a+b \log (c (e+f x)))}{d f^5}+\frac{i^4 (e+f x)^4 (a+b \log (c (e+f x)))}{4 d f^5}-\frac{3 b i^2 (e+f x)^2 (f h-e i)^2}{2 d f^5}-\frac{4 b i^3 (e+f x)^3 (f h-e i)}{9 d f^5}-\frac{4 b i x (f h-e i)^3}{d f^4}-\frac{b (f h-e i)^4 \log ^2(e+f x)}{2 d f^5}-\frac{b i^4 (e+f x)^4}{16 d f^5}",1,"(-4*b*i*(f*h - e*i)^3*x)/(d*f^4) - (3*b*i^2*(f*h - e*i)^2*(e + f*x)^2)/(2*d*f^5) - (4*b*i^3*(f*h - e*i)*(e + f*x)^3)/(9*d*f^5) - (b*i^4*(e + f*x)^4)/(16*d*f^5) - (b*(f*h - e*i)^4*Log[e + f*x]^2)/(2*d*f^5) + (((48*i*(f*h - e*i)^3*(e + f*x))/f^4 + (36*i^2*(f*h - e*i)^2*(e + f*x)^2)/f^4 + (16*i^3*(f*h - e*i)*(e + f*x)^3)/f^4 + (3*i^4*(e + f*x)^4)/f^4 + (12*(f*h - e*i)^4*Log[e + f*x])/f^4)*(a + b*Log[c*(e + f*x)]))/(12*d*f)","A",6,5,30,0.1667,1,"{2411, 12, 43, 2334, 2301}"
176,1,204,0,0.3838512,"\int \frac{(h+i x)^3 (a+b \log (c (e+f x)))}{d e+d f x} \, dx","Int[((h + i*x)^3*(a + b*Log[c*(e + f*x)]))/(d*e + d*f*x),x]","\frac{\left(\frac{9 i^2 (e+f x)^2 (f h-e i)}{f^3}+\frac{18 i (e+f x) (f h-e i)^2}{f^3}+\frac{6 (f h-e i)^3 \log (e+f x)}{f^3}+\frac{2 i^3 (e+f x)^3}{f^3}\right) (a+b \log (c (e+f x)))}{6 d f}-\frac{3 b i^2 (e+f x)^2 (f h-e i)}{4 d f^4}-\frac{3 b i x (f h-e i)^2}{d f^3}-\frac{b (f h-e i)^3 \log ^2(e+f x)}{2 d f^4}-\frac{b i^3 (e+f x)^3}{9 d f^4}","\frac{3 i^2 (e+f x)^2 (f h-e i) (a+b \log (c (e+f x)))}{2 d f^4}+\frac{(f h-e i)^3 \log (e+f x) (a+b \log (c (e+f x)))}{d f^4}+\frac{3 i (e+f x) (f h-e i)^2 (a+b \log (c (e+f x)))}{d f^4}+\frac{i^3 (e+f x)^3 (a+b \log (c (e+f x)))}{3 d f^4}-\frac{3 b i^2 (e+f x)^2 (f h-e i)}{4 d f^4}-\frac{3 b i x (f h-e i)^2}{d f^3}-\frac{b (f h-e i)^3 \log ^2(e+f x)}{2 d f^4}-\frac{b i^3 (e+f x)^3}{9 d f^4}",1,"(-3*b*i*(f*h - e*i)^2*x)/(d*f^3) - (3*b*i^2*(f*h - e*i)*(e + f*x)^2)/(4*d*f^4) - (b*i^3*(e + f*x)^3)/(9*d*f^4) - (b*(f*h - e*i)^3*Log[e + f*x]^2)/(2*d*f^4) + (((18*i*(f*h - e*i)^2*(e + f*x))/f^3 + (9*i^2*(f*h - e*i)*(e + f*x)^2)/f^3 + (2*i^3*(e + f*x)^3)/f^3 + (6*(f*h - e*i)^3*Log[e + f*x])/f^3)*(a + b*Log[c*(e + f*x)]))/(6*d*f)","A",8,6,30,0.2000,1,"{2411, 12, 43, 2334, 14, 2301}"
177,1,133,0,0.2629257,"\int \frac{(h+i x)^2 (a+b \log (c (e+f x)))}{d e+d f x} \, dx","Int[((h + i*x)^2*(a + b*Log[c*(e + f*x)]))/(d*e + d*f*x),x]","\frac{\left(\frac{4 i (e+f x) (f h-e i)}{f^2}+\frac{2 (f h-e i)^2 \log (e+f x)}{f^2}+\frac{i^2 (e+f x)^2}{f^2}\right) (a+b \log (c (e+f x)))}{2 d f}-\frac{b (-3 e i+4 f h+f i x)^2}{4 d f^3}-\frac{b (f h-e i)^2 \log ^2(e+f x)}{2 d f^3}","\frac{(f h-e i)^2 \log (e+f x) (a+b \log (c (e+f x)))}{d f^3}+\frac{2 i (e+f x) (f h-e i) (a+b \log (c (e+f x)))}{d f^3}+\frac{i^2 (e+f x)^2 (a+b \log (c (e+f x)))}{2 d f^3}-\frac{b (-3 e i+4 f h+f i x)^2}{4 d f^3}-\frac{b (f h-e i)^2 \log ^2(e+f x)}{2 d f^3}",1,"-(b*(4*f*h - 3*e*i + f*i*x)^2)/(4*d*f^3) - (b*(f*h - e*i)^2*Log[e + f*x]^2)/(2*d*f^3) + (((4*i*(f*h - e*i)*(e + f*x))/f^2 + (i^2*(e + f*x)^2)/f^2 + (2*(f*h - e*i)^2*Log[e + f*x])/f^2)*(a + b*Log[c*(e + f*x)]))/(2*d*f)","A",7,6,30,0.2000,1,"{2411, 12, 43, 2334, 14, 2301}"
178,1,79,0,0.1290905,"\int \frac{(h+i x) (a+b \log (c (e+f x)))}{d e+d f x} \, dx","Int[((h + i*x)*(a + b*Log[c*(e + f*x)]))/(d*e + d*f*x),x]","\frac{(f h-e i) (a+b \log (c (e+f x)))^2}{2 b d f^2}+\frac{a i x}{d f}+\frac{b i (e+f x) \log (c (e+f x))}{d f^2}-\frac{b i x}{d f}","\frac{(f h-e i) (a+b \log (c (e+f x)))^2}{2 b d f^2}+\frac{a i x}{d f}+\frac{b i (e+f x) \log (c (e+f x))}{d f^2}-\frac{b i x}{d f}",1,"(a*i*x)/(d*f) - (b*i*x)/(d*f) + (b*i*(e + f*x)*Log[c*(e + f*x)])/(d*f^2) + ((f*h - e*i)*(a + b*Log[c*(e + f*x)])^2)/(2*b*d*f^2)","A",6,5,28,0.1786,1,"{2411, 12, 2346, 2301, 2295}"
179,1,27,0,0.0343237,"\int \frac{a+b \log (c (e+f x))}{d e+d f x} \, dx","Int[(a + b*Log[c*(e + f*x)])/(d*e + d*f*x),x]","\frac{(a+b \log (c (e+f x)))^2}{2 b d f}","\frac{(a+b \log (c (e+f x)))^2}{2 b d f}",1,"(a + b*Log[c*(e + f*x)])^2/(2*b*d*f)","A",3,3,23,0.1304,1,"{2390, 12, 2301}"
180,1,116,0,0.2343063,"\int \frac{a+b \log (c (e+f x))}{(d e+d f x) (h+i x)} \, dx","Int[(a + b*Log[c*(e + f*x)])/((d*e + d*f*x)*(h + i*x)),x]","-\frac{b \text{PolyLog}\left(2,-\frac{i (e+f x)}{f h-e i}\right)}{d (f h-e i)}+\frac{(a+b \log (c (e+f x)))^2}{2 b d (f h-e i)}-\frac{\log \left(\frac{f (h+i x)}{f h-e i}\right) (a+b \log (c (e+f x)))}{d (f h-e i)}","\frac{b \text{PolyLog}\left(2,-\frac{f h-e i}{i (e+f x)}\right)}{d (f h-e i)}-\frac{\log \left(\frac{f h-e i}{i (e+f x)}+1\right) (a+b \log (c (e+f x)))}{d (f h-e i)}",1,"(a + b*Log[c*(e + f*x)])^2/(2*b*d*(f*h - e*i)) - ((a + b*Log[c*(e + f*x)])*Log[(f*(h + i*x))/(f*h - e*i)])/(d*(f*h - e*i)) - (b*PolyLog[2, -((i*(e + f*x))/(f*h - e*i))])/(d*(f*h - e*i))","A",6,6,30,0.2000,1,"{2411, 12, 2344, 2301, 2317, 2391}"
181,1,181,0,0.3640538,"\int \frac{a+b \log (c (e+f x))}{(d e+d f x) (h+i x)^2} \, dx","Int[(a + b*Log[c*(e + f*x)])/((d*e + d*f*x)*(h + i*x)^2),x]","-\frac{b f \text{PolyLog}\left(2,-\frac{i (e+f x)}{f h-e i}\right)}{d (f h-e i)^2}+\frac{f (a+b \log (c (e+f x)))^2}{2 b d (f h-e i)^2}-\frac{f \log \left(\frac{f (h+i x)}{f h-e i}\right) (a+b \log (c (e+f x)))}{d (f h-e i)^2}-\frac{i (e+f x) (a+b \log (c (e+f x)))}{d (h+i x) (f h-e i)^2}+\frac{b f \log (h+i x)}{d (f h-e i)^2}","\frac{b f \text{PolyLog}\left(2,-\frac{f h-e i}{i (e+f x)}\right)}{d (f h-e i)^2}-\frac{f \log \left(\frac{f h-e i}{i (e+f x)}+1\right) (a+b \log (c (e+f x)))}{d (f h-e i)^2}-\frac{i (e+f x) (a+b \log (c (e+f x)))}{d (h+i x) (f h-e i)^2}+\frac{b f \log (h+i x)}{d (f h-e i)^2}",1,"-((i*(e + f*x)*(a + b*Log[c*(e + f*x)]))/(d*(f*h - e*i)^2*(h + i*x))) + (f*(a + b*Log[c*(e + f*x)])^2)/(2*b*d*(f*h - e*i)^2) + (b*f*Log[h + i*x])/(d*(f*h - e*i)^2) - (f*(a + b*Log[c*(e + f*x)])*Log[(f*(h + i*x))/(f*h - e*i)])/(d*(f*h - e*i)^2) - (b*f*PolyLog[2, -((i*(e + f*x))/(f*h - e*i))])/(d*(f*h - e*i)^2)","A",9,9,30,0.3000,1,"{2411, 12, 2347, 2344, 2301, 2317, 2391, 2314, 31}"
182,1,282,0,0.5719775,"\int \frac{a+b \log (c (e+f x))}{(d e+d f x) (h+i x)^3} \, dx","Int[(a + b*Log[c*(e + f*x)])/((d*e + d*f*x)*(h + i*x)^3),x]","-\frac{b f^2 \text{PolyLog}\left(2,-\frac{i (e+f x)}{f h-e i}\right)}{d (f h-e i)^3}+\frac{f^2 (a+b \log (c (e+f x)))^2}{2 b d (f h-e i)^3}-\frac{f^2 \log \left(\frac{f (h+i x)}{f h-e i}\right) (a+b \log (c (e+f x)))}{d (f h-e i)^3}-\frac{f i (e+f x) (a+b \log (c (e+f x)))}{d (h+i x) (f h-e i)^3}+\frac{a+b \log (c (e+f x))}{2 d (h+i x)^2 (f h-e i)}-\frac{b f^2 \log (e+f x)}{2 d (f h-e i)^3}+\frac{3 b f^2 \log (h+i x)}{2 d (f h-e i)^3}-\frac{b f}{2 d (h+i x) (f h-e i)^2}","\frac{b f^2 \text{PolyLog}\left(2,-\frac{f h-e i}{i (e+f x)}\right)}{d (f h-e i)^3}-\frac{f^2 \log \left(\frac{f h-e i}{i (e+f x)}+1\right) (a+b \log (c (e+f x)))}{d (f h-e i)^3}-\frac{f i (e+f x) (a+b \log (c (e+f x)))}{d (h+i x) (f h-e i)^3}+\frac{a+b \log (c (e+f x))}{2 d (h+i x)^2 (f h-e i)}-\frac{b f^2 \log (e+f x)}{2 d (f h-e i)^3}+\frac{3 b f^2 \log (h+i x)}{2 d (f h-e i)^3}-\frac{b f}{2 d (h+i x) (f h-e i)^2}",1,"-(b*f)/(2*d*(f*h - e*i)^2*(h + i*x)) - (b*f^2*Log[e + f*x])/(2*d*(f*h - e*i)^3) + (a + b*Log[c*(e + f*x)])/(2*d*(f*h - e*i)*(h + i*x)^2) - (f*i*(e + f*x)*(a + b*Log[c*(e + f*x)]))/(d*(f*h - e*i)^3*(h + i*x)) + (f^2*(a + b*Log[c*(e + f*x)])^2)/(2*b*d*(f*h - e*i)^3) + (3*b*f^2*Log[h + i*x])/(2*d*(f*h - e*i)^3) - (f^2*(a + b*Log[c*(e + f*x)])*Log[(f*(h + i*x))/(f*h - e*i)])/(d*(f*h - e*i)^3) - (b*f^2*PolyLog[2, -((i*(e + f*x))/(f*h - e*i))])/(d*(f*h - e*i)^3)","A",13,11,30,0.3667,1,"{2411, 12, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
183,1,672,0,1.6744497,"\int \frac{(h+i x)^4 (a+b \log (c (e+f x)))^2}{d e+d f x} \, dx","Int[((h + i*x)^4*(a + b*Log[c*(e + f*x)])^2)/(d*e + d*f*x),x]","\frac{i^2 (e+f x)^2 (f h-e i)^2 (a+b \log (c (e+f x)))^2}{2 d f^5}-\frac{b i^2 (e+f x)^2 (f h-e i)^2 (a+b \log (c (e+f x)))}{2 d f^5}-\frac{b (f h-e i) \left(\frac{9 i^2 (e+f x)^2 (f h-e i)}{f^2}+\frac{18 i (e+f x) (f h-e i)^2}{f^2}+\frac{6 (f h-e i)^3 \log (e+f x)}{f^2}+\frac{2 i^3 (e+f x)^3}{f^2}\right) (a+b \log (c (e+f x)))}{9 d f^3}-\frac{b \left(\frac{36 i^2 (e+f x)^2 (f h-e i)^2}{f^3}+\frac{16 i^3 (e+f x)^3 (f h-e i)}{f^3}+\frac{48 i (e+f x) (f h-e i)^3}{f^3}+\frac{12 (f h-e i)^4 \log (e+f x)}{f^3}+\frac{3 i^4 (e+f x)^4}{f^3}\right) (a+b \log (c (e+f x)))}{24 d f^2}+\frac{(f h-e i)^4 (a+b \log (c (e+f x)))^3}{3 b d f^5}+\frac{2 i (e+f x) (f h-e i)^3 (a+b \log (c (e+f x)))^2}{d f^5}+\frac{(h+i x)^3 (f h-e i) (a+b \log (c (e+f x)))^2}{3 d f^2}+\frac{(h+i x)^4 (a+b \log (c (e+f x)))^2}{4 d f}-\frac{4 a b i x (f h-e i)^3}{d f^4}-\frac{4 b^2 i (e+f x) (f h-e i)^3 \log (c (e+f x))}{d f^5}+\frac{3 b^2 i^2 (e+f x)^2 (f h-e i)^2}{2 d f^5}+\frac{8 b^2 i^3 (e+f x)^3 (f h-e i)}{27 d f^5}+\frac{8 b^2 i x (f h-e i)^3}{d f^4}+\frac{7 b^2 (f h-e i)^4 \log ^2(e+f x)}{12 d f^5}+\frac{b^2 i^4 (e+f x)^4}{32 d f^5}","\frac{i^2 (e+f x)^2 (f h-e i)^2 (a+b \log (c (e+f x)))^2}{2 d f^5}-\frac{3 b i^2 (e+f x)^2 (f h-e i)^2 (a+b \log (c (e+f x)))}{d f^5}-\frac{8 b i^3 (e+f x)^3 (f h-e i) (a+b \log (c (e+f x)))}{9 d f^5}+\frac{(f h-e i)^4 (a+b \log (c (e+f x)))^3}{3 b d f^5}-\frac{7 b (f h-e i)^4 \log (e+f x) (a+b \log (c (e+f x)))}{6 d f^5}+\frac{2 i (e+f x) (f h-e i)^3 (a+b \log (c (e+f x)))^2}{d f^5}-\frac{4 b i (e+f x) (f h-e i)^3 (a+b \log (c (e+f x)))}{d f^5}+\frac{(h+i x)^3 (f h-e i) (a+b \log (c (e+f x)))^2}{3 d f^2}-\frac{b i^4 (e+f x)^4 (a+b \log (c (e+f x)))}{8 d f^5}+\frac{(h+i x)^4 (a+b \log (c (e+f x)))^2}{4 d f}-\frac{4 a b i x (f h-e i)^3}{d f^4}-\frac{4 b^2 i (e+f x) (f h-e i)^3 \log (c (e+f x))}{d f^5}+\frac{3 b^2 i^2 (e+f x)^2 (f h-e i)^2}{2 d f^5}+\frac{8 b^2 i^3 (e+f x)^3 (f h-e i)}{27 d f^5}+\frac{8 b^2 i x (f h-e i)^3}{d f^4}+\frac{7 b^2 (f h-e i)^4 \log ^2(e+f x)}{12 d f^5}+\frac{b^2 i^4 (e+f x)^4}{32 d f^5}",1,"(-4*a*b*i*(f*h - e*i)^3*x)/(d*f^4) + (8*b^2*i*(f*h - e*i)^3*x)/(d*f^4) + (3*b^2*i^2*(f*h - e*i)^2*(e + f*x)^2)/(2*d*f^5) + (8*b^2*i^3*(f*h - e*i)*(e + f*x)^3)/(27*d*f^5) + (b^2*i^4*(e + f*x)^4)/(32*d*f^5) + (7*b^2*(f*h - e*i)^4*Log[e + f*x]^2)/(12*d*f^5) - (4*b^2*i*(f*h - e*i)^3*(e + f*x)*Log[c*(e + f*x)])/(d*f^5) - (b*i^2*(f*h - e*i)^2*(e + f*x)^2*(a + b*Log[c*(e + f*x)]))/(2*d*f^5) - (b*(f*h - e*i)*((18*i*(f*h - e*i)^2*(e + f*x))/f^2 + (9*i^2*(f*h - e*i)*(e + f*x)^2)/f^2 + (2*i^3*(e + f*x)^3)/f^2 + (6*(f*h - e*i)^3*Log[e + f*x])/f^2)*(a + b*Log[c*(e + f*x)]))/(9*d*f^3) - (b*((48*i*(f*h - e*i)^3*(e + f*x))/f^3 + (36*i^2*(f*h - e*i)^2*(e + f*x)^2)/f^3 + (16*i^3*(f*h - e*i)*(e + f*x)^3)/f^3 + (3*i^4*(e + f*x)^4)/f^3 + (12*(f*h - e*i)^4*Log[e + f*x])/f^3)*(a + b*Log[c*(e + f*x)]))/(24*d*f^2) + (2*i*(f*h - e*i)^3*(e + f*x)*(a + b*Log[c*(e + f*x)])^2)/(d*f^5) + (i^2*(f*h - e*i)^2*(e + f*x)^2*(a + b*Log[c*(e + f*x)])^2)/(2*d*f^5) + ((f*h - e*i)*(h + i*x)^3*(a + b*Log[c*(e + f*x)])^2)/(3*d*f^2) + ((h + i*x)^4*(a + b*Log[c*(e + f*x)])^2)/(4*d*f) + ((f*h - e*i)^4*(a + b*Log[c*(e + f*x)])^3)/(3*b*d*f^5)","A",30,15,32,0.4688,1,"{2411, 12, 2346, 2302, 30, 2296, 2295, 2330, 2305, 2304, 2319, 43, 2334, 14, 2301}"
184,1,459,0,0.981334,"\int \frac{(h+i x)^3 (a+b \log (c (e+f x)))^2}{d e+d f x} \, dx","Int[((h + i*x)^3*(a + b*Log[c*(e + f*x)])^2)/(d*e + d*f*x),x]","\frac{i^2 (e+f x)^2 (f h-e i) (a+b \log (c (e+f x)))^2}{2 d f^4}-\frac{b i^2 (e+f x)^2 (f h-e i) (a+b \log (c (e+f x)))}{2 d f^4}-\frac{b \left(\frac{9 i^2 (e+f x)^2 (f h-e i)}{f^2}+\frac{18 i (e+f x) (f h-e i)^2}{f^2}+\frac{6 (f h-e i)^3 \log (e+f x)}{f^2}+\frac{2 i^3 (e+f x)^3}{f^2}\right) (a+b \log (c (e+f x)))}{9 d f^2}+\frac{(f h-e i)^3 (a+b \log (c (e+f x)))^3}{3 b d f^4}+\frac{2 i (e+f x) (f h-e i)^2 (a+b \log (c (e+f x)))^2}{d f^4}+\frac{(h+i x)^3 (a+b \log (c (e+f x)))^2}{3 d f}-\frac{4 a b i x (f h-e i)^2}{d f^3}-\frac{4 b^2 i (e+f x) (f h-e i)^2 \log (c (e+f x))}{d f^4}+\frac{3 b^2 i^2 (e+f x)^2 (f h-e i)}{4 d f^4}+\frac{6 b^2 i x (f h-e i)^2}{d f^3}+\frac{b^2 (f h-e i)^3 \log ^2(e+f x)}{3 d f^4}+\frac{2 b^2 i^3 (e+f x)^3}{27 d f^4}","\frac{i^2 (e+f x)^2 (f h-e i) (a+b \log (c (e+f x)))^2}{2 d f^4}-\frac{3 b i^2 (e+f x)^2 (f h-e i) (a+b \log (c (e+f x)))}{2 d f^4}+\frac{(f h-e i)^3 (a+b \log (c (e+f x)))^3}{3 b d f^4}-\frac{2 b (f h-e i)^3 \log (e+f x) (a+b \log (c (e+f x)))}{3 d f^4}+\frac{2 i (e+f x) (f h-e i)^2 (a+b \log (c (e+f x)))^2}{d f^4}-\frac{2 b i (e+f x) (f h-e i)^2 (a+b \log (c (e+f x)))}{d f^4}-\frac{2 b i^3 (e+f x)^3 (a+b \log (c (e+f x)))}{9 d f^4}+\frac{(h+i x)^3 (a+b \log (c (e+f x)))^2}{3 d f}-\frac{4 a b i x (f h-e i)^2}{d f^3}-\frac{4 b^2 i (e+f x) (f h-e i)^2 \log (c (e+f x))}{d f^4}+\frac{3 b^2 i^2 (e+f x)^2 (f h-e i)}{4 d f^4}+\frac{6 b^2 i x (f h-e i)^2}{d f^3}+\frac{b^2 (f h-e i)^3 \log ^2(e+f x)}{3 d f^4}+\frac{2 b^2 i^3 (e+f x)^3}{27 d f^4}",1,"(-4*a*b*i*(f*h - e*i)^2*x)/(d*f^3) + (6*b^2*i*(f*h - e*i)^2*x)/(d*f^3) + (3*b^2*i^2*(f*h - e*i)*(e + f*x)^2)/(4*d*f^4) + (2*b^2*i^3*(e + f*x)^3)/(27*d*f^4) + (b^2*(f*h - e*i)^3*Log[e + f*x]^2)/(3*d*f^4) - (4*b^2*i*(f*h - e*i)^2*(e + f*x)*Log[c*(e + f*x)])/(d*f^4) - (b*i^2*(f*h - e*i)*(e + f*x)^2*(a + b*Log[c*(e + f*x)]))/(2*d*f^4) - (b*((18*i*(f*h - e*i)^2*(e + f*x))/f^2 + (9*i^2*(f*h - e*i)*(e + f*x)^2)/f^2 + (2*i^3*(e + f*x)^3)/f^2 + (6*(f*h - e*i)^3*Log[e + f*x])/f^2)*(a + b*Log[c*(e + f*x)]))/(9*d*f^2) + (2*i*(f*h - e*i)^2*(e + f*x)*(a + b*Log[c*(e + f*x)])^2)/(d*f^4) + (i^2*(f*h - e*i)*(e + f*x)^2*(a + b*Log[c*(e + f*x)])^2)/(2*d*f^4) + ((h + i*x)^3*(a + b*Log[c*(e + f*x)])^2)/(3*d*f) + ((f*h - e*i)^3*(a + b*Log[c*(e + f*x)])^3)/(3*b*d*f^4)","A",24,15,32,0.4688,1,"{2411, 12, 2346, 2302, 30, 2296, 2295, 2330, 2305, 2304, 2319, 43, 2334, 14, 2301}"
185,1,238,0,0.5134415,"\int \frac{(h+i x)^2 (a+b \log (c (e+f x)))^2}{d e+d f x} \, dx","Int[((h + i*x)^2*(a + b*Log[c*(e + f*x)])^2)/(d*e + d*f*x),x]","\frac{(f h-e i)^2 (a+b \log (c (e+f x)))^3}{3 b d f^3}+\frac{2 i (e+f x) (f h-e i) (a+b \log (c (e+f x)))^2}{d f^3}+\frac{i^2 (e+f x)^2 (a+b \log (c (e+f x)))^2}{2 d f^3}-\frac{b i^2 (e+f x)^2 (a+b \log (c (e+f x)))}{2 d f^3}-\frac{4 a b i x (f h-e i)}{d f^2}-\frac{4 b^2 i (e+f x) (f h-e i) \log (c (e+f x))}{d f^3}+\frac{4 b^2 i x (f h-e i)}{d f^2}+\frac{b^2 i^2 (e+f x)^2}{4 d f^3}","\frac{(f h-e i)^2 (a+b \log (c (e+f x)))^3}{3 b d f^3}+\frac{2 i (e+f x) (f h-e i) (a+b \log (c (e+f x)))^2}{d f^3}+\frac{i^2 (e+f x)^2 (a+b \log (c (e+f x)))^2}{2 d f^3}-\frac{b i^2 (e+f x)^2 (a+b \log (c (e+f x)))}{2 d f^3}-\frac{4 a b i x (f h-e i)}{d f^2}-\frac{4 b^2 i (e+f x) (f h-e i) \log (c (e+f x))}{d f^3}+\frac{4 b^2 i x (f h-e i)}{d f^2}+\frac{b^2 i^2 (e+f x)^2}{4 d f^3}",1,"(-4*a*b*i*(f*h - e*i)*x)/(d*f^2) + (4*b^2*i*(f*h - e*i)*x)/(d*f^2) + (b^2*i^2*(e + f*x)^2)/(4*d*f^3) - (4*b^2*i*(f*h - e*i)*(e + f*x)*Log[c*(e + f*x)])/(d*f^3) - (b*i^2*(e + f*x)^2*(a + b*Log[c*(e + f*x)]))/(2*d*f^3) + (2*i*(f*h - e*i)*(e + f*x)*(a + b*Log[c*(e + f*x)])^2)/(d*f^3) + (i^2*(e + f*x)^2*(a + b*Log[c*(e + f*x)])^2)/(2*d*f^3) + ((f*h - e*i)^2*(a + b*Log[c*(e + f*x)])^3)/(3*b*d*f^3)","A",16,10,32,0.3125,1,"{2411, 12, 2346, 2302, 30, 2296, 2295, 2330, 2305, 2304}"
186,1,113,0,0.2019752,"\int \frac{(h+i x) (a+b \log (c (e+f x)))^2}{d e+d f x} \, dx","Int[((h + i*x)*(a + b*Log[c*(e + f*x)])^2)/(d*e + d*f*x),x]","\frac{(f h-e i) (a+b \log (c (e+f x)))^3}{3 b d f^2}+\frac{i (e+f x) (a+b \log (c (e+f x)))^2}{d f^2}-\frac{2 a b i x}{d f}-\frac{2 b^2 i (e+f x) \log (c (e+f x))}{d f^2}+\frac{2 b^2 i x}{d f}","\frac{(f h-e i) (a+b \log (c (e+f x)))^3}{3 b d f^2}+\frac{i (e+f x) (a+b \log (c (e+f x)))^2}{d f^2}-\frac{2 a b i x}{d f}-\frac{2 b^2 i (e+f x) \log (c (e+f x))}{d f^2}+\frac{2 b^2 i x}{d f}",1,"(-2*a*b*i*x)/(d*f) + (2*b^2*i*x)/(d*f) - (2*b^2*i*(e + f*x)*Log[c*(e + f*x)])/(d*f^2) + (i*(e + f*x)*(a + b*Log[c*(e + f*x)])^2)/(d*f^2) + ((f*h - e*i)*(a + b*Log[c*(e + f*x)])^3)/(3*b*d*f^2)","A",8,7,30,0.2333,1,"{2411, 12, 2346, 2302, 30, 2296, 2295}"
187,1,27,0,0.0595308,"\int \frac{(a+b \log (c (e+f x)))^2}{d e+d f x} \, dx","Int[(a + b*Log[c*(e + f*x)])^2/(d*e + d*f*x),x]","\frac{(a+b \log (c (e+f x)))^3}{3 b d f}","\frac{(a+b \log (c (e+f x)))^3}{3 b d f}",1,"(a + b*Log[c*(e + f*x)])^3/(3*b*d*f)","A",4,4,25,0.1600,1,"{2390, 12, 2302, 30}"
188,1,168,0,0.3834633,"\int \frac{(a+b \log (c (e+f x)))^2}{(d e+d f x) (h+i x)} \, dx","Int[(a + b*Log[c*(e + f*x)])^2/((d*e + d*f*x)*(h + i*x)),x]","-\frac{2 b \text{PolyLog}\left(2,-\frac{i (e+f x)}{f h-e i}\right) (a+b \log (c (e+f x)))}{d (f h-e i)}+\frac{2 b^2 \text{PolyLog}\left(3,-\frac{i (e+f x)}{f h-e i}\right)}{d (f h-e i)}+\frac{(a+b \log (c (e+f x)))^3}{3 b d (f h-e i)}-\frac{\log \left(\frac{f (h+i x)}{f h-e i}\right) (a+b \log (c (e+f x)))^2}{d (f h-e i)}","\frac{2 b \text{PolyLog}\left(2,-\frac{f h-e i}{i (e+f x)}\right) (a+b \log (c (e+f x)))}{d (f h-e i)}+\frac{2 b^2 \text{PolyLog}\left(3,-\frac{f h-e i}{i (e+f x)}\right)}{d (f h-e i)}-\frac{\log \left(\frac{f h-e i}{i (e+f x)}+1\right) (a+b \log (c (e+f x)))^2}{d (f h-e i)}",1,"(a + b*Log[c*(e + f*x)])^3/(3*b*d*(f*h - e*i)) - ((a + b*Log[c*(e + f*x)])^2*Log[(f*(h + i*x))/(f*h - e*i)])/(d*(f*h - e*i)) - (2*b*(a + b*Log[c*(e + f*x)])*PolyLog[2, -((i*(e + f*x))/(f*h - e*i))])/(d*(f*h - e*i)) + (2*b^2*PolyLog[3, -((i*(e + f*x))/(f*h - e*i))])/(d*(f*h - e*i))","A",8,8,32,0.2500,1,"{2411, 12, 2344, 2302, 30, 2317, 2374, 6589}"
189,1,300,0,0.6370807,"\int \frac{(a+b \log (c (e+f x)))^2}{(d e+d f x) (h+i x)^2} \, dx","Int[(a + b*Log[c*(e + f*x)])^2/((d*e + d*f*x)*(h + i*x)^2),x]","-\frac{2 b f \text{PolyLog}\left(2,-\frac{i (e+f x)}{f h-e i}\right) (a+b \log (c (e+f x)))}{d (f h-e i)^2}+\frac{2 b^2 f \text{PolyLog}\left(2,-\frac{i (e+f x)}{f h-e i}\right)}{d (f h-e i)^2}+\frac{2 b^2 f \text{PolyLog}\left(3,-\frac{i (e+f x)}{f h-e i}\right)}{d (f h-e i)^2}+\frac{f (a+b \log (c (e+f x)))^3}{3 b d (f h-e i)^2}-\frac{f \log \left(\frac{f (h+i x)}{f h-e i}\right) (a+b \log (c (e+f x)))^2}{d (f h-e i)^2}-\frac{i (e+f x) (a+b \log (c (e+f x)))^2}{d (h+i x) (f h-e i)^2}+\frac{2 b f \log \left(\frac{f (h+i x)}{f h-e i}\right) (a+b \log (c (e+f x)))}{d (f h-e i)^2}","\frac{2 b f \text{PolyLog}\left(2,-\frac{f h-e i}{i (e+f x)}\right) (a+b \log (c (e+f x)))}{d (f h-e i)^2}+\frac{2 b^2 f \text{PolyLog}\left(2,-\frac{i (e+f x)}{f h-e i}\right)}{d (f h-e i)^2}+\frac{2 b^2 f \text{PolyLog}\left(3,-\frac{f h-e i}{i (e+f x)}\right)}{d (f h-e i)^2}+\frac{2 b f \log \left(\frac{f (h+i x)}{f h-e i}\right) (a+b \log (c (e+f x)))}{d (f h-e i)^2}-\frac{i (e+f x) (a+b \log (c (e+f x)))^2}{d (h+i x) (f h-e i)^2}-\frac{f \log \left(\frac{f h-e i}{i (e+f x)}+1\right) (a+b \log (c (e+f x)))^2}{d (f h-e i)^2}",1,"-((i*(e + f*x)*(a + b*Log[c*(e + f*x)])^2)/(d*(f*h - e*i)^2*(h + i*x))) + (f*(a + b*Log[c*(e + f*x)])^3)/(3*b*d*(f*h - e*i)^2) + (2*b*f*(a + b*Log[c*(e + f*x)])*Log[(f*(h + i*x))/(f*h - e*i)])/(d*(f*h - e*i)^2) - (f*(a + b*Log[c*(e + f*x)])^2*Log[(f*(h + i*x))/(f*h - e*i)])/(d*(f*h - e*i)^2) + (2*b^2*f*PolyLog[2, -((i*(e + f*x))/(f*h - e*i))])/(d*(f*h - e*i)^2) - (2*b*f*(a + b*Log[c*(e + f*x)])*PolyLog[2, -((i*(e + f*x))/(f*h - e*i))])/(d*(f*h - e*i)^2) + (2*b^2*f*PolyLog[3, -((i*(e + f*x))/(f*h - e*i))])/(d*(f*h - e*i)^2)","A",12,11,32,0.3438,1,"{2411, 12, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391}"
190,1,453,0,1.0920092,"\int \frac{(a+b \log (c (e+f x)))^2}{(d e+d f x) (h+i x)^3} \, dx","Int[(a + b*Log[c*(e + f*x)])^2/((d*e + d*f*x)*(h + i*x)^3),x]","-\frac{2 b f^2 \text{PolyLog}\left(2,-\frac{i (e+f x)}{f h-e i}\right) (a+b \log (c (e+f x)))}{d (f h-e i)^3}+\frac{3 b^2 f^2 \text{PolyLog}\left(2,-\frac{i (e+f x)}{f h-e i}\right)}{d (f h-e i)^3}+\frac{2 b^2 f^2 \text{PolyLog}\left(3,-\frac{i (e+f x)}{f h-e i}\right)}{d (f h-e i)^3}+\frac{f^2 (a+b \log (c (e+f x)))^3}{3 b d (f h-e i)^3}-\frac{f^2 \log \left(\frac{f (h+i x)}{f h-e i}\right) (a+b \log (c (e+f x)))^2}{d (f h-e i)^3}-\frac{f^2 (a+b \log (c (e+f x)))^2}{2 d (f h-e i)^3}+\frac{3 b f^2 \log \left(\frac{f (h+i x)}{f h-e i}\right) (a+b \log (c (e+f x)))}{d (f h-e i)^3}-\frac{f i (e+f x) (a+b \log (c (e+f x)))^2}{d (h+i x) (f h-e i)^3}+\frac{(a+b \log (c (e+f x)))^2}{2 d (h+i x)^2 (f h-e i)}+\frac{b f i (e+f x) (a+b \log (c (e+f x)))}{d (h+i x) (f h-e i)^3}-\frac{b^2 f^2 \log (h+i x)}{d (f h-e i)^3}","\frac{2 b f^2 \text{PolyLog}\left(2,-\frac{f h-e i}{i (e+f x)}\right) (a+b \log (c (e+f x)))}{d (f h-e i)^3}-\frac{b^2 f^2 \text{PolyLog}\left(2,-\frac{f h-e i}{i (e+f x)}\right)}{d (f h-e i)^3}+\frac{2 b^2 f^2 \text{PolyLog}\left(2,-\frac{i (e+f x)}{f h-e i}\right)}{d (f h-e i)^3}+\frac{2 b^2 f^2 \text{PolyLog}\left(3,-\frac{f h-e i}{i (e+f x)}\right)}{d (f h-e i)^3}+\frac{2 b f^2 \log \left(\frac{f (h+i x)}{f h-e i}\right) (a+b \log (c (e+f x)))}{d (f h-e i)^3}-\frac{f^2 \log \left(\frac{f h-e i}{i (e+f x)}+1\right) (a+b \log (c (e+f x)))^2}{d (f h-e i)^3}+\frac{b f^2 \log \left(\frac{f h-e i}{i (e+f x)}+1\right) (a+b \log (c (e+f x)))}{d (f h-e i)^3}-\frac{f i (e+f x) (a+b \log (c (e+f x)))^2}{d (h+i x) (f h-e i)^3}+\frac{b f i (e+f x) (a+b \log (c (e+f x)))}{d (h+i x) (f h-e i)^3}+\frac{(a+b \log (c (e+f x)))^2}{2 d (h+i x)^2 (f h-e i)}-\frac{b^2 f^2 \log (h+i x)}{d (f h-e i)^3}",1,"(b*f*i*(e + f*x)*(a + b*Log[c*(e + f*x)]))/(d*(f*h - e*i)^3*(h + i*x)) - (f^2*(a + b*Log[c*(e + f*x)])^2)/(2*d*(f*h - e*i)^3) + (a + b*Log[c*(e + f*x)])^2/(2*d*(f*h - e*i)*(h + i*x)^2) - (f*i*(e + f*x)*(a + b*Log[c*(e + f*x)])^2)/(d*(f*h - e*i)^3*(h + i*x)) + (f^2*(a + b*Log[c*(e + f*x)])^3)/(3*b*d*(f*h - e*i)^3) - (b^2*f^2*Log[h + i*x])/(d*(f*h - e*i)^3) + (3*b*f^2*(a + b*Log[c*(e + f*x)])*Log[(f*(h + i*x))/(f*h - e*i)])/(d*(f*h - e*i)^3) - (f^2*(a + b*Log[c*(e + f*x)])^2*Log[(f*(h + i*x))/(f*h - e*i)])/(d*(f*h - e*i)^3) + (3*b^2*f^2*PolyLog[2, -((i*(e + f*x))/(f*h - e*i))])/(d*(f*h - e*i)^3) - (2*b*f^2*(a + b*Log[c*(e + f*x)])*PolyLog[2, -((i*(e + f*x))/(f*h - e*i))])/(d*(f*h - e*i)^3) + (2*b^2*f^2*PolyLog[3, -((i*(e + f*x))/(f*h - e*i))])/(d*(f*h - e*i)^3)","A",21,15,32,0.4688,1,"{2411, 12, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391, 2319, 2301, 2314, 31}"
191,1,230,0,0.6680643,"\int \frac{(h+i x)^4}{(d e+d f x) (a+b \log (c (e+f x)))} \, dx","Int[(h + i*x)^4/((d*e + d*f*x)*(a + b*Log[c*(e + f*x)])),x]","\frac{4 i^3 e^{-\frac{3 a}{b}} (f h-e i) \text{Ei}\left(\frac{3 (a+b \log (c (e+f x)))}{b}\right)}{b c^3 d f^5}+\frac{6 i^2 e^{-\frac{2 a}{b}} (f h-e i)^2 \text{Ei}\left(\frac{2 (a+b \log (c (e+f x)))}{b}\right)}{b c^2 d f^5}+\frac{i^4 e^{-\frac{4 a}{b}} \text{Ei}\left(\frac{4 (a+b \log (c (e+f x)))}{b}\right)}{b c^4 d f^5}+\frac{4 i e^{-\frac{a}{b}} (f h-e i)^3 \text{Ei}\left(\frac{a+b \log (c (e+f x))}{b}\right)}{b c d f^5}+\frac{(f h-e i)^4 \log (a+b \log (c (e+f x)))}{b d f^5}","\frac{4 i^3 e^{-\frac{3 a}{b}} (f h-e i) \text{Ei}\left(\frac{3 (a+b \log (c (e+f x)))}{b}\right)}{b c^3 d f^5}+\frac{6 i^2 e^{-\frac{2 a}{b}} (f h-e i)^2 \text{Ei}\left(\frac{2 (a+b \log (c (e+f x)))}{b}\right)}{b c^2 d f^5}+\frac{i^4 e^{-\frac{4 a}{b}} \text{Ei}\left(\frac{4 (a+b \log (c (e+f x)))}{b}\right)}{b c^4 d f^5}+\frac{4 i e^{-\frac{a}{b}} (f h-e i)^3 \text{Ei}\left(\frac{a+b \log (c (e+f x))}{b}\right)}{b c d f^5}+\frac{(f h-e i)^4 \log (a+b \log (c (e+f x)))}{b d f^5}",1,"(4*i*(f*h - e*i)^3*ExpIntegralEi[(a + b*Log[c*(e + f*x)])/b])/(b*c*d*E^(a/b)*f^5) + (6*i^2*(f*h - e*i)^2*ExpIntegralEi[(2*(a + b*Log[c*(e + f*x)]))/b])/(b*c^2*d*E^((2*a)/b)*f^5) + (4*i^3*(f*h - e*i)*ExpIntegralEi[(3*(a + b*Log[c*(e + f*x)]))/b])/(b*c^3*d*E^((3*a)/b)*f^5) + (i^4*ExpIntegralEi[(4*(a + b*Log[c*(e + f*x)]))/b])/(b*c^4*d*E^((4*a)/b)*f^5) + ((f*h - e*i)^4*Log[a + b*Log[c*(e + f*x)]])/(b*d*f^5)","A",14,8,32,0.2500,1,"{2411, 12, 2353, 2299, 2178, 2302, 29, 2309}"
192,1,177,0,0.4840221,"\int \frac{(h+i x)^3}{(d e+d f x) (a+b \log (c (e+f x)))} \, dx","Int[(h + i*x)^3/((d*e + d*f*x)*(a + b*Log[c*(e + f*x)])),x]","\frac{3 i^2 e^{-\frac{2 a}{b}} (f h-e i) \text{Ei}\left(\frac{2 (a+b \log (c (e+f x)))}{b}\right)}{b c^2 d f^4}+\frac{i^3 e^{-\frac{3 a}{b}} \text{Ei}\left(\frac{3 (a+b \log (c (e+f x)))}{b}\right)}{b c^3 d f^4}+\frac{3 i e^{-\frac{a}{b}} (f h-e i)^2 \text{Ei}\left(\frac{a+b \log (c (e+f x))}{b}\right)}{b c d f^4}+\frac{(f h-e i)^3 \log (a+b \log (c (e+f x)))}{b d f^4}","\frac{3 i^2 e^{-\frac{2 a}{b}} (f h-e i) \text{Ei}\left(\frac{2 (a+b \log (c (e+f x)))}{b}\right)}{b c^2 d f^4}+\frac{i^3 e^{-\frac{3 a}{b}} \text{Ei}\left(\frac{3 (a+b \log (c (e+f x)))}{b}\right)}{b c^3 d f^4}+\frac{3 i e^{-\frac{a}{b}} (f h-e i)^2 \text{Ei}\left(\frac{a+b \log (c (e+f x))}{b}\right)}{b c d f^4}+\frac{(f h-e i)^3 \log (a+b \log (c (e+f x)))}{b d f^4}",1,"(3*i*(f*h - e*i)^2*ExpIntegralEi[(a + b*Log[c*(e + f*x)])/b])/(b*c*d*E^(a/b)*f^4) + (3*i^2*(f*h - e*i)*ExpIntegralEi[(2*(a + b*Log[c*(e + f*x)]))/b])/(b*c^2*d*E^((2*a)/b)*f^4) + (i^3*ExpIntegralEi[(3*(a + b*Log[c*(e + f*x)]))/b])/(b*c^3*d*E^((3*a)/b)*f^4) + ((f*h - e*i)^3*Log[a + b*Log[c*(e + f*x)]])/(b*d*f^4)","A",12,8,32,0.2500,1,"{2411, 12, 2353, 2299, 2178, 2302, 29, 2309}"
193,1,124,0,0.3793456,"\int \frac{(h+i x)^2}{(d e+d f x) (a+b \log (c (e+f x)))} \, dx","Int[(h + i*x)^2/((d*e + d*f*x)*(a + b*Log[c*(e + f*x)])),x]","\frac{i^2 e^{-\frac{2 a}{b}} \text{Ei}\left(\frac{2 (a+b \log (c (e+f x)))}{b}\right)}{b c^2 d f^3}+\frac{2 i e^{-\frac{a}{b}} (f h-e i) \text{Ei}\left(\frac{a+b \log (c (e+f x))}{b}\right)}{b c d f^3}+\frac{(f h-e i)^2 \log (a+b \log (c (e+f x)))}{b d f^3}","\frac{i^2 e^{-\frac{2 a}{b}} \text{Ei}\left(\frac{2 (a+b \log (c (e+f x)))}{b}\right)}{b c^2 d f^3}+\frac{2 i e^{-\frac{a}{b}} (f h-e i) \text{Ei}\left(\frac{a+b \log (c (e+f x))}{b}\right)}{b c d f^3}+\frac{(f h-e i)^2 \log (a+b \log (c (e+f x)))}{b d f^3}",1,"(2*i*(f*h - e*i)*ExpIntegralEi[(a + b*Log[c*(e + f*x)])/b])/(b*c*d*E^(a/b)*f^3) + (i^2*ExpIntegralEi[(2*(a + b*Log[c*(e + f*x)]))/b])/(b*c^2*d*E^((2*a)/b)*f^3) + ((f*h - e*i)^2*Log[a + b*Log[c*(e + f*x)]])/(b*d*f^3)","A",10,8,32,0.2500,1,"{2411, 12, 2353, 2299, 2178, 2302, 29, 2309}"
194,1,71,0,0.2183097,"\int \frac{h+i x}{(d e+d f x) (a+b \log (c (e+f x)))} \, dx","Int[(h + i*x)/((d*e + d*f*x)*(a + b*Log[c*(e + f*x)])),x]","\frac{i e^{-\frac{a}{b}} \text{Ei}\left(\frac{a+b \log (c (e+f x))}{b}\right)}{b c d f^2}+\frac{(f h-e i) \log (a+b \log (c (e+f x)))}{b d f^2}","\frac{i e^{-\frac{a}{b}} \text{Ei}\left(\frac{a+b \log (c (e+f x))}{b}\right)}{b c d f^2}+\frac{(f h-e i) \log (a+b \log (c (e+f x)))}{b d f^2}",1,"(i*ExpIntegralEi[(a + b*Log[c*(e + f*x)])/b])/(b*c*d*E^(a/b)*f^2) + ((f*h - e*i)*Log[a + b*Log[c*(e + f*x)]])/(b*d*f^2)","A",8,7,30,0.2333,1,"{2411, 12, 2353, 2299, 2178, 2302, 29}"
195,1,23,0,0.0663648,"\int \frac{1}{(d e+d f x) (a+b \log (c (e+f x)))} \, dx","Int[1/((d*e + d*f*x)*(a + b*Log[c*(e + f*x)])),x]","\frac{\log (a+b \log (c (e+f x)))}{b d f}","\frac{\log (a+b \log (c (e+f x)))}{b d f}",1,"Log[a + b*Log[c*(e + f*x)]]/(b*d*f)","A",4,4,25,0.1600,1,"{2390, 12, 2302, 29}"
196,0,0,0,0.2405868,"\int \frac{1}{(d e+d f x) (h+i x) (a+b \log (c (e+f x)))} \, dx","Int[1/((d*e + d*f*x)*(h + i*x)*(a + b*Log[c*(e + f*x)])),x]","\int \frac{1}{(d e+d f x) (h+i x) (a+b \log (c (e+f x)))} \, dx","\frac{\log (a+b \log (c (e+f x)))}{b d (f h-e i)}-\frac{i \text{Int}\left(\frac{1}{(h+i x) (a+b \log (c (e+f x)))},x\right)}{d (f h-e i)}",0,"Log[a + b*Log[c*(e + f*x)]]/(b*d*(f*h - e*i)) - (i*Defer[Int][1/((h + i*x)*(a + b*Log[c*(e + f*x)])), x])/(d*(f*h - e*i))","A",0,0,0,0,-1,"{}"
197,0,0,0,0.2948415,"\int \frac{1}{(d e+d f x) (h+i x)^2 (a+b \log (c (e+f x)))} \, dx","Int[1/((d*e + d*f*x)*(h + i*x)^2*(a + b*Log[c*(e + f*x)])),x]","\int \frac{1}{(d e+d f x) (h+i x)^2 (a+b \log (c (e+f x)))} \, dx","-\frac{i \text{Int}\left(\frac{1}{(h+i x)^2 (a+b \log (c (e+f x)))},x\right)}{d (f h-e i)}-\frac{f i \text{Int}\left(\frac{1}{(h+i x) (a+b \log (c (e+f x)))},x\right)}{d (f h-e i)^2}+\frac{f \log (a+b \log (c (e+f x)))}{b d (f h-e i)^2}",0,"(f*Log[a + b*Log[c*(e + f*x)]])/(b*d*(f*h - e*i)^2) - (i*Defer[Int][1/((h + i*x)^2*(a + b*Log[c*(e + f*x)])), x])/(d*(f*h - e*i)) - (f*i*Defer[Int][1/((h + i*x)*(a + b*Log[c*(e + f*x)])), x])/(d*(f*h - e*i)^2)","A",0,0,0,0,-1,"{}"
198,1,485,0,2.045088,"\int \frac{(f+g x)^{5/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{d+e x} \, dx","Int[((f + g*x)^(5/2)*(a + b*Log[c*(d + e*x)^n]))/(d + e*x),x]","-\frac{2 b n (e f-d g)^{5/2} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{e^{7/2}}+\frac{2 \sqrt{f+g x} (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^3}+\frac{2 (f+g x)^{3/2} (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 e^2}-\frac{2 (e f-d g)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^{7/2}}+\frac{2 (f+g x)^{5/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 e}-\frac{92 b n \sqrt{f+g x} (e f-d g)^2}{15 e^3}-\frac{32 b n (f+g x)^{3/2} (e f-d g)}{45 e^2}+\frac{2 b n (e f-d g)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{e^{7/2}}+\frac{92 b n (e f-d g)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{15 e^{7/2}}-\frac{4 b n (e f-d g)^{5/2} \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{7/2}}-\frac{4 b n (f+g x)^{5/2}}{25 e}","-\frac{2 b n (e f-d g)^{5/2} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{e^{7/2}}+\frac{2 \sqrt{f+g x} (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^3}+\frac{2 (f+g x)^{3/2} (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 e^2}-\frac{2 (e f-d g)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^{7/2}}+\frac{2 (f+g x)^{5/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 e}-\frac{92 b n \sqrt{f+g x} (e f-d g)^2}{15 e^3}-\frac{32 b n (f+g x)^{3/2} (e f-d g)}{45 e^2}+\frac{2 b n (e f-d g)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{e^{7/2}}+\frac{92 b n (e f-d g)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{15 e^{7/2}}-\frac{4 b n (e f-d g)^{5/2} \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{7/2}}-\frac{4 b n (f+g x)^{5/2}}{25 e}",1,"(-92*b*(e*f - d*g)^2*n*Sqrt[f + g*x])/(15*e^3) - (32*b*(e*f - d*g)*n*(f + g*x)^(3/2))/(45*e^2) - (4*b*n*(f + g*x)^(5/2))/(25*e) + (92*b*(e*f - d*g)^(5/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(15*e^(7/2)) + (2*b*(e*f - d*g)^(5/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]^2)/e^(7/2) + (2*(e*f - d*g)^2*Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n]))/e^3 + (2*(e*f - d*g)*(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n]))/(3*e^2) + (2*(f + g*x)^(5/2)*(a + b*Log[c*(d + e*x)^n]))/(5*e) - (2*(e*f - d*g)^(5/2)*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*(a + b*Log[c*(d + e*x)^n]))/e^(7/2) - (4*b*(e*f - d*g)^(5/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*Log[2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/e^(7/2) - (2*b*(e*f - d*g)^(5/2)*n*PolyLog[2, 1 - 2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/e^(7/2)","A",27,14,31,0.4516,1,"{2411, 2346, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 50}"
199,1,417,0,1.377619,"\int \frac{(f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{d+e x} \, dx","Int[((f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n]))/(d + e*x),x]","-\frac{2 b n (e f-d g)^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{e^{5/2}}+\frac{2 \sqrt{f+g x} (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^2}-\frac{2 (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^{5/2}}+\frac{2 (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 e}-\frac{16 b n \sqrt{f+g x} (e f-d g)}{3 e^2}+\frac{2 b n (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{e^{5/2}}+\frac{16 b n (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{3 e^{5/2}}-\frac{4 b n (e f-d g)^{3/2} \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{5/2}}-\frac{4 b n (f+g x)^{3/2}}{9 e}","-\frac{2 b n (e f-d g)^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{e^{5/2}}+\frac{2 \sqrt{f+g x} (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^2}-\frac{2 (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^{5/2}}+\frac{2 (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 e}-\frac{16 b n \sqrt{f+g x} (e f-d g)}{3 e^2}+\frac{2 b n (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{e^{5/2}}+\frac{16 b n (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{3 e^{5/2}}-\frac{4 b n (e f-d g)^{3/2} \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{5/2}}-\frac{4 b n (f+g x)^{3/2}}{9 e}",1,"(-16*b*(e*f - d*g)*n*Sqrt[f + g*x])/(3*e^2) - (4*b*n*(f + g*x)^(3/2))/(9*e) + (16*b*(e*f - d*g)^(3/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(3*e^(5/2)) + (2*b*(e*f - d*g)^(3/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]^2)/e^(5/2) + (2*(e*f - d*g)*Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n]))/e^2 + (2*(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n]))/(3*e) - (2*(e*f - d*g)^(3/2)*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*(a + b*Log[c*(d + e*x)^n]))/e^(5/2) - (4*b*(e*f - d*g)^(3/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*Log[2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/e^(5/2) - (2*b*(e*f - d*g)^(3/2)*n*PolyLog[2, 1 - 2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/e^(5/2)","A",20,14,31,0.4516,1,"{2411, 2346, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 50}"
200,1,349,0,0.9859006,"\int \frac{\sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)}{d+e x} \, dx","Int[(Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n]))/(d + e*x),x]","-\frac{2 b n \sqrt{e f-d g} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{e^{3/2}}-\frac{2 \sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^{3/2}}+\frac{2 \sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)}{e}+\frac{2 b n \sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{e^{3/2}}+\frac{4 b n \sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{3/2}}-\frac{4 b n \sqrt{e f-d g} \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{3/2}}-\frac{4 b n \sqrt{f+g x}}{e}","-\frac{2 b n \sqrt{e f-d g} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{e^{3/2}}-\frac{2 \sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^{3/2}}+\frac{2 \sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)}{e}+\frac{2 b n \sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{e^{3/2}}+\frac{4 b n \sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{3/2}}-\frac{4 b n \sqrt{e f-d g} \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{3/2}}-\frac{4 b n \sqrt{f+g x}}{e}",1,"(-4*b*n*Sqrt[f + g*x])/e + (4*b*Sqrt[e*f - d*g]*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/e^(3/2) + (2*b*Sqrt[e*f - d*g]*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]^2)/e^(3/2) + (2*Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n]))/e - (2*Sqrt[e*f - d*g]*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*(a + b*Log[c*(d + e*x)^n]))/e^(3/2) - (4*b*Sqrt[e*f - d*g]*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*Log[2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/e^(3/2) - (2*b*Sqrt[e*f - d*g]*n*PolyLog[2, 1 - 2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/e^(3/2)","A",14,14,31,0.4516,1,"{2411, 2346, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 50}"
201,1,256,0,0.6937561,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(d+e x) \sqrt{f+g x}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/((d + e*x)*Sqrt[f + g*x]),x]","-\frac{2 b n \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{\sqrt{e} \sqrt{e f-d g}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{e} \sqrt{e f-d g}}+\frac{2 b n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{\sqrt{e} \sqrt{e f-d g}}-\frac{4 b n \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{\sqrt{e} \sqrt{e f-d g}}","-\frac{2 b n \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{\sqrt{e} \sqrt{e f-d g}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{e} \sqrt{e f-d g}}+\frac{2 b n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{\sqrt{e} \sqrt{e f-d g}}-\frac{4 b n \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{\sqrt{e} \sqrt{e f-d g}}",1,"(2*b*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]^2)/(Sqrt[e]*Sqrt[e*f - d*g]) - (2*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*(a + b*Log[c*(d + e*x)^n]))/(Sqrt[e]*Sqrt[e*f - d*g]) - (4*b*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*Log[2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(Sqrt[e]*Sqrt[e*f - d*g]) - (2*b*n*PolyLog[2, 1 - 2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(Sqrt[e]*Sqrt[e*f - d*g])","A",9,11,31,0.3548,1,"{2411, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315}"
202,1,340,0,1.0255498,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(d+e x) (f+g x)^{3/2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/((d + e*x)*(f + g*x)^(3/2)),x]","-\frac{2 b \sqrt{e} n \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{(e f-d g)^{3/2}}+\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{f+g x} (e f-d g)}-\frac{2 \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(e f-d g)^{3/2}}+\frac{2 b \sqrt{e} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{(e f-d g)^{3/2}}+\frac{4 b \sqrt{e} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{(e f-d g)^{3/2}}-\frac{4 b \sqrt{e} n \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{(e f-d g)^{3/2}}","-\frac{2 b \sqrt{e} n \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{(e f-d g)^{3/2}}+\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{f+g x} (e f-d g)}-\frac{2 \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(e f-d g)^{3/2}}+\frac{2 b \sqrt{e} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{(e f-d g)^{3/2}}+\frac{4 b \sqrt{e} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{(e f-d g)^{3/2}}-\frac{4 b \sqrt{e} n \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{(e f-d g)^{3/2}}",1,"(4*b*Sqrt[e]*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(e*f - d*g)^(3/2) + (2*b*Sqrt[e]*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]^2)/(e*f - d*g)^(3/2) + (2*(a + b*Log[c*(d + e*x)^n]))/((e*f - d*g)*Sqrt[f + g*x]) - (2*Sqrt[e]*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*(a + b*Log[c*(d + e*x)^n]))/(e*f - d*g)^(3/2) - (4*b*Sqrt[e]*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*Log[2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(e*f - d*g)^(3/2) - (2*b*Sqrt[e]*n*PolyLog[2, 1 - 2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(e*f - d*g)^(3/2)","A",13,13,31,0.4194,1,"{2411, 2347, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319}"
203,1,406,0,1.3877248,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(d+e x) (f+g x)^{5/2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/((d + e*x)*(f + g*x)^(5/2)),x]","-\frac{2 b e^{3/2} n \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{(e f-d g)^{5/2}}-\frac{2 e^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(e f-d g)^{5/2}}+\frac{2 e \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{f+g x} (e f-d g)^2}+\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 (f+g x)^{3/2} (e f-d g)}+\frac{2 b e^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{(e f-d g)^{5/2}}+\frac{16 b e^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{3 (e f-d g)^{5/2}}-\frac{4 b e^{3/2} n \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{(e f-d g)^{5/2}}-\frac{4 b e n}{3 \sqrt{f+g x} (e f-d g)^2}","-\frac{2 b e^{3/2} n \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{(e f-d g)^{5/2}}-\frac{2 e^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(e f-d g)^{5/2}}+\frac{2 e \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{f+g x} (e f-d g)^2}+\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 (f+g x)^{3/2} (e f-d g)}+\frac{2 b e^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)^2}{(e f-d g)^{5/2}}+\frac{16 b e^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{3 (e f-d g)^{5/2}}-\frac{4 b e^{3/2} n \log \left(\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{(e f-d g)^{5/2}}-\frac{4 b e n}{3 \sqrt{f+g x} (e f-d g)^2}",1,"(-4*b*e*n)/(3*(e*f - d*g)^2*Sqrt[f + g*x]) + (16*b*e^(3/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(3*(e*f - d*g)^(5/2)) + (2*b*e^(3/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]^2)/(e*f - d*g)^(5/2) + (2*(a + b*Log[c*(d + e*x)^n]))/(3*(e*f - d*g)*(f + g*x)^(3/2)) + (2*e*(a + b*Log[c*(d + e*x)^n]))/((e*f - d*g)^2*Sqrt[f + g*x]) - (2*e^(3/2)*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*(a + b*Log[c*(d + e*x)^n]))/(e*f - d*g)^(5/2) - (4*b*e^(3/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]*Log[2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(e*f - d*g)^(5/2) - (2*b*e^(3/2)*n*PolyLog[2, 1 - 2/(1 - (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])])/(e*f - d*g)^(5/2)","A",18,14,31,0.4516,1,"{2411, 2347, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 51}"
204,1,381,0,1.5299026,"\int \frac{(d+e x)^{3/2} \log (a+b x)}{a+b x} \, dx","Int[((d + e*x)^(3/2)*Log[a + b*x])/(a + b*x),x]","-\frac{2 (b d-a e)^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right)}{b^{5/2}}-\frac{16 \sqrt{d+e x} (b d-a e)}{3 b^2}+\frac{2 \sqrt{d+e x} (b d-a e) \log (a+b x)}{b^2}+\frac{2 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)^2}{b^{5/2}}+\frac{16 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{3 b^{5/2}}-\frac{2 (b d-a e)^{3/2} \log (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2}}-\frac{4 (b d-a e)^{3/2} \log \left(\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2}}+\frac{2 (d+e x)^{3/2} \log (a+b x)}{3 b}-\frac{4 (d+e x)^{3/2}}{9 b}","-\frac{2 (b d-a e)^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right)}{b^{5/2}}-\frac{16 \sqrt{d+e x} (b d-a e)}{3 b^2}+\frac{2 \sqrt{d+e x} (b d-a e) \log (a+b x)}{b^2}+\frac{2 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)^2}{b^{5/2}}+\frac{16 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{3 b^{5/2}}-\frac{2 (b d-a e)^{3/2} \log (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2}}-\frac{4 (b d-a e)^{3/2} \log \left(\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2}}+\frac{2 (d+e x)^{3/2} \log (a+b x)}{3 b}-\frac{4 (d+e x)^{3/2}}{9 b}",1,"(-16*(b*d - a*e)*Sqrt[d + e*x])/(3*b^2) - (4*(d + e*x)^(3/2))/(9*b) + (16*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(3*b^(5/2)) + (2*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]^2)/b^(5/2) + (2*(b*d - a*e)*Sqrt[d + e*x]*Log[a + b*x])/b^2 + (2*(d + e*x)^(3/2)*Log[a + b*x])/(3*b) - (2*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]*Log[a + b*x])/b^(5/2) - (4*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]*Log[2/(1 - (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])])/b^(5/2) - (2*(b*d - a*e)^(3/2)*PolyLog[2, 1 - 2/(1 - (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])])/b^(5/2)","A",20,14,23,0.6087,1,"{2411, 2346, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 50}"
205,1,323,0,0.9130332,"\int \frac{\sqrt{d+e x} \log (a+b x)}{a+b x} \, dx","Int[(Sqrt[d + e*x]*Log[a + b*x])/(a + b*x),x]","-\frac{2 \sqrt{b d-a e} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right)}{b^{3/2}}+\frac{2 \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)^2}{b^{3/2}}+\frac{4 \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2}}-\frac{2 \sqrt{b d-a e} \log (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2}}-\frac{4 \sqrt{b d-a e} \log \left(\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2}}+\frac{2 \sqrt{d+e x} \log (a+b x)}{b}-\frac{4 \sqrt{d+e x}}{b}","-\frac{2 \sqrt{b d-a e} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right)}{b^{3/2}}+\frac{2 \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)^2}{b^{3/2}}+\frac{4 \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2}}-\frac{2 \sqrt{b d-a e} \log (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2}}-\frac{4 \sqrt{b d-a e} \log \left(\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2}}+\frac{2 \sqrt{d+e x} \log (a+b x)}{b}-\frac{4 \sqrt{d+e x}}{b}",1,"(-4*Sqrt[d + e*x])/b + (4*Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/b^(3/2) + (2*Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]^2)/b^(3/2) + (2*Sqrt[d + e*x]*Log[a + b*x])/b - (2*Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]*Log[a + b*x])/b^(3/2) - (4*Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]*Log[2/(1 - (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])])/b^(3/2) - (2*Sqrt[b*d - a*e]*PolyLog[2, 1 - 2/(1 - (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])])/b^(3/2)","A",14,14,23,0.6087,1,"{2411, 2346, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 50}"
206,1,242,0,0.6453226,"\int \frac{\log (a+b x)}{(a+b x) \sqrt{d+e x}} \, dx","Int[Log[a + b*x]/((a + b*x)*Sqrt[d + e*x]),x]","-\frac{2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right)}{\sqrt{b} \sqrt{b d-a e}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)^2}{\sqrt{b} \sqrt{b d-a e}}-\frac{2 \log (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} \sqrt{b d-a e}}-\frac{4 \log \left(\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} \sqrt{b d-a e}}","-\frac{2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right)}{\sqrt{b} \sqrt{b d-a e}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)^2}{\sqrt{b} \sqrt{b d-a e}}-\frac{2 \log (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} \sqrt{b d-a e}}-\frac{4 \log \left(\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} \sqrt{b d-a e}}",1,"(2*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]^2)/(Sqrt[b]*Sqrt[b*d - a*e]) - (2*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]*Log[a + b*x])/(Sqrt[b]*Sqrt[b*d - a*e]) - (4*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]*Log[2/(1 - (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])])/(Sqrt[b]*Sqrt[b*d - a*e]) - (2*PolyLog[2, 1 - 2/(1 - (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])])/(Sqrt[b]*Sqrt[b*d - a*e])","A",9,11,23,0.4783,1,"{2411, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315}"
207,1,316,0,0.9445305,"\int \frac{\log (a+b x)}{(a+b x) (d+e x)^{3/2}} \, dx","Int[Log[a + b*x]/((a + b*x)*(d + e*x)^(3/2)),x]","-\frac{2 \sqrt{b} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right)}{(b d-a e)^{3/2}}+\frac{2 \log (a+b x)}{\sqrt{d+e x} (b d-a e)}+\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)^2}{(b d-a e)^{3/2}}+\frac{4 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{3/2}}-\frac{2 \sqrt{b} \log (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{3/2}}-\frac{4 \sqrt{b} \log \left(\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{3/2}}","-\frac{2 \sqrt{b} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right)}{(b d-a e)^{3/2}}+\frac{2 \log (a+b x)}{\sqrt{d+e x} (b d-a e)}+\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)^2}{(b d-a e)^{3/2}}+\frac{4 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{3/2}}-\frac{2 \sqrt{b} \log (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{3/2}}-\frac{4 \sqrt{b} \log \left(\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{3/2}}",1,"(4*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b*d - a*e)^(3/2) + (2*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]^2)/(b*d - a*e)^(3/2) + (2*Log[a + b*x])/((b*d - a*e)*Sqrt[d + e*x]) - (2*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]*Log[a + b*x])/(b*d - a*e)^(3/2) - (4*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]*Log[2/(1 - (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])])/(b*d - a*e)^(3/2) - (2*Sqrt[b]*PolyLog[2, 1 - 2/(1 - (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])])/(b*d - a*e)^(3/2)","A",13,13,23,0.5652,1,"{2411, 2347, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319}"
208,1,372,0,1.2573892,"\int \frac{\log (a+b x)}{(a+b x) (d+e x)^{5/2}} \, dx","Int[Log[a + b*x]/((a + b*x)*(d + e*x)^(5/2)),x]","-\frac{2 b^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right)}{(b d-a e)^{5/2}}+\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)^2}{(b d-a e)^{5/2}}+\frac{16 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{3 (b d-a e)^{5/2}}-\frac{2 b^{3/2} \log (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{5/2}}-\frac{4 b^{3/2} \log \left(\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{5/2}}-\frac{4 b}{3 \sqrt{d+e x} (b d-a e)^2}+\frac{2 b \log (a+b x)}{\sqrt{d+e x} (b d-a e)^2}+\frac{2 \log (a+b x)}{3 (d+e x)^{3/2} (b d-a e)}","-\frac{2 b^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right)}{(b d-a e)^{5/2}}+\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)^2}{(b d-a e)^{5/2}}+\frac{16 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{3 (b d-a e)^{5/2}}-\frac{2 b^{3/2} \log (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{5/2}}-\frac{4 b^{3/2} \log \left(\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{5/2}}-\frac{4 b}{3 \sqrt{d+e x} (b d-a e)^2}+\frac{2 b \log (a+b x)}{\sqrt{d+e x} (b d-a e)^2}+\frac{2 \log (a+b x)}{3 (d+e x)^{3/2} (b d-a e)}",1,"(-4*b)/(3*(b*d - a*e)^2*Sqrt[d + e*x]) + (16*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(3*(b*d - a*e)^(5/2)) + (2*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]^2)/(b*d - a*e)^(5/2) + (2*Log[a + b*x])/(3*(b*d - a*e)*(d + e*x)^(3/2)) + (2*b*Log[a + b*x])/((b*d - a*e)^2*Sqrt[d + e*x]) - (2*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]*Log[a + b*x])/(b*d - a*e)^(5/2) - (4*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]*Log[2/(1 - (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])])/(b*d - a*e)^(5/2) - (2*b^(3/2)*PolyLog[2, 1 - 2/(1 - (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])])/(b*d - a*e)^(5/2)","A",18,14,23,0.6087,1,"{2411, 2347, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 51}"
209,0,0,0,0.1105334,"\int \frac{(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx","Int[((h + i*x)^q*(a + b*Log[c*(e + f*x)])^p)/(d*e + d*f*x),x]","\int \frac{(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx","\text{Int}\left(\frac{(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x},x\right)",0,"Defer[Int][((h + i*x)^q*(a + b*Log[c*(e + f*x)])^p)/(d*e + d*f*x), x]","A",0,0,0,0,-1,"{}"
210,1,305,0,0.6639426,"\int \frac{(h+i x)^3 (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx","Int[((h + i*x)^3*(a + b*Log[c*(e + f*x)])^p)/(d*e + d*f*x),x]","\frac{3 i^2 2^{-p-1} e^{-\frac{2 a}{b}} (f h-e i) (a+b \log (c (e+f x)))^p \left(-\frac{a+b \log (c (e+f x))}{b}\right)^{-p} \text{Gamma}\left(p+1,-\frac{2 (a+b \log (c (e+f x)))}{b}\right)}{c^2 d f^4}+\frac{i^3 3^{-p-1} e^{-\frac{3 a}{b}} (a+b \log (c (e+f x)))^p \left(-\frac{a+b \log (c (e+f x))}{b}\right)^{-p} \text{Gamma}\left(p+1,-\frac{3 (a+b \log (c (e+f x)))}{b}\right)}{c^3 d f^4}+\frac{3 i e^{-\frac{a}{b}} (f h-e i)^2 (a+b \log (c (e+f x)))^p \left(-\frac{a+b \log (c (e+f x))}{b}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a+b \log (c (e+f x))}{b}\right)}{c d f^4}+\frac{(f h-e i)^3 (a+b \log (c (e+f x)))^{p+1}}{b d f^4 (p+1)}","\frac{3 i^2 2^{-p-1} e^{-\frac{2 a}{b}} (f h-e i) (a+b \log (c (e+f x)))^p \left(-\frac{a+b \log (c (e+f x))}{b}\right)^{-p} \text{Gamma}\left(p+1,-\frac{2 (a+b \log (c (e+f x)))}{b}\right)}{c^2 d f^4}+\frac{i^3 3^{-p-1} e^{-\frac{3 a}{b}} (a+b \log (c (e+f x)))^p \left(-\frac{a+b \log (c (e+f x))}{b}\right)^{-p} \text{Gamma}\left(p+1,-\frac{3 (a+b \log (c (e+f x)))}{b}\right)}{c^3 d f^4}+\frac{3 i e^{-\frac{a}{b}} (f h-e i)^2 (a+b \log (c (e+f x)))^p \left(-\frac{a+b \log (c (e+f x))}{b}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a+b \log (c (e+f x))}{b}\right)}{c d f^4}+\frac{(f h-e i)^3 (a+b \log (c (e+f x)))^{p+1}}{b d f^4 (p+1)}",1,"((f*h - e*i)^3*(a + b*Log[c*(e + f*x)])^(1 + p))/(b*d*f^4*(1 + p)) + (3^(-1 - p)*i^3*Gamma[1 + p, (-3*(a + b*Log[c*(e + f*x)]))/b]*(a + b*Log[c*(e + f*x)])^p)/(c^3*d*E^((3*a)/b)*f^4*(-((a + b*Log[c*(e + f*x)])/b))^p) + (3*2^(-1 - p)*i^2*(f*h - e*i)*Gamma[1 + p, (-2*(a + b*Log[c*(e + f*x)]))/b]*(a + b*Log[c*(e + f*x)])^p)/(c^2*d*E^((2*a)/b)*f^4*(-((a + b*Log[c*(e + f*x)])/b))^p) + (3*i*(f*h - e*i)^2*Gamma[1 + p, -((a + b*Log[c*(e + f*x)])/b)]*(a + b*Log[c*(e + f*x)])^p)/(c*d*E^(a/b)*f^4*(-((a + b*Log[c*(e + f*x)])/b))^p)","A",12,8,32,0.2500,1,"{2411, 12, 2353, 2299, 2181, 2302, 30, 2309}"
211,1,210,0,0.4722887,"\int \frac{(h+i x)^2 (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx","Int[((h + i*x)^2*(a + b*Log[c*(e + f*x)])^p)/(d*e + d*f*x),x]","\frac{i^2 2^{-p-1} e^{-\frac{2 a}{b}} (a+b \log (c (e+f x)))^p \left(-\frac{a+b \log (c (e+f x))}{b}\right)^{-p} \text{Gamma}\left(p+1,-\frac{2 (a+b \log (c (e+f x)))}{b}\right)}{c^2 d f^3}+\frac{2 i e^{-\frac{a}{b}} (f h-e i) (a+b \log (c (e+f x)))^p \left(-\frac{a+b \log (c (e+f x))}{b}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a+b \log (c (e+f x))}{b}\right)}{c d f^3}+\frac{(f h-e i)^2 (a+b \log (c (e+f x)))^{p+1}}{b d f^3 (p+1)}","\frac{i^2 2^{-p-1} e^{-\frac{2 a}{b}} (a+b \log (c (e+f x)))^p \left(-\frac{a+b \log (c (e+f x))}{b}\right)^{-p} \text{Gamma}\left(p+1,-\frac{2 (a+b \log (c (e+f x)))}{b}\right)}{c^2 d f^3}+\frac{2 i e^{-\frac{a}{b}} (f h-e i) (a+b \log (c (e+f x)))^p \left(-\frac{a+b \log (c (e+f x))}{b}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a+b \log (c (e+f x))}{b}\right)}{c d f^3}+\frac{(f h-e i)^2 (a+b \log (c (e+f x)))^{p+1}}{b d f^3 (p+1)}",1,"((f*h - e*i)^2*(a + b*Log[c*(e + f*x)])^(1 + p))/(b*d*f^3*(1 + p)) + (2^(-1 - p)*i^2*Gamma[1 + p, (-2*(a + b*Log[c*(e + f*x)]))/b]*(a + b*Log[c*(e + f*x)])^p)/(c^2*d*E^((2*a)/b)*f^3*(-((a + b*Log[c*(e + f*x)])/b))^p) + (2*i*(f*h - e*i)*Gamma[1 + p, -((a + b*Log[c*(e + f*x)])/b)]*(a + b*Log[c*(e + f*x)])^p)/(c*d*E^(a/b)*f^3*(-((a + b*Log[c*(e + f*x)])/b))^p)","A",10,8,32,0.2500,1,"{2411, 12, 2353, 2299, 2181, 2302, 30, 2309}"
212,1,115,0,0.2818804,"\int \frac{(h+i x) (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx","Int[((h + i*x)*(a + b*Log[c*(e + f*x)])^p)/(d*e + d*f*x),x]","\frac{i e^{-\frac{a}{b}} (a+b \log (c (e+f x)))^p \left(-\frac{a+b \log (c (e+f x))}{b}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a+b \log (c (e+f x))}{b}\right)}{c d f^2}+\frac{(f h-e i) (a+b \log (c (e+f x)))^{p+1}}{b d f^2 (p+1)}","\frac{i e^{-\frac{a}{b}} (a+b \log (c (e+f x)))^p \left(-\frac{a+b \log (c (e+f x))}{b}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a+b \log (c (e+f x))}{b}\right)}{c d f^2}+\frac{(f h-e i) (a+b \log (c (e+f x)))^{p+1}}{b d f^2 (p+1)}",1,"((f*h - e*i)*(a + b*Log[c*(e + f*x)])^(1 + p))/(b*d*f^2*(1 + p)) + (i*Gamma[1 + p, -((a + b*Log[c*(e + f*x)])/b)]*(a + b*Log[c*(e + f*x)])^p)/(c*d*E^(a/b)*f^2*(-((a + b*Log[c*(e + f*x)])/b))^p)","A",8,7,30,0.2333,1,"{2411, 12, 2353, 2299, 2181, 2302, 30}"
213,1,31,0,0.0751913,"\int \frac{(a+b \log (c (e+f x)))^p}{d e+d f x} \, dx","Int[(a + b*Log[c*(e + f*x)])^p/(d*e + d*f*x),x]","\frac{(a+b \log (c (e+f x)))^{p+1}}{b d f (p+1)}","\frac{(a+b \log (c (e+f x)))^{p+1}}{b d f (p+1)}",1,"(a + b*Log[c*(e + f*x)])^(1 + p)/(b*d*f*(1 + p))","A",4,4,25,0.1600,1,"{2390, 12, 2302, 30}"
214,0,0,0,0.1302061,"\int \frac{(a+b \log (c (e+f x)))^p}{(d e+d f x) (h+i x)} \, dx","Int[(a + b*Log[c*(e + f*x)])^p/((d*e + d*f*x)*(h + i*x)),x]","\int \frac{(a+b \log (c (e+f x)))^p}{(d e+d f x) (h+i x)} \, dx","\text{Int}\left(\frac{(a+b \log (c (e+f x)))^p}{(h+i x) (d e+d f x)},x\right)",0,"Defer[Int][(a + b*Log[c*(e + f*x)])^p/((d*e + d*f*x)*(h + i*x)), x]","A",0,0,0,0,-1,"{}"
215,0,0,0,0.126725,"\int \frac{(a+b \log (c (e+f x)))^p}{(d e+d f x) (h+i x)^2} \, dx","Int[(a + b*Log[c*(e + f*x)])^p/((d*e + d*f*x)*(h + i*x)^2),x]","\int \frac{(a+b \log (c (e+f x)))^p}{(d e+d f x) (h+i x)^2} \, dx","\text{Int}\left(\frac{(a+b \log (c (e+f x)))^p}{(h+i x)^2 (d e+d f x)},x\right)",0,"Defer[Int][(a + b*Log[c*(e + f*x)])^p/((d*e + d*f*x)*(h + i*x)^2), x]","A",0,0,0,0,-1,"{}"
216,0,0,0,0.1286565,"\int \frac{(a+b \log (c (e+f x)))^p}{(d e+d f x) (h+i x)^3} \, dx","Int[(a + b*Log[c*(e + f*x)])^p/((d*e + d*f*x)*(h + i*x)^3),x]","\int \frac{(a+b \log (c (e+f x)))^p}{(d e+d f x) (h+i x)^3} \, dx","\text{Int}\left(\frac{(a+b \log (c (e+f x)))^p}{(h+i x)^3 (d e+d f x)},x\right)",0,"Defer[Int][(a + b*Log[c*(e + f*x)])^p/((d*e + d*f*x)*(h + i*x)^3), x]","A",0,0,0,0,-1,"{}"
217,1,402,0,0.3636828,"\int \frac{(h+i x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x} \, dx","Int[((h + i*x)^3*(a + b*Log[c*(d + e*x)^n]))/(f + g*x),x]","\frac{b n (g h-f i)^3 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^4}+\frac{(h+i x)^2 (g h-f i) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}+\frac{(g h-f i)^3 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^4}+\frac{(h+i x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g}+\frac{a i x (g h-f i)^2}{g^3}+\frac{b i (d+e x) (g h-f i)^2 \log \left(c (d+e x)^n\right)}{e g^3}-\frac{b n (e h-d i)^2 \log (d+e x) (g h-f i)}{2 e^2 g^2}-\frac{b i n x (e h-d i)^2}{3 e^2 g}-\frac{b n (e h-d i)^3 \log (d+e x)}{3 e^3 g}-\frac{b i n x (e h-d i) (g h-f i)}{2 e g^2}-\frac{b n (h+i x)^2 (e h-d i)}{6 e g}-\frac{b n (h+i x)^2 (g h-f i)}{4 g^2}-\frac{b i n x (g h-f i)^2}{g^3}-\frac{b n (h+i x)^3}{9 g}","\frac{b n (g h-f i)^3 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^4}+\frac{(h+i x)^2 (g h-f i) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}+\frac{(g h-f i)^3 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^4}+\frac{(h+i x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g}+\frac{a i x (g h-f i)^2}{g^3}+\frac{b i (d+e x) (g h-f i)^2 \log \left(c (d+e x)^n\right)}{e g^3}-\frac{b n (e h-d i)^2 \log (d+e x) (g h-f i)}{2 e^2 g^2}-\frac{b i n x (e h-d i)^2}{3 e^2 g}-\frac{b n (e h-d i)^3 \log (d+e x)}{3 e^3 g}-\frac{b i n x (e h-d i) (g h-f i)}{2 e g^2}-\frac{b n (h+i x)^2 (e h-d i)}{6 e g}-\frac{b n (h+i x)^2 (g h-f i)}{4 g^2}-\frac{b i n x (g h-f i)^2}{g^3}-\frac{b n (h+i x)^3}{9 g}",1,"(a*i*(g*h - f*i)^2*x)/g^3 - (b*i*(e*h - d*i)^2*n*x)/(3*e^2*g) - (b*i*(e*h - d*i)*(g*h - f*i)*n*x)/(2*e*g^2) - (b*i*(g*h - f*i)^2*n*x)/g^3 - (b*(e*h - d*i)*n*(h + i*x)^2)/(6*e*g) - (b*(g*h - f*i)*n*(h + i*x)^2)/(4*g^2) - (b*n*(h + i*x)^3)/(9*g) - (b*(e*h - d*i)^3*n*Log[d + e*x])/(3*e^3*g) - (b*(e*h - d*i)^2*(g*h - f*i)*n*Log[d + e*x])/(2*e^2*g^2) + (b*i*(g*h - f*i)^2*(d + e*x)*Log[c*(d + e*x)^n])/(e*g^3) + ((g*h - f*i)*(h + i*x)^2*(a + b*Log[c*(d + e*x)^n]))/(2*g^2) + ((h + i*x)^3*(a + b*Log[c*(d + e*x)^n]))/(3*g) + ((g*h - f*i)^3*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/g^4 + (b*(g*h - f*i)^3*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g^4","A",14,8,29,0.2759,1,"{2418, 2389, 2295, 2394, 2393, 2391, 2395, 43}"
218,1,241,0,0.2229425,"\int \frac{(h+i x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x} \, dx","Int[((h + i*x)^2*(a + b*Log[c*(d + e*x)^n]))/(f + g*x),x]","\frac{b n (g h-f i)^2 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^3}+\frac{(g h-f i)^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3}+\frac{(h+i x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g}+\frac{a i x (g h-f i)}{g^2}+\frac{b i (d+e x) (g h-f i) \log \left(c (d+e x)^n\right)}{e g^2}-\frac{b n (e h-d i)^2 \log (d+e x)}{2 e^2 g}-\frac{b i n x (e h-d i)}{2 e g}-\frac{b i n x (g h-f i)}{g^2}-\frac{b n (h+i x)^2}{4 g}","\frac{b n (g h-f i)^2 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^3}+\frac{(g h-f i)^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3}+\frac{(h+i x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g}+\frac{a i x (g h-f i)}{g^2}+\frac{b i (d+e x) (g h-f i) \log \left(c (d+e x)^n\right)}{e g^2}-\frac{b n (e h-d i)^2 \log (d+e x)}{2 e^2 g}-\frac{b i n x (e h-d i)}{2 e g}-\frac{b i n x (g h-f i)}{g^2}-\frac{b n (h+i x)^2}{4 g}",1,"(a*i*(g*h - f*i)*x)/g^2 - (b*i*(e*h - d*i)*n*x)/(2*e*g) - (b*i*(g*h - f*i)*n*x)/g^2 - (b*n*(h + i*x)^2)/(4*g) - (b*(e*h - d*i)^2*n*Log[d + e*x])/(2*e^2*g) + (b*i*(g*h - f*i)*(d + e*x)*Log[c*(d + e*x)^n])/(e*g^2) + ((h + i*x)^2*(a + b*Log[c*(d + e*x)^n]))/(2*g) + ((g*h - f*i)^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/g^3 + (b*(g*h - f*i)^2*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g^3","A",11,8,29,0.2759,1,"{2418, 2389, 2295, 2394, 2393, 2391, 2395, 43}"
219,1,119,0,0.1389209,"\int \frac{(h+i x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x} \, dx","Int[((h + i*x)*(a + b*Log[c*(d + e*x)^n]))/(f + g*x),x]","\frac{b n (g h-f i) \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^2}+\frac{(g h-f i) \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}+\frac{a i x}{g}+\frac{b i (d+e x) \log \left(c (d+e x)^n\right)}{e g}-\frac{b i n x}{g}","\frac{b n (g h-f i) \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^2}+\frac{(g h-f i) \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}+\frac{a i x}{g}+\frac{b i (d+e x) \log \left(c (d+e x)^n\right)}{e g}-\frac{b i n x}{g}",1,"(a*i*x)/g - (b*i*n*x)/g + (b*i*(d + e*x)*Log[c*(d + e*x)^n])/(e*g) + ((g*h - f*i)*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/g^2 + (b*(g*h - f*i)*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g^2","A",8,6,27,0.2222,1,"{2418, 2389, 2295, 2394, 2393, 2391}"
220,1,63,0,0.0453695,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{f+g x} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(f + g*x),x]","\frac{b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}","\frac{b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}",1,"((a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/g + (b*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g","A",3,3,22,0.1364,1,"{2394, 2393, 2391}"
221,1,155,0,0.1953035,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x) (h+i x)} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/((f + g*x)*(h + i*x)),x]","\frac{b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g h-f i}-\frac{b n \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right)}{g h-f i}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g h-f i}-\frac{\log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g h-f i}","\frac{b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g h-f i}-\frac{b n \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right)}{g h-f i}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g h-f i}-\frac{\log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g h-f i}",1,"((a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/(g*h - f*i) - ((a + b*Log[c*(d + e*x)^n])*Log[(e*(h + i*x))/(e*h - d*i)])/(g*h - f*i) + (b*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/(g*h - f*i) - (b*n*PolyLog[2, -((i*(d + e*x))/(e*h - d*i))])/(g*h - f*i)","A",8,4,29,0.1379,1,"{2418, 2394, 2393, 2391}"
222,1,252,0,0.2586947,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x) (h+i x)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/((f + g*x)*(h + i*x)^2),x]","\frac{b g n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{(g h-f i)^2}-\frac{b g n \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right)}{(g h-f i)^2}+\frac{a+b \log \left(c (d+e x)^n\right)}{(h+i x) (g h-f i)}+\frac{g \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(g h-f i)^2}-\frac{g \log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(g h-f i)^2}-\frac{b e n \log (d+e x)}{(e h-d i) (g h-f i)}+\frac{b e n \log (h+i x)}{(e h-d i) (g h-f i)}","\frac{b g n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{(g h-f i)^2}-\frac{b g n \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right)}{(g h-f i)^2}+\frac{a+b \log \left(c (d+e x)^n\right)}{(h+i x) (g h-f i)}+\frac{g \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(g h-f i)^2}-\frac{g \log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(g h-f i)^2}-\frac{b e n \log (d+e x)}{(e h-d i) (g h-f i)}+\frac{b e n \log (h+i x)}{(e h-d i) (g h-f i)}",1,"-((b*e*n*Log[d + e*x])/((e*h - d*i)*(g*h - f*i))) + (a + b*Log[c*(d + e*x)^n])/((g*h - f*i)*(h + i*x)) + (g*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/(g*h - f*i)^2 + (b*e*n*Log[h + i*x])/((e*h - d*i)*(g*h - f*i)) - (g*(a + b*Log[c*(d + e*x)^n])*Log[(e*(h + i*x))/(e*h - d*i)])/(g*h - f*i)^2 + (b*g*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/(g*h - f*i)^2 - (b*g*n*PolyLog[2, -((i*(d + e*x))/(e*h - d*i))])/(g*h - f*i)^2","A",12,7,29,0.2414,1,"{2418, 2394, 2393, 2391, 2395, 36, 31}"
223,1,402,0,0.3710579,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x) (h+i x)^3} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/((f + g*x)*(h + i*x)^3),x]","\frac{b g^2 n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{(g h-f i)^3}-\frac{b g^2 n \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right)}{(g h-f i)^3}+\frac{g^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(g h-f i)^3}-\frac{g^2 \log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(g h-f i)^3}+\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)}{(h+i x) (g h-f i)^2}+\frac{a+b \log \left(c (d+e x)^n\right)}{2 (h+i x)^2 (g h-f i)}-\frac{b e^2 n \log (d+e x)}{2 (e h-d i)^2 (g h-f i)}+\frac{b e^2 n \log (h+i x)}{2 (e h-d i)^2 (g h-f i)}-\frac{b e n}{2 (h+i x) (e h-d i) (g h-f i)}-\frac{b e g n \log (d+e x)}{(e h-d i) (g h-f i)^2}+\frac{b e g n \log (h+i x)}{(e h-d i) (g h-f i)^2}","\frac{b g^2 n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{(g h-f i)^3}-\frac{b g^2 n \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right)}{(g h-f i)^3}+\frac{g^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(g h-f i)^3}-\frac{g^2 \log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(g h-f i)^3}+\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)}{(h+i x) (g h-f i)^2}+\frac{a+b \log \left(c (d+e x)^n\right)}{2 (h+i x)^2 (g h-f i)}-\frac{b e^2 n \log (d+e x)}{2 (e h-d i)^2 (g h-f i)}+\frac{b e^2 n \log (h+i x)}{2 (e h-d i)^2 (g h-f i)}-\frac{b e n}{2 (h+i x) (e h-d i) (g h-f i)}-\frac{b e g n \log (d+e x)}{(e h-d i) (g h-f i)^2}+\frac{b e g n \log (h+i x)}{(e h-d i) (g h-f i)^2}",1,"-(b*e*n)/(2*(e*h - d*i)*(g*h - f*i)*(h + i*x)) - (b*e*g*n*Log[d + e*x])/((e*h - d*i)*(g*h - f*i)^2) - (b*e^2*n*Log[d + e*x])/(2*(e*h - d*i)^2*(g*h - f*i)) + (a + b*Log[c*(d + e*x)^n])/(2*(g*h - f*i)*(h + i*x)^2) + (g*(a + b*Log[c*(d + e*x)^n]))/((g*h - f*i)^2*(h + i*x)) + (g^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/(g*h - f*i)^3 + (b*e*g*n*Log[h + i*x])/((e*h - d*i)*(g*h - f*i)^2) + (b*e^2*n*Log[h + i*x])/(2*(e*h - d*i)^2*(g*h - f*i)) - (g^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(h + i*x))/(e*h - d*i)])/(g*h - f*i)^3 + (b*g^2*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/(g*h - f*i)^3 - (b*g^2*n*PolyLog[2, -((i*(d + e*x))/(e*h - d*i))])/(g*h - f*i)^3","A",15,8,29,0.2759,1,"{2418, 2394, 2393, 2391, 2395, 44, 36, 31}"
224,1,469,0,0.5547932,"\int \frac{(h+i x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x} \, dx","Int[((h + i*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x),x]","\frac{2 b n (g h-f i)^2 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3}-\frac{2 b^2 n^2 (g h-f i)^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{g^3}+\frac{i (d+e x) (e h-d i) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2 g}-\frac{b i^2 n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^2 g}+\frac{i^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2 g}+\frac{i (d+e x) (g h-f i) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e g^2}+\frac{(g h-f i)^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g^3}-\frac{2 a b i n x (e h-d i)}{e g}-\frac{2 a b i n x (g h-f i)}{g^2}-\frac{2 b^2 i n (d+e x) (e h-d i) \log \left(c (d+e x)^n\right)}{e^2 g}-\frac{2 b^2 i n (d+e x) (g h-f i) \log \left(c (d+e x)^n\right)}{e g^2}+\frac{b^2 i^2 n^2 (d+e x)^2}{4 e^2 g}+\frac{2 b^2 i n^2 x (e h-d i)}{e g}+\frac{2 b^2 i n^2 x (g h-f i)}{g^2}","\frac{2 b n (g h-f i)^2 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3}-\frac{2 b^2 n^2 (g h-f i)^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{g^3}+\frac{i (d+e x) (e h-d i) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2 g}-\frac{b i^2 n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^2 g}+\frac{i^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2 g}+\frac{i (d+e x) (g h-f i) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e g^2}+\frac{(g h-f i)^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g^3}-\frac{2 a b i n x (e h-d i)}{e g}-\frac{2 a b i n x (g h-f i)}{g^2}-\frac{2 b^2 i n (d+e x) (e h-d i) \log \left(c (d+e x)^n\right)}{e^2 g}-\frac{2 b^2 i n (d+e x) (g h-f i) \log \left(c (d+e x)^n\right)}{e g^2}+\frac{b^2 i^2 n^2 (d+e x)^2}{4 e^2 g}+\frac{2 b^2 i n^2 x (e h-d i)}{e g}+\frac{2 b^2 i n^2 x (g h-f i)}{g^2}",1,"(-2*a*b*i*(e*h - d*i)*n*x)/(e*g) - (2*a*b*i*(g*h - f*i)*n*x)/g^2 + (2*b^2*i*(e*h - d*i)*n^2*x)/(e*g) + (2*b^2*i*(g*h - f*i)*n^2*x)/g^2 + (b^2*i^2*n^2*(d + e*x)^2)/(4*e^2*g) - (2*b^2*i*(e*h - d*i)*n*(d + e*x)*Log[c*(d + e*x)^n])/(e^2*g) - (2*b^2*i*(g*h - f*i)*n*(d + e*x)*Log[c*(d + e*x)^n])/(e*g^2) - (b*i^2*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(2*e^2*g) + (i*(e*h - d*i)*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(e^2*g) + (i*(g*h - f*i)*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(e*g^2) + (i^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(2*e^2*g) + ((g*h - f*i)^2*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(f + g*x))/(e*f - d*g)])/g^3 + (2*b*(g*h - f*i)^2*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g^3 - (2*b^2*(g*h - f*i)^2*n^2*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/g^3","A",19,12,31,0.3871,1,"{2418, 2389, 2296, 2295, 2396, 2433, 2374, 6589, 2401, 2390, 2305, 2304}"
225,1,215,0,0.2742688,"\int \frac{(h+i x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x} \, dx","Int[((h + i*x)*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x),x]","\frac{2 b n (g h-f i) \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}-\frac{2 b^2 n^2 (g h-f i) \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{g^2}+\frac{(g h-f i) \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g^2}+\frac{i (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e g}-\frac{2 a b i n x}{g}-\frac{2 b^2 i n (d+e x) \log \left(c (d+e x)^n\right)}{e g}+\frac{2 b^2 i n^2 x}{g}","\frac{2 b n (g h-f i) \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}-\frac{2 b^2 n^2 (g h-f i) \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{g^2}+\frac{(g h-f i) \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g^2}+\frac{i (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e g}-\frac{2 a b i n x}{g}-\frac{2 b^2 i n (d+e x) \log \left(c (d+e x)^n\right)}{e g}+\frac{2 b^2 i n^2 x}{g}",1,"(-2*a*b*i*n*x)/g + (2*b^2*i*n^2*x)/g - (2*b^2*i*n*(d + e*x)*Log[c*(d + e*x)^n])/(e*g) + (i*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(e*g) + ((g*h - f*i)*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(f + g*x))/(e*f - d*g)])/g^2 + (2*b*(g*h - f*i)*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g^2 - (2*b^2*(g*h - f*i)*n^2*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/g^2","A",10,8,29,0.2759,1,"{2418, 2389, 2296, 2295, 2396, 2433, 2374, 6589}"
226,1,111,0,0.1136606,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x),x]","\frac{2 b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{g}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g}","\frac{2 b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{g}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g}",1,"((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(f + g*x))/(e*f - d*g)])/g + (2*b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g - (2*b^2*n^2*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/g","A",4,4,24,0.1667,1,"{2396, 2433, 2374, 6589}"
227,1,264,0,0.370723,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x) (h+i x)} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/((f + g*x)*(h + i*x)),x]","\frac{2 b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g h-f i}-\frac{2 b n \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g h-f i}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{g h-f i}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{i (d+e x)}{e h-d i}\right)}{g h-f i}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g h-f i}-\frac{\log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g h-f i}","\frac{2 b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g h-f i}-\frac{2 b n \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g h-f i}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{g h-f i}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{i (d+e x)}{e h-d i}\right)}{g h-f i}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g h-f i}-\frac{\log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g h-f i}",1,"((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(f + g*x))/(e*f - d*g)])/(g*h - f*i) - ((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(h + i*x))/(e*h - d*i)])/(g*h - f*i) + (2*b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/(g*h - f*i) - (2*b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((i*(d + e*x))/(e*h - d*i))])/(g*h - f*i) - (2*b^2*n^2*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/(g*h - f*i) + (2*b^2*n^2*PolyLog[3, -((i*(d + e*x))/(e*h - d*i))])/(g*h - f*i)","A",10,5,31,0.1613,1,"{2418, 2396, 2433, 2374, 6589}"
228,1,427,0,0.4907683,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x) (h+i x)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/((f + g*x)*(h + i*x)^2),x]","\frac{2 b g n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(g h-f i)^2}-\frac{2 b g n \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(g h-f i)^2}+\frac{2 b^2 e n^2 \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right)}{(e h-d i) (g h-f i)}-\frac{2 b^2 g n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{(g h-f i)^2}+\frac{2 b^2 g n^2 \text{PolyLog}\left(3,-\frac{i (d+e x)}{e h-d i}\right)}{(g h-f i)^2}+\frac{2 b e n \log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(e h-d i) (g h-f i)}-\frac{i (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(h+i x) (e h-d i) (g h-f i)}+\frac{g \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(g h-f i)^2}-\frac{g \log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(g h-f i)^2}","\frac{2 b g n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(g h-f i)^2}-\frac{2 b g n \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(g h-f i)^2}+\frac{2 b^2 e n^2 \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right)}{(e h-d i) (g h-f i)}-\frac{2 b^2 g n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{(g h-f i)^2}+\frac{2 b^2 g n^2 \text{PolyLog}\left(3,-\frac{i (d+e x)}{e h-d i}\right)}{(g h-f i)^2}+\frac{2 b e n \log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(e h-d i) (g h-f i)}-\frac{i (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(h+i x) (e h-d i) (g h-f i)}+\frac{g \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(g h-f i)^2}-\frac{g \log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(g h-f i)^2}",1,"-((i*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/((e*h - d*i)*(g*h - f*i)*(h + i*x))) + (g*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(f + g*x))/(e*f - d*g)])/(g*h - f*i)^2 + (2*b*e*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(h + i*x))/(e*h - d*i)])/((e*h - d*i)*(g*h - f*i)) - (g*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(h + i*x))/(e*h - d*i)])/(g*h - f*i)^2 + (2*b*g*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/(g*h - f*i)^2 + (2*b^2*e*n^2*PolyLog[2, -((i*(d + e*x))/(e*h - d*i))])/((e*h - d*i)*(g*h - f*i)) - (2*b*g*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((i*(d + e*x))/(e*h - d*i))])/(g*h - f*i)^2 - (2*b^2*g*n^2*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/(g*h - f*i)^2 + (2*b^2*g*n^2*PolyLog[3, -((i*(d + e*x))/(e*h - d*i))])/(g*h - f*i)^2","A",14,9,31,0.2903,1,"{2418, 2396, 2433, 2374, 6589, 2397, 2394, 2393, 2391}"
229,1,660,0,0.7335613,"\int \frac{(h+i x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{f+g x} \, dx","Int[((h + i*x)^2*(a + b*Log[c*(d + e*x)^n])^3)/(f + g*x),x]","-\frac{6 b^2 n^2 (g h-f i)^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3}+\frac{3 b n (g h-f i)^2 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g^3}+\frac{6 b^3 n^3 (g h-f i)^2 \text{PolyLog}\left(4,-\frac{g (d+e x)}{e f-d g}\right)}{g^3}+\frac{3 b^2 i^2 n^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 e^2 g}+\frac{6 a b^2 i n^2 x (e h-d i)}{e g}+\frac{6 a b^2 i n^2 x (g h-f i)}{g^2}-\frac{3 b i n (d+e x) (e h-d i) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2 g}+\frac{i (d+e x) (e h-d i) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e^2 g}-\frac{3 b i^2 n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 e^2 g}+\frac{i^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{2 e^2 g}-\frac{3 b i n (d+e x) (g h-f i) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e g^2}+\frac{i (d+e x) (g h-f i) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e g^2}+\frac{(g h-f i)^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{g^3}+\frac{6 b^3 i n^2 (d+e x) (e h-d i) \log \left(c (d+e x)^n\right)}{e^2 g}+\frac{6 b^3 i n^2 (d+e x) (g h-f i) \log \left(c (d+e x)^n\right)}{e g^2}-\frac{3 b^3 i^2 n^3 (d+e x)^2}{8 e^2 g}-\frac{6 b^3 i n^3 x (e h-d i)}{e g}-\frac{6 b^3 i n^3 x (g h-f i)}{g^2}","-\frac{6 b^2 n^2 (g h-f i)^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3}+\frac{3 b n (g h-f i)^2 \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g^3}+\frac{6 b^3 n^3 (g h-f i)^2 \text{PolyLog}\left(4,-\frac{g (d+e x)}{e f-d g}\right)}{g^3}+\frac{3 b^2 i^2 n^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 e^2 g}+\frac{6 a b^2 i n^2 x (e h-d i)}{e g}+\frac{6 a b^2 i n^2 x (g h-f i)}{g^2}-\frac{3 b i n (d+e x) (e h-d i) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2 g}+\frac{i (d+e x) (e h-d i) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e^2 g}-\frac{3 b i^2 n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 e^2 g}+\frac{i^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{2 e^2 g}-\frac{3 b i n (d+e x) (g h-f i) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e g^2}+\frac{i (d+e x) (g h-f i) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e g^2}+\frac{(g h-f i)^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{g^3}+\frac{6 b^3 i n^2 (d+e x) (e h-d i) \log \left(c (d+e x)^n\right)}{e^2 g}+\frac{6 b^3 i n^2 (d+e x) (g h-f i) \log \left(c (d+e x)^n\right)}{e g^2}-\frac{3 b^3 i^2 n^3 (d+e x)^2}{8 e^2 g}-\frac{6 b^3 i n^3 x (e h-d i)}{e g}-\frac{6 b^3 i n^3 x (g h-f i)}{g^2}",1,"(6*a*b^2*i*(e*h - d*i)*n^2*x)/(e*g) + (6*a*b^2*i*(g*h - f*i)*n^2*x)/g^2 - (6*b^3*i*(e*h - d*i)*n^3*x)/(e*g) - (6*b^3*i*(g*h - f*i)*n^3*x)/g^2 - (3*b^3*i^2*n^3*(d + e*x)^2)/(8*e^2*g) + (6*b^3*i*(e*h - d*i)*n^2*(d + e*x)*Log[c*(d + e*x)^n])/(e^2*g) + (6*b^3*i*(g*h - f*i)*n^2*(d + e*x)*Log[c*(d + e*x)^n])/(e*g^2) + (3*b^2*i^2*n^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(4*e^2*g) - (3*b*i*(e*h - d*i)*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(e^2*g) - (3*b*i*(g*h - f*i)*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(e*g^2) - (3*b*i^2*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(4*e^2*g) + (i*(e*h - d*i)*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/(e^2*g) + (i*(g*h - f*i)*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/(e*g^2) + (i^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^3)/(2*e^2*g) + ((g*h - f*i)^2*(a + b*Log[c*(d + e*x)^n])^3*Log[(e*(f + g*x))/(e*f - d*g)])/g^3 + (3*b*(g*h - f*i)^2*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g^3 - (6*b^2*(g*h - f*i)^2*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/g^3 + (6*b^3*(g*h - f*i)^2*n^3*PolyLog[4, -((g*(d + e*x))/(e*f - d*g))])/g^3","A",23,13,31,0.4194,1,"{2418, 2389, 2296, 2295, 2396, 2433, 2374, 2383, 6589, 2401, 2390, 2305, 2304}"
230,1,308,0,0.3639522,"\int \frac{(h+i x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{f+g x} \, dx","Int[((h + i*x)*(a + b*Log[c*(d + e*x)^n])^3)/(f + g*x),x]","-\frac{6 b^2 n^2 (g h-f i) \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}+\frac{3 b n (g h-f i) \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g^2}+\frac{6 b^3 n^3 (g h-f i) \text{PolyLog}\left(4,-\frac{g (d+e x)}{e f-d g}\right)}{g^2}+\frac{6 a b^2 i n^2 x}{g}+\frac{(g h-f i) \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{g^2}-\frac{3 b i n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e g}+\frac{i (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e g}+\frac{6 b^3 i n^2 (d+e x) \log \left(c (d+e x)^n\right)}{e g}-\frac{6 b^3 i n^3 x}{g}","-\frac{6 b^2 n^2 (g h-f i) \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}+\frac{3 b n (g h-f i) \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g^2}+\frac{6 b^3 n^3 (g h-f i) \text{PolyLog}\left(4,-\frac{g (d+e x)}{e f-d g}\right)}{g^2}+\frac{6 a b^2 i n^2 x}{g}+\frac{(g h-f i) \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{g^2}-\frac{3 b i n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e g}+\frac{i (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e g}+\frac{6 b^3 i n^2 (d+e x) \log \left(c (d+e x)^n\right)}{e g}-\frac{6 b^3 i n^3 x}{g}",1,"(6*a*b^2*i*n^2*x)/g - (6*b^3*i*n^3*x)/g + (6*b^3*i*n^2*(d + e*x)*Log[c*(d + e*x)^n])/(e*g) - (3*b*i*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(e*g) + (i*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/(e*g) + ((g*h - f*i)*(a + b*Log[c*(d + e*x)^n])^3*Log[(e*(f + g*x))/(e*f - d*g)])/g^2 + (3*b*(g*h - f*i)*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g^2 - (6*b^2*(g*h - f*i)*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/g^2 + (6*b^3*(g*h - f*i)*n^3*PolyLog[4, -((g*(d + e*x))/(e*f - d*g))])/g^2","A",12,9,29,0.3103,1,"{2418, 2389, 2296, 2295, 2396, 2433, 2374, 2383, 6589}"
231,1,158,0,0.1798916,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{f+g x} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^3/(f + g*x),x]","-\frac{6 b^2 n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}+\frac{3 b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g}+\frac{6 b^3 n^3 \text{PolyLog}\left(4,-\frac{g (d+e x)}{e f-d g}\right)}{g}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{g}","-\frac{6 b^2 n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}+\frac{3 b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g}+\frac{6 b^3 n^3 \text{PolyLog}\left(4,-\frac{g (d+e x)}{e f-d g}\right)}{g}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{g}",1,"((a + b*Log[c*(d + e*x)^n])^3*Log[(e*(f + g*x))/(e*f - d*g)])/g + (3*b*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g - (6*b^2*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/g + (6*b^3*n^3*PolyLog[4, -((g*(d + e*x))/(e*f - d*g))])/g","A",5,5,24,0.2083,1,"{2396, 2433, 2374, 2383, 6589}"
232,1,372,0,0.5222065,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(f+g x) (h+i x)} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^3/((f + g*x)*(h + i*x)),x]","-\frac{6 b^2 n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g h-f i}+\frac{6 b^2 n^2 \text{PolyLog}\left(3,-\frac{i (d+e x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g h-f i}+\frac{3 b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g h-f i}-\frac{3 b n \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g h-f i}+\frac{6 b^3 n^3 \text{PolyLog}\left(4,-\frac{g (d+e x)}{e f-d g}\right)}{g h-f i}-\frac{6 b^3 n^3 \text{PolyLog}\left(4,-\frac{i (d+e x)}{e h-d i}\right)}{g h-f i}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{g h-f i}-\frac{\log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{g h-f i}","-\frac{6 b^2 n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g h-f i}+\frac{6 b^2 n^2 \text{PolyLog}\left(3,-\frac{i (d+e x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g h-f i}+\frac{3 b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g h-f i}-\frac{3 b n \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{g h-f i}+\frac{6 b^3 n^3 \text{PolyLog}\left(4,-\frac{g (d+e x)}{e f-d g}\right)}{g h-f i}-\frac{6 b^3 n^3 \text{PolyLog}\left(4,-\frac{i (d+e x)}{e h-d i}\right)}{g h-f i}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{g h-f i}-\frac{\log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{g h-f i}",1,"((a + b*Log[c*(d + e*x)^n])^3*Log[(e*(f + g*x))/(e*f - d*g)])/(g*h - f*i) - ((a + b*Log[c*(d + e*x)^n])^3*Log[(e*(h + i*x))/(e*h - d*i)])/(g*h - f*i) + (3*b*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/(g*h - f*i) - (3*b*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((i*(d + e*x))/(e*h - d*i))])/(g*h - f*i) - (6*b^2*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/(g*h - f*i) + (6*b^2*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[3, -((i*(d + e*x))/(e*h - d*i))])/(g*h - f*i) + (6*b^3*n^3*PolyLog[4, -((g*(d + e*x))/(e*f - d*g))])/(g*h - f*i) - (6*b^3*n^3*PolyLog[4, -((i*(d + e*x))/(e*h - d*i))])/(g*h - f*i)","A",12,6,31,0.1935,1,"{2418, 2396, 2433, 2374, 2383, 6589}"
233,1,602,0,0.7251293,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(f+g x) (h+i x)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^3/((f + g*x)*(h + i*x)^2),x]","\frac{6 b^2 e n^2 \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(e h-d i) (g h-f i)}-\frac{6 b^2 g n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(g h-f i)^2}+\frac{6 b^2 g n^2 \text{PolyLog}\left(3,-\frac{i (d+e x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(g h-f i)^2}+\frac{3 b g n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(g h-f i)^2}-\frac{3 b g n \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(g h-f i)^2}-\frac{6 b^3 e n^3 \text{PolyLog}\left(3,-\frac{i (d+e x)}{e h-d i}\right)}{(e h-d i) (g h-f i)}+\frac{6 b^3 g n^3 \text{PolyLog}\left(4,-\frac{g (d+e x)}{e f-d g}\right)}{(g h-f i)^2}-\frac{6 b^3 g n^3 \text{PolyLog}\left(4,-\frac{i (d+e x)}{e h-d i}\right)}{(g h-f i)^2}+\frac{3 b e n \log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(e h-d i) (g h-f i)}-\frac{i (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(h+i x) (e h-d i) (g h-f i)}+\frac{g \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(g h-f i)^2}-\frac{g \log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(g h-f i)^2}","\frac{6 b^2 e n^2 \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(e h-d i) (g h-f i)}-\frac{6 b^2 g n^2 \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(g h-f i)^2}+\frac{6 b^2 g n^2 \text{PolyLog}\left(3,-\frac{i (d+e x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(g h-f i)^2}+\frac{3 b g n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(g h-f i)^2}-\frac{3 b g n \text{PolyLog}\left(2,-\frac{i (d+e x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(g h-f i)^2}-\frac{6 b^3 e n^3 \text{PolyLog}\left(3,-\frac{i (d+e x)}{e h-d i}\right)}{(e h-d i) (g h-f i)}+\frac{6 b^3 g n^3 \text{PolyLog}\left(4,-\frac{g (d+e x)}{e f-d g}\right)}{(g h-f i)^2}-\frac{6 b^3 g n^3 \text{PolyLog}\left(4,-\frac{i (d+e x)}{e h-d i}\right)}{(g h-f i)^2}+\frac{3 b e n \log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(e h-d i) (g h-f i)}-\frac{i (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(h+i x) (e h-d i) (g h-f i)}+\frac{g \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(g h-f i)^2}-\frac{g \log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(g h-f i)^2}",1,"-((i*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/((e*h - d*i)*(g*h - f*i)*(h + i*x))) + (g*(a + b*Log[c*(d + e*x)^n])^3*Log[(e*(f + g*x))/(e*f - d*g)])/(g*h - f*i)^2 + (3*b*e*n*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(h + i*x))/(e*h - d*i)])/((e*h - d*i)*(g*h - f*i)) - (g*(a + b*Log[c*(d + e*x)^n])^3*Log[(e*(h + i*x))/(e*h - d*i)])/(g*h - f*i)^2 + (3*b*g*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/(g*h - f*i)^2 + (6*b^2*e*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((i*(d + e*x))/(e*h - d*i))])/((e*h - d*i)*(g*h - f*i)) - (3*b*g*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((i*(d + e*x))/(e*h - d*i))])/(g*h - f*i)^2 - (6*b^2*g*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/(g*h - f*i)^2 - (6*b^3*e*n^3*PolyLog[3, -((i*(d + e*x))/(e*h - d*i))])/((e*h - d*i)*(g*h - f*i)) + (6*b^2*g*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[3, -((i*(d + e*x))/(e*h - d*i))])/(g*h - f*i)^2 + (6*b^3*g*n^3*PolyLog[4, -((g*(d + e*x))/(e*f - d*g))])/(g*h - f*i)^2 - (6*b^3*g*n^3*PolyLog[4, -((i*(d + e*x))/(e*h - d*i))])/(g*h - f*i)^2","A",17,7,31,0.2258,1,"{2418, 2396, 2433, 2374, 2383, 6589, 2397}"
234,0,0,0,0.1761092,"\int \frac{h+i x}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","Int[(h + i*x)/((f + g*x)*(a + b*Log[c*(d + e*x)^n])),x]","\int \frac{h+i x}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","\frac{(g h-f i) \text{Int}\left(\frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)},x\right)}{g}+\frac{i e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b e g n}",0,"(i*(d + e*x)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)])/(b*e*E^(a/(b*n))*g*n*(c*(d + e*x)^n)^n^(-1)) + ((g*h - f*i)*Defer[Int][1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])), x])/g","A",0,0,0,0,-1,"{}"
235,0,0,0,0.0367887,"\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","Int[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])),x]","\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)},x\right)",0,"Defer[Int][1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])), x]","A",0,0,0,0,-1,"{}"
236,0,0,0,0.1894578,"\int \frac{1}{(f+g x) (h+i x) \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","Int[1/((f + g*x)*(h + i*x)*(a + b*Log[c*(d + e*x)^n])),x]","\int \frac{1}{(f+g x) (h+i x) \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","\frac{g \text{Int}\left(\frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)},x\right)}{g h-f i}-\frac{i \text{Int}\left(\frac{1}{(h+i x) \left(a+b \log \left(c (d+e x)^n\right)\right)},x\right)}{g h-f i}",0,"(g*Defer[Int][1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])), x])/(g*h - f*i) - (i*Defer[Int][1/((h + i*x)*(a + b*Log[c*(d + e*x)^n])), x])/(g*h - f*i)","A",0,0,0,0,-1,"{}"
237,0,0,0,0.2335832,"\int \frac{1}{(f+g x) (h+i x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","Int[1/((f + g*x)*(h + i*x)^2*(a + b*Log[c*(d + e*x)^n])),x]","\int \frac{1}{(f+g x) (h+i x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","\frac{g^2 \text{Int}\left(\frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)},x\right)}{(g h-f i)^2}-\frac{g i \text{Int}\left(\frac{1}{(h+i x) \left(a+b \log \left(c (d+e x)^n\right)\right)},x\right)}{(g h-f i)^2}-\frac{i \text{Int}\left(\frac{1}{(h+i x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)},x\right)}{g h-f i}",0,"(g^2*Defer[Int][1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])), x])/(g*h - f*i)^2 - (i*Defer[Int][1/((h + i*x)^2*(a + b*Log[c*(d + e*x)^n])), x])/(g*h - f*i) - (g*i*Defer[Int][1/((h + i*x)*(a + b*Log[c*(d + e*x)^n])), x])/(g*h - f*i)^2","A",0,0,0,0,-1,"{}"
238,0,0,0,0.196317,"\int \frac{h+i x}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Int[(h + i*x)/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^2),x]","\int \frac{h+i x}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","\frac{(g h-f i) \text{Int}\left(\frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2},x\right)}{g}+\frac{i e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)}{b^2 e g n^2}-\frac{i (d+e x)}{b e g n \left(a+b \log \left(c (d+e x)^n\right)\right)}",0,"(i*(d + e*x)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)])/(b^2*e*E^(a/(b*n))*g*n^2*(c*(d + e*x)^n)^n^(-1)) - (i*(d + e*x))/(b*e*g*n*(a + b*Log[c*(d + e*x)^n])) + ((g*h - f*i)*Defer[Int][1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^2), x])/g","A",0,0,0,0,-1,"{}"
239,0,0,0,0.0338843,"\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Int[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^2),x]","\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2},x\right)",0,"Defer[Int][1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^2), x]","A",0,0,0,0,-1,"{}"
240,0,0,0,0.1827066,"\int \frac{1}{(f+g x) (h+i x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Int[1/((f + g*x)*(h + i*x)*(a + b*Log[c*(d + e*x)^n])^2),x]","\int \frac{1}{(f+g x) (h+i x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","\frac{g \text{Int}\left(\frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2},x\right)}{g h-f i}-\frac{i \text{Int}\left(\frac{1}{(h+i x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2},x\right)}{g h-f i}",0,"(g*Defer[Int][1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^2), x])/(g*h - f*i) - (i*Defer[Int][1/((h + i*x)*(a + b*Log[c*(d + e*x)^n])^2), x])/(g*h - f*i)","A",0,0,0,0,-1,"{}"
241,0,0,0,0.2240477,"\int \frac{1}{(f+g x) (h+i x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Int[1/((f + g*x)*(h + i*x)^2*(a + b*Log[c*(d + e*x)^n])^2),x]","\int \frac{1}{(f+g x) (h+i x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","\frac{g^2 \text{Int}\left(\frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2},x\right)}{(g h-f i)^2}-\frac{g i \text{Int}\left(\frac{1}{(h+i x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2},x\right)}{(g h-f i)^2}-\frac{i \text{Int}\left(\frac{1}{(h+i x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2},x\right)}{g h-f i}",0,"(g^2*Defer[Int][1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^2), x])/(g*h - f*i)^2 - (i*Defer[Int][1/((h + i*x)^2*(a + b*Log[c*(d + e*x)^n])^2), x])/(g*h - f*i) - (g*i*Defer[Int][1/((h + i*x)*(a + b*Log[c*(d + e*x)^n])^2), x])/(g*h - f*i)^2","A",0,0,0,0,-1,"{}"
242,1,281,0,0.2776523,"\int \frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x} \, dx","Int[(x^3*(a + b*Log[c*(d + e*x)^n]))/(f + g*x),x]","-\frac{b f^3 n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^4}-\frac{f^3 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^4}-\frac{f x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}+\frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g}+\frac{a f^2 x}{g^3}+\frac{b f^2 (d+e x) \log \left(c (d+e x)^n\right)}{e g^3}+\frac{b d^2 f n \log (d+e x)}{2 e^2 g^2}-\frac{b d^2 n x}{3 e^2 g}+\frac{b d^3 n \log (d+e x)}{3 e^3 g}-\frac{b d f n x}{2 e g^2}+\frac{b d n x^2}{6 e g}-\frac{b f^2 n x}{g^3}+\frac{b f n x^2}{4 g^2}-\frac{b n x^3}{9 g}","-\frac{b f^3 n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^4}-\frac{f^3 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^4}-\frac{f x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}+\frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g}+\frac{a f^2 x}{g^3}+\frac{b f^2 (d+e x) \log \left(c (d+e x)^n\right)}{e g^3}+\frac{b d^2 f n \log (d+e x)}{2 e^2 g^2}-\frac{b d^2 n x}{3 e^2 g}+\frac{b d^3 n \log (d+e x)}{3 e^3 g}-\frac{b d f n x}{2 e g^2}+\frac{b d n x^2}{6 e g}-\frac{b f^2 n x}{g^3}+\frac{b f n x^2}{4 g^2}-\frac{b n x^3}{9 g}",1,"(a*f^2*x)/g^3 - (b*f^2*n*x)/g^3 - (b*d*f*n*x)/(2*e*g^2) - (b*d^2*n*x)/(3*e^2*g) + (b*f*n*x^2)/(4*g^2) + (b*d*n*x^2)/(6*e*g) - (b*n*x^3)/(9*g) + (b*d^2*f*n*Log[d + e*x])/(2*e^2*g^2) + (b*d^3*n*Log[d + e*x])/(3*e^3*g) + (b*f^2*(d + e*x)*Log[c*(d + e*x)^n])/(e*g^3) - (f*x^2*(a + b*Log[c*(d + e*x)^n]))/(2*g^2) + (x^3*(a + b*Log[c*(d + e*x)^n]))/(3*g) - (f^3*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/g^4 - (b*f^3*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g^4","A",14,8,25,0.3200,1,"{43, 2416, 2389, 2295, 2395, 2394, 2393, 2391}"
243,1,181,0,0.1933299,"\int \frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x} \, dx","Int[(x^2*(a + b*Log[c*(d + e*x)^n]))/(f + g*x),x]","\frac{b f^2 n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^3}+\frac{f^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3}+\frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g}-\frac{a f x}{g^2}-\frac{b f (d+e x) \log \left(c (d+e x)^n\right)}{e g^2}-\frac{b d^2 n \log (d+e x)}{2 e^2 g}+\frac{b d n x}{2 e g}+\frac{b f n x}{g^2}-\frac{b n x^2}{4 g}","\frac{b f^2 n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^3}+\frac{f^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3}+\frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g}-\frac{a f x}{g^2}-\frac{b f (d+e x) \log \left(c (d+e x)^n\right)}{e g^2}-\frac{b d^2 n \log (d+e x)}{2 e^2 g}+\frac{b d n x}{2 e g}+\frac{b f n x}{g^2}-\frac{b n x^2}{4 g}",1,"-((a*f*x)/g^2) + (b*f*n*x)/g^2 + (b*d*n*x)/(2*e*g) - (b*n*x^2)/(4*g) - (b*d^2*n*Log[d + e*x])/(2*e^2*g) - (b*f*(d + e*x)*Log[c*(d + e*x)^n])/(e*g^2) + (x^2*(a + b*Log[c*(d + e*x)^n]))/(2*g) + (f^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/g^3 + (b*f^2*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g^3","A",11,8,25,0.3200,1,"{43, 2416, 2389, 2295, 2395, 2394, 2393, 2391}"
244,1,104,0,0.1307022,"\int \frac{x \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x} \, dx","Int[(x*(a + b*Log[c*(d + e*x)^n]))/(f + g*x),x]","-\frac{b f n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^2}-\frac{f \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}+\frac{a x}{g}+\frac{b (d+e x) \log \left(c (d+e x)^n\right)}{e g}-\frac{b n x}{g}","-\frac{b f n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^2}-\frac{f \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}+\frac{a x}{g}+\frac{b (d+e x) \log \left(c (d+e x)^n\right)}{e g}-\frac{b n x}{g}",1,"(a*x)/g - (b*n*x)/g + (b*(d + e*x)*Log[c*(d + e*x)^n])/(e*g) - (f*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/g^2 - (b*f*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g^2","A",8,7,23,0.3043,1,"{43, 2416, 2389, 2295, 2394, 2393, 2391}"
245,1,63,0,0.0476132,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{f+g x} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(f + g*x),x]","\frac{b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}","\frac{b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}",1,"((a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/g + (b*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g","A",3,3,22,0.1364,1,"{2394, 2393, 2391}"
246,1,107,0,0.1436997,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x (f+g x)} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(x*(f + g*x)),x]","-\frac{b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{f}+\frac{b n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f}-\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f}+\frac{\log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f}","-\frac{b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{f}+\frac{b n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f}-\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f}+\frac{\log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f}",1,"(Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/f - ((a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/f - (b*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/f + (b*n*PolyLog[2, 1 + (e*x)/d])/f","A",7,8,25,0.3200,1,"{36, 29, 31, 2416, 2394, 2315, 2393, 2391}"
247,1,162,0,0.1911032,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^2 (f+g x)} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(x^2*(f + g*x)),x]","\frac{b g n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{f^2}-\frac{b g n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^2}-\frac{g \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}+\frac{g \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}-\frac{a+b \log \left(c (d+e x)^n\right)}{f x}+\frac{b e n \log (x)}{d f}-\frac{b e n \log (d+e x)}{d f}","\frac{b g n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{f^2}-\frac{b g n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^2}-\frac{g \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}+\frac{g \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}-\frac{a+b \log \left(c (d+e x)^n\right)}{f x}+\frac{b e n \log (x)}{d f}-\frac{b e n \log (d+e x)}{d f}",1,"(b*e*n*Log[x])/(d*f) - (b*e*n*Log[d + e*x])/(d*f) - (a + b*Log[c*(d + e*x)^n])/(f*x) - (g*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/f^2 + (g*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/f^2 + (b*g*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/f^2 - (b*g*n*PolyLog[2, 1 + (e*x)/d])/f^2","A",11,10,25,0.4000,1,"{44, 2416, 2395, 36, 29, 31, 2394, 2315, 2393, 2391}"
248,1,250,0,0.2521837,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^3 (f+g x)} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(x^3*(f + g*x)),x]","-\frac{b g^2 n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{f^3}+\frac{b g^2 n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^3}+\frac{g^2 \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3}-\frac{g^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3}+\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2 x}-\frac{a+b \log \left(c (d+e x)^n\right)}{2 f x^2}-\frac{b e^2 n \log (x)}{2 d^2 f}+\frac{b e^2 n \log (d+e x)}{2 d^2 f}-\frac{b e g n \log (x)}{d f^2}+\frac{b e g n \log (d+e x)}{d f^2}-\frac{b e n}{2 d f x}","-\frac{b g^2 n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{f^3}+\frac{b g^2 n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^3}+\frac{g^2 \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3}-\frac{g^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3}+\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2 x}-\frac{a+b \log \left(c (d+e x)^n\right)}{2 f x^2}-\frac{b e^2 n \log (x)}{2 d^2 f}+\frac{b e^2 n \log (d+e x)}{2 d^2 f}-\frac{b e g n \log (x)}{d f^2}+\frac{b e g n \log (d+e x)}{d f^2}-\frac{b e n}{2 d f x}",1,"-(b*e*n)/(2*d*f*x) - (b*e^2*n*Log[x])/(2*d^2*f) - (b*e*g*n*Log[x])/(d*f^2) + (b*e^2*n*Log[d + e*x])/(2*d^2*f) + (b*e*g*n*Log[d + e*x])/(d*f^2) - (a + b*Log[c*(d + e*x)^n])/(2*f*x^2) + (g*(a + b*Log[c*(d + e*x)^n]))/(f^2*x) + (g^2*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/f^3 - (g^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/f^3 - (b*g^2*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/f^3 + (b*g^2*n*PolyLog[2, 1 + (e*x)/d])/f^3","A",14,10,25,0.4000,1,"{44, 2416, 2395, 36, 29, 31, 2394, 2315, 2393, 2391}"
249,1,265,0,0.2603844,"\int \frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{(f+g x)^2} \, dx","Int[(x^3*(a + b*Log[c*(d + e*x)^n]))/(f + g*x)^2,x]","\frac{3 b f^2 n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^4}+\frac{f^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^4 (f+g x)}+\frac{3 f^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^4}+\frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}-\frac{2 a f x}{g^3}-\frac{2 b f (d+e x) \log \left(c (d+e x)^n\right)}{e g^3}-\frac{b d^2 n \log (d+e x)}{2 e^2 g^2}-\frac{b e f^3 n \log (d+e x)}{g^4 (e f-d g)}+\frac{b e f^3 n \log (f+g x)}{g^4 (e f-d g)}+\frac{b d n x}{2 e g^2}+\frac{2 b f n x}{g^3}-\frac{b n x^2}{4 g^2}","\frac{3 b f^2 n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^4}+\frac{f^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^4 (f+g x)}+\frac{3 f^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^4}+\frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}-\frac{2 a f x}{g^3}-\frac{2 b f (d+e x) \log \left(c (d+e x)^n\right)}{e g^3}-\frac{b d^2 n \log (d+e x)}{2 e^2 g^2}-\frac{b e f^3 n \log (d+e x)}{g^4 (e f-d g)}+\frac{b e f^3 n \log (f+g x)}{g^4 (e f-d g)}+\frac{b d n x}{2 e g^2}+\frac{2 b f n x}{g^3}-\frac{b n x^2}{4 g^2}",1,"(-2*a*f*x)/g^3 + (2*b*f*n*x)/g^3 + (b*d*n*x)/(2*e*g^2) - (b*n*x^2)/(4*g^2) - (b*d^2*n*Log[d + e*x])/(2*e^2*g^2) - (b*e*f^3*n*Log[d + e*x])/(g^4*(e*f - d*g)) - (2*b*f*(d + e*x)*Log[c*(d + e*x)^n])/(e*g^3) + (x^2*(a + b*Log[c*(d + e*x)^n]))/(2*g^2) + (f^3*(a + b*Log[c*(d + e*x)^n]))/(g^4*(f + g*x)) + (b*e*f^3*n*Log[f + g*x])/(g^4*(e*f - d*g)) + (3*f^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/g^4 + (3*b*f^2*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g^4","A",15,10,25,0.4000,1,"{43, 2416, 2389, 2295, 2395, 36, 31, 2394, 2393, 2391}"
250,1,186,0,0.2033054,"\int \frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{(f+g x)^2} \, dx","Int[(x^2*(a + b*Log[c*(d + e*x)^n]))/(f + g*x)^2,x]","-\frac{2 b f n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^3}-\frac{f^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3 (f+g x)}-\frac{2 f \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3}+\frac{a x}{g^2}+\frac{b (d+e x) \log \left(c (d+e x)^n\right)}{e g^2}+\frac{b e f^2 n \log (d+e x)}{g^3 (e f-d g)}-\frac{b e f^2 n \log (f+g x)}{g^3 (e f-d g)}-\frac{b n x}{g^2}","-\frac{2 b f n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^3}-\frac{f^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3 (f+g x)}-\frac{2 f \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3}+\frac{a x}{g^2}+\frac{b (d+e x) \log \left(c (d+e x)^n\right)}{e g^2}+\frac{b e f^2 n \log (d+e x)}{g^3 (e f-d g)}-\frac{b e f^2 n \log (f+g x)}{g^3 (e f-d g)}-\frac{b n x}{g^2}",1,"(a*x)/g^2 - (b*n*x)/g^2 + (b*e*f^2*n*Log[d + e*x])/(g^3*(e*f - d*g)) + (b*(d + e*x)*Log[c*(d + e*x)^n])/(e*g^2) - (f^2*(a + b*Log[c*(d + e*x)^n]))/(g^3*(f + g*x)) - (b*e*f^2*n*Log[f + g*x])/(g^3*(e*f - d*g)) - (2*f*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/g^3 - (2*b*f*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g^3","A",12,10,25,0.4000,1,"{43, 2416, 2389, 2295, 2395, 36, 31, 2394, 2393, 2391}"
251,1,138,0,0.1521761,"\int \frac{x \left(a+b \log \left(c (d+e x)^n\right)\right)}{(f+g x)^2} \, dx","Int[(x*(a + b*Log[c*(d + e*x)^n]))/(f + g*x)^2,x]","\frac{b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^2}+\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2 (f+g x)}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}-\frac{b e f n \log (d+e x)}{g^2 (e f-d g)}+\frac{b e f n \log (f+g x)}{g^2 (e f-d g)}","\frac{b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{g^2}+\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2 (f+g x)}+\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}-\frac{b e f n \log (d+e x)}{g^2 (e f-d g)}+\frac{b e f n \log (f+g x)}{g^2 (e f-d g)}",1,"-((b*e*f*n*Log[d + e*x])/(g^2*(e*f - d*g))) + (f*(a + b*Log[c*(d + e*x)^n]))/(g^2*(f + g*x)) + (b*e*f*n*Log[f + g*x])/(g^2*(e*f - d*g)) + ((a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/g^2 + (b*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/g^2","A",9,8,23,0.3478,1,"{43, 2416, 2395, 36, 31, 2394, 2393, 2391}"
252,1,74,0,0.0284328,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(f + g*x)^2,x]","-\frac{a+b \log \left(c (d+e x)^n\right)}{g (f+g x)}+\frac{b e n \log (d+e x)}{g (e f-d g)}-\frac{b e n \log (f+g x)}{g (e f-d g)}","-\frac{a+b \log \left(c (d+e x)^n\right)}{g (f+g x)}+\frac{b e n \log (d+e x)}{g (e f-d g)}-\frac{b e n \log (f+g x)}{g (e f-d g)}",1,"(b*e*n*Log[d + e*x])/(g*(e*f - d*g)) - (a + b*Log[c*(d + e*x)^n])/(g*(f + g*x)) - (b*e*n*Log[f + g*x])/(g*(e*f - d*g))","A",4,3,22,0.1364,1,"{2395, 36, 31}"
253,1,179,0,0.2015283,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x (f+g x)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(x*(f + g*x)^2),x]","-\frac{b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{f^2}+\frac{b n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^2}-\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}+\frac{\log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}+\frac{a+b \log \left(c (d+e x)^n\right)}{f (f+g x)}-\frac{b e n \log (d+e x)}{f (e f-d g)}+\frac{b e n \log (f+g x)}{f (e f-d g)}","-\frac{b n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{f^2}+\frac{b n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^2}-\frac{\log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}+\frac{\log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}+\frac{a+b \log \left(c (d+e x)^n\right)}{f (f+g x)}-\frac{b e n \log (d+e x)}{f (e f-d g)}+\frac{b e n \log (f+g x)}{f (e f-d g)}",1,"-((b*e*n*Log[d + e*x])/(f*(e*f - d*g))) + (a + b*Log[c*(d + e*x)^n])/(f*(f + g*x)) + (Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/f^2 + (b*e*n*Log[f + g*x])/(f*(e*f - d*g)) - ((a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/f^2 - (b*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/f^2 + (b*n*PolyLog[2, 1 + (e*x)/d])/f^2","A",11,9,25,0.3600,1,"{44, 2416, 2394, 2315, 2395, 36, 31, 2393, 2391}"
254,1,240,0,0.244097,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^2 (f+g x)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(x^2*(f + g*x)^2),x]","\frac{2 b g n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{f^3}-\frac{2 b g n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^3}-\frac{2 g \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3}-\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2 (f+g x)}+\frac{2 g \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3}-\frac{a+b \log \left(c (d+e x)^n\right)}{f^2 x}+\frac{b e g n \log (d+e x)}{f^2 (e f-d g)}-\frac{b e g n \log (f+g x)}{f^2 (e f-d g)}+\frac{b e n \log (x)}{d f^2}-\frac{b e n \log (d+e x)}{d f^2}","\frac{2 b g n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{f^3}-\frac{2 b g n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^3}-\frac{2 g \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3}-\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2 (f+g x)}+\frac{2 g \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3}-\frac{a+b \log \left(c (d+e x)^n\right)}{f^2 x}+\frac{b e g n \log (d+e x)}{f^2 (e f-d g)}-\frac{b e g n \log (f+g x)}{f^2 (e f-d g)}+\frac{b e n \log (x)}{d f^2}-\frac{b e n \log (d+e x)}{d f^2}",1,"(b*e*n*Log[x])/(d*f^2) - (b*e*n*Log[d + e*x])/(d*f^2) + (b*e*g*n*Log[d + e*x])/(f^2*(e*f - d*g)) - (a + b*Log[c*(d + e*x)^n])/(f^2*x) - (g*(a + b*Log[c*(d + e*x)^n]))/(f^2*(f + g*x)) - (2*g*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/f^3 - (b*e*g*n*Log[f + g*x])/(f^2*(e*f - d*g)) + (2*g*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/f^3 + (2*b*g*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/f^3 - (2*b*g*n*PolyLog[2, 1 + (e*x)/d])/f^3","A",15,10,25,0.4000,1,"{44, 2416, 2395, 36, 29, 31, 2394, 2315, 2393, 2391}"
255,1,335,0,0.3141223,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^3 (f+g x)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(x^3*(f + g*x)^2),x]","-\frac{3 b g^2 n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{f^4}+\frac{3 b g^2 n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^4}+\frac{3 g^2 \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^4}+\frac{g^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3 (f+g x)}-\frac{3 g^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^4}+\frac{2 g \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3 x}-\frac{a+b \log \left(c (d+e x)^n\right)}{2 f^2 x^2}-\frac{b e^2 n \log (x)}{2 d^2 f^2}+\frac{b e^2 n \log (d+e x)}{2 d^2 f^2}-\frac{b e g^2 n \log (d+e x)}{f^3 (e f-d g)}+\frac{b e g^2 n \log (f+g x)}{f^3 (e f-d g)}-\frac{2 b e g n \log (x)}{d f^3}+\frac{2 b e g n \log (d+e x)}{d f^3}-\frac{b e n}{2 d f^2 x}","-\frac{3 b g^2 n \text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right)}{f^4}+\frac{3 b g^2 n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^4}+\frac{3 g^2 \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^4}+\frac{g^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3 (f+g x)}-\frac{3 g^2 \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^4}+\frac{2 g \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3 x}-\frac{a+b \log \left(c (d+e x)^n\right)}{2 f^2 x^2}-\frac{b e^2 n \log (x)}{2 d^2 f^2}+\frac{b e^2 n \log (d+e x)}{2 d^2 f^2}-\frac{b e g^2 n \log (d+e x)}{f^3 (e f-d g)}+\frac{b e g^2 n \log (f+g x)}{f^3 (e f-d g)}-\frac{2 b e g n \log (x)}{d f^3}+\frac{2 b e g n \log (d+e x)}{d f^3}-\frac{b e n}{2 d f^2 x}",1,"-(b*e*n)/(2*d*f^2*x) - (b*e^2*n*Log[x])/(2*d^2*f^2) - (2*b*e*g*n*Log[x])/(d*f^3) + (b*e^2*n*Log[d + e*x])/(2*d^2*f^2) + (2*b*e*g*n*Log[d + e*x])/(d*f^3) - (b*e*g^2*n*Log[d + e*x])/(f^3*(e*f - d*g)) - (a + b*Log[c*(d + e*x)^n])/(2*f^2*x^2) + (2*g*(a + b*Log[c*(d + e*x)^n]))/(f^3*x) + (g^2*(a + b*Log[c*(d + e*x)^n]))/(f^3*(f + g*x)) + (3*g^2*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/f^4 + (b*e*g^2*n*Log[f + g*x])/(f^3*(e*f - d*g)) - (3*g^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/f^4 - (3*b*g^2*n*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/f^4 + (3*b*g^2*n*PolyLog[2, 1 + (e*x)/d])/f^4","A",18,10,25,0.4000,1,"{44, 2416, 2395, 36, 29, 31, 2394, 2315, 2393, 2391}"
256,1,397,0,0.5102948,"\int \frac{x^5 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x^2} \, dx","Int[(x^5*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2),x]","\frac{b f^2 n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^3}+\frac{b f^2 n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 g^3}+\frac{f^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^3}+\frac{f^2 \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^3}-\frac{f x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}+\frac{x^4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 g}+\frac{b d^2 f n \log (d+e x)}{2 e^2 g^2}-\frac{b d^2 n x^2}{8 e^2 g}+\frac{b d^3 n x}{4 e^3 g}-\frac{b d^4 n \log (d+e x)}{4 e^4 g}-\frac{b d f n x}{2 e g^2}+\frac{b d n x^3}{12 e g}+\frac{b f n x^2}{4 g^2}-\frac{b n x^4}{16 g}","\frac{b f^2 n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^3}+\frac{b f^2 n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 g^3}+\frac{f^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^3}+\frac{f^2 \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^3}-\frac{f x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}+\frac{x^4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 g}+\frac{b d^2 f n \log (d+e x)}{2 e^2 g^2}-\frac{b d^2 n x^2}{8 e^2 g}+\frac{b d^3 n x}{4 e^3 g}-\frac{b d^4 n \log (d+e x)}{4 e^4 g}-\frac{b d f n x}{2 e g^2}+\frac{b d n x^3}{12 e g}+\frac{b f n x^2}{4 g^2}-\frac{b n x^4}{16 g}",1,"-(b*d*f*n*x)/(2*e*g^2) + (b*d^3*n*x)/(4*e^3*g) + (b*f*n*x^2)/(4*g^2) - (b*d^2*n*x^2)/(8*e^2*g) + (b*d*n*x^3)/(12*e*g) - (b*n*x^4)/(16*g) + (b*d^2*f*n*Log[d + e*x])/(2*e^2*g^2) - (b*d^4*n*Log[d + e*x])/(4*e^4*g) - (f*x^2*(a + b*Log[c*(d + e*x)^n]))/(2*g^2) + (x^4*(a + b*Log[c*(d + e*x)^n]))/(4*g) + (f^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^3) + (f^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*g^3) + (b*f^2*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*g^3) + (b*f^2*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^3)","A",16,8,27,0.2963,1,"{266, 43, 2416, 2395, 260, 2394, 2393, 2391}"
257,1,278,0,0.3250937,"\int \frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x^2} \, dx","Int[(x^3*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2),x]","-\frac{b f n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^2}-\frac{b f n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 g^2}-\frac{f \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}-\frac{f \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}+\frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g}-\frac{b d^2 n \log (d+e x)}{2 e^2 g}+\frac{b d n x}{2 e g}-\frac{b n x^2}{4 g}","-\frac{b f n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^2}-\frac{b f n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 g^2}-\frac{f \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}-\frac{f \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}+\frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g}-\frac{b d^2 n \log (d+e x)}{2 e^2 g}+\frac{b d n x}{2 e g}-\frac{b n x^2}{4 g}",1,"(b*d*n*x)/(2*e*g) - (b*n*x^2)/(4*g) - (b*d^2*n*Log[d + e*x])/(2*e^2*g) + (x^2*(a + b*Log[c*(d + e*x)^n]))/(2*g) - (f*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^2) - (f*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*g^2) - (b*f*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*g^2) - (b*f*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^2)","A",13,8,27,0.2963,1,"{266, 43, 2416, 2395, 260, 2394, 2393, 2391}"
258,1,203,0,0.1796264,"\int \frac{x \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x^2} \, dx","Int[(x*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2),x]","\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g}+\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 g}+\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g}+\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g}","\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g}+\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 g}+\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g}+\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g}",1,"((a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g) + ((a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*g) + (b*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*g) + (b*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g)","A",8,5,25,0.2000,1,"{260, 2416, 2394, 2393, 2391}"
259,1,245,0,0.3163593,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x \left(f+g x^2\right)} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(x*(f + g*x^2)),x]","-\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f}-\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 f}+\frac{b n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f}-\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f}-\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f}+\frac{\log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f}","-\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f}-\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 f}+\frac{b n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f}-\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f}-\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f}+\frac{\log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f}",1,"(Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/f - ((a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f) - ((a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*f) - (b*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*f) - (b*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f) + (b*n*PolyLog[2, 1 + (e*x)/d])/f","A",12,10,27,0.3704,1,"{266, 36, 29, 31, 2416, 2394, 2315, 260, 2393, 2391}"
260,1,331,0,0.3680749,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^3 \left(f+g x^2\right)} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(x^3*(f + g*x^2)),x]","\frac{b g n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f^2}+\frac{b g n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 f^2}-\frac{b g n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^2}-\frac{g \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}+\frac{g \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f^2}+\frac{g \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f^2}-\frac{a+b \log \left(c (d+e x)^n\right)}{2 f x^2}-\frac{b e^2 n \log (x)}{2 d^2 f}+\frac{b e^2 n \log (d+e x)}{2 d^2 f}-\frac{b e n}{2 d f x}","\frac{b g n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f^2}+\frac{b g n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 f^2}-\frac{b g n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^2}-\frac{g \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}+\frac{g \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f^2}+\frac{g \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f^2}-\frac{a+b \log \left(c (d+e x)^n\right)}{2 f x^2}-\frac{b e^2 n \log (x)}{2 d^2 f}+\frac{b e^2 n \log (d+e x)}{2 d^2 f}-\frac{b e n}{2 d f x}",1,"-(b*e*n)/(2*d*f*x) - (b*e^2*n*Log[x])/(2*d^2*f) + (b*e^2*n*Log[d + e*x])/(2*d^2*f) - (a + b*Log[c*(d + e*x)^n])/(2*f*x^2) - (g*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/f^2 + (g*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f^2) + (g*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*f^2) + (b*g*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*f^2) + (b*g*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f^2) - (b*g*n*PolyLog[2, 1 + (e*x)/d])/f^2","A",15,9,27,0.3333,1,"{266, 44, 2416, 2395, 2394, 2315, 260, 2393, 2391}"
261,1,369,0,0.3947067,"\int \frac{x^4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x^2} \, dx","Int[(x^4*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2),x]","-\frac{b (-f)^{3/2} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^{5/2}}+\frac{b (-f)^{3/2} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 g^{5/2}}+\frac{(-f)^{3/2} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^{5/2}}-\frac{(-f)^{3/2} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^{5/2}}+\frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g}-\frac{a f x}{g^2}-\frac{b f (d+e x) \log \left(c (d+e x)^n\right)}{e g^2}-\frac{b d^2 n x}{3 e^2 g}+\frac{b d^3 n \log (d+e x)}{3 e^3 g}+\frac{b d n x^2}{6 e g}+\frac{b f n x}{g^2}-\frac{b n x^3}{9 g}","-\frac{b (-f)^{3/2} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^{5/2}}+\frac{b (-f)^{3/2} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 g^{5/2}}+\frac{(-f)^{3/2} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^{5/2}}-\frac{(-f)^{3/2} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^{5/2}}+\frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g}-\frac{a f x}{g^2}-\frac{b f (d+e x) \log \left(c (d+e x)^n\right)}{e g^2}-\frac{b d^2 n x}{3 e^2 g}+\frac{b d^3 n \log (d+e x)}{3 e^3 g}+\frac{b d n x^2}{6 e g}+\frac{b f n x}{g^2}-\frac{b n x^3}{9 g}",1,"-((a*f*x)/g^2) + (b*f*n*x)/g^2 - (b*d^2*n*x)/(3*e^2*g) + (b*d*n*x^2)/(6*e*g) - (b*n*x^3)/(9*g) + (b*d^3*n*Log[d + e*x])/(3*e^3*g) - (b*f*(d + e*x)*Log[c*(d + e*x)^n])/(e*g^2) + (x^3*(a + b*Log[c*(d + e*x)^n]))/(3*g) + ((-f)^(3/2)*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^(5/2)) - ((-f)^(3/2)*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*g^(5/2)) - (b*(-f)^(3/2)*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*g^(5/2)) + (b*(-f)^(3/2)*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^(5/2))","A",16,11,27,0.4074,1,"{302, 205, 2416, 2389, 2295, 2395, 43, 2409, 2394, 2393, 2391}"
262,1,276,0,0.3093999,"\int \frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x^2} \, dx","Int[(x^2*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2),x]","-\frac{b \sqrt{-f} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^{3/2}}+\frac{b \sqrt{-f} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 g^{3/2}}+\frac{\sqrt{-f} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^{3/2}}-\frac{\sqrt{-f} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^{3/2}}+\frac{a x}{g}+\frac{b (d+e x) \log \left(c (d+e x)^n\right)}{e g}-\frac{b n x}{g}","-\frac{b \sqrt{-f} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^{3/2}}+\frac{b \sqrt{-f} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 g^{3/2}}+\frac{\sqrt{-f} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^{3/2}}-\frac{\sqrt{-f} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^{3/2}}+\frac{a x}{g}+\frac{b (d+e x) \log \left(c (d+e x)^n\right)}{e g}-\frac{b n x}{g}",1,"(a*x)/g - (b*n*x)/g + (b*(d + e*x)*Log[c*(d + e*x)^n])/(e*g) + (Sqrt[-f]*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^(3/2)) - (Sqrt[-f]*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*g^(3/2)) - (b*Sqrt[-f]*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*g^(3/2)) + (b*Sqrt[-f]*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^(3/2))","A",13,9,27,0.3333,1,"{321, 205, 2416, 2389, 2295, 2409, 2394, 2393, 2391}"
263,1,239,0,0.1682507,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{f+g x^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(f + g*x^2),x]","-\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 \sqrt{-f} \sqrt{g}}-\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 \sqrt{-f} \sqrt{g}}","-\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 \sqrt{-f} \sqrt{g}}-\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 \sqrt{-f} \sqrt{g}}",1,"((a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*Sqrt[-f]*Sqrt[g]) - ((a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*Sqrt[-f]*Sqrt[g]) - (b*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*Sqrt[-f]*Sqrt[g]) + (b*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*Sqrt[-f]*Sqrt[g])","A",8,4,24,0.1667,1,"{2409, 2394, 2393, 2391}"
264,1,290,0,0.315934,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^2 \left(f+g x^2\right)} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(x^2*(f + g*x^2)),x]","-\frac{b \sqrt{g} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 (-f)^{3/2}}+\frac{b \sqrt{g} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 (-f)^{3/2}}+\frac{\sqrt{g} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 (-f)^{3/2}}-\frac{\sqrt{g} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 (-f)^{3/2}}-\frac{a+b \log \left(c (d+e x)^n\right)}{f x}+\frac{b e n \log (x)}{d f}-\frac{b e n \log (d+e x)}{d f}","-\frac{b \sqrt{g} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 (-f)^{3/2}}+\frac{b \sqrt{g} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 (-f)^{3/2}}+\frac{\sqrt{g} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 (-f)^{3/2}}-\frac{\sqrt{g} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 (-f)^{3/2}}-\frac{a+b \log \left(c (d+e x)^n\right)}{f x}+\frac{b e n \log (x)}{d f}-\frac{b e n \log (d+e x)}{d f}",1,"(b*e*n*Log[x])/(d*f) - (b*e*n*Log[d + e*x])/(d*f) - (a + b*Log[c*(d + e*x)^n])/(f*x) + (Sqrt[g]*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*(-f)^(3/2)) - (Sqrt[g]*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*(-f)^(3/2)) - (b*Sqrt[g]*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*(-f)^(3/2)) + (b*Sqrt[g]*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*(-f)^(3/2))","A",14,11,27,0.4074,1,"{325, 205, 2416, 2395, 36, 29, 31, 2409, 2394, 2393, 2391}"
265,1,388,0,0.3759496,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^4 \left(f+g x^2\right)} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(x^4*(f + g*x^2)),x]","-\frac{b g^{3/2} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 (-f)^{5/2}}+\frac{b g^{3/2} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 (-f)^{5/2}}+\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2 x}+\frac{g^{3/2} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 (-f)^{5/2}}-\frac{g^{3/2} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 (-f)^{5/2}}-\frac{a+b \log \left(c (d+e x)^n\right)}{3 f x^3}+\frac{b e^2 n}{3 d^2 f x}+\frac{b e^3 n \log (x)}{3 d^3 f}-\frac{b e^3 n \log (d+e x)}{3 d^3 f}-\frac{b e g n \log (x)}{d f^2}+\frac{b e g n \log (d+e x)}{d f^2}-\frac{b e n}{6 d f x^2}","-\frac{b g^{3/2} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 (-f)^{5/2}}+\frac{b g^{3/2} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 (-f)^{5/2}}+\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2 x}+\frac{g^{3/2} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 (-f)^{5/2}}-\frac{g^{3/2} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 (-f)^{5/2}}-\frac{a+b \log \left(c (d+e x)^n\right)}{3 f x^3}+\frac{b e^2 n}{3 d^2 f x}+\frac{b e^3 n \log (x)}{3 d^3 f}-\frac{b e^3 n \log (d+e x)}{3 d^3 f}-\frac{b e g n \log (x)}{d f^2}+\frac{b e g n \log (d+e x)}{d f^2}-\frac{b e n}{6 d f x^2}",1,"-(b*e*n)/(6*d*f*x^2) + (b*e^2*n)/(3*d^2*f*x) + (b*e^3*n*Log[x])/(3*d^3*f) - (b*e*g*n*Log[x])/(d*f^2) - (b*e^3*n*Log[d + e*x])/(3*d^3*f) + (b*e*g*n*Log[d + e*x])/(d*f^2) - (a + b*Log[c*(d + e*x)^n])/(3*f*x^3) + (g*(a + b*Log[c*(d + e*x)^n]))/(f^2*x) + (g^(3/2)*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*(-f)^(5/2)) - (g^(3/2)*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*(-f)^(5/2)) - (b*g^(3/2)*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*(-f)^(5/2)) + (b*g^(3/2)*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*(-f)^(5/2))","A",17,12,27,0.4444,1,"{325, 205, 2416, 2395, 44, 36, 29, 31, 2409, 2394, 2393, 2391}"
266,1,417,0,0.4872622,"\int \frac{x^5 \left(a+b \log \left(c (d+e x)^n\right)\right)}{\left(f+g x^2\right)^2} \, dx","Int[(x^5*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2)^2,x]","-\frac{b f n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^3}-\frac{b f n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{g^3}-\frac{f^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^3 \left(f+g x^2\right)}-\frac{f \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3}-\frac{f \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3}+\frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}-\frac{b e^2 f^2 n \log \left(f+g x^2\right)}{4 g^3 \left(d^2 g+e^2 f\right)}+\frac{b e^2 f^2 n \log (d+e x)}{2 g^3 \left(d^2 g+e^2 f\right)}+\frac{b d e f^{3/2} n \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{2 g^{5/2} \left(d^2 g+e^2 f\right)}-\frac{b d^2 n \log (d+e x)}{2 e^2 g^2}+\frac{b d n x}{2 e g^2}-\frac{b n x^2}{4 g^2}","-\frac{b f n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^3}-\frac{b f n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{g^3}-\frac{f^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^3 \left(f+g x^2\right)}-\frac{f \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3}-\frac{f \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3}+\frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}-\frac{b e^2 f^2 n \log \left(f+g x^2\right)}{4 g^3 \left(d^2 g+e^2 f\right)}+\frac{b e^2 f^2 n \log (d+e x)}{2 g^3 \left(d^2 g+e^2 f\right)}+\frac{b d e f^{3/2} n \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{2 g^{5/2} \left(d^2 g+e^2 f\right)}-\frac{b d^2 n \log (d+e x)}{2 e^2 g^2}+\frac{b d n x}{2 e g^2}-\frac{b n x^2}{4 g^2}",1,"(b*d*n*x)/(2*e*g^2) - (b*n*x^2)/(4*g^2) + (b*d*e*f^(3/2)*n*ArcTan[(Sqrt[g]*x)/Sqrt[f]])/(2*g^(5/2)*(e^2*f + d^2*g)) - (b*d^2*n*Log[d + e*x])/(2*e^2*g^2) + (b*e^2*f^2*n*Log[d + e*x])/(2*g^3*(e^2*f + d^2*g)) + (x^2*(a + b*Log[c*(d + e*x)^n]))/(2*g^2) - (f^2*(a + b*Log[c*(d + e*x)^n]))/(2*g^3*(f + g*x^2)) - (f*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g^3 - (f*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/g^3 - (b*e^2*f^2*n*Log[f + g*x^2])/(4*g^3*(e^2*f + d^2*g)) - (b*f*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/g^3 - (b*f*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g^3","A",19,13,27,0.4815,1,"{266, 43, 2416, 2395, 2413, 706, 31, 635, 205, 260, 2394, 2393, 2391}"
267,1,344,0,0.4074494,"\int \frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{\left(f+g x^2\right)^2} \, dx","Int[(x^3*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2)^2,x]","\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^2}+\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 g^2}+\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2 \left(f+g x^2\right)}+\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}+\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}+\frac{b e^2 f n \log \left(f+g x^2\right)}{4 g^2 \left(d^2 g+e^2 f\right)}-\frac{b e^2 f n \log (d+e x)}{2 g^2 \left(d^2 g+e^2 f\right)}-\frac{b d e \sqrt{f} n \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{2 g^{3/2} \left(d^2 g+e^2 f\right)}","\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^2}+\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 g^2}+\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2 \left(f+g x^2\right)}+\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}+\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}+\frac{b e^2 f n \log \left(f+g x^2\right)}{4 g^2 \left(d^2 g+e^2 f\right)}-\frac{b e^2 f n \log (d+e x)}{2 g^2 \left(d^2 g+e^2 f\right)}-\frac{b d e \sqrt{f} n \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{2 g^{3/2} \left(d^2 g+e^2 f\right)}",1,"-(b*d*e*Sqrt[f]*n*ArcTan[(Sqrt[g]*x)/Sqrt[f]])/(2*g^(3/2)*(e^2*f + d^2*g)) - (b*e^2*f*n*Log[d + e*x])/(2*g^2*(e^2*f + d^2*g)) + (f*(a + b*Log[c*(d + e*x)^n]))/(2*g^2*(f + g*x^2)) + ((a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^2) + ((a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*g^2) + (b*e^2*f*n*Log[f + g*x^2])/(4*g^2*(e^2*f + d^2*g)) + (b*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*g^2) + (b*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^2)","A",16,12,27,0.4444,1,"{266, 43, 2416, 2413, 706, 31, 635, 205, 260, 2394, 2393, 2391}"
268,1,139,0,0.0783081,"\int \frac{x \left(a+b \log \left(c (d+e x)^n\right)\right)}{\left(f+g x^2\right)^2} \, dx","Int[(x*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2)^2,x]","-\frac{a+b \log \left(c (d+e x)^n\right)}{2 g \left(f+g x^2\right)}-\frac{b e^2 n \log \left(f+g x^2\right)}{4 g \left(d^2 g+e^2 f\right)}+\frac{b e^2 n \log (d+e x)}{2 g \left(d^2 g+e^2 f\right)}+\frac{b d e n \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{2 \sqrt{f} \sqrt{g} \left(d^2 g+e^2 f\right)}","-\frac{a+b \log \left(c (d+e x)^n\right)}{2 g \left(f+g x^2\right)}-\frac{b e^2 n \log \left(f+g x^2\right)}{4 g \left(d^2 g+e^2 f\right)}+\frac{b e^2 n \log (d+e x)}{2 g \left(d^2 g+e^2 f\right)}+\frac{b d e n \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{2 \sqrt{f} \sqrt{g} \left(d^2 g+e^2 f\right)}",1,"(b*d*e*n*ArcTan[(Sqrt[g]*x)/Sqrt[f]])/(2*Sqrt[f]*Sqrt[g]*(e^2*f + d^2*g)) + (b*e^2*n*Log[d + e*x])/(2*g*(e^2*f + d^2*g)) - (a + b*Log[c*(d + e*x)^n])/(2*g*(f + g*x^2)) - (b*e^2*n*Log[f + g*x^2])/(4*g*(e^2*f + d^2*g))","A",6,6,25,0.2400,1,"{2413, 706, 31, 635, 205, 260}"
269,1,383,0,0.4533942,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x \left(f+g x^2\right)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(x*(f + g*x^2)^2),x]","-\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f^2}-\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 f^2}+\frac{b n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^2}-\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f^2}-\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f^2}+\frac{\log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}+\frac{a+b \log \left(c (d+e x)^n\right)}{2 f \left(f+g x^2\right)}-\frac{b d e \sqrt{g} n \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{2 f^{3/2} \left(d^2 g+e^2 f\right)}+\frac{b e^2 n \log \left(f+g x^2\right)}{4 f \left(d^2 g+e^2 f\right)}-\frac{b e^2 n \log (d+e x)}{2 f \left(d^2 g+e^2 f\right)}","-\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f^2}-\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 f^2}+\frac{b n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^2}-\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f^2}-\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f^2}+\frac{\log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}+\frac{a+b \log \left(c (d+e x)^n\right)}{2 f \left(f+g x^2\right)}-\frac{b d e \sqrt{g} n \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{2 f^{3/2} \left(d^2 g+e^2 f\right)}+\frac{b e^2 n \log \left(f+g x^2\right)}{4 f \left(d^2 g+e^2 f\right)}-\frac{b e^2 n \log (d+e x)}{2 f \left(d^2 g+e^2 f\right)}",1,"-(b*d*e*Sqrt[g]*n*ArcTan[(Sqrt[g]*x)/Sqrt[f]])/(2*f^(3/2)*(e^2*f + d^2*g)) - (b*e^2*n*Log[d + e*x])/(2*f*(e^2*f + d^2*g)) + (a + b*Log[c*(d + e*x)^n])/(2*f*(f + g*x^2)) + (Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/f^2 - ((a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f^2) - ((a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*f^2) + (b*e^2*n*Log[f + g*x^2])/(4*f*(e^2*f + d^2*g)) - (b*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*f^2) - (b*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f^2) + (b*n*PolyLog[2, 1 + (e*x)/d])/f^2","A",18,13,27,0.4815,1,"{266, 44, 2416, 2394, 2315, 2413, 706, 31, 635, 205, 260, 2393, 2391}"
270,1,460,0,0.5168323,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^3 \left(f+g x^2\right)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(x^3*(f + g*x^2)^2),x]","\frac{b g n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{f^3}+\frac{b g n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{f^3}-\frac{2 b g n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^3}-\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f^2 \left(f+g x^2\right)}-\frac{2 g \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3}+\frac{g \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3}+\frac{g \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3}-\frac{a+b \log \left(c (d+e x)^n\right)}{2 f^2 x^2}+\frac{b d e g^{3/2} n \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{2 f^{5/2} \left(d^2 g+e^2 f\right)}-\frac{b e^2 g n \log \left(f+g x^2\right)}{4 f^2 \left(d^2 g+e^2 f\right)}+\frac{b e^2 g n \log (d+e x)}{2 f^2 \left(d^2 g+e^2 f\right)}-\frac{b e^2 n \log (x)}{2 d^2 f^2}+\frac{b e^2 n \log (d+e x)}{2 d^2 f^2}-\frac{b e n}{2 d f^2 x}","\frac{b g n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{f^3}+\frac{b g n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{f^3}-\frac{2 b g n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^3}-\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f^2 \left(f+g x^2\right)}-\frac{2 g \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3}+\frac{g \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3}+\frac{g \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3}-\frac{a+b \log \left(c (d+e x)^n\right)}{2 f^2 x^2}+\frac{b d e g^{3/2} n \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{2 f^{5/2} \left(d^2 g+e^2 f\right)}-\frac{b e^2 g n \log \left(f+g x^2\right)}{4 f^2 \left(d^2 g+e^2 f\right)}+\frac{b e^2 g n \log (d+e x)}{2 f^2 \left(d^2 g+e^2 f\right)}-\frac{b e^2 n \log (x)}{2 d^2 f^2}+\frac{b e^2 n \log (d+e x)}{2 d^2 f^2}-\frac{b e n}{2 d f^2 x}",1,"-(b*e*n)/(2*d*f^2*x) + (b*d*e*g^(3/2)*n*ArcTan[(Sqrt[g]*x)/Sqrt[f]])/(2*f^(5/2)*(e^2*f + d^2*g)) - (b*e^2*n*Log[x])/(2*d^2*f^2) + (b*e^2*n*Log[d + e*x])/(2*d^2*f^2) + (b*e^2*g*n*Log[d + e*x])/(2*f^2*(e^2*f + d^2*g)) - (a + b*Log[c*(d + e*x)^n])/(2*f^2*x^2) - (g*(a + b*Log[c*(d + e*x)^n]))/(2*f^2*(f + g*x^2)) - (2*g*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/f^3 + (g*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/f^3 + (g*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/f^3 - (b*e^2*g*n*Log[f + g*x^2])/(4*f^2*(e^2*f + d^2*g)) + (b*g*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/f^3 + (b*g*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/f^3 - (2*b*g*n*PolyLog[2, 1 + (e*x)/d])/f^3","A",21,14,27,0.5185,1,"{266, 44, 2416, 2395, 2394, 2315, 2413, 706, 31, 635, 205, 260, 2393, 2391}"
271,1,534,0,0.9299538,"\int \frac{x^4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{\left(f+g x^2\right)^2} \, dx","Int[(x^4*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2)^2,x]","-\frac{3 b \sqrt{-f} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 g^{5/2}}+\frac{3 b \sqrt{-f} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{4 g^{5/2}}-\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 g^{5/2} \left(\sqrt{-f}-\sqrt{g} x\right)}+\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 g^{5/2} \left(\sqrt{-f}+\sqrt{g} x\right)}+\frac{3 \sqrt{-f} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 g^{5/2}}-\frac{3 \sqrt{-f} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 g^{5/2}}+\frac{a x}{g^2}+\frac{b (d+e x) \log \left(c (d+e x)^n\right)}{e g^2}-\frac{b e f n \log (d+e x)}{4 g^{5/2} \left(e \sqrt{-f}-d \sqrt{g}\right)}+\frac{b e f n \log (d+e x)}{4 g^{5/2} \left(d \sqrt{g}+e \sqrt{-f}\right)}-\frac{b e f n \log \left(\sqrt{-f}-\sqrt{g} x\right)}{4 g^{5/2} \left(d \sqrt{g}+e \sqrt{-f}\right)}+\frac{b e f n \log \left(\sqrt{-f}+\sqrt{g} x\right)}{4 g^{5/2} \left(e \sqrt{-f}-d \sqrt{g}\right)}-\frac{b n x}{g^2}","-\frac{3 b \sqrt{-f} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 g^{5/2}}+\frac{3 b \sqrt{-f} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{4 g^{5/2}}-\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 g^{5/2} \left(\sqrt{-f}-\sqrt{g} x\right)}+\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 g^{5/2} \left(\sqrt{-f}+\sqrt{g} x\right)}+\frac{3 \sqrt{-f} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 g^{5/2}}-\frac{3 \sqrt{-f} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 g^{5/2}}+\frac{a x}{g^2}+\frac{b (d+e x) \log \left(c (d+e x)^n\right)}{e g^2}-\frac{b e f n \log (d+e x)}{4 g^{5/2} \left(e \sqrt{-f}-d \sqrt{g}\right)}+\frac{b e f n \log (d+e x)}{4 g^{5/2} \left(d \sqrt{g}+e \sqrt{-f}\right)}-\frac{b e f n \log \left(\sqrt{-f}-\sqrt{g} x\right)}{4 g^{5/2} \left(d \sqrt{g}+e \sqrt{-f}\right)}+\frac{b e f n \log \left(\sqrt{-f}+\sqrt{g} x\right)}{4 g^{5/2} \left(e \sqrt{-f}-d \sqrt{g}\right)}-\frac{b n x}{g^2}",1,"(a*x)/g^2 - (b*n*x)/g^2 - (b*e*f*n*Log[d + e*x])/(4*(e*Sqrt[-f] - d*Sqrt[g])*g^(5/2)) + (b*e*f*n*Log[d + e*x])/(4*(e*Sqrt[-f] + d*Sqrt[g])*g^(5/2)) + (b*(d + e*x)*Log[c*(d + e*x)^n])/(e*g^2) - (f*(a + b*Log[c*(d + e*x)^n]))/(4*g^(5/2)*(Sqrt[-f] - Sqrt[g]*x)) + (f*(a + b*Log[c*(d + e*x)^n]))/(4*g^(5/2)*(Sqrt[-f] + Sqrt[g]*x)) - (b*e*f*n*Log[Sqrt[-f] - Sqrt[g]*x])/(4*(e*Sqrt[-f] + d*Sqrt[g])*g^(5/2)) + (3*Sqrt[-f]*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(4*g^(5/2)) + (b*e*f*n*Log[Sqrt[-f] + Sqrt[g]*x])/(4*(e*Sqrt[-f] - d*Sqrt[g])*g^(5/2)) - (3*Sqrt[-f]*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(4*g^(5/2)) - (3*b*Sqrt[-f]*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(4*g^(5/2)) + (3*b*Sqrt[-f]*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(4*g^(5/2))","A",31,13,27,0.4815,1,"{288, 321, 205, 2416, 2389, 2295, 2409, 2395, 36, 31, 2394, 2393, 2391}"
272,1,491,0,0.7599756,"\int \frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{\left(f+g x^2\right)^2} \, dx","Int[(x^2*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2)^2,x]","-\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 \sqrt{-f} g^{3/2}}+\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{4 \sqrt{-f} g^{3/2}}+\frac{a+b \log \left(c (d+e x)^n\right)}{4 g^{3/2} \left(\sqrt{-f}-\sqrt{g} x\right)}-\frac{a+b \log \left(c (d+e x)^n\right)}{4 g^{3/2} \left(\sqrt{-f}+\sqrt{g} x\right)}+\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 \sqrt{-f} g^{3/2}}-\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 \sqrt{-f} g^{3/2}}+\frac{b e n \log (d+e x)}{4 g^{3/2} \left(e \sqrt{-f}-d \sqrt{g}\right)}-\frac{b e n \log (d+e x)}{4 g^{3/2} \left(d \sqrt{g}+e \sqrt{-f}\right)}+\frac{b e n \log \left(\sqrt{-f}-\sqrt{g} x\right)}{4 g^{3/2} \left(d \sqrt{g}+e \sqrt{-f}\right)}-\frac{b e n \log \left(\sqrt{-f}+\sqrt{g} x\right)}{4 g^{3/2} \left(e \sqrt{-f}-d \sqrt{g}\right)}","-\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 \sqrt{-f} g^{3/2}}+\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{4 \sqrt{-f} g^{3/2}}+\frac{a+b \log \left(c (d+e x)^n\right)}{4 g^{3/2} \left(\sqrt{-f}-\sqrt{g} x\right)}-\frac{a+b \log \left(c (d+e x)^n\right)}{4 g^{3/2} \left(\sqrt{-f}+\sqrt{g} x\right)}+\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 \sqrt{-f} g^{3/2}}-\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 \sqrt{-f} g^{3/2}}+\frac{b e n \log (d+e x)}{4 g^{3/2} \left(e \sqrt{-f}-d \sqrt{g}\right)}-\frac{b e n \log (d+e x)}{4 g^{3/2} \left(d \sqrt{g}+e \sqrt{-f}\right)}+\frac{b e n \log \left(\sqrt{-f}-\sqrt{g} x\right)}{4 g^{3/2} \left(d \sqrt{g}+e \sqrt{-f}\right)}-\frac{b e n \log \left(\sqrt{-f}+\sqrt{g} x\right)}{4 g^{3/2} \left(e \sqrt{-f}-d \sqrt{g}\right)}",1,"(b*e*n*Log[d + e*x])/(4*(e*Sqrt[-f] - d*Sqrt[g])*g^(3/2)) - (b*e*n*Log[d + e*x])/(4*(e*Sqrt[-f] + d*Sqrt[g])*g^(3/2)) + (a + b*Log[c*(d + e*x)^n])/(4*g^(3/2)*(Sqrt[-f] - Sqrt[g]*x)) - (a + b*Log[c*(d + e*x)^n])/(4*g^(3/2)*(Sqrt[-f] + Sqrt[g]*x)) + (b*e*n*Log[Sqrt[-f] - Sqrt[g]*x])/(4*(e*Sqrt[-f] + d*Sqrt[g])*g^(3/2)) + ((a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(4*Sqrt[-f]*g^(3/2)) - (b*e*n*Log[Sqrt[-f] + Sqrt[g]*x])/(4*(e*Sqrt[-f] - d*Sqrt[g])*g^(3/2)) - ((a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(4*Sqrt[-f]*g^(3/2)) - (b*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(4*Sqrt[-f]*g^(3/2)) + (b*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(4*Sqrt[-f]*g^(3/2))","A",28,10,27,0.3704,1,"{288, 205, 2416, 2409, 2395, 36, 31, 2394, 2393, 2391}"
273,1,503,0,0.3935755,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\left(f+g x^2\right)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(f + g*x^2)^2,x]","\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 (-f)^{3/2} \sqrt{g}}-\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{4 (-f)^{3/2} \sqrt{g}}-\frac{a+b \log \left(c (d+e x)^n\right)}{4 f \sqrt{g} \left(\sqrt{-f}-\sqrt{g} x\right)}+\frac{a+b \log \left(c (d+e x)^n\right)}{4 f \sqrt{g} \left(\sqrt{-f}+\sqrt{g} x\right)}-\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 (-f)^{3/2} \sqrt{g}}+\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 (-f)^{3/2} \sqrt{g}}+\frac{b e n \log (d+e x)}{4 f \sqrt{g} \left(d \sqrt{g}+e \sqrt{-f}\right)}+\frac{b e n \log (d+e x)}{4 \sqrt{g} \left(d f \sqrt{g}+e (-f)^{3/2}\right)}-\frac{b e n \log \left(\sqrt{-f}-\sqrt{g} x\right)}{4 f \sqrt{g} \left(d \sqrt{g}+e \sqrt{-f}\right)}-\frac{b e n \log \left(\sqrt{-f}+\sqrt{g} x\right)}{4 \sqrt{g} \left(d f \sqrt{g}+e (-f)^{3/2}\right)}","\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 (-f)^{3/2} \sqrt{g}}-\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{4 (-f)^{3/2} \sqrt{g}}-\frac{a+b \log \left(c (d+e x)^n\right)}{4 f \sqrt{g} \left(\sqrt{-f}-\sqrt{g} x\right)}+\frac{a+b \log \left(c (d+e x)^n\right)}{4 f \sqrt{g} \left(\sqrt{-f}+\sqrt{g} x\right)}-\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 (-f)^{3/2} \sqrt{g}}+\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 (-f)^{3/2} \sqrt{g}}+\frac{b e n \log (d+e x)}{4 f \sqrt{g} \left(d \sqrt{g}+e \sqrt{-f}\right)}+\frac{b e n \log (d+e x)}{4 \sqrt{g} \left(d f \sqrt{g}+e (-f)^{3/2}\right)}-\frac{b e n \log \left(\sqrt{-f}-\sqrt{g} x\right)}{4 f \sqrt{g} \left(d \sqrt{g}+e \sqrt{-f}\right)}-\frac{b e n \log \left(\sqrt{-f}+\sqrt{g} x\right)}{4 \sqrt{g} \left(d f \sqrt{g}+e (-f)^{3/2}\right)}",1,"(b*e*n*Log[d + e*x])/(4*f*(e*Sqrt[-f] + d*Sqrt[g])*Sqrt[g]) + (b*e*n*Log[d + e*x])/(4*(e*(-f)^(3/2) + d*f*Sqrt[g])*Sqrt[g]) - (a + b*Log[c*(d + e*x)^n])/(4*f*Sqrt[g]*(Sqrt[-f] - Sqrt[g]*x)) + (a + b*Log[c*(d + e*x)^n])/(4*f*Sqrt[g]*(Sqrt[-f] + Sqrt[g]*x)) - (b*e*n*Log[Sqrt[-f] - Sqrt[g]*x])/(4*f*(e*Sqrt[-f] + d*Sqrt[g])*Sqrt[g]) - ((a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(4*(-f)^(3/2)*Sqrt[g]) - (b*e*n*Log[Sqrt[-f] + Sqrt[g]*x])/(4*(e*(-f)^(3/2) + d*f*Sqrt[g])*Sqrt[g]) + ((a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(4*(-f)^(3/2)*Sqrt[g]) + (b*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(4*(-f)^(3/2)*Sqrt[g]) - (b*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(4*(-f)^(3/2)*Sqrt[g])","A",18,7,24,0.2917,1,"{2409, 2395, 36, 31, 2394, 2393, 2391}"
274,1,560,0,0.8192673,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^2 \left(f+g x^2\right)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(x^2*(f + g*x^2)^2),x]","\frac{3 b \sqrt{g} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 (-f)^{5/2}}-\frac{3 b \sqrt{g} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{4 (-f)^{5/2}}+\frac{\sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 f^2 \left(\sqrt{-f}-\sqrt{g} x\right)}-\frac{\sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 f^2 \left(\sqrt{-f}+\sqrt{g} x\right)}-\frac{a+b \log \left(c (d+e x)^n\right)}{f^2 x}-\frac{3 \sqrt{g} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 (-f)^{5/2}}+\frac{3 \sqrt{g} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 (-f)^{5/2}}-\frac{b e \sqrt{g} n \log (d+e x)}{4 f^2 \left(d \sqrt{g}+e \sqrt{-f}\right)}+\frac{b e \sqrt{g} n \log \left(\sqrt{-f}-\sqrt{g} x\right)}{4 f^2 \left(d \sqrt{g}+e \sqrt{-f}\right)}+\frac{b e n \log (x)}{d f^2}-\frac{b e n \log (d+e x)}{d f^2}-\frac{b e \sqrt{g} n \log (d+e x)}{4 f \left(d f \sqrt{g}+e (-f)^{3/2}\right)}+\frac{b e \sqrt{g} n \log \left(\sqrt{-f}+\sqrt{g} x\right)}{4 f \left(d f \sqrt{g}+e (-f)^{3/2}\right)}","\frac{3 b \sqrt{g} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 (-f)^{5/2}}-\frac{3 b \sqrt{g} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{4 (-f)^{5/2}}+\frac{\sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 f^2 \left(\sqrt{-f}-\sqrt{g} x\right)}-\frac{\sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 f^2 \left(\sqrt{-f}+\sqrt{g} x\right)}-\frac{a+b \log \left(c (d+e x)^n\right)}{f^2 x}-\frac{3 \sqrt{g} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 (-f)^{5/2}}+\frac{3 \sqrt{g} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 (-f)^{5/2}}-\frac{b e \sqrt{g} n \log (d+e x)}{4 f^2 \left(d \sqrt{g}+e \sqrt{-f}\right)}+\frac{b e \sqrt{g} n \log \left(\sqrt{-f}-\sqrt{g} x\right)}{4 f^2 \left(d \sqrt{g}+e \sqrt{-f}\right)}+\frac{b e n \log (x)}{d f^2}-\frac{b e n \log (d+e x)}{d f^2}-\frac{b e \sqrt{g} n \log (d+e x)}{4 f \left(d f \sqrt{g}+e (-f)^{3/2}\right)}+\frac{b e \sqrt{g} n \log \left(\sqrt{-f}+\sqrt{g} x\right)}{4 f \left(d f \sqrt{g}+e (-f)^{3/2}\right)}",1,"(b*e*n*Log[x])/(d*f^2) - (b*e*n*Log[d + e*x])/(d*f^2) - (b*e*Sqrt[g]*n*Log[d + e*x])/(4*f^2*(e*Sqrt[-f] + d*Sqrt[g])) - (b*e*Sqrt[g]*n*Log[d + e*x])/(4*f*(e*(-f)^(3/2) + d*f*Sqrt[g])) - (a + b*Log[c*(d + e*x)^n])/(f^2*x) + (Sqrt[g]*(a + b*Log[c*(d + e*x)^n]))/(4*f^2*(Sqrt[-f] - Sqrt[g]*x)) - (Sqrt[g]*(a + b*Log[c*(d + e*x)^n]))/(4*f^2*(Sqrt[-f] + Sqrt[g]*x)) + (b*e*Sqrt[g]*n*Log[Sqrt[-f] - Sqrt[g]*x])/(4*f^2*(e*Sqrt[-f] + d*Sqrt[g])) - (3*Sqrt[g]*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(4*(-f)^(5/2)) + (b*e*Sqrt[g]*n*Log[Sqrt[-f] + Sqrt[g]*x])/(4*f*(e*(-f)^(3/2) + d*f*Sqrt[g])) + (3*Sqrt[g]*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(4*(-f)^(5/2)) + (3*b*Sqrt[g]*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(4*(-f)^(5/2)) - (3*b*Sqrt[g]*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(4*(-f)^(5/2))","A",32,12,27,0.4444,1,"{290, 325, 205, 2416, 2395, 36, 29, 31, 2409, 2394, 2393, 2391}"
275,1,326,0,0.4205629,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\sqrt{2+g x^2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/Sqrt[2 + g*x^2],x]","-\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{2} e e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right)}}{d \sqrt{g}-\sqrt{d^2 g+2 e^2}}\right)}{\sqrt{g}}-\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{2} e e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right)}}{\sqrt{d^2 g+2 e^2}+d \sqrt{g}}\right)}{\sqrt{g}}+\frac{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{g}}-\frac{b n \sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right) \log \left(\frac{\sqrt{2} e e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right)}}{d \sqrt{g}-\sqrt{d^2 g+2 e^2}}+1\right)}{\sqrt{g}}-\frac{b n \sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right) \log \left(\frac{\sqrt{2} e e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right)}}{\sqrt{d^2 g+2 e^2}+d \sqrt{g}}+1\right)}{\sqrt{g}}+\frac{b n \sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right)^2}{2 \sqrt{g}}","-\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{2} e e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right)}}{d \sqrt{g}-\sqrt{d^2 g+2 e^2}}\right)}{\sqrt{g}}-\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{2} e e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right)}}{\sqrt{d^2 g+2 e^2}+d \sqrt{g}}\right)}{\sqrt{g}}+\frac{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{g}}-\frac{b n \sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right) \log \left(\frac{\sqrt{2} e e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right)}}{d \sqrt{g}-\sqrt{d^2 g+2 e^2}}+1\right)}{\sqrt{g}}-\frac{b n \sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right) \log \left(\frac{\sqrt{2} e e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right)}}{\sqrt{d^2 g+2 e^2}+d \sqrt{g}}+1\right)}{\sqrt{g}}+\frac{b n \sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right)^2}{2 \sqrt{g}}",1,"(b*n*ArcSinh[(Sqrt[g]*x)/Sqrt[2]]^2)/(2*Sqrt[g]) - (b*n*ArcSinh[(Sqrt[g]*x)/Sqrt[2]]*Log[1 + (Sqrt[2]*e*E^ArcSinh[(Sqrt[g]*x)/Sqrt[2]])/(d*Sqrt[g] - Sqrt[2*e^2 + d^2*g])])/Sqrt[g] - (b*n*ArcSinh[(Sqrt[g]*x)/Sqrt[2]]*Log[1 + (Sqrt[2]*e*E^ArcSinh[(Sqrt[g]*x)/Sqrt[2]])/(d*Sqrt[g] + Sqrt[2*e^2 + d^2*g])])/Sqrt[g] + (ArcSinh[(Sqrt[g]*x)/Sqrt[2]]*(a + b*Log[c*(d + e*x)^n]))/Sqrt[g] - (b*n*PolyLog[2, -((Sqrt[2]*e*E^ArcSinh[(Sqrt[g]*x)/Sqrt[2]])/(d*Sqrt[g] - Sqrt[2*e^2 + d^2*g]))])/Sqrt[g] - (b*n*PolyLog[2, -((Sqrt[2]*e*E^ArcSinh[(Sqrt[g]*x)/Sqrt[2]])/(d*Sqrt[g] + Sqrt[2*e^2 + d^2*g]))])/Sqrt[g]","A",10,8,26,0.3077,1,"{215, 2404, 12, 5799, 5561, 2190, 2279, 2391}"
276,1,506,0,0.5568193,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\sqrt{f+g x^2}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/Sqrt[f + g*x^2],x]","-\frac{b \sqrt{f} n \sqrt{\frac{g x^2}{f}+1} \text{PolyLog}\left(2,-\frac{e \sqrt{f} e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}}{d \sqrt{g}-\sqrt{d^2 g+e^2 f}}\right)}{\sqrt{g} \sqrt{f+g x^2}}-\frac{b \sqrt{f} n \sqrt{\frac{g x^2}{f}+1} \text{PolyLog}\left(2,-\frac{e \sqrt{f} e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}}{\sqrt{d^2 g+e^2 f}+d \sqrt{g}}\right)}{\sqrt{g} \sqrt{f+g x^2}}+\frac{\sqrt{f} \sqrt{\frac{g x^2}{f}+1} \sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{g} \sqrt{f+g x^2}}-\frac{b \sqrt{f} n \sqrt{\frac{g x^2}{f}+1} \sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{e \sqrt{f} e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}}{d \sqrt{g}-\sqrt{d^2 g+e^2 f}}+1\right)}{\sqrt{g} \sqrt{f+g x^2}}-\frac{b \sqrt{f} n \sqrt{\frac{g x^2}{f}+1} \sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{e \sqrt{f} e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}}{\sqrt{d^2 g+e^2 f}+d \sqrt{g}}+1\right)}{\sqrt{g} \sqrt{f+g x^2}}+\frac{b \sqrt{f} n \sqrt{\frac{g x^2}{f}+1} \sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)^2}{2 \sqrt{g} \sqrt{f+g x^2}}","-\frac{b \sqrt{f} n \sqrt{\frac{g x^2}{f}+1} \text{PolyLog}\left(2,-\frac{e \sqrt{f} e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}}{d \sqrt{g}-\sqrt{d^2 g+e^2 f}}\right)}{\sqrt{g} \sqrt{f+g x^2}}-\frac{b \sqrt{f} n \sqrt{\frac{g x^2}{f}+1} \text{PolyLog}\left(2,-\frac{e \sqrt{f} e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}}{\sqrt{d^2 g+e^2 f}+d \sqrt{g}}\right)}{\sqrt{g} \sqrt{f+g x^2}}+\frac{\sqrt{f} \sqrt{\frac{g x^2}{f}+1} \sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{g} \sqrt{f+g x^2}}-\frac{b \sqrt{f} n \sqrt{\frac{g x^2}{f}+1} \sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{e \sqrt{f} e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}}{d \sqrt{g}-\sqrt{d^2 g+e^2 f}}+1\right)}{\sqrt{g} \sqrt{f+g x^2}}-\frac{b \sqrt{f} n \sqrt{\frac{g x^2}{f}+1} \sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{e \sqrt{f} e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}}{\sqrt{d^2 g+e^2 f}+d \sqrt{g}}+1\right)}{\sqrt{g} \sqrt{f+g x^2}}+\frac{b \sqrt{f} n \sqrt{\frac{g x^2}{f}+1} \sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)^2}{2 \sqrt{g} \sqrt{f+g x^2}}",1,"(b*Sqrt[f]*n*Sqrt[1 + (g*x^2)/f]*ArcSinh[(Sqrt[g]*x)/Sqrt[f]]^2)/(2*Sqrt[g]*Sqrt[f + g*x^2]) - (b*Sqrt[f]*n*Sqrt[1 + (g*x^2)/f]*ArcSinh[(Sqrt[g]*x)/Sqrt[f]]*Log[1 + (e*E^ArcSinh[(Sqrt[g]*x)/Sqrt[f]]*Sqrt[f])/(d*Sqrt[g] - Sqrt[e^2*f + d^2*g])])/(Sqrt[g]*Sqrt[f + g*x^2]) - (b*Sqrt[f]*n*Sqrt[1 + (g*x^2)/f]*ArcSinh[(Sqrt[g]*x)/Sqrt[f]]*Log[1 + (e*E^ArcSinh[(Sqrt[g]*x)/Sqrt[f]]*Sqrt[f])/(d*Sqrt[g] + Sqrt[e^2*f + d^2*g])])/(Sqrt[g]*Sqrt[f + g*x^2]) + (Sqrt[f]*Sqrt[1 + (g*x^2)/f]*ArcSinh[(Sqrt[g]*x)/Sqrt[f]]*(a + b*Log[c*(d + e*x)^n]))/(Sqrt[g]*Sqrt[f + g*x^2]) - (b*Sqrt[f]*n*Sqrt[1 + (g*x^2)/f]*PolyLog[2, -((e*E^ArcSinh[(Sqrt[g]*x)/Sqrt[f]]*Sqrt[f])/(d*Sqrt[g] - Sqrt[e^2*f + d^2*g]))])/(Sqrt[g]*Sqrt[f + g*x^2]) - (b*Sqrt[f]*n*Sqrt[1 + (g*x^2)/f]*PolyLog[2, -((e*E^ArcSinh[(Sqrt[g]*x)/Sqrt[f]]*Sqrt[f])/(d*Sqrt[g] + Sqrt[e^2*f + d^2*g]))])/(Sqrt[g]*Sqrt[f + g*x^2])","A",11,9,26,0.3462,1,"{2406, 215, 2404, 12, 5799, 5561, 2190, 2279, 2391}"
277,1,278,0,0.4744535,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\sqrt{2-g x} \sqrt{2+g x}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(Sqrt[2 - g*x]*Sqrt[2 + g*x]),x]","\frac{i b n \text{PolyLog}\left(2,-\frac{2 e e^{i \sin ^{-1}\left(\frac{g x}{2}\right)}}{-\sqrt{4 e^2-d^2 g^2}+i d g}\right)}{g}+\frac{i b n \text{PolyLog}\left(2,-\frac{2 e e^{i \sin ^{-1}\left(\frac{g x}{2}\right)}}{\sqrt{4 e^2-d^2 g^2}+i d g}\right)}{g}+\frac{\sin ^{-1}\left(\frac{g x}{2}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}-\frac{b n \sin ^{-1}\left(\frac{g x}{2}\right) \log \left(1+\frac{2 e e^{i \sin ^{-1}\left(\frac{g x}{2}\right)}}{-\sqrt{4 e^2-d^2 g^2}+i d g}\right)}{g}-\frac{b n \sin ^{-1}\left(\frac{g x}{2}\right) \log \left(1+\frac{2 e e^{i \sin ^{-1}\left(\frac{g x}{2}\right)}}{\sqrt{4 e^2-d^2 g^2}+i d g}\right)}{g}+\frac{i b n \sin ^{-1}\left(\frac{g x}{2}\right)^2}{2 g}","\frac{i b n \text{PolyLog}\left(2,-\frac{2 e e^{i \sin ^{-1}\left(\frac{g x}{2}\right)}}{-\sqrt{4 e^2-d^2 g^2}+i d g}\right)}{g}+\frac{i b n \text{PolyLog}\left(2,-\frac{2 e e^{i \sin ^{-1}\left(\frac{g x}{2}\right)}}{\sqrt{4 e^2-d^2 g^2}+i d g}\right)}{g}+\frac{\sin ^{-1}\left(\frac{g x}{2}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}-\frac{b n \sin ^{-1}\left(\frac{g x}{2}\right) \log \left(1+\frac{2 e e^{i \sin ^{-1}\left(\frac{g x}{2}\right)}}{-\sqrt{4 e^2-d^2 g^2}+i d g}\right)}{g}-\frac{b n \sin ^{-1}\left(\frac{g x}{2}\right) \log \left(1+\frac{2 e e^{i \sin ^{-1}\left(\frac{g x}{2}\right)}}{\sqrt{4 e^2-d^2 g^2}+i d g}\right)}{g}+\frac{i b n \sin ^{-1}\left(\frac{g x}{2}\right)^2}{2 g}",1,"((I/2)*b*n*ArcSin[(g*x)/2]^2)/g - (b*n*ArcSin[(g*x)/2]*Log[1 + (2*e*E^(I*ArcSin[(g*x)/2]))/(I*d*g - Sqrt[4*e^2 - d^2*g^2])])/g - (b*n*ArcSin[(g*x)/2]*Log[1 + (2*e*E^(I*ArcSin[(g*x)/2]))/(I*d*g + Sqrt[4*e^2 - d^2*g^2])])/g + (ArcSin[(g*x)/2]*(a + b*Log[c*(d + e*x)^n]))/g + (I*b*n*PolyLog[2, (-2*e*E^(I*ArcSin[(g*x)/2]))/(I*d*g - Sqrt[4*e^2 - d^2*g^2])])/g + (I*b*n*PolyLog[2, (-2*e*E^(I*ArcSin[(g*x)/2]))/(I*d*g + Sqrt[4*e^2 - d^2*g^2])])/g","A",9,7,34,0.2059,1,"{216, 2405, 4741, 4521, 2190, 2279, 2391}"
278,1,510,0,0.6436739,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\sqrt{f-g x} \sqrt{f+g x}} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/(Sqrt[f - g*x]*Sqrt[f + g*x]),x]","\frac{i b f n \sqrt{1-\frac{g^2 x^2}{f^2}} \text{PolyLog}\left(2,-\frac{e f e^{i \sin ^{-1}\left(\frac{g x}{f}\right)}}{-\sqrt{e^2 f^2-d^2 g^2}+i d g}\right)}{g \sqrt{f-g x} \sqrt{f+g x}}+\frac{i b f n \sqrt{1-\frac{g^2 x^2}{f^2}} \text{PolyLog}\left(2,-\frac{e f e^{i \sin ^{-1}\left(\frac{g x}{f}\right)}}{\sqrt{e^2 f^2-d^2 g^2}+i d g}\right)}{g \sqrt{f-g x} \sqrt{f+g x}}+\frac{f \sqrt{1-\frac{g^2 x^2}{f^2}} \sin ^{-1}\left(\frac{g x}{f}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g \sqrt{f-g x} \sqrt{f+g x}}-\frac{b f n \sqrt{1-\frac{g^2 x^2}{f^2}} \sin ^{-1}\left(\frac{g x}{f}\right) \log \left(1+\frac{e f e^{i \sin ^{-1}\left(\frac{g x}{f}\right)}}{-\sqrt{e^2 f^2-d^2 g^2}+i d g}\right)}{g \sqrt{f-g x} \sqrt{f+g x}}-\frac{b f n \sqrt{1-\frac{g^2 x^2}{f^2}} \sin ^{-1}\left(\frac{g x}{f}\right) \log \left(1+\frac{e f e^{i \sin ^{-1}\left(\frac{g x}{f}\right)}}{\sqrt{e^2 f^2-d^2 g^2}+i d g}\right)}{g \sqrt{f-g x} \sqrt{f+g x}}+\frac{i b f n \sqrt{1-\frac{g^2 x^2}{f^2}} \sin ^{-1}\left(\frac{g x}{f}\right)^2}{2 g \sqrt{f-g x} \sqrt{f+g x}}","\frac{i b f n \sqrt{1-\frac{g^2 x^2}{f^2}} \text{PolyLog}\left(2,-\frac{e f e^{i \sin ^{-1}\left(\frac{g x}{f}\right)}}{-\sqrt{e^2 f^2-d^2 g^2}+i d g}\right)}{g \sqrt{f-g x} \sqrt{f+g x}}+\frac{i b f n \sqrt{1-\frac{g^2 x^2}{f^2}} \text{PolyLog}\left(2,-\frac{e f e^{i \sin ^{-1}\left(\frac{g x}{f}\right)}}{\sqrt{e^2 f^2-d^2 g^2}+i d g}\right)}{g \sqrt{f-g x} \sqrt{f+g x}}+\frac{f \sqrt{1-\frac{g^2 x^2}{f^2}} \sin ^{-1}\left(\frac{g x}{f}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g \sqrt{f-g x} \sqrt{f+g x}}-\frac{b f n \sqrt{1-\frac{g^2 x^2}{f^2}} \sin ^{-1}\left(\frac{g x}{f}\right) \log \left(1+\frac{e f e^{i \sin ^{-1}\left(\frac{g x}{f}\right)}}{-\sqrt{e^2 f^2-d^2 g^2}+i d g}\right)}{g \sqrt{f-g x} \sqrt{f+g x}}-\frac{b f n \sqrt{1-\frac{g^2 x^2}{f^2}} \sin ^{-1}\left(\frac{g x}{f}\right) \log \left(1+\frac{e f e^{i \sin ^{-1}\left(\frac{g x}{f}\right)}}{\sqrt{e^2 f^2-d^2 g^2}+i d g}\right)}{g \sqrt{f-g x} \sqrt{f+g x}}+\frac{i b f n \sqrt{1-\frac{g^2 x^2}{f^2}} \sin ^{-1}\left(\frac{g x}{f}\right)^2}{2 g \sqrt{f-g x} \sqrt{f+g x}}",1,"((I/2)*b*f*n*Sqrt[1 - (g^2*x^2)/f^2]*ArcSin[(g*x)/f]^2)/(g*Sqrt[f - g*x]*Sqrt[f + g*x]) - (b*f*n*Sqrt[1 - (g^2*x^2)/f^2]*ArcSin[(g*x)/f]*Log[1 + (e*E^(I*ArcSin[(g*x)/f])*f)/(I*d*g - Sqrt[e^2*f^2 - d^2*g^2])])/(g*Sqrt[f - g*x]*Sqrt[f + g*x]) - (b*f*n*Sqrt[1 - (g^2*x^2)/f^2]*ArcSin[(g*x)/f]*Log[1 + (e*E^(I*ArcSin[(g*x)/f])*f)/(I*d*g + Sqrt[e^2*f^2 - d^2*g^2])])/(g*Sqrt[f - g*x]*Sqrt[f + g*x]) + (f*Sqrt[1 - (g^2*x^2)/f^2]*ArcSin[(g*x)/f]*(a + b*Log[c*(d + e*x)^n]))/(g*Sqrt[f - g*x]*Sqrt[f + g*x]) + (I*b*f*n*Sqrt[1 - (g^2*x^2)/f^2]*PolyLog[2, -((e*E^(I*ArcSin[(g*x)/f])*f)/(I*d*g - Sqrt[e^2*f^2 - d^2*g^2]))])/(g*Sqrt[f - g*x]*Sqrt[f + g*x]) + (I*b*f*n*Sqrt[1 - (g^2*x^2)/f^2]*PolyLog[2, -((e*E^(I*ArcSin[(g*x)/f])*f)/(I*d*g + Sqrt[e^2*f^2 - d^2*g^2]))])/(g*Sqrt[f - g*x]*Sqrt[f + g*x])","A",11,9,34,0.2647,1,"{2407, 216, 2404, 12, 4741, 4521, 2190, 2279, 2391}"
279,1,24,0,0.0314029,"\int \frac{\log \left(\frac{2 e}{e+f x}\right)}{e^2-f^2 x^2} \, dx","Int[Log[(2*e)/(e + f*x)]/(e^2 - f^2*x^2),x]","\frac{\text{PolyLog}\left(2,1-\frac{2 e}{e+f x}\right)}{2 e f}","\frac{\text{PolyLog}\left(2,1-\frac{2 e}{e+f x}\right)}{2 e f}",1,"PolyLog[2, 1 - (2*e)/(e + f*x)]/(2*e*f)","A",2,2,26,0.07692,1,"{2402, 2315}"
280,1,42,0,0.0544162,"\int \frac{\log \left(\frac{e}{e+f x}\right)}{e^2-f^2 x^2} \, dx","Int[Log[e/(e + f*x)]/(e^2 - f^2*x^2),x]","\frac{\text{PolyLog}\left(2,1-\frac{2 e}{e+f x}\right)}{2 e f}-\frac{\log (2) \tanh ^{-1}\left(\frac{f x}{e}\right)}{e f}","\frac{\text{PolyLog}\left(2,1-\frac{2 e}{e+f x}\right)}{2 e f}-\frac{\log (2) \tanh ^{-1}\left(\frac{f x}{e}\right)}{e f}",1,"-((ArcTanh[(f*x)/e]*Log[2])/(e*f)) + PolyLog[2, 1 - (2*e)/(e + f*x)]/(2*e*f)","A",4,4,25,0.1600,1,"{2403, 208, 2402, 2315}"
281,1,41,0,0.0605801,"\int \frac{a+b \log \left(\frac{2 e}{e+f x}\right)}{e^2-f^2 x^2} \, dx","Int[(a + b*Log[(2*e)/(e + f*x)])/(e^2 - f^2*x^2),x]","\frac{b \text{PolyLog}\left(2,1-\frac{2 e}{e+f x}\right)}{2 e f}+\frac{a \tanh ^{-1}\left(\frac{f x}{e}\right)}{e f}","\frac{b \text{PolyLog}\left(2,1-\frac{2 e}{e+f x}\right)}{2 e f}+\frac{a \tanh ^{-1}\left(\frac{f x}{e}\right)}{e f}",1,"(a*ArcTanh[(f*x)/e])/(e*f) + (b*PolyLog[2, 1 - (2*e)/(e + f*x)])/(2*e*f)","A",4,4,30,0.1333,1,"{2403, 208, 2402, 2315}"
282,1,47,0,0.0648044,"\int \frac{a+b \log \left(\frac{e}{e+f x}\right)}{e^2-f^2 x^2} \, dx","Int[(a + b*Log[e/(e + f*x)])/(e^2 - f^2*x^2),x]","\frac{b \text{PolyLog}\left(2,1-\frac{2 e}{e+f x}\right)}{2 e f}+\frac{(a-b \log (2)) \tanh ^{-1}\left(\frac{f x}{e}\right)}{e f}","\frac{b \text{PolyLog}\left(2,1-\frac{2 e}{e+f x}\right)}{2 e f}+\frac{(a-b \log (2)) \tanh ^{-1}\left(\frac{f x}{e}\right)}{e f}",1,"(ArcTanh[(f*x)/e]*(a - b*Log[2]))/(e*f) + (b*PolyLog[2, 1 - (2*e)/(e + f*x)])/(2*e*f)","A",4,4,29,0.1379,1,"{2403, 208, 2402, 2315}"
283,1,371,0,0.5958238,"\int \frac{x^5 \log (c+d x)}{a+b x^3} \, dx","Int[(x^5*Log[c + d*x])/(a + b*x^3),x]","-\frac{a \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^2}-\frac{a \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)}{3 b^2}-\frac{a \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 b^2}-\frac{a \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^2}-\frac{a \log (c+d x) \log \left(-\frac{d \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 b^2}-\frac{a \log (c+d x) \log \left(\frac{\sqrt[3]{-1} d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)}{3 b^2}-\frac{c^2 x}{3 b d^2}+\frac{c^3 \log (c+d x)}{3 b d^3}+\frac{c x^2}{6 b d}+\frac{x^3 \log (c+d x)}{3 b}-\frac{x^3}{9 b}","-\frac{a \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^2}-\frac{a \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)}{3 b^2}-\frac{a \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 b^2}-\frac{a \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^2}-\frac{a \log (c+d x) \log \left(-\frac{d \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 b^2}-\frac{a \log (c+d x) \log \left(\frac{\sqrt[3]{-1} d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)}{3 b^2}-\frac{c^2 x}{3 b d^2}+\frac{c^3 \log (c+d x)}{3 b d^3}+\frac{c x^2}{6 b d}+\frac{x^3 \log (c+d x)}{3 b}-\frac{x^3}{9 b}",1,"-(c^2*x)/(3*b*d^2) + (c*x^2)/(6*b*d) - x^3/(9*b) + (c^3*Log[c + d*x])/(3*b*d^3) + (x^3*Log[c + d*x])/(3*b) - (a*Log[-((d*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*c - a^(1/3)*d))]*Log[c + d*x])/(3*b^2) - (a*Log[-((d*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(b^(1/3)*c - (-1)^(2/3)*a^(1/3)*d))]*Log[c + d*x])/(3*b^2) - (a*Log[((-1)^(1/3)*d*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/(b^(1/3)*c + (-1)^(1/3)*a^(1/3)*d)]*Log[c + d*x])/(3*b^2) - (a*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)])/(3*b^2) - (a*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c + (-1)^(1/3)*a^(1/3)*d)])/(3*b^2) - (a*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - (-1)^(2/3)*a^(1/3)*d)])/(3*b^2)","A",16,8,19,0.4211,1,"{266, 43, 2416, 2395, 260, 2394, 2393, 2391}"
284,1,292,0,0.2772186,"\int \frac{x^2 \log (c+d x)}{a+b x^3} \, dx","Int[(x^2*Log[c + d*x])/(a + b*x^3),x]","\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)}{3 b}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 b}+\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b}+\frac{\log (c+d x) \log \left(-\frac{d \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 b}+\frac{\log (c+d x) \log \left(\frac{\sqrt[3]{-1} d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)}{3 b}","\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)}{3 b}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 b}+\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b}+\frac{\log (c+d x) \log \left(-\frac{d \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 b}+\frac{\log (c+d x) \log \left(\frac{\sqrt[3]{-1} d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)}{3 b}",1,"(Log[-((d*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*c - a^(1/3)*d))]*Log[c + d*x])/(3*b) + (Log[-((d*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(b^(1/3)*c - (-1)^(2/3)*a^(1/3)*d))]*Log[c + d*x])/(3*b) + (Log[((-1)^(1/3)*d*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/(b^(1/3)*c + (-1)^(1/3)*a^(1/3)*d)]*Log[c + d*x])/(3*b) + PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)]/(3*b) + PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c + (-1)^(1/3)*a^(1/3)*d)]/(3*b) + PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - (-1)^(2/3)*a^(1/3)*d)]/(3*b)","A",11,5,19,0.2632,1,"{260, 2416, 2394, 2393, 2391}"
285,1,324,0,0.4294025,"\int \frac{\log (c+d x)}{x \left(a+b x^3\right)} \, dx","Int[Log[c + d*x]/(x*(a + b*x^3)),x]","-\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a}-\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)}{3 a}-\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 a}+\frac{\text{PolyLog}\left(2,\frac{d x}{c}+1\right)}{a}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a}-\frac{\log (c+d x) \log \left(-\frac{d \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 a}-\frac{\log (c+d x) \log \left(\frac{\sqrt[3]{-1} d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)}{3 a}+\frac{\log \left(-\frac{d x}{c}\right) \log (c+d x)}{a}","-\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a}-\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)}{3 a}-\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 a}+\frac{\text{PolyLog}\left(2,\frac{d x}{c}+1\right)}{a}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a}-\frac{\log (c+d x) \log \left(-\frac{d \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 a}-\frac{\log (c+d x) \log \left(\frac{\sqrt[3]{-1} d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)}{3 a}+\frac{\log \left(-\frac{d x}{c}\right) \log (c+d x)}{a}",1,"(Log[-((d*x)/c)]*Log[c + d*x])/a - (Log[-((d*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*c - a^(1/3)*d))]*Log[c + d*x])/(3*a) - (Log[-((d*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(b^(1/3)*c - (-1)^(2/3)*a^(1/3)*d))]*Log[c + d*x])/(3*a) - (Log[((-1)^(1/3)*d*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/(b^(1/3)*c + (-1)^(1/3)*a^(1/3)*d)]*Log[c + d*x])/(3*a) - PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)]/(3*a) - PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c + (-1)^(1/3)*a^(1/3)*d)]/(3*a) - PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - (-1)^(2/3)*a^(1/3)*d)]/(3*a) + PolyLog[2, 1 + (d*x)/c]/a","A",15,10,19,0.5263,1,"{266, 36, 29, 31, 2416, 2394, 2315, 260, 2393, 2391}"
286,1,414,0,0.4956311,"\int \frac{\log (c+d x)}{x^4 \left(a+b x^3\right)} \, dx","Int[Log[c + d*x]/(x^4*(a + b*x^3)),x]","\frac{b \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^2}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)}{3 a^2}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 a^2}-\frac{b \text{PolyLog}\left(2,\frac{d x}{c}+1\right)}{a^2}-\frac{b \log \left(-\frac{d x}{c}\right) \log (c+d x)}{a^2}+\frac{b \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^2}+\frac{b \log (c+d x) \log \left(-\frac{d \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 a^2}+\frac{b \log (c+d x) \log \left(\frac{\sqrt[3]{-1} d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)}{3 a^2}+\frac{d^2}{3 a c^2 x}+\frac{d^3 \log (x)}{3 a c^3}-\frac{d^3 \log (c+d x)}{3 a c^3}-\frac{d}{6 a c x^2}-\frac{\log (c+d x)}{3 a x^3}","\frac{b \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^2}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)}{3 a^2}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 a^2}-\frac{b \text{PolyLog}\left(2,\frac{d x}{c}+1\right)}{a^2}-\frac{b \log \left(-\frac{d x}{c}\right) \log (c+d x)}{a^2}+\frac{b \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^2}+\frac{b \log (c+d x) \log \left(-\frac{d \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 a^2}+\frac{b \log (c+d x) \log \left(\frac{\sqrt[3]{-1} d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)}{3 a^2}+\frac{d^2}{3 a c^2 x}+\frac{d^3 \log (x)}{3 a c^3}-\frac{d^3 \log (c+d x)}{3 a c^3}-\frac{d}{6 a c x^2}-\frac{\log (c+d x)}{3 a x^3}",1,"-d/(6*a*c*x^2) + d^2/(3*a*c^2*x) + (d^3*Log[x])/(3*a*c^3) - (d^3*Log[c + d*x])/(3*a*c^3) - Log[c + d*x]/(3*a*x^3) - (b*Log[-((d*x)/c)]*Log[c + d*x])/a^2 + (b*Log[-((d*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*c - a^(1/3)*d))]*Log[c + d*x])/(3*a^2) + (b*Log[-((d*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(b^(1/3)*c - (-1)^(2/3)*a^(1/3)*d))]*Log[c + d*x])/(3*a^2) + (b*Log[((-1)^(1/3)*d*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/(b^(1/3)*c + (-1)^(1/3)*a^(1/3)*d)]*Log[c + d*x])/(3*a^2) + (b*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)])/(3*a^2) + (b*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c + (-1)^(1/3)*a^(1/3)*d)])/(3*a^2) + (b*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - (-1)^(2/3)*a^(1/3)*d)])/(3*a^2) - (b*PolyLog[2, 1 + (d*x)/c])/a^2","A",18,9,19,0.4737,1,"{266, 44, 2416, 2395, 2394, 2315, 260, 2393, 2391}"
287,1,416,0,0.7005643,"\int \frac{x^4 \log (c+d x)}{a+b x^3} \, dx","Int[(x^4*Log[c + d*x])/(a + b*x^3),x]","\frac{a^{2/3} \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{5/3}}+\frac{(-1)^{2/3} a^{2/3} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{5/3}}-\frac{\sqrt[3]{-1} a^{2/3} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 b^{5/3}}+\frac{a^{2/3} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{5/3}}-\frac{\sqrt[3]{-1} a^{2/3} \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 b^{5/3}}+\frac{(-1)^{2/3} a^{2/3} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{5/3}}-\frac{c^2 \log (c+d x)}{2 b d^2}+\frac{x^2 \log (c+d x)}{2 b}+\frac{c x}{2 b d}-\frac{x^2}{4 b}","\frac{a^{2/3} \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{5/3}}+\frac{(-1)^{2/3} a^{2/3} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{5/3}}-\frac{\sqrt[3]{-1} a^{2/3} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 b^{5/3}}+\frac{a^{2/3} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{5/3}}-\frac{\sqrt[3]{-1} a^{2/3} \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 b^{5/3}}+\frac{(-1)^{2/3} a^{2/3} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{5/3}}-\frac{c^2 \log (c+d x)}{2 b d^2}+\frac{x^2 \log (c+d x)}{2 b}+\frac{c x}{2 b d}-\frac{x^2}{4 b}",1,"(c*x)/(2*b*d) - x^2/(4*b) - (c^2*Log[c + d*x])/(2*b*d^2) + (x^2*Log[c + d*x])/(2*b) + (a^(2/3)*Log[-((d*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*c - a^(1/3)*d))]*Log[c + d*x])/(3*b^(5/3)) - ((-1)^(1/3)*a^(2/3)*Log[(d*(a^(1/3) - (-1)^(1/3)*b^(1/3)*x))/((-1)^(1/3)*b^(1/3)*c + a^(1/3)*d)]*Log[c + d*x])/(3*b^(5/3)) + ((-1)^(2/3)*a^(2/3)*Log[-((d*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/((-1)^(2/3)*b^(1/3)*c - a^(1/3)*d))]*Log[c + d*x])/(3*b^(5/3)) + (a^(2/3)*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)])/(3*b^(5/3)) + ((-1)^(2/3)*a^(2/3)*PolyLog[2, ((-1)^(2/3)*b^(1/3)*(c + d*x))/((-1)^(2/3)*b^(1/3)*c - a^(1/3)*d)])/(3*b^(5/3)) - ((-1)^(1/3)*a^(2/3)*PolyLog[2, ((-1)^(1/3)*b^(1/3)*(c + d*x))/((-1)^(1/3)*b^(1/3)*c + a^(1/3)*d)])/(3*b^(5/3))","A",16,13,19,0.6842,1,"{321, 292, 31, 634, 617, 204, 628, 2416, 2395, 43, 2394, 2393, 2391}"
288,1,383,0,0.4461209,"\int \frac{x^3 \log (c+d x)}{a+b x^3} \, dx","Int[(x^3*Log[c + d*x])/(a + b*x^3),x]","-\frac{\sqrt[3]{a} \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{4/3}}+\frac{\sqrt[3]{-1} \sqrt[3]{a} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{a} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 b^{4/3}}-\frac{\sqrt[3]{a} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{a} \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 b^{4/3}}+\frac{\sqrt[3]{-1} \sqrt[3]{a} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{4/3}}+\frac{(c+d x) \log (c+d x)}{b d}-\frac{x}{b}","-\frac{\sqrt[3]{a} \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{4/3}}+\frac{\sqrt[3]{-1} \sqrt[3]{a} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{a} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 b^{4/3}}-\frac{\sqrt[3]{a} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{a} \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 b^{4/3}}+\frac{\sqrt[3]{-1} \sqrt[3]{a} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{4/3}}+\frac{(c+d x) \log (c+d x)}{b d}-\frac{x}{b}",1,"-(x/b) + ((c + d*x)*Log[c + d*x])/(b*d) - (a^(1/3)*Log[-((d*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*c - a^(1/3)*d))]*Log[c + d*x])/(3*b^(4/3)) - ((-1)^(2/3)*a^(1/3)*Log[(d*(a^(1/3) - (-1)^(1/3)*b^(1/3)*x))/((-1)^(1/3)*b^(1/3)*c + a^(1/3)*d)]*Log[c + d*x])/(3*b^(4/3)) + ((-1)^(1/3)*a^(1/3)*Log[-((d*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/((-1)^(2/3)*b^(1/3)*c - a^(1/3)*d))]*Log[c + d*x])/(3*b^(4/3)) - (a^(1/3)*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)])/(3*b^(4/3)) + ((-1)^(1/3)*a^(1/3)*PolyLog[2, ((-1)^(2/3)*b^(1/3)*(c + d*x))/((-1)^(2/3)*b^(1/3)*c - a^(1/3)*d)])/(3*b^(4/3)) - ((-1)^(2/3)*a^(1/3)*PolyLog[2, ((-1)^(1/3)*b^(1/3)*(c + d*x))/((-1)^(1/3)*b^(1/3)*c + a^(1/3)*d)])/(3*b^(4/3))","A",15,14,19,0.7368,1,"{321, 200, 31, 634, 617, 204, 628, 2416, 2389, 2295, 2409, 2394, 2393, 2391}"
289,1,359,0,0.3145359,"\int \frac{x \log (c+d x)}{a+b x^3} \, dx","Int[(x*Log[c + d*x])/(a + b*x^3),x]","-\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{(-1)^{2/3} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 \sqrt[3]{a} b^{2/3}}+\frac{\sqrt[3]{-1} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 \sqrt[3]{a} b^{2/3}}+\frac{\sqrt[3]{-1} \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{(-1)^{2/3} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 \sqrt[3]{a} b^{2/3}}","-\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{(-1)^{2/3} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 \sqrt[3]{a} b^{2/3}}+\frac{\sqrt[3]{-1} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 \sqrt[3]{a} b^{2/3}}+\frac{\sqrt[3]{-1} \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{(-1)^{2/3} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 \sqrt[3]{a} b^{2/3}}",1,"-(Log[-((d*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*c - a^(1/3)*d))]*Log[c + d*x])/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*Log[(d*(a^(1/3) - (-1)^(1/3)*b^(1/3)*x))/((-1)^(1/3)*b^(1/3)*c + a^(1/3)*d)]*Log[c + d*x])/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*Log[-((d*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/((-1)^(2/3)*b^(1/3)*c - a^(1/3)*d))]*Log[c + d*x])/(3*a^(1/3)*b^(2/3)) - PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)]/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*PolyLog[2, ((-1)^(2/3)*b^(1/3)*(c + d*x))/((-1)^(2/3)*b^(1/3)*c - a^(1/3)*d)])/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*PolyLog[2, ((-1)^(1/3)*b^(1/3)*(c + d*x))/((-1)^(1/3)*b^(1/3)*c + a^(1/3)*d)])/(3*a^(1/3)*b^(2/3))","A",11,10,17,0.5882,1,"{292, 31, 634, 617, 204, 628, 2416, 2394, 2393, 2391}"
290,1,359,0,0.2388275,"\int \frac{\log (c+d x)}{a+b x^3} \, dx","Int[Log[c + d*x]/(a + b*x^3),x]","\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{2/3} \sqrt[3]{b}}-\frac{\sqrt[3]{-1} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{(-1)^{2/3} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{(-1)^{2/3} \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 a^{2/3} \sqrt[3]{b}}-\frac{\sqrt[3]{-1} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{2/3} \sqrt[3]{b}}","\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{2/3} \sqrt[3]{b}}-\frac{\sqrt[3]{-1} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{(-1)^{2/3} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{(-1)^{2/3} \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 a^{2/3} \sqrt[3]{b}}-\frac{\sqrt[3]{-1} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{2/3} \sqrt[3]{b}}",1,"(Log[-((d*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*c - a^(1/3)*d))]*Log[c + d*x])/(3*a^(2/3)*b^(1/3)) + ((-1)^(2/3)*Log[(d*(a^(1/3) - (-1)^(1/3)*b^(1/3)*x))/((-1)^(1/3)*b^(1/3)*c + a^(1/3)*d)]*Log[c + d*x])/(3*a^(2/3)*b^(1/3)) - ((-1)^(1/3)*Log[-((d*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/((-1)^(2/3)*b^(1/3)*c - a^(1/3)*d))]*Log[c + d*x])/(3*a^(2/3)*b^(1/3)) + PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)]/(3*a^(2/3)*b^(1/3)) - ((-1)^(1/3)*PolyLog[2, ((-1)^(2/3)*b^(1/3)*(c + d*x))/((-1)^(2/3)*b^(1/3)*c - a^(1/3)*d)])/(3*a^(2/3)*b^(1/3)) + ((-1)^(2/3)*PolyLog[2, ((-1)^(1/3)*b^(1/3)*(c + d*x))/((-1)^(1/3)*b^(1/3)*c + a^(1/3)*d)])/(3*a^(2/3)*b^(1/3))","A",11,4,16,0.2500,1,"{2409, 2394, 2393, 2391}"
291,1,398,0,0.4937229,"\int \frac{\log (c+d x)}{x^2 \left(a+b x^3\right)} \, dx","Int[Log[c + d*x]/(x^2*(a + b*x^3)),x]","\frac{\sqrt[3]{b} \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{4/3}}+\frac{(-1)^{2/3} \sqrt[3]{b} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{b} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 a^{4/3}}+\frac{\sqrt[3]{b} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{b} \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 a^{4/3}}+\frac{(-1)^{2/3} \sqrt[3]{b} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{4/3}}+\frac{d \log (x)}{a c}-\frac{d \log (c+d x)}{a c}-\frac{\log (c+d x)}{a x}","\frac{\sqrt[3]{b} \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{4/3}}+\frac{(-1)^{2/3} \sqrt[3]{b} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{b} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 a^{4/3}}+\frac{\sqrt[3]{b} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{b} \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 a^{4/3}}+\frac{(-1)^{2/3} \sqrt[3]{b} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{4/3}}+\frac{d \log (x)}{a c}-\frac{d \log (c+d x)}{a c}-\frac{\log (c+d x)}{a x}",1,"(d*Log[x])/(a*c) - (d*Log[c + d*x])/(a*c) - Log[c + d*x]/(a*x) + (b^(1/3)*Log[-((d*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*c - a^(1/3)*d))]*Log[c + d*x])/(3*a^(4/3)) - ((-1)^(1/3)*b^(1/3)*Log[(d*(a^(1/3) - (-1)^(1/3)*b^(1/3)*x))/((-1)^(1/3)*b^(1/3)*c + a^(1/3)*d)]*Log[c + d*x])/(3*a^(4/3)) + ((-1)^(2/3)*b^(1/3)*Log[-((d*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/((-1)^(2/3)*b^(1/3)*c - a^(1/3)*d))]*Log[c + d*x])/(3*a^(4/3)) + (b^(1/3)*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)])/(3*a^(4/3)) + ((-1)^(2/3)*b^(1/3)*PolyLog[2, ((-1)^(2/3)*b^(1/3)*(c + d*x))/((-1)^(2/3)*b^(1/3)*c - a^(1/3)*d)])/(3*a^(4/3)) - ((-1)^(1/3)*b^(1/3)*PolyLog[2, ((-1)^(1/3)*b^(1/3)*(c + d*x))/((-1)^(1/3)*b^(1/3)*c + a^(1/3)*d)])/(3*a^(4/3))","A",17,14,19,0.7368,1,"{325, 292, 31, 634, 617, 204, 628, 2416, 2395, 36, 29, 2394, 2393, 2391}"
292,1,423,0,0.4376093,"\int \frac{\log (c+d x)}{x^3 \left(a+b x^3\right)} \, dx","Int[Log[c + d*x]/(x^3*(a + b*x^3)),x]","-\frac{b^{2/3} \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{5/3}}+\frac{\sqrt[3]{-1} b^{2/3} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{5/3}}-\frac{(-1)^{2/3} b^{2/3} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 a^{5/3}}-\frac{b^{2/3} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{5/3}}-\frac{(-1)^{2/3} b^{2/3} \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 a^{5/3}}+\frac{\sqrt[3]{-1} b^{2/3} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{5/3}}-\frac{d^2 \log (x)}{2 a c^2}+\frac{d^2 \log (c+d x)}{2 a c^2}-\frac{\log (c+d x)}{2 a x^2}-\frac{d}{2 a c x}","-\frac{b^{2/3} \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{5/3}}+\frac{\sqrt[3]{-1} b^{2/3} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{5/3}}-\frac{(-1)^{2/3} b^{2/3} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 a^{5/3}}-\frac{b^{2/3} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{5/3}}-\frac{(-1)^{2/3} b^{2/3} \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} c}\right)}{3 a^{5/3}}+\frac{\sqrt[3]{-1} b^{2/3} \log (c+d x) \log \left(-\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^{5/3}}-\frac{d^2 \log (x)}{2 a c^2}+\frac{d^2 \log (c+d x)}{2 a c^2}-\frac{\log (c+d x)}{2 a x^2}-\frac{d}{2 a c x}",1,"-d/(2*a*c*x) - (d^2*Log[x])/(2*a*c^2) + (d^2*Log[c + d*x])/(2*a*c^2) - Log[c + d*x]/(2*a*x^2) - (b^(2/3)*Log[-((d*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*c - a^(1/3)*d))]*Log[c + d*x])/(3*a^(5/3)) - ((-1)^(2/3)*b^(2/3)*Log[(d*(a^(1/3) - (-1)^(1/3)*b^(1/3)*x))/((-1)^(1/3)*b^(1/3)*c + a^(1/3)*d)]*Log[c + d*x])/(3*a^(5/3)) + ((-1)^(1/3)*b^(2/3)*Log[-((d*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/((-1)^(2/3)*b^(1/3)*c - a^(1/3)*d))]*Log[c + d*x])/(3*a^(5/3)) - (b^(2/3)*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)])/(3*a^(5/3)) + ((-1)^(1/3)*b^(2/3)*PolyLog[2, ((-1)^(2/3)*b^(1/3)*(c + d*x))/((-1)^(2/3)*b^(1/3)*c - a^(1/3)*d)])/(3*a^(5/3)) - ((-1)^(2/3)*b^(2/3)*PolyLog[2, ((-1)^(1/3)*b^(1/3)*(c + d*x))/((-1)^(1/3)*b^(1/3)*c + a^(1/3)*d)])/(3*a^(5/3))","A",16,14,19,0.7368,1,"{325, 200, 31, 634, 617, 204, 628, 2416, 2395, 44, 2409, 2394, 2393, 2391}"
293,1,498,0,0.810366,"\int \frac{x^7 \log (c+d x)}{a+b x^4} \, dx","Int[(x^7*Log[c + d*x])/(a + b*x^4),x]","-\frac{a \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^2}-\frac{a \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 b^2}-\frac{a \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^2}-\frac{a \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 b^2}-\frac{a \log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 b^2}-\frac{a \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 b^2}-\frac{a \log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^2}-\frac{a \log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^2}-\frac{c^2 x^2}{8 b d^2}+\frac{c^3 x}{4 b d^3}-\frac{c^4 \log (c+d x)}{4 b d^4}+\frac{c x^3}{12 b d}+\frac{x^4 \log (c+d x)}{4 b}-\frac{x^4}{16 b}","-\frac{a \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^2}-\frac{a \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 b^2}-\frac{a \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^2}-\frac{a \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 b^2}-\frac{a \log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 b^2}-\frac{a \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 b^2}-\frac{a \log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^2}-\frac{a \log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^2}-\frac{c^2 x^2}{8 b d^2}+\frac{c^3 x}{4 b d^3}-\frac{c^4 \log (c+d x)}{4 b d^4}+\frac{c x^3}{12 b d}+\frac{x^4 \log (c+d x)}{4 b}-\frac{x^4}{16 b}",1,"(c^3*x)/(4*b*d^3) - (c^2*x^2)/(8*b*d^2) + (c*x^3)/(12*b*d) - x^4/(16*b) - (c^4*Log[c + d*x])/(4*b*d^4) + (x^4*Log[c + d*x])/(4*b) - (a*Log[(d*(Sqrt[-Sqrt[-a]] - b^(1/4)*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)]*Log[c + d*x])/(4*b^2) - (a*Log[(d*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x])/(4*b^2) - (a*Log[-((d*(Sqrt[-Sqrt[-a]] + b^(1/4)*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d))]*Log[c + d*x])/(4*b^2) - (a*Log[-((d*((-a)^(1/4) + b^(1/4)*x))/(b^(1/4)*c - (-a)^(1/4)*d))]*Log[c + d*x])/(4*b^2) - (a*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d)])/(4*b^2) - (a*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)])/(4*b^2) - (a*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)])/(4*b^2) - (a*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)])/(4*b^2)","A",23,8,19,0.4211,1,"{266, 43, 2416, 2395, 260, 2394, 2393, 2391}"
294,1,401,0,0.4601359,"\int \frac{x^3 \log (c+d x)}{a+b x^4} \, dx","Int[(x^3*Log[c + d*x])/(a + b*x^4),x]","\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 b}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 b}+\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 b}+\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 b}+\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b}+\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b}","\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 b}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 b}+\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 b}+\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 b}+\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b}+\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b}",1,"(Log[(d*(Sqrt[-Sqrt[-a]] - b^(1/4)*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)]*Log[c + d*x])/(4*b) + (Log[(d*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x])/(4*b) + (Log[-((d*(Sqrt[-Sqrt[-a]] + b^(1/4)*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d))]*Log[c + d*x])/(4*b) + (Log[-((d*((-a)^(1/4) + b^(1/4)*x))/(b^(1/4)*c - (-a)^(1/4)*d))]*Log[c + d*x])/(4*b) + PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d)]/(4*b) + PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)]/(4*b) + PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)]/(4*b) + PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)]/(4*b)","A",18,5,19,0.2632,1,"{260, 2416, 2394, 2393, 2391}"
295,1,433,0,0.5945847,"\int \frac{\log (c+d x)}{x \left(a+b x^4\right)} \, dx","Int[Log[c + d*x]/(x*(a + b*x^4)),x]","-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 a}-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 a}-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 a}-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 a}+\frac{\text{PolyLog}\left(2,\frac{d x}{c}+1\right)}{a}-\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 a}-\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 a}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 a}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 a}+\frac{\log \left(-\frac{d x}{c}\right) \log (c+d x)}{a}","-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 a}-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 a}-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 a}-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 a}+\frac{\text{PolyLog}\left(2,\frac{d x}{c}+1\right)}{a}-\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 a}-\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 a}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 a}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 a}+\frac{\log \left(-\frac{d x}{c}\right) \log (c+d x)}{a}",1,"(Log[-((d*x)/c)]*Log[c + d*x])/a - (Log[(d*(Sqrt[-Sqrt[-a]] - b^(1/4)*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)]*Log[c + d*x])/(4*a) - (Log[(d*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x])/(4*a) - (Log[-((d*(Sqrt[-Sqrt[-a]] + b^(1/4)*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d))]*Log[c + d*x])/(4*a) - (Log[-((d*((-a)^(1/4) + b^(1/4)*x))/(b^(1/4)*c - (-a)^(1/4)*d))]*Log[c + d*x])/(4*a) - PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d)]/(4*a) - PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)]/(4*a) - PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)]/(4*a) - PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)]/(4*a) + PolyLog[2, 1 + (d*x)/c]/a","A",22,10,19,0.5263,1,"{266, 36, 29, 31, 2416, 2394, 2315, 260, 2393, 2391}"
296,1,530,0,0.6478872,"\int \frac{x^5 \log (c+d x)}{a+b x^4} \, dx","Int[(x^5*Log[c + d*x])/(a + b*x^4),x]","-\frac{\sqrt{-a} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^{3/2}}-\frac{\sqrt{-a} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 b^{3/2}}+\frac{\sqrt{-a} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^{3/2}}+\frac{\sqrt{-a} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 b^{3/2}}-\frac{\sqrt{-a} \log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 b^{3/2}}+\frac{\sqrt{-a} \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 b^{3/2}}-\frac{\sqrt{-a} \log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^{3/2}}+\frac{\sqrt{-a} \log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^{3/2}}-\frac{c^2 \log (c+d x)}{2 b d^2}+\frac{x^2 \log (c+d x)}{2 b}+\frac{c x}{2 b d}-\frac{x^2}{4 b}","-\frac{\sqrt{-a} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^{3/2}}-\frac{\sqrt{-a} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 b^{3/2}}+\frac{\sqrt{-a} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^{3/2}}+\frac{\sqrt{-a} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 b^{3/2}}-\frac{\sqrt{-a} \log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 b^{3/2}}+\frac{\sqrt{-a} \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 b^{3/2}}-\frac{\sqrt{-a} \log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^{3/2}}+\frac{\sqrt{-a} \log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^{3/2}}-\frac{c^2 \log (c+d x)}{2 b d^2}+\frac{x^2 \log (c+d x)}{2 b}+\frac{c x}{2 b d}-\frac{x^2}{4 b}",1,"(c*x)/(2*b*d) - x^2/(4*b) - (c^2*Log[c + d*x])/(2*b*d^2) + (x^2*Log[c + d*x])/(2*b) - (Sqrt[-a]*Log[(d*(Sqrt[-Sqrt[-a]] - b^(1/4)*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)]*Log[c + d*x])/(4*b^(3/2)) + (Sqrt[-a]*Log[(d*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x])/(4*b^(3/2)) - (Sqrt[-a]*Log[-((d*(Sqrt[-Sqrt[-a]] + b^(1/4)*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d))]*Log[c + d*x])/(4*b^(3/2)) + (Sqrt[-a]*Log[-((d*((-a)^(1/4) + b^(1/4)*x))/(b^(1/4)*c - (-a)^(1/4)*d))]*Log[c + d*x])/(4*b^(3/2)) - (Sqrt[-a]*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d)])/(4*b^(3/2)) - (Sqrt[-a]*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)])/(4*b^(3/2)) + (Sqrt[-a]*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)])/(4*b^(3/2)) + (Sqrt[-a]*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)])/(4*b^(3/2))","A",23,10,19,0.5263,1,"{275, 321, 205, 2416, 2395, 43, 260, 2394, 2393, 2391}"
297,1,473,0,0.4727922,"\int \frac{x \log (c+d x)}{a+b x^4} \, dx","Int[(x*Log[c + d*x])/(a + b*x^4),x]","-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 \sqrt{-a} \sqrt{b}}","-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 \sqrt{-a} \sqrt{b}}",1,"-(Log[(d*(Sqrt[-Sqrt[-a]] - b^(1/4)*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)]*Log[c + d*x])/(4*Sqrt[-a]*Sqrt[b]) + (Log[(d*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x])/(4*Sqrt[-a]*Sqrt[b]) - (Log[-((d*(Sqrt[-Sqrt[-a]] + b^(1/4)*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d))]*Log[c + d*x])/(4*Sqrt[-a]*Sqrt[b]) + (Log[-((d*((-a)^(1/4) + b^(1/4)*x))/(b^(1/4)*c - (-a)^(1/4)*d))]*Log[c + d*x])/(4*Sqrt[-a]*Sqrt[b]) - PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d)]/(4*Sqrt[-a]*Sqrt[b]) - PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)]/(4*Sqrt[-a]*Sqrt[b]) + PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)]/(4*Sqrt[-a]*Sqrt[b]) + PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)]/(4*Sqrt[-a]*Sqrt[b])","A",18,7,17,0.4118,1,"{275, 205, 2416, 260, 2394, 2393, 2391}"
298,1,537,0,0.6509771,"\int \frac{\log (c+d x)}{x^3 \left(a+b x^4\right)} \, dx","Int[Log[c + d*x]/(x^3*(a + b*x^4)),x]","-\frac{\sqrt{b} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 (-a)^{3/2}}-\frac{\sqrt{b} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 (-a)^{3/2}}+\frac{\sqrt{b} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 (-a)^{3/2}}+\frac{\sqrt{b} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 (-a)^{3/2}}-\frac{\sqrt{b} \log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 (-a)^{3/2}}+\frac{\sqrt{b} \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 (-a)^{3/2}}-\frac{\sqrt{b} \log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 (-a)^{3/2}}+\frac{\sqrt{b} \log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 (-a)^{3/2}}-\frac{d^2 \log (x)}{2 a c^2}+\frac{d^2 \log (c+d x)}{2 a c^2}-\frac{\log (c+d x)}{2 a x^2}-\frac{d}{2 a c x}","-\frac{\sqrt{b} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 (-a)^{3/2}}-\frac{\sqrt{b} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 (-a)^{3/2}}+\frac{\sqrt{b} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 (-a)^{3/2}}+\frac{\sqrt{b} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 (-a)^{3/2}}-\frac{\sqrt{b} \log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 (-a)^{3/2}}+\frac{\sqrt{b} \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 (-a)^{3/2}}-\frac{\sqrt{b} \log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 (-a)^{3/2}}+\frac{\sqrt{b} \log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 (-a)^{3/2}}-\frac{d^2 \log (x)}{2 a c^2}+\frac{d^2 \log (c+d x)}{2 a c^2}-\frac{\log (c+d x)}{2 a x^2}-\frac{d}{2 a c x}",1,"-d/(2*a*c*x) - (d^2*Log[x])/(2*a*c^2) + (d^2*Log[c + d*x])/(2*a*c^2) - Log[c + d*x]/(2*a*x^2) - (Sqrt[b]*Log[(d*(Sqrt[-Sqrt[-a]] - b^(1/4)*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)]*Log[c + d*x])/(4*(-a)^(3/2)) + (Sqrt[b]*Log[(d*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x])/(4*(-a)^(3/2)) - (Sqrt[b]*Log[-((d*(Sqrt[-Sqrt[-a]] + b^(1/4)*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d))]*Log[c + d*x])/(4*(-a)^(3/2)) + (Sqrt[b]*Log[-((d*((-a)^(1/4) + b^(1/4)*x))/(b^(1/4)*c - (-a)^(1/4)*d))]*Log[c + d*x])/(4*(-a)^(3/2)) - (Sqrt[b]*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d)])/(4*(-a)^(3/2)) - (Sqrt[b]*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)])/(4*(-a)^(3/2)) + (Sqrt[b]*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)])/(4*(-a)^(3/2)) + (Sqrt[b]*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)])/(4*(-a)^(3/2))","A",23,10,19,0.5263,1,"{275, 325, 205, 2416, 2395, 44, 260, 2394, 2393, 2391}"
299,1,521,0,0.7556263,"\int \frac{x^4 \log (c+d x)}{a+b x^4} \, dx","Int[(x^4*Log[c + d*x])/(a + b*x^4),x]","-\frac{\sqrt{-\sqrt{-a}} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^{5/4}}+\frac{\sqrt{-\sqrt{-a}} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 b^{5/4}}-\frac{\sqrt[4]{-a} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^{5/4}}+\frac{\sqrt[4]{-a} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 b^{5/4}}+\frac{\sqrt{-\sqrt{-a}} \log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 b^{5/4}}+\frac{\sqrt[4]{-a} \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 b^{5/4}}-\frac{\sqrt{-\sqrt{-a}} \log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^{5/4}}-\frac{\sqrt[4]{-a} \log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^{5/4}}+\frac{(c+d x) \log (c+d x)}{b d}-\frac{x}{b}","-\frac{\sqrt{-\sqrt{-a}} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^{5/4}}+\frac{\sqrt{-\sqrt{-a}} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 b^{5/4}}-\frac{\sqrt[4]{-a} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^{5/4}}+\frac{\sqrt[4]{-a} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 b^{5/4}}+\frac{\sqrt{-\sqrt{-a}} \log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 b^{5/4}}+\frac{\sqrt[4]{-a} \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 b^{5/4}}-\frac{\sqrt{-\sqrt{-a}} \log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^{5/4}}-\frac{\sqrt[4]{-a} \log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^{5/4}}+\frac{(c+d x) \log (c+d x)}{b d}-\frac{x}{b}",1,"-(x/b) + ((c + d*x)*Log[c + d*x])/(b*d) + (Sqrt[-Sqrt[-a]]*Log[(d*(Sqrt[-Sqrt[-a]] - b^(1/4)*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)]*Log[c + d*x])/(4*b^(5/4)) + ((-a)^(1/4)*Log[(d*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x])/(4*b^(5/4)) - (Sqrt[-Sqrt[-a]]*Log[-((d*(Sqrt[-Sqrt[-a]] + b^(1/4)*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d))]*Log[c + d*x])/(4*b^(5/4)) - ((-a)^(1/4)*Log[-((d*((-a)^(1/4) + b^(1/4)*x))/(b^(1/4)*c - (-a)^(1/4)*d))]*Log[c + d*x])/(4*b^(5/4)) - (Sqrt[-Sqrt[-a]]*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d)])/(4*b^(5/4)) + (Sqrt[-Sqrt[-a]]*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)])/(4*b^(5/4)) - ((-a)^(1/4)*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)])/(4*b^(5/4)) + ((-a)^(1/4)*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)])/(4*b^(5/4))","A",22,14,19,0.7368,1,"{321, 211, 1165, 628, 1162, 617, 204, 2416, 2389, 2295, 2409, 2394, 2393, 2391}"
300,1,497,0,0.5406136,"\int \frac{x^2 \log (c+d x)}{a+b x^4} \, dx","Int[(x^2*Log[c + d*x])/(a + b*x^4),x]","-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \sqrt{-\sqrt{-a}} b^{3/4}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 \sqrt{-\sqrt{-a}} b^{3/4}}-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 \sqrt[4]{-a} b^{3/4}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 \sqrt[4]{-a} b^{3/4}}+\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 \sqrt{-\sqrt{-a}} b^{3/4}}+\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 \sqrt[4]{-a} b^{3/4}}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \sqrt{-\sqrt{-a}} b^{3/4}}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 \sqrt[4]{-a} b^{3/4}}","-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \sqrt{-\sqrt{-a}} b^{3/4}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 \sqrt{-\sqrt{-a}} b^{3/4}}-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 \sqrt[4]{-a} b^{3/4}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 \sqrt[4]{-a} b^{3/4}}+\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 \sqrt{-\sqrt{-a}} b^{3/4}}+\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 \sqrt[4]{-a} b^{3/4}}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \sqrt{-\sqrt{-a}} b^{3/4}}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 \sqrt[4]{-a} b^{3/4}}",1,"(Log[(d*(Sqrt[-Sqrt[-a]] - b^(1/4)*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)]*Log[c + d*x])/(4*Sqrt[-Sqrt[-a]]*b^(3/4)) + (Log[(d*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x])/(4*(-a)^(1/4)*b^(3/4)) - (Log[-((d*(Sqrt[-Sqrt[-a]] + b^(1/4)*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d))]*Log[c + d*x])/(4*Sqrt[-Sqrt[-a]]*b^(3/4)) - (Log[-((d*((-a)^(1/4) + b^(1/4)*x))/(b^(1/4)*c - (-a)^(1/4)*d))]*Log[c + d*x])/(4*(-a)^(1/4)*b^(3/4)) - PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d)]/(4*Sqrt[-Sqrt[-a]]*b^(3/4)) + PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)]/(4*Sqrt[-Sqrt[-a]]*b^(3/4)) - PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)]/(4*(-a)^(1/4)*b^(3/4)) + PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)]/(4*(-a)^(1/4)*b^(3/4))","A",18,11,19,0.5789,1,"{297, 1162, 617, 204, 1165, 628, 2416, 2409, 2394, 2393, 2391}"
301,1,497,0,0.4156273,"\int \frac{\log (c+d x)}{a+b x^4} \, dx","Int[Log[c + d*x]/(a + b*x^4),x]","-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \left(-\sqrt{-a}\right)^{3/2} \sqrt[4]{b}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 \left(-\sqrt{-a}\right)^{3/2} \sqrt[4]{b}}-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 (-a)^{3/4} \sqrt[4]{b}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 (-a)^{3/4} \sqrt[4]{b}}+\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 \left(-\sqrt{-a}\right)^{3/2} \sqrt[4]{b}}+\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 (-a)^{3/4} \sqrt[4]{b}}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \left(-\sqrt{-a}\right)^{3/2} \sqrt[4]{b}}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 (-a)^{3/4} \sqrt[4]{b}}","-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \left(-\sqrt{-a}\right)^{3/2} \sqrt[4]{b}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 \left(-\sqrt{-a}\right)^{3/2} \sqrt[4]{b}}-\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 (-a)^{3/4} \sqrt[4]{b}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 (-a)^{3/4} \sqrt[4]{b}}+\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 \left(-\sqrt{-a}\right)^{3/2} \sqrt[4]{b}}+\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 (-a)^{3/4} \sqrt[4]{b}}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \left(-\sqrt{-a}\right)^{3/2} \sqrt[4]{b}}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 (-a)^{3/4} \sqrt[4]{b}}",1,"(Log[(d*(Sqrt[-Sqrt[-a]] - b^(1/4)*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)]*Log[c + d*x])/(4*(-Sqrt[-a])^(3/2)*b^(1/4)) + (Log[(d*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x])/(4*(-a)^(3/4)*b^(1/4)) - (Log[-((d*(Sqrt[-Sqrt[-a]] + b^(1/4)*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d))]*Log[c + d*x])/(4*(-Sqrt[-a])^(3/2)*b^(1/4)) - (Log[-((d*((-a)^(1/4) + b^(1/4)*x))/(b^(1/4)*c - (-a)^(1/4)*d))]*Log[c + d*x])/(4*(-a)^(3/4)*b^(1/4)) - PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d)]/(4*(-Sqrt[-a])^(3/2)*b^(1/4)) + PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)]/(4*(-Sqrt[-a])^(3/2)*b^(1/4)) - PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)]/(4*(-a)^(3/4)*b^(1/4)) + PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)]/(4*(-a)^(3/4)*b^(1/4))","A",18,4,16,0.2500,1,"{2409, 2394, 2393, 2391}"
302,1,536,0,0.816492,"\int \frac{\log (c+d x)}{x^2 \left(a+b x^4\right)} \, dx","Int[Log[c + d*x]/(x^2*(a + b*x^4)),x]","-\frac{\sqrt[4]{b} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \left(-\sqrt{-a}\right)^{5/2}}+\frac{\sqrt[4]{b} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 \left(-\sqrt{-a}\right)^{5/2}}-\frac{\sqrt[4]{b} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 (-a)^{5/4}}+\frac{\sqrt[4]{b} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 (-a)^{5/4}}+\frac{\sqrt[4]{b} \log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 \left(-\sqrt{-a}\right)^{5/2}}+\frac{\sqrt[4]{b} \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 (-a)^{5/4}}-\frac{\sqrt[4]{b} \log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \left(-\sqrt{-a}\right)^{5/2}}-\frac{\sqrt[4]{b} \log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 (-a)^{5/4}}+\frac{d \log (x)}{a c}-\frac{d \log (c+d x)}{a c}-\frac{\log (c+d x)}{a x}","-\frac{\sqrt[4]{b} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \left(-\sqrt{-a}\right)^{5/2}}+\frac{\sqrt[4]{b} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 \left(-\sqrt{-a}\right)^{5/2}}-\frac{\sqrt[4]{b} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 (-a)^{5/4}}+\frac{\sqrt[4]{b} \text{PolyLog}\left(2,\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 (-a)^{5/4}}+\frac{\sqrt[4]{b} \log (c+d x) \log \left(\frac{d \left(\sqrt{-\sqrt{-a}}-\sqrt[4]{b} x\right)}{\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c}\right)}{4 \left(-\sqrt{-a}\right)^{5/2}}+\frac{\sqrt[4]{b} \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-\sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+\sqrt[4]{b} c}\right)}{4 (-a)^{5/4}}-\frac{\sqrt[4]{b} \log (c+d x) \log \left(-\frac{d \left(\sqrt{-\sqrt{-a}}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \left(-\sqrt{-a}\right)^{5/2}}-\frac{\sqrt[4]{b} \log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{-a}+\sqrt[4]{b} x\right)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 (-a)^{5/4}}+\frac{d \log (x)}{a c}-\frac{d \log (c+d x)}{a c}-\frac{\log (c+d x)}{a x}",1,"(d*Log[x])/(a*c) - (d*Log[c + d*x])/(a*c) - Log[c + d*x]/(a*x) + (b^(1/4)*Log[(d*(Sqrt[-Sqrt[-a]] - b^(1/4)*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)]*Log[c + d*x])/(4*(-Sqrt[-a])^(5/2)) + (b^(1/4)*Log[(d*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x])/(4*(-a)^(5/4)) - (b^(1/4)*Log[-((d*(Sqrt[-Sqrt[-a]] + b^(1/4)*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d))]*Log[c + d*x])/(4*(-Sqrt[-a])^(5/2)) - (b^(1/4)*Log[-((d*((-a)^(1/4) + b^(1/4)*x))/(b^(1/4)*c - (-a)^(1/4)*d))]*Log[c + d*x])/(4*(-a)^(5/4)) - (b^(1/4)*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d)])/(4*(-Sqrt[-a])^(5/2)) + (b^(1/4)*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)])/(4*(-Sqrt[-a])^(5/2)) - (b^(1/4)*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)])/(4*(-a)^(5/4)) + (b^(1/4)*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)])/(4*(-a)^(5/4))","A",24,16,19,0.8421,1,"{325, 297, 1162, 617, 204, 1165, 628, 2416, 2395, 36, 29, 31, 2409, 2394, 2393, 2391}"
303,1,91,0,0.0639724,"\int \left(f+\frac{g}{x}\right) x \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Int[(f + g/x)*x*(a + b*Log[c*(d + e*x)^n]),x]","\frac{(f x+g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f}-\frac{b n (d f-e g)^2 \log (d+e x)}{2 e^2 f}+\frac{b n x (d f-e g)}{2 e}-\frac{b n (f x+g)^2}{4 f}","\frac{(f x+g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f}-\frac{b n (d f-e g)^2 \log (d+e x)}{2 e^2 f}+\frac{b n x (d f-e g)}{2 e}-\frac{b n (f x+g)^2}{4 f}",1,"(b*(d*f - e*g)*n*x)/(2*e) - (b*n*(g + f*x)^2)/(4*f) - (b*(d*f - e*g)^2*n*Log[d + e*x])/(2*e^2*f) + ((g + f*x)^2*(a + b*Log[c*(d + e*x)^n]))/(2*f)","A",4,3,23,0.1304,1,"{2412, 2395, 43}"
304,1,120,0,0.1131226,"\int \left(f+\frac{g}{x}\right)^2 x^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Int[(f + g/x)^2*x^2*(a + b*Log[c*(d + e*x)^n]),x]","\frac{(f x+g)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 f}-\frac{b n x (d f-e g)^2}{3 e^2}+\frac{b n (d f-e g)^3 \log (d+e x)}{3 e^3 f}+\frac{b n (f x+g)^2 (d f-e g)}{6 e f}-\frac{b n (f x+g)^3}{9 f}","\frac{(f x+g)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 f}-\frac{b n x (d f-e g)^2}{3 e^2}+\frac{b n (d f-e g)^3 \log (d+e x)}{3 e^3 f}+\frac{b n (f x+g)^2 (d f-e g)}{6 e f}-\frac{b n (f x+g)^3}{9 f}",1,"-(b*(d*f - e*g)^2*n*x)/(3*e^2) + (b*(d*f - e*g)*n*(g + f*x)^2)/(6*e*f) - (b*n*(g + f*x)^3)/(9*f) + (b*(d*f - e*g)^3*n*Log[d + e*x])/(3*e^3*f) + ((g + f*x)^3*(a + b*Log[c*(d + e*x)^n]))/(3*f)","A",4,3,27,0.1111,1,"{2412, 2395, 43}"
305,1,149,0,0.1226603,"\int \left(f+\frac{g}{x}\right)^3 x^3 \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Int[(f + g/x)^3*x^3*(a + b*Log[c*(d + e*x)^n]),x]","\frac{(f x+g)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 f}+\frac{b n x (d f-e g)^3}{4 e^3}-\frac{b n (f x+g)^2 (d f-e g)^2}{8 e^2 f}-\frac{b n (d f-e g)^4 \log (d+e x)}{4 e^4 f}+\frac{b n (f x+g)^3 (d f-e g)}{12 e f}-\frac{b n (f x+g)^4}{16 f}","\frac{(f x+g)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 f}+\frac{b n x (d f-e g)^3}{4 e^3}-\frac{b n (f x+g)^2 (d f-e g)^2}{8 e^2 f}-\frac{b n (d f-e g)^4 \log (d+e x)}{4 e^4 f}+\frac{b n (f x+g)^3 (d f-e g)}{12 e f}-\frac{b n (f x+g)^4}{16 f}",1,"(b*(d*f - e*g)^3*n*x)/(4*e^3) - (b*(d*f - e*g)^2*n*(g + f*x)^2)/(8*e^2*f) + (b*(d*f - e*g)*n*(g + f*x)^3)/(12*e*f) - (b*n*(g + f*x)^4)/(16*f) - (b*(d*f - e*g)^4*n*Log[d + e*x])/(4*e^4*f) + ((g + f*x)^4*(a + b*Log[c*(d + e*x)^n]))/(4*f)","A",4,3,27,0.1111,1,"{2412, 2395, 43}"
306,1,63,0,0.1004083,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\left(f+\frac{g}{x}\right) x} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/((f + g/x)*x),x]","\frac{b n \text{PolyLog}\left(2,\frac{f (d+e x)}{d f-e g}\right)}{f}+\frac{\log \left(-\frac{e (f x+g)}{d f-e g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f}","\frac{b n \text{PolyLog}\left(2,\frac{f (d+e x)}{d f-e g}\right)}{f}+\frac{\log \left(-\frac{e (f x+g)}{d f-e g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f}",1,"((a + b*Log[c*(d + e*x)^n])*Log[-((e*(g + f*x))/(d*f - e*g))])/f + (b*n*PolyLog[2, (f*(d + e*x))/(d*f - e*g)])/f","A",4,4,27,0.1481,1,"{2412, 2394, 2393, 2391}"
307,1,74,0,0.0830582,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\left(f+\frac{g}{x}\right)^2 x^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/((f + g/x)^2*x^2),x]","-\frac{a+b \log \left(c (d+e x)^n\right)}{f (f x+g)}-\frac{b e n \log (d+e x)}{f (d f-e g)}+\frac{b e n \log (f x+g)}{f (d f-e g)}","-\frac{a+b \log \left(c (d+e x)^n\right)}{f (f x+g)}-\frac{b e n \log (d+e x)}{f (d f-e g)}+\frac{b e n \log (f x+g)}{f (d f-e g)}",1,"-((b*e*n*Log[d + e*x])/(f*(d*f - e*g))) - (a + b*Log[c*(d + e*x)^n])/(f*(g + f*x)) + (b*e*n*Log[g + f*x])/(f*(d*f - e*g))","A",5,4,27,0.1481,1,"{2412, 2395, 36, 31}"
308,1,112,0,0.1177602,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\left(f+\frac{g}{x}\right)^3 x^3} \, dx","Int[(a + b*Log[c*(d + e*x)^n])/((f + g/x)^3*x^3),x]","-\frac{a+b \log \left(c (d+e x)^n\right)}{2 f (f x+g)^2}+\frac{b e^2 n \log (d+e x)}{2 f (d f-e g)^2}-\frac{b e^2 n \log (f x+g)}{2 f (d f-e g)^2}-\frac{b e n}{2 f (f x+g) (d f-e g)}","-\frac{a+b \log \left(c (d+e x)^n\right)}{2 f (f x+g)^2}+\frac{b e^2 n \log (d+e x)}{2 f (d f-e g)^2}-\frac{b e^2 n \log (f x+g)}{2 f (d f-e g)^2}-\frac{b e n}{2 f (f x+g) (d f-e g)}",1,"-(b*e*n)/(2*f*(d*f - e*g)*(g + f*x)) + (b*e^2*n*Log[d + e*x])/(2*f*(d*f - e*g)^2) - (a + b*Log[c*(d + e*x)^n])/(2*f*(g + f*x)^2) - (b*e^2*n*Log[g + f*x])/(2*f*(d*f - e*g)^2)","A",4,3,27,0.1111,1,"{2412, 2395, 44}"
309,1,247,0,0.3365484,"\int \frac{\log (a+b x)}{c+\frac{d}{x^2}} \, dx","Int[Log[a + b*x]/(c + d/x^2),x]","\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (a+b x)}{a \sqrt{-c}-b \sqrt{d}}\right)}{2 (-c)^{3/2}}-\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (a+b x)}{a \sqrt{-c}+b \sqrt{d}}\right)}{2 (-c)^{3/2}}-\frac{\sqrt{d} \log (a+b x) \log \left(\frac{b \left(\sqrt{d}-\sqrt{-c} x\right)}{a \sqrt{-c}+b \sqrt{d}}\right)}{2 (-c)^{3/2}}+\frac{\sqrt{d} \log (a+b x) \log \left(-\frac{b \left(\sqrt{-c} x+\sqrt{d}\right)}{a \sqrt{-c}-b \sqrt{d}}\right)}{2 (-c)^{3/2}}+\frac{(a+b x) \log (a+b x)}{b c}-\frac{x}{c}","\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (a+b x)}{a \sqrt{-c}-b \sqrt{d}}\right)}{2 (-c)^{3/2}}-\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (a+b x)}{a \sqrt{-c}+b \sqrt{d}}\right)}{2 (-c)^{3/2}}-\frac{\sqrt{d} \log (a+b x) \log \left(\frac{b \left(\sqrt{d}-\sqrt{-c} x\right)}{a \sqrt{-c}+b \sqrt{d}}\right)}{2 (-c)^{3/2}}+\frac{\sqrt{d} \log (a+b x) \log \left(-\frac{b \left(\sqrt{-c} x+\sqrt{d}\right)}{a \sqrt{-c}-b \sqrt{d}}\right)}{2 (-c)^{3/2}}+\frac{(a+b x) \log (a+b x)}{b c}-\frac{x}{c}",1,"-(x/c) + ((a + b*x)*Log[a + b*x])/(b*c) - (Sqrt[d]*Log[a + b*x]*Log[(b*(Sqrt[d] - Sqrt[-c]*x))/(a*Sqrt[-c] + b*Sqrt[d])])/(2*(-c)^(3/2)) + (Sqrt[d]*Log[a + b*x]*Log[-((b*(Sqrt[d] + Sqrt[-c]*x))/(a*Sqrt[-c] - b*Sqrt[d]))])/(2*(-c)^(3/2)) + (Sqrt[d]*PolyLog[2, (Sqrt[-c]*(a + b*x))/(a*Sqrt[-c] - b*Sqrt[d])])/(2*(-c)^(3/2)) - (Sqrt[d]*PolyLog[2, (Sqrt[-c]*(a + b*x))/(a*Sqrt[-c] + b*Sqrt[d])])/(2*(-c)^(3/2))","A",12,6,16,0.3750,1,"{2409, 2389, 2295, 2394, 2393, 2391}"
310,1,752,0,1.0852721,"\int \frac{x^5 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x^2} \, dx","Int[(x^5*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2),x]","\frac{b f^2 n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3}+\frac{b f^2 n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^3}-\frac{b^2 f^2 n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^3}-\frac{b^2 f^2 n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{g^3}+\frac{b n \left(\frac{48 d^3 (d+e x)}{e^4}-\frac{36 d^2 (d+e x)^2}{e^4}-\frac{12 d^4 \log (d+e x)}{e^4}+\frac{16 d (d+e x)^3}{e^4}-\frac{3 (d+e x)^4}{e^4}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{24 g}+\frac{d f (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2 g^2}-\frac{f (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2 g^2}+\frac{b f n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^2 g^2}+\frac{f^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^3}+\frac{f^2 \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^3}+\frac{x^4 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 g}-\frac{2 a b d f n x}{e g^2}-\frac{2 b^2 d f n (d+e x) \log \left(c (d+e x)^n\right)}{e^2 g^2}-\frac{2 b^2 d^3 n^2 x}{e^3 g}+\frac{3 b^2 d^2 n^2 (d+e x)^2}{4 e^4 g}+\frac{b^2 d^4 n^2 \log ^2(d+e x)}{4 e^4 g}-\frac{b^2 f n^2 (d+e x)^2}{4 e^2 g^2}-\frac{2 b^2 d n^2 (d+e x)^3}{9 e^4 g}+\frac{b^2 n^2 (d+e x)^4}{32 e^4 g}+\frac{2 b^2 d f n^2 x}{e g^2}","\frac{b^2 n^2 \log ^2(d+e x) d^4}{4 e^4 g}-\frac{b n \log (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right) d^4}{2 e^4 g}-\frac{2 b^2 n^2 x d^3}{e^3 g}+\frac{2 b n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right) d^3}{e^4 g}+\frac{3 b^2 n^2 (d+e x)^2 d^2}{4 e^4 g}-\frac{3 b n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right) d^2}{2 e^4 g}-\frac{2 b^2 n^2 (d+e x)^3 d}{9 e^4 g}+\frac{f (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 d}{e^2 g^2}+\frac{2 b^2 f n^2 x d}{e g^2}-\frac{2 a b f n x d}{e g^2}-\frac{2 b^2 f n (d+e x) \log \left(c (d+e x)^n\right) d}{e^2 g^2}+\frac{2 b n (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right) d}{3 e^4 g}+\frac{b^2 n^2 (d+e x)^4}{32 e^4 g}-\frac{b^2 f n^2 (d+e x)^2}{4 e^2 g^2}+\frac{x^4 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 g}-\frac{f (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2 g^2}-\frac{b n (d+e x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{8 e^4 g}+\frac{b f n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^2 g^2}+\frac{f^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 g^3}+\frac{f^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^3}+\frac{b f^2 n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^3}+\frac{b f^2 n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{g^3}-\frac{b^2 f^2 n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^3}-\frac{b^2 f^2 n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{g^3}",1,"(-2*a*b*d*f*n*x)/(e*g^2) + (2*b^2*d*f*n^2*x)/(e*g^2) - (2*b^2*d^3*n^2*x)/(e^3*g) - (b^2*f*n^2*(d + e*x)^2)/(4*e^2*g^2) + (3*b^2*d^2*n^2*(d + e*x)^2)/(4*e^4*g) - (2*b^2*d*n^2*(d + e*x)^3)/(9*e^4*g) + (b^2*n^2*(d + e*x)^4)/(32*e^4*g) + (b^2*d^4*n^2*Log[d + e*x]^2)/(4*e^4*g) - (2*b^2*d*f*n*(d + e*x)*Log[c*(d + e*x)^n])/(e^2*g^2) + (b*f*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(2*e^2*g^2) + (b*n*((48*d^3*(d + e*x))/e^4 - (36*d^2*(d + e*x)^2)/e^4 + (16*d*(d + e*x)^3)/e^4 - (3*(d + e*x)^4)/e^4 - (12*d^4*Log[d + e*x])/e^4)*(a + b*Log[c*(d + e*x)^n]))/(24*g) + (x^4*(a + b*Log[c*(d + e*x)^n])^2)/(4*g) + (d*f*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(e^2*g^2) - (f*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(2*e^2*g^2) + (f^2*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^3) + (f^2*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*g^3) + (b*f^2*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/g^3 + (b*f^2*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g^3 - (b^2*f^2*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/g^3 - (b^2*f^2*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g^3","A",28,19,29,0.6552,1,"{2416, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2398, 2411, 43, 2334, 12, 14, 2301, 2396, 2433, 2374, 6589}"
311,1,499,0,0.6878014,"\int \frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x^2} \, dx","Int[(x^3*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2),x]","-\frac{b f n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}-\frac{b f n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}+\frac{b^2 f n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^2}+\frac{b^2 f n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{g^2}-\frac{b n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^2 g}+\frac{(d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2 g}-\frac{d (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2 g}-\frac{f \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^2}-\frac{f \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^2}+\frac{2 a b d n x}{e g}+\frac{2 b^2 d n (d+e x) \log \left(c (d+e x)^n\right)}{e^2 g}+\frac{b^2 n^2 (d+e x)^2}{4 e^2 g}-\frac{2 b^2 d n^2 x}{e g}","-\frac{b f n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}-\frac{b f n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}+\frac{b^2 f n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^2}+\frac{b^2 f n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{g^2}-\frac{b n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^2 g}+\frac{(d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2 g}-\frac{d (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2 g}-\frac{f \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^2}-\frac{f \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^2}+\frac{2 a b d n x}{e g}+\frac{2 b^2 d n (d+e x) \log \left(c (d+e x)^n\right)}{e^2 g}+\frac{b^2 n^2 (d+e x)^2}{4 e^2 g}-\frac{2 b^2 d n^2 x}{e g}",1,"(2*a*b*d*n*x)/(e*g) - (2*b^2*d*n^2*x)/(e*g) + (b^2*n^2*(d + e*x)^2)/(4*e^2*g) + (2*b^2*d*n*(d + e*x)*Log[c*(d + e*x)^n])/(e^2*g) - (b*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(2*e^2*g) - (d*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(e^2*g) + ((d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(2*e^2*g) - (f*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^2) - (f*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*g^2) - (b*f*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/g^2 - (b*f*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g^2 + (b^2*f*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/g^2 + (b^2*f*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g^2","A",21,12,29,0.4138,1,"{2416, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2396, 2433, 2374, 6589}"
312,1,317,0,0.3712151,"\int \frac{x \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x^2} \, dx","Int[(x*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2),x]","\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}+\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}-\frac{b^2 n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g}-\frac{b^2 n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{g}+\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g}+\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g}","\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}+\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}-\frac{b^2 n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g}-\frac{b^2 n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{g}+\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g}+\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g}",1,"((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g) + ((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*g) + (b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/g + (b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g - (b^2*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/g - (b^2*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g","A",10,5,27,0.1852,1,"{2416, 2396, 2433, 2374, 6589}"
313,1,397,0,0.596786,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x \left(f+g x^2\right)} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(x*(f + g*x^2)),x]","-\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f}-\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f}+\frac{2 b n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f}+\frac{b^2 n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{f}+\frac{b^2 n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{f}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)}{f}-\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f}-\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f}+\frac{\log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f}","-\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f}-\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f}+\frac{2 b n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f}+\frac{b^2 n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{f}+\frac{b^2 n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{f}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)}{f}-\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f}-\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f}+\frac{\log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f}",1,"(Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n])^2)/f - ((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f) - ((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*f) - (b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/f - (b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/f + (2*b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, 1 + (e*x)/d])/f + (b^2*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/f + (b^2*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/f - (2*b^2*n^2*PolyLog[3, 1 + (e*x)/d])/f","A",16,5,29,0.1724,1,"{2416, 2396, 2433, 2374, 6589}"
314,1,575,0,0.9456393,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x^3 \left(f+g x^2\right)} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(x^3*(f + g*x^2)),x]","\frac{b g n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}+\frac{b g n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}-\frac{2 b g n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}-\frac{b^2 e^2 n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{d^2 f}-\frac{b^2 g n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{f^2}-\frac{b^2 g n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{f^2}+\frac{2 b^2 g n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)}{f^2}+\frac{e^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 d^2 f}-\frac{b e^2 n \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{d^2 f}-\frac{b e n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{d^2 f x}-\frac{g \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f^2}+\frac{g \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f^2}+\frac{g \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f^2}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f x^2}+\frac{b^2 e^2 n^2 \log (x)}{d^2 f}","\frac{b g n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}+\frac{b g n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}-\frac{2 b g n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}+\frac{b^2 e^2 n^2 \text{PolyLog}\left(2,\frac{d}{d+e x}\right)}{d^2 f}-\frac{b^2 g n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{f^2}-\frac{b^2 g n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{f^2}+\frac{2 b^2 g n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)}{f^2}-\frac{b e^2 n \log \left(1-\frac{d}{d+e x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{d^2 f}-\frac{b e n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{d^2 f x}-\frac{g \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f^2}+\frac{g \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f^2}+\frac{g \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f^2}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f x^2}+\frac{b^2 e^2 n^2 \log (x)}{d^2 f}",1,"(b^2*e^2*n^2*Log[x])/(d^2*f) - (b*e*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n]))/(d^2*f*x) - (b*e^2*n*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/(d^2*f) + (e^2*(a + b*Log[c*(d + e*x)^n])^2)/(2*d^2*f) - (a + b*Log[c*(d + e*x)^n])^2/(2*f*x^2) - (g*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n])^2)/f^2 + (g*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f^2) + (g*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*f^2) + (b*g*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/f^2 + (b*g*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/f^2 - (b^2*e^2*n^2*PolyLog[2, 1 + (e*x)/d])/(d^2*f) - (2*b*g*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, 1 + (e*x)/d])/f^2 - (b^2*g*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/f^2 - (b^2*g*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/f^2 + (2*b^2*g*n^2*PolyLog[3, 1 + (e*x)/d])/f^2","A",25,14,29,0.4828,1,"{2416, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2396, 2433, 2374, 6589}"
315,1,646,0,0.921698,"\int \frac{x^4 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x^2} \, dx","Int[(x^4*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2),x]","-\frac{b (-f)^{3/2} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^{5/2}}+\frac{b (-f)^{3/2} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^{5/2}}+\frac{b^2 (-f)^{3/2} n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^{5/2}}-\frac{b^2 (-f)^{3/2} n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{g^{5/2}}-\frac{b n \left(\frac{18 d^2 (d+e x)}{e^3}-\frac{6 d^3 \log (d+e x)}{e^3}-\frac{9 d (d+e x)^2}{e^3}+\frac{2 (d+e x)^3}{e^3}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{9 g}-\frac{f (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e g^2}+\frac{(-f)^{3/2} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^{5/2}}-\frac{(-f)^{3/2} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^{5/2}}+\frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 g}+\frac{2 a b f n x}{g^2}+\frac{2 b^2 f n (d+e x) \log \left(c (d+e x)^n\right)}{e g^2}+\frac{2 b^2 d^2 n^2 x}{e^2 g}-\frac{b^2 d^3 n^2 \log ^2(d+e x)}{3 e^3 g}-\frac{b^2 d n^2 (d+e x)^2}{2 e^3 g}+\frac{2 b^2 n^2 (d+e x)^3}{27 e^3 g}-\frac{2 b^2 f n^2 x}{g^2}","-\frac{b (-f)^{3/2} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^{5/2}}+\frac{b (-f)^{3/2} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^{5/2}}+\frac{b^2 (-f)^{3/2} n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^{5/2}}-\frac{b^2 (-f)^{3/2} n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{g^{5/2}}+\frac{2 b d^3 n \log (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 e^3 g}-\frac{2 b d^2 n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^3 g}+\frac{b d n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^3 g}-\frac{2 b n (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{9 e^3 g}-\frac{f (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e g^2}+\frac{(-f)^{3/2} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^{5/2}}-\frac{(-f)^{3/2} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^{5/2}}+\frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 g}+\frac{2 a b f n x}{g^2}+\frac{2 b^2 f n (d+e x) \log \left(c (d+e x)^n\right)}{e g^2}+\frac{2 b^2 d^2 n^2 x}{e^2 g}-\frac{b^2 d^3 n^2 \log ^2(d+e x)}{3 e^3 g}-\frac{b^2 d n^2 (d+e x)^2}{2 e^3 g}+\frac{2 b^2 n^2 (d+e x)^3}{27 e^3 g}-\frac{2 b^2 f n^2 x}{g^2}",1,"(2*a*b*f*n*x)/g^2 - (2*b^2*f*n^2*x)/g^2 + (2*b^2*d^2*n^2*x)/(e^2*g) - (b^2*d*n^2*(d + e*x)^2)/(2*e^3*g) + (2*b^2*n^2*(d + e*x)^3)/(27*e^3*g) - (b^2*d^3*n^2*Log[d + e*x]^2)/(3*e^3*g) + (2*b^2*f*n*(d + e*x)*Log[c*(d + e*x)^n])/(e*g^2) - (b*n*((18*d^2*(d + e*x))/e^3 - (9*d*(d + e*x)^2)/e^3 + (2*(d + e*x)^3)/e^3 - (6*d^3*Log[d + e*x])/e^3)*(a + b*Log[c*(d + e*x)^n]))/(9*g) + (x^3*(a + b*Log[c*(d + e*x)^n])^2)/(3*g) - (f*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(e*g^2) + ((-f)^(3/2)*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^(5/2)) - ((-f)^(3/2)*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*g^(5/2)) - (b*(-f)^(3/2)*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/g^(5/2) + (b*(-f)^(3/2)*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g^(5/2) + (b^2*(-f)^(3/2)*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/g^(5/2) - (b^2*(-f)^(3/2)*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g^(5/2)","A",23,16,29,0.5517,1,"{2416, 2389, 2296, 2295, 2398, 2411, 43, 2334, 12, 14, 2301, 2409, 2396, 2433, 2374, 6589}"
316,1,447,0,0.5921316,"\int \frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x^2} \, dx","Int[(x^2*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2),x]","-\frac{b \sqrt{-f} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^{3/2}}+\frac{b \sqrt{-f} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^{3/2}}+\frac{b^2 \sqrt{-f} n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^{3/2}}-\frac{b^2 \sqrt{-f} n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{g^{3/2}}+\frac{\sqrt{-f} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^{3/2}}-\frac{\sqrt{-f} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^{3/2}}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e g}-\frac{2 a b n x}{g}-\frac{2 b^2 n (d+e x) \log \left(c (d+e x)^n\right)}{e g}+\frac{2 b^2 n^2 x}{g}","-\frac{b \sqrt{-f} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^{3/2}}+\frac{b \sqrt{-f} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^{3/2}}+\frac{b^2 \sqrt{-f} n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^{3/2}}-\frac{b^2 \sqrt{-f} n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{g^{3/2}}+\frac{\sqrt{-f} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^{3/2}}-\frac{\sqrt{-f} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^{3/2}}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e g}-\frac{2 a b n x}{g}-\frac{2 b^2 n (d+e x) \log \left(c (d+e x)^n\right)}{e g}+\frac{2 b^2 n^2 x}{g}",1,"(-2*a*b*n*x)/g + (2*b^2*n^2*x)/g - (2*b^2*n*(d + e*x)*Log[c*(d + e*x)^n])/(e*g) + ((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(e*g) + (Sqrt[-f]*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^(3/2)) - (Sqrt[-f]*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*g^(3/2)) - (b*Sqrt[-f]*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/g^(3/2) + (b*Sqrt[-f]*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g^(3/2) + (b^2*Sqrt[-f]*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/g^(3/2) - (b^2*Sqrt[-f]*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g^(3/2)","A",16,9,29,0.3103,1,"{2416, 2389, 2296, 2295, 2409, 2396, 2433, 2374, 6589}"
317,1,371,0,0.3755059,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x^2),x]","-\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{-f} \sqrt{g}}+\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{-f} \sqrt{g}}+\frac{b^2 n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{\sqrt{-f} \sqrt{g}}-\frac{b^2 n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{\sqrt{-f} \sqrt{g}}+\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 \sqrt{-f} \sqrt{g}}-\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 \sqrt{-f} \sqrt{g}}","-\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{-f} \sqrt{g}}+\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{-f} \sqrt{g}}+\frac{b^2 n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{\sqrt{-f} \sqrt{g}}-\frac{b^2 n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{\sqrt{-f} \sqrt{g}}+\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 \sqrt{-f} \sqrt{g}}-\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 \sqrt{-f} \sqrt{g}}",1,"((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*Sqrt[-f]*Sqrt[g]) - ((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*Sqrt[-f]*Sqrt[g]) - (b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(Sqrt[-f]*Sqrt[g]) + (b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(Sqrt[-f]*Sqrt[g]) + (b^2*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(Sqrt[-f]*Sqrt[g]) - (b^2*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(Sqrt[-f]*Sqrt[g])","A",10,5,26,0.1923,1,"{2409, 2396, 2433, 2374, 6589}"
318,1,461,0,0.6337783,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x^2 \left(f+g x^2\right)} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(x^2*(f + g*x^2)),x]","-\frac{b \sqrt{g} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(-f)^{3/2}}+\frac{b \sqrt{g} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(-f)^{3/2}}+\frac{b^2 \sqrt{g} n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{(-f)^{3/2}}-\frac{b^2 \sqrt{g} n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{(-f)^{3/2}}+\frac{2 b^2 e n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{d f}+\frac{\sqrt{g} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 (-f)^{3/2}}-\frac{\sqrt{g} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 (-f)^{3/2}}+\frac{2 b e n \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{d f}-\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{d f x}","-\frac{b \sqrt{g} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(-f)^{3/2}}+\frac{b \sqrt{g} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(-f)^{3/2}}+\frac{b^2 \sqrt{g} n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{(-f)^{3/2}}-\frac{b^2 \sqrt{g} n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{(-f)^{3/2}}+\frac{2 b^2 e n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{d f}+\frac{\sqrt{g} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 (-f)^{3/2}}-\frac{\sqrt{g} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 (-f)^{3/2}}+\frac{2 b e n \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{d f}-\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{d f x}",1,"(2*b*e*n*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/(d*f) - ((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(d*f*x) + (Sqrt[g]*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*(-f)^(3/2)) - (Sqrt[g]*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*(-f)^(3/2)) - (b*Sqrt[g]*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(-f)^(3/2) + (b*Sqrt[g]*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(-f)^(3/2) + (2*b^2*e*n^2*PolyLog[2, 1 + (e*x)/d])/(d*f) + (b^2*Sqrt[g]*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(-f)^(3/2) - (b^2*Sqrt[g]*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(-f)^(3/2)","A",15,9,29,0.3103,1,"{2416, 2397, 2394, 2315, 2409, 2396, 2433, 2374, 6589}"
319,1,717,0,1.1144844,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x^4 \left(f+g x^2\right)} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(x^4*(f + g*x^2)),x]","-\frac{b g^{3/2} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(-f)^{5/2}}+\frac{b g^{3/2} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(-f)^{5/2}}+\frac{2 b^2 e^3 n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{3 d^3 f}-\frac{2 b^2 e g n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{d f^2}+\frac{b^2 g^{3/2} n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{(-f)^{5/2}}-\frac{b^2 g^{3/2} n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{(-f)^{5/2}}-\frac{e^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 d^3 f}+\frac{2 b e^3 n \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 d^3 f}+\frac{2 b e^2 n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 d^3 f x}-\frac{2 b e g n \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{d f^2}+\frac{g (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{d f^2 x}+\frac{g^{3/2} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 (-f)^{5/2}}-\frac{g^{3/2} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 (-f)^{5/2}}-\frac{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 d f x^2}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 f x^3}-\frac{b^2 e^2 n^2}{3 d^2 f x}-\frac{b^2 e^3 n^2 \log (x)}{d^3 f}+\frac{b^2 e^3 n^2 \log (d+e x)}{3 d^3 f}","-\frac{b g^{3/2} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(-f)^{5/2}}+\frac{b g^{3/2} n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(-f)^{5/2}}-\frac{2 b^2 e^3 n^2 \text{PolyLog}\left(2,\frac{d}{d+e x}\right)}{3 d^3 f}-\frac{2 b^2 e g n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{d f^2}+\frac{b^2 g^{3/2} n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{(-f)^{5/2}}-\frac{b^2 g^{3/2} n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{(-f)^{5/2}}+\frac{2 b e^3 n \log \left(1-\frac{d}{d+e x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 d^3 f}+\frac{2 b e^2 n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 d^3 f x}-\frac{2 b e g n \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{d f^2}+\frac{g (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{d f^2 x}+\frac{g^{3/2} \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 (-f)^{5/2}}-\frac{g^{3/2} \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 (-f)^{5/2}}-\frac{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 d f x^2}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 f x^3}-\frac{b^2 e^2 n^2}{3 d^2 f x}-\frac{b^2 e^3 n^2 \log (x)}{d^3 f}+\frac{b^2 e^3 n^2 \log (d+e x)}{3 d^3 f}",1,"-(b^2*e^2*n^2)/(3*d^2*f*x) - (b^2*e^3*n^2*Log[x])/(d^3*f) + (b^2*e^3*n^2*Log[d + e*x])/(3*d^3*f) - (b*e*n*(a + b*Log[c*(d + e*x)^n]))/(3*d*f*x^2) + (2*b*e^2*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n]))/(3*d^3*f*x) + (2*b*e^3*n*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/(3*d^3*f) - (2*b*e*g*n*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/(d*f^2) - (e^3*(a + b*Log[c*(d + e*x)^n])^2)/(3*d^3*f) - (a + b*Log[c*(d + e*x)^n])^2/(3*f*x^3) + (g*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(d*f^2*x) + (g^(3/2)*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*(-f)^(5/2)) - (g^(3/2)*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*(-f)^(5/2)) - (b*g^(3/2)*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(-f)^(5/2) + (b*g^(3/2)*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(-f)^(5/2) + (2*b^2*e^3*n^2*PolyLog[2, 1 + (e*x)/d])/(3*d^3*f) - (2*b^2*e*g*n^2*PolyLog[2, 1 + (e*x)/d])/(d*f^2) + (b^2*g^(3/2)*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(-f)^(5/2) - (b^2*g^(3/2)*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(-f)^(5/2)","A",28,20,29,0.6897,1,"{2416, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44, 2397, 2394, 2315, 2409, 2396, 2433, 2374, 6589}"
320,1,936,0,1.5296691,"\int \frac{x^5 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{\left(f+g x^2\right)^2} \, dx","Int[(x^5*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2)^2,x]","\frac{n^2 (d+e x)^2 b^2}{4 e^2 g^2}-\frac{2 d n^2 x b^2}{e g^2}+\frac{2 d n (d+e x) \log \left(c (d+e x)^n\right) b^2}{e^2 g^2}-\frac{e (-f)^{3/2} \left(\sqrt{g} d+e \sqrt{-f}\right) n^2 \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) b^2}{2 g^3 \left(g d^2+e^2 f\right)}-\frac{e (-f)^{3/2} \left(e \sqrt{-f}-d \sqrt{g}\right) n^2 \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) b^2}{2 g^3 \left(g d^2+e^2 f\right)}+\frac{2 f n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) b^2}{g^3}+\frac{2 f n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) b^2}{g^3}+\frac{2 a d n x b}{e g^2}-\frac{n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right) b}{2 e^2 g^2}-\frac{e f \left(\sqrt{-f} \sqrt{g} d+e f\right) n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right) b}{2 g^3 \left(g d^2+e^2 f\right)}-\frac{e (-f)^{3/2} \left(\sqrt{g} d+e \sqrt{-f}\right) n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right) b}{2 g^3 \left(g d^2+e^2 f\right)}-\frac{2 f n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) b}{g^3}-\frac{2 f n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) b}{g^3}+\frac{(d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2 g^2}-\frac{d (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2 g^2}+\frac{e^2 f^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^3 \left(g d^2+e^2 f\right)}-\frac{f^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^3 \left(g x^2+f\right)}-\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{g^3}-\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^3}","\frac{n^2 (d+e x)^2 b^2}{4 e^2 g^2}-\frac{2 d n^2 x b^2}{e g^2}+\frac{2 d n (d+e x) \log \left(c (d+e x)^n\right) b^2}{e^2 g^2}-\frac{e (-f)^{3/2} \left(\sqrt{g} d+e \sqrt{-f}\right) n^2 \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) b^2}{2 g^3 \left(g d^2+e^2 f\right)}-\frac{e (-f)^{3/2} \left(e \sqrt{-f}-d \sqrt{g}\right) n^2 \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) b^2}{2 g^3 \left(g d^2+e^2 f\right)}+\frac{2 f n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) b^2}{g^3}+\frac{2 f n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) b^2}{g^3}+\frac{2 a d n x b}{e g^2}-\frac{n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right) b}{2 e^2 g^2}-\frac{e f \left(\sqrt{-f} \sqrt{g} d+e f\right) n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right) b}{2 g^3 \left(g d^2+e^2 f\right)}-\frac{e (-f)^{3/2} \left(\sqrt{g} d+e \sqrt{-f}\right) n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right) b}{2 g^3 \left(g d^2+e^2 f\right)}-\frac{2 f n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) b}{g^3}-\frac{2 f n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) b}{g^3}+\frac{(d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2 g^2}-\frac{d (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2 g^2}+\frac{e^2 f^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^3 \left(g d^2+e^2 f\right)}-\frac{f^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^3 \left(g x^2+f\right)}-\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{g^3}-\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^3}",1,"(2*a*b*d*n*x)/(e*g^2) - (2*b^2*d*n^2*x)/(e*g^2) + (b^2*n^2*(d + e*x)^2)/(4*e^2*g^2) + (2*b^2*d*n*(d + e*x)*Log[c*(d + e*x)^n])/(e^2*g^2) - (b*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(2*e^2*g^2) + (e^2*f^2*(a + b*Log[c*(d + e*x)^n])^2)/(2*g^3*(e^2*f + d^2*g)) - (d*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(e^2*g^2) + ((d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(2*e^2*g^2) - (f^2*(a + b*Log[c*(d + e*x)^n])^2)/(2*g^3*(f + g*x^2)) - (b*e*f*(e*f + d*Sqrt[-f]*Sqrt[g])*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^3*(e^2*f + d^2*g)) - (f*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g^3 - (b*e*(-f)^(3/2)*(e*Sqrt[-f] + d*Sqrt[g])*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*g^3*(e^2*f + d^2*g)) - (f*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/g^3 - (b^2*e*(-f)^(3/2)*(e*Sqrt[-f] + d*Sqrt[g])*n^2*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*g^3*(e^2*f + d^2*g)) - (2*b*f*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/g^3 - (b^2*e*(-f)^(3/2)*(e*Sqrt[-f] - d*Sqrt[g])*n^2*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^3*(e^2*f + d^2*g)) - (2*b*f*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g^3 + (2*b^2*f*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/g^3 + (2*b^2*f*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g^3","A",34,18,29,0.6207,1,"{2416, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2413, 2418, 2301, 2394, 2393, 2391, 2396, 2433, 2374, 6589}"
321,1,739,0,1.1951155,"\int \frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{\left(f+g x^2\right)^2} \, dx","Int[(x^3*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2)^2,x]","\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}+\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}-\frac{b^2 e \sqrt{-f} n^2 \left(d \sqrt{g}+e \sqrt{-f}\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^2 \left(d^2 g+e^2 f\right)}+\frac{b^2 e n^2 \left(d \sqrt{-f} \sqrt{g}+e f\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 g^2 \left(d^2 g+e^2 f\right)}-\frac{b^2 n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^2}-\frac{b^2 n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{g^2}+\frac{b e n \left(d \sqrt{-f} \sqrt{g}+e f\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2 \left(d^2 g+e^2 f\right)}+\frac{b e n \left(e f-d \sqrt{-f} \sqrt{g}\right) \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2 \left(d^2 g+e^2 f\right)}-\frac{e^2 f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^2 \left(d^2 g+e^2 f\right)}+\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^2 \left(f+g x^2\right)}+\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^2}+\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^2}","\frac{b n \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}+\frac{b n \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}-\frac{b^2 e \sqrt{-f} n^2 \left(d \sqrt{g}+e \sqrt{-f}\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^2 \left(d^2 g+e^2 f\right)}+\frac{b^2 e n^2 \left(d \sqrt{-f} \sqrt{g}+e f\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 g^2 \left(d^2 g+e^2 f\right)}-\frac{b^2 n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^2}-\frac{b^2 n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{g^2}+\frac{b e n \left(d \sqrt{-f} \sqrt{g}+e f\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2 \left(d^2 g+e^2 f\right)}+\frac{b e n \left(e f-d \sqrt{-f} \sqrt{g}\right) \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2 \left(d^2 g+e^2 f\right)}-\frac{e^2 f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^2 \left(d^2 g+e^2 f\right)}+\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^2 \left(f+g x^2\right)}+\frac{\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^2}+\frac{\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g^2}",1,"-(e^2*f*(a + b*Log[c*(d + e*x)^n])^2)/(2*g^2*(e^2*f + d^2*g)) + (f*(a + b*Log[c*(d + e*x)^n])^2)/(2*g^2*(f + g*x^2)) + (b*e*(e*f + d*Sqrt[-f]*Sqrt[g])*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^2*(e^2*f + d^2*g)) + ((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^2) + (b*e*(e*f - d*Sqrt[-f]*Sqrt[g])*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*g^2*(e^2*f + d^2*g)) + ((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*g^2) - (b^2*e*Sqrt[-f]*(e*Sqrt[-f] + d*Sqrt[g])*n^2*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*g^2*(e^2*f + d^2*g)) + (b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/g^2 + (b^2*e*(e*f + d*Sqrt[-f]*Sqrt[g])*n^2*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^2*(e^2*f + d^2*g)) + (b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g^2 - (b^2*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/g^2 - (b^2*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g^2","A",25,12,29,0.4138,1,"{2416, 2413, 2418, 2390, 2301, 2394, 2393, 2391, 2396, 2433, 2374, 6589}"
322,1,430,0,0.5469761,"\int \frac{x \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{\left(f+g x^2\right)^2} \, dx","Int[(x*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2)^2,x]","-\frac{b^2 e n^2 \left(d \sqrt{g}+e \sqrt{-f}\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 \sqrt{-f} g \left(d^2 g+e^2 f\right)}-\frac{b^2 e n^2 \left(d \sqrt{-f} \sqrt{g}+e f\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 f g \left(d^2 g+e^2 f\right)}-\frac{b e n \left(d \sqrt{-f} \sqrt{g}+e f\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f g \left(d^2 g+e^2 f\right)}-\frac{b e n \left(e f-d \sqrt{-f} \sqrt{g}\right) \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f g \left(d^2 g+e^2 f\right)}+\frac{e^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g \left(d^2 g+e^2 f\right)}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g \left(f+g x^2\right)}","-\frac{b^2 e n^2 \left(d \sqrt{g}+e \sqrt{-f}\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 \sqrt{-f} g \left(d^2 g+e^2 f\right)}-\frac{b^2 e n^2 \left(d \sqrt{-f} \sqrt{g}+e f\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 f g \left(d^2 g+e^2 f\right)}-\frac{b e n \left(d \sqrt{-f} \sqrt{g}+e f\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f g \left(d^2 g+e^2 f\right)}-\frac{b e n \left(e f-d \sqrt{-f} \sqrt{g}\right) \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f g \left(d^2 g+e^2 f\right)}+\frac{e^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g \left(d^2 g+e^2 f\right)}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g \left(f+g x^2\right)}",1,"(e^2*(a + b*Log[c*(d + e*x)^n])^2)/(2*g*(e^2*f + d^2*g)) - (a + b*Log[c*(d + e*x)^n])^2/(2*g*(f + g*x^2)) - (b*e*(e*f + d*Sqrt[-f]*Sqrt[g])*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f*g*(e^2*f + d^2*g)) - (b*e*(e*f - d*Sqrt[-f]*Sqrt[g])*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*f*g*(e^2*f + d^2*g)) - (b^2*e*(e*Sqrt[-f] + d*Sqrt[g])*n^2*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*Sqrt[-f]*g*(e^2*f + d^2*g)) - (b^2*e*(e*f + d*Sqrt[-f]*Sqrt[g])*n^2*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f*g*(e^2*f + d^2*g))","A",13,7,27,0.2593,1,"{2413, 2418, 2390, 2301, 2394, 2393, 2391}"
323,1,814,0,1.3003858,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x \left(f+g x^2\right)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(x*(f + g*x^2)^2),x]","-\frac{b^2 e \left(\sqrt{g} d+e \sqrt{-f}\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{2 (-f)^{3/2} \left(g d^2+e^2 f\right)}+\frac{b^2 e \left(\sqrt{-f} \sqrt{g} d+e f\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{2 f^2 \left(g d^2+e^2 f\right)}+\frac{b^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{f^2}+\frac{b^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{f^2}-\frac{2 b^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right) n^2}{f^2}+\frac{b e \left(\sqrt{-f} \sqrt{g} d+e f\right) \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right) n}{2 f^2 \left(g d^2+e^2 f\right)}+\frac{b e \left(e f-d \sqrt{-f} \sqrt{g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right) n}{2 f^2 \left(g d^2+e^2 f\right)}-\frac{b \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n}{f^2}-\frac{b \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n}{f^2}+\frac{2 b \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{e x}{d}+1\right) n}{f^2}+\frac{\log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f^2}-\frac{e^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f \left(g d^2+e^2 f\right)}+\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f \left(g x^2+f\right)}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 f^2}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f^2}","-\frac{b^2 e \left(\sqrt{g} d+e \sqrt{-f}\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{2 (-f)^{3/2} \left(g d^2+e^2 f\right)}+\frac{b^2 e \left(\sqrt{-f} \sqrt{g} d+e f\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{2 f^2 \left(g d^2+e^2 f\right)}+\frac{b^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{f^2}+\frac{b^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{f^2}-\frac{2 b^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right) n^2}{f^2}+\frac{b e \left(\sqrt{-f} \sqrt{g} d+e f\right) \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right) n}{2 f^2 \left(g d^2+e^2 f\right)}+\frac{b e \left(e f-d \sqrt{-f} \sqrt{g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right) n}{2 f^2 \left(g d^2+e^2 f\right)}-\frac{b \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n}{f^2}-\frac{b \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n}{f^2}+\frac{2 b \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{e x}{d}+1\right) n}{f^2}+\frac{\log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f^2}-\frac{e^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f \left(g d^2+e^2 f\right)}+\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f \left(g x^2+f\right)}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 f^2}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f^2}",1,"-(e^2*(a + b*Log[c*(d + e*x)^n])^2)/(2*f*(e^2*f + d^2*g)) + (a + b*Log[c*(d + e*x)^n])^2/(2*f*(f + g*x^2)) + (Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n])^2)/f^2 + (b*e*(e*f + d*Sqrt[-f]*Sqrt[g])*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f^2*(e^2*f + d^2*g)) - ((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f^2) + (b*e*(e*f - d*Sqrt[-f]*Sqrt[g])*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*f^2*(e^2*f + d^2*g)) - ((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*f^2) - (b^2*e*(e*Sqrt[-f] + d*Sqrt[g])*n^2*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*(-f)^(3/2)*(e^2*f + d^2*g)) - (b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/f^2 + (b^2*e*(e*f + d*Sqrt[-f]*Sqrt[g])*n^2*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f^2*(e^2*f + d^2*g)) - (b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/f^2 + (2*b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, 1 + (e*x)/d])/f^2 + (b^2*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/f^2 + (b^2*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/f^2 - (2*b^2*n^2*PolyLog[3, 1 + (e*x)/d])/f^2","A",29,12,29,0.4138,1,"{2416, 2396, 2433, 2374, 6589, 2413, 2418, 2390, 2301, 2394, 2393, 2391}"
324,1,994,0,1.6531613,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x^3 \left(f+g x^2\right)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(x^3*(f + g*x^2)^2),x]","\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)^2 e^2}{2 f^2 \left(g d^2+e^2 f\right)}+\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 e^2}{2 d^2 f^2}+\frac{b^2 n^2 \log (x) e^2}{d^2 f^2}-\frac{b n \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right) e^2}{d^2 f^2}-\frac{b^2 n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right) e^2}{d^2 f^2}-\frac{b n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right) e}{d^2 f^2 x}-\frac{b \left(\sqrt{-f} \sqrt{g} d+e f\right) g n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right) e}{2 f^3 \left(g d^2+e^2 f\right)}-\frac{b \left(e f-d \sqrt{-f} \sqrt{g}\right) g n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right) e}{2 f^3 \left(g d^2+e^2 f\right)}-\frac{b^2 \left(\sqrt{g} d+e \sqrt{-f}\right) g n^2 \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) e}{2 (-f)^{5/2} \left(g d^2+e^2 f\right)}-\frac{b^2 \left(\sqrt{-f} \sqrt{g} d+e f\right) g n^2 \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) e}{2 f^3 \left(g d^2+e^2 f\right)}-\frac{2 g \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f^3}-\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f^2 \left(g x^2+f\right)}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f^2 x^2}+\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{f^3}+\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{f^3}+\frac{2 b g n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{f^3}+\frac{2 b g n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{f^3}-\frac{4 b g n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^3}-\frac{2 b^2 g n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{f^3}-\frac{2 b^2 g n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{f^3}+\frac{4 b^2 g n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)}{f^3}","\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)^2 e^2}{2 f^2 \left(g d^2+e^2 f\right)}+\frac{b^2 n^2 \log (x) e^2}{d^2 f^2}-\frac{b n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(1-\frac{d}{d+e x}\right) e^2}{d^2 f^2}+\frac{b^2 n^2 \text{PolyLog}\left(2,\frac{d}{d+e x}\right) e^2}{d^2 f^2}-\frac{b n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right) e}{d^2 f^2 x}-\frac{b \left(\sqrt{-f} \sqrt{g} d+e f\right) g n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right) e}{2 f^3 \left(g d^2+e^2 f\right)}-\frac{b \left(e f-d \sqrt{-f} \sqrt{g}\right) g n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right) e}{2 f^3 \left(g d^2+e^2 f\right)}-\frac{b^2 \left(\sqrt{g} d+e \sqrt{-f}\right) g n^2 \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) e}{2 (-f)^{5/2} \left(g d^2+e^2 f\right)}-\frac{b^2 \left(\sqrt{-f} \sqrt{g} d+e f\right) g n^2 \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) e}{2 f^3 \left(g d^2+e^2 f\right)}-\frac{2 g \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f^3}-\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f^2 \left(g x^2+f\right)}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 f^2 x^2}+\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{f^3}+\frac{g \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{f^3}+\frac{2 b g n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{f^3}+\frac{2 b g n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{f^3}-\frac{4 b g n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{f^3}-\frac{2 b^2 g n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{f^3}-\frac{2 b^2 g n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{f^3}+\frac{4 b^2 g n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)}{f^3}",1,"(b^2*e^2*n^2*Log[x])/(d^2*f^2) - (b*e*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n]))/(d^2*f^2*x) - (b*e^2*n*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/(d^2*f^2) + (e^2*(a + b*Log[c*(d + e*x)^n])^2)/(2*d^2*f^2) + (e^2*g*(a + b*Log[c*(d + e*x)^n])^2)/(2*f^2*(e^2*f + d^2*g)) - (a + b*Log[c*(d + e*x)^n])^2/(2*f^2*x^2) - (g*(a + b*Log[c*(d + e*x)^n])^2)/(2*f^2*(f + g*x^2)) - (2*g*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n])^2)/f^3 - (b*e*(e*f + d*Sqrt[-f]*Sqrt[g])*g*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f^3*(e^2*f + d^2*g)) + (g*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/f^3 - (b*e*(e*f - d*Sqrt[-f]*Sqrt[g])*g*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*f^3*(e^2*f + d^2*g)) + (g*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/f^3 - (b^2*e*(e*Sqrt[-f] + d*Sqrt[g])*g*n^2*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*(-f)^(5/2)*(e^2*f + d^2*g)) + (2*b*g*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/f^3 - (b^2*e*(e*f + d*Sqrt[-f]*Sqrt[g])*g*n^2*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f^3*(e^2*f + d^2*g)) + (2*b*g*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/f^3 - (b^2*e^2*n^2*PolyLog[2, 1 + (e*x)/d])/(d^2*f^2) - (4*b*g*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, 1 + (e*x)/d])/f^3 - (2*b^2*g*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/f^3 - (2*b^2*g*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/f^3 + (4*b^2*g*n^2*PolyLog[3, 1 + (e*x)/d])/f^3","A",38,19,29,0.6552,1,"{2416, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2396, 2433, 2374, 6589, 2413, 2418, 2390, 2394, 2393}"
325,1,897,0,1.7838983,"\int \frac{x^4 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{\left(f+g x^2\right)^2} \, dx","Int[(x^4*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2)^2,x]","\frac{2 n^2 x b^2}{g^2}-\frac{2 n (d+e x) \log \left(c (d+e x)^n\right) b^2}{e g^2}+\frac{e f n^2 \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) b^2}{2 \left(e \sqrt{-f}-d \sqrt{g}\right) g^{5/2}}-\frac{e f n^2 \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) b^2}{2 \left(\sqrt{g} d+e \sqrt{-f}\right) g^{5/2}}+\frac{3 \sqrt{-f} n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) b^2}{2 g^{5/2}}-\frac{3 \sqrt{-f} n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) b^2}{2 g^{5/2}}-\frac{2 a n x b}{g^2}-\frac{e f n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right) b}{2 \left(\sqrt{g} d+e \sqrt{-f}\right) g^{5/2}}+\frac{e f n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right) b}{2 \left(e \sqrt{-f}-d \sqrt{g}\right) g^{5/2}}-\frac{3 \sqrt{-f} n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) b}{2 g^{5/2}}+\frac{3 \sqrt{-f} n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) b}{2 g^{5/2}}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e g^2}-\frac{f (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 \left(\sqrt{g} d+e \sqrt{-f}\right) g^2 \left(\sqrt{-f}-\sqrt{g} x\right)}-\frac{f (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 \left(e \sqrt{-f}-d \sqrt{g}\right) g^2 \left(\sqrt{g} x+\sqrt{-f}\right)}+\frac{3 \sqrt{-f} \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{4 g^{5/2}}-\frac{3 \sqrt{-f} \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 g^{5/2}}","\frac{2 n^2 x b^2}{g^2}-\frac{2 n (d+e x) \log \left(c (d+e x)^n\right) b^2}{e g^2}+\frac{e f n^2 \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) b^2}{2 \left(e \sqrt{-f}-d \sqrt{g}\right) g^{5/2}}-\frac{e f n^2 \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) b^2}{2 \left(\sqrt{g} d+e \sqrt{-f}\right) g^{5/2}}+\frac{3 \sqrt{-f} n^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) b^2}{2 g^{5/2}}-\frac{3 \sqrt{-f} n^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) b^2}{2 g^{5/2}}-\frac{2 a n x b}{g^2}-\frac{e f n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right) b}{2 \left(\sqrt{g} d+e \sqrt{-f}\right) g^{5/2}}+\frac{e f n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right) b}{2 \left(e \sqrt{-f}-d \sqrt{g}\right) g^{5/2}}-\frac{3 \sqrt{-f} n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) b}{2 g^{5/2}}+\frac{3 \sqrt{-f} n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) b}{2 g^{5/2}}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e g^2}-\frac{f (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 \left(\sqrt{g} d+e \sqrt{-f}\right) g^2 \left(\sqrt{-f}-\sqrt{g} x\right)}-\frac{f (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 \left(e \sqrt{-f}-d \sqrt{g}\right) g^2 \left(\sqrt{g} x+\sqrt{-f}\right)}+\frac{3 \sqrt{-f} \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{4 g^{5/2}}-\frac{3 \sqrt{-f} \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 g^{5/2}}",1,"(-2*a*b*n*x)/g^2 + (2*b^2*n^2*x)/g^2 - (2*b^2*n*(d + e*x)*Log[c*(d + e*x)^n])/(e*g^2) + ((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(e*g^2) - (f*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(4*(e*Sqrt[-f] + d*Sqrt[g])*g^2*(Sqrt[-f] - Sqrt[g]*x)) - (f*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(4*(e*Sqrt[-f] - d*Sqrt[g])*g^2*(Sqrt[-f] + Sqrt[g]*x)) - (b*e*f*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*(e*Sqrt[-f] + d*Sqrt[g])*g^(5/2)) + (3*Sqrt[-f]*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(4*g^(5/2)) + (b*e*f*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*(e*Sqrt[-f] - d*Sqrt[g])*g^(5/2)) - (3*Sqrt[-f]*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(4*g^(5/2)) + (b^2*e*f*n^2*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*(e*Sqrt[-f] - d*Sqrt[g])*g^(5/2)) - (3*b*Sqrt[-f]*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*g^(5/2)) - (b^2*e*f*n^2*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*(e*Sqrt[-f] + d*Sqrt[g])*g^(5/2)) + (3*b*Sqrt[-f]*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^(5/2)) + (3*b^2*Sqrt[-f]*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*g^(5/2)) - (3*b^2*Sqrt[-f]*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^(5/2))","A",36,13,29,0.4483,1,"{2416, 2389, 2296, 2295, 2409, 2397, 2394, 2393, 2391, 2396, 2433, 2374, 6589}"
326,1,815,0,1.5444667,"\int \frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{\left(f+g x^2\right)^2} \, dx","Int[(x^2*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2)^2,x]","-\frac{b^2 e \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{2 \left(e \sqrt{-f}-d \sqrt{g}\right) g^{3/2}}+\frac{b^2 e \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{2 \left(\sqrt{g} d+e \sqrt{-f}\right) g^{3/2}}+\frac{b^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{2 \sqrt{-f} g^{3/2}}-\frac{b^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{2 \sqrt{-f} g^{3/2}}+\frac{b e \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right) n}{2 \left(\sqrt{g} d+e \sqrt{-f}\right) g^{3/2}}-\frac{b e \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right) n}{2 \left(e \sqrt{-f}-d \sqrt{g}\right) g^{3/2}}-\frac{b \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n}{2 \sqrt{-f} g^{3/2}}+\frac{b \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n}{2 \sqrt{-f} g^{3/2}}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 \left(\sqrt{g} d+e \sqrt{-f}\right) g \left(\sqrt{-f}-\sqrt{g} x\right)}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 \left(e \sqrt{-f}-d \sqrt{g}\right) g \left(\sqrt{g} x+\sqrt{-f}\right)}+\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{4 \sqrt{-f} g^{3/2}}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 \sqrt{-f} g^{3/2}}","-\frac{b^2 e \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{2 \left(e \sqrt{-f}-d \sqrt{g}\right) g^{3/2}}+\frac{b^2 e \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{2 \left(\sqrt{g} d+e \sqrt{-f}\right) g^{3/2}}+\frac{b^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{2 \sqrt{-f} g^{3/2}}-\frac{b^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{2 \sqrt{-f} g^{3/2}}+\frac{b e \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right) n}{2 \left(\sqrt{g} d+e \sqrt{-f}\right) g^{3/2}}-\frac{b e \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right) n}{2 \left(e \sqrt{-f}-d \sqrt{g}\right) g^{3/2}}-\frac{b \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n}{2 \sqrt{-f} g^{3/2}}+\frac{b \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n}{2 \sqrt{-f} g^{3/2}}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 \left(\sqrt{g} d+e \sqrt{-f}\right) g \left(\sqrt{-f}-\sqrt{g} x\right)}+\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 \left(e \sqrt{-f}-d \sqrt{g}\right) g \left(\sqrt{g} x+\sqrt{-f}\right)}+\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{4 \sqrt{-f} g^{3/2}}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 \sqrt{-f} g^{3/2}}",1,"((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(4*(e*Sqrt[-f] + d*Sqrt[g])*g*(Sqrt[-f] - Sqrt[g]*x)) + ((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(4*(e*Sqrt[-f] - d*Sqrt[g])*g*(Sqrt[-f] + Sqrt[g]*x)) + (b*e*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*(e*Sqrt[-f] + d*Sqrt[g])*g^(3/2)) + ((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(4*Sqrt[-f]*g^(3/2)) - (b*e*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*(e*Sqrt[-f] - d*Sqrt[g])*g^(3/2)) - ((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(4*Sqrt[-f]*g^(3/2)) - (b^2*e*n^2*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*(e*Sqrt[-f] - d*Sqrt[g])*g^(3/2)) - (b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*Sqrt[-f]*g^(3/2)) + (b^2*e*n^2*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*(e*Sqrt[-f] + d*Sqrt[g])*g^(3/2)) + (b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*Sqrt[-f]*g^(3/2)) + (b^2*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*Sqrt[-f]*g^(3/2)) - (b^2*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*Sqrt[-f]*g^(3/2))","A",32,10,29,0.3448,1,"{2416, 2409, 2397, 2394, 2393, 2391, 2396, 2433, 2374, 6589}"
327,1,821,0,0.8461605,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{\left(f+g x^2\right)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x^2)^2,x]","-\frac{b^2 e \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{2 \left(e (-f)^{3/2}+d f \sqrt{g}\right) \sqrt{g}}-\frac{b^2 e \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{2 f \left(\sqrt{g} d+e \sqrt{-f}\right) \sqrt{g}}-\frac{b^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{2 (-f)^{3/2} \sqrt{g}}+\frac{b^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{2 (-f)^{3/2} \sqrt{g}}-\frac{b e \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right) n}{2 f \left(\sqrt{g} d+e \sqrt{-f}\right) \sqrt{g}}-\frac{b e \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right) n}{2 \left(e (-f)^{3/2}+d f \sqrt{g}\right) \sqrt{g}}+\frac{b \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n}{2 (-f)^{3/2} \sqrt{g}}-\frac{b \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n}{2 (-f)^{3/2} \sqrt{g}}-\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 f \left(\sqrt{g} d+e \sqrt{-f}\right) \left(\sqrt{-f}-\sqrt{g} x\right)}-\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 f \left(e \sqrt{-f}-d \sqrt{g}\right) \left(\sqrt{g} x+\sqrt{-f}\right)}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{4 (-f)^{3/2} \sqrt{g}}+\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 (-f)^{3/2} \sqrt{g}}","-\frac{b^2 e \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{2 \left(e (-f)^{3/2}+d f \sqrt{g}\right) \sqrt{g}}-\frac{b^2 e \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{2 f \left(\sqrt{g} d+e \sqrt{-f}\right) \sqrt{g}}-\frac{b^2 \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{2 (-f)^{3/2} \sqrt{g}}+\frac{b^2 \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{2 (-f)^{3/2} \sqrt{g}}-\frac{b e \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right) n}{2 f \left(\sqrt{g} d+e \sqrt{-f}\right) \sqrt{g}}-\frac{b e \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right) n}{2 \left(e (-f)^{3/2}+d f \sqrt{g}\right) \sqrt{g}}+\frac{b \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n}{2 (-f)^{3/2} \sqrt{g}}-\frac{b \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n}{2 (-f)^{3/2} \sqrt{g}}-\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 f \left(\sqrt{g} d+e \sqrt{-f}\right) \left(\sqrt{-f}-\sqrt{g} x\right)}-\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 f \left(e \sqrt{-f}-d \sqrt{g}\right) \left(\sqrt{g} x+\sqrt{-f}\right)}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{4 (-f)^{3/2} \sqrt{g}}+\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 (-f)^{3/2} \sqrt{g}}",1,"-((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(4*f*(e*Sqrt[-f] + d*Sqrt[g])*(Sqrt[-f] - Sqrt[g]*x)) - ((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(4*f*(e*Sqrt[-f] - d*Sqrt[g])*(Sqrt[-f] + Sqrt[g]*x)) - (b*e*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f*(e*Sqrt[-f] + d*Sqrt[g])*Sqrt[g]) - ((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(4*(-f)^(3/2)*Sqrt[g]) - (b*e*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*(e*(-f)^(3/2) + d*f*Sqrt[g])*Sqrt[g]) + ((a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(4*(-f)^(3/2)*Sqrt[g]) - (b^2*e*n^2*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*(e*(-f)^(3/2) + d*f*Sqrt[g])*Sqrt[g]) + (b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*(-f)^(3/2)*Sqrt[g]) - (b^2*e*n^2*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f*(e*Sqrt[-f] + d*Sqrt[g])*Sqrt[g]) - (b*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*(-f)^(3/2)*Sqrt[g]) - (b^2*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*(-f)^(3/2)*Sqrt[g]) + (b^2*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*(-f)^(3/2)*Sqrt[g])","A",20,9,26,0.3462,1,"{2409, 2397, 2394, 2393, 2391, 2396, 2433, 2374, 6589}"
328,1,919,0,1.6129307,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x^2 \left(f+g x^2\right)^2} \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2/(x^2*(f + g*x^2)^2),x]","\frac{b^2 e \sqrt{g} \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{2 f \left(e (-f)^{3/2}+d f \sqrt{g}\right)}+\frac{b^2 e \sqrt{g} \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{2 f^2 \left(\sqrt{g} d+e \sqrt{-f}\right)}+\frac{2 b^2 e \text{PolyLog}\left(2,\frac{e x}{d}+1\right) n^2}{d f^2}-\frac{3 b^2 \sqrt{g} \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{2 (-f)^{5/2}}+\frac{3 b^2 \sqrt{g} \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{2 (-f)^{5/2}}+\frac{2 b e \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right) n}{d f^2}+\frac{b e \sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right) n}{2 f^2 \left(\sqrt{g} d+e \sqrt{-f}\right)}+\frac{b e \sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right) n}{2 f \left(e (-f)^{3/2}+d f \sqrt{g}\right)}+\frac{3 b \sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n}{2 (-f)^{5/2}}-\frac{3 b \sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n}{2 (-f)^{5/2}}-\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{d f^2 x}+\frac{g (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 f^2 \left(\sqrt{g} d+e \sqrt{-f}\right) \left(\sqrt{-f}-\sqrt{g} x\right)}+\frac{g (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 f^2 \left(e \sqrt{-f}-d \sqrt{g}\right) \left(\sqrt{g} x+\sqrt{-f}\right)}-\frac{3 \sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{4 (-f)^{5/2}}+\frac{3 \sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 (-f)^{5/2}}","\frac{b^2 e \sqrt{g} \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{2 f \left(e (-f)^{3/2}+d f \sqrt{g}\right)}+\frac{b^2 e \sqrt{g} \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{2 f^2 \left(\sqrt{g} d+e \sqrt{-f}\right)}+\frac{2 b^2 e \text{PolyLog}\left(2,\frac{e x}{d}+1\right) n^2}{d f^2}-\frac{3 b^2 \sqrt{g} \text{PolyLog}\left(3,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{2 (-f)^{5/2}}+\frac{3 b^2 \sqrt{g} \text{PolyLog}\left(3,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{2 (-f)^{5/2}}+\frac{2 b e \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right) n}{d f^2}+\frac{b e \sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right) n}{2 f^2 \left(\sqrt{g} d+e \sqrt{-f}\right)}+\frac{b e \sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right) n}{2 f \left(e (-f)^{3/2}+d f \sqrt{g}\right)}+\frac{3 b \sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n}{2 (-f)^{5/2}}-\frac{3 b \sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n}{2 (-f)^{5/2}}-\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{d f^2 x}+\frac{g (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 f^2 \left(\sqrt{g} d+e \sqrt{-f}\right) \left(\sqrt{-f}-\sqrt{g} x\right)}+\frac{g (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 f^2 \left(e \sqrt{-f}-d \sqrt{g}\right) \left(\sqrt{g} x+\sqrt{-f}\right)}-\frac{3 \sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{4 (-f)^{5/2}}+\frac{3 \sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e \left(\sqrt{g} x+\sqrt{-f}\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 (-f)^{5/2}}",1,"(2*b*e*n*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/(d*f^2) - ((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(d*f^2*x) + (g*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(4*f^2*(e*Sqrt[-f] + d*Sqrt[g])*(Sqrt[-f] - Sqrt[g]*x)) + (g*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(4*f^2*(e*Sqrt[-f] - d*Sqrt[g])*(Sqrt[-f] + Sqrt[g]*x)) + (b*e*Sqrt[g]*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f^2*(e*Sqrt[-f] + d*Sqrt[g])) - (3*Sqrt[g]*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(4*(-f)^(5/2)) + (b*e*Sqrt[g]*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*f*(e*(-f)^(3/2) + d*f*Sqrt[g])) + (3*Sqrt[g]*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(4*(-f)^(5/2)) + (b^2*e*Sqrt[g]*n^2*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*f*(e*(-f)^(3/2) + d*f*Sqrt[g])) + (3*b*Sqrt[g]*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*(-f)^(5/2)) + (b^2*e*Sqrt[g]*n^2*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f^2*(e*Sqrt[-f] + d*Sqrt[g])) - (3*b*Sqrt[g]*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*(-f)^(5/2)) + (2*b^2*e*n^2*PolyLog[2, 1 + (e*x)/d])/(d*f^2) - (3*b^2*Sqrt[g]*n^2*PolyLog[3, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*(-f)^(5/2)) + (3*b^2*Sqrt[g]*n^2*PolyLog[3, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*(-f)^(5/2))","A",35,11,29,0.3793,1,"{2416, 2397, 2394, 2315, 2409, 2393, 2391, 2396, 2433, 2374, 6589}"
329,1,477,0,0.5373322,"\int \frac{\log ^3\left(c (a+b x)^n\right)}{d+e x^2} \, dx","Int[Log[c*(a + b*x)^n]^3/(d + e*x^2),x]","\frac{3 n^2 \log \left(c (a+b x)^n\right) \text{PolyLog}\left(3,-\frac{\sqrt{e} (a+b x)}{b \sqrt{-d}-a \sqrt{e}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{3 n^2 \log \left(c (a+b x)^n\right) \text{PolyLog}\left(3,\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+b \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{3 n \log ^2\left(c (a+b x)^n\right) \text{PolyLog}\left(2,-\frac{\sqrt{e} (a+b x)}{b \sqrt{-d}-a \sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{3 n \log ^2\left(c (a+b x)^n\right) \text{PolyLog}\left(2,\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+b \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{3 n^3 \text{PolyLog}\left(4,-\frac{\sqrt{e} (a+b x)}{b \sqrt{-d}-a \sqrt{e}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{3 n^3 \text{PolyLog}\left(4,\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+b \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{\log ^3\left(c (a+b x)^n\right) \log \left(\frac{b \left(\sqrt{-d}-\sqrt{e} x\right)}{a \sqrt{e}+b \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\log ^3\left(c (a+b x)^n\right) \log \left(\frac{b \left(\sqrt{-d}+\sqrt{e} x\right)}{b \sqrt{-d}-a \sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}","\frac{3 n^2 \log \left(c (a+b x)^n\right) \text{PolyLog}\left(3,-\frac{\sqrt{e} (a+b x)}{b \sqrt{-d}-a \sqrt{e}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{3 n^2 \log \left(c (a+b x)^n\right) \text{PolyLog}\left(3,\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+b \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{3 n \log ^2\left(c (a+b x)^n\right) \text{PolyLog}\left(2,-\frac{\sqrt{e} (a+b x)}{b \sqrt{-d}-a \sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{3 n \log ^2\left(c (a+b x)^n\right) \text{PolyLog}\left(2,\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+b \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{3 n^3 \text{PolyLog}\left(4,-\frac{\sqrt{e} (a+b x)}{b \sqrt{-d}-a \sqrt{e}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{3 n^3 \text{PolyLog}\left(4,\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+b \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{\log ^3\left(c (a+b x)^n\right) \log \left(\frac{b \left(\sqrt{-d}-\sqrt{e} x\right)}{a \sqrt{e}+b \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\log ^3\left(c (a+b x)^n\right) \log \left(\frac{b \left(\sqrt{-d}+\sqrt{e} x\right)}{b \sqrt{-d}-a \sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}",1,"(Log[c*(a + b*x)^n]^3*Log[(b*(Sqrt[-d] - Sqrt[e]*x))/(b*Sqrt[-d] + a*Sqrt[e])])/(2*Sqrt[-d]*Sqrt[e]) - (Log[c*(a + b*x)^n]^3*Log[(b*(Sqrt[-d] + Sqrt[e]*x))/(b*Sqrt[-d] - a*Sqrt[e])])/(2*Sqrt[-d]*Sqrt[e]) - (3*n*Log[c*(a + b*x)^n]^2*PolyLog[2, -((Sqrt[e]*(a + b*x))/(b*Sqrt[-d] - a*Sqrt[e]))])/(2*Sqrt[-d]*Sqrt[e]) + (3*n*Log[c*(a + b*x)^n]^2*PolyLog[2, (Sqrt[e]*(a + b*x))/(b*Sqrt[-d] + a*Sqrt[e])])/(2*Sqrt[-d]*Sqrt[e]) + (3*n^2*Log[c*(a + b*x)^n]*PolyLog[3, -((Sqrt[e]*(a + b*x))/(b*Sqrt[-d] - a*Sqrt[e]))])/(Sqrt[-d]*Sqrt[e]) - (3*n^2*Log[c*(a + b*x)^n]*PolyLog[3, (Sqrt[e]*(a + b*x))/(b*Sqrt[-d] + a*Sqrt[e])])/(Sqrt[-d]*Sqrt[e]) - (3*n^3*PolyLog[4, -((Sqrt[e]*(a + b*x))/(b*Sqrt[-d] - a*Sqrt[e]))])/(Sqrt[-d]*Sqrt[e]) + (3*n^3*PolyLog[4, (Sqrt[e]*(a + b*x))/(b*Sqrt[-d] + a*Sqrt[e])])/(Sqrt[-d]*Sqrt[e])","A",12,6,22,0.2727,1,"{2409, 2396, 2433, 2374, 2383, 6589}"
330,1,347,0,0.316108,"\int \frac{\log ^2\left(c (a+b x)^n\right)}{d+e x^2} \, dx","Int[Log[c*(a + b*x)^n]^2/(d + e*x^2),x]","-\frac{n \log \left(c (a+b x)^n\right) \text{PolyLog}\left(2,-\frac{\sqrt{e} (a+b x)}{b \sqrt{-d}-a \sqrt{e}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{n \log \left(c (a+b x)^n\right) \text{PolyLog}\left(2,\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+b \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{n^2 \text{PolyLog}\left(3,-\frac{\sqrt{e} (a+b x)}{b \sqrt{-d}-a \sqrt{e}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{n^2 \text{PolyLog}\left(3,\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+b \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{\log ^2\left(c (a+b x)^n\right) \log \left(\frac{b \left(\sqrt{-d}-\sqrt{e} x\right)}{a \sqrt{e}+b \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\log ^2\left(c (a+b x)^n\right) \log \left(\frac{b \left(\sqrt{-d}+\sqrt{e} x\right)}{b \sqrt{-d}-a \sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}","-\frac{n \log \left(c (a+b x)^n\right) \text{PolyLog}\left(2,-\frac{\sqrt{e} (a+b x)}{b \sqrt{-d}-a \sqrt{e}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{n \log \left(c (a+b x)^n\right) \text{PolyLog}\left(2,\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+b \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{n^2 \text{PolyLog}\left(3,-\frac{\sqrt{e} (a+b x)}{b \sqrt{-d}-a \sqrt{e}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{n^2 \text{PolyLog}\left(3,\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+b \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{\log ^2\left(c (a+b x)^n\right) \log \left(\frac{b \left(\sqrt{-d}-\sqrt{e} x\right)}{a \sqrt{e}+b \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\log ^2\left(c (a+b x)^n\right) \log \left(\frac{b \left(\sqrt{-d}+\sqrt{e} x\right)}{b \sqrt{-d}-a \sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}",1,"(Log[c*(a + b*x)^n]^2*Log[(b*(Sqrt[-d] - Sqrt[e]*x))/(b*Sqrt[-d] + a*Sqrt[e])])/(2*Sqrt[-d]*Sqrt[e]) - (Log[c*(a + b*x)^n]^2*Log[(b*(Sqrt[-d] + Sqrt[e]*x))/(b*Sqrt[-d] - a*Sqrt[e])])/(2*Sqrt[-d]*Sqrt[e]) - (n*Log[c*(a + b*x)^n]*PolyLog[2, -((Sqrt[e]*(a + b*x))/(b*Sqrt[-d] - a*Sqrt[e]))])/(Sqrt[-d]*Sqrt[e]) + (n*Log[c*(a + b*x)^n]*PolyLog[2, (Sqrt[e]*(a + b*x))/(b*Sqrt[-d] + a*Sqrt[e])])/(Sqrt[-d]*Sqrt[e]) + (n^2*PolyLog[3, -((Sqrt[e]*(a + b*x))/(b*Sqrt[-d] - a*Sqrt[e]))])/(Sqrt[-d]*Sqrt[e]) - (n^2*PolyLog[3, (Sqrt[e]*(a + b*x))/(b*Sqrt[-d] + a*Sqrt[e])])/(Sqrt[-d]*Sqrt[e])","A",10,5,22,0.2273,1,"{2409, 2396, 2433, 2374, 6589}"
331,1,229,0,0.164198,"\int \frac{\log \left(c (a+b x)^n\right)}{d+e x^2} \, dx","Int[Log[c*(a + b*x)^n]/(d + e*x^2),x]","-\frac{n \text{PolyLog}\left(2,-\frac{\sqrt{e} (a+b x)}{b \sqrt{-d}-a \sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{n \text{PolyLog}\left(2,\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+b \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\log \left(c (a+b x)^n\right) \log \left(\frac{b \left(\sqrt{-d}-\sqrt{e} x\right)}{a \sqrt{e}+b \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\log \left(c (a+b x)^n\right) \log \left(\frac{b \left(\sqrt{-d}+\sqrt{e} x\right)}{b \sqrt{-d}-a \sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}","-\frac{n \text{PolyLog}\left(2,-\frac{\sqrt{e} (a+b x)}{b \sqrt{-d}-a \sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{n \text{PolyLog}\left(2,\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+b \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\log \left(c (a+b x)^n\right) \log \left(\frac{b \left(\sqrt{-d}-\sqrt{e} x\right)}{a \sqrt{e}+b \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\log \left(c (a+b x)^n\right) \log \left(\frac{b \left(\sqrt{-d}+\sqrt{e} x\right)}{b \sqrt{-d}-a \sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}",1,"(Log[c*(a + b*x)^n]*Log[(b*(Sqrt[-d] - Sqrt[e]*x))/(b*Sqrt[-d] + a*Sqrt[e])])/(2*Sqrt[-d]*Sqrt[e]) - (Log[c*(a + b*x)^n]*Log[(b*(Sqrt[-d] + Sqrt[e]*x))/(b*Sqrt[-d] - a*Sqrt[e])])/(2*Sqrt[-d]*Sqrt[e]) - (n*PolyLog[2, -((Sqrt[e]*(a + b*x))/(b*Sqrt[-d] - a*Sqrt[e]))])/(2*Sqrt[-d]*Sqrt[e]) + (n*PolyLog[2, (Sqrt[e]*(a + b*x))/(b*Sqrt[-d] + a*Sqrt[e])])/(2*Sqrt[-d]*Sqrt[e])","A",8,4,20,0.2000,1,"{2409, 2394, 2393, 2391}"
332,0,0,0,0.114693,"\int \frac{1}{\left(d+e x^2\right) \log \left(c (a+b x)^n\right)} \, dx","Int[1/((d + e*x^2)*Log[c*(a + b*x)^n]),x]","\int \frac{1}{\left(d+e x^2\right) \log \left(c (a+b x)^n\right)} \, dx","-\frac{\text{Int}\left(\frac{1}{\left(\sqrt{-d}-\sqrt{e} x\right) \log \left(c (a+b x)^n\right)},x\right)}{2 \sqrt{-d}}-\frac{\text{Int}\left(\frac{1}{\left(\sqrt{-d}+\sqrt{e} x\right) \log \left(c (a+b x)^n\right)},x\right)}{2 \sqrt{-d}}",0,"-Defer[Int][1/((Sqrt[-d] - Sqrt[e]*x)*Log[c*(a + b*x)^n]), x]/(2*Sqrt[-d]) - Defer[Int][1/((Sqrt[-d] + Sqrt[e]*x)*Log[c*(a + b*x)^n]), x]/(2*Sqrt[-d])","A",0,0,0,0,-1,"{}"
333,1,27,0,0.1300073,"\int \frac{\log \left(c-\frac{a (1-c) x^{-m}}{b}\right)}{x \left(a+b x^m\right)} \, dx","Int[Log[c - (a*(1 - c))/(b*x^m)]/(x*(a + b*x^m)),x]","\frac{\text{PolyLog}\left(2,\frac{(1-c) \left(a x^{-m}+b\right)}{b}\right)}{a m}","\frac{\text{PolyLog}\left(2,\frac{(1-c) \left(a x^{-m}+b\right)}{b}\right)}{a m}",1,"PolyLog[2, ((1 - c)*(b + a/x^m))/b]/(a*m)","A",4,4,32,0.1250,1,"{2475, 2412, 2393, 2391}"
334,1,27,0,0.1802167,"\int \frac{\log \left(\frac{x^{-m} \left(-a+a c+b c x^m\right)}{b}\right)}{x \left(a+b x^m\right)} \, dx","Int[Log[(-a + a*c + b*c*x^m)/(b*x^m)]/(x*(a + b*x^m)),x]","\frac{\text{PolyLog}\left(2,\frac{(1-c) \left(a x^{-m}+b\right)}{b}\right)}{a m}","\frac{\text{PolyLog}\left(2,\frac{(1-c) \left(a x^{-m}+b\right)}{b}\right)}{a m}",1,"PolyLog[2, ((1 - c)*(b + a/x^m))/b]/(a*m)","A",5,5,36,0.1389,1,"{2480, 2475, 2412, 2393, 2391}"
335,1,28,0,0.1349786,"\int \frac{\log \left(c \left(a-\frac{(d-a c d) x^{-m}}{c e}\right)\right)}{x \left(d+e x^m\right)} \, dx","Int[Log[c*(a - (d - a*c*d)/(c*e*x^m))]/(x*(d + e*x^m)),x]","\frac{\text{PolyLog}\left(2,\frac{(1-a c) \left(d x^{-m}+e\right)}{e}\right)}{d m}","\frac{\text{PolyLog}\left(2,\frac{(1-a c) \left(d x^{-m}+e\right)}{e}\right)}{d m}",1,"PolyLog[2, ((1 - a*c)*(e + d/x^m))/e]/(d*m)","A",4,4,38,0.1053,1,"{2475, 2412, 2393, 2391}"
336,1,28,0,0.1829424,"\int \frac{\log \left(\frac{x^{-m} \left(-d+a c d+a c e x^m\right)}{e}\right)}{x \left(d+e x^m\right)} \, dx","Int[Log[(-d + a*c*d + a*c*e*x^m)/(e*x^m)]/(x*(d + e*x^m)),x]","\frac{\text{PolyLog}\left(2,\frac{(1-a c) \left(d x^{-m}+e\right)}{e}\right)}{d m}","\frac{\text{PolyLog}\left(2,\frac{(1-a c) \left(d x^{-m}+e\right)}{e}\right)}{d m}",1,"PolyLog[2, ((1 - a*c)*(e + d/x^m))/e]/(d*m)","A",5,5,38,0.1316,1,"{2480, 2475, 2412, 2393, 2391}"
337,1,24,0,0.0309399,"\int \frac{\log \left(\frac{2 a}{a+b x}\right)}{a^2-b^2 x^2} \, dx","Int[Log[(2*a)/(a + b*x)]/(a^2 - b^2*x^2),x]","\frac{\text{PolyLog}\left(2,1-\frac{2 a}{a+b x}\right)}{2 a b}","\frac{\text{PolyLog}\left(2,1-\frac{2 a}{a+b x}\right)}{2 a b}",1,"PolyLog[2, 1 - (2*a)/(a + b*x)]/(2*a*b)","A",2,2,26,0.07692,1,"{2402, 2315}"
338,1,24,0,0.1332368,"\int \frac{\log \left(\frac{2 a}{a+b x}\right)}{(a-b x) (a+b x)} \, dx","Int[Log[(2*a)/(a + b*x)]/((a - b*x)*(a + b*x)),x]","\frac{\text{PolyLog}\left(2,1-\frac{2 a}{a+b x}\right)}{2 a b}","\frac{\text{PolyLog}\left(2,1-\frac{2 a}{a+b x}\right)}{2 a b}",1,"PolyLog[2, 1 - (2*a)/(a + b*x)]/(2*a*b)","A",4,4,27,0.1481,1,"{2411, 2343, 2333, 2315}"
339,1,37,0,0.0250285,"\int \frac{\log \left(\frac{a (1-c)+b (1+c) x}{a+b x}\right)}{a^2-b^2 x^2} \, dx","Int[Log[(a*(1 - c) + b*(1 + c)*x)/(a + b*x)]/(a^2 - b^2*x^2),x]","\frac{\text{PolyLog}\left(2,1-\frac{a (1-c)+b (c+1) x}{a+b x}\right)}{2 a b}","\frac{\text{PolyLog}\left(2,1-\frac{a (1-c)+b (c+1) x}{a+b x}\right)}{2 a b}",1,"PolyLog[2, 1 - (a*(1 - c) + b*(1 + c)*x)/(a + b*x)]/(2*a*b)","A",1,1,38,0.02632,1,"{2447}"
340,1,27,0,0.0739229,"\int \frac{\log \left(\frac{a (1-c)+b (1+c) x}{a+b x}\right)}{(a-b x) (a+b x)} \, dx","Int[Log[(a*(1 - c) + b*(1 + c)*x)/(a + b*x)]/((a - b*x)*(a + b*x)),x]","\frac{\text{PolyLog}\left(2,\frac{c (a-b x)}{a+b x}\right)}{2 a b}","\frac{\text{PolyLog}\left(2,\frac{c (a-b x)}{a+b x}\right)}{2 a b}",1,"PolyLog[2, (c*(a - b*x))/(a + b*x)]/(2*a*b)","A",2,2,39,0.05128,1,"{2502, 2315}"
341,1,27,0,0.019532,"\int \frac{\log \left(1-\frac{c (a-b x)}{a+b x}\right)}{a^2-b^2 x^2} \, dx","Int[Log[1 - (c*(a - b*x))/(a + b*x)]/(a^2 - b^2*x^2),x]","\frac{\text{PolyLog}\left(2,\frac{c (a-b x)}{a+b x}\right)}{2 a b}","\frac{\text{PolyLog}\left(2,\frac{c (a-b x)}{a+b x}\right)}{2 a b}",1,"PolyLog[2, (c*(a - b*x))/(a + b*x)]/(2*a*b)","A",1,1,34,0.02941,1,"{2447}"
342,1,27,0,0.127099,"\int \frac{\log \left(1-\frac{c (a-b x)}{a+b x}\right)}{(a-b x) (a+b x)} \, dx","Int[Log[1 - (c*(a - b*x))/(a + b*x)]/((a - b*x)*(a + b*x)),x]","\frac{\text{PolyLog}\left(2,\frac{c (a-b x)}{a+b x}\right)}{2 a b}","\frac{\text{PolyLog}\left(2,\frac{c (a-b x)}{a+b x}\right)}{2 a b}",1,"PolyLog[2, (c*(a - b*x))/(a + b*x)]/(2*a*b)","A",3,3,35,0.08571,1,"{2517, 2502, 2315}"
343,1,238,0,0.3513503,"\int \frac{\log ^3\left(c (a+b x)^n\right)}{d x+e x^2} \, dx","Int[Log[c*(a + b*x)^n]^3/(d*x + e*x^2),x]","\frac{6 n^2 \log \left(c (a+b x)^n\right) \text{PolyLog}\left(3,-\frac{e (a+b x)}{b d-a e}\right)}{d}-\frac{3 n \log ^2\left(c (a+b x)^n\right) \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{d}-\frac{6 n^2 \text{PolyLog}\left(3,\frac{b x}{a}+1\right) \log \left(c (a+b x)^n\right)}{d}+\frac{3 n \text{PolyLog}\left(2,\frac{b x}{a}+1\right) \log ^2\left(c (a+b x)^n\right)}{d}-\frac{6 n^3 \text{PolyLog}\left(4,-\frac{e (a+b x)}{b d-a e}\right)}{d}+\frac{6 n^3 \text{PolyLog}\left(4,\frac{b x}{a}+1\right)}{d}-\frac{\log ^3\left(c (a+b x)^n\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{d}+\frac{\log \left(-\frac{b x}{a}\right) \log ^3\left(c (a+b x)^n\right)}{d}","\frac{6 n^2 \log \left(c (a+b x)^n\right) \text{PolyLog}\left(3,-\frac{e (a+b x)}{b d-a e}\right)}{d}-\frac{3 n \log ^2\left(c (a+b x)^n\right) \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{d}-\frac{6 n^2 \text{PolyLog}\left(3,\frac{b x}{a}+1\right) \log \left(c (a+b x)^n\right)}{d}+\frac{3 n \text{PolyLog}\left(2,\frac{b x}{a}+1\right) \log ^2\left(c (a+b x)^n\right)}{d}-\frac{6 n^3 \text{PolyLog}\left(4,-\frac{e (a+b x)}{b d-a e}\right)}{d}+\frac{6 n^3 \text{PolyLog}\left(4,\frac{b x}{a}+1\right)}{d}-\frac{\log ^3\left(c (a+b x)^n\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{d}+\frac{\log \left(-\frac{b x}{a}\right) \log ^3\left(c (a+b x)^n\right)}{d}",1,"(Log[-((b*x)/a)]*Log[c*(a + b*x)^n]^3)/d - (Log[c*(a + b*x)^n]^3*Log[(b*(d + e*x))/(b*d - a*e)])/d - (3*n*Log[c*(a + b*x)^n]^2*PolyLog[2, -((e*(a + b*x))/(b*d - a*e))])/d + (3*n*Log[c*(a + b*x)^n]^2*PolyLog[2, 1 + (b*x)/a])/d + (6*n^2*Log[c*(a + b*x)^n]*PolyLog[3, -((e*(a + b*x))/(b*d - a*e))])/d - (6*n^2*Log[c*(a + b*x)^n]*PolyLog[3, 1 + (b*x)/a])/d - (6*n^3*PolyLog[4, -((e*(a + b*x))/(b*d - a*e))])/d + (6*n^3*PolyLog[4, 1 + (b*x)/a])/d","A",13,7,24,0.2917,1,"{1593, 2416, 2396, 2433, 2374, 2383, 6589}"
344,1,168,0,0.2480682,"\int \frac{\log ^2\left(c (a+b x)^n\right)}{d x+e x^2} \, dx","Int[Log[c*(a + b*x)^n]^2/(d*x + e*x^2),x]","-\frac{2 n \log \left(c (a+b x)^n\right) \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{d}+\frac{2 n \text{PolyLog}\left(2,\frac{b x}{a}+1\right) \log \left(c (a+b x)^n\right)}{d}+\frac{2 n^2 \text{PolyLog}\left(3,-\frac{e (a+b x)}{b d-a e}\right)}{d}-\frac{2 n^2 \text{PolyLog}\left(3,\frac{b x}{a}+1\right)}{d}-\frac{\log ^2\left(c (a+b x)^n\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{d}+\frac{\log \left(-\frac{b x}{a}\right) \log ^2\left(c (a+b x)^n\right)}{d}","-\frac{2 n \log \left(c (a+b x)^n\right) \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{d}+\frac{2 n \text{PolyLog}\left(2,\frac{b x}{a}+1\right) \log \left(c (a+b x)^n\right)}{d}+\frac{2 n^2 \text{PolyLog}\left(3,-\frac{e (a+b x)}{b d-a e}\right)}{d}-\frac{2 n^2 \text{PolyLog}\left(3,\frac{b x}{a}+1\right)}{d}-\frac{\log ^2\left(c (a+b x)^n\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{d}+\frac{\log \left(-\frac{b x}{a}\right) \log ^2\left(c (a+b x)^n\right)}{d}",1,"(Log[-((b*x)/a)]*Log[c*(a + b*x)^n]^2)/d - (Log[c*(a + b*x)^n]^2*Log[(b*(d + e*x))/(b*d - a*e)])/d - (2*n*Log[c*(a + b*x)^n]*PolyLog[2, -((e*(a + b*x))/(b*d - a*e))])/d + (2*n*Log[c*(a + b*x)^n]*PolyLog[2, 1 + (b*x)/a])/d + (2*n^2*PolyLog[3, -((e*(a + b*x))/(b*d - a*e))])/d - (2*n^2*PolyLog[3, 1 + (b*x)/a])/d","A",11,6,24,0.2500,1,"{1593, 2416, 2396, 2433, 2374, 6589}"
345,1,97,0,0.1235384,"\int \frac{\log \left(c (a+b x)^n\right)}{d x+e x^2} \, dx","Int[Log[c*(a + b*x)^n]/(d*x + e*x^2),x]","-\frac{n \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{d}+\frac{n \text{PolyLog}\left(2,\frac{b x}{a}+1\right)}{d}-\frac{\log \left(c (a+b x)^n\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{d}+\frac{\log \left(-\frac{b x}{a}\right) \log \left(c (a+b x)^n\right)}{d}","-\frac{n \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{d}+\frac{n \text{PolyLog}\left(2,\frac{b x}{a}+1\right)}{d}-\frac{\log \left(c (a+b x)^n\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{d}+\frac{\log \left(-\frac{b x}{a}\right) \log \left(c (a+b x)^n\right)}{d}",1,"(Log[-((b*x)/a)]*Log[c*(a + b*x)^n])/d - (Log[c*(a + b*x)^n]*Log[(b*(d + e*x))/(b*d - a*e)])/d - (n*PolyLog[2, -((e*(a + b*x))/(b*d - a*e))])/d + (n*PolyLog[2, 1 + (b*x)/a])/d","A",8,9,22,0.4091,1,"{1593, 36, 29, 31, 2416, 2394, 2315, 2393, 2391}"
346,0,0,0,0.1098904,"\int \frac{1}{\left(d x+e x^2\right) \log \left(c (a+b x)^n\right)} \, dx","Int[1/((d*x + e*x^2)*Log[c*(a + b*x)^n]),x]","\int \frac{1}{\left(d x+e x^2\right) \log \left(c (a+b x)^n\right)} \, dx","\frac{\text{Int}\left(\frac{1}{x \log \left(c (a+b x)^n\right)},x\right)}{d}-\frac{e \text{Int}\left(\frac{1}{(d+e x) \log \left(c (a+b x)^n\right)},x\right)}{d}",0,"Defer[Int][1/(x*Log[c*(a + b*x)^n]), x]/d - (e*Defer[Int][1/((d + e*x)*Log[c*(a + b*x)^n]), x])/d","A",0,0,0,0,-1,"{}"
347,1,500,0,0.7007867,"\int \frac{\log ^3\left(c (a+b x)^n\right)}{d+e x+f x^2} \, dx","Int[Log[c*(a + b*x)^n]^3/(d + e*x + f*x^2),x]","-\frac{6 n^2 \log \left(c (a+b x)^n\right) \text{PolyLog}\left(3,\frac{2 f (a+b x)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{6 n^2 \log \left(c (a+b x)^n\right) \text{PolyLog}\left(3,\frac{2 f (a+b x)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{3 n \log ^2\left(c (a+b x)^n\right) \text{PolyLog}\left(2,\frac{2 f (a+b x)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{3 n \log ^2\left(c (a+b x)^n\right) \text{PolyLog}\left(2,\frac{2 f (a+b x)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{6 n^3 \text{PolyLog}\left(4,\frac{2 f (a+b x)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{6 n^3 \text{PolyLog}\left(4,\frac{2 f (a+b x)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{\log ^3\left(c (a+b x)^n\right) \log \left(-\frac{b \left(-\sqrt{e^2-4 d f}+e+2 f x\right)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{\log ^3\left(c (a+b x)^n\right) \log \left(-\frac{b \left(\sqrt{e^2-4 d f}+e+2 f x\right)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}","-\frac{6 n^2 \log \left(c (a+b x)^n\right) \text{PolyLog}\left(3,\frac{2 f (a+b x)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{6 n^2 \log \left(c (a+b x)^n\right) \text{PolyLog}\left(3,\frac{2 f (a+b x)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{3 n \log ^2\left(c (a+b x)^n\right) \text{PolyLog}\left(2,\frac{2 f (a+b x)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{3 n \log ^2\left(c (a+b x)^n\right) \text{PolyLog}\left(2,\frac{2 f (a+b x)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{6 n^3 \text{PolyLog}\left(4,\frac{2 f (a+b x)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{6 n^3 \text{PolyLog}\left(4,\frac{2 f (a+b x)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{\log ^3\left(c (a+b x)^n\right) \log \left(-\frac{b \left(-\sqrt{e^2-4 d f}+e+2 f x\right)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{\log ^3\left(c (a+b x)^n\right) \log \left(-\frac{b \left(\sqrt{e^2-4 d f}+e+2 f x\right)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}",1,"(Log[c*(a + b*x)^n]^3*Log[-((b*(e - Sqrt[e^2 - 4*d*f] + 2*f*x))/(2*a*f - b*(e - Sqrt[e^2 - 4*d*f])))])/Sqrt[e^2 - 4*d*f] - (Log[c*(a + b*x)^n]^3*Log[-((b*(e + Sqrt[e^2 - 4*d*f] + 2*f*x))/(2*a*f - b*(e + Sqrt[e^2 - 4*d*f])))])/Sqrt[e^2 - 4*d*f] + (3*n*Log[c*(a + b*x)^n]^2*PolyLog[2, (2*f*(a + b*x))/(2*a*f - b*(e - Sqrt[e^2 - 4*d*f]))])/Sqrt[e^2 - 4*d*f] - (3*n*Log[c*(a + b*x)^n]^2*PolyLog[2, (2*f*(a + b*x))/(2*a*f - b*(e + Sqrt[e^2 - 4*d*f]))])/Sqrt[e^2 - 4*d*f] - (6*n^2*Log[c*(a + b*x)^n]*PolyLog[3, (2*f*(a + b*x))/(2*a*f - b*(e - Sqrt[e^2 - 4*d*f]))])/Sqrt[e^2 - 4*d*f] + (6*n^2*Log[c*(a + b*x)^n]*PolyLog[3, (2*f*(a + b*x))/(2*a*f - b*(e + Sqrt[e^2 - 4*d*f]))])/Sqrt[e^2 - 4*d*f] + (6*n^3*PolyLog[4, (2*f*(a + b*x))/(2*a*f - b*(e - Sqrt[e^2 - 4*d*f]))])/Sqrt[e^2 - 4*d*f] - (6*n^3*PolyLog[4, (2*f*(a + b*x))/(2*a*f - b*(e + Sqrt[e^2 - 4*d*f]))])/Sqrt[e^2 - 4*d*f]","A",12,6,25,0.2400,1,"{2418, 2396, 2433, 2374, 2383, 6589}"
348,1,372,0,0.4055321,"\int \frac{\log ^2\left(c (a+b x)^n\right)}{d+e x+f x^2} \, dx","Int[Log[c*(a + b*x)^n]^2/(d + e*x + f*x^2),x]","\frac{2 n \log \left(c (a+b x)^n\right) \text{PolyLog}\left(2,\frac{2 f (a+b x)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{2 n \log \left(c (a+b x)^n\right) \text{PolyLog}\left(2,\frac{2 f (a+b x)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{2 n^2 \text{PolyLog}\left(3,\frac{2 f (a+b x)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{2 n^2 \text{PolyLog}\left(3,\frac{2 f (a+b x)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{\log ^2\left(c (a+b x)^n\right) \log \left(-\frac{b \left(-\sqrt{e^2-4 d f}+e+2 f x\right)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{\log ^2\left(c (a+b x)^n\right) \log \left(-\frac{b \left(\sqrt{e^2-4 d f}+e+2 f x\right)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}","\frac{2 n \log \left(c (a+b x)^n\right) \text{PolyLog}\left(2,\frac{2 f (a+b x)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{2 n \log \left(c (a+b x)^n\right) \text{PolyLog}\left(2,\frac{2 f (a+b x)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{2 n^2 \text{PolyLog}\left(3,\frac{2 f (a+b x)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{2 n^2 \text{PolyLog}\left(3,\frac{2 f (a+b x)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{\log ^2\left(c (a+b x)^n\right) \log \left(-\frac{b \left(-\sqrt{e^2-4 d f}+e+2 f x\right)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{\log ^2\left(c (a+b x)^n\right) \log \left(-\frac{b \left(\sqrt{e^2-4 d f}+e+2 f x\right)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}",1,"(Log[c*(a + b*x)^n]^2*Log[-((b*(e - Sqrt[e^2 - 4*d*f] + 2*f*x))/(2*a*f - b*(e - Sqrt[e^2 - 4*d*f])))])/Sqrt[e^2 - 4*d*f] - (Log[c*(a + b*x)^n]^2*Log[-((b*(e + Sqrt[e^2 - 4*d*f] + 2*f*x))/(2*a*f - b*(e + Sqrt[e^2 - 4*d*f])))])/Sqrt[e^2 - 4*d*f] + (2*n*Log[c*(a + b*x)^n]*PolyLog[2, (2*f*(a + b*x))/(2*a*f - b*(e - Sqrt[e^2 - 4*d*f]))])/Sqrt[e^2 - 4*d*f] - (2*n*Log[c*(a + b*x)^n]*PolyLog[2, (2*f*(a + b*x))/(2*a*f - b*(e + Sqrt[e^2 - 4*d*f]))])/Sqrt[e^2 - 4*d*f] - (2*n^2*PolyLog[3, (2*f*(a + b*x))/(2*a*f - b*(e - Sqrt[e^2 - 4*d*f]))])/Sqrt[e^2 - 4*d*f] + (2*n^2*PolyLog[3, (2*f*(a + b*x))/(2*a*f - b*(e + Sqrt[e^2 - 4*d*f]))])/Sqrt[e^2 - 4*d*f]","A",10,5,25,0.2000,1,"{2418, 2396, 2433, 2374, 6589}"
349,1,243,0,0.2288929,"\int \frac{\log \left(c (a+b x)^n\right)}{d+e x+f x^2} \, dx","Int[Log[c*(a + b*x)^n]/(d + e*x + f*x^2),x]","\frac{n \text{PolyLog}\left(2,\frac{2 f (a+b x)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{n \text{PolyLog}\left(2,\frac{2 f (a+b x)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{\log \left(c (a+b x)^n\right) \log \left(-\frac{b \left(-\sqrt{e^2-4 d f}+e+2 f x\right)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{\log \left(c (a+b x)^n\right) \log \left(-\frac{b \left(\sqrt{e^2-4 d f}+e+2 f x\right)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}","\frac{n \text{PolyLog}\left(2,\frac{2 f (a+b x)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{n \text{PolyLog}\left(2,\frac{2 f (a+b x)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{\log \left(c (a+b x)^n\right) \log \left(-\frac{b \left(-\sqrt{e^2-4 d f}+e+2 f x\right)}{2 a f-b \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{\log \left(c (a+b x)^n\right) \log \left(-\frac{b \left(\sqrt{e^2-4 d f}+e+2 f x\right)}{2 a f-b \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}",1,"(Log[c*(a + b*x)^n]*Log[-((b*(e - Sqrt[e^2 - 4*d*f] + 2*f*x))/(2*a*f - b*(e - Sqrt[e^2 - 4*d*f])))])/Sqrt[e^2 - 4*d*f] - (Log[c*(a + b*x)^n]*Log[-((b*(e + Sqrt[e^2 - 4*d*f] + 2*f*x))/(2*a*f - b*(e + Sqrt[e^2 - 4*d*f])))])/Sqrt[e^2 - 4*d*f] + (n*PolyLog[2, (2*f*(a + b*x))/(2*a*f - b*(e - Sqrt[e^2 - 4*d*f]))])/Sqrt[e^2 - 4*d*f] - (n*PolyLog[2, (2*f*(a + b*x))/(2*a*f - b*(e + Sqrt[e^2 - 4*d*f]))])/Sqrt[e^2 - 4*d*f]","A",8,4,23,0.1739,1,"{2418, 2394, 2393, 2391}"
350,0,0,0,0.1990322,"\int \frac{1}{\left(d+e x+f x^2\right) \log \left(c (a+b x)^n\right)} \, dx","Int[1/((d + e*x + f*x^2)*Log[c*(a + b*x)^n]),x]","\int \frac{1}{\left(d+e x+f x^2\right) \log \left(c (a+b x)^n\right)} \, dx","\frac{2 f \text{Int}\left(\frac{1}{\left(-\sqrt{e^2-4 d f}+e+2 f x\right) \log \left(c (a+b x)^n\right)},x\right)}{\sqrt{e^2-4 d f}}-\frac{2 f \text{Int}\left(\frac{1}{\left(\sqrt{e^2-4 d f}+e+2 f x\right) \log \left(c (a+b x)^n\right)},x\right)}{\sqrt{e^2-4 d f}}",0,"(2*f*Defer[Int][1/((e - Sqrt[e^2 - 4*d*f] + 2*f*x)*Log[c*(a + b*x)^n]), x])/Sqrt[e^2 - 4*d*f] - (2*f*Defer[Int][1/((e + Sqrt[e^2 - 4*d*f] + 2*f*x)*Log[c*(a + b*x)^n]), x])/Sqrt[e^2 - 4*d*f]","A",0,0,0,0,-1,"{}"
351,1,286,0,0.443137,"\int \frac{x^3 \log (x)}{a+b x+c x^2} \, dx","Int[(x^3*Log[x])/(a + b*x + c*x^2),x]","\frac{\left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \text{PolyLog}\left(2,-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{2 c^3}+\frac{\left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \text{PolyLog}\left(2,-\frac{2 c x}{\sqrt{b^2-4 a c}+b}\right)}{2 c^3}+\frac{\log (x) \left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \log \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)}{2 c^3}+\frac{\log (x) \left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \log \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)}{2 c^3}+\frac{b x}{c^2}-\frac{b x \log (x)}{c^2}-\frac{x^2}{4 c}+\frac{x^2 \log (x)}{2 c}","\frac{\left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \text{PolyLog}\left(2,-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{2 c^3}+\frac{\left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \text{PolyLog}\left(2,-\frac{2 c x}{\sqrt{b^2-4 a c}+b}\right)}{2 c^3}+\frac{\log (x) \left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \log \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)}{2 c^3}+\frac{\log (x) \left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \log \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)}{2 c^3}+\frac{b x}{c^2}-\frac{b x \log (x)}{c^2}-\frac{x^2}{4 c}+\frac{x^2 \log (x)}{2 c}",1,"(b*x)/c^2 - x^2/(4*c) - (b*x*Log[x])/c^2 + (x^2*Log[x])/(2*c) + ((b^2 - a*c - (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*Log[x]*Log[1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(2*c^3) + ((b^2 - a*c + (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*Log[x]*Log[1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(2*c^3) + ((b^2 - a*c - (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(2*c^3) + ((b^2 - a*c + (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(2*c^3)","A",10,5,18,0.2778,1,"{2357, 2295, 2304, 2317, 2391}"
352,1,234,0,0.355269,"\int \frac{x^2 \log (x)}{a+b x+c x^2} \, dx","Int[(x^2*Log[x])/(a + b*x + c*x^2),x]","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \text{PolyLog}\left(2,-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{2 c^2}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \text{PolyLog}\left(2,-\frac{2 c x}{\sqrt{b^2-4 a c}+b}\right)}{2 c^2}-\frac{\log (x) \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)}{2 c^2}-\frac{\log (x) \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)}{2 c^2}-\frac{x}{c}+\frac{x \log (x)}{c}","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \text{PolyLog}\left(2,-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{2 c^2}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \text{PolyLog}\left(2,-\frac{2 c x}{\sqrt{b^2-4 a c}+b}\right)}{2 c^2}-\frac{\log (x) \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)}{2 c^2}-\frac{\log (x) \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)}{2 c^2}-\frac{x}{c}+\frac{x \log (x)}{c}",1,"-(x/c) + (x*Log[x])/c - ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[x]*Log[1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(2*c^2) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[x]*Log[1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(2*c^2) - ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(2*c^2) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(2*c^2)","A",9,4,18,0.2222,1,"{2357, 2295, 2317, 2391}"
353,1,193,0,0.1805221,"\int \frac{x \log (x)}{a+b x+c x^2} \, dx","Int[(x*Log[x])/(a + b*x + c*x^2),x]","\frac{\left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \text{PolyLog}\left(2,-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{2 c}+\frac{\left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \text{PolyLog}\left(2,-\frac{2 c x}{\sqrt{b^2-4 a c}+b}\right)}{2 c}+\frac{\log (x) \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \log \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)}{2 c}+\frac{\log (x) \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \log \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)}{2 c}","\frac{\left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \text{PolyLog}\left(2,-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{2 c}+\frac{\left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \text{PolyLog}\left(2,-\frac{2 c x}{\sqrt{b^2-4 a c}+b}\right)}{2 c}+\frac{\log (x) \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \log \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)}{2 c}+\frac{\log (x) \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \log \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)}{2 c}",1,"((1 - b/Sqrt[b^2 - 4*a*c])*Log[x]*Log[1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(2*c) + ((1 + b/Sqrt[b^2 - 4*a*c])*Log[x]*Log[1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(2*c) + ((1 - b/Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(2*c) + ((1 + b/Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(2*c)","A",6,3,16,0.1875,1,"{2357, 2317, 2391}"
354,1,153,0,0.1374238,"\int \frac{\log (x)}{a+b x+c x^2} \, dx","Int[Log[x]/(a + b*x + c*x^2),x]","\frac{\text{PolyLog}\left(2,-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}-\frac{\text{PolyLog}\left(2,-\frac{2 c x}{\sqrt{b^2-4 a c}+b}\right)}{\sqrt{b^2-4 a c}}+\frac{\log (x) \log \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)}{\sqrt{b^2-4 a c}}-\frac{\log (x) \log \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)}{\sqrt{b^2-4 a c}}","\frac{\text{PolyLog}\left(2,-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}-\frac{\text{PolyLog}\left(2,-\frac{2 c x}{\sqrt{b^2-4 a c}+b}\right)}{\sqrt{b^2-4 a c}}+\frac{\log (x) \log \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)}{\sqrt{b^2-4 a c}}-\frac{\log (x) \log \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)}{\sqrt{b^2-4 a c}}",1,"(Log[x]*Log[1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/Sqrt[b^2 - 4*a*c] - (Log[x]*Log[1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[b^2 - 4*a*c] + PolyLog[2, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c])]/Sqrt[b^2 - 4*a*c] - PolyLog[2, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])]/Sqrt[b^2 - 4*a*c]","A",6,3,15,0.2000,1,"{2357, 2317, 2391}"
355,1,204,0,0.2822381,"\int \frac{\log (x)}{x \left(a+b x+c x^2\right)} \, dx","Int[Log[x]/(x*(a + b*x + c*x^2)),x]","-\frac{\left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \text{PolyLog}\left(2,-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{2 a}-\frac{\left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \text{PolyLog}\left(2,-\frac{2 c x}{\sqrt{b^2-4 a c}+b}\right)}{2 a}-\frac{\log (x) \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \log \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)}{2 a}-\frac{\log (x) \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \log \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)}{2 a}+\frac{\log ^2(x)}{2 a}","-\frac{\left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \text{PolyLog}\left(2,-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{2 a}-\frac{\left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \text{PolyLog}\left(2,-\frac{2 c x}{\sqrt{b^2-4 a c}+b}\right)}{2 a}-\frac{\log (x) \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \log \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)}{2 a}-\frac{\log (x) \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \log \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)}{2 a}+\frac{\log ^2(x)}{2 a}",1,"Log[x]^2/(2*a) - ((1 + b/Sqrt[b^2 - 4*a*c])*Log[x]*Log[1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(2*a) - ((1 - b/Sqrt[b^2 - 4*a*c])*Log[x]*Log[1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(2*a) - ((1 + b/Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(2*a) - ((1 - b/Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(2*a)","A",9,4,18,0.2222,1,"{2357, 2301, 2317, 2391}"
356,1,251,0,0.3912196,"\int \frac{\log (x)}{x^2 \left(a+b x+c x^2\right)} \, dx","Int[Log[x]/(x^2*(a + b*x + c*x^2)),x]","\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \text{PolyLog}\left(2,-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{2 a^2}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \text{PolyLog}\left(2,-\frac{2 c x}{\sqrt{b^2-4 a c}+b}\right)}{2 a^2}+\frac{\log (x) \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)}{2 a^2}+\frac{\log (x) \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)}{2 a^2}-\frac{b \log ^2(x)}{2 a^2}-\frac{1}{a x}-\frac{\log (x)}{a x}","\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \text{PolyLog}\left(2,-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{2 a^2}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \text{PolyLog}\left(2,-\frac{2 c x}{\sqrt{b^2-4 a c}+b}\right)}{2 a^2}+\frac{\log (x) \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)}{2 a^2}+\frac{\log (x) \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)}{2 a^2}-\frac{b \log ^2(x)}{2 a^2}-\frac{1}{a x}-\frac{\log (x)}{a x}",1,"-(1/(a*x)) - Log[x]/(a*x) - (b*Log[x]^2)/(2*a^2) + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[x]*Log[1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(2*a^2) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[x]*Log[1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(2*a^2) + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(2*a^2) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(2*a^2)","A",10,5,18,0.2778,1,"{2357, 2304, 2301, 2317, 2391}"
357,1,308,0,0.5124126,"\int \frac{\log (x)}{x^3 \left(a+b x+c x^2\right)} \, dx","Int[Log[x]/(x^3*(a + b*x + c*x^2)),x]","-\frac{\left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \text{PolyLog}\left(2,-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{2 a^3}-\frac{\left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \text{PolyLog}\left(2,-\frac{2 c x}{\sqrt{b^2-4 a c}+b}\right)}{2 a^3}+\frac{\log ^2(x) \left(b^2-a c\right)}{2 a^3}-\frac{\log (x) \left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \log \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)}{2 a^3}-\frac{\log (x) \left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \log \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)}{2 a^3}+\frac{b}{a^2 x}+\frac{b \log (x)}{a^2 x}-\frac{1}{4 a x^2}-\frac{\log (x)}{2 a x^2}","-\frac{\left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \text{PolyLog}\left(2,-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{2 a^3}-\frac{\left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \text{PolyLog}\left(2,-\frac{2 c x}{\sqrt{b^2-4 a c}+b}\right)}{2 a^3}+\frac{\log ^2(x) \left(b^2-a c\right)}{2 a^3}-\frac{\log (x) \left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \log \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)}{2 a^3}-\frac{\log (x) \left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \log \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)}{2 a^3}+\frac{b}{a^2 x}+\frac{b \log (x)}{a^2 x}-\frac{1}{4 a x^2}-\frac{\log (x)}{2 a x^2}",1,"-1/(4*a*x^2) + b/(a^2*x) - Log[x]/(2*a*x^2) + (b*Log[x])/(a^2*x) + ((b^2 - a*c)*Log[x]^2)/(2*a^3) - ((b^2 - a*c + (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*Log[x]*Log[1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(2*a^3) - ((b^2 - a*c - (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*Log[x]*Log[1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(2*a^3) - ((b^2 - a*c + (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(2*a^3) - ((b^2 - a*c - (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(2*a^3)","A",11,5,18,0.2778,1,"{2357, 2304, 2301, 2317, 2391}"
358,1,232,0,0.2202414,"\int x^3 \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Int[x^3*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]),x]","-\frac{b d^4 m n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{4 e^4}-\frac{1}{16} \left(m x^4-4 x^4 \log \left(f x^m\right)\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-\frac{b d^4 n \log \left(\frac{e x}{d}+1\right) \log \left(f x^m\right)}{4 e^4}+\frac{b d^3 n x \log \left(f x^m\right)}{4 e^3}-\frac{b d^2 n x^2 \log \left(f x^m\right)}{8 e^2}+\frac{3 b d^2 m n x^2}{32 e^2}-\frac{5 b d^3 m n x}{16 e^3}+\frac{b d^4 m n \log (d+e x)}{16 e^4}+\frac{b d n x^3 \log \left(f x^m\right)}{12 e}-\frac{7 b d m n x^3}{144 e}-\frac{1}{16} b n x^4 \log \left(f x^m\right)+\frac{1}{32} b m n x^4","-\frac{b d^4 m n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{4 e^4}-\frac{1}{16} \left(m x^4-4 x^4 \log \left(f x^m\right)\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-\frac{b d^4 n \log \left(\frac{e x}{d}+1\right) \log \left(f x^m\right)}{4 e^4}+\frac{b d^3 n x \log \left(f x^m\right)}{4 e^3}-\frac{b d^2 n x^2 \log \left(f x^m\right)}{8 e^2}+\frac{3 b d^2 m n x^2}{32 e^2}-\frac{5 b d^3 m n x}{16 e^3}+\frac{b d^4 m n \log (d+e x)}{16 e^4}+\frac{b d n x^3 \log \left(f x^m\right)}{12 e}-\frac{7 b d m n x^3}{144 e}-\frac{1}{16} b n x^4 \log \left(f x^m\right)+\frac{1}{32} b m n x^4",1,"(-5*b*d^3*m*n*x)/(16*e^3) + (3*b*d^2*m*n*x^2)/(32*e^2) - (7*b*d*m*n*x^3)/(144*e) + (b*m*n*x^4)/32 + (b*d^3*n*x*Log[f*x^m])/(4*e^3) - (b*d^2*n*x^2*Log[f*x^m])/(8*e^2) + (b*d*n*x^3*Log[f*x^m])/(12*e) - (b*n*x^4*Log[f*x^m])/16 + (b*d^4*m*n*Log[d + e*x])/(16*e^4) - ((m*x^4 - 4*x^4*Log[f*x^m])*(a + b*Log[c*(d + e*x)^n]))/16 - (b*d^4*n*Log[f*x^m]*Log[1 + (e*x)/d])/(4*e^4) - (b*d^4*m*n*PolyLog[2, -((e*x)/d)])/(4*e^4)","A",11,7,24,0.2917,1,"{2426, 43, 2351, 2295, 2304, 2317, 2391}"
359,1,195,0,0.1830983,"\int x^2 \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Int[x^2*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]),x]","\frac{b d^3 m n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{3 e^3}-\frac{1}{9} \left(m x^3-3 x^3 \log \left(f x^m\right)\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{b d^3 n \log \left(\frac{e x}{d}+1\right) \log \left(f x^m\right)}{3 e^3}-\frac{b d^2 n x \log \left(f x^m\right)}{3 e^2}+\frac{4 b d^2 m n x}{9 e^2}-\frac{b d^3 m n \log (d+e x)}{9 e^3}+\frac{b d n x^2 \log \left(f x^m\right)}{6 e}-\frac{5 b d m n x^2}{36 e}-\frac{1}{9} b n x^3 \log \left(f x^m\right)+\frac{2}{27} b m n x^3","\frac{b d^3 m n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{3 e^3}-\frac{1}{9} \left(m x^3-3 x^3 \log \left(f x^m\right)\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{b d^3 n \log \left(\frac{e x}{d}+1\right) \log \left(f x^m\right)}{3 e^3}-\frac{b d^2 n x \log \left(f x^m\right)}{3 e^2}+\frac{4 b d^2 m n x}{9 e^2}-\frac{b d^3 m n \log (d+e x)}{9 e^3}+\frac{b d n x^2 \log \left(f x^m\right)}{6 e}-\frac{5 b d m n x^2}{36 e}-\frac{1}{9} b n x^3 \log \left(f x^m\right)+\frac{2}{27} b m n x^3",1,"(4*b*d^2*m*n*x)/(9*e^2) - (5*b*d*m*n*x^2)/(36*e) + (2*b*m*n*x^3)/27 - (b*d^2*n*x*Log[f*x^m])/(3*e^2) + (b*d*n*x^2*Log[f*x^m])/(6*e) - (b*n*x^3*Log[f*x^m])/9 - (b*d^3*m*n*Log[d + e*x])/(9*e^3) - ((m*x^3 - 3*x^3*Log[f*x^m])*(a + b*Log[c*(d + e*x)^n]))/9 + (b*d^3*n*Log[f*x^m]*Log[1 + (e*x)/d])/(3*e^3) + (b*d^3*m*n*PolyLog[2, -((e*x)/d)])/(3*e^3)","A",10,7,24,0.2917,1,"{2426, 43, 2351, 2295, 2304, 2317, 2391}"
360,1,158,0,0.1378499,"\int x \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Int[x*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]),x]","-\frac{b d^2 m n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{2 e^2}-\frac{1}{4} \left(m x^2-2 x^2 \log \left(f x^m\right)\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-\frac{b d^2 n \log \left(\frac{e x}{d}+1\right) \log \left(f x^m\right)}{2 e^2}+\frac{b d^2 m n \log (d+e x)}{4 e^2}+\frac{b d n x \log \left(f x^m\right)}{2 e}-\frac{3 b d m n x}{4 e}-\frac{1}{4} b n x^2 \log \left(f x^m\right)+\frac{1}{4} b m n x^2","-\frac{b d^2 m n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{2 e^2}-\frac{1}{4} \left(m x^2-2 x^2 \log \left(f x^m\right)\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-\frac{b d^2 n \log \left(\frac{e x}{d}+1\right) \log \left(f x^m\right)}{2 e^2}+\frac{b d^2 m n \log (d+e x)}{4 e^2}+\frac{b d n x \log \left(f x^m\right)}{2 e}-\frac{3 b d m n x}{4 e}-\frac{1}{4} b n x^2 \log \left(f x^m\right)+\frac{1}{4} b m n x^2",1,"(-3*b*d*m*n*x)/(4*e) + (b*m*n*x^2)/4 + (b*d*n*x*Log[f*x^m])/(2*e) - (b*n*x^2*Log[f*x^m])/4 + (b*d^2*m*n*Log[d + e*x])/(4*e^2) - ((m*x^2 - 2*x^2*Log[f*x^m])*(a + b*Log[c*(d + e*x)^n]))/4 - (b*d^2*n*Log[f*x^m]*Log[1 + (e*x)/d])/(2*e^2) - (b*d^2*m*n*PolyLog[2, -((e*x)/d)])/(2*e^2)","A",9,7,22,0.3182,1,"{2426, 43, 2351, 2295, 2304, 2317, 2391}"
361,1,99,0,0.0938871,"\int \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Int[Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]),x]","\frac{b d m n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e}-x \left(m-\log \left(f x^m\right)\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{b d n \log \left(\frac{e x}{d}+1\right) \log \left(f x^m\right)}{e}-\frac{b d m n \log (d+e x)}{e}-b n x \log \left(f x^m\right)+2 b m n x","\frac{b d m n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e}-x \left(m-\log \left(f x^m\right)\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{b d n \log \left(\frac{e x}{d}+1\right) \log \left(f x^m\right)}{e}-\frac{b d m n \log (d+e x)}{e}-b n x \log \left(f x^m\right)+2 b m n x",1,"2*b*m*n*x - b*n*x*Log[f*x^m] - (b*d*m*n*Log[d + e*x])/e - x*(m - Log[f*x^m])*(a + b*Log[c*(d + e*x)^n]) + (b*d*n*Log[f*x^m]*Log[1 + (e*x)/d])/e + (b*d*m*n*PolyLog[2, -((e*x)/d)])/e","A",8,6,21,0.2857,1,"{2422, 43, 2351, 2295, 2317, 2391}"
362,1,88,0,0.0742769,"\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{x} \, dx","Int[(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]))/x,x]","-b n \log \left(f x^m\right) \text{PolyLog}\left(2,-\frac{e x}{d}\right)+b m n \text{PolyLog}\left(3,-\frac{e x}{d}\right)+\frac{\log ^2\left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 m}-\frac{b n \log \left(\frac{e x}{d}+1\right) \log ^2\left(f x^m\right)}{2 m}","-b n \log \left(f x^m\right) \text{PolyLog}\left(2,-\frac{e x}{d}\right)+b m n \text{PolyLog}\left(3,-\frac{e x}{d}\right)+\frac{\log ^2\left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 m}-\frac{b n \log \left(\frac{e x}{d}+1\right) \log ^2\left(f x^m\right)}{2 m}",1,"(Log[f*x^m]^2*(a + b*Log[c*(d + e*x)^n]))/(2*m) - (b*n*Log[f*x^m]^2*Log[1 + (e*x)/d])/(2*m) - b*n*Log[f*x^m]*PolyLog[2, -((e*x)/d)] + b*m*n*PolyLog[3, -((e*x)/d)]","A",4,4,24,0.1667,1,"{2425, 2317, 2374, 6589}"
363,1,120,0,0.0954819,"\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{x^2} \, dx","Int[(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]))/x^2,x]","-\frac{b e m n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d}-\left(\frac{\log \left(f x^m\right)}{x}+\frac{m}{x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{b e n \log ^2\left(f x^m\right)}{2 d m}-\frac{b e n \log \left(\frac{e x}{d}+1\right) \log \left(f x^m\right)}{d}+\frac{b e m n \log (x)}{d}-\frac{b e m n \log (d+e x)}{d}","\frac{b e m n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{d}-\left(\frac{\log \left(f x^m\right)}{x}+\frac{m}{x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-\frac{b e n \log \left(\frac{d}{e x}+1\right) \log \left(f x^m\right)}{d}+\frac{b e m n \log (x)}{d}-\frac{b e m n \log (d+e x)}{d}",1,"(b*e*m*n*Log[x])/d + (b*e*n*Log[f*x^m]^2)/(2*d*m) - (b*e*m*n*Log[d + e*x])/d - (m/x + Log[f*x^m]/x)*(a + b*Log[c*(d + e*x)^n]) - (b*e*n*Log[f*x^m]*Log[1 + (e*x)/d])/d - (b*e*m*n*PolyLog[2, -((e*x)/d)])/d","A",8,8,24,0.3333,1,"{2426, 2344, 2301, 2317, 2391, 36, 29, 31}"
364,1,175,0,0.1510566,"\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{x^3} \, dx","Int[(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]))/x^3,x]","\frac{b e^2 m n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{2 d^2}-\frac{1}{4} \left(\frac{2 \log \left(f x^m\right)}{x^2}+\frac{m}{x^2}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-\frac{b e^2 n \log ^2\left(f x^m\right)}{4 d^2 m}+\frac{b e^2 n \log \left(\frac{e x}{d}+1\right) \log \left(f x^m\right)}{2 d^2}-\frac{b e^2 m n \log (x)}{4 d^2}+\frac{b e^2 m n \log (d+e x)}{4 d^2}-\frac{b e n \log \left(f x^m\right)}{2 d x}-\frac{3 b e m n}{4 d x}","-\frac{b e^2 m n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{2 d^2}-\frac{1}{4} \left(\frac{2 \log \left(f x^m\right)}{x^2}+\frac{m}{x^2}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{b e^2 n \log \left(\frac{d}{e x}+1\right) \log \left(f x^m\right)}{2 d^2}-\frac{b e^2 m n \log (x)}{4 d^2}+\frac{b e^2 m n \log (d+e x)}{4 d^2}-\frac{b e n \log \left(f x^m\right)}{2 d x}-\frac{3 b e m n}{4 d x}",1,"(-3*b*e*m*n)/(4*d*x) - (b*e^2*m*n*Log[x])/(4*d^2) - (b*e*n*Log[f*x^m])/(2*d*x) - (b*e^2*n*Log[f*x^m]^2)/(4*d^2*m) + (b*e^2*m*n*Log[d + e*x])/(4*d^2) - ((m/x^2 + (2*Log[f*x^m])/x^2)*(a + b*Log[c*(d + e*x)^n]))/4 + (b*e^2*n*Log[f*x^m]*Log[1 + (e*x)/d])/(2*d^2) + (b*e^2*m*n*PolyLog[2, -((e*x)/d)])/(2*d^2)","A",9,7,24,0.2917,1,"{2426, 44, 2351, 2304, 2301, 2317, 2391}"
365,1,212,0,0.1814869,"\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{x^4} \, dx","Int[(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]))/x^4,x]","-\frac{b e^3 m n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{3 d^3}-\frac{1}{9} \left(\frac{3 \log \left(f x^m\right)}{x^3}+\frac{m}{x^3}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{b e^3 n \log ^2\left(f x^m\right)}{6 d^3 m}-\frac{b e^3 n \log \left(\frac{e x}{d}+1\right) \log \left(f x^m\right)}{3 d^3}+\frac{b e^2 n \log \left(f x^m\right)}{3 d^2 x}+\frac{4 b e^2 m n}{9 d^2 x}+\frac{b e^3 m n \log (x)}{9 d^3}-\frac{b e^3 m n \log (d+e x)}{9 d^3}-\frac{b e n \log \left(f x^m\right)}{6 d x^2}-\frac{5 b e m n}{36 d x^2}","\frac{b e^3 m n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{3 d^3}-\frac{1}{9} \left(\frac{3 \log \left(f x^m\right)}{x^3}+\frac{m}{x^3}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-\frac{b e^3 n \log \left(\frac{d}{e x}+1\right) \log \left(f x^m\right)}{3 d^3}+\frac{b e^2 n \log \left(f x^m\right)}{3 d^2 x}+\frac{4 b e^2 m n}{9 d^2 x}+\frac{b e^3 m n \log (x)}{9 d^3}-\frac{b e^3 m n \log (d+e x)}{9 d^3}-\frac{b e n \log \left(f x^m\right)}{6 d x^2}-\frac{5 b e m n}{36 d x^2}",1,"(-5*b*e*m*n)/(36*d*x^2) + (4*b*e^2*m*n)/(9*d^2*x) + (b*e^3*m*n*Log[x])/(9*d^3) - (b*e*n*Log[f*x^m])/(6*d*x^2) + (b*e^2*n*Log[f*x^m])/(3*d^2*x) + (b*e^3*n*Log[f*x^m]^2)/(6*d^3*m) - (b*e^3*m*n*Log[d + e*x])/(9*d^3) - ((m/x^3 + (3*Log[f*x^m])/x^3)*(a + b*Log[c*(d + e*x)^n]))/9 - (b*e^3*n*Log[f*x^m]*Log[1 + (e*x)/d])/(3*d^3) - (b*e^3*m*n*PolyLog[2, -((e*x)/d)])/(3*d^3)","A",10,7,24,0.2917,1,"{2426, 44, 2351, 2304, 2301, 2317, 2391}"
366,1,249,0,0.2189461,"\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{x^5} \, dx","Int[(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]))/x^5,x]","\frac{b e^4 m n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{4 d^4}-\frac{1}{16} \left(\frac{4 \log \left(f x^m\right)}{x^4}+\frac{m}{x^4}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-\frac{b e^4 n \log ^2\left(f x^m\right)}{8 d^4 m}+\frac{b e^4 n \log \left(\frac{e x}{d}+1\right) \log \left(f x^m\right)}{4 d^4}-\frac{b e^3 n \log \left(f x^m\right)}{4 d^3 x}+\frac{b e^2 n \log \left(f x^m\right)}{8 d^2 x^2}+\frac{3 b e^2 m n}{32 d^2 x^2}-\frac{5 b e^3 m n}{16 d^3 x}-\frac{b e^4 m n \log (x)}{16 d^4}+\frac{b e^4 m n \log (d+e x)}{16 d^4}-\frac{b e n \log \left(f x^m\right)}{12 d x^3}-\frac{7 b e m n}{144 d x^3}","-\frac{b e^4 m n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{4 d^4}-\frac{1}{16} \left(\frac{4 \log \left(f x^m\right)}{x^4}+\frac{m}{x^4}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{b e^4 n \log \left(\frac{d}{e x}+1\right) \log \left(f x^m\right)}{4 d^4}-\frac{b e^3 n \log \left(f x^m\right)}{4 d^3 x}+\frac{b e^2 n \log \left(f x^m\right)}{8 d^2 x^2}+\frac{3 b e^2 m n}{32 d^2 x^2}-\frac{5 b e^3 m n}{16 d^3 x}-\frac{b e^4 m n \log (x)}{16 d^4}+\frac{b e^4 m n \log (d+e x)}{16 d^4}-\frac{b e n \log \left(f x^m\right)}{12 d x^3}-\frac{7 b e m n}{144 d x^3}",1,"(-7*b*e*m*n)/(144*d*x^3) + (3*b*e^2*m*n)/(32*d^2*x^2) - (5*b*e^3*m*n)/(16*d^3*x) - (b*e^4*m*n*Log[x])/(16*d^4) - (b*e*n*Log[f*x^m])/(12*d*x^3) + (b*e^2*n*Log[f*x^m])/(8*d^2*x^2) - (b*e^3*n*Log[f*x^m])/(4*d^3*x) - (b*e^4*n*Log[f*x^m]^2)/(8*d^4*m) + (b*e^4*m*n*Log[d + e*x])/(16*d^4) - ((m/x^4 + (4*Log[f*x^m])/x^4)*(a + b*Log[c*(d + e*x)^n]))/16 + (b*e^4*n*Log[f*x^m]*Log[1 + (e*x)/d])/(4*d^4) + (b*e^4*m*n*PolyLog[2, -((e*x)/d)])/(4*d^4)","A",11,7,24,0.2917,1,"{2426, 44, 2351, 2304, 2301, 2317, 2391}"
367,1,902,0,2.1890846,"\int x^2 \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Int[x^2*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{b^2 m n^2 \log ^2(d+e x) d^3}{9 e^3}+\frac{b^2 m n^2 \log (x) \log ^2(d+e x) d^3}{3 e^3}-\frac{b^2 n^2 \log \left(f x^m\right) \log ^2(d+e x) d^3}{3 e^3}+\frac{b^2 m \log (x) \log ^2\left(c (d+e x)^n\right) d^3}{3 e^3}-\frac{b^2 m \log \left(-\frac{e x}{d}\right) \log ^2\left(c (d+e x)^n\right) d^3}{3 e^3}+\frac{23 b^2 m n^2 \log (x) d^3}{54 e^3}+\frac{11 a b m n \log (x) d^3}{9 e^3}+\frac{13 b^2 m n^2 \log (d+e x) d^3}{54 e^3}-\frac{2 a b m n \log \left(-\frac{e x}{d}\right) \log (d+e x) d^3}{3 e^3}+\frac{11 b^2 m n \log \left(-\frac{e x}{d}\right) \log \left(c (d+e x)^n\right) d^3}{9 e^3}-\frac{2 b^2 m n \log (x) \log (d+e x) \log \left(c (d+e x)^n\right) d^3}{3 e^3}+\frac{11 b^2 m n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right) d^3}{9 e^3}-\frac{2 a b m n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) d^3}{3 e^3}-\frac{2 b^2 m n \log \left(c (d+e x)^n\right) \text{PolyLog}\left(2,\frac{e x}{d}+1\right) d^3}{3 e^3}+\frac{2 b^2 m n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right) d^3}{3 e^3}-\frac{151 b^2 m n^2 x d^2}{54 e^2}+\frac{2 a b m n x d^2}{3 e^2}+\frac{2 b^2 n^2 x \log \left(f x^m\right) d^2}{e^2}+\frac{2 b^2 m n (d+e x) \log \left(c (d+e x)^n\right) d^2}{3 e^3}+\frac{7 b^2 m n^2 x^2 d}{27 e}-\frac{a b m n x^2 d}{6 e}+\frac{b^2 m n^2 (d+e x)^2 d}{6 e^3}-\frac{b^2 n^2 (d+e x)^2 \log \left(f x^m\right) d}{2 e^3}-\frac{b^2 m n x^2 \log \left(c (d+e x)^n\right) d}{6 e}-\frac{4}{81} b^2 m n^2 x^3+\frac{2}{27} a b m n x^3-\frac{2 b^2 m n^2 (d+e x)^3}{81 e^3}-\frac{1}{9} m x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2+\frac{1}{3} x^3 \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2+\frac{2 b^2 n^2 (d+e x)^3 \log \left(f x^m\right)}{27 e^3}+\frac{2}{27} b^2 m n x^3 \log \left(c (d+e x)^n\right)+\frac{1}{27} b m n \left(-\frac{6 \log (d+e x) d^3}{e^3}+\frac{18 (d+e x) d^2}{e^3}-\frac{9 (d+e x)^2 d}{e^3}+\frac{2 (d+e x)^3}{e^3}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-\frac{1}{9} b n \log \left(f x^m\right) \left(-\frac{6 \log (d+e x) d^3}{e^3}+\frac{18 (d+e x) d^2}{e^3}-\frac{9 (d+e x)^2 d}{e^3}+\frac{2 (d+e x)^3}{e^3}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)","-\frac{2 b d^3 m n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 e^3}+\frac{11 b^2 d^3 m n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{9 e^3}+\frac{2 b^2 d^3 m n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)}{3 e^3}+\frac{d^3 \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 e^3}-\frac{d^3 m \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{9 e^3}-\frac{d^3 m \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 e^3}+\frac{b d n x^2 \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 e}+\frac{1}{3} x^3 \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2-\frac{2}{9} b n x^3 \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-\frac{5 b d m n x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{18 e}-\frac{1}{9} m x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2+\frac{4}{27} b m n x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)-\frac{2 a b d^2 n x \log \left(f x^m\right)}{3 e^2}+\frac{2 a b d^2 m n x}{9 e^2}+\frac{b d^2 m n x (6 a-11 b n)}{9 e^2}-\frac{2 b^2 d^2 n (d+e x) \log \left(f x^m\right) \log \left(c (d+e x)^n\right)}{3 e^3}+\frac{2 b^2 d^3 m n \log \left(-\frac{e x}{d}\right) \log \left(c (d+e x)^n\right)}{3 e^3}+\frac{8 b^2 d^2 m n (d+e x) \log \left(c (d+e x)^n\right)}{9 e^3}-\frac{5 b^2 d^3 n^2 \log (d+e x) \log \left(f x^m\right)}{9 e^3}+\frac{11 b^2 d^2 n^2 x \log \left(f x^m\right)}{9 e^2}-\frac{71 b^2 d^2 m n^2 x}{54 e^2}+\frac{23 b^2 d^3 m n^2 \log (d+e x)}{54 e^3}+\frac{5 b^2 d^3 m n^2 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{9 e^3}-\frac{5 b^2 d n^2 x^2 \log \left(f x^m\right)}{18 e}+\frac{19 b^2 d m n^2 x^2}{54 e}+\frac{2}{27} b^2 n^2 x^3 \log \left(f x^m\right)-\frac{2}{27} b^2 m n^2 x^3",1,"(2*a*b*d^2*m*n*x)/(3*e^2) - (151*b^2*d^2*m*n^2*x)/(54*e^2) - (a*b*d*m*n*x^2)/(6*e) + (7*b^2*d*m*n^2*x^2)/(27*e) + (2*a*b*m*n*x^3)/27 - (4*b^2*m*n^2*x^3)/81 + (b^2*d*m*n^2*(d + e*x)^2)/(6*e^3) - (2*b^2*m*n^2*(d + e*x)^3)/(81*e^3) + (11*a*b*d^3*m*n*Log[x])/(9*e^3) + (23*b^2*d^3*m*n^2*Log[x])/(54*e^3) + (2*b^2*d^2*n^2*x*Log[f*x^m])/e^2 - (b^2*d*n^2*(d + e*x)^2*Log[f*x^m])/(2*e^3) + (2*b^2*n^2*(d + e*x)^3*Log[f*x^m])/(27*e^3) + (13*b^2*d^3*m*n^2*Log[d + e*x])/(54*e^3) - (2*a*b*d^3*m*n*Log[-((e*x)/d)]*Log[d + e*x])/(3*e^3) + (b^2*d^3*m*n^2*Log[d + e*x]^2)/(9*e^3) + (b^2*d^3*m*n^2*Log[x]*Log[d + e*x]^2)/(3*e^3) - (b^2*d^3*n^2*Log[f*x^m]*Log[d + e*x]^2)/(3*e^3) - (b^2*d*m*n*x^2*Log[c*(d + e*x)^n])/(6*e) + (2*b^2*m*n*x^3*Log[c*(d + e*x)^n])/27 + (2*b^2*d^2*m*n*(d + e*x)*Log[c*(d + e*x)^n])/(3*e^3) + (11*b^2*d^3*m*n*Log[-((e*x)/d)]*Log[c*(d + e*x)^n])/(9*e^3) - (2*b^2*d^3*m*n*Log[x]*Log[d + e*x]*Log[c*(d + e*x)^n])/(3*e^3) + (b^2*d^3*m*Log[x]*Log[c*(d + e*x)^n]^2)/(3*e^3) - (b^2*d^3*m*Log[-((e*x)/d)]*Log[c*(d + e*x)^n]^2)/(3*e^3) + (b*m*n*((18*d^2*(d + e*x))/e^3 - (9*d*(d + e*x)^2)/e^3 + (2*(d + e*x)^3)/e^3 - (6*d^3*Log[d + e*x])/e^3)*(a + b*Log[c*(d + e*x)^n]))/27 - (b*n*Log[f*x^m]*((18*d^2*(d + e*x))/e^3 - (9*d*(d + e*x)^2)/e^3 + (2*(d + e*x)^3)/e^3 - (6*d^3*Log[d + e*x])/e^3)*(a + b*Log[c*(d + e*x)^n]))/9 - (m*x^3*(a + b*Log[c*(d + e*x)^n])^2)/9 + (x^3*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2)/3 - (2*a*b*d^3*m*n*PolyLog[2, 1 + (e*x)/d])/(3*e^3) + (11*b^2*d^3*m*n^2*PolyLog[2, 1 + (e*x)/d])/(9*e^3) - (2*b^2*d^3*m*n*Log[c*(d + e*x)^n]*PolyLog[2, 1 + (e*x)/d])/(3*e^3) + (2*b^2*d^3*m*n^2*PolyLog[3, 1 + (e*x)/d])/(3*e^3)","A",50,22,26,0.8462,1,"{2398, 2411, 43, 2334, 12, 14, 2301, 2428, 2396, 2433, 2374, 6589, 6741, 6742, 2394, 2315, 2389, 2295, 2395, 2434, 2375, 2317}"
368,1,602,0,1.2931332,"\int x \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Int[x*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{b d^2 m n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^2}-\frac{3 b^2 d^2 m n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{2 e^2}-\frac{b^2 d^2 m n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)}{e^2}+\frac{b d^2 m n \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^2}+\frac{d^2 m \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2}-\frac{b n (d+e x)^2 \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^2}+\frac{(d+e x)^2 \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2}-\frac{d (d+e x) \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2}+\frac{b m n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^2}-\frac{m (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 e^2}+\frac{d m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2}+\frac{2 a b d n x \log \left(f x^m\right)}{e}-\frac{a b d m n x}{2 e}-\frac{2 b d m n x (a-b n)}{e}-\frac{2 b^2 d^2 m n \log \left(-\frac{e x}{d}\right) \log \left(c (d+e x)^n\right)}{e^2}+\frac{2 b^2 d n (d+e x) \log \left(f x^m\right) \log \left(c (d+e x)^n\right)}{e^2}-\frac{5 b^2 d m n (d+e x) \log \left(c (d+e x)^n\right)}{2 e^2}-\frac{b^2 d^2 m n^2 \log (x)}{4 e^2}+\frac{b^2 n^2 (d+e x)^2 \log \left(f x^m\right)}{4 e^2}-\frac{b^2 m n^2 (d+e x)^2}{4 e^2}-\frac{2 b^2 d n^2 x \log \left(f x^m\right)}{e}+\frac{2 b^2 d m n^2 x}{e}-\frac{1}{8} b^2 m n^2 x^2","\frac{b d^2 m n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^2}-\frac{3 b^2 d^2 m n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{2 e^2}-\frac{b^2 d^2 m n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)}{e^2}+\frac{b d^2 m n \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^2}+\frac{d^2 m \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2}-\frac{b n (d+e x)^2 \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^2}+\frac{(d+e x)^2 \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2}-\frac{d (d+e x) \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e^2}+\frac{b m n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 e^2}-\frac{m (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 e^2}+\frac{d m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2}+\frac{2 a b d n x \log \left(f x^m\right)}{e}-\frac{a b d m n x}{2 e}-\frac{2 b d m n x (a-b n)}{e}-\frac{2 b^2 d^2 m n \log \left(-\frac{e x}{d}\right) \log \left(c (d+e x)^n\right)}{e^2}+\frac{2 b^2 d n (d+e x) \log \left(f x^m\right) \log \left(c (d+e x)^n\right)}{e^2}-\frac{5 b^2 d m n (d+e x) \log \left(c (d+e x)^n\right)}{2 e^2}-\frac{b^2 d^2 m n^2 \log (x)}{4 e^2}+\frac{b^2 n^2 (d+e x)^2 \log \left(f x^m\right)}{4 e^2}-\frac{b^2 m n^2 (d+e x)^2}{4 e^2}-\frac{2 b^2 d n^2 x \log \left(f x^m\right)}{e}+\frac{2 b^2 d m n^2 x}{e}-\frac{1}{8} b^2 m n^2 x^2",1,"-(a*b*d*m*n*x)/(2*e) + (2*b^2*d*m*n^2*x)/e - (2*b*d*m*n*(a - b*n)*x)/e - (b^2*m*n^2*x^2)/8 - (b^2*m*n^2*(d + e*x)^2)/(4*e^2) - (b^2*d^2*m*n^2*Log[x])/(4*e^2) + (2*a*b*d*n*x*Log[f*x^m])/e - (2*b^2*d*n^2*x*Log[f*x^m])/e + (b^2*n^2*(d + e*x)^2*Log[f*x^m])/(4*e^2) - (5*b^2*d*m*n*(d + e*x)*Log[c*(d + e*x)^n])/(2*e^2) - (2*b^2*d^2*m*n*Log[-((e*x)/d)]*Log[c*(d + e*x)^n])/e^2 + (2*b^2*d*n*(d + e*x)*Log[f*x^m]*Log[c*(d + e*x)^n])/e^2 + (b*m*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(2*e^2) + (b*d^2*m*n*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/(2*e^2) - (b*n*(d + e*x)^2*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]))/(2*e^2) + (d*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(2*e^2) - (m*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(4*e^2) + (d^2*m*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n])^2)/(2*e^2) - (d*(d + e*x)*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2)/e^2 + ((d + e*x)^2*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2)/(2*e^2) - (3*b^2*d^2*m*n^2*PolyLog[2, 1 + (e*x)/d])/(2*e^2) + (b*d^2*m*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, 1 + (e*x)/d])/e^2 - (b^2*d^2*m*n^2*PolyLog[3, 1 + (e*x)/d])/e^2","A",38,16,24,0.6667,1,"{2401, 2389, 2296, 2295, 2390, 2305, 2304, 2428, 43, 2411, 2351, 2317, 2391, 2353, 2374, 6589}"
369,1,309,0,0.4525421,"\int \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Int[Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2,x]","-\frac{2 b d m n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e}+\frac{2 b^2 d m n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e}+\frac{2 b^2 d m n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)}{e}+\frac{(d+e x) \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-\frac{m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-\frac{d m \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-2 a b n x \log \left(f x^m\right)+2 a b m n x+2 b m n x (a-b n)-\frac{2 b^2 n (d+e x) \log \left(f x^m\right) \log \left(c (d+e x)^n\right)}{e}+\frac{4 b^2 m n (d+e x) \log \left(c (d+e x)^n\right)}{e}+\frac{2 b^2 d m n \log \left(-\frac{e x}{d}\right) \log \left(c (d+e x)^n\right)}{e}+2 b^2 n^2 x \log \left(f x^m\right)-4 b^2 m n^2 x","-\frac{2 b d m n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e}+\frac{2 b^2 d m n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e}+\frac{2 b^2 d m n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)}{e}+\frac{(d+e x) \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-\frac{m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-\frac{d m \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-2 a b n x \log \left(f x^m\right)+2 a b m n x+2 b m n x (a-b n)-\frac{2 b^2 n (d+e x) \log \left(f x^m\right) \log \left(c (d+e x)^n\right)}{e}+\frac{4 b^2 m n (d+e x) \log \left(c (d+e x)^n\right)}{e}+\frac{2 b^2 d m n \log \left(-\frac{e x}{d}\right) \log \left(c (d+e x)^n\right)}{e}+2 b^2 n^2 x \log \left(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 - 2*a*b*n*x*Log[f*x^m] + 2*b^2*n^2*x*Log[f*x^m] + (4*b^2*m*n*(d + e*x)*Log[c*(d + e*x)^n])/e + (2*b^2*d*m*n*Log[-((e*x)/d)]*Log[c*(d + e*x)^n])/e - (2*b^2*n*(d + e*x)*Log[f*x^m]*Log[c*(d + e*x)^n])/e - (m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e - (d*m*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n])^2)/e + ((d + e*x)*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2)/e + (2*b^2*d*m*n^2*PolyLog[2, 1 + (e*x)/d])/e - (2*b*d*m*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, 1 + (e*x)/d])/e + (2*b^2*d*m*n^2*PolyLog[3, 1 + (e*x)/d])/e","A",17,12,23,0.5217,1,"{2389, 2296, 2295, 2423, 2411, 43, 2351, 2317, 2391, 2353, 2374, 6589}"
370,0,0,0,0.0659637,"\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x} \, dx","Int[(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2)/x,x]","\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x} \, dx","-b^2 \left(m \log (x)-\log \left(f x^m\right)\right) \left(\log \left(-\frac{e x}{d}\right) \log ^2(d+e x)+2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \log (d+e x)-2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)\right) n^2+\frac{1}{12} b^2 m \left(\log ^4\left(-\frac{e x}{d}\right)+6 \log ^2\left(-\frac{e x}{d+e x}\right) \log ^2\left(-\frac{e x}{d}\right)-4 \log \left(-\frac{e x}{d+e x}\right) \left(\log \left(-\frac{e x}{d}\right)+3 \log \left(\frac{e x}{d}+1\right)\right) \log ^2\left(-\frac{e x}{d}\right)+\log ^4\left(-\frac{e x}{d+e x}\right)-4 \left(\log \left(-\frac{e x}{d}\right)+\log \left(\frac{d}{d+e x}\right)\right) \log ^3\left(-\frac{e x}{d+e x}\right)+6 \log ^2(x) \log ^2(d+e x)+6 \left(\log (x)-\log \left(-\frac{e x}{d}\right)\right) \left(\log (x)+3 \log \left(-\frac{e x}{d}\right)\right) \log ^2\left(\frac{e x}{d}+1\right)+4 \left(2 \log ^3\left(-\frac{e x}{d}\right)-3 \log ^2(x) \log (d+e x)\right) \log \left(\frac{e x}{d}+1\right)+12 \left(\log ^2\left(-\frac{e x}{d}\right)-2 \left(\log \left(-\frac{e x}{d+e x}\right)+\log \left(\frac{e x}{d}+1\right)\right) \log \left(-\frac{e x}{d}\right)+2 \log (x) \left(\log \left(\frac{e x}{d}+1\right)-\log (d+e x)\right)\right) \text{PolyLog}\left(2,-\frac{e x}{d}\right)-12 \log ^2\left(-\frac{e x}{d+e x}\right) \text{PolyLog}\left(2,\frac{e x}{d+e x}\right)+12 \left(\log \left(-\frac{e x}{d}\right)-\log \left(-\frac{e x}{d+e x}\right)\right)^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)+24 \left(\log (x)-\log \left(-\frac{e x}{d}\right)\right) \log \left(\frac{e x}{d}+1\right) \text{PolyLog}\left(2,\frac{e x}{d}+1\right)+24 \left(\log \left(-\frac{e x}{d+e x}\right)+\log (d+e x)\right) \text{PolyLog}\left(3,-\frac{e x}{d}\right)+24 \log \left(-\frac{e x}{d+e x}\right) \text{PolyLog}\left(3,\frac{e x}{d+e x}\right)+24 \left(\log \left(-\frac{e x}{d+e x}\right)-\log (x)\right) \text{PolyLog}\left(3,\frac{e x}{d}+1\right)-24 \left(\text{PolyLog}\left(4,-\frac{e x}{d}\right)+\text{PolyLog}\left(4,\frac{e x}{d+e x}\right)-\text{PolyLog}\left(4,\frac{e x}{d}+1\right)\right)\right) n^2+2 b \left(\log \left(f x^m\right)-m \log (x)\right) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(\log (x) \left(\log (d+e x)-\log \left(\frac{e x}{d}+1\right)\right)-\text{PolyLog}\left(2,-\frac{e x}{d}\right)\right) n+2 b m \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(\frac{1}{2} \left(\log (d+e x)-\log \left(\frac{e x}{d}+1\right)\right) \log ^2(x)-\text{PolyLog}\left(2,-\frac{e x}{d}\right) \log (x)+\text{PolyLog}\left(3,-\frac{e x}{d}\right)\right) n+\frac{1}{2} m \log ^2(x) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2+\log (x) \left(\log \left(f x^m\right)-m \log (x)\right) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2",1,"(Log[f*x^m]^2*(a + b*Log[c*(d + e*x)^n])^2)/(2*m) - (b*e*n*Defer[Int][(Log[f*x^m]^2*(a + b*Log[c*(d + e*x)^n]))/(d + e*x), x])/m","F",0,0,0,0,-1,"{}"
371,0,0,0,0.0289378,"\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x^2} \, dx","Int[(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2)/x^2,x]","\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x^2} \, dx","\frac{b m n \left(e x \left(\log ^2(x)-2 \left(\text{PolyLog}\left(2,-\frac{e x}{d}\right)+\log (x) \log \left(\frac{e x}{d}+1\right)\right)\right)+2 e x \log \left(-\frac{e x}{d}\right)-2 (d+e x) \log (d+e x)-2 d \log (x) \log (d+e x)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)}{d x}-\frac{2 b^2 e n^2 \log \left(f x^m\right) \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d}+\frac{2 b^2 e m n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{d}-\frac{2 b^2 e m n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)}{d}+\frac{2 b^2 e m n^2 (\log (d+e x)+1) \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{d}-\frac{2 b n \left(e x \log \left(-\frac{e x}{d}\right)-(d+e x) \log (d+e x)\right) \left(m \log (x)-\log \left(f x^m\right)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)}{d x}-\frac{\left(\log \left(f x^m\right)+m (-\log (x))+m\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2}{x}-\frac{m \log (x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2}{x}-\frac{b^2 e n^2 \log ^2(d+e x) \log \left(f x^m\right)}{d}-\frac{b^2 n^2 \log ^2(d+e x) \log \left(f x^m\right)}{x}+\frac{2 b^2 e n^2 \log (x) \log (d+e x) \log \left(f x^m\right)}{d}-\frac{2 b^2 e n^2 \log (x) \log \left(\frac{e x}{d}+1\right) \log \left(f x^m\right)}{d}-\frac{b^2 e m n^2 \log ^2(d+e x)}{d}+\frac{b^2 e m n^2 \log \left(-\frac{e x}{d}\right) \log ^2(d+e x)}{d}-\frac{b^2 m n^2 \log ^2(d+e x)}{x}-\frac{b^2 e m n^2 \log ^2(x) \log (d+e x)}{d}+\frac{b^2 e m n^2 \log ^2(x) \log \left(\frac{e x}{d}+1\right)}{d}+\frac{2 b^2 e m n^2 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d}",1,"Defer[Int][(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2)/x^2, x]","F",0,0,0,0,-1,"{}"
372,0,0,0,0.0295654,"\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x^3} \, dx","Int[(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2)/x^3,x]","\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x^3} \, dx","-\frac{b^2 e^2 m \log ^2(x) n^2}{2 d^2}+\frac{b^2 e^2 m \log ^2(d+e x) n^2}{4 d^2}-\frac{b^2 e^2 m \log \left(-\frac{e x}{d}\right) \log ^2(d+e x) n^2}{2 d^2}+\frac{b^2 e^2 \log \left(f x^m\right) \log ^2(d+e x) n^2}{2 d^2}-\frac{b^2 \log \left(f x^m\right) \log ^2(d+e x) n^2}{2 x^2}-\frac{b^2 m \log ^2(d+e x) n^2}{4 x^2}+\frac{b^2 e^2 m \log (x) n^2}{d^2}+\frac{b^2 e^2 m \log \left(-\frac{e x}{d}\right) n^2}{2 d^2}+\frac{b^2 e^2 \log (x) \log \left(f x^m\right) n^2}{d^2}+\frac{b^2 e^2 m \log ^2(x) \log (d+e x) n^2}{2 d^2}-\frac{3 b^2 e^2 m \log (d+e x) n^2}{2 d^2}+\frac{b^2 e^2 m \log (x) \log (d+e x) n^2}{d^2}-\frac{b^2 e^2 m \log \left(-\frac{e x}{d}\right) \log (d+e x) n^2}{2 d^2}-\frac{b^2 e^2 \log \left(f x^m\right) \log (d+e x) n^2}{d^2}-\frac{b^2 e^2 \log (x) \log \left(f x^m\right) \log (d+e x) n^2}{d^2}-\frac{b^2 e \log \left(f x^m\right) \log (d+e x) n^2}{d x}-\frac{3 b^2 e m \log (d+e x) n^2}{2 d x}-\frac{b^2 e^2 m \log ^2(x) \log \left(\frac{e x}{d}+1\right) n^2}{2 d^2}-\frac{b^2 e^2 m \log (x) \log \left(\frac{e x}{d}+1\right) n^2}{d^2}+\frac{b^2 e^2 \log (x) \log \left(f x^m\right) \log \left(\frac{e x}{d}+1\right) n^2}{d^2}-\frac{b^2 e^2 \left(m-\log \left(f x^m\right)\right) \text{PolyLog}\left(2,-\frac{e x}{d}\right) n^2}{d^2}-\frac{b^2 e^2 m (2 \log (d+e x)+1) \text{PolyLog}\left(2,\frac{e x}{d}+1\right) n^2}{2 d^2}-\frac{b^2 e^2 m \text{PolyLog}\left(3,-\frac{e x}{d}\right) n^2}{d^2}+\frac{b^2 e^2 m \text{PolyLog}\left(3,\frac{e x}{d}+1\right) n^2}{d^2}+\frac{b \left(m \log (x)-\log \left(f x^m\right)\right) \left(e^2 \log \left(-\frac{e x}{d}\right) x^2+(d+e x) (e x+(d-e x) \log (d+e x))\right) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) n}{d^2 x^2}-\frac{b m \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(2 \log (x) \log (d+e x) d^2+e x (d+e x)+e^2 x^2 \log \left(-\frac{e x}{d}\right)+\left(d^2-e^2 x^2\right) \log (d+e x)+e x \left(e x \log ^2(x)+2 d (\log (x)+1)-2 e x \left(\log (x) \log \left(\frac{e x}{d}+1\right)+\text{PolyLog}\left(2,-\frac{e x}{d}\right)\right)\right)\right) n}{2 d^2 x^2}-\frac{m \log (x) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2}{2 x^2}-\frac{\left(-2 \log (x) m+m+2 \log \left(f x^m\right)\right) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2}{4 x^2}",1,"Defer[Int][(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2)/x^3, x]","F",0,0,0,0,-1,"{}"
373,1,522,0,0.8579523,"\int \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \, dx","Int[Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^3,x]","\frac{6 b^2 d m n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e}+\frac{6 b^2 d m n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e}-\frac{3 b d m n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-\frac{6 b^3 d m n^3 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e}-\frac{6 b^3 d m n^3 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)}{e}-\frac{6 b^3 d m n^3 \text{PolyLog}\left(4,\frac{e x}{d}+1\right)}{e}+6 a b^2 n^2 x \log \left(f x^m\right)-12 a b^2 m n^2 x-6 b^2 m n^2 x (a-b n)-\frac{3 b n (d+e x) \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}+\frac{(d+e x) \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}+\frac{6 b m n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}+\frac{3 b d m n \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-\frac{m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}-\frac{d m \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}+\frac{6 b^3 n^2 (d+e x) \log \left(f x^m\right) \log \left(c (d+e x)^n\right)}{e}-\frac{18 b^3 m n^2 (d+e x) \log \left(c (d+e x)^n\right)}{e}-\frac{6 b^3 d m n^2 \log \left(-\frac{e x}{d}\right) \log \left(c (d+e x)^n\right)}{e}-6 b^3 n^3 x \log \left(f x^m\right)+18 b^3 m n^3 x","\frac{6 b^2 d m n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e}+\frac{6 b^2 d m n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e}-\frac{3 b d m n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-\frac{6 b^3 d m n^3 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e}-\frac{6 b^3 d m n^3 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)}{e}-\frac{6 b^3 d m n^3 \text{PolyLog}\left(4,\frac{e x}{d}+1\right)}{e}+6 a b^2 n^2 x \log \left(f x^m\right)-12 a b^2 m n^2 x-6 b^2 m n^2 x (a-b n)-\frac{3 b n (d+e x) \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}+\frac{(d+e x) \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}+\frac{6 b m n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}+\frac{3 b d m n \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-\frac{m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}-\frac{d m \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}+\frac{6 b^3 n^2 (d+e x) \log \left(f x^m\right) \log \left(c (d+e x)^n\right)}{e}-\frac{18 b^3 m n^2 (d+e x) \log \left(c (d+e x)^n\right)}{e}-\frac{6 b^3 d m n^2 \log \left(-\frac{e x}{d}\right) \log \left(c (d+e x)^n\right)}{e}-6 b^3 n^3 x \log \left(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 + 6*a*b^2*n^2*x*Log[f*x^m] - 6*b^3*n^3*x*Log[f*x^m] - (18*b^3*m*n^2*(d + e*x)*Log[c*(d + e*x)^n])/e - (6*b^3*d*m*n^2*Log[-((e*x)/d)]*Log[c*(d + e*x)^n])/e + (6*b^3*n^2*(d + e*x)*Log[f*x^m]*Log[c*(d + e*x)^n])/e + (6*b*m*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e + (3*b*d*m*n*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n])^2)/e - (3*b*n*(d + e*x)*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2)/e - (m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/e - (d*m*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n])^3)/e + ((d + e*x)*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^3)/e - (6*b^3*d*m*n^3*PolyLog[2, 1 + (e*x)/d])/e + (6*b^2*d*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, 1 + (e*x)/d])/e - (3*b*d*m*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, 1 + (e*x)/d])/e - (6*b^3*d*m*n^3*PolyLog[3, 1 + (e*x)/d])/e + (6*b^2*d*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[3, 1 + (e*x)/d])/e - (6*b^3*d*m*n^3*PolyLog[4, 1 + (e*x)/d])/e","A",28,13,23,0.5652,1,"{2389, 2296, 2295, 2423, 2411, 43, 2351, 2317, 2391, 2353, 2374, 6589, 2383}"
374,0,0,0,0.048933,"\int \frac{\log (x) \log ^2(a+b x)}{x} \, dx","Int[(Log[x]*Log[a + b*x]^2)/x,x]","\int \frac{\log (x) \log ^2(a+b x)}{x} \, dx","\frac{1}{12} \left(-24 \left(\text{PolyLog}\left(4,-\frac{b x}{a}\right)+\text{PolyLog}\left(4,\frac{b x}{a+b x}\right)-\text{PolyLog}\left(4,\frac{b x}{a}+1\right)\right)+12 \left(\log ^2\left(-\frac{b x}{a}\right)-2 \left(\log \left(-\frac{b x}{a+b x}\right)+\log \left(\frac{b x}{a}+1\right)\right) \log \left(-\frac{b x}{a}\right)+2 \log (x) \left(\log \left(\frac{b x}{a}+1\right)-\log (a+b x)\right)\right) \text{PolyLog}\left(2,-\frac{b x}{a}\right)-12 \log ^2\left(-\frac{b x}{a+b x}\right) \text{PolyLog}\left(2,\frac{b x}{a+b x}\right)+12 \left(\log \left(-\frac{b x}{a}\right)-\log \left(-\frac{b x}{a+b x}\right)\right)^2 \text{PolyLog}\left(2,\frac{b x}{a}+1\right)+24 \left(\log (x)-\log \left(-\frac{b x}{a}\right)\right) \log \left(\frac{b x}{a}+1\right) \text{PolyLog}\left(2,\frac{b x}{a}+1\right)+24 \left(\log \left(-\frac{b x}{a+b x}\right)+\log (a+b x)\right) \text{PolyLog}\left(3,-\frac{b x}{a}\right)+24 \log \left(-\frac{b x}{a+b x}\right) \text{PolyLog}\left(3,\frac{b x}{a+b x}\right)+24 \left(\log \left(-\frac{b x}{a+b x}\right)-\log (x)\right) \text{PolyLog}\left(3,\frac{b x}{a}+1\right)+\log ^4\left(-\frac{b x}{a}\right)+6 \log ^2\left(-\frac{b x}{a+b x}\right) \log ^2\left(-\frac{b x}{a}\right)-4 \log \left(-\frac{b x}{a+b x}\right) \left(\log \left(-\frac{b x}{a}\right)+3 \log \left(\frac{b x}{a}+1\right)\right) \log ^2\left(-\frac{b x}{a}\right)+\log ^4\left(-\frac{b x}{a+b x}\right)-4 \left(\log \left(-\frac{b x}{a}\right)+\log \left(\frac{a}{a+b x}\right)\right) \log ^3\left(-\frac{b x}{a+b x}\right)+6 \log ^2(x) \log ^2(a+b x)+6 \left(\log (x)-\log \left(-\frac{b x}{a}\right)\right) \left(3 \log \left(-\frac{b x}{a}\right)+\log (x)\right) \log ^2\left(\frac{b x}{a}+1\right)+4 \left(2 \log ^3\left(-\frac{b x}{a}\right)-3 \log ^2(x) \log (a+b x)\right) \log \left(\frac{b x}{a}+1\right)\right)",1,"(Log[x]^2*Log[a + b*x]^2)/2 - b*Defer[Int][(Log[x]^2*Log[a + b*x])/(a + b*x), x]","F",0,0,0,0,-1,"{}"
375,0,0,0,0.0112972,"\int \frac{\log \left(f x^m\right)}{a+b \log \left(c (d+e x)^n\right)} \, dx","Int[Log[f*x^m]/(a + b*Log[c*(d + e*x)^n]),x]","\int \frac{\log \left(f x^m\right)}{a+b \log \left(c (d+e x)^n\right)} \, dx","\text{Int}\left(\frac{\log \left(f x^m\right)}{a+b \log \left(c (d+e x)^n\right)},x\right)",0,"Defer[Int][Log[f*x^m]/(a + b*Log[c*(d + e*x)^n]), x]","A",0,0,0,0,-1,"{}"
376,0,0,0,0.0108033,"\int \frac{\log \left(f x^m\right)}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Int[Log[f*x^m]/(a + b*Log[c*(d + e*x)^n])^2,x]","\int \frac{\log \left(f x^m\right)}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{\log \left(f x^m\right)}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2},x\right)",0,"Defer[Int][Log[f*x^m]/(a + b*Log[c*(d + e*x)^n])^2, x]","A",0,0,0,0,-1,"{}"
377,0,0,0,0.0101469,"\int \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^p \, dx","Int[Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^p,x]","\int \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^p \, dx","\text{Int}\left(\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^p,x\right)",0,"Defer[Int][Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^p, x]","A",0,0,0,0,-1,"{}"
378,1,364,0,0.0545108,"\int \frac{\log (a+b x) \log (c+d x)}{x} \, dx","Int[(Log[a + b*x]*Log[c + d*x])/x,x]","\text{PolyLog}\left(3,\frac{c (a+b x)}{a (c+d x)}\right)-\text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right)+\log \left(\frac{a (c+d x)}{c (a+b x)}\right) \text{PolyLog}\left(2,\frac{c (a+b x)}{a (c+d x)}\right)-\log \left(\frac{a (c+d x)}{c (a+b x)}\right) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)+\text{PolyLog}\left(2,\frac{b x}{a}+1\right) \left(\log (c+d x)-\log \left(\frac{a (c+d x)}{c (a+b x)}\right)\right)+\text{PolyLog}\left(2,\frac{d x}{c}+1\right) \left(\log \left(\frac{a (c+d x)}{c (a+b x)}\right)+\log (a+b x)\right)-\text{PolyLog}\left(3,\frac{b x}{a}+1\right)-\text{PolyLog}\left(3,\frac{d x}{c}+1\right)+\frac{1}{2} \left(\log \left(\frac{b c-a d}{b (c+d x)}\right)-\log \left(-\frac{x (b c-a d)}{a (c+d x)}\right)+\log \left(-\frac{b x}{a}\right)\right) \log ^2\left(\frac{a (c+d x)}{c (a+b x)}\right)-\frac{1}{2} \left(\log \left(-\frac{b x}{a}\right)-\log \left(-\frac{d x}{c}\right)\right) \left(\log \left(\frac{a (c+d x)}{c (a+b x)}\right)+\log (a+b x)\right)^2+\log \left(-\frac{b x}{a}\right) \log (a+b x) \log (c+d x)","\text{PolyLog}\left(3,\frac{c (a+b x)}{a (c+d x)}\right)-\text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right)+\log \left(\frac{a (c+d x)}{c (a+b x)}\right) \text{PolyLog}\left(2,\frac{c (a+b x)}{a (c+d x)}\right)-\log \left(\frac{a (c+d x)}{c (a+b x)}\right) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)+\text{PolyLog}\left(2,\frac{b x}{a}+1\right) \left(\log (c+d x)-\log \left(\frac{a (c+d x)}{c (a+b x)}\right)\right)+\text{PolyLog}\left(2,\frac{d x}{c}+1\right) \left(\log \left(\frac{a (c+d x)}{c (a+b x)}\right)+\log (a+b x)\right)-\text{PolyLog}\left(3,\frac{b x}{a}+1\right)-\text{PolyLog}\left(3,\frac{d x}{c}+1\right)+\frac{1}{2} \left(\log \left(\frac{b c-a d}{b (c+d x)}\right)-\log \left(-\frac{x (b c-a d)}{a (c+d x)}\right)+\log \left(-\frac{b x}{a}\right)\right) \log ^2\left(\frac{a (c+d x)}{c (a+b x)}\right)-\frac{1}{2} \left(\log \left(-\frac{b x}{a}\right)-\log \left(-\frac{d x}{c}\right)\right) \left(\log \left(\frac{a (c+d x)}{c (a+b x)}\right)+\log (a+b x)\right)^2+\log \left(-\frac{b x}{a}\right) \log (a+b x) \log (c+d x)",1,"Log[-((b*x)/a)]*Log[a + b*x]*Log[c + d*x] + ((Log[-((b*x)/a)] + Log[(b*c - a*d)/(b*(c + d*x))] - Log[-(((b*c - a*d)*x)/(a*(c + d*x)))])*Log[(a*(c + d*x))/(c*(a + b*x))]^2)/2 - ((Log[-((b*x)/a)] - Log[-((d*x)/c)])*(Log[a + b*x] + Log[(a*(c + d*x))/(c*(a + b*x))])^2)/2 + (Log[c + d*x] - Log[(a*(c + d*x))/(c*(a + b*x))])*PolyLog[2, 1 + (b*x)/a] + Log[(a*(c + d*x))/(c*(a + b*x))]*PolyLog[2, (c*(a + b*x))/(a*(c + d*x))] - Log[(a*(c + d*x))/(c*(a + b*x))]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] + (Log[a + b*x] + Log[(a*(c + d*x))/(c*(a + b*x))])*PolyLog[2, 1 + (d*x)/c] - PolyLog[3, 1 + (b*x)/a] + PolyLog[3, (c*(a + b*x))/(a*(c + d*x))] - PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] - PolyLog[3, 1 + (d*x)/c]","A",1,1,16,0.06250,1,"{2435}"
379,1,258,0,0.4352761,"\int x^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(c (d+e x)^n\right)\right) \, dx","Int[x^2*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]),x]","-\frac{1}{18} g n \left(\frac{18 d^2 (d+e x)}{e^3}-\frac{6 d^3 \log (d+e x)}{e^3}-\frac{9 d (d+e x)^2}{e^3}+\frac{2 (d+e x)^3}{e^3}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{1}{3} x^3 \left(a+b \log \left(c (d+e x)^n\right)\right) \left(g \log \left(c (d+e x)^n\right)+f\right)-\frac{1}{18} b n \left(\frac{18 d^2 (d+e x)}{e^3}-\frac{6 d^3 \log (d+e x)}{e^3}-\frac{9 d (d+e x)^2}{e^3}+\frac{2 (d+e x)^3}{e^3}\right) \left(g \log \left(c (d+e x)^n\right)+f\right)+\frac{2 b d^2 g n^2 x}{e^2}-\frac{b d^3 g n^2 \log ^2(d+e x)}{3 e^3}-\frac{b d g n^2 (d+e x)^2}{2 e^3}+\frac{2 b g n^2 (d+e x)^3}{27 e^3}","\frac{d^3 n \log (d+e x) \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)}{3 e^3}-\frac{d^2 n (d+e x) \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)}{e^3}+\frac{d n (d+e x)^2 \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)}{2 e^3}-\frac{n (d+e x)^3 \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)}{9 e^3}+\frac{1}{3} x^3 \left(a+b \log \left(c (d+e x)^n\right)\right) \left(g \log \left(c (d+e x)^n\right)+f\right)+\frac{2 b d^2 g n^2 x}{e^2}-\frac{b d^3 g n^2 \log ^2(d+e x)}{3 e^3}-\frac{b d g n^2 (d+e x)^2}{2 e^3}+\frac{2 b g n^2 (d+e x)^3}{27 e^3}",1,"(2*b*d^2*g*n^2*x)/e^2 - (b*d*g*n^2*(d + e*x)^2)/(2*e^3) + (2*b*g*n^2*(d + e*x)^3)/(27*e^3) - (b*d^3*g*n^2*Log[d + e*x]^2)/(3*e^3) - (g*n*((18*d^2*(d + e*x))/e^3 - (9*d*(d + e*x)^2)/e^3 + (2*(d + e*x)^3)/e^3 - (6*d^3*Log[d + e*x])/e^3)*(a + b*Log[c*(d + e*x)^n]))/18 - (b*n*((18*d^2*(d + e*x))/e^3 - (9*d*(d + e*x)^2)/e^3 + (2*(d + e*x)^3)/e^3 - (6*d^3*Log[d + e*x])/e^3)*(f + g*Log[c*(d + e*x)^n]))/18 + (x^3*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]))/3","A",13,7,32,0.2188,1,"{2439, 2411, 43, 2334, 12, 14, 2301}"
380,1,206,0,0.3709048,"\int x \left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(c (d+e x)^n\right)\right) \, dx","Int[x*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]),x]","\frac{1}{4} g n \left(-\frac{2 d^2 \log (d+e x)}{e^2}+\frac{4 d (d+e x)}{e^2}-\frac{(d+e x)^2}{e^2}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{1}{2} x^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \left(g \log \left(c (d+e x)^n\right)+f\right)+\frac{1}{4} b n \left(-\frac{2 d^2 \log (d+e x)}{e^2}+\frac{4 d (d+e x)}{e^2}-\frac{(d+e x)^2}{e^2}\right) \left(g \log \left(c (d+e x)^n\right)+f\right)+\frac{b d^2 g n^2 \log ^2(d+e x)}{2 e^2}+\frac{b g n^2 (d+e x)^2}{4 e^2}-\frac{2 b d g n^2 x}{e}","-\frac{d^2 n \log (d+e x) \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)}{2 e^2}+\frac{d n (d+e x) \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)}{e^2}-\frac{n (d+e x)^2 \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)}{4 e^2}+\frac{1}{2} x^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \left(g \log \left(c (d+e x)^n\right)+f\right)+\frac{b d^2 g n^2 \log ^2(d+e x)}{2 e^2}+\frac{b g n^2 (d+e x)^2}{4 e^2}-\frac{2 b d g n^2 x}{e}",1,"(-2*b*d*g*n^2*x)/e + (b*g*n^2*(d + e*x)^2)/(4*e^2) + (b*d^2*g*n^2*Log[d + e*x]^2)/(2*e^2) + (g*n*((4*d*(d + e*x))/e^2 - (d + e*x)^2/e^2 - (2*d^2*Log[d + e*x])/e^2)*(a + b*Log[c*(d + e*x)^n]))/4 + (b*n*((4*d*(d + e*x))/e^2 - (d + e*x)^2/e^2 - (2*d^2*Log[d + e*x])/e^2)*(f + g*Log[c*(d + e*x)^n]))/4 + (x^2*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]))/2","A",13,7,30,0.2333,1,"{2439, 2411, 43, 2334, 12, 14, 2301}"
381,1,130,0,0.2221667,"\int \left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(c (d+e x)^n\right)\right) \, dx","Int[(a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]),x]","x \left(a+b \log \left(c (d+e x)^n\right)\right) \left(g \log \left(c (d+e x)^n\right)+f\right)+\frac{d g \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 b e}-a g n x+\frac{b d \left(g \log \left(c (d+e x)^n\right)+f\right)^2}{2 e g}-\frac{2 b g n (d+e x) \log \left(c (d+e x)^n\right)}{e}-b f n x+2 b g n^2 x","\frac{d \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)^2}{4 b e g}+x \left(a+b \log \left(c (d+e x)^n\right)\right) \left(g \log \left(c (d+e x)^n\right)+f\right)-n x (a g+b f)-\frac{2 b g n (d+e x) \log \left(c (d+e x)^n\right)}{e}+2 b g n^2 x",1,"-(b*f*n*x) - a*g*n*x + 2*b*g*n^2*x - (2*b*g*n*(d + e*x)*Log[c*(d + e*x)^n])/e + (d*g*(a + b*Log[c*(d + e*x)^n])^2)/(2*b*e) + x*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]) + (b*d*(f + g*Log[c*(d + e*x)^n])^2)/(2*e*g)","A",11,5,29,0.1724,1,"{2430, 2411, 2346, 2301, 2295}"
382,1,219,0,0.3259949,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(c (d+e x)^n\right)\right)}{x} \, dx","Int[((a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]))/x,x]","g n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+b n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(g \log \left(c (d+e x)^n\right)+f\right)-2 b g n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)+\log (x) \left(a+b \log \left(c (d+e x)^n\right)\right) \left(g \log \left(c (d+e x)^n\right)+f\right)-\frac{g \log (x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 b}+\frac{g \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 b}-\frac{b \log (x) \left(g \log \left(c (d+e x)^n\right)+f\right)^2}{2 g}+\frac{b \log \left(-\frac{e x}{d}\right) \left(g \log \left(c (d+e x)^n\right)+f\right)^2}{2 g}","n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)-2 b g n^2 \text{PolyLog}\left(3,\frac{e x}{d}+1\right)-\frac{\log (x) \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)^2}{4 b g}+\frac{\log \left(-\frac{e x}{d}\right) \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)^2}{4 b g}+\log (x) \left(a+b \log \left(c (d+e x)^n\right)\right) \left(g \log \left(c (d+e x)^n\right)+f\right)",1,"-(g*Log[x]*(a + b*Log[c*(d + e*x)^n])^2)/(2*b) + (g*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n])^2)/(2*b) + Log[x]*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]) - (b*Log[x]*(f + g*Log[c*(d + e*x)^n])^2)/(2*g) + (b*Log[-((e*x)/d)]*(f + g*Log[c*(d + e*x)^n])^2)/(2*g) + g*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, 1 + (e*x)/d] + b*n*(f + g*Log[c*(d + e*x)^n])*PolyLog[2, 1 + (e*x)/d] - 2*b*g*n^2*PolyLog[3, 1 + (e*x)/d]","A",11,6,32,0.1875,1,"{2434, 2433, 2375, 2317, 2374, 6589}"
383,1,169,0,0.3460254,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(c (d+e x)^n\right)\right)}{x^2} \, dx","Int[((a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]))/x^2,x]","\frac{2 b e g n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{d}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(g \log \left(c (d+e x)^n\right)+f\right)}{x}+\frac{e g n \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{d}-\frac{e g \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 b d}+\frac{b e n \log \left(-\frac{e x}{d}\right) \left(g \log \left(c (d+e x)^n\right)+f\right)}{d}-\frac{b e \left(g \log \left(c (d+e x)^n\right)+f\right)^2}{2 d g}","-\frac{2 b e g n^2 \text{PolyLog}\left(2,\frac{d}{d+e x}\right)}{d}+\frac{e n \log \left(1-\frac{d}{d+e x}\right) \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)}{d}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(g \log \left(c (d+e x)^n\right)+f\right)}{x}",1,"(e*g*n*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/d - (e*g*(a + b*Log[c*(d + e*x)^n])^2)/(2*b*d) + (b*e*n*Log[-((e*x)/d)]*(f + g*Log[c*(d + e*x)^n]))/d - ((a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]))/x - (b*e*(f + g*Log[c*(d + e*x)^n])^2)/(2*d*g) + (2*b*e*g*n^2*PolyLog[2, 1 + (e*x)/d])/d","A",11,6,32,0.1875,1,"{2439, 2411, 2344, 2301, 2317, 2391}"
384,1,265,0,0.5568684,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(c (d+e x)^n\right)\right)}{x^3} \, dx","Int[((a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]))/x^3,x]","-\frac{b e^2 g n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{d^2}+\frac{e^2 g \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 b d^2}-\frac{e^2 g n \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 d^2}-\frac{e g n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 d^2 x}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(g \log \left(c (d+e x)^n\right)+f\right)}{2 x^2}+\frac{b e^2 \left(g \log \left(c (d+e x)^n\right)+f\right)^2}{4 d^2 g}-\frac{b e^2 n \log \left(-\frac{e x}{d}\right) \left(g \log \left(c (d+e x)^n\right)+f\right)}{2 d^2}-\frac{b e n (d+e x) \left(g \log \left(c (d+e x)^n\right)+f\right)}{2 d^2 x}+\frac{b e^2 g n^2 \log (x)}{d^2}","\frac{b e^2 g n^2 \text{PolyLog}\left(2,\frac{d}{d+e x}\right)}{d^2}-\frac{e^2 n \log \left(1-\frac{d}{d+e x}\right) \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)}{2 d^2}-\frac{e n (d+e x) \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)}{2 d^2 x}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(g \log \left(c (d+e x)^n\right)+f\right)}{2 x^2}+\frac{b e^2 g n^2 \log (x)}{d^2}",1,"(b*e^2*g*n^2*Log[x])/d^2 - (e*g*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n]))/(2*d^2*x) - (e^2*g*n*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/(2*d^2) + (e^2*g*(a + b*Log[c*(d + e*x)^n])^2)/(4*b*d^2) - (b*e*n*(d + e*x)*(f + g*Log[c*(d + e*x)^n]))/(2*d^2*x) - (b*e^2*n*Log[-((e*x)/d)]*(f + g*Log[c*(d + e*x)^n]))/(2*d^2) - ((a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]))/(2*x^2) + (b*e^2*(f + g*Log[c*(d + e*x)^n])^2)/(4*d^2*g) - (b*e^2*g*n^2*PolyLog[2, 1 + (e*x)/d])/d^2","A",17,9,32,0.2812,1,"{2439, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31}"
385,1,365,0,0.8222587,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(c (d+e x)^n\right)\right)}{x^4} \, dx","Int[((a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]))/x^4,x]","\frac{2 b e^3 g n^2 \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{3 d^3}-\frac{e^3 g \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{6 b d^3}+\frac{e^3 g n \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 d^3}+\frac{e^2 g n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 d^3 x}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(g \log \left(c (d+e x)^n\right)+f\right)}{3 x^3}-\frac{e g n \left(a+b \log \left(c (d+e x)^n\right)\right)}{6 d x^2}-\frac{b e^3 \left(g \log \left(c (d+e x)^n\right)+f\right)^2}{6 d^3 g}+\frac{b e^3 n \log \left(-\frac{e x}{d}\right) \left(g \log \left(c (d+e x)^n\right)+f\right)}{3 d^3}+\frac{b e^2 n (d+e x) \left(g \log \left(c (d+e x)^n\right)+f\right)}{3 d^3 x}-\frac{b e n \left(g \log \left(c (d+e x)^n\right)+f\right)}{6 d x^2}-\frac{b e^2 g n^2}{3 d^2 x}-\frac{b e^3 g n^2 \log (x)}{d^3}+\frac{b e^3 g n^2 \log (d+e x)}{3 d^3}","-\frac{2 b e^3 g n^2 \text{PolyLog}\left(2,\frac{d}{d+e x}\right)}{3 d^3}+\frac{e^3 n \log \left(1-\frac{d}{d+e x}\right) \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)}{3 d^3}+\frac{e^2 n (d+e x) \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)}{3 d^3 x}-\frac{e n \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)}{6 d x^2}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(g \log \left(c (d+e x)^n\right)+f\right)}{3 x^3}-\frac{b e^2 g n^2}{3 d^2 x}-\frac{b e^3 g n^2 \log (x)}{d^3}+\frac{b e^3 g n^2 \log (d+e x)}{3 d^3}",1,"-(b*e^2*g*n^2)/(3*d^2*x) - (b*e^3*g*n^2*Log[x])/d^3 + (b*e^3*g*n^2*Log[d + e*x])/(3*d^3) - (e*g*n*(a + b*Log[c*(d + e*x)^n]))/(6*d*x^2) + (e^2*g*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n]))/(3*d^3*x) + (e^3*g*n*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/(3*d^3) - (e^3*g*(a + b*Log[c*(d + e*x)^n])^2)/(6*b*d^3) - (b*e*n*(f + g*Log[c*(d + e*x)^n]))/(6*d*x^2) + (b*e^2*n*(d + e*x)*(f + g*Log[c*(d + e*x)^n]))/(3*d^3*x) + (b*e^3*n*Log[-((e*x)/d)]*(f + g*Log[c*(d + e*x)^n]))/(3*d^3) - ((a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]))/(3*x^3) - (b*e^3*(f + g*Log[c*(d + e*x)^n])^2)/(6*d^3*g) + (2*b*e^3*g*n^2*PolyLog[2, 1 + (e*x)/d])/(3*d^3)","A",25,11,32,0.3438,1,"{2439, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
386,1,742,0,0.8721771,"\int x^3 \left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right) \, dx","Int[x^3*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]),x]","-\frac{b d^4 g m n \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right)}{4 e^4}-\frac{b g i^4 m n \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right)}{4 j^4}+\frac{1}{4} x^4 \left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right)-\frac{g i^2 m x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{8 j^2}-\frac{g i^4 m \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 j^4}+\frac{g i m x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{12 j}-\frac{1}{16} g m x^4 \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{a g i^3 m x}{4 j^3}+\frac{b g i^3 m (d+e x) \log \left(c (d+e x)^n\right)}{4 e j^3}-\frac{b d^2 n x^2 \left(f+g \log \left(h (i+j x)^m\right)\right)}{8 e^2}-\frac{b d^4 n \log \left(-\frac{j (d+e x)}{e i-d j}\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{4 e^4}+\frac{b d^3 f n x}{4 e^3}+\frac{b d^3 g n (i+j x) \log \left(h (i+j x)^m\right)}{4 e^3 j}+\frac{b d^2 g i^2 m n \log (d+e x)}{8 e^2 j^2}+\frac{b d^2 g i^2 m n \log (i+j x)}{8 e^2 j^2}-\frac{5 b d^2 g i m n x}{24 e^2 j}+\frac{b d^3 g i m n \log (d+e x)}{12 e^3 j}+\frac{3 b d^2 g m n x^2}{32 e^2}-\frac{5 b d^3 g m n x}{16 e^3}+\frac{b d^4 g m n \log (d+e x)}{16 e^4}+\frac{b d n x^3 \left(f+g \log \left(h (i+j x)^m\right)\right)}{12 e}-\frac{5 b d g i^2 m n x}{24 e j^2}+\frac{b d g i^3 m n \log (i+j x)}{12 e j^3}+\frac{b d g i m n x^2}{12 e j}-\frac{7 b d g m n x^3}{144 e}-\frac{1}{16} b n x^4 \left(f+g \log \left(h (i+j x)^m\right)\right)+\frac{3 b g i^2 m n x^2}{32 j^2}-\frac{5 b g i^3 m n x}{16 j^3}+\frac{b g i^4 m n \log (i+j x)}{16 j^4}-\frac{7 b g i m n x^3}{144 j}+\frac{1}{32} b g m n x^4","-\frac{b d^4 g m n \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right)}{4 e^4}-\frac{b g i^4 m n \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right)}{4 j^4}+\frac{1}{4} x^4 \left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right)-\frac{g i^2 m x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{8 j^2}-\frac{g i^4 m \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 j^4}+\frac{g i m x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{12 j}-\frac{1}{16} g m x^4 \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{a g i^3 m x}{4 j^3}+\frac{b g i^3 m (d+e x) \log \left(c (d+e x)^n\right)}{4 e j^3}-\frac{b d^2 n x^2 \left(f+g \log \left(h (i+j x)^m\right)\right)}{8 e^2}-\frac{b d^4 n \log \left(-\frac{j (d+e x)}{e i-d j}\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{4 e^4}+\frac{b d^3 f n x}{4 e^3}+\frac{b d^3 g n (i+j x) \log \left(h (i+j x)^m\right)}{4 e^3 j}+\frac{b d^2 g i^2 m n \log (d+e x)}{8 e^2 j^2}+\frac{b d^2 g i^2 m n \log (i+j x)}{8 e^2 j^2}-\frac{5 b d^2 g i m n x}{24 e^2 j}+\frac{b d^3 g i m n \log (d+e x)}{12 e^3 j}+\frac{3 b d^2 g m n x^2}{32 e^2}-\frac{5 b d^3 g m n x}{16 e^3}+\frac{b d^4 g m n \log (d+e x)}{16 e^4}+\frac{b d n x^3 \left(f+g \log \left(h (i+j x)^m\right)\right)}{12 e}-\frac{5 b d g i^2 m n x}{24 e j^2}+\frac{b d g i^3 m n \log (i+j x)}{12 e j^3}+\frac{b d g i m n x^2}{12 e j}-\frac{7 b d g m n x^3}{144 e}-\frac{1}{16} b n x^4 \left(f+g \log \left(h (i+j x)^m\right)\right)+\frac{3 b g i^2 m n x^2}{32 j^2}-\frac{5 b g i^3 m n x}{16 j^3}+\frac{b g i^4 m n \log (i+j x)}{16 j^4}-\frac{7 b g i m n x^3}{144 j}+\frac{1}{32} b g m n x^4",1,"(a*g*i^3*m*x)/(4*j^3) + (b*d^3*f*n*x)/(4*e^3) - (5*b*d^3*g*m*n*x)/(16*e^3) - (5*b*g*i^3*m*n*x)/(16*j^3) - (5*b*d*g*i^2*m*n*x)/(24*e*j^2) - (5*b*d^2*g*i*m*n*x)/(24*e^2*j) + (3*b*d^2*g*m*n*x^2)/(32*e^2) + (3*b*g*i^2*m*n*x^2)/(32*j^2) + (b*d*g*i*m*n*x^2)/(12*e*j) - (7*b*d*g*m*n*x^3)/(144*e) - (7*b*g*i*m*n*x^3)/(144*j) + (b*g*m*n*x^4)/32 + (b*d^4*g*m*n*Log[d + e*x])/(16*e^4) + (b*d^2*g*i^2*m*n*Log[d + e*x])/(8*e^2*j^2) + (b*d^3*g*i*m*n*Log[d + e*x])/(12*e^3*j) + (b*g*i^3*m*(d + e*x)*Log[c*(d + e*x)^n])/(4*e*j^3) - (g*i^2*m*x^2*(a + b*Log[c*(d + e*x)^n]))/(8*j^2) + (g*i*m*x^3*(a + b*Log[c*(d + e*x)^n]))/(12*j) - (g*m*x^4*(a + b*Log[c*(d + e*x)^n]))/16 + (b*g*i^4*m*n*Log[i + j*x])/(16*j^4) + (b*d*g*i^3*m*n*Log[i + j*x])/(12*e*j^3) + (b*d^2*g*i^2*m*n*Log[i + j*x])/(8*e^2*j^2) - (g*i^4*m*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(4*j^4) + (b*d^3*g*n*(i + j*x)*Log[h*(i + j*x)^m])/(4*e^3*j) - (b*d^2*n*x^2*(f + g*Log[h*(i + j*x)^m]))/(8*e^2) + (b*d*n*x^3*(f + g*Log[h*(i + j*x)^m]))/(12*e) - (b*n*x^4*(f + g*Log[h*(i + j*x)^m]))/16 - (b*d^4*n*Log[-((j*(d + e*x))/(e*i - d*j))]*(f + g*Log[h*(i + j*x)^m]))/(4*e^4) + (x^4*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]))/4 - (b*g*i^4*m*n*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(4*j^4) - (b*d^4*g*m*n*PolyLog[2, (e*(i + j*x))/(e*i - d*j)])/(4*e^4)","A",35,9,32,0.2812,1,"{2439, 43, 2416, 2389, 2295, 2395, 2394, 2393, 2391}"
387,1,558,0,0.609394,"\int x^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right) \, dx","Int[x^2*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]),x]","\frac{b d^3 g m n \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right)}{3 e^3}+\frac{b g i^3 m n \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right)}{3 j^3}+\frac{1}{3} x^3 \left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right)+\frac{g i^3 m \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 j^3}+\frac{g i m x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{6 j}-\frac{1}{9} g m x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)-\frac{a g i^2 m x}{3 j^2}-\frac{b g i^2 m (d+e x) \log \left(c (d+e x)^n\right)}{3 e j^2}+\frac{b d^3 n \log \left(-\frac{j (d+e x)}{e i-d j}\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{3 e^3}-\frac{b d^2 f n x}{3 e^2}-\frac{b d^2 g n (i+j x) \log \left(h (i+j x)^m\right)}{3 e^2 j}-\frac{b d^2 g i m n \log (d+e x)}{6 e^2 j}+\frac{4 b d^2 g m n x}{9 e^2}-\frac{b d^3 g m n \log (d+e x)}{9 e^3}+\frac{b d n x^2 \left(f+g \log \left(h (i+j x)^m\right)\right)}{6 e}-\frac{b d g i^2 m n \log (i+j x)}{6 e j^2}+\frac{b d g i m n x}{3 e j}-\frac{5 b d g m n x^2}{36 e}-\frac{1}{9} b n x^3 \left(f+g \log \left(h (i+j x)^m\right)\right)+\frac{4 b g i^2 m n x}{9 j^2}-\frac{b g i^3 m n \log (i+j x)}{9 j^3}-\frac{5 b g i m n x^2}{36 j}+\frac{2}{27} b g m n x^3","\frac{b d^3 g m n \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right)}{3 e^3}+\frac{b g i^3 m n \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right)}{3 j^3}+\frac{1}{3} x^3 \left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right)+\frac{g i^3 m \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 j^3}+\frac{g i m x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{6 j}-\frac{1}{9} g m x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)-\frac{a g i^2 m x}{3 j^2}-\frac{b g i^2 m (d+e x) \log \left(c (d+e x)^n\right)}{3 e j^2}+\frac{b d^3 n \log \left(-\frac{j (d+e x)}{e i-d j}\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{3 e^3}-\frac{b d^2 f n x}{3 e^2}-\frac{b d^2 g n (i+j x) \log \left(h (i+j x)^m\right)}{3 e^2 j}-\frac{b d^2 g i m n \log (d+e x)}{6 e^2 j}+\frac{4 b d^2 g m n x}{9 e^2}-\frac{b d^3 g m n \log (d+e x)}{9 e^3}+\frac{b d n x^2 \left(f+g \log \left(h (i+j x)^m\right)\right)}{6 e}-\frac{b d g i^2 m n \log (i+j x)}{6 e j^2}+\frac{b d g i m n x}{3 e j}-\frac{5 b d g m n x^2}{36 e}-\frac{1}{9} b n x^3 \left(f+g \log \left(h (i+j x)^m\right)\right)+\frac{4 b g i^2 m n x}{9 j^2}-\frac{b g i^3 m n \log (i+j x)}{9 j^3}-\frac{5 b g i m n x^2}{36 j}+\frac{2}{27} b g m n x^3",1,"-(a*g*i^2*m*x)/(3*j^2) - (b*d^2*f*n*x)/(3*e^2) + (4*b*d^2*g*m*n*x)/(9*e^2) + (4*b*g*i^2*m*n*x)/(9*j^2) + (b*d*g*i*m*n*x)/(3*e*j) - (5*b*d*g*m*n*x^2)/(36*e) - (5*b*g*i*m*n*x^2)/(36*j) + (2*b*g*m*n*x^3)/27 - (b*d^3*g*m*n*Log[d + e*x])/(9*e^3) - (b*d^2*g*i*m*n*Log[d + e*x])/(6*e^2*j) - (b*g*i^2*m*(d + e*x)*Log[c*(d + e*x)^n])/(3*e*j^2) + (g*i*m*x^2*(a + b*Log[c*(d + e*x)^n]))/(6*j) - (g*m*x^3*(a + b*Log[c*(d + e*x)^n]))/9 - (b*g*i^3*m*n*Log[i + j*x])/(9*j^3) - (b*d*g*i^2*m*n*Log[i + j*x])/(6*e*j^2) + (g*i^3*m*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(3*j^3) - (b*d^2*g*n*(i + j*x)*Log[h*(i + j*x)^m])/(3*e^2*j) + (b*d*n*x^2*(f + g*Log[h*(i + j*x)^m]))/(6*e) - (b*n*x^3*(f + g*Log[h*(i + j*x)^m]))/9 + (b*d^3*n*Log[-((j*(d + e*x))/(e*i - d*j))]*(f + g*Log[h*(i + j*x)^m]))/(3*e^3) + (x^3*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]))/3 + (b*g*i^3*m*n*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(3*j^3) + (b*d^3*g*m*n*PolyLog[2, (e*(i + j*x))/(e*i - d*j)])/(3*e^3)","A",29,9,32,0.2812,1,"{2439, 43, 2416, 2389, 2295, 2395, 2394, 2393, 2391}"
388,1,397,0,0.4334557,"\int x \left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right) \, dx","Int[x*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]),x]","-\frac{b d^2 g m n \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right)}{2 e^2}-\frac{b g i^2 m n \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right)}{2 j^2}+\frac{1}{2} x^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right)-\frac{g i^2 m \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 j^2}-\frac{1}{4} g m x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{a g i m x}{2 j}+\frac{b g i m (d+e x) \log \left(c (d+e x)^n\right)}{2 e j}-\frac{b d^2 n \log \left(-\frac{j (d+e x)}{e i-d j}\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{2 e^2}+\frac{b d^2 g m n \log (d+e x)}{4 e^2}+\frac{b d f n x}{2 e}+\frac{b d g n (i+j x) \log \left(h (i+j x)^m\right)}{2 e j}-\frac{3 b d g m n x}{4 e}-\frac{1}{4} b n x^2 \left(f+g \log \left(h (i+j x)^m\right)\right)+\frac{b g i^2 m n \log (i+j x)}{4 j^2}-\frac{3 b g i m n x}{4 j}+\frac{1}{4} b g m n x^2","-\frac{b d^2 g m n \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right)}{2 e^2}-\frac{b g i^2 m n \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right)}{2 j^2}+\frac{1}{2} x^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right)-\frac{g i^2 m \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 j^2}-\frac{1}{4} g m x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{a g i m x}{2 j}+\frac{b g i m (d+e x) \log \left(c (d+e x)^n\right)}{2 e j}-\frac{b d^2 n \log \left(-\frac{j (d+e x)}{e i-d j}\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{2 e^2}+\frac{b d^2 g m n \log (d+e x)}{4 e^2}+\frac{b d f n x}{2 e}+\frac{b d g n (i+j x) \log \left(h (i+j x)^m\right)}{2 e j}-\frac{3 b d g m n x}{4 e}-\frac{1}{4} b n x^2 \left(f+g \log \left(h (i+j x)^m\right)\right)+\frac{b g i^2 m n \log (i+j x)}{4 j^2}-\frac{3 b g i m n x}{4 j}+\frac{1}{4} b g m n x^2",1,"(a*g*i*m*x)/(2*j) + (b*d*f*n*x)/(2*e) - (3*b*d*g*m*n*x)/(4*e) - (3*b*g*i*m*n*x)/(4*j) + (b*g*m*n*x^2)/4 + (b*d^2*g*m*n*Log[d + e*x])/(4*e^2) + (b*g*i*m*(d + e*x)*Log[c*(d + e*x)^n])/(2*e*j) - (g*m*x^2*(a + b*Log[c*(d + e*x)^n]))/4 + (b*g*i^2*m*n*Log[i + j*x])/(4*j^2) - (g*i^2*m*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(2*j^2) + (b*d*g*n*(i + j*x)*Log[h*(i + j*x)^m])/(2*e*j) - (b*n*x^2*(f + g*Log[h*(i + j*x)^m]))/4 - (b*d^2*n*Log[-((j*(d + e*x))/(e*i - d*j))]*(f + g*Log[h*(i + j*x)^m]))/(2*e^2) + (x^2*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]))/2 - (b*g*i^2*m*n*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(2*j^2) - (b*d^2*g*m*n*PolyLog[2, (e*(i + j*x))/(e*i - d*j)])/(2*e^2)","A",23,9,30,0.3000,1,"{2439, 43, 2416, 2389, 2295, 2395, 2394, 2393, 2391}"
389,1,232,0,0.284739,"\int \left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right) \, dx","Int[(a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]),x]","\frac{b g i m n \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right)}{j}+\frac{b d g m n \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right)}{e}+x \left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right)+\frac{g i m \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{j}-a g m x-\frac{b g m (d+e x) \log \left(c (d+e x)^n\right)}{e}+\frac{b d n \log \left(-\frac{j (d+e x)}{e i-d j}\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{e}-b f n x-\frac{b g n (i+j x) \log \left(h (i+j x)^m\right)}{j}+2 b g m n x","\frac{b g i m n \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right)}{j}+\frac{b d g m n \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right)}{e}+x \left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right)+\frac{g i m \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{j}-a g m x-\frac{b g m (d+e x) \log \left(c (d+e x)^n\right)}{e}+\frac{b d n \log \left(-\frac{j (d+e x)}{e i-d j}\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{e}-b f n x-\frac{b g n (i+j x) \log \left(h (i+j x)^m\right)}{j}+2 b g m n x",1,"-(a*g*m*x) - b*f*n*x + 2*b*g*m*n*x - (b*g*m*(d + e*x)*Log[c*(d + e*x)^n])/e + (g*i*m*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/j - (b*g*n*(i + j*x)*Log[h*(i + j*x)^m])/j + (b*d*n*Log[-((j*(d + e*x))/(e*i - d*j))]*(f + g*Log[h*(i + j*x)^m]))/e + x*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]) + (b*g*i*m*n*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/j + (b*d*g*m*n*PolyLog[2, (e*(i + j*x))/(e*i - d*j)])/e","A",17,8,29,0.2759,1,"{2430, 43, 2416, 2389, 2295, 2394, 2393, 2391}"
390,1,637,0,0.432721,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{x} \, dx","Int[((a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]))/x,x]","a g m \text{PolyLog}\left(2,\frac{j x}{i}+1\right)-b g m \text{PolyLog}\left(2,\frac{j x}{i}+1\right) \left(n \log (d+e x)-\log \left(c (d+e x)^n\right)\right)+b f n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)-b g n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(m \log (i+j x)-\log \left(h (i+j x)^m\right)\right)+b g m n \text{PolyLog}\left(3,\frac{i (d+e x)}{d (i+j x)}\right)-b g m n \text{PolyLog}\left(3,\frac{j (d+e x)}{e (i+j x)}\right)+b g m n \log \left(\frac{d (i+j x)}{i (d+e x)}\right) \text{PolyLog}\left(2,\frac{i (d+e x)}{d (i+j x)}\right)-b g m n \log \left(\frac{d (i+j x)}{i (d+e x)}\right) \text{PolyLog}\left(2,\frac{j (d+e x)}{e (i+j x)}\right)+b g m n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(\log (i+j x)-\log \left(\frac{d (i+j x)}{i (d+e x)}\right)\right)+b g m n \text{PolyLog}\left(2,\frac{j x}{i}+1\right) \left(\log \left(\frac{d (i+j x)}{i (d+e x)}\right)+\log (d+e x)\right)-b g m n \text{PolyLog}\left(3,\frac{e x}{d}+1\right)-b g m n \text{PolyLog}\left(3,\frac{j x}{i}+1\right)+f \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+a g \log \left(-\frac{j x}{i}\right) \log \left(h (i+j x)^m\right)-b g \log \left(-\frac{e x}{d}\right) \log \left(c (d+e x)^n\right) \left(m \log (i+j x)-\log \left(h (i+j x)^m\right)\right)-b g m \log \left(-\frac{j x}{i}\right) \log (i+j x) \left(n \log (d+e x)-\log \left(c (d+e x)^n\right)\right)+\frac{1}{2} b g m n \left(\log \left(\frac{e i-d j}{e (i+j x)}\right)-\log \left(-\frac{x (e i-d j)}{d (i+j x)}\right)+\log \left(-\frac{e x}{d}\right)\right) \log ^2\left(\frac{d (i+j x)}{i (d+e x)}\right)-\frac{1}{2} b g m n \left(\log \left(-\frac{e x}{d}\right)-\log \left(-\frac{j x}{i}\right)\right) \left(\log \left(\frac{d (i+j x)}{i (d+e x)}\right)+\log (d+e x)\right)^2+b g m n \log \left(-\frac{e x}{d}\right) \log (d+e x) \log (i+j x)","a g m \text{PolyLog}\left(2,\frac{j x}{i}+1\right)-b g m \text{PolyLog}\left(2,\frac{j x}{i}+1\right) \left(n \log (d+e x)-\log \left(c (d+e x)^n\right)\right)+b f n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)-b g n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(m \log (i+j x)-\log \left(h (i+j x)^m\right)\right)+b g m n \text{PolyLog}\left(3,\frac{i (d+e x)}{d (i+j x)}\right)-b g m n \text{PolyLog}\left(3,\frac{j (d+e x)}{e (i+j x)}\right)+b g m n \log \left(\frac{d (i+j x)}{i (d+e x)}\right) \text{PolyLog}\left(2,\frac{i (d+e x)}{d (i+j x)}\right)-b g m n \log \left(\frac{d (i+j x)}{i (d+e x)}\right) \text{PolyLog}\left(2,\frac{j (d+e x)}{e (i+j x)}\right)+b g m n \text{PolyLog}\left(2,\frac{e x}{d}+1\right) \left(\log (i+j x)-\log \left(\frac{d (i+j x)}{i (d+e x)}\right)\right)+b g m n \text{PolyLog}\left(2,\frac{j x}{i}+1\right) \left(\log \left(\frac{d (i+j x)}{i (d+e x)}\right)+\log (d+e x)\right)-b g m n \text{PolyLog}\left(3,\frac{e x}{d}+1\right)-b g m n \text{PolyLog}\left(3,\frac{j x}{i}+1\right)+f \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+a g \log \left(-\frac{j x}{i}\right) \log \left(h (i+j x)^m\right)-b g \log \left(-\frac{e x}{d}\right) \log \left(c (d+e x)^n\right) \left(m \log (i+j x)-\log \left(h (i+j x)^m\right)\right)-b g m \log \left(-\frac{j x}{i}\right) \log (i+j x) \left(n \log (d+e x)-\log \left(c (d+e x)^n\right)\right)+\frac{1}{2} b g m n \left(\log \left(\frac{e i-d j}{e (i+j x)}\right)-\log \left(-\frac{x (e i-d j)}{d (i+j x)}\right)+\log \left(-\frac{e x}{d}\right)\right) \log ^2\left(\frac{d (i+j x)}{i (d+e x)}\right)-\frac{1}{2} b g m n \left(\log \left(-\frac{e x}{d}\right)-\log \left(-\frac{j x}{i}\right)\right) \left(\log \left(\frac{d (i+j x)}{i (d+e x)}\right)+\log (d+e x)\right)^2+b g m n \log \left(-\frac{e x}{d}\right) \log (d+e x) \log (i+j x)",1,"f*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]) + b*g*m*n*Log[-((e*x)/d)]*Log[d + e*x]*Log[i + j*x] - b*g*m*Log[-((j*x)/i)]*(n*Log[d + e*x] - Log[c*(d + e*x)^n])*Log[i + j*x] + (b*g*m*n*(Log[-((e*x)/d)] + Log[(e*i - d*j)/(e*(i + j*x))] - Log[-(((e*i - d*j)*x)/(d*(i + j*x)))])*Log[(d*(i + j*x))/(i*(d + e*x))]^2)/2 - (b*g*m*n*(Log[-((e*x)/d)] - Log[-((j*x)/i)])*(Log[d + e*x] + Log[(d*(i + j*x))/(i*(d + e*x))])^2)/2 - b*g*Log[-((e*x)/d)]*Log[c*(d + e*x)^n]*(m*Log[i + j*x] - Log[h*(i + j*x)^m]) + a*g*Log[-((j*x)/i)]*Log[h*(i + j*x)^m] + b*f*n*PolyLog[2, 1 + (e*x)/d] + b*g*m*n*(Log[i + j*x] - Log[(d*(i + j*x))/(i*(d + e*x))])*PolyLog[2, 1 + (e*x)/d] - b*g*n*(m*Log[i + j*x] - Log[h*(i + j*x)^m])*PolyLog[2, 1 + (e*x)/d] + b*g*m*n*Log[(d*(i + j*x))/(i*(d + e*x))]*PolyLog[2, (i*(d + e*x))/(d*(i + j*x))] - b*g*m*n*Log[(d*(i + j*x))/(i*(d + e*x))]*PolyLog[2, (j*(d + e*x))/(e*(i + j*x))] + a*g*m*PolyLog[2, 1 + (j*x)/i] - b*g*m*(n*Log[d + e*x] - Log[c*(d + e*x)^n])*PolyLog[2, 1 + (j*x)/i] + b*g*m*n*(Log[d + e*x] + Log[(d*(i + j*x))/(i*(d + e*x))])*PolyLog[2, 1 + (j*x)/i] - b*g*m*n*PolyLog[3, 1 + (e*x)/d] + b*g*m*n*PolyLog[3, (i*(d + e*x))/(d*(i + j*x))] - b*g*m*n*PolyLog[3, (j*(d + e*x))/(e*(i + j*x))] - b*g*m*n*PolyLog[3, 1 + (j*x)/i]","A",13,5,32,0.1562,1,"{2438, 2394, 2315, 2437, 2435}"
391,1,270,0,0.3326088,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{x^2} \, dx","Int[((a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]))/x^2,x]","-\frac{b g j m n \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right)}{i}+\frac{b g j m n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{i}-\frac{b e g m n \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right)}{d}+\frac{b e g m n \text{PolyLog}\left(2,\frac{j x}{i}+1\right)}{d}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{x}+\frac{g j m \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{i}-\frac{g j m \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{i}+\frac{b e n \log \left(-\frac{j x}{i}\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{d}-\frac{b e n \log \left(-\frac{j (d+e x)}{e i-d j}\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{d}","-\frac{b g j m n \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right)}{i}+\frac{b g j m n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{i}-\frac{b e g m n \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right)}{d}+\frac{b e g m n \text{PolyLog}\left(2,\frac{j x}{i}+1\right)}{d}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{x}+\frac{g j m \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{i}-\frac{g j m \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{i}+\frac{b e n \log \left(-\frac{j x}{i}\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{d}-\frac{b e n \log \left(-\frac{j (d+e x)}{e i-d j}\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{d}",1,"(g*j*m*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/i - (g*j*m*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/i + (b*e*n*Log[-((j*x)/i)]*(f + g*Log[h*(i + j*x)^m]))/d - (b*e*n*Log[-((j*(d + e*x))/(e*i - d*j))]*(f + g*Log[h*(i + j*x)^m]))/d - ((a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]))/x - (b*g*j*m*n*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/i + (b*g*j*m*n*PolyLog[2, 1 + (e*x)/d])/i - (b*e*g*m*n*PolyLog[2, (e*(i + j*x))/(e*i - d*j)])/d + (b*e*g*m*n*PolyLog[2, 1 + (j*x)/i])/d","A",15,9,32,0.2812,1,"{2439, 36, 29, 31, 2416, 2394, 2315, 2393, 2391}"
392,1,421,0,0.4551791,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{x^3} \, dx","Int[((a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]))/x^3,x]","\frac{b e^2 g m n \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right)}{2 d^2}-\frac{b e^2 g m n \text{PolyLog}\left(2,\frac{j x}{i}+1\right)}{2 d^2}+\frac{b g j^2 m n \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right)}{2 i^2}-\frac{b g j^2 m n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{2 i^2}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{2 x^2}-\frac{g j^2 m \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 i^2}+\frac{g j^2 m \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 i^2}-\frac{g j m \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 i x}-\frac{b e^2 n \log \left(-\frac{j x}{i}\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{2 d^2}+\frac{b e^2 n \log \left(-\frac{j (d+e x)}{e i-d j}\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{2 d^2}-\frac{b e n \left(f+g \log \left(h (i+j x)^m\right)\right)}{2 d x}+\frac{b e g j m n \log (x)}{d i}-\frac{b e g j m n \log (d+e x)}{2 d i}-\frac{b e g j m n \log (i+j x)}{2 d i}","\frac{b e^2 g m n \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right)}{2 d^2}-\frac{b e^2 g m n \text{PolyLog}\left(2,\frac{j x}{i}+1\right)}{2 d^2}+\frac{b g j^2 m n \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right)}{2 i^2}-\frac{b g j^2 m n \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{2 i^2}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{2 x^2}-\frac{g j^2 m \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 i^2}+\frac{g j^2 m \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 i^2}-\frac{g j m \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 i x}-\frac{b e^2 n \log \left(-\frac{j x}{i}\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{2 d^2}+\frac{b e^2 n \log \left(-\frac{j (d+e x)}{e i-d j}\right) \left(f+g \log \left(h (i+j x)^m\right)\right)}{2 d^2}-\frac{b e n \left(f+g \log \left(h (i+j x)^m\right)\right)}{2 d x}+\frac{b e g j m n \log (x)}{d i}-\frac{b e g j m n \log (d+e x)}{2 d i}-\frac{b e g j m n \log (i+j x)}{2 d i}",1,"(b*e*g*j*m*n*Log[x])/(d*i) - (b*e*g*j*m*n*Log[d + e*x])/(2*d*i) - (g*j*m*(a + b*Log[c*(d + e*x)^n]))/(2*i*x) - (g*j^2*m*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]))/(2*i^2) - (b*e*g*j*m*n*Log[i + j*x])/(2*d*i) + (g*j^2*m*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(2*i^2) - (b*e*n*(f + g*Log[h*(i + j*x)^m]))/(2*d*x) - (b*e^2*n*Log[-((j*x)/i)]*(f + g*Log[h*(i + j*x)^m]))/(2*d^2) + (b*e^2*n*Log[-((j*(d + e*x))/(e*i - d*j))]*(f + g*Log[h*(i + j*x)^m]))/(2*d^2) - ((a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]))/(2*x^2) + (b*g*j^2*m*n*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(2*i^2) - (b*g*j^2*m*n*PolyLog[2, 1 + (e*x)/d])/(2*i^2) + (b*e^2*g*m*n*PolyLog[2, (e*(i + j*x))/(e*i - d*j)])/(2*d^2) - (b*e^2*g*m*n*PolyLog[2, 1 + (j*x)/i])/(2*d^2)","A",23,11,32,0.3438,1,"{2439, 44, 2416, 2395, 36, 29, 31, 2394, 2315, 2393, 2391}"
393,1,1179,0,2.7902401,"\int x \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \left(f+g \log \left(h (i+j x)^m\right)\right) \, dx","Int[x*(a + b*Log[c*(d + e*x)^n])^2*(f + g*Log[h*(i + j*x)^m]),x]","-\frac{1}{4} g m n^2 x^2 b^2+\frac{f n^2 (d+e x)^2 b^2}{4 e^2}-\frac{g m n^2 (d+e x)^2 b^2}{8 e^2}+\frac{d^2 f n^2 \log ^2(d+e x) b^2}{2 e^2}-\frac{2 d f n^2 x b^2}{e}+\frac{15 d g m n^2 x b^2}{4 e}+\frac{7 g i m n^2 x b^2}{4 j}-\frac{d^2 g m n^2 \log (d+e x) b^2}{4 e^2}-\frac{2 d g m n (d+e x) \log \left(c (d+e x)^n\right) b^2}{e^2}-\frac{3 g i m n (d+e x) \log \left(c (d+e x)^n\right) b^2}{2 e j}-\frac{g i^2 m n^2 \log (i+j x) b^2}{4 j^2}+\frac{1}{4} g n^2 x^2 \log \left(h (i+j x)^m\right) b^2-\frac{3 d g n^2 (i+j x) \log \left(h (i+j x)^m\right) b^2}{2 e j}+\frac{3 d^2 g n^2 \log \left(-\frac{j (d+e x)}{e i-d j}\right) \log \left(h (i+j x)^m\right) b^2}{2 e^2}+\frac{d g i m n^2 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^2}{e j}+\frac{g i^2 m n^2 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^2}{2 j^2}+\frac{3 d^2 g m n^2 \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right) b^2}{2 e^2}-\frac{d^2 g m n^2 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^2}{e^2}+\frac{g i^2 m n^2 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^2}{j^2}-\frac{2 a d g m n x b}{e}-\frac{3 a g i m n x b}{2 j}+\frac{1}{4} g m n x^2 \left(a+b \log \left(c (d+e x)^n\right)\right) b+\frac{g m n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right) b}{4 e^2}+\frac{1}{2} f n \left(-\frac{2 \log (d+e x) d^2}{e^2}+\frac{4 (d+e x) d}{e^2}-\frac{(d+e x)^2}{e^2}\right) \left(a+b \log \left(c (d+e x)^n\right)\right) b+\frac{d g i m n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e (i+j x)}{e i-d j}\right) b}{e j}+\frac{g i^2 m n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e (i+j x)}{e i-d j}\right) b}{2 j^2}-\frac{1}{2} g n x^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(h (i+j x)^m\right) b+\frac{d g n x \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(h (i+j x)^m\right) b}{e}+\frac{d^2 g m n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b}{e^2}-\frac{g i^2 m n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b}{j^2}-\frac{g m (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 e^2}+\frac{d g m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2}+\frac{g i m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e j}+\frac{d^2 g m \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e (i+j x)}{e i-d j}\right)}{2 e^2}-\frac{g i^2 m \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e (i+j x)}{e i-d j}\right)}{2 j^2}-\frac{d^2 g \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(h (i+j x)^m\right)}{2 e^2}+\frac{1}{2} x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \left(f+g \log \left(h (i+j x)^m\right)\right)","-\frac{1}{4} g m n^2 x^2 b^2+\frac{f n^2 (d+e x)^2 b^2}{4 e^2}-\frac{g m n^2 (d+e x)^2 b^2}{8 e^2}+\frac{d^2 f n^2 \log ^2(d+e x) b^2}{2 e^2}-\frac{2 d f n^2 x b^2}{e}+\frac{15 d g m n^2 x b^2}{4 e}+\frac{7 g i m n^2 x b^2}{4 j}-\frac{d^2 g m n^2 \log (d+e x) b^2}{4 e^2}-\frac{2 d g m n (d+e x) \log \left(c (d+e x)^n\right) b^2}{e^2}-\frac{3 g i m n (d+e x) \log \left(c (d+e x)^n\right) b^2}{2 e j}-\frac{g i^2 m n^2 \log (i+j x) b^2}{4 j^2}+\frac{1}{4} g n^2 x^2 \log \left(h (i+j x)^m\right) b^2-\frac{3 d g n^2 (i+j x) \log \left(h (i+j x)^m\right) b^2}{2 e j}+\frac{3 d^2 g n^2 \log \left(-\frac{j (d+e x)}{e i-d j}\right) \log \left(h (i+j x)^m\right) b^2}{2 e^2}+\frac{d g i m n^2 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^2}{e j}+\frac{g i^2 m n^2 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^2}{2 j^2}+\frac{3 d^2 g m n^2 \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right) b^2}{2 e^2}-\frac{d^2 g m n^2 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^2}{e^2}+\frac{g i^2 m n^2 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^2}{j^2}-\frac{2 a d g m n x b}{e}-\frac{3 a g i m n x b}{2 j}+\frac{1}{4} g m n x^2 \left(a+b \log \left(c (d+e x)^n\right)\right) b-\frac{f n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right) b}{2 e^2}+\frac{g m n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right) b}{4 e^2}+\frac{2 d f n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right) b}{e^2}-\frac{d^2 f n \log (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right) b}{e^2}+\frac{d g i m n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e (i+j x)}{e i-d j}\right) b}{e j}+\frac{g i^2 m n \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e (i+j x)}{e i-d j}\right) b}{2 j^2}-\frac{1}{2} g n x^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(h (i+j x)^m\right) b+\frac{d g n x \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(h (i+j x)^m\right) b}{e}+\frac{d^2 g m n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b}{e^2}-\frac{g i^2 m n \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b}{j^2}-\frac{g m (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{4 e^2}+\frac{d g m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e^2}+\frac{g i m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 e j}+\frac{d^2 g m \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e (i+j x)}{e i-d j}\right)}{2 e^2}-\frac{g i^2 m \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e (i+j x)}{e i-d j}\right)}{2 j^2}-\frac{d^2 g \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(h (i+j x)^m\right)}{2 e^2}+\frac{1}{2} x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \left(f+g \log \left(h (i+j x)^m\right)\right)",1,"(-2*a*b*d*g*m*n*x)/e - (3*a*b*g*i*m*n*x)/(2*j) - (2*b^2*d*f*n^2*x)/e + (15*b^2*d*g*m*n^2*x)/(4*e) + (7*b^2*g*i*m*n^2*x)/(4*j) - (b^2*g*m*n^2*x^2)/4 + (b^2*f*n^2*(d + e*x)^2)/(4*e^2) - (b^2*g*m*n^2*(d + e*x)^2)/(8*e^2) - (b^2*d^2*g*m*n^2*Log[d + e*x])/(4*e^2) + (b^2*d^2*f*n^2*Log[d + e*x]^2)/(2*e^2) - (2*b^2*d*g*m*n*(d + e*x)*Log[c*(d + e*x)^n])/e^2 - (3*b^2*g*i*m*n*(d + e*x)*Log[c*(d + e*x)^n])/(2*e*j) + (b*g*m*n*x^2*(a + b*Log[c*(d + e*x)^n]))/4 + (b*g*m*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(4*e^2) + (b*f*n*((4*d*(d + e*x))/e^2 - (d + e*x)^2/e^2 - (2*d^2*Log[d + e*x])/e^2)*(a + b*Log[c*(d + e*x)^n]))/2 + (d*g*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(2*e^2) + (g*i*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(2*e*j) - (g*m*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(4*e^2) - (b^2*g*i^2*m*n^2*Log[i + j*x])/(4*j^2) + (b*g*i^2*m*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(2*j^2) + (b*d*g*i*m*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(e*j) + (d^2*g*m*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/(2*e^2) - (g*i^2*m*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/(2*j^2) + (b^2*g*n^2*x^2*Log[h*(i + j*x)^m])/4 - (3*b^2*d*g*n^2*(i + j*x)*Log[h*(i + j*x)^m])/(2*e*j) + (3*b^2*d^2*g*n^2*Log[-((j*(d + e*x))/(e*i - d*j))]*Log[h*(i + j*x)^m])/(2*e^2) + (b*d*g*n*x*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m])/e - (b*g*n*x^2*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m])/2 - (d^2*g*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m])/(2*e^2) + (x^2*(a + b*Log[c*(d + e*x)^n])^2*(f + g*Log[h*(i + j*x)^m]))/2 + (b^2*g*i^2*m*n^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(2*j^2) + (b^2*d*g*i*m*n^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(e*j) + (b*d^2*g*m*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/e^2 - (b*g*i^2*m*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/j^2 + (3*b^2*d^2*g*m*n^2*PolyLog[2, (e*(i + j*x))/(e*i - d*j)])/(2*e^2) - (b^2*d^2*g*m*n^2*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/e^2 + (b^2*g*i^2*m*n^2*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/j^2","A",73,27,32,0.8438,1,"{2439, 2416, 2389, 2296, 2295, 2401, 2390, 2305, 2304, 2396, 2433, 2374, 6589, 6742, 2411, 43, 2334, 12, 14, 2301, 2430, 2394, 2393, 2391, 2395, 2375, 2317}"
394,1,649,0,1.4812806,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \left(f+g \log \left(h (i+j x)^m\right)\right) \, dx","Int[(a + b*Log[c*(d + e*x)^n])^2*(f + g*Log[h*(i + j*x)^m]),x]","-\frac{2 b d g m n \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e}+\frac{2 b g i m n \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{j}-\frac{2 b^2 g i m n^2 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right)}{j}-\frac{2 b^2 d g m n^2 \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right)}{e}+\frac{2 b^2 d g m n^2 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right)}{e}-\frac{2 b^2 g i m n^2 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right)}{j}+x \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \left(f+g \log \left(h (i+j x)^m\right)\right)+\frac{d f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-2 b g n x \log \left(h (i+j x)^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{d g \log \left(h (i+j x)^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-\frac{2 b g i m n \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{j}-\frac{d g m \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}+\frac{g i m \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{j}-\frac{g m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-2 a b f n x+4 a b g m n x-\frac{2 b^2 f n (d+e x) \log \left(c (d+e x)^n\right)}{e}+\frac{4 b^2 g m n (d+e x) \log \left(c (d+e x)^n\right)}{e}-\frac{2 b^2 d g n^2 \log \left(-\frac{j (d+e x)}{e i-d j}\right) \log \left(h (i+j x)^m\right)}{e}+2 b^2 f n^2 x+\frac{2 b^2 g n^2 (i+j x) \log \left(h (i+j x)^m\right)}{j}-6 b^2 g m n^2 x","-\frac{2 b d g m n \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e}+\frac{2 b g i m n \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{j}-\frac{2 b^2 g i m n^2 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right)}{j}-\frac{2 b^2 d g m n^2 \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right)}{e}+\frac{2 b^2 d g m n^2 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right)}{e}-\frac{2 b^2 g i m n^2 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right)}{j}+x \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \left(f+g \log \left(h (i+j x)^m\right)\right)+\frac{d f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-2 b g n x \log \left(h (i+j x)^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{d g \log \left(h (i+j x)^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-\frac{2 b g i m n \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{j}-\frac{d g m \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}+\frac{g i m \log \left(\frac{e (i+j x)}{e i-d j}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{j}-\frac{g m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-2 a b f n x+4 a b g m n x-\frac{2 b^2 f n (d+e x) \log \left(c (d+e x)^n\right)}{e}+\frac{4 b^2 g m n (d+e x) \log \left(c (d+e x)^n\right)}{e}-\frac{2 b^2 d g n^2 \log \left(-\frac{j (d+e x)}{e i-d j}\right) \log \left(h (i+j x)^m\right)}{e}+2 b^2 f n^2 x+\frac{2 b^2 g n^2 (i+j x) \log \left(h (i+j x)^m\right)}{j}-6 b^2 g m n^2 x",1,"-2*a*b*f*n*x + 4*a*b*g*m*n*x + 2*b^2*f*n^2*x - 6*b^2*g*m*n^2*x - (2*b^2*f*n*(d + e*x)*Log[c*(d + e*x)^n])/e + (4*b^2*g*m*n*(d + e*x)*Log[c*(d + e*x)^n])/e + (d*f*(a + b*Log[c*(d + e*x)^n])^2)/e - (g*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e - (2*b*g*i*m*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/j - (d*g*m*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/e + (g*i*m*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/j + (2*b^2*g*n^2*(i + j*x)*Log[h*(i + j*x)^m])/j - (2*b^2*d*g*n^2*Log[-((j*(d + e*x))/(e*i - d*j))]*Log[h*(i + j*x)^m])/e - 2*b*g*n*x*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m] + (d*g*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m])/e + x*(a + b*Log[c*(d + e*x)^n])^2*(f + g*Log[h*(i + j*x)^m]) - (2*b^2*g*i*m*n^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/j - (2*b*d*g*m*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/e + (2*b*g*i*m*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/j - (2*b^2*d*g*m*n^2*PolyLog[2, (e*(i + j*x))/(e*i - d*j)])/e + (2*b^2*d*g*m*n^2*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/e - (2*b^2*g*i*m*n^2*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/j","A",41,19,31,0.6129,1,"{2430, 2416, 2389, 2296, 2295, 2396, 2433, 2374, 6589, 6742, 2411, 2346, 2301, 43, 2394, 2393, 2391, 2375, 2317}"
395,0,0,0,0.0370585,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \left(f+g \log \left(h (i+j x)^m\right)\right)}{x} \, dx","Int[((a + b*Log[c*(d + e*x)^n])^2*(f + g*Log[h*(i + j*x)^m]))/x,x]","\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \left(f+g \log \left(h (i+j x)^m\right)\right)}{x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \left(f+g \log \left(h (i+j x)^m\right)\right)}{x},x\right)",0,"Defer[Int][((a + b*Log[c*(d + e*x)^n])^2*(f + g*Log[h*(i + j*x)^m]))/x, x]","A",0,0,0,0,-1,"{}"
396,0,0,0,0.0396986,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \left(f+g \log \left(h (i+j x)^m\right)\right)}{x^2} \, dx","Int[((a + b*Log[c*(d + e*x)^n])^2*(f + g*Log[h*(i + j*x)^m]))/x^2,x]","\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \left(f+g \log \left(h (i+j x)^m\right)\right)}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \left(f+g \log \left(h (i+j x)^m\right)\right)}{x^2},x\right)",0,"Defer[Int][((a + b*Log[c*(d + e*x)^n])^2*(f + g*Log[h*(i + j*x)^m]))/x^2, x]","A",0,0,0,0,-1,"{}"
397,1,2050,0,6.8906854,"\int x \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \left(f+g \log \left(h (i+j x)^m\right)\right) \, dx","Int[x*(a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]),x]","\frac{3}{8} g m n^3 x^2 b^3-\frac{3 f n^3 (d+e x)^2 b^3}{8 e^2}+\frac{3 g m n^3 (d+e x)^2 b^3}{8 e^2}+\frac{6 d f n^3 x b^3}{e}-\frac{141 d g m n^3 x b^3}{8 e}-\frac{45 g i m n^3 x b^3}{8 j}+\frac{3 d^2 g m n^3 \log (d+e x) b^3}{8 e^2}-\frac{6 d f n^2 (d+e x) \log \left(c (d+e x)^n\right) b^3}{e^2}+\frac{12 d g m n^2 (d+e x) \log \left(c (d+e x)^n\right) b^3}{e^2}+\frac{21 g i m n^2 (d+e x) \log \left(c (d+e x)^n\right) b^3}{4 e j}+\frac{3 g i^2 m n^3 \log (i+j x) b^3}{8 j^2}-\frac{3}{8} g n^3 x^2 \log \left(h (i+j x)^m\right) b^3+\frac{21 d g n^3 (i+j x) \log \left(h (i+j x)^m\right) b^3}{4 e j}-\frac{21 d^2 g n^3 \log \left(-\frac{j (d+e x)}{e i-d j}\right) \log \left(h (i+j x)^m\right) b^3}{4 e^2}-\frac{9 d g i m n^3 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^3}{2 e j}-\frac{3 g i^2 m n^3 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^3}{4 j^2}-\frac{21 d^2 g m n^3 \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right) b^3}{4 e^2}+\frac{9 d^2 g m n^3 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^3}{2 e^2}-\frac{3 d g i m n^3 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^3}{e j}-\frac{3 g i^2 m n^3 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^3}{2 j^2}+\frac{3 d^2 g m n^3 \text{PolyLog}\left(4,-\frac{j (d+e x)}{e i-d j}\right) b^3}{e^2}-\frac{3 g i^2 m n^3 \text{PolyLog}\left(4,-\frac{j (d+e x)}{e i-d j}\right) b^3}{j^2}-\frac{6 a d f n^2 x b^2}{e}+\frac{12 a d g m n^2 x b^2}{e}+\frac{21 a g i m n^2 x b^2}{4 j}-\frac{3}{8} g m n^2 x^2 \left(a+b \log \left(c (d+e x)^n\right)\right) b^2+\frac{3 f n^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right) b^2}{4 e^2}-\frac{3 g m n^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right) b^2}{4 e^2}-\frac{9 d g i m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e (i+j x)}{e i-d j}\right) b^2}{2 e j}-\frac{3 g i^2 m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e (i+j x)}{e i-d j}\right) b^2}{4 j^2}+\frac{3}{4} g n^2 x^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(h (i+j x)^m\right) b^2-\frac{9 d g n^2 x \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(h (i+j x)^m\right) b^2}{2 e}-\frac{9 d^2 g m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^2}{2 e^2}+\frac{3 d g i m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^2}{e j}+\frac{3 g i^2 m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^2}{2 j^2}-\frac{3 d^2 g m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^2}{e^2}+\frac{3 g i^2 m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^2}{j^2}-\frac{3 f n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2 b}{4 e^2}+\frac{3 g m n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2 b}{4 e^2}+\frac{3 d f n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 b}{e^2}-\frac{15 d g m n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 b}{4 e^2}-\frac{9 g i m n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 b}{4 e j}-\frac{9 d^2 g m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e (i+j x)}{e i-d j}\right) b}{4 e^2}+\frac{3 d g i m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e (i+j x)}{e i-d j}\right) b}{2 e j}+\frac{3 g i^2 m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e (i+j x)}{e i-d j}\right) b}{4 j^2}-\frac{3}{4} g n x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(h (i+j x)^m\right) b+\frac{9 d^2 g n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(h (i+j x)^m\right) b}{4 e^2}+\frac{3 d g n x \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(h (i+j x)^m\right) b}{2 e}+\frac{3 d^2 g m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b}{2 e^2}-\frac{3 g i^2 m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b}{2 j^2}-\frac{g m (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{4 e^2}-\frac{d^2 f \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{2 e^2}+\frac{d g m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{2 e^2}+\frac{g i m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{2 e j}+\frac{d^2 g m \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \log \left(\frac{e (i+j x)}{e i-d j}\right)}{2 e^2}-\frac{g i^2 m \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \log \left(\frac{e (i+j x)}{e i-d j}\right)}{2 j^2}-\frac{d^2 g \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \log \left(h (i+j x)^m\right)}{2 e^2}+\frac{1}{2} x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \left(f+g \log \left(h (i+j x)^m\right)\right)","\frac{3}{8} g m n^3 x^2 b^3-\frac{3 f n^3 (d+e x)^2 b^3}{8 e^2}+\frac{3 g m n^3 (d+e x)^2 b^3}{8 e^2}+\frac{6 d f n^3 x b^3}{e}-\frac{141 d g m n^3 x b^3}{8 e}-\frac{45 g i m n^3 x b^3}{8 j}+\frac{3 d^2 g m n^3 \log (d+e x) b^3}{8 e^2}-\frac{6 d f n^2 (d+e x) \log \left(c (d+e x)^n\right) b^3}{e^2}+\frac{12 d g m n^2 (d+e x) \log \left(c (d+e x)^n\right) b^3}{e^2}+\frac{21 g i m n^2 (d+e x) \log \left(c (d+e x)^n\right) b^3}{4 e j}+\frac{3 g i^2 m n^3 \log (i+j x) b^3}{8 j^2}-\frac{3}{8} g n^3 x^2 \log \left(h (i+j x)^m\right) b^3+\frac{21 d g n^3 (i+j x) \log \left(h (i+j x)^m\right) b^3}{4 e j}-\frac{21 d^2 g n^3 \log \left(-\frac{j (d+e x)}{e i-d j}\right) \log \left(h (i+j x)^m\right) b^3}{4 e^2}-\frac{9 d g i m n^3 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^3}{2 e j}-\frac{3 g i^2 m n^3 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^3}{4 j^2}-\frac{21 d^2 g m n^3 \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right) b^3}{4 e^2}+\frac{9 d^2 g m n^3 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^3}{2 e^2}-\frac{3 d g i m n^3 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^3}{e j}-\frac{3 g i^2 m n^3 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^3}{2 j^2}+\frac{3 d^2 g m n^3 \text{PolyLog}\left(4,-\frac{j (d+e x)}{e i-d j}\right) b^3}{e^2}-\frac{3 g i^2 m n^3 \text{PolyLog}\left(4,-\frac{j (d+e x)}{e i-d j}\right) b^3}{j^2}-\frac{6 a d f n^2 x b^2}{e}+\frac{12 a d g m n^2 x b^2}{e}+\frac{21 a g i m n^2 x b^2}{4 j}-\frac{3}{8} g m n^2 x^2 \left(a+b \log \left(c (d+e x)^n\right)\right) b^2+\frac{3 f n^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right) b^2}{4 e^2}-\frac{3 g m n^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right) b^2}{4 e^2}-\frac{9 d g i m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e (i+j x)}{e i-d j}\right) b^2}{2 e j}-\frac{3 g i^2 m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e (i+j x)}{e i-d j}\right) b^2}{4 j^2}+\frac{3}{4} g n^2 x^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(h (i+j x)^m\right) b^2-\frac{9 d g n^2 x \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(h (i+j x)^m\right) b^2}{2 e}-\frac{9 d^2 g m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^2}{2 e^2}+\frac{3 d g i m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^2}{e j}+\frac{3 g i^2 m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^2}{2 j^2}-\frac{3 d^2 g m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^2}{e^2}+\frac{3 g i^2 m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^2}{j^2}-\frac{3 f n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2 b}{4 e^2}+\frac{3 g m n (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2 b}{4 e^2}+\frac{3 d f n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 b}{e^2}-\frac{15 d g m n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 b}{4 e^2}-\frac{9 g i m n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 b}{4 e j}-\frac{9 d^2 g m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e (i+j x)}{e i-d j}\right) b}{4 e^2}+\frac{3 d g i m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e (i+j x)}{e i-d j}\right) b}{2 e j}+\frac{3 g i^2 m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e (i+j x)}{e i-d j}\right) b}{4 j^2}-\frac{3}{4} g n x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(h (i+j x)^m\right) b+\frac{9 d^2 g n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(h (i+j x)^m\right) b}{4 e^2}+\frac{3 d g n x \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(h (i+j x)^m\right) b}{2 e}+\frac{3 d^2 g m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b}{2 e^2}-\frac{3 g i^2 m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b}{2 j^2}-\frac{g m (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{4 e^2}-\frac{d^2 f \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{2 e^2}+\frac{d g m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{2 e^2}+\frac{g i m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{2 e j}+\frac{d^2 g m \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \log \left(\frac{e (i+j x)}{e i-d j}\right)}{2 e^2}-\frac{g i^2 m \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \log \left(\frac{e (i+j x)}{e i-d j}\right)}{2 j^2}-\frac{d^2 g \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \log \left(h (i+j x)^m\right)}{2 e^2}+\frac{1}{2} x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \left(f+g \log \left(h (i+j x)^m\right)\right)",1,"(-6*a*b^2*d*f*n^2*x)/e + (12*a*b^2*d*g*m*n^2*x)/e + (21*a*b^2*g*i*m*n^2*x)/(4*j) + (6*b^3*d*f*n^3*x)/e - (141*b^3*d*g*m*n^3*x)/(8*e) - (45*b^3*g*i*m*n^3*x)/(8*j) + (3*b^3*g*m*n^3*x^2)/8 - (3*b^3*f*n^3*(d + e*x)^2)/(8*e^2) + (3*b^3*g*m*n^3*(d + e*x)^2)/(8*e^2) + (3*b^3*d^2*g*m*n^3*Log[d + e*x])/(8*e^2) - (6*b^3*d*f*n^2*(d + e*x)*Log[c*(d + e*x)^n])/e^2 + (12*b^3*d*g*m*n^2*(d + e*x)*Log[c*(d + e*x)^n])/e^2 + (21*b^3*g*i*m*n^2*(d + e*x)*Log[c*(d + e*x)^n])/(4*e*j) - (3*b^2*g*m*n^2*x^2*(a + b*Log[c*(d + e*x)^n]))/8 + (3*b^2*f*n^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(4*e^2) - (3*b^2*g*m*n^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(4*e^2) + (3*b*d*f*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e^2 - (15*b*d*g*m*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(4*e^2) - (9*b*g*i*m*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(4*e*j) - (3*b*f*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(4*e^2) + (3*b*g*m*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(4*e^2) - (d^2*f*(a + b*Log[c*(d + e*x)^n])^3)/(2*e^2) + (d*g*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/(2*e^2) + (g*i*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/(2*e*j) - (g*m*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^3)/(4*e^2) + (3*b^3*g*i^2*m*n^3*Log[i + j*x])/(8*j^2) - (3*b^2*g*i^2*m*n^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(4*j^2) - (9*b^2*d*g*i*m*n^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(2*e*j) - (9*b*d^2*g*m*n*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/(4*e^2) + (3*b*g*i^2*m*n*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/(4*j^2) + (3*b*d*g*i*m*n*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/(2*e*j) + (d^2*g*m*(a + b*Log[c*(d + e*x)^n])^3*Log[(e*(i + j*x))/(e*i - d*j)])/(2*e^2) - (g*i^2*m*(a + b*Log[c*(d + e*x)^n])^3*Log[(e*(i + j*x))/(e*i - d*j)])/(2*j^2) - (3*b^3*g*n^3*x^2*Log[h*(i + j*x)^m])/8 + (21*b^3*d*g*n^3*(i + j*x)*Log[h*(i + j*x)^m])/(4*e*j) - (21*b^3*d^2*g*n^3*Log[-((j*(d + e*x))/(e*i - d*j))]*Log[h*(i + j*x)^m])/(4*e^2) - (9*b^2*d*g*n^2*x*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m])/(2*e) + (3*b^2*g*n^2*x^2*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m])/4 + (9*b*d^2*g*n*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m])/(4*e^2) + (3*b*d*g*n*x*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m])/(2*e) - (3*b*g*n*x^2*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m])/4 - (d^2*g*(a + b*Log[c*(d + e*x)^n])^3*Log[h*(i + j*x)^m])/(2*e^2) + (x^2*(a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]))/2 - (3*b^3*g*i^2*m*n^3*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(4*j^2) - (9*b^3*d*g*i*m*n^3*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(2*e*j) - (9*b^2*d^2*g*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(2*e^2) + (3*b^2*g*i^2*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(2*j^2) + (3*b^2*d*g*i*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(e*j) + (3*b*d^2*g*m*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(2*e^2) - (3*b*g*i^2*m*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(2*j^2) - (21*b^3*d^2*g*m*n^3*PolyLog[2, (e*(i + j*x))/(e*i - d*j)])/(4*e^2) + (9*b^3*d^2*g*m*n^3*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/(2*e^2) - (3*b^3*g*i^2*m*n^3*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/(2*j^2) - (3*b^3*d*g*i*m*n^3*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/(e*j) - (3*b^2*d^2*g*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/e^2 + (3*b^2*g*i^2*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/j^2 + (3*b^3*d^2*g*m*n^3*PolyLog[4, -((j*(d + e*x))/(e*i - d*j))])/e^2 - (3*b^3*g*i^2*m*n^3*PolyLog[4, -((j*(d + e*x))/(e*i - d*j))])/j^2","A",148,32,32,1.000,1,"{2439, 2416, 2389, 2296, 2295, 2401, 2390, 2305, 2304, 2396, 2433, 2374, 2383, 6589, 6742, 2411, 2346, 2302, 30, 2330, 2430, 2301, 43, 2394, 2393, 2391, 2375, 2317, 2334, 12, 14, 2395}"
398,1,1147,0,3.1229464,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \left(f+g \log \left(h (i+j x)^m\right)\right) \, dx","Int[(a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]),x]","-6 f n^3 x b^3+24 g m n^3 x b^3+\frac{6 f n^2 (d+e x) \log \left(c (d+e x)^n\right) b^3}{e}-\frac{18 g m n^2 (d+e x) \log \left(c (d+e x)^n\right) b^3}{e}-\frac{6 g n^3 (i+j x) \log \left(h (i+j x)^m\right) b^3}{j}+\frac{6 d g n^3 \log \left(-\frac{j (d+e x)}{e i-d j}\right) \log \left(h (i+j x)^m\right) b^3}{e}+\frac{6 g i m n^3 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^3}{j}+\frac{6 d g m n^3 \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right) b^3}{e}-\frac{6 d g m n^3 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^3}{e}+\frac{6 g i m n^3 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^3}{j}-\frac{6 d g m n^3 \text{PolyLog}\left(4,-\frac{j (d+e x)}{e i-d j}\right) b^3}{e}+\frac{6 g i m n^3 \text{PolyLog}\left(4,-\frac{j (d+e x)}{e i-d j}\right) b^3}{j}+6 a f n^2 x b^2-18 a g m n^2 x b^2+\frac{6 g i m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e (i+j x)}{e i-d j}\right) b^2}{j}+6 g n^2 x \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(h (i+j x)^m\right) b^2+\frac{6 d g m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^2}{e}-\frac{6 g i m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^2}{j}+\frac{6 d g m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^2}{e}-\frac{6 g i m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^2}{j}-\frac{3 f n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 b}{e}+\frac{6 g m n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 b}{e}+\frac{3 d g m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e (i+j x)}{e i-d j}\right) b}{e}-\frac{3 g i m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e (i+j x)}{e i-d j}\right) b}{j}-\frac{3 d g n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(h (i+j x)^m\right) b}{e}-3 g n x \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(h (i+j x)^m\right) b-\frac{3 d g m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b}{e}+\frac{3 g i m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b}{j}+\frac{d f \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}-\frac{g m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}-\frac{d g m \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \log \left(\frac{e (i+j x)}{e i-d j}\right)}{e}+\frac{g i m \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \log \left(\frac{e (i+j x)}{e i-d j}\right)}{j}+\frac{d g \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \log \left(h (i+j x)^m\right)}{e}+x \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \left(f+g \log \left(h (i+j x)^m\right)\right)","-6 f n^3 x b^3+24 g m n^3 x b^3+\frac{6 f n^2 (d+e x) \log \left(c (d+e x)^n\right) b^3}{e}-\frac{18 g m n^2 (d+e x) \log \left(c (d+e x)^n\right) b^3}{e}-\frac{6 g n^3 (i+j x) \log \left(h (i+j x)^m\right) b^3}{j}+\frac{6 d g n^3 \log \left(-\frac{j (d+e x)}{e i-d j}\right) \log \left(h (i+j x)^m\right) b^3}{e}+\frac{6 g i m n^3 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^3}{j}+\frac{6 d g m n^3 \text{PolyLog}\left(2,\frac{e (i+j x)}{e i-d j}\right) b^3}{e}-\frac{6 d g m n^3 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^3}{e}+\frac{6 g i m n^3 \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^3}{j}-\frac{6 d g m n^3 \text{PolyLog}\left(4,-\frac{j (d+e x)}{e i-d j}\right) b^3}{e}+\frac{6 g i m n^3 \text{PolyLog}\left(4,-\frac{j (d+e x)}{e i-d j}\right) b^3}{j}+6 a f n^2 x b^2-18 a g m n^2 x b^2+\frac{6 g i m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e (i+j x)}{e i-d j}\right) b^2}{j}+6 g n^2 x \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(h (i+j x)^m\right) b^2+\frac{6 d g m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^2}{e}-\frac{6 g i m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b^2}{j}+\frac{6 d g m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^2}{e}-\frac{6 g i m n^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \text{PolyLog}\left(3,-\frac{j (d+e x)}{e i-d j}\right) b^2}{j}-\frac{3 f n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 b}{e}+\frac{6 g m n (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 b}{e}+\frac{3 d g m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e (i+j x)}{e i-d j}\right) b}{e}-\frac{3 g i m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(\frac{e (i+j x)}{e i-d j}\right) b}{j}-\frac{3 d g n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(h (i+j x)^m\right) b}{e}-3 g n x \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(h (i+j x)^m\right) b-\frac{3 d g m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b}{e}+\frac{3 g i m n \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{j (d+e x)}{e i-d j}\right) b}{j}+\frac{d f \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}-\frac{g m (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{e}-\frac{d g m \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \log \left(\frac{e (i+j x)}{e i-d j}\right)}{e}+\frac{g i m \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \log \left(\frac{e (i+j x)}{e i-d j}\right)}{j}+\frac{d g \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \log \left(h (i+j x)^m\right)}{e}+x \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \left(f+g \log \left(h (i+j x)^m\right)\right)",1,"6*a*b^2*f*n^2*x - 18*a*b^2*g*m*n^2*x - 6*b^3*f*n^3*x + 24*b^3*g*m*n^3*x + (6*b^3*f*n^2*(d + e*x)*Log[c*(d + e*x)^n])/e - (18*b^3*g*m*n^2*(d + e*x)*Log[c*(d + e*x)^n])/e - (3*b*f*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e + (6*b*g*m*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e + (d*f*(a + b*Log[c*(d + e*x)^n])^3)/e - (g*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/e + (6*b^2*g*i*m*n^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/j + (3*b*d*g*m*n*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/e - (3*b*g*i*m*n*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/j - (d*g*m*(a + b*Log[c*(d + e*x)^n])^3*Log[(e*(i + j*x))/(e*i - d*j)])/e + (g*i*m*(a + b*Log[c*(d + e*x)^n])^3*Log[(e*(i + j*x))/(e*i - d*j)])/j - (6*b^3*g*n^3*(i + j*x)*Log[h*(i + j*x)^m])/j + (6*b^3*d*g*n^3*Log[-((j*(d + e*x))/(e*i - d*j))]*Log[h*(i + j*x)^m])/e + 6*b^2*g*n^2*x*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m] - (3*b*d*g*n*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m])/e - 3*b*g*n*x*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m] + (d*g*(a + b*Log[c*(d + e*x)^n])^3*Log[h*(i + j*x)^m])/e + x*(a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]) + (6*b^3*g*i*m*n^3*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/j + (6*b^2*d*g*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/e - (6*b^2*g*i*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/j - (3*b*d*g*m*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/e + (3*b*g*i*m*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/j + (6*b^3*d*g*m*n^3*PolyLog[2, (e*(i + j*x))/(e*i - d*j)])/e - (6*b^3*d*g*m*n^3*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/e + (6*b^3*g*i*m*n^3*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/j + (6*b^2*d*g*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/e - (6*b^2*g*i*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/j - (6*b^3*d*g*m*n^3*PolyLog[4, -((j*(d + e*x))/(e*i - d*j))])/e + (6*b^3*g*i*m*n^3*PolyLog[4, -((j*(d + e*x))/(e*i - d*j))])/j","A",64,22,31,0.7097,1,"{2430, 2416, 2389, 2296, 2295, 2396, 2433, 2374, 2383, 6589, 6742, 2411, 2346, 2302, 30, 2301, 43, 2394, 2393, 2391, 2375, 2317}"
399,0,0,0,0.0396653,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3 \left(f+g \log \left(h (i+j x)^m\right)\right)}{x} \, dx","Int[((a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]))/x,x]","\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3 \left(f+g \log \left(h (i+j x)^m\right)\right)}{x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3 \left(f+g \log \left(h (i+j x)^m\right)\right)}{x},x\right)",0,"Defer[Int][((a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]))/x, x]","A",0,0,0,0,-1,"{}"
400,0,0,0,0.0411003,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3 \left(f+g \log \left(h (i+j x)^m\right)\right)}{x^2} \, dx","Int[((a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]))/x^2,x]","\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3 \left(f+g \log \left(h (i+j x)^m\right)\right)}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3 \left(f+g \log \left(h (i+j x)^m\right)\right)}{x^2},x\right)",0,"Defer[Int][((a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]))/x^2, x]","A",0,0,0,0,-1,"{}"
401,1,66,0,0.083694,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\frac{e (f+g x)}{e f-d g}\right)}{d+e x} \, dx","Int[((a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)])/(d + e*x),x]","\frac{b n \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{e}-\frac{\text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e}","\frac{b n \text{PolyLog}\left(3,-\frac{g (d+e x)}{e f-d g}\right)}{e}-\frac{\text{PolyLog}\left(2,-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e}",1,"-(((a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((g*(d + e*x))/(e*f - d*g))])/e) + (b*n*PolyLog[3, -((g*(d + e*x))/(e*f - d*g))])/e","A",3,3,40,0.07500,1,"{2433, 2374, 6589}"
402,1,92,0,0.0945195,"\int \frac{\log (c (d+e x)) (a+b \log (c (d+e x)))}{(d+e x)^2} \, dx","Int[(Log[c*(d + e*x)]*(a + b*Log[c*(d + e*x)]))/(d + e*x)^2,x]","-\frac{\log (c (d+e x)) (a+b \log (c (d+e x)))}{e (d+e x)}-\frac{a+b \log (c (d+e x))+b}{e (d+e x)}-\frac{b \log (c (d+e x))}{e (d+e x)}-\frac{b}{e (d+e x)}","-\frac{\log (c (d+e x)) (a+b \log (c (d+e x)))}{e (d+e x)}-\frac{a+b \log (c (d+e x))+b}{e (d+e x)}-\frac{b \log (c (d+e x))}{e (d+e x)}-\frac{b}{e (d+e x)}",1,"-(b/(e*(d + e*x))) - (b*Log[c*(d + e*x)])/(e*(d + e*x)) - (Log[c*(d + e*x)]*(a + b*Log[c*(d + e*x)]))/(e*(d + e*x)) - (a + b + b*Log[c*(d + e*x)])/(e*(d + e*x))","A",4,4,28,0.1429,1,"{2369, 12, 2304, 2366}"
403,1,102,0,0.1108583,"\int \frac{(a+b \log (c (d+e x))) (f+g \log (c (d+e x)))}{(d+e x)^2} \, dx","Int[((a + b*Log[c*(d + e*x)])*(f + g*Log[c*(d + e*x)]))/(d + e*x)^2,x]","-\frac{(a+b \log (c (d+e x))) (g \log (c (d+e x))+f)}{e (d+e x)}-\frac{g (a+b \log (c (d+e x))+b)}{e (d+e x)}-\frac{b (g \log (c (d+e x))+f)}{e (d+e x)}-\frac{b g}{e (d+e x)}","-\frac{(a+b \log (c (d+e x))) (g \log (c (d+e x))+f)}{e (d+e x)}-\frac{g (a+b \log (c (d+e x))+b)}{e (d+e x)}-\frac{b (g \log (c (d+e x))+f)}{e (d+e x)}-\frac{b g}{e (d+e x)}",1,"-((b*g)/(e*(d + e*x))) - (g*(a + b + b*Log[c*(d + e*x)]))/(e*(d + e*x)) - (b*(f + g*Log[c*(d + e*x)]))/(e*(d + e*x)) - ((a + b*Log[c*(d + e*x)])*(f + g*Log[c*(d + e*x)]))/(e*(d + e*x))","A",4,4,32,0.1250,1,"{2369, 12, 2304, 2366}"
404,1,160,0,0.2008172,"\int \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^4 \, dx","Int[(a + b*Log[c*(d*(e + f*x)^m)^n])^4,x]","\frac{12 b^2 m^2 n^2 (e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^2}{f}-24 a b^3 m^3 n^3 x-\frac{4 b m n (e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^3}{f}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^4}{f}-\frac{24 b^4 m^3 n^3 (e+f x) \log \left(c \left(d (e+f x)^m\right)^n\right)}{f}+24 b^4 m^4 n^4 x","\frac{12 b^2 m^2 n^2 (e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^2}{f}-24 a b^3 m^3 n^3 x-\frac{4 b m n (e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^3}{f}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^4}{f}-\frac{24 b^4 m^3 n^3 (e+f x) \log \left(c \left(d (e+f x)^m\right)^n\right)}{f}+24 b^4 m^4 n^4 x",1,"-24*a*b^3*m^3*n^3*x + 24*b^4*m^4*n^4*x - (24*b^4*m^3*n^3*(e + f*x)*Log[c*(d*(e + f*x)^m)^n])/f + (12*b^2*m^2*n^2*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^m)^n])^2)/f - (4*b*m*n*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^m)^n])^3)/f + ((e + f*x)*(a + b*Log[c*(d*(e + f*x)^m)^n])^4)/f","A",7,4,20,0.2000,1,"{2389, 2296, 2295, 2445}"
405,1,121,0,0.1406378,"\int \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^3 \, dx","Int[(a + b*Log[c*(d*(e + f*x)^m)^n])^3,x]","6 a b^2 m^2 n^2 x-\frac{3 b m n (e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^2}{f}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^3}{f}+\frac{6 b^3 m^2 n^2 (e+f x) \log \left(c \left(d (e+f x)^m\right)^n\right)}{f}-6 b^3 m^3 n^3 x","6 a b^2 m^2 n^2 x-\frac{3 b m n (e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^2}{f}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^3}{f}+\frac{6 b^3 m^2 n^2 (e+f x) \log \left(c \left(d (e+f x)^m\right)^n\right)}{f}-6 b^3 m^3 n^3 x",1,"6*a*b^2*m^2*n^2*x - 6*b^3*m^3*n^3*x + (6*b^3*m^2*n^2*(e + f*x)*Log[c*(d*(e + f*x)^m)^n])/f - (3*b*m*n*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^m)^n])^2)/f + ((e + f*x)*(a + b*Log[c*(d*(e + f*x)^m)^n])^3)/f","A",6,4,20,0.2000,1,"{2389, 2296, 2295, 2445}"
406,1,78,0,0.0944507,"\int \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^2 \, dx","Int[(a + b*Log[c*(d*(e + f*x)^m)^n])^2,x]","\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^2}{f}-2 a b m n x-\frac{2 b^2 m n (e+f x) \log \left(c \left(d (e+f x)^m\right)^n\right)}{f}+2 b^2 m^2 n^2 x","\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^2}{f}-2 a b m n x-\frac{2 b^2 m n (e+f x) \log \left(c \left(d (e+f x)^m\right)^n\right)}{f}+2 b^2 m^2 n^2 x",1,"-2*a*b*m*n*x + 2*b^2*m^2*n^2*x - (2*b^2*m*n*(e + f*x)*Log[c*(d*(e + f*x)^m)^n])/f + ((e + f*x)*(a + b*Log[c*(d*(e + f*x)^m)^n])^2)/f","A",5,4,20,0.2000,1,"{2389, 2296, 2295, 2445}"
407,1,34,0,0.0315224,"\int \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right) \, dx","Int[a + b*Log[c*(d*(e + f*x)^m)^n],x]","a x+\frac{b (e+f x) \log \left(c \left(d (e+f x)^m\right)^n\right)}{f}-b m n x","a x+\frac{b (e+f x) \log \left(c \left(d (e+f x)^m\right)^n\right)}{f}-b m n x",1,"a*x - b*m*n*x + (b*(e + f*x)*Log[c*(d*(e + f*x)^m)^n])/f","A",4,3,18,0.1667,1,"{2389, 2295, 2445}"
408,1,83,0,0.1315985,"\int \frac{1}{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^m)^n])^(-1),x]","\frac{(e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}\right)}{b f m n}","\frac{(e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}\right)}{b f m n}",1,"((e + f*x)*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^m)^n])/(b*m*n)])/(b*E^(a/(b*m*n))*f*m*n*(c*(d*(e + f*x)^m)^n)^(1/(m*n)))","A",4,4,20,0.2000,1,"{2389, 2300, 2178, 2445}"
409,1,123,0,0.1675331,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^2} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^m)^n])^(-2),x]","\frac{(e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}\right)}{b^2 f m^2 n^2}-\frac{e+f x}{b f m n \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)}","\frac{(e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}\right)}{b^2 f m^2 n^2}-\frac{e+f x}{b f m n \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)}",1,"((e + f*x)*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^m)^n])/(b*m*n)])/(b^2*E^(a/(b*m*n))*f*m^2*n^2*(c*(d*(e + f*x)^m)^n)^(1/(m*n))) - (e + f*x)/(b*f*m*n*(a + b*Log[c*(d*(e + f*x)^m)^n]))","A",5,5,20,0.2500,1,"{2389, 2297, 2300, 2178, 2445}"
410,1,169,0,0.2227231,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^3} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^m)^n])^(-3),x]","\frac{(e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}\right)}{2 b^3 f m^3 n^3}-\frac{e+f x}{2 b^2 f m^2 n^2 \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)}-\frac{e+f x}{2 b f m n \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^2}","\frac{(e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}\right)}{2 b^3 f m^3 n^3}-\frac{e+f x}{2 b^2 f m^2 n^2 \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)}-\frac{e+f x}{2 b f m n \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^2}",1,"((e + f*x)*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^m)^n])/(b*m*n)])/(2*b^3*E^(a/(b*m*n))*f*m^3*n^3*(c*(d*(e + f*x)^m)^n)^(1/(m*n))) - (e + f*x)/(2*b*f*m*n*(a + b*Log[c*(d*(e + f*x)^m)^n])^2) - (e + f*x)/(2*b^2*f*m^2*n^2*(a + b*Log[c*(d*(e + f*x)^m)^n]))","A",6,5,20,0.2500,1,"{2389, 2297, 2300, 2178, 2445}"
411,1,219,0,0.3676999,"\int \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{5/2} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^m)^n])^(5/2),x]","-\frac{15 \sqrt{\pi } b^{5/2} m^{5/2} n^{5/2} (e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{\sqrt{b} \sqrt{m} \sqrt{n}}\right)}{8 f}+\frac{15 b^2 m^2 n^2 (e+f x) \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{4 f}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{5/2}}{f}-\frac{5 b m n (e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{3/2}}{2 f}","-\frac{15 \sqrt{\pi } b^{5/2} m^{5/2} n^{5/2} (e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{\sqrt{b} \sqrt{m} \sqrt{n}}\right)}{8 f}+\frac{15 b^2 m^2 n^2 (e+f x) \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{4 f}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{5/2}}{f}-\frac{5 b m n (e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{3/2}}{2 f}",1,"(-15*b^(5/2)*m^(5/2)*n^(5/2)*Sqrt[Pi]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]]/(Sqrt[b]*Sqrt[m]*Sqrt[n])])/(8*E^(a/(b*m*n))*f*(c*(d*(e + f*x)^m)^n)^(1/(m*n))) + (15*b^2*m^2*n^2*(e + f*x)*Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]])/(4*f) - (5*b*m*n*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^m)^n])^(3/2))/(2*f) + ((e + f*x)*(a + b*Log[c*(d*(e + f*x)^m)^n])^(5/2))/f","A",8,6,22,0.2727,1,"{2389, 2296, 2300, 2180, 2204, 2445}"
412,1,176,0,0.2758945,"\int \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{3/2} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^m)^n])^(3/2),x]","\frac{3 \sqrt{\pi } b^{3/2} m^{3/2} n^{3/2} (e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{\sqrt{b} \sqrt{m} \sqrt{n}}\right)}{4 f}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{3/2}}{f}-\frac{3 b m n (e+f x) \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{2 f}","\frac{3 \sqrt{\pi } b^{3/2} m^{3/2} n^{3/2} (e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{\sqrt{b} \sqrt{m} \sqrt{n}}\right)}{4 f}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{3/2}}{f}-\frac{3 b m n (e+f x) \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{2 f}",1,"(3*b^(3/2)*m^(3/2)*n^(3/2)*Sqrt[Pi]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]]/(Sqrt[b]*Sqrt[m]*Sqrt[n])])/(4*E^(a/(b*m*n))*f*(c*(d*(e + f*x)^m)^n)^(1/(m*n))) - (3*b*m*n*(e + f*x)*Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]])/(2*f) + ((e + f*x)*(a + b*Log[c*(d*(e + f*x)^m)^n])^(3/2))/f","A",7,6,22,0.2727,1,"{2389, 2296, 2300, 2180, 2204, 2445}"
413,1,139,0,0.2195058,"\int \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)} \, dx","Int[Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]],x]","\frac{(e+f x) \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{f}-\frac{\sqrt{\pi } \sqrt{b} \sqrt{m} \sqrt{n} (e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{\sqrt{b} \sqrt{m} \sqrt{n}}\right)}{2 f}","\frac{(e+f x) \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{f}-\frac{\sqrt{\pi } \sqrt{b} \sqrt{m} \sqrt{n} (e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{\sqrt{b} \sqrt{m} \sqrt{n}}\right)}{2 f}",1,"-(Sqrt[b]*Sqrt[m]*Sqrt[n]*Sqrt[Pi]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]]/(Sqrt[b]*Sqrt[m]*Sqrt[n])])/(2*E^(a/(b*m*n))*f*(c*(d*(e + f*x)^m)^n)^(1/(m*n))) + ((e + f*x)*Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]])/f","A",6,6,22,0.2727,1,"{2389, 2296, 2300, 2180, 2204, 2445}"
414,1,104,0,0.1823531,"\int \frac{1}{\sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}} \, dx","Int[1/Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]],x]","\frac{\sqrt{\pi } (e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{\sqrt{b} \sqrt{m} \sqrt{n}}\right)}{\sqrt{b} f \sqrt{m} \sqrt{n}}","\frac{\sqrt{\pi } (e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{\sqrt{b} \sqrt{m} \sqrt{n}}\right)}{\sqrt{b} f \sqrt{m} \sqrt{n}}",1,"(Sqrt[Pi]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]]/(Sqrt[b]*Sqrt[m]*Sqrt[n])])/(Sqrt[b]*E^(a/(b*m*n))*f*Sqrt[m]*Sqrt[n]*(c*(d*(e + f*x)^m)^n)^(1/(m*n)))","A",5,5,22,0.2273,1,"{2389, 2300, 2180, 2204, 2445}"
415,1,147,0,0.2455908,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{3/2}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^m)^n])^(-3/2),x]","\frac{2 \sqrt{\pi } (e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{\sqrt{b} \sqrt{m} \sqrt{n}}\right)}{b^{3/2} f m^{3/2} n^{3/2}}-\frac{2 (e+f x)}{b f m n \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}","\frac{2 \sqrt{\pi } (e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{\sqrt{b} \sqrt{m} \sqrt{n}}\right)}{b^{3/2} f m^{3/2} n^{3/2}}-\frac{2 (e+f x)}{b f m n \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}",1,"(2*Sqrt[Pi]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]]/(Sqrt[b]*Sqrt[m]*Sqrt[n])])/(b^(3/2)*E^(a/(b*m*n))*f*m^(3/2)*n^(3/2)*(c*(d*(e + f*x)^m)^n)^(1/(m*n))) - (2*(e + f*x))/(b*f*m*n*Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]])","A",6,6,22,0.2727,1,"{2389, 2297, 2300, 2180, 2204, 2445}"
416,1,194,0,0.3124276,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{5/2}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^m)^n])^(-5/2),x]","\frac{4 \sqrt{\pi } (e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{\sqrt{b} \sqrt{m} \sqrt{n}}\right)}{3 b^{5/2} f m^{5/2} n^{5/2}}-\frac{4 (e+f x)}{3 b^2 f m^2 n^2 \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}-\frac{2 (e+f x)}{3 b f m n \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{3/2}}","\frac{4 \sqrt{\pi } (e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{\sqrt{b} \sqrt{m} \sqrt{n}}\right)}{3 b^{5/2} f m^{5/2} n^{5/2}}-\frac{4 (e+f x)}{3 b^2 f m^2 n^2 \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}-\frac{2 (e+f x)}{3 b f m n \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{3/2}}",1,"(4*Sqrt[Pi]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]]/(Sqrt[b]*Sqrt[m]*Sqrt[n])])/(3*b^(5/2)*E^(a/(b*m*n))*f*m^(5/2)*n^(5/2)*(c*(d*(e + f*x)^m)^n)^(1/(m*n))) - (2*(e + f*x))/(3*b*f*m*n*(a + b*Log[c*(d*(e + f*x)^m)^n])^(3/2)) - (4*(e + f*x))/(3*b^2*f*m^2*n^2*Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]])","A",7,6,22,0.2727,1,"{2389, 2297, 2300, 2180, 2204, 2445}"
417,1,237,0,0.3846232,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{7/2}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^m)^n])^(-7/2),x]","\frac{8 \sqrt{\pi } (e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{\sqrt{b} \sqrt{m} \sqrt{n}}\right)}{15 b^{7/2} f m^{7/2} n^{7/2}}-\frac{8 (e+f x)}{15 b^3 f m^3 n^3 \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}-\frac{4 (e+f x)}{15 b^2 f m^2 n^2 \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{3/2}}-\frac{2 (e+f x)}{5 b f m n \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{5/2}}","\frac{8 \sqrt{\pi } (e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}{\sqrt{b} \sqrt{m} \sqrt{n}}\right)}{15 b^{7/2} f m^{7/2} n^{7/2}}-\frac{8 (e+f x)}{15 b^3 f m^3 n^3 \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}}-\frac{4 (e+f x)}{15 b^2 f m^2 n^2 \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{3/2}}-\frac{2 (e+f x)}{5 b f m n \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{5/2}}",1,"(8*Sqrt[Pi]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]]/(Sqrt[b]*Sqrt[m]*Sqrt[n])])/(15*b^(7/2)*E^(a/(b*m*n))*f*m^(7/2)*n^(7/2)*(c*(d*(e + f*x)^m)^n)^(1/(m*n))) - (2*(e + f*x))/(5*b*f*m*n*(a + b*Log[c*(d*(e + f*x)^m)^n])^(5/2)) - (4*(e + f*x))/(15*b^2*f*m^2*n^2*(a + b*Log[c*(d*(e + f*x)^m)^n])^(3/2)) - (8*(e + f*x))/(15*b^3*f*m^3*n^3*Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]])","A",8,6,22,0.2727,1,"{2389, 2297, 2300, 2180, 2204, 2445}"
418,1,131,0,0.1469501,"\int \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^p \, dx","Int[(a + b*Log[c*(d*(e + f*x)^m)^n])^p,x]","\frac{(e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^p \left(-\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}\right)}{f}","\frac{(e+f x) e^{-\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{-\frac{1}{m n}} \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^p \left(-\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}\right)}{f}",1,"((e + f*x)*Gamma[1 + p, -((a + b*Log[c*(d*(e + f*x)^m)^n])/(b*m*n))]*(a + b*Log[c*(d*(e + f*x)^m)^n])^p)/(E^(a/(b*m*n))*f*(c*(d*(e + f*x)^m)^n)^(1/(m*n))*(-((a + b*Log[c*(d*(e + f*x)^m)^n])/(b*m*n)))^p)","A",4,4,20,0.2000,1,"{2389, 2300, 2181, 2445}"
419,1,109,0,0.1386491,"\int \left(a+b \log \left(c \sqrt{d \sqrt{e+f x}}\right)\right)^p \, dx","Int[(a + b*Log[c*Sqrt[d*Sqrt[e + f*x]]])^p,x]","\frac{4^{-p} e^{-\frac{4 a}{b}} \left(a+b \log \left(c \sqrt{d \sqrt{e+f x}}\right)\right)^p \left(-\frac{a+b \log \left(c \sqrt{d \sqrt{e+f x}}\right)}{b}\right)^{-p} \text{Gamma}\left(p+1,-\frac{4 \left(a+b \log \left(c \sqrt{d \sqrt{e+f x}}\right)\right)}{b}\right)}{c^4 d^2 f}","\frac{4^{-p} e^{-\frac{4 a}{b}} \left(a+b \log \left(c \sqrt{d \sqrt{e+f x}}\right)\right)^p \left(-\frac{a+b \log \left(c \sqrt{d \sqrt{e+f x}}\right)}{b}\right)^{-p} \text{Gamma}\left(p+1,-\frac{4 \left(a+b \log \left(c \sqrt{d \sqrt{e+f x}}\right)\right)}{b}\right)}{c^4 d^2 f}",1,"(Gamma[1 + p, (-4*(a + b*Log[c*Sqrt[d*Sqrt[e + f*x]]]))/b]*(a + b*Log[c*Sqrt[d*Sqrt[e + f*x]]])^p)/(4^p*c^4*d^2*E^((4*a)/b)*f*(-((a + b*Log[c*Sqrt[d*Sqrt[e + f*x]]])/b))^p)","A",4,4,24,0.1667,1,"{2389, 2299, 2181, 2445}"
420,1,158,0,0.1636419,"\int (g+h x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \, dx","Int[(g + h*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\frac{(g+h x)^4 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{4 h}-\frac{b p q x (f g-e h)^3}{4 f^3}-\frac{b p q (g+h x)^2 (f g-e h)^2}{8 f^2 h}-\frac{b p q (f g-e h)^4 \log (e+f x)}{4 f^4 h}-\frac{b p q (g+h x)^3 (f g-e h)}{12 f h}-\frac{b p q (g+h x)^4}{16 h}","\frac{(g+h x)^4 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{4 h}-\frac{b p q x (f g-e h)^3}{4 f^3}-\frac{b p q (g+h x)^2 (f g-e h)^2}{8 f^2 h}-\frac{b p q (f g-e h)^4 \log (e+f x)}{4 f^4 h}-\frac{b p q (g+h x)^3 (f g-e h)}{12 f h}-\frac{b p q (g+h x)^4}{16 h}",1,"-(b*(f*g - e*h)^3*p*q*x)/(4*f^3) - (b*(f*g - e*h)^2*p*q*(g + h*x)^2)/(8*f^2*h) - (b*(f*g - e*h)*p*q*(g + h*x)^3)/(12*f*h) - (b*p*q*(g + h*x)^4)/(16*h) - (b*(f*g - e*h)^4*p*q*Log[e + f*x])/(4*f^4*h) + ((g + h*x)^4*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(4*h)","A",4,3,26,0.1154,1,"{2395, 43, 2445}"
421,1,128,0,0.1252214,"\int (g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \, dx","Int[(g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\frac{(g+h x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 h}-\frac{b p q x (f g-e h)^2}{3 f^2}-\frac{b p q (f g-e h)^3 \log (e+f x)}{3 f^3 h}-\frac{b p q (g+h x)^2 (f g-e h)}{6 f h}-\frac{b p q (g+h x)^3}{9 h}","\frac{(g+h x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 h}-\frac{b p q x (f g-e h)^2}{3 f^2}-\frac{b p q (f g-e h)^3 \log (e+f x)}{3 f^3 h}-\frac{b p q (g+h x)^2 (f g-e h)}{6 f h}-\frac{b p q (g+h x)^3}{9 h}",1,"-(b*(f*g - e*h)^2*p*q*x)/(3*f^2) - (b*(f*g - e*h)*p*q*(g + h*x)^2)/(6*f*h) - (b*p*q*(g + h*x)^3)/(9*h) - (b*(f*g - e*h)^3*p*q*Log[e + f*x])/(3*f^3*h) + ((g + h*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(3*h)","A",4,3,26,0.1154,1,"{2395, 43, 2445}"
422,1,98,0,0.0813518,"\int (g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \, dx","Int[(g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\frac{(g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 h}-\frac{b p q (f g-e h)^2 \log (e+f x)}{2 f^2 h}-\frac{b p q x (f g-e h)}{2 f}-\frac{b p q (g+h x)^2}{4 h}","\frac{(g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 h}-\frac{b p q (f g-e h)^2 \log (e+f x)}{2 f^2 h}-\frac{b p q x (f g-e h)}{2 f}-\frac{b p q (g+h x)^2}{4 h}",1,"-(b*(f*g - e*h)*p*q*x)/(2*f) - (b*p*q*(g + h*x)^2)/(4*h) - (b*(f*g - e*h)^2*p*q*Log[e + f*x])/(2*f^2*h) + ((g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(2*h)","A",4,3,24,0.1250,1,"{2395, 43, 2445}"
423,1,34,0,0.0294347,"\int \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \, dx","Int[a + b*Log[c*(d*(e + f*x)^p)^q],x]","a x+\frac{b (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f}-b p q x","a x+\frac{b (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f}-b p q x",1,"a*x - b*p*q*x + (b*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/f","A",4,3,18,0.1667,1,"{2389, 2295, 2445}"
424,1,68,0,0.1124867,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{g+h x} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x),x]","\frac{b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}","\frac{b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}",1,"((a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(g + h*x))/(f*g - e*h)])/h + (b*p*q*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/h","A",4,4,26,0.1538,1,"{2394, 2393, 2391, 2445}"
425,1,80,0,0.0762221,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x)^2} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x)^2,x]","-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{h (g+h x)}+\frac{b f p q \log (e+f x)}{h (f g-e h)}-\frac{b f p q \log (g+h x)}{h (f g-e h)}","-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{h (g+h x)}+\frac{b f p q \log (e+f x)}{h (f g-e h)}-\frac{b f p q \log (g+h x)}{h (f g-e h)}",1,"(b*f*p*q*Log[e + f*x])/(h*(f*g - e*h)) - (a + b*Log[c*(d*(e + f*x)^p)^q])/(h*(g + h*x)) - (b*f*p*q*Log[g + h*x])/(h*(f*g - e*h))","A",5,4,26,0.1538,1,"{2395, 36, 31, 2445}"
426,1,119,0,0.129398,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x)^3} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x)^3,x]","-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{2 h (g+h x)^2}+\frac{b f^2 p q \log (e+f x)}{2 h (f g-e h)^2}-\frac{b f^2 p q \log (g+h x)}{2 h (f g-e h)^2}+\frac{b f p q}{2 h (g+h x) (f g-e h)}","-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{2 h (g+h x)^2}+\frac{b f^2 p q \log (e+f x)}{2 h (f g-e h)^2}-\frac{b f^2 p q \log (g+h x)}{2 h (f g-e h)^2}+\frac{b f p q}{2 h (g+h x) (f g-e h)}",1,"(b*f*p*q)/(2*h*(f*g - e*h)*(g + h*x)) + (b*f^2*p*q*Log[e + f*x])/(2*h*(f*g - e*h)^2) - (a + b*Log[c*(d*(e + f*x)^p)^q])/(2*h*(g + h*x)^2) - (b*f^2*p*q*Log[g + h*x])/(2*h*(f*g - e*h)^2)","A",4,3,26,0.1154,1,"{2395, 44, 2445}"
427,1,149,0,0.1669194,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x)^4} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x)^4,x]","-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{3 h (g+h x)^3}+\frac{b f^2 p q}{3 h (g+h x) (f g-e h)^2}+\frac{b f^3 p q \log (e+f x)}{3 h (f g-e h)^3}-\frac{b f^3 p q \log (g+h x)}{3 h (f g-e h)^3}+\frac{b f p q}{6 h (g+h x)^2 (f g-e h)}","-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{3 h (g+h x)^3}+\frac{b f^2 p q}{3 h (g+h x) (f g-e h)^2}+\frac{b f^3 p q \log (e+f x)}{3 h (f g-e h)^3}-\frac{b f^3 p q \log (g+h x)}{3 h (f g-e h)^3}+\frac{b f p q}{6 h (g+h x)^2 (f g-e h)}",1,"(b*f*p*q)/(6*h*(f*g - e*h)*(g + h*x)^2) + (b*f^2*p*q)/(3*h*(f*g - e*h)^2*(g + h*x)) + (b*f^3*p*q*Log[e + f*x])/(3*h*(f*g - e*h)^3) - (a + b*Log[c*(d*(e + f*x)^p)^q])/(3*h*(g + h*x)^3) - (b*f^3*p*q*Log[g + h*x])/(3*h*(f*g - e*h)^3)","A",4,3,26,0.1154,1,"{2395, 44, 2445}"
428,1,325,0,1.0376919,"\int (g+h x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \, dx","Int[(g + h*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q])^2,x]","-\frac{b p q \left(\frac{36 h^2 (e+f x)^2 (f g-e h)^2}{f^4}+\frac{16 h^3 (e+f x)^3 (f g-e h)}{f^4}+\frac{48 h (e+f x) (f g-e h)^3}{f^4}+\frac{12 (f g-e h)^4 \log (e+f x)}{f^4}+\frac{3 h^4 (e+f x)^4}{f^4}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{24 h}+\frac{(g+h x)^4 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{4 h}+\frac{2 b^2 h^2 p^2 q^2 (e+f x)^3 (f g-e h)}{9 f^4}+\frac{2 b^2 p^2 q^2 x (f g-e h)^3}{f^3}+\frac{3 b^2 h p^2 q^2 (e+f x)^2 (f g-e h)^2}{4 f^4}+\frac{b^2 p^2 q^2 (f g-e h)^4 \log ^2(e+f x)}{4 f^4 h}+\frac{b^2 h^3 p^2 q^2 (e+f x)^4}{32 f^4}","-\frac{2 b h^2 p q (e+f x)^3 (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 f^4}-\frac{b p q (f g-e h)^4 \log (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 f^4 h}-\frac{2 b p q (e+f x) (f g-e h)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{f^4}-\frac{3 b h p q (e+f x)^2 (f g-e h)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 f^4}-\frac{b h^3 p q (e+f x)^4 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{8 f^4}+\frac{(g+h x)^4 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{4 h}+\frac{2 b^2 h^2 p^2 q^2 (e+f x)^3 (f g-e h)}{9 f^4}+\frac{2 b^2 p^2 q^2 x (f g-e h)^3}{f^3}+\frac{3 b^2 h p^2 q^2 (e+f x)^2 (f g-e h)^2}{4 f^4}+\frac{b^2 p^2 q^2 (f g-e h)^4 \log ^2(e+f x)}{4 f^4 h}+\frac{b^2 h^3 p^2 q^2 (e+f x)^4}{32 f^4}",1,"(2*b^2*(f*g - e*h)^3*p^2*q^2*x)/f^3 + (3*b^2*h*(f*g - e*h)^2*p^2*q^2*(e + f*x)^2)/(4*f^4) + (2*b^2*h^2*(f*g - e*h)*p^2*q^2*(e + f*x)^3)/(9*f^4) + (b^2*h^3*p^2*q^2*(e + f*x)^4)/(32*f^4) + (b^2*(f*g - e*h)^4*p^2*q^2*Log[e + f*x]^2)/(4*f^4*h) - (b*p*q*((48*h*(f*g - e*h)^3*(e + f*x))/f^4 + (36*h^2*(f*g - e*h)^2*(e + f*x)^2)/f^4 + (16*h^3*(f*g - e*h)*(e + f*x)^3)/f^4 + (3*h^4*(e + f*x)^4)/f^4 + (12*(f*g - e*h)^4*Log[e + f*x])/f^4)*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(24*h) + ((g + h*x)^4*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(4*h)","A",7,7,28,0.2500,1,"{2398, 2411, 43, 2334, 12, 2301, 2445}"
429,1,264,0,0.8345714,"\int (g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \, dx","Int[(g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2,x]","-\frac{b p q \left(\frac{9 h^2 (e+f x)^2 (f g-e h)}{f^3}+\frac{18 h (e+f x) (f g-e h)^2}{f^3}+\frac{6 (f g-e h)^3 \log (e+f x)}{f^3}+\frac{2 h^3 (e+f x)^3}{f^3}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{9 h}+\frac{(g+h x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{3 h}+\frac{2 b^2 p^2 q^2 x (f g-e h)^2}{f^2}+\frac{b^2 h p^2 q^2 (e+f x)^2 (f g-e h)}{2 f^3}+\frac{b^2 p^2 q^2 (f g-e h)^3 \log ^2(e+f x)}{3 f^3 h}+\frac{2 b^2 h^2 p^2 q^2 (e+f x)^3}{27 f^3}","-\frac{2 b p q (f g-e h)^3 \log (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 f^3 h}-\frac{2 b p q (e+f x) (f g-e h)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{f^3}-\frac{b h p q (e+f x)^2 (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{f^3}-\frac{2 b h^2 p q (e+f x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{9 f^3}+\frac{(g+h x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{3 h}+\frac{2 b^2 p^2 q^2 x (f g-e h)^2}{f^2}+\frac{b^2 h p^2 q^2 (e+f x)^2 (f g-e h)}{2 f^3}+\frac{b^2 p^2 q^2 (f g-e h)^3 \log ^2(e+f x)}{3 f^3 h}+\frac{2 b^2 h^2 p^2 q^2 (e+f x)^3}{27 f^3}",1,"(2*b^2*(f*g - e*h)^2*p^2*q^2*x)/f^2 + (b^2*h*(f*g - e*h)*p^2*q^2*(e + f*x)^2)/(2*f^3) + (2*b^2*h^2*p^2*q^2*(e + f*x)^3)/(27*f^3) + (b^2*(f*g - e*h)^3*p^2*q^2*Log[e + f*x]^2)/(3*f^3*h) - (b*p*q*((18*h*(f*g - e*h)^2*(e + f*x))/f^3 + (9*h^2*(f*g - e*h)*(e + f*x)^2)/f^3 + (2*h^3*(e + f*x)^3)/f^3 + (6*(f*g - e*h)^3*Log[e + f*x])/f^3)*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(9*h) + ((g + h*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(3*h)","A",9,8,28,0.2857,1,"{2398, 2411, 43, 2334, 12, 14, 2301, 2445}"
430,1,211,0,0.3893342,"\int (g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \, dx","Int[(g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2,x]","\frac{(e+f x) (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f^2}-\frac{b h p q (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 f^2}+\frac{h (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{2 f^2}-\frac{2 a b p q x (f g-e h)}{f}-\frac{2 b^2 p q (e+f x) (f g-e h) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f^2}+\frac{b^2 h p^2 q^2 (e+f x)^2}{4 f^2}+\frac{2 b^2 p^2 q^2 x (f g-e h)}{f}","\frac{(e+f x) (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f^2}-\frac{b h p q (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 f^2}+\frac{h (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{2 f^2}-\frac{2 a b p q x (f g-e h)}{f}-\frac{2 b^2 p q (e+f x) (f g-e h) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f^2}+\frac{b^2 h p^2 q^2 (e+f x)^2}{4 f^2}+\frac{2 b^2 p^2 q^2 x (f g-e h)}{f}",1,"(-2*a*b*(f*g - e*h)*p*q*x)/f + (2*b^2*(f*g - e*h)*p^2*q^2*x)/f + (b^2*h*p^2*q^2*(e + f*x)^2)/(4*f^2) - (2*b^2*(f*g - e*h)*p*q*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/f^2 - (b*h*p*q*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(2*f^2) + ((f*g - e*h)*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/f^2 + (h*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(2*f^2)","A",10,8,26,0.3077,1,"{2401, 2389, 2296, 2295, 2390, 2305, 2304, 2445}"
431,1,78,0,0.0963122,"\int \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^2,x]","\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f}-2 a b p q x-\frac{2 b^2 p q (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f}+2 b^2 p^2 q^2 x","\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f}-2 a b p q x-\frac{2 b^2 p q (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f}+2 b^2 p^2 q^2 x",1,"-2*a*b*p*q*x + 2*b^2*p^2*q^2*x - (2*b^2*p*q*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/f + ((e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/f","A",5,4,20,0.2000,1,"{2389, 2296, 2295, 2445}"
432,1,123,0,0.2650715,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{g+h x} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/(g + h*x),x]","\frac{2 b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}-\frac{2 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right)}{h}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h}","\frac{2 b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}-\frac{2 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right)}{h}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h}",1,"((a + b*Log[c*(d*(e + f*x)^p)^q])^2*Log[(f*(g + h*x))/(f*g - e*h)])/h + (2*b*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/h - (2*b^2*p^2*q^2*PolyLog[3, -((h*(e + f*x))/(f*g - e*h))])/h","A",5,5,28,0.1786,1,"{2396, 2433, 2374, 6589, 2445}"
433,1,144,0,0.2004085,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(g+h x)^2} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/(g + h*x)^2,x]","-\frac{2 b^2 f p^2 q^2 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h (f g-e h)}-\frac{2 b f p q \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h (f g-e h)}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(g+h x) (f g-e h)}","-\frac{2 b^2 f p^2 q^2 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h (f g-e h)}-\frac{2 b f p q \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h (f g-e h)}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(g+h x) (f g-e h)}",1,"((e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/((f*g - e*h)*(g + h*x)) - (2*b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(g + h*x))/(f*g - e*h)])/(h*(f*g - e*h)) - (2*b^2*f*p^2*q^2*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/(h*(f*g - e*h))","A",5,5,28,0.1786,1,"{2397, 2394, 2393, 2391, 2445}"
434,1,257,0,0.8168031,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(g+h x)^3} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/(g + h*x)^3,x]","-\frac{b^2 f^2 p^2 q^2 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h (f g-e h)^2}+\frac{f^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{2 h (f g-e h)^2}-\frac{b f^2 p q \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h (f g-e h)^2}-\frac{b f p q (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(g+h x) (f g-e h)^2}-\frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{2 h (g+h x)^2}+\frac{b^2 f^2 p^2 q^2 \log (g+h x)}{h (f g-e h)^2}","\frac{b^2 f^2 p^2 q^2 \text{PolyLog}\left(2,-\frac{f g-e h}{h (e+f x)}\right)}{h (f g-e h)^2}-\frac{b f^2 p q \log \left(\frac{f g-e h}{h (e+f x)}+1\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h (f g-e h)^2}-\frac{b f p q (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(g+h x) (f g-e h)^2}-\frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{2 h (g+h x)^2}+\frac{b^2 f^2 p^2 q^2 \log (g+h x)}{h (f g-e h)^2}",1,"-((b*f*p*q*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q]))/((f*g - e*h)^2*(g + h*x))) + (f^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(2*h*(f*g - e*h)^2) - (a + b*Log[c*(d*(e + f*x)^p)^q])^2/(2*h*(g + h*x)^2) + (b^2*f^2*p^2*q^2*Log[g + h*x])/(h*(f*g - e*h)^2) - (b*f^2*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(g + h*x))/(f*g - e*h)])/(h*(f*g - e*h)^2) - (b^2*f^2*p^2*q^2*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/(h*(f*g - e*h)^2)","A",10,10,28,0.3571,1,"{2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2445}"
435,1,492,0,0.9483404,"\int (g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3 \, dx","Int[(g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^3,x]","\frac{3 b^2 h p^2 q^2 (e+f x)^2 (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 f^3}+\frac{2 b^2 h^2 p^2 q^2 (e+f x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{9 f^3}+\frac{6 a b^2 p^2 q^2 x (f g-e h)^2}{f^2}-\frac{3 b h p q (e+f x)^2 (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{2 f^3}-\frac{3 b p q (e+f x) (f g-e h)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f^3}+\frac{h (e+f x)^2 (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{f^3}+\frac{(e+f x) (f g-e h)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{f^3}-\frac{b h^2 p q (e+f x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{3 f^3}+\frac{h^2 (e+f x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{3 f^3}+\frac{6 b^3 p^2 q^2 (e+f x) (f g-e h)^2 \log \left(c \left(d (e+f x)^p\right)^q\right)}{f^3}-\frac{3 b^3 h p^3 q^3 (e+f x)^2 (f g-e h)}{4 f^3}-\frac{6 b^3 p^3 q^3 x (f g-e h)^2}{f^2}-\frac{2 b^3 h^2 p^3 q^3 (e+f x)^3}{27 f^3}","\frac{3 b^2 h p^2 q^2 (e+f x)^2 (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 f^3}+\frac{2 b^2 h^2 p^2 q^2 (e+f x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{9 f^3}+\frac{6 a b^2 p^2 q^2 x (f g-e h)^2}{f^2}-\frac{3 b h p q (e+f x)^2 (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{2 f^3}-\frac{3 b p q (e+f x) (f g-e h)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f^3}+\frac{h (e+f x)^2 (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{f^3}+\frac{(e+f x) (f g-e h)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{f^3}-\frac{b h^2 p q (e+f x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{3 f^3}+\frac{h^2 (e+f x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{3 f^3}+\frac{6 b^3 p^2 q^2 (e+f x) (f g-e h)^2 \log \left(c \left(d (e+f x)^p\right)^q\right)}{f^3}-\frac{3 b^3 h p^3 q^3 (e+f x)^2 (f g-e h)}{4 f^3}-\frac{6 b^3 p^3 q^3 x (f g-e h)^2}{f^2}-\frac{2 b^3 h^2 p^3 q^3 (e+f x)^3}{27 f^3}",1,"(6*a*b^2*(f*g - e*h)^2*p^2*q^2*x)/f^2 - (6*b^3*(f*g - e*h)^2*p^3*q^3*x)/f^2 - (3*b^3*h*(f*g - e*h)*p^3*q^3*(e + f*x)^2)/(4*f^3) - (2*b^3*h^2*p^3*q^3*(e + f*x)^3)/(27*f^3) + (6*b^3*(f*g - e*h)^2*p^2*q^2*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/f^3 + (3*b^2*h*(f*g - e*h)*p^2*q^2*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(2*f^3) + (2*b^2*h^2*p^2*q^2*(e + f*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(9*f^3) - (3*b*(f*g - e*h)^2*p*q*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/f^3 - (3*b*h*(f*g - e*h)*p*q*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(2*f^3) - (b*h^2*p*q*(e + f*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(3*f^3) + ((f*g - e*h)^2*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/f^3 + (h*(f*g - e*h)*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/f^3 + (h^2*(e + f*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/(3*f^3)","A",16,8,28,0.2857,1,"{2401, 2389, 2296, 2295, 2390, 2305, 2304, 2445}"
436,1,306,0,0.534299,"\int (g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3 \, dx","Int[(g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3,x]","\frac{3 b^2 h p^2 q^2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{4 f^2}+\frac{6 a b^2 p^2 q^2 x (f g-e h)}{f}-\frac{3 b p q (e+f x) (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f^2}+\frac{(e+f x) (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{f^2}-\frac{3 b h p q (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{4 f^2}+\frac{h (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{2 f^2}+\frac{6 b^3 p^2 q^2 (e+f x) (f g-e h) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f^2}-\frac{3 b^3 h p^3 q^3 (e+f x)^2}{8 f^2}-\frac{6 b^3 p^3 q^3 x (f g-e h)}{f}","\frac{3 b^2 h p^2 q^2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{4 f^2}+\frac{6 a b^2 p^2 q^2 x (f g-e h)}{f}-\frac{3 b p q (e+f x) (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f^2}+\frac{(e+f x) (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{f^2}-\frac{3 b h p q (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{4 f^2}+\frac{h (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{2 f^2}+\frac{6 b^3 p^2 q^2 (e+f x) (f g-e h) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f^2}-\frac{3 b^3 h p^3 q^3 (e+f x)^2}{8 f^2}-\frac{6 b^3 p^3 q^3 x (f g-e h)}{f}",1,"(6*a*b^2*(f*g - e*h)*p^2*q^2*x)/f - (6*b^3*(f*g - e*h)*p^3*q^3*x)/f - (3*b^3*h*p^3*q^3*(e + f*x)^2)/(8*f^2) + (6*b^3*(f*g - e*h)*p^2*q^2*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/f^2 + (3*b^2*h*p^2*q^2*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(4*f^2) - (3*b*(f*g - e*h)*p*q*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/f^2 - (3*b*h*p*q*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(4*f^2) + ((f*g - e*h)*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/f^2 + (h*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/(2*f^2)","A",12,8,26,0.3077,1,"{2401, 2389, 2296, 2295, 2390, 2305, 2304, 2445}"
437,1,121,0,0.1414718,"\int \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3 \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^3,x]","6 a b^2 p^2 q^2 x-\frac{3 b p q (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{f}+\frac{6 b^3 p^2 q^2 (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f}-6 b^3 p^3 q^3 x","6 a b^2 p^2 q^2 x-\frac{3 b p q (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{f}+\frac{6 b^3 p^2 q^2 (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f}-6 b^3 p^3 q^3 x",1,"6*a*b^2*p^2*q^2*x - 6*b^3*p^3*q^3*x + (6*b^3*p^2*q^2*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/f - (3*b*p*q*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/f + ((e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/f","A",6,4,20,0.2000,1,"{2389, 2296, 2295, 2445}"
438,1,177,0,0.412099,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{g+h x} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^3/(g + h*x),x]","-\frac{6 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}+\frac{3 b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h}+\frac{6 b^3 p^3 q^3 \text{PolyLog}\left(4,-\frac{h (e+f x)}{f g-e h}\right)}{h}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{h}","-\frac{6 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}+\frac{3 b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h}+\frac{6 b^3 p^3 q^3 \text{PolyLog}\left(4,-\frac{h (e+f x)}{f g-e h}\right)}{h}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{h}",1,"((a + b*Log[c*(d*(e + f*x)^p)^q])^3*Log[(f*(g + h*x))/(f*g - e*h)])/h + (3*b*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/h - (6*b^2*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[3, -((h*(e + f*x))/(f*g - e*h))])/h + (6*b^3*p^3*q^3*PolyLog[4, -((h*(e + f*x))/(f*g - e*h))])/h","A",6,6,28,0.2143,1,"{2396, 2433, 2374, 2383, 6589, 2445}"
439,1,209,0,0.3656585,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{(g+h x)^2} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^3/(g + h*x)^2,x]","-\frac{6 b^2 f p^2 q^2 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h (f g-e h)}+\frac{6 b^3 f p^3 q^3 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right)}{h (f g-e h)}-\frac{3 b f p q \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h (f g-e h)}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{(g+h x) (f g-e h)}","-\frac{6 b^2 f p^2 q^2 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h (f g-e h)}+\frac{6 b^3 f p^3 q^3 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right)}{h (f g-e h)}-\frac{3 b f p q \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h (f g-e h)}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{(g+h x) (f g-e h)}",1,"((e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/((f*g - e*h)*(g + h*x)) - (3*b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*Log[(f*(g + h*x))/(f*g - e*h)])/(h*(f*g - e*h)) - (6*b^2*f*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/(h*(f*g - e*h)) + (6*b^3*f*p^3*q^3*PolyLog[3, -((h*(e + f*x))/(f*g - e*h))])/(h*(f*g - e*h))","A",6,6,28,0.2143,1,"{2397, 2396, 2433, 2374, 6589, 2445}"
440,1,408,0,1.3897224,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{(g+h x)^3} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^3/(g + h*x)^3,x]","-\frac{3 b^2 f^2 p^2 q^2 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h (f g-e h)^2}+\frac{3 b^3 f^2 p^3 q^3 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h (f g-e h)^2}+\frac{3 b^3 f^2 p^3 q^3 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right)}{h (f g-e h)^2}+\frac{3 b^2 f^2 p^2 q^2 \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h (f g-e h)^2}-\frac{3 b f^2 p q \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{2 h (f g-e h)^2}+\frac{f^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{2 h (f g-e h)^2}-\frac{3 b f p q (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{2 (g+h x) (f g-e h)^2}-\frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{2 h (g+h x)^2}","\frac{3 b^2 f^2 p^2 q^2 \text{PolyLog}\left(2,-\frac{f g-e h}{h (e+f x)}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h (f g-e h)^2}+\frac{3 b^3 f^2 p^3 q^3 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h (f g-e h)^2}+\frac{3 b^3 f^2 p^3 q^3 \text{PolyLog}\left(3,-\frac{f g-e h}{h (e+f x)}\right)}{h (f g-e h)^2}+\frac{3 b^2 f^2 p^2 q^2 \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h (f g-e h)^2}-\frac{3 b f^2 p q \log \left(\frac{f g-e h}{h (e+f x)}+1\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{2 h (f g-e h)^2}-\frac{3 b f p q (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{2 (g+h x) (f g-e h)^2}-\frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{2 h (g+h x)^2}",1,"(-3*b*f*p*q*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(2*(f*g - e*h)^2*(g + h*x)) + (f^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/(2*h*(f*g - e*h)^2) - (a + b*Log[c*(d*(e + f*x)^p)^q])^3/(2*h*(g + h*x)^2) + (3*b^2*f^2*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(g + h*x))/(f*g - e*h)])/(h*(f*g - e*h)^2) - (3*b*f^2*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*Log[(f*(g + h*x))/(f*g - e*h)])/(2*h*(f*g - e*h)^2) + (3*b^3*f^2*p^3*q^3*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/(h*(f*g - e*h)^2) - (3*b^2*f^2*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/(h*(f*g - e*h)^2) + (3*b^3*f^2*p^3*q^3*PolyLog[3, -((h*(e + f*x))/(f*g - e*h))])/(h*(f*g - e*h)^2)","A",13,12,28,0.4286,1,"{2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391, 2445}"
441,1,160,0,0.2013874,"\int \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^4 \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^4,x]","\frac{12 b^2 p^2 q^2 (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f}-24 a b^3 p^3 q^3 x-\frac{4 b p q (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{f}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^4}{f}-\frac{24 b^4 p^3 q^3 (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f}+24 b^4 p^4 q^4 x","\frac{12 b^2 p^2 q^2 (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f}-24 a b^3 p^3 q^3 x-\frac{4 b p q (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{f}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^4}{f}-\frac{24 b^4 p^3 q^3 (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f}+24 b^4 p^4 q^4 x",1,"-24*a*b^3*p^3*q^3*x + 24*b^4*p^4*q^4*x - (24*b^4*p^3*q^3*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/f + (12*b^2*p^2*q^2*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/f - (4*b*p*q*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/f + ((e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^4)/f","A",7,4,20,0.2000,1,"{2389, 2296, 2295, 2445}"
442,1,231,0,0.5342943,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^4}{g+h x} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^4/(g + h*x),x]","\frac{24 b^3 p^3 q^3 \text{PolyLog}\left(4,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}-\frac{12 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h}+\frac{4 b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{h}-\frac{24 b^4 p^4 q^4 \text{PolyLog}\left(5,-\frac{h (e+f x)}{f g-e h}\right)}{h}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^4}{h}","\frac{24 b^3 p^3 q^3 \text{PolyLog}\left(4,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}-\frac{12 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h}+\frac{4 b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{h}-\frac{24 b^4 p^4 q^4 \text{PolyLog}\left(5,-\frac{h (e+f x)}{f g-e h}\right)}{h}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^4}{h}",1,"((a + b*Log[c*(d*(e + f*x)^p)^q])^4*Log[(f*(g + h*x))/(f*g - e*h)])/h + (4*b*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^3*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/h - (12*b^2*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*PolyLog[3, -((h*(e + f*x))/(f*g - e*h))])/h + (24*b^3*p^3*q^3*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[4, -((h*(e + f*x))/(f*g - e*h))])/h - (24*b^4*p^4*q^4*PolyLog[5, -((h*(e + f*x))/(f*g - e*h))])/h","A",7,6,28,0.2143,1,"{2396, 2433, 2374, 2383, 6589, 2445}"
443,1,274,0,0.52508,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^4}{(g+h x)^2} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^4/(g + h*x)^2,x]","\frac{24 b^3 f p^3 q^3 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h (f g-e h)}-\frac{12 b^2 f p^2 q^2 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h (f g-e h)}-\frac{24 b^4 f p^4 q^4 \text{PolyLog}\left(4,-\frac{h (e+f x)}{f g-e h}\right)}{h (f g-e h)}-\frac{4 b f p q \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{h (f g-e h)}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^4}{(g+h x) (f g-e h)}","\frac{24 b^3 f p^3 q^3 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h (f g-e h)}-\frac{12 b^2 f p^2 q^2 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h (f g-e h)}-\frac{24 b^4 f p^4 q^4 \text{PolyLog}\left(4,-\frac{h (e+f x)}{f g-e h}\right)}{h (f g-e h)}-\frac{4 b f p q \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{h (f g-e h)}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^4}{(g+h x) (f g-e h)}",1,"((e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^4)/((f*g - e*h)*(g + h*x)) - (4*b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^3*Log[(f*(g + h*x))/(f*g - e*h)])/(h*(f*g - e*h)) - (12*b^2*f*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/(h*(f*g - e*h)) + (24*b^3*f*p^3*q^3*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[3, -((h*(e + f*x))/(f*g - e*h))])/(h*(f*g - e*h)) - (24*b^4*f*p^4*q^4*PolyLog[4, -((h*(e + f*x))/(f*g - e*h))])/(h*(f*g - e*h))","A",7,7,28,0.2500,1,"{2397, 2396, 2433, 2374, 2383, 6589, 2445}"
444,1,29,0,0.0230847,"\int \log \left(c \left(d (e+f x)^p\right)^q\right) \, dx","Int[Log[c*(d*(e + f*x)^p)^q],x]","\frac{(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f}-p q x","\frac{(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f}-p q x",1,"-(p*q*x) + ((e + f*x)*Log[c*(d*(e + f*x)^p)^q])/f","A",3,3,14,0.2143,1,"{2389, 2295, 2445}"
445,1,279,0,0.7789383,"\int \frac{(g+h x)^2}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Int[(g + h*x)^2/(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\frac{2 h (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Ei}\left(\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{b f^3 p q}+\frac{(e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{b f^3 p q}+\frac{h^2 (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \text{Ei}\left(\frac{3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{b f^3 p q}","\frac{2 h (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Ei}\left(\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{b f^3 p q}+\frac{(e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{b f^3 p q}+\frac{h^2 (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \text{Ei}\left(\frac{3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{b f^3 p q}",1,"((f*g - e*h)^2*(e + f*x)*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)])/(b*E^(a/(b*p*q))*f^3*p*q*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (2*h*(f*g - e*h)*(e + f*x)^2*ExpIntegralEi[(2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)])/(b*E^((2*a)/(b*p*q))*f^3*p*q*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) + (h^2*(e + f*x)^3*ExpIntegralEi[(3*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)])/(b*E^((3*a)/(b*p*q))*f^3*p*q*(c*(d*(e + f*x)^p)^q)^(3/(p*q)))","A",12,7,28,0.2500,1,"{2399, 2389, 2300, 2178, 2390, 2310, 2445}"
446,1,179,0,0.4161353,"\int \frac{g+h x}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Int[(g + h*x)/(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\frac{(e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{b f^2 p q}+\frac{h (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Ei}\left(\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{b f^2 p q}","\frac{(e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{b f^2 p q}+\frac{h (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Ei}\left(\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{b f^2 p q}",1,"((f*g - e*h)*(e + f*x)*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)])/(b*E^(a/(b*p*q))*f^2*p*q*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (h*(e + f*x)^2*ExpIntegralEi[(2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)])/(b*E^((2*a)/(b*p*q))*f^2*p*q*(c*(d*(e + f*x)^p)^q)^(2/(p*q)))","A",9,7,26,0.2692,1,"{2399, 2389, 2300, 2178, 2390, 2310, 2445}"
447,1,83,0,0.1190179,"\int \frac{1}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^(-1),x]","\frac{(e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{b f p q}","\frac{(e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{b f p q}",1,"((e + f*x)*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)])/(b*E^(a/(b*p*q))*f*p*q*(c*(d*(e + f*x)^p)^q)^(1/(p*q)))","A",4,4,20,0.2000,1,"{2389, 2300, 2178, 2445}"
448,0,0,0,0.0699271,"\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","Int[1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])),x]","\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","\text{Int}\left(\frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)},x\right)",0,"Defer[Int][1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])), x]","A",0,0,0,0,-1,"{}"
449,0,0,0,0.0657543,"\int \frac{1}{(g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","Int[1/((g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])),x]","\int \frac{1}{(g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","\text{Int}\left(\frac{1}{(g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)},x\right)",0,"Defer[Int][1/((g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])), x]","A",0,0,0,0,-1,"{}"
450,1,326,0,1.2918197,"\int \frac{(g+h x)^2}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","Int[(g + h*x)^2/(a + b*Log[c*(d*(e + f*x)^p)^q])^2,x]","\frac{4 h (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Ei}\left(\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{b^2 f^3 p^2 q^2}+\frac{(e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{b^2 f^3 p^2 q^2}+\frac{3 h^2 (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \text{Ei}\left(\frac{3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{b^2 f^3 p^2 q^2}-\frac{(e+f x) (g+h x)^2}{b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}","\frac{4 h (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Ei}\left(\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{b^2 f^3 p^2 q^2}+\frac{(e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{b^2 f^3 p^2 q^2}+\frac{3 h^2 (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \text{Ei}\left(\frac{3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{b^2 f^3 p^2 q^2}-\frac{(e+f x) (g+h x)^2}{b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}",1,"((f*g - e*h)^2*(e + f*x)*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)])/(b^2*E^(a/(b*p*q))*f^3*p^2*q^2*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (4*h*(f*g - e*h)*(e + f*x)^2*ExpIntegralEi[(2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)])/(b^2*E^((2*a)/(b*p*q))*f^3*p^2*q^2*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) + (3*h^2*(e + f*x)^3*ExpIntegralEi[(3*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)])/(b^2*E^((3*a)/(b*p*q))*f^3*p^2*q^2*(c*(d*(e + f*x)^p)^q)^(3/(p*q))) - ((e + f*x)*(g + h*x)^2)/(b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q]))","A",21,8,28,0.2857,1,"{2400, 2399, 2389, 2300, 2178, 2390, 2310, 2445}"
451,1,224,0,0.6214234,"\int \frac{g+h x}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","Int[(g + h*x)/(a + b*Log[c*(d*(e + f*x)^p)^q])^2,x]","\frac{(e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{b^2 f^2 p^2 q^2}+\frac{2 h (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Ei}\left(\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{b^2 f^2 p^2 q^2}-\frac{(e+f x) (g+h x)}{b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}","\frac{(e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{b^2 f^2 p^2 q^2}+\frac{2 h (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Ei}\left(\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{b^2 f^2 p^2 q^2}-\frac{(e+f x) (g+h x)}{b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}",1,"((f*g - e*h)*(e + f*x)*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)])/(b^2*E^(a/(b*p*q))*f^2*p^2*q^2*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (2*h*(e + f*x)^2*ExpIntegralEi[(2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)])/(b^2*E^((2*a)/(b*p*q))*f^2*p^2*q^2*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) - ((e + f*x)*(g + h*x))/(b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q]))","A",13,8,26,0.3077,1,"{2400, 2399, 2389, 2300, 2178, 2390, 2310, 2445}"
452,1,123,0,0.161389,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^(-2),x]","\frac{(e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{b^2 f p^2 q^2}-\frac{e+f x}{b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}","\frac{(e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{b^2 f p^2 q^2}-\frac{e+f x}{b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}",1,"((e + f*x)*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)])/(b^2*E^(a/(b*p*q))*f*p^2*q^2*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) - (e + f*x)/(b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q]))","A",5,5,20,0.2500,1,"{2389, 2297, 2300, 2178, 2445}"
453,0,0,0,0.0646748,"\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","Int[1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2),x]","\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2},x\right)",0,"Defer[Int][1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2), x]","A",0,0,0,0,-1,"{}"
454,0,0,0,0.0621928,"\int \frac{1}{(g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","Int[1/((g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2),x]","\int \frac{1}{(g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2},x\right)",0,"Defer[Int][1/((g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2), x]","A",0,0,0,0,-1,"{}"
455,1,432,0,2.134211,"\int \frac{(g+h x)^2}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3} \, dx","Int[(g + h*x)^2/(a + b*Log[c*(d*(e + f*x)^p)^q])^3,x]","\frac{4 h (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Ei}\left(\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{b^3 f^3 p^3 q^3}+\frac{(e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{2 b^3 f^3 p^3 q^3}+\frac{9 h^2 (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \text{Ei}\left(\frac{3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{2 b^3 f^3 p^3 q^3}+\frac{(e+f x) (g+h x) (f g-e h)}{b^2 f^2 p^2 q^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}-\frac{3 (e+f x) (g+h x)^2}{2 b^2 f p^2 q^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}-\frac{(e+f x) (g+h x)^2}{2 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}","\frac{4 h (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Ei}\left(\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{b^3 f^3 p^3 q^3}+\frac{(e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{2 b^3 f^3 p^3 q^3}+\frac{9 h^2 (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \text{Ei}\left(\frac{3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{2 b^3 f^3 p^3 q^3}+\frac{(e+f x) (g+h x) (f g-e h)}{b^2 f^2 p^2 q^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}-\frac{3 (e+f x) (g+h x)^2}{2 b^2 f p^2 q^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}-\frac{(e+f x) (g+h x)^2}{2 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}",1,"((f*g - e*h)^2*(e + f*x)*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)])/(2*b^3*E^(a/(b*p*q))*f^3*p^3*q^3*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (4*h*(f*g - e*h)*(e + f*x)^2*ExpIntegralEi[(2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)])/(b^3*E^((2*a)/(b*p*q))*f^3*p^3*q^3*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) + (9*h^2*(e + f*x)^3*ExpIntegralEi[(3*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)])/(2*b^3*E^((3*a)/(b*p*q))*f^3*p^3*q^3*(c*(d*(e + f*x)^p)^q)^(3/(p*q))) - ((e + f*x)*(g + h*x)^2)/(2*b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^2) + ((f*g - e*h)*(e + f*x)*(g + h*x))/(b^2*f^2*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q])) - (3*(e + f*x)*(g + h*x)^2)/(2*b^2*f*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q]))","A",34,8,28,0.2857,1,"{2400, 2399, 2389, 2300, 2178, 2390, 2310, 2445}"
456,1,322,0,0.9255353,"\int \frac{g+h x}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3} \, dx","Int[(g + h*x)/(a + b*Log[c*(d*(e + f*x)^p)^q])^3,x]","\frac{(e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{2 b^3 f^2 p^3 q^3}+\frac{2 h (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Ei}\left(\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{b^3 f^2 p^3 q^3}+\frac{(e+f x) (f g-e h)}{2 b^2 f^2 p^2 q^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}-\frac{(e+f x) (g+h x)}{b^2 f p^2 q^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}-\frac{(e+f x) (g+h x)}{2 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}","\frac{(e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{2 b^3 f^2 p^3 q^3}+\frac{2 h (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Ei}\left(\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{b^3 f^2 p^3 q^3}+\frac{(e+f x) (f g-e h)}{2 b^2 f^2 p^2 q^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}-\frac{(e+f x) (g+h x)}{b^2 f p^2 q^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}-\frac{(e+f x) (g+h x)}{2 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}",1,"((f*g - e*h)*(e + f*x)*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)])/(2*b^3*E^(a/(b*p*q))*f^2*p^3*q^3*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (2*h*(e + f*x)^2*ExpIntegralEi[(2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)])/(b^3*E^((2*a)/(b*p*q))*f^2*p^3*q^3*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) - ((e + f*x)*(g + h*x))/(2*b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^2) + ((f*g - e*h)*(e + f*x))/(2*b^2*f^2*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q])) - ((e + f*x)*(g + h*x))/(b^2*f*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q]))","A",18,9,26,0.3462,1,"{2400, 2399, 2389, 2300, 2178, 2390, 2310, 2297, 2445}"
457,1,169,0,0.2149203,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^(-3),x]","\frac{(e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{2 b^3 f p^3 q^3}-\frac{e+f x}{2 b^2 f p^2 q^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}-\frac{e+f x}{2 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}","\frac{(e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{2 b^3 f p^3 q^3}-\frac{e+f x}{2 b^2 f p^2 q^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}-\frac{e+f x}{2 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}",1,"((e + f*x)*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)])/(2*b^3*E^(a/(b*p*q))*f*p^3*q^3*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) - (e + f*x)/(2*b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^2) - (e + f*x)/(2*b^2*f*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q]))","A",6,5,20,0.2500,1,"{2389, 2297, 2300, 2178, 2445}"
458,0,0,0,0.0653549,"\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3} \, dx","Int[1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3),x]","\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3} \, dx","\text{Int}\left(\frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3},x\right)",0,"Defer[Int][1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3), x]","A",0,0,0,0,-1,"{}"
459,0,0,0,0.062645,"\int \frac{1}{(g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3} \, dx","Int[1/((g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^3),x]","\int \frac{1}{(g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3} \, dx","\text{Int}\left(\frac{1}{(g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3},x\right)",0,"Defer[Int][1/((g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^3), x]","A",0,0,0,0,-1,"{}"
460,1,488,0,1.6147603,"\int (g+h x)^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Int[(g + h*x)^2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} h \sqrt{p} \sqrt{q} (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{2 f^3}-\frac{\sqrt{\pi } \sqrt{b} \sqrt{p} \sqrt{q} (e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{2 f^3}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} h^2 \sqrt{p} \sqrt{q} (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{6 f^3}+\frac{h (e+f x)^2 (f g-e h) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{f^3}+\frac{(e+f x) (f g-e h)^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{f^3}+\frac{h^2 (e+f x)^3 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{3 f^3}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} h \sqrt{p} \sqrt{q} (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{2 f^3}-\frac{\sqrt{\pi } \sqrt{b} \sqrt{p} \sqrt{q} (e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{2 f^3}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} h^2 \sqrt{p} \sqrt{q} (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{6 f^3}+\frac{h (e+f x)^2 (f g-e h) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{f^3}+\frac{(e+f x) (f g-e h)^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{f^3}+\frac{h^2 (e+f x)^3 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{3 f^3}",1,"-(Sqrt[b]*(f*g - e*h)^2*Sqrt[p]*Sqrt[Pi]*Sqrt[q]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(2*E^(a/(b*p*q))*f^3*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) - (Sqrt[b]*h*(f*g - e*h)*Sqrt[p]*Sqrt[Pi/2]*Sqrt[q]*(e + f*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(2*E^((2*a)/(b*p*q))*f^3*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) - (Sqrt[b]*h^2*Sqrt[p]*Sqrt[Pi/3]*Sqrt[q]*(e + f*x)^3*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(6*E^((3*a)/(b*p*q))*f^3*(c*(d*(e + f*x)^p)^q)^(3/(p*q))) + ((f*g - e*h)^2*(e + f*x)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/f^3 + (h*(f*g - e*h)*(e + f*x)^2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/f^3 + (h^2*(e + f*x)^3*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(3*f^3)","A",18,10,30,0.3333,1,"{2401, 2389, 2296, 2300, 2180, 2204, 2390, 2305, 2310, 2445}"
461,1,311,0,0.8112268,"\int (g+h x) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Int[(g + h*x)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]","-\frac{\sqrt{\pi } \sqrt{b} \sqrt{p} \sqrt{q} (e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{2 f^2}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} h \sqrt{p} \sqrt{q} (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{4 f^2}+\frac{(e+f x) (f g-e h) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{f^2}+\frac{h (e+f x)^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{2 f^2}","-\frac{\sqrt{\pi } \sqrt{b} \sqrt{p} \sqrt{q} (e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{2 f^2}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} h \sqrt{p} \sqrt{q} (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{4 f^2}+\frac{(e+f x) (f g-e h) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{f^2}+\frac{h (e+f x)^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{2 f^2}",1,"-(Sqrt[b]*(f*g - e*h)*Sqrt[p]*Sqrt[Pi]*Sqrt[q]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(2*E^(a/(b*p*q))*f^2*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) - (Sqrt[b]*h*Sqrt[p]*Sqrt[Pi/2]*Sqrt[q]*(e + f*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(4*E^((2*a)/(b*p*q))*f^2*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) + ((f*g - e*h)*(e + f*x)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/f^2 + (h*(e + f*x)^2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(2*f^2)","A",13,10,28,0.3571,1,"{2401, 2389, 2296, 2300, 2180, 2204, 2390, 2305, 2310, 2445}"
462,1,139,0,0.222615,"\int \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Int[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]","\frac{(e+f x) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{f}-\frac{\sqrt{\pi } \sqrt{b} \sqrt{p} \sqrt{q} (e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{2 f}","\frac{(e+f x) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{f}-\frac{\sqrt{\pi } \sqrt{b} \sqrt{p} \sqrt{q} (e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{2 f}",1,"-(Sqrt[b]*Sqrt[p]*Sqrt[Pi]*Sqrt[q]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(2*E^(a/(b*p*q))*f*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + ((e + f*x)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/f","A",6,6,22,0.2727,1,"{2389, 2296, 2300, 2180, 2204, 2445}"
463,0,0,0,0.0955348,"\int \frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{g+h x} \, dx","Int[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(g + h*x),x]","\int \frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{g+h x} \, dx","\text{Int}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{g+h x},x\right)",0,"Defer[Int][Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(g + h*x), x]","A",0,0,0,0,-1,"{}"
464,0,0,0,0.1489753,"\int \frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{(g+h x)^2} \, dx","Int[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(g + h*x)^2,x]","\int \frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{(g+h x)^2} \, dx","\text{Int}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{(g+h x)^2},x\right)",0,"Defer[Int][Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(g + h*x)^2, x]","A",0,0,0,0,-1,"{}"
465,1,625,0,1.9160488,"\int (g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2} \, dx","Int[(g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2),x]","\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} h p^{3/2} q^{3/2} (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{8 f^3}+\frac{3 \sqrt{\pi } b^{3/2} p^{3/2} q^{3/2} (e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{4 f^3}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} h^2 p^{3/2} q^{3/2} (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{12 f^3}+\frac{h (e+f x)^2 (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{f^3}+\frac{(e+f x) (f g-e h)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{f^3}-\frac{3 b h p q (e+f x)^2 (f g-e h) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{4 f^3}-\frac{3 b p q (e+f x) (f g-e h)^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{2 f^3}+\frac{h^2 (e+f x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{3 f^3}-\frac{b h^2 p q (e+f x)^3 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{6 f^3}","\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} h p^{3/2} q^{3/2} (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{8 f^3}+\frac{3 \sqrt{\pi } b^{3/2} p^{3/2} q^{3/2} (e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{4 f^3}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} h^2 p^{3/2} q^{3/2} (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{12 f^3}+\frac{h (e+f x)^2 (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{f^3}+\frac{(e+f x) (f g-e h)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{f^3}-\frac{3 b h p q (e+f x)^2 (f g-e h) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{4 f^3}-\frac{3 b p q (e+f x) (f g-e h)^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{2 f^3}+\frac{h^2 (e+f x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{3 f^3}-\frac{b h^2 p q (e+f x)^3 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{6 f^3}",1,"(3*b^(3/2)*(f*g - e*h)^2*p^(3/2)*Sqrt[Pi]*q^(3/2)*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(4*E^(a/(b*p*q))*f^3*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (3*b^(3/2)*h*(f*g - e*h)*p^(3/2)*Sqrt[Pi/2]*q^(3/2)*(e + f*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(8*E^((2*a)/(b*p*q))*f^3*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) + (b^(3/2)*h^2*p^(3/2)*Sqrt[Pi/3]*q^(3/2)*(e + f*x)^3*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(12*E^((3*a)/(b*p*q))*f^3*(c*(d*(e + f*x)^p)^q)^(3/(p*q))) - (3*b*(f*g - e*h)^2*p*q*(e + f*x)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(2*f^3) - (3*b*h*(f*g - e*h)*p*q*(e + f*x)^2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(4*f^3) - (b*h^2*p*q*(e + f*x)^3*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(6*f^3) + ((f*g - e*h)^2*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2))/f^3 + (h*(f*g - e*h)*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2))/f^3 + (h^2*(e + f*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2))/(3*f^3)","A",21,10,30,0.3333,1,"{2401, 2389, 2296, 2300, 2180, 2204, 2390, 2305, 2310, 2445}"
466,1,396,0,1.0178485,"\int (g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2} \, dx","Int[(g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2),x]","\frac{3 \sqrt{\pi } b^{3/2} p^{3/2} q^{3/2} (e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{4 f^2}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} h p^{3/2} q^{3/2} (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{16 f^2}+\frac{(e+f x) (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{f^2}-\frac{3 b p q (e+f x) (f g-e h) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{2 f^2}+\frac{h (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{2 f^2}-\frac{3 b h p q (e+f x)^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{8 f^2}","\frac{3 \sqrt{\pi } b^{3/2} p^{3/2} q^{3/2} (e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{4 f^2}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} h p^{3/2} q^{3/2} (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{16 f^2}+\frac{(e+f x) (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{f^2}-\frac{3 b p q (e+f x) (f g-e h) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{2 f^2}+\frac{h (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{2 f^2}-\frac{3 b h p q (e+f x)^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{8 f^2}",1,"(3*b^(3/2)*(f*g - e*h)*p^(3/2)*Sqrt[Pi]*q^(3/2)*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(4*E^(a/(b*p*q))*f^2*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (3*b^(3/2)*h*p^(3/2)*Sqrt[Pi/2]*q^(3/2)*(e + f*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(16*E^((2*a)/(b*p*q))*f^2*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) - (3*b*(f*g - e*h)*p*q*(e + f*x)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(2*f^2) - (3*b*h*p*q*(e + f*x)^2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(8*f^2) + ((f*g - e*h)*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2))/f^2 + (h*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2))/(2*f^2)","A",15,10,28,0.3571,1,"{2401, 2389, 2296, 2300, 2180, 2204, 2390, 2305, 2310, 2445}"
467,1,176,0,0.2695852,"\int \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2),x]","\frac{3 \sqrt{\pi } b^{3/2} p^{3/2} q^{3/2} (e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{4 f}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{f}-\frac{3 b p q (e+f x) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{2 f}","\frac{3 \sqrt{\pi } b^{3/2} p^{3/2} q^{3/2} (e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{4 f}+\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{f}-\frac{3 b p q (e+f x) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{2 f}",1,"(3*b^(3/2)*p^(3/2)*Sqrt[Pi]*q^(3/2)*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(4*E^(a/(b*p*q))*f*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) - (3*b*p*q*(e + f*x)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(2*f) + ((e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2))/f","A",7,6,22,0.2727,1,"{2389, 2296, 2300, 2180, 2204, 2445}"
468,0,0,0,0.1155627,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{g+h x} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2)/(g + h*x),x]","\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{g+h x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{g+h x},x\right)",0,"Defer[Int][(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2)/(g + h*x), x]","A",0,0,0,0,-1,"{}"
469,0,0,0,0.1630674,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{(g+h x)^2} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2)/(g + h*x)^2,x]","\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{(g+h x)^2} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{(g+h x)^2},x\right)",0,"Defer[Int][(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2)/(g + h*x)^2, x]","A",0,0,0,0,-1,"{}"
470,1,355,0,1.3072492,"\int \frac{(g+h x)^2}{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","Int[(g + h*x)^2/Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]","\frac{\sqrt{2 \pi } h (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{\sqrt{b} f^3 \sqrt{p} \sqrt{q}}+\frac{\sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{\sqrt{b} f^3 \sqrt{p} \sqrt{q}}+\frac{\sqrt{\frac{\pi }{3}} h^2 (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{\sqrt{b} f^3 \sqrt{p} \sqrt{q}}","\frac{\sqrt{2 \pi } h (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{\sqrt{b} f^3 \sqrt{p} \sqrt{q}}+\frac{\sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{\sqrt{b} f^3 \sqrt{p} \sqrt{q}}+\frac{\sqrt{\frac{\pi }{3}} h^2 (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{\sqrt{b} f^3 \sqrt{p} \sqrt{q}}",1,"((f*g - e*h)^2*Sqrt[Pi]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(Sqrt[b]*E^(a/(b*p*q))*f^3*Sqrt[p]*Sqrt[q]*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (h*(f*g - e*h)*Sqrt[2*Pi]*(e + f*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(Sqrt[b]*E^((2*a)/(b*p*q))*f^3*Sqrt[p]*Sqrt[q]*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) + (h^2*Sqrt[Pi/3]*(e + f*x)^3*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(Sqrt[b]*E^((3*a)/(b*p*q))*f^3*Sqrt[p]*Sqrt[q]*(c*(d*(e + f*x)^p)^q)^(3/(p*q)))","A",15,8,30,0.2667,1,"{2401, 2389, 2300, 2180, 2204, 2390, 2310, 2445}"
471,1,229,0,0.6657037,"\int \frac{g+h x}{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","Int[(g + h*x)/Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]","\frac{\sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{\sqrt{b} f^2 \sqrt{p} \sqrt{q}}+\frac{\sqrt{\frac{\pi }{2}} h (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{\sqrt{b} f^2 \sqrt{p} \sqrt{q}}","\frac{\sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{\sqrt{b} f^2 \sqrt{p} \sqrt{q}}+\frac{\sqrt{\frac{\pi }{2}} h (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{\sqrt{b} f^2 \sqrt{p} \sqrt{q}}",1,"((f*g - e*h)*Sqrt[Pi]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(Sqrt[b]*E^(a/(b*p*q))*f^2*Sqrt[p]*Sqrt[q]*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (h*Sqrt[Pi/2]*(e + f*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(Sqrt[b]*E^((2*a)/(b*p*q))*f^2*Sqrt[p]*Sqrt[q]*(c*(d*(e + f*x)^p)^q)^(2/(p*q)))","A",11,8,28,0.2857,1,"{2401, 2389, 2300, 2180, 2204, 2390, 2310, 2445}"
472,1,104,0,0.1794999,"\int \frac{1}{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","Int[1/Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]","\frac{\sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{\sqrt{b} f \sqrt{p} \sqrt{q}}","\frac{\sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{\sqrt{b} f \sqrt{p} \sqrt{q}}",1,"(Sqrt[Pi]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(Sqrt[b]*E^(a/(b*p*q))*f*Sqrt[p]*Sqrt[q]*(c*(d*(e + f*x)^p)^q)^(1/(p*q)))","A",5,5,22,0.2273,1,"{2389, 2300, 2180, 2204, 2445}"
473,0,0,0,0.104327,"\int \frac{1}{(g+h x) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","Int[1/((g + h*x)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]),x]","\int \frac{1}{(g+h x) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","\text{Int}\left(\frac{1}{(g+h x) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}},x\right)",0,"Defer[Int][1/((g + h*x)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]), x]","A",0,0,0,0,-1,"{}"
474,1,404,0,2.2498797,"\int \frac{(g+h x)^2}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}} \, dx","Int[(g + h*x)^2/(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2),x]","\frac{4 \sqrt{2 \pi } h (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{b^{3/2} f^3 p^{3/2} q^{3/2}}+\frac{2 \sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{b^{3/2} f^3 p^{3/2} q^{3/2}}+\frac{2 \sqrt{3 \pi } h^2 (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{b^{3/2} f^3 p^{3/2} q^{3/2}}-\frac{2 (e+f x) (g+h x)^2}{b f p q \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}","\frac{4 \sqrt{2 \pi } h (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{b^{3/2} f^3 p^{3/2} q^{3/2}}+\frac{2 \sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{b^{3/2} f^3 p^{3/2} q^{3/2}}+\frac{2 \sqrt{3 \pi } h^2 (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{b^{3/2} f^3 p^{3/2} q^{3/2}}-\frac{2 (e+f x) (g+h x)^2}{b f p q \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}",1,"(2*(f*g - e*h)^2*Sqrt[Pi]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(b^(3/2)*E^(a/(b*p*q))*f^3*p^(3/2)*q^(3/2)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (4*h*(f*g - e*h)*Sqrt[2*Pi]*(e + f*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(b^(3/2)*E^((2*a)/(b*p*q))*f^3*p^(3/2)*q^(3/2)*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) + (2*h^2*Sqrt[3*Pi]*(e + f*x)^3*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(b^(3/2)*E^((3*a)/(b*p*q))*f^3*p^(3/2)*q^(3/2)*(c*(d*(e + f*x)^p)^q)^(3/(p*q))) - (2*(e + f*x)*(g + h*x)^2)/(b*f*p*q*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])","A",26,9,30,0.3000,1,"{2400, 2401, 2389, 2300, 2180, 2204, 2390, 2310, 2445}"
475,1,275,0,1.0118631,"\int \frac{g+h x}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}} \, dx","Int[(g + h*x)/(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2),x]","\frac{2 \sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{b^{3/2} f^2 p^{3/2} q^{3/2}}+\frac{2 \sqrt{2 \pi } h (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{b^{3/2} f^2 p^{3/2} q^{3/2}}-\frac{2 (e+f x) (g+h x)}{b f p q \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}","\frac{2 \sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{b^{3/2} f^2 p^{3/2} q^{3/2}}+\frac{2 \sqrt{2 \pi } h (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{b^{3/2} f^2 p^{3/2} q^{3/2}}-\frac{2 (e+f x) (g+h x)}{b f p q \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}",1,"(2*(f*g - e*h)*Sqrt[Pi]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(b^(3/2)*E^(a/(b*p*q))*f^2*p^(3/2)*q^(3/2)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (2*h*Sqrt[2*Pi]*(e + f*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(b^(3/2)*E^((2*a)/(b*p*q))*f^2*p^(3/2)*q^(3/2)*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) - (2*(e + f*x)*(g + h*x))/(b*f*p*q*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])","A",16,9,28,0.3214,1,"{2400, 2401, 2389, 2300, 2180, 2204, 2390, 2310, 2445}"
476,1,147,0,0.2479216,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^(-3/2),x]","\frac{2 \sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{b^{3/2} f p^{3/2} q^{3/2}}-\frac{2 (e+f x)}{b f p q \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}","\frac{2 \sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{b^{3/2} f p^{3/2} q^{3/2}}-\frac{2 (e+f x)}{b f p q \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}",1,"(2*Sqrt[Pi]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(b^(3/2)*E^(a/(b*p*q))*f*p^(3/2)*q^(3/2)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) - (2*(e + f*x))/(b*f*p*q*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])","A",6,6,22,0.2727,1,"{2389, 2297, 2300, 2180, 2204, 2445}"
477,0,0,0,0.1226765,"\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}} \, dx","Int[1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2)),x]","\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}} \, dx","\text{Int}\left(\frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}},x\right)",0,"Defer[Int][1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2)), x]","A",0,0,0,0,-1,"{}"
478,1,514,0,3.8564512,"\int \frac{(g+h x)^2}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{5/2}} \, dx","Int[(g + h*x)^2/(a + b*Log[c*(d*(e + f*x)^p)^q])^(5/2),x]","\frac{16 \sqrt{2 \pi } h (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{3 b^{5/2} f^3 p^{5/2} q^{5/2}}+\frac{4 \sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{3 b^{5/2} f^3 p^{5/2} q^{5/2}}+\frac{4 \sqrt{3 \pi } h^2 (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{b^{5/2} f^3 p^{5/2} q^{5/2}}+\frac{8 (e+f x) (g+h x) (f g-e h)}{3 b^2 f^2 p^2 q^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}-\frac{4 (e+f x) (g+h x)^2}{b^2 f p^2 q^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}-\frac{2 (e+f x) (g+h x)^2}{3 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}","\frac{16 \sqrt{2 \pi } h (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{3 b^{5/2} f^3 p^{5/2} q^{5/2}}+\frac{4 \sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{3 b^{5/2} f^3 p^{5/2} q^{5/2}}+\frac{4 \sqrt{3 \pi } h^2 (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{b^{5/2} f^3 p^{5/2} q^{5/2}}+\frac{8 (e+f x) (g+h x) (f g-e h)}{3 b^2 f^2 p^2 q^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}-\frac{4 (e+f x) (g+h x)^2}{b^2 f p^2 q^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}-\frac{2 (e+f x) (g+h x)^2}{3 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}",1,"(4*(f*g - e*h)^2*Sqrt[Pi]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(3*b^(5/2)*E^(a/(b*p*q))*f^3*p^(5/2)*q^(5/2)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (16*h*(f*g - e*h)*Sqrt[2*Pi]*(e + f*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(3*b^(5/2)*E^((2*a)/(b*p*q))*f^3*p^(5/2)*q^(5/2)*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) + (4*h^2*Sqrt[3*Pi]*(e + f*x)^3*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(b^(5/2)*E^((3*a)/(b*p*q))*f^3*p^(5/2)*q^(5/2)*(c*(d*(e + f*x)^p)^q)^(3/(p*q))) - (2*(e + f*x)*(g + h*x)^2)/(3*b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2)) + (8*(f*g - e*h)*(e + f*x)*(g + h*x))/(3*b^2*f^2*p^2*q^2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]) - (4*(e + f*x)*(g + h*x)^2)/(b^2*f*p^2*q^2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])","A",42,9,30,0.3000,1,"{2400, 2401, 2389, 2300, 2180, 2204, 2390, 2310, 2445}"
479,1,380,0,1.5979538,"\int \frac{g+h x}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{5/2}} \, dx","Int[(g + h*x)/(a + b*Log[c*(d*(e + f*x)^p)^q])^(5/2),x]","\frac{4 \sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{3 b^{5/2} f^2 p^{5/2} q^{5/2}}+\frac{8 \sqrt{2 \pi } h (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{3 b^{5/2} f^2 p^{5/2} q^{5/2}}+\frac{4 (e+f x) (f g-e h)}{3 b^2 f^2 p^2 q^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}-\frac{8 (e+f x) (g+h x)}{3 b^2 f p^2 q^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}-\frac{2 (e+f x) (g+h x)}{3 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}","\frac{4 \sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{3 b^{5/2} f^2 p^{5/2} q^{5/2}}+\frac{8 \sqrt{2 \pi } h (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{3 b^{5/2} f^2 p^{5/2} q^{5/2}}+\frac{4 (e+f x) (f g-e h)}{3 b^2 f^2 p^2 q^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}-\frac{8 (e+f x) (g+h x)}{3 b^2 f p^2 q^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}-\frac{2 (e+f x) (g+h x)}{3 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}",1,"(4*(f*g - e*h)*Sqrt[Pi]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(3*b^(5/2)*E^(a/(b*p*q))*f^2*p^(5/2)*q^(5/2)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (8*h*Sqrt[2*Pi]*(e + f*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(3*b^(5/2)*E^((2*a)/(b*p*q))*f^2*p^(5/2)*q^(5/2)*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) - (2*(e + f*x)*(g + h*x))/(3*b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2)) + (4*(f*g - e*h)*(e + f*x))/(3*b^2*f^2*p^2*q^2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]) - (8*(e + f*x)*(g + h*x))/(3*b^2*f*p^2*q^2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])","A",22,10,28,0.3571,1,"{2400, 2401, 2389, 2300, 2180, 2204, 2390, 2310, 2297, 2445}"
480,1,194,0,0.3392867,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{5/2}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^(-5/2),x]","\frac{4 \sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{3 b^{5/2} f p^{5/2} q^{5/2}}-\frac{4 (e+f x)}{3 b^2 f p^2 q^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}-\frac{2 (e+f x)}{3 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}","\frac{4 \sqrt{\pi } (e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \text{Erfi}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)}{3 b^{5/2} f p^{5/2} q^{5/2}}-\frac{4 (e+f x)}{3 b^2 f p^2 q^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}-\frac{2 (e+f x)}{3 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}",1,"(4*Sqrt[Pi]*(e + f*x)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(3*b^(5/2)*E^(a/(b*p*q))*f*p^(5/2)*q^(5/2)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) - (2*(e + f*x))/(3*b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2)) - (4*(e + f*x))/(3*b^2*f*p^2*q^2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])","A",7,6,22,0.2727,1,"{2389, 2297, 2300, 2180, 2204, 2445}"
481,0,0,0,0.1301299,"\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{5/2}} \, dx","Int[1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^(5/2)),x]","\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{5/2}} \, dx","\text{Int}\left(\frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{5/2}},x\right)",0,"Defer[Int][1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^(5/2)), x]","A",0,0,0,0,-1,"{}"
482,1,171,0,0.3345502,"\int (g+h x)^{3/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \, dx","Int[(g + h*x)^(3/2)*(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\frac{2 (g+h x)^{5/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{5 h}-\frac{4 b p q \sqrt{g+h x} (f g-e h)^2}{5 f^2 h}+\frac{4 b p q (f g-e h)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{5 f^{5/2} h}-\frac{4 b p q (g+h x)^{3/2} (f g-e h)}{15 f h}-\frac{4 b p q (g+h x)^{5/2}}{25 h}","\frac{2 (g+h x)^{5/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{5 h}-\frac{4 b p q \sqrt{g+h x} (f g-e h)^2}{5 f^2 h}+\frac{4 b p q (f g-e h)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{5 f^{5/2} h}-\frac{4 b p q (g+h x)^{3/2} (f g-e h)}{15 f h}-\frac{4 b p q (g+h x)^{5/2}}{25 h}",1,"(-4*b*(f*g - e*h)^2*p*q*Sqrt[g + h*x])/(5*f^2*h) - (4*b*(f*g - e*h)*p*q*(g + h*x)^(3/2))/(15*f*h) - (4*b*p*q*(g + h*x)^(5/2))/(25*h) + (4*b*(f*g - e*h)^(5/2)*p*q*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]])/(5*f^(5/2)*h) + (2*(g + h*x)^(5/2)*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(5*h)","A",7,5,28,0.1786,1,"{2395, 50, 63, 208, 2445}"
483,1,139,0,0.182752,"\int \sqrt{g+h x} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \, dx","Int[Sqrt[g + h*x]*(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\frac{2 (g+h x)^{3/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 h}+\frac{4 b p q (f g-e h)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{3 f^{3/2} h}-\frac{4 b p q \sqrt{g+h x} (f g-e h)}{3 f h}-\frac{4 b p q (g+h x)^{3/2}}{9 h}","\frac{2 (g+h x)^{3/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 h}+\frac{4 b p q (f g-e h)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{3 f^{3/2} h}-\frac{4 b p q \sqrt{g+h x} (f g-e h)}{3 f h}-\frac{4 b p q (g+h x)^{3/2}}{9 h}",1,"(-4*b*(f*g - e*h)*p*q*Sqrt[g + h*x])/(3*f*h) - (4*b*p*q*(g + h*x)^(3/2))/(9*h) + (4*b*(f*g - e*h)^(3/2)*p*q*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]])/(3*f^(3/2)*h) + (2*(g + h*x)^(3/2)*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(3*h)","A",6,5,28,0.1786,1,"{2395, 50, 63, 208, 2445}"
484,1,103,0,0.1369616,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{\sqrt{g+h x}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/Sqrt[g + h*x],x]","\frac{2 \sqrt{g+h x} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}+\frac{4 b p q \sqrt{f g-e h} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{\sqrt{f} h}-\frac{4 b p q \sqrt{g+h x}}{h}","\frac{2 \sqrt{g+h x} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}+\frac{4 b p q \sqrt{f g-e h} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{\sqrt{f} h}-\frac{4 b p q \sqrt{g+h x}}{h}",1,"(-4*b*p*q*Sqrt[g + h*x])/h + (4*b*Sqrt[f*g - e*h]*p*q*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]])/(Sqrt[f]*h) + (2*Sqrt[g + h*x]*(a + b*Log[c*(d*(e + f*x)^p)^q]))/h","A",5,5,28,0.1786,1,"{2395, 50, 63, 208, 2445}"
485,1,86,0,0.126199,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x)^{3/2}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x)^(3/2),x]","-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h \sqrt{g+h x}}-\frac{4 b \sqrt{f} p q \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{h \sqrt{f g-e h}}","-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h \sqrt{g+h x}}-\frac{4 b \sqrt{f} p q \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{h \sqrt{f g-e h}}",1,"(-4*b*Sqrt[f]*p*q*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]])/(h*Sqrt[f*g - e*h]) - (2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(h*Sqrt[g + h*x])","A",4,4,28,0.1429,1,"{2395, 63, 208, 2445}"
486,1,120,0,0.159532,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x)^{5/2}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x)^(5/2),x]","-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 h (g+h x)^{3/2}}-\frac{4 b f^{3/2} p q \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{3 h (f g-e h)^{3/2}}+\frac{4 b f p q}{3 h \sqrt{g+h x} (f g-e h)}","-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 h (g+h x)^{3/2}}-\frac{4 b f^{3/2} p q \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{3 h (f g-e h)^{3/2}}+\frac{4 b f p q}{3 h \sqrt{g+h x} (f g-e h)}",1,"(4*b*f*p*q)/(3*h*(f*g - e*h)*Sqrt[g + h*x]) - (4*b*f^(3/2)*p*q*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]])/(3*h*(f*g - e*h)^(3/2)) - (2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(3*h*(g + h*x)^(3/2))","A",5,5,28,0.1786,1,"{2395, 51, 63, 208, 2445}"
487,1,152,0,0.1994167,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x)^{7/2}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x)^(7/2),x]","-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{5 h (g+h x)^{5/2}}+\frac{4 b f^2 p q}{5 h \sqrt{g+h x} (f g-e h)^2}-\frac{4 b f^{5/2} p q \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{5 h (f g-e h)^{5/2}}+\frac{4 b f p q}{15 h (g+h x)^{3/2} (f g-e h)}","-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{5 h (g+h x)^{5/2}}+\frac{4 b f^2 p q}{5 h \sqrt{g+h x} (f g-e h)^2}-\frac{4 b f^{5/2} p q \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{5 h (f g-e h)^{5/2}}+\frac{4 b f p q}{15 h (g+h x)^{3/2} (f g-e h)}",1,"(4*b*f*p*q)/(15*h*(f*g - e*h)*(g + h*x)^(3/2)) + (4*b*f^2*p*q)/(5*h*(f*g - e*h)^2*Sqrt[g + h*x]) - (4*b*f^(5/2)*p*q*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]])/(5*h*(f*g - e*h)^(5/2)) - (2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(5*h*(g + h*x)^(5/2))","A",6,5,28,0.1786,1,"{2395, 51, 63, 208, 2445}"
488,1,184,0,0.2777488,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x)^{9/2}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x)^(9/2),x]","-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{7 h (g+h x)^{7/2}}+\frac{4 b f^3 p q}{7 h \sqrt{g+h x} (f g-e h)^3}+\frac{4 b f^2 p q}{21 h (g+h x)^{3/2} (f g-e h)^2}-\frac{4 b f^{7/2} p q \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{7 h (f g-e h)^{7/2}}+\frac{4 b f p q}{35 h (g+h x)^{5/2} (f g-e h)}","-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{7 h (g+h x)^{7/2}}+\frac{4 b f^3 p q}{7 h \sqrt{g+h x} (f g-e h)^3}+\frac{4 b f^2 p q}{21 h (g+h x)^{3/2} (f g-e h)^2}-\frac{4 b f^{7/2} p q \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{7 h (f g-e h)^{7/2}}+\frac{4 b f p q}{35 h (g+h x)^{5/2} (f g-e h)}",1,"(4*b*f*p*q)/(35*h*(f*g - e*h)*(g + h*x)^(5/2)) + (4*b*f^2*p*q)/(21*h*(f*g - e*h)^2*(g + h*x)^(3/2)) + (4*b*f^3*p*q)/(7*h*(f*g - e*h)^3*Sqrt[g + h*x]) - (4*b*f^(7/2)*p*q*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]])/(7*h*(f*g - e*h)^(7/2)) - (2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(7*h*(g + h*x)^(7/2))","A",7,5,28,0.1786,1,"{2395, 51, 63, 208, 2445}"
489,1,635,0,4.3478225,"\int (g+h x)^{3/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \, dx","Int[(g + h*x)^(3/2)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2,x]","\frac{8 b^2 p^2 q^2 (f g-e h)^{5/2} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right)}{5 f^{5/2} h}-\frac{8 b p q \sqrt{g+h x} (f g-e h)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{5 f^2 h}+\frac{8 b p q (f g-e h)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{5 f^{5/2} h}-\frac{8 b p q (g+h x)^{3/2} (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{15 f h}+\frac{2 (g+h x)^{5/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{5 h}-\frac{8 b p q (g+h x)^{5/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{25 h}+\frac{368 b^2 p^2 q^2 \sqrt{g+h x} (f g-e h)^2}{75 f^2 h}-\frac{8 b^2 p^2 q^2 (f g-e h)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)^2}{5 f^{5/2} h}-\frac{368 b^2 p^2 q^2 (f g-e h)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{75 f^{5/2} h}+\frac{16 b^2 p^2 q^2 (f g-e h)^{5/2} \log \left(\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{5 f^{5/2} h}+\frac{128 b^2 p^2 q^2 (g+h x)^{3/2} (f g-e h)}{225 f h}+\frac{16 b^2 p^2 q^2 (g+h x)^{5/2}}{125 h}","\frac{8 b^2 p^2 q^2 (f g-e h)^{5/2} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right)}{5 f^{5/2} h}-\frac{8 b p q \sqrt{g+h x} (f g-e h)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{5 f^2 h}+\frac{8 b p q (f g-e h)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{5 f^{5/2} h}-\frac{8 b p q (g+h x)^{3/2} (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{15 f h}+\frac{2 (g+h x)^{5/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{5 h}-\frac{8 b p q (g+h x)^{5/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{25 h}+\frac{368 b^2 p^2 q^2 \sqrt{g+h x} (f g-e h)^2}{75 f^2 h}-\frac{8 b^2 p^2 q^2 (f g-e h)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)^2}{5 f^{5/2} h}-\frac{368 b^2 p^2 q^2 (f g-e h)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{75 f^{5/2} h}+\frac{16 b^2 p^2 q^2 (f g-e h)^{5/2} \log \left(\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{5 f^{5/2} h}+\frac{128 b^2 p^2 q^2 (g+h x)^{3/2} (f g-e h)}{225 f h}+\frac{16 b^2 p^2 q^2 (g+h x)^{5/2}}{125 h}",1,"(368*b^2*(f*g - e*h)^2*p^2*q^2*Sqrt[g + h*x])/(75*f^2*h) + (128*b^2*(f*g - e*h)*p^2*q^2*(g + h*x)^(3/2))/(225*f*h) + (16*b^2*p^2*q^2*(g + h*x)^(5/2))/(125*h) - (368*b^2*(f*g - e*h)^(5/2)*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]])/(75*f^(5/2)*h) - (8*b^2*(f*g - e*h)^(5/2)*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]^2)/(5*f^(5/2)*h) - (8*b*(f*g - e*h)^2*p*q*Sqrt[g + h*x]*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(5*f^2*h) - (8*b*(f*g - e*h)*p*q*(g + h*x)^(3/2)*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(15*f*h) - (8*b*p*q*(g + h*x)^(5/2)*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(25*h) + (8*b*(f*g - e*h)^(5/2)*p*q*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(5*f^(5/2)*h) + (2*(g + h*x)^(5/2)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(5*h) + (16*b^2*(f*g - e*h)^(5/2)*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*Log[2/(1 - (Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h])])/(5*f^(5/2)*h) + (8*b^2*(f*g - e*h)^(5/2)*p^2*q^2*PolyLog[2, 1 - 2/(1 - (Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h])])/(5*f^(5/2)*h)","A",29,16,30,0.5333,1,"{2398, 2411, 2346, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 50, 2445}"
490,1,547,0,2.9826729,"\int \sqrt{g+h x} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \, dx","Int[Sqrt[g + h*x]*(a + b*Log[c*(d*(e + f*x)^p)^q])^2,x]","\frac{8 b^2 p^2 q^2 (f g-e h)^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right)}{3 f^{3/2} h}+\frac{8 b p q (f g-e h)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 f^{3/2} h}-\frac{8 b p q (g+h x)^{3/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{9 h}-\frac{8 b p q \sqrt{g+h x} (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 f h}+\frac{2 (g+h x)^{3/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{3 h}-\frac{8 b^2 p^2 q^2 (f g-e h)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)^2}{3 f^{3/2} h}-\frac{64 b^2 p^2 q^2 (f g-e h)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{9 f^{3/2} h}+\frac{16 b^2 p^2 q^2 (f g-e h)^{3/2} \log \left(\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{3 f^{3/2} h}+\frac{64 b^2 p^2 q^2 \sqrt{g+h x} (f g-e h)}{9 f h}+\frac{16 b^2 p^2 q^2 (g+h x)^{3/2}}{27 h}","\frac{8 b^2 p^2 q^2 (f g-e h)^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right)}{3 f^{3/2} h}+\frac{8 b p q (f g-e h)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 f^{3/2} h}-\frac{8 b p q (g+h x)^{3/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{9 h}-\frac{8 b p q \sqrt{g+h x} (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 f h}+\frac{2 (g+h x)^{3/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{3 h}-\frac{8 b^2 p^2 q^2 (f g-e h)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)^2}{3 f^{3/2} h}-\frac{64 b^2 p^2 q^2 (f g-e h)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{9 f^{3/2} h}+\frac{16 b^2 p^2 q^2 (f g-e h)^{3/2} \log \left(\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{3 f^{3/2} h}+\frac{64 b^2 p^2 q^2 \sqrt{g+h x} (f g-e h)}{9 f h}+\frac{16 b^2 p^2 q^2 (g+h x)^{3/2}}{27 h}",1,"(64*b^2*(f*g - e*h)*p^2*q^2*Sqrt[g + h*x])/(9*f*h) + (16*b^2*p^2*q^2*(g + h*x)^(3/2))/(27*h) - (64*b^2*(f*g - e*h)^(3/2)*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]])/(9*f^(3/2)*h) - (8*b^2*(f*g - e*h)^(3/2)*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]^2)/(3*f^(3/2)*h) - (8*b*(f*g - e*h)*p*q*Sqrt[g + h*x]*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(3*f*h) - (8*b*p*q*(g + h*x)^(3/2)*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(9*h) + (8*b*(f*g - e*h)^(3/2)*p*q*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(3*f^(3/2)*h) + (2*(g + h*x)^(3/2)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(3*h) + (16*b^2*(f*g - e*h)^(3/2)*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*Log[2/(1 - (Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h])])/(3*f^(3/2)*h) + (8*b^2*(f*g - e*h)^(3/2)*p^2*q^2*PolyLog[2, 1 - 2/(1 - (Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h])])/(3*f^(3/2)*h)","A",22,16,30,0.5333,1,"{2398, 2411, 2346, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 50, 2445}"
491,1,447,0,2.2173701,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{\sqrt{g+h x}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/Sqrt[g + h*x],x]","\frac{8 b^2 p^2 q^2 \sqrt{f g-e h} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right)}{\sqrt{f} h}-\frac{8 b p q \sqrt{g+h x} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}+\frac{2 \sqrt{g+h x} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h}+\frac{8 b p q \sqrt{f g-e h} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{\sqrt{f} h}-\frac{8 b^2 p^2 q^2 \sqrt{f g-e h} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)^2}{\sqrt{f} h}-\frac{16 b^2 p^2 q^2 \sqrt{f g-e h} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{\sqrt{f} h}+\frac{16 b^2 p^2 q^2 \sqrt{f g-e h} \log \left(\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{\sqrt{f} h}+\frac{16 b^2 p^2 q^2 \sqrt{g+h x}}{h}","\frac{8 b^2 p^2 q^2 \sqrt{f g-e h} \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right)}{\sqrt{f} h}-\frac{8 b p q \sqrt{g+h x} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}+\frac{2 \sqrt{g+h x} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h}+\frac{8 b p q \sqrt{f g-e h} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{\sqrt{f} h}-\frac{8 b^2 p^2 q^2 \sqrt{f g-e h} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)^2}{\sqrt{f} h}-\frac{16 b^2 p^2 q^2 \sqrt{f g-e h} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{\sqrt{f} h}+\frac{16 b^2 p^2 q^2 \sqrt{f g-e h} \log \left(\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{\sqrt{f} h}+\frac{16 b^2 p^2 q^2 \sqrt{g+h x}}{h}",1,"(16*b^2*p^2*q^2*Sqrt[g + h*x])/h - (16*b^2*Sqrt[f*g - e*h]*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]])/(Sqrt[f]*h) - (8*b^2*Sqrt[f*g - e*h]*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]^2)/(Sqrt[f]*h) - (8*b*p*q*Sqrt[g + h*x]*(a + b*Log[c*(d*(e + f*x)^p)^q]))/h + (8*b*Sqrt[f*g - e*h]*p*q*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(Sqrt[f]*h) + (2*Sqrt[g + h*x]*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/h + (16*b^2*Sqrt[f*g - e*h]*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*Log[2/(1 - (Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h])])/(Sqrt[f]*h) + (8*b^2*Sqrt[f*g - e*h]*p^2*q^2*PolyLog[2, 1 - 2/(1 - (Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h])])/(Sqrt[f]*h)","A",16,16,30,0.5333,1,"{2398, 2411, 2346, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 50, 2445}"
492,1,330,0,1.6202924,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(g+h x)^{3/2}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/(g + h*x)^(3/2),x]","-\frac{8 b^2 \sqrt{f} p^2 q^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right)}{h \sqrt{f g-e h}}-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h \sqrt{g+h x}}-\frac{8 b \sqrt{f} p q \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h \sqrt{f g-e h}}+\frac{8 b^2 \sqrt{f} p^2 q^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)^2}{h \sqrt{f g-e h}}-\frac{16 b^2 \sqrt{f} p^2 q^2 \log \left(\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{h \sqrt{f g-e h}}","-\frac{8 b^2 \sqrt{f} p^2 q^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right)}{h \sqrt{f g-e h}}-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h \sqrt{g+h x}}-\frac{8 b \sqrt{f} p q \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h \sqrt{f g-e h}}+\frac{8 b^2 \sqrt{f} p^2 q^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)^2}{h \sqrt{f g-e h}}-\frac{16 b^2 \sqrt{f} p^2 q^2 \log \left(\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{h \sqrt{f g-e h}}",1,"(8*b^2*Sqrt[f]*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]^2)/(h*Sqrt[f*g - e*h]) - (8*b*Sqrt[f]*p*q*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(h*Sqrt[f*g - e*h]) - (2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(h*Sqrt[g + h*x]) - (16*b^2*Sqrt[f]*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*Log[2/(1 - (Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h])])/(h*Sqrt[f*g - e*h]) - (8*b^2*Sqrt[f]*p^2*q^2*PolyLog[2, 1 - 2/(1 - (Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h])])/(h*Sqrt[f*g - e*h])","A",11,13,30,0.4333,1,"{2398, 2411, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2445}"
493,1,449,0,2.3779118,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(g+h x)^{5/2}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/(g + h*x)^(5/2),x]","-\frac{8 b^2 f^{3/2} p^2 q^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right)}{3 h (f g-e h)^{3/2}}-\frac{8 b f^{3/2} p q \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 h (f g-e h)^{3/2}}+\frac{8 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 h \sqrt{g+h x} (f g-e h)}-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{3 h (g+h x)^{3/2}}+\frac{8 b^2 f^{3/2} p^2 q^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)^2}{3 h (f g-e h)^{3/2}}+\frac{16 b^2 f^{3/2} p^2 q^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{3 h (f g-e h)^{3/2}}-\frac{16 b^2 f^{3/2} p^2 q^2 \log \left(\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{3 h (f g-e h)^{3/2}}","-\frac{8 b^2 f^{3/2} p^2 q^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right)}{3 h (f g-e h)^{3/2}}-\frac{8 b f^{3/2} p q \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 h (f g-e h)^{3/2}}+\frac{8 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 h \sqrt{g+h x} (f g-e h)}-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{3 h (g+h x)^{3/2}}+\frac{8 b^2 f^{3/2} p^2 q^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)^2}{3 h (f g-e h)^{3/2}}+\frac{16 b^2 f^{3/2} p^2 q^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{3 h (f g-e h)^{3/2}}-\frac{16 b^2 f^{3/2} p^2 q^2 \log \left(\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{3 h (f g-e h)^{3/2}}",1,"(16*b^2*f^(3/2)*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]])/(3*h*(f*g - e*h)^(3/2)) + (8*b^2*f^(3/2)*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]^2)/(3*h*(f*g - e*h)^(3/2)) + (8*b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(3*h*(f*g - e*h)*Sqrt[g + h*x]) - (8*b*f^(3/2)*p*q*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(3*h*(f*g - e*h)^(3/2)) - (2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(3*h*(g + h*x)^(3/2)) - (16*b^2*f^(3/2)*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*Log[2/(1 - (Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h])])/(3*h*(f*g - e*h)^(3/2)) - (8*b^2*f^(3/2)*p^2*q^2*PolyLog[2, 1 - 2/(1 - (Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h])])/(3*h*(f*g - e*h)^(3/2))","A",15,15,30,0.5000,1,"{2398, 2411, 2347, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 2445}"
494,1,537,0,3.0839221,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(g+h x)^{7/2}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/(g + h*x)^(7/2),x]","-\frac{8 b^2 f^{5/2} p^2 q^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right)}{5 h (f g-e h)^{5/2}}+\frac{8 b f^2 p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{5 h \sqrt{g+h x} (f g-e h)^2}-\frac{8 b f^{5/2} p q \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{5 h (f g-e h)^{5/2}}+\frac{8 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{15 h (g+h x)^{3/2} (f g-e h)}-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{5 h (g+h x)^{5/2}}-\frac{16 b^2 f^2 p^2 q^2}{15 h \sqrt{g+h x} (f g-e h)^2}+\frac{8 b^2 f^{5/2} p^2 q^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)^2}{5 h (f g-e h)^{5/2}}+\frac{64 b^2 f^{5/2} p^2 q^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{15 h (f g-e h)^{5/2}}-\frac{16 b^2 f^{5/2} p^2 q^2 \log \left(\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{5 h (f g-e h)^{5/2}}","-\frac{8 b^2 f^{5/2} p^2 q^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right)}{5 h (f g-e h)^{5/2}}+\frac{8 b f^2 p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{5 h \sqrt{g+h x} (f g-e h)^2}-\frac{8 b f^{5/2} p q \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{5 h (f g-e h)^{5/2}}+\frac{8 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{15 h (g+h x)^{3/2} (f g-e h)}-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{5 h (g+h x)^{5/2}}-\frac{16 b^2 f^2 p^2 q^2}{15 h \sqrt{g+h x} (f g-e h)^2}+\frac{8 b^2 f^{5/2} p^2 q^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)^2}{5 h (f g-e h)^{5/2}}+\frac{64 b^2 f^{5/2} p^2 q^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{15 h (f g-e h)^{5/2}}-\frac{16 b^2 f^{5/2} p^2 q^2 \log \left(\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{5 h (f g-e h)^{5/2}}",1,"(-16*b^2*f^2*p^2*q^2)/(15*h*(f*g - e*h)^2*Sqrt[g + h*x]) + (64*b^2*f^(5/2)*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]])/(15*h*(f*g - e*h)^(5/2)) + (8*b^2*f^(5/2)*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]^2)/(5*h*(f*g - e*h)^(5/2)) + (8*b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(15*h*(f*g - e*h)*(g + h*x)^(3/2)) + (8*b*f^2*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(5*h*(f*g - e*h)^2*Sqrt[g + h*x]) - (8*b*f^(5/2)*p*q*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(5*h*(f*g - e*h)^(5/2)) - (2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(5*h*(g + h*x)^(5/2)) - (16*b^2*f^(5/2)*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*Log[2/(1 - (Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h])])/(5*h*(f*g - e*h)^(5/2)) - (8*b^2*f^(5/2)*p^2*q^2*PolyLog[2, 1 - 2/(1 - (Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h])])/(5*h*(f*g - e*h)^(5/2))","A",20,16,30,0.5333,1,"{2398, 2411, 2347, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 51, 2445}"
495,1,625,0,3.9271635,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(g+h x)^{9/2}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/(g + h*x)^(9/2),x]","-\frac{8 b^2 f^{7/2} p^2 q^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right)}{7 h (f g-e h)^{7/2}}+\frac{8 b f^3 p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{7 h \sqrt{g+h x} (f g-e h)^3}+\frac{8 b f^2 p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{21 h (g+h x)^{3/2} (f g-e h)^2}-\frac{8 b f^{7/2} p q \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{7 h (f g-e h)^{7/2}}+\frac{8 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{35 h (g+h x)^{5/2} (f g-e h)}-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{7 h (g+h x)^{7/2}}-\frac{128 b^2 f^3 p^2 q^2}{105 h \sqrt{g+h x} (f g-e h)^3}-\frac{16 b^2 f^2 p^2 q^2}{105 h (g+h x)^{3/2} (f g-e h)^2}+\frac{8 b^2 f^{7/2} p^2 q^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)^2}{7 h (f g-e h)^{7/2}}+\frac{368 b^2 f^{7/2} p^2 q^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{105 h (f g-e h)^{7/2}}-\frac{16 b^2 f^{7/2} p^2 q^2 \log \left(\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{7 h (f g-e h)^{7/2}}","-\frac{8 b^2 f^{7/2} p^2 q^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right)}{7 h (f g-e h)^{7/2}}+\frac{8 b f^3 p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{7 h \sqrt{g+h x} (f g-e h)^3}+\frac{8 b f^2 p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{21 h (g+h x)^{3/2} (f g-e h)^2}-\frac{8 b f^{7/2} p q \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{7 h (f g-e h)^{7/2}}+\frac{8 b f p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{35 h (g+h x)^{5/2} (f g-e h)}-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{7 h (g+h x)^{7/2}}-\frac{128 b^2 f^3 p^2 q^2}{105 h \sqrt{g+h x} (f g-e h)^3}-\frac{16 b^2 f^2 p^2 q^2}{105 h (g+h x)^{3/2} (f g-e h)^2}+\frac{8 b^2 f^{7/2} p^2 q^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)^2}{7 h (f g-e h)^{7/2}}+\frac{368 b^2 f^{7/2} p^2 q^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{105 h (f g-e h)^{7/2}}-\frac{16 b^2 f^{7/2} p^2 q^2 \log \left(\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)}{7 h (f g-e h)^{7/2}}",1,"(-16*b^2*f^2*p^2*q^2)/(105*h*(f*g - e*h)^2*(g + h*x)^(3/2)) - (128*b^2*f^3*p^2*q^2)/(105*h*(f*g - e*h)^3*Sqrt[g + h*x]) + (368*b^2*f^(7/2)*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]])/(105*h*(f*g - e*h)^(7/2)) + (8*b^2*f^(7/2)*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]^2)/(7*h*(f*g - e*h)^(7/2)) + (8*b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(35*h*(f*g - e*h)*(g + h*x)^(5/2)) + (8*b*f^2*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(21*h*(f*g - e*h)^2*(g + h*x)^(3/2)) + (8*b*f^3*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(7*h*(f*g - e*h)^3*Sqrt[g + h*x]) - (8*b*f^(7/2)*p*q*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(7*h*(f*g - e*h)^(7/2)) - (2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(7*h*(g + h*x)^(7/2)) - (16*b^2*f^(7/2)*p^2*q^2*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*Log[2/(1 - (Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h])])/(7*h*(f*g - e*h)^(7/2)) - (8*b^2*f^(7/2)*p^2*q^2*PolyLog[2, 1 - 2/(1 - (Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h])])/(7*h*(f*g - e*h)^(7/2))","A",26,16,30,0.5333,1,"{2398, 2411, 2347, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 51, 2445}"
496,0,0,0,0.0882588,"\int \frac{(g+h x)^{3/2}}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Int[(g + h*x)^(3/2)/(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\int \frac{(g+h x)^{3/2}}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","\text{Int}\left(\frac{(g+h x)^{3/2}}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)},x\right)",0,"Defer[Int][(g + h*x)^(3/2)/(a + b*Log[c*(d*(e + f*x)^p)^q]), x]","A",0,0,0,0,-1,"{}"
497,0,0,0,0.0781728,"\int \frac{\sqrt{g+h x}}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Int[Sqrt[g + h*x]/(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\int \frac{\sqrt{g+h x}}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","\text{Int}\left(\frac{\sqrt{g+h x}}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)},x\right)",0,"Defer[Int][Sqrt[g + h*x]/(a + b*Log[c*(d*(e + f*x)^p)^q]), x]","A",0,0,0,0,-1,"{}"
498,0,0,0,0.0819394,"\int \frac{1}{\sqrt{g+h x} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","Int[1/(Sqrt[g + h*x]*(a + b*Log[c*(d*(e + f*x)^p)^q])),x]","\int \frac{1}{\sqrt{g+h x} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","\text{Int}\left(\frac{1}{\sqrt{g+h x} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)},x\right)",0,"Defer[Int][1/(Sqrt[g + h*x]*(a + b*Log[c*(d*(e + f*x)^p)^q])), x]","A",0,0,0,0,-1,"{}"
499,0,0,0,0.0873596,"\int \frac{1}{(g+h x)^{3/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","Int[1/((g + h*x)^(3/2)*(a + b*Log[c*(d*(e + f*x)^p)^q])),x]","\int \frac{1}{(g+h x)^{3/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","\text{Int}\left(\frac{1}{(g+h x)^{3/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)},x\right)",0,"Defer[Int][1/((g + h*x)^(3/2)*(a + b*Log[c*(d*(e + f*x)^p)^q])), x]","A",0,0,0,0,-1,"{}"
500,0,0,0,0.3324875,"\int \sqrt{g+h x} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Int[Sqrt[g + h*x]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]","\int \sqrt{g+h x} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","\text{Int}\left(\sqrt{g+h x} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)},x\right)",0,"Defer[Int][Sqrt[g + h*x]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]], x]","A",0,0,0,0,-1,"{}"
501,0,0,0,0.309956,"\int \frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{g+h x}} \, dx","Int[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/Sqrt[g + h*x],x]","\int \frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{g+h x}} \, dx","\text{Int}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{g+h x}},x\right)",0,"Defer[Int][Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/Sqrt[g + h*x], x]","A",0,0,0,0,-1,"{}"
502,0,0,0,0.3242211,"\int \frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{(g+h x)^{3/2}} \, dx","Int[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(g + h*x)^(3/2),x]","\int \frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{(g+h x)^{3/2}} \, dx","\text{Int}\left(\frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{(g+h x)^{3/2}},x\right)",0,"Defer[Int][Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(g + h*x)^(3/2), x]","A",0,0,0,0,-1,"{}"
503,0,0,0,0.1121124,"\int \frac{\sqrt{g+h x}}{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","Int[Sqrt[g + h*x]/Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]","\int \frac{\sqrt{g+h x}}{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","\text{Int}\left(\frac{\sqrt{g+h x}}{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}},x\right)",0,"Defer[Int][Sqrt[g + h*x]/Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]], x]","A",0,0,0,0,-1,"{}"
504,0,0,0,0.1169008,"\int \frac{1}{\sqrt{g+h x} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","Int[1/(Sqrt[g + h*x]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]),x]","\int \frac{1}{\sqrt{g+h x} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","\text{Int}\left(\frac{1}{\sqrt{g+h x} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}},x\right)",0,"Defer[Int][1/(Sqrt[g + h*x]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]), x]","A",0,0,0,0,-1,"{}"
505,0,0,0,0.120249,"\int \frac{1}{(g+h x)^{3/2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","Int[1/((g + h*x)^(3/2)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]),x]","\int \frac{1}{(g+h x)^{3/2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","\text{Int}\left(\frac{1}{(g+h x)^{3/2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}},x\right)",0,"Defer[Int][1/((g + h*x)^(3/2)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]), x]","A",0,0,0,0,-1,"{}"
506,1,99,0,0.1059242,"\int (g+h x)^m \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \, dx","Int[(g + h*x)^m*(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\frac{(g+h x)^{m+1} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h (m+1)}+\frac{b f p q (g+h x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{f (g+h x)}{f g-e h}\right)}{h (m+1) (m+2) (f g-e h)}","\frac{(g+h x)^{m+1} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h (m+1)}+\frac{b f p q (g+h x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{f (g+h x)}{f g-e h}\right)}{h (m+1) (m+2) (f g-e h)}",1,"(b*f*p*q*(g + h*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (f*(g + h*x))/(f*g - e*h)])/(h*(f*g - e*h)*(1 + m)*(2 + m)) + ((g + h*x)^(1 + m)*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(h*(1 + m))","A",3,3,26,0.1154,1,"{2395, 68, 2445}"
507,0,0,0,0.0573508,"\int \frac{(g+h x)^m}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Int[(g + h*x)^m/(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\int \frac{(g+h x)^m}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","\text{Int}\left(\frac{(g+h x)^m}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)},x\right)",0,"Defer[Int][(g + h*x)^m/(a + b*Log[c*(d*(e + f*x)^p)^q]), x]","A",0,0,0,0,-1,"{}"
508,0,0,0,0.0552597,"\int \frac{(g+h x)^m}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","Int[(g + h*x)^m/(a + b*Log[c*(d*(e + f*x)^p)^q])^2,x]","\int \frac{(g+h x)^m}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","\text{Int}\left(\frac{(g+h x)^m}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2},x\right)",0,"Defer[Int][(g + h*x)^m/(a + b*Log[c*(d*(e + f*x)^p)^q])^2, x]","A",0,0,0,0,-1,"{}"
509,0,0,0,0.1106552,"\int (g+h x)^m \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2} \, dx","Int[(g + h*x)^m*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2),x]","\int (g+h x)^m \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2} \, dx","\text{Int}\left((g+h x)^m \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2},x\right)",0,"Defer[Int][(g + h*x)^m*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2), x]","A",0,0,0,0,-1,"{}"
510,0,0,0,0.0900227,"\int (g+h x)^m \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Int[(g + h*x)^m*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]","\int (g+h x)^m \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","\text{Int}\left((g+h x)^m \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)},x\right)",0,"Defer[Int][(g + h*x)^m*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]], x]","A",0,0,0,0,-1,"{}"
511,0,0,0,0.0968894,"\int \frac{(g+h x)^m}{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","Int[(g + h*x)^m/Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]","\int \frac{(g+h x)^m}{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","\text{Int}\left(\frac{(g+h x)^m}{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}},x\right)",0,"Defer[Int][(g + h*x)^m/Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]], x]","A",0,0,0,0,-1,"{}"
512,0,0,0,0.1142303,"\int \frac{(g+h x)^m}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}} \, dx","Int[(g + h*x)^m/(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2),x]","\int \frac{(g+h x)^m}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}} \, dx","\text{Int}\left(\frac{(g+h x)^m}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}},x\right)",0,"Defer[Int][(g + h*x)^m/(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2), x]","A",0,0,0,0,-1,"{}"
513,0,0,0,0.0548252,"\int (g+h x)^m \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \, dx","Int[(g + h*x)^m*(a + b*Log[c*(d*(e + f*x)^p)^q])^n,x]","\int (g+h x)^m \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \, dx","\text{Int}\left((g+h x)^m \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n,x\right)",0,"Defer[Int][(g + h*x)^m*(a + b*Log[c*(d*(e + f*x)^p)^q])^n, x]","A",0,0,0,0,-1,"{}"
514,1,432,0,0.9572876,"\int (g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \, dx","Int[(g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^n,x]","\frac{h 2^{-n} (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \left(-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{f^3}+\frac{(e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \left(-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{f^3}+\frac{h^2 3^{-n-1} (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \left(-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{f^3}","\frac{h 2^{-n} (e+f x)^2 e^{-\frac{2 a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \left(-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{f^3}+\frac{(e+f x) e^{-\frac{a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \left(-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{f^3}+\frac{h^2 3^{-n-1} (e+f x)^3 e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \left(-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{f^3}",1,"(3^(-1 - n)*h^2*(e + f*x)^3*Gamma[1 + n, (-3*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)]*(a + b*Log[c*(d*(e + f*x)^p)^q])^n)/(E^((3*a)/(b*p*q))*f^3*(c*(d*(e + f*x)^p)^q)^(3/(p*q))*(-((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)))^n) + (h*(f*g - e*h)*(e + f*x)^2*Gamma[1 + n, (-2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)]*(a + b*Log[c*(d*(e + f*x)^p)^q])^n)/(2^n*E^((2*a)/(b*p*q))*f^3*(c*(d*(e + f*x)^p)^q)^(2/(p*q))*(-((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)))^n) + ((f*g - e*h)^2*(e + f*x)*Gamma[1 + n, -((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q))]*(a + b*Log[c*(d*(e + f*x)^p)^q])^n)/(E^(a/(b*p*q))*f^3*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*(-((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)))^n)","A",12,7,28,0.2500,1,"{2401, 2389, 2300, 2181, 2390, 2310, 2445}"
515,1,281,0,0.5290452,"\int (g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \, dx","Int[(g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^n,x]","\frac{(e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \left(-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{f^2}+\frac{h 2^{-n-1} (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \left(-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{f^2}","\frac{(e+f x) e^{-\frac{a}{b p q}} (f g-e h) \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \left(-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{f^2}+\frac{h 2^{-n-1} (e+f x)^2 e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \left(-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)}{f^2}",1,"(2^(-1 - n)*h*(e + f*x)^2*Gamma[1 + n, (-2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)]*(a + b*Log[c*(d*(e + f*x)^p)^q])^n)/(E^((2*a)/(b*p*q))*f^2*(c*(d*(e + f*x)^p)^q)^(2/(p*q))*(-((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)))^n) + ((f*g - e*h)*(e + f*x)*Gamma[1 + n, -((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q))]*(a + b*Log[c*(d*(e + f*x)^p)^q])^n)/(E^(a/(b*p*q))*f^2*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*(-((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)))^n)","A",9,7,26,0.2692,1,"{2401, 2389, 2300, 2181, 2390, 2310, 2445}"
516,1,131,0,0.1514473,"\int \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^n,x]","\frac{(e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \left(-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{f}","\frac{(e+f x) e^{-\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \left(-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)}{f}",1,"((e + f*x)*Gamma[1 + n, -((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q))]*(a + b*Log[c*(d*(e + f*x)^p)^q])^n)/(E^(a/(b*p*q))*f*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*(-((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)))^n)","A",4,4,20,0.2000,1,"{2389, 2300, 2181, 2445}"
517,0,0,0,0.0622584,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n}{g+h x} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^n/(g + h*x),x]","\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n}{g+h x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n}{g+h x},x\right)",0,"Defer[Int][(a + b*Log[c*(d*(e + f*x)^p)^q])^n/(g + h*x), x]","A",0,0,0,0,-1,"{}"
518,1,249,0,0.5039936,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{g+h x^2} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x^2),x]","-\frac{b p q \text{PolyLog}\left(2,-\frac{\sqrt{h} (e+f x)}{f \sqrt{-g}-e \sqrt{h}}\right)}{2 \sqrt{-g} \sqrt{h}}+\frac{b p q \text{PolyLog}\left(2,\frac{\sqrt{h} (e+f x)}{e \sqrt{h}+f \sqrt{-g}}\right)}{2 \sqrt{-g} \sqrt{h}}+\frac{\log \left(\frac{f \left(\sqrt{-g}-\sqrt{h} x\right)}{e \sqrt{h}+f \sqrt{-g}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 \sqrt{-g} \sqrt{h}}-\frac{\log \left(\frac{f \left(\sqrt{-g}+\sqrt{h} x\right)}{f \sqrt{-g}-e \sqrt{h}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 \sqrt{-g} \sqrt{h}}","-\frac{b p q \text{PolyLog}\left(2,-\frac{\sqrt{h} (e+f x)}{f \sqrt{-g}-e \sqrt{h}}\right)}{2 \sqrt{-g} \sqrt{h}}+\frac{b p q \text{PolyLog}\left(2,\frac{\sqrt{h} (e+f x)}{e \sqrt{h}+f \sqrt{-g}}\right)}{2 \sqrt{-g} \sqrt{h}}+\frac{\log \left(\frac{f \left(\sqrt{-g}-\sqrt{h} x\right)}{e \sqrt{h}+f \sqrt{-g}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 \sqrt{-g} \sqrt{h}}-\frac{\log \left(\frac{f \left(\sqrt{-g}+\sqrt{h} x\right)}{f \sqrt{-g}-e \sqrt{h}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 \sqrt{-g} \sqrt{h}}",1,"((a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(Sqrt[-g] - Sqrt[h]*x))/(f*Sqrt[-g] + e*Sqrt[h])])/(2*Sqrt[-g]*Sqrt[h]) - ((a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(Sqrt[-g] + Sqrt[h]*x))/(f*Sqrt[-g] - e*Sqrt[h])])/(2*Sqrt[-g]*Sqrt[h]) - (b*p*q*PolyLog[2, -((Sqrt[h]*(e + f*x))/(f*Sqrt[-g] - e*Sqrt[h]))])/(2*Sqrt[-g]*Sqrt[h]) + (b*p*q*PolyLog[2, (Sqrt[h]*(e + f*x))/(f*Sqrt[-g] + e*Sqrt[h])])/(2*Sqrt[-g]*Sqrt[h])","A",9,5,28,0.1786,1,"{2409, 2394, 2393, 2391, 2445}"
519,1,335,0,0.831641,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{\sqrt{2+h x^2}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/Sqrt[2 + h*x^2],x]","-\frac{b p q \text{PolyLog}\left(2,-\frac{\sqrt{2} f e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right)}}{e \sqrt{h}-\sqrt{e^2 h+2 f^2}}\right)}{\sqrt{h}}-\frac{b p q \text{PolyLog}\left(2,-\frac{\sqrt{2} f e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right)}}{\sqrt{e^2 h+2 f^2}+e \sqrt{h}}\right)}{\sqrt{h}}+\frac{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{\sqrt{h}}-\frac{b p q \sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right) \log \left(\frac{\sqrt{2} f e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right)}}{e \sqrt{h}-\sqrt{e^2 h+2 f^2}}+1\right)}{\sqrt{h}}-\frac{b p q \sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right) \log \left(\frac{\sqrt{2} f e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right)}}{\sqrt{e^2 h+2 f^2}+e \sqrt{h}}+1\right)}{\sqrt{h}}+\frac{b p q \sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right)^2}{2 \sqrt{h}}","-\frac{b p q \text{PolyLog}\left(2,-\frac{\sqrt{2} f e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right)}}{e \sqrt{h}-\sqrt{e^2 h+2 f^2}}\right)}{\sqrt{h}}-\frac{b p q \text{PolyLog}\left(2,-\frac{\sqrt{2} f e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right)}}{\sqrt{e^2 h+2 f^2}+e \sqrt{h}}\right)}{\sqrt{h}}+\frac{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{\sqrt{h}}-\frac{b p q \sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right) \log \left(\frac{\sqrt{2} f e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right)}}{e \sqrt{h}-\sqrt{e^2 h+2 f^2}}+1\right)}{\sqrt{h}}-\frac{b p q \sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right) \log \left(\frac{\sqrt{2} f e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right)}}{\sqrt{e^2 h+2 f^2}+e \sqrt{h}}+1\right)}{\sqrt{h}}+\frac{b p q \sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right)^2}{2 \sqrt{h}}",1,"(b*p*q*ArcSinh[(Sqrt[h]*x)/Sqrt[2]]^2)/(2*Sqrt[h]) - (b*p*q*ArcSinh[(Sqrt[h]*x)/Sqrt[2]]*Log[1 + (Sqrt[2]*E^ArcSinh[(Sqrt[h]*x)/Sqrt[2]]*f)/(e*Sqrt[h] - Sqrt[2*f^2 + e^2*h])])/Sqrt[h] - (b*p*q*ArcSinh[(Sqrt[h]*x)/Sqrt[2]]*Log[1 + (Sqrt[2]*E^ArcSinh[(Sqrt[h]*x)/Sqrt[2]]*f)/(e*Sqrt[h] + Sqrt[2*f^2 + e^2*h])])/Sqrt[h] + (ArcSinh[(Sqrt[h]*x)/Sqrt[2]]*(a + b*Log[c*(d*(e + f*x)^p)^q]))/Sqrt[h] - (b*p*q*PolyLog[2, -((Sqrt[2]*E^ArcSinh[(Sqrt[h]*x)/Sqrt[2]]*f)/(e*Sqrt[h] - Sqrt[2*f^2 + e^2*h]))])/Sqrt[h] - (b*p*q*PolyLog[2, -((Sqrt[2]*E^ArcSinh[(Sqrt[h]*x)/Sqrt[2]]*f)/(e*Sqrt[h] + Sqrt[2*f^2 + e^2*h]))])/Sqrt[h]","A",11,9,30,0.3000,1,"{215, 2404, 12, 5799, 5561, 2190, 2279, 2391, 2445}"
520,1,515,0,1.2005029,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{\sqrt{g+h x^2}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/Sqrt[g + h*x^2],x]","-\frac{b \sqrt{g} p q \sqrt{\frac{h x^2}{g}+1} \text{PolyLog}\left(2,-\frac{f \sqrt{g} e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right)}}{e \sqrt{h}-\sqrt{e^2 h+f^2 g}}\right)}{\sqrt{h} \sqrt{g+h x^2}}-\frac{b \sqrt{g} p q \sqrt{\frac{h x^2}{g}+1} \text{PolyLog}\left(2,-\frac{f \sqrt{g} e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right)}}{\sqrt{e^2 h+f^2 g}+e \sqrt{h}}\right)}{\sqrt{h} \sqrt{g+h x^2}}+\frac{\sqrt{g} \sqrt{\frac{h x^2}{g}+1} \sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{\sqrt{h} \sqrt{g+h x^2}}-\frac{b \sqrt{g} p q \sqrt{\frac{h x^2}{g}+1} \sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right) \log \left(\frac{f \sqrt{g} e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right)}}{e \sqrt{h}-\sqrt{e^2 h+f^2 g}}+1\right)}{\sqrt{h} \sqrt{g+h x^2}}-\frac{b \sqrt{g} p q \sqrt{\frac{h x^2}{g}+1} \sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right) \log \left(\frac{f \sqrt{g} e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right)}}{\sqrt{e^2 h+f^2 g}+e \sqrt{h}}+1\right)}{\sqrt{h} \sqrt{g+h x^2}}+\frac{b \sqrt{g} p q \sqrt{\frac{h x^2}{g}+1} \sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right)^2}{2 \sqrt{h} \sqrt{g+h x^2}}","-\frac{b \sqrt{g} p q \sqrt{\frac{h x^2}{g}+1} \text{PolyLog}\left(2,-\frac{f \sqrt{g} e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right)}}{e \sqrt{h}-\sqrt{e^2 h+f^2 g}}\right)}{\sqrt{h} \sqrt{g+h x^2}}-\frac{b \sqrt{g} p q \sqrt{\frac{h x^2}{g}+1} \text{PolyLog}\left(2,-\frac{f \sqrt{g} e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right)}}{\sqrt{e^2 h+f^2 g}+e \sqrt{h}}\right)}{\sqrt{h} \sqrt{g+h x^2}}+\frac{\sqrt{g} \sqrt{\frac{h x^2}{g}+1} \sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{\sqrt{h} \sqrt{g+h x^2}}-\frac{b \sqrt{g} p q \sqrt{\frac{h x^2}{g}+1} \sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right) \log \left(\frac{f \sqrt{g} e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right)}}{e \sqrt{h}-\sqrt{e^2 h+f^2 g}}+1\right)}{\sqrt{h} \sqrt{g+h x^2}}-\frac{b \sqrt{g} p q \sqrt{\frac{h x^2}{g}+1} \sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right) \log \left(\frac{f \sqrt{g} e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right)}}{\sqrt{e^2 h+f^2 g}+e \sqrt{h}}+1\right)}{\sqrt{h} \sqrt{g+h x^2}}+\frac{b \sqrt{g} p q \sqrt{\frac{h x^2}{g}+1} \sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right)^2}{2 \sqrt{h} \sqrt{g+h x^2}}",1,"(b*Sqrt[g]*p*q*Sqrt[1 + (h*x^2)/g]*ArcSinh[(Sqrt[h]*x)/Sqrt[g]]^2)/(2*Sqrt[h]*Sqrt[g + h*x^2]) - (b*Sqrt[g]*p*q*Sqrt[1 + (h*x^2)/g]*ArcSinh[(Sqrt[h]*x)/Sqrt[g]]*Log[1 + (E^ArcSinh[(Sqrt[h]*x)/Sqrt[g]]*f*Sqrt[g])/(e*Sqrt[h] - Sqrt[f^2*g + e^2*h])])/(Sqrt[h]*Sqrt[g + h*x^2]) - (b*Sqrt[g]*p*q*Sqrt[1 + (h*x^2)/g]*ArcSinh[(Sqrt[h]*x)/Sqrt[g]]*Log[1 + (E^ArcSinh[(Sqrt[h]*x)/Sqrt[g]]*f*Sqrt[g])/(e*Sqrt[h] + Sqrt[f^2*g + e^2*h])])/(Sqrt[h]*Sqrt[g + h*x^2]) + (Sqrt[g]*Sqrt[1 + (h*x^2)/g]*ArcSinh[(Sqrt[h]*x)/Sqrt[g]]*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(Sqrt[h]*Sqrt[g + h*x^2]) - (b*Sqrt[g]*p*q*Sqrt[1 + (h*x^2)/g]*PolyLog[2, -((E^ArcSinh[(Sqrt[h]*x)/Sqrt[g]]*f*Sqrt[g])/(e*Sqrt[h] - Sqrt[f^2*g + e^2*h]))])/(Sqrt[h]*Sqrt[g + h*x^2]) - (b*Sqrt[g]*p*q*Sqrt[1 + (h*x^2)/g]*PolyLog[2, -((E^ArcSinh[(Sqrt[h]*x)/Sqrt[g]]*f*Sqrt[g])/(e*Sqrt[h] + Sqrt[f^2*g + e^2*h]))])/(Sqrt[h]*Sqrt[g + h*x^2])","A",12,10,30,0.3333,1,"{2406, 215, 2404, 12, 5799, 5561, 2190, 2279, 2391, 2445}"
521,1,287,0,1.0594265,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{\sqrt{2-h x} \sqrt{2+h x}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/(Sqrt[2 - h*x]*Sqrt[2 + h*x]),x]","\frac{i b p q \text{PolyLog}\left(2,-\frac{2 f e^{i \sin ^{-1}\left(\frac{h x}{2}\right)}}{-\sqrt{4 f^2-e^2 h^2}+i e h}\right)}{h}+\frac{i b p q \text{PolyLog}\left(2,-\frac{2 f e^{i \sin ^{-1}\left(\frac{h x}{2}\right)}}{\sqrt{4 f^2-e^2 h^2}+i e h}\right)}{h}+\frac{\sin ^{-1}\left(\frac{h x}{2}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}-\frac{b p q \sin ^{-1}\left(\frac{h x}{2}\right) \log \left(1+\frac{2 f e^{i \sin ^{-1}\left(\frac{h x}{2}\right)}}{-\sqrt{4 f^2-e^2 h^2}+i e h}\right)}{h}-\frac{b p q \sin ^{-1}\left(\frac{h x}{2}\right) \log \left(1+\frac{2 f e^{i \sin ^{-1}\left(\frac{h x}{2}\right)}}{\sqrt{4 f^2-e^2 h^2}+i e h}\right)}{h}+\frac{i b p q \sin ^{-1}\left(\frac{h x}{2}\right)^2}{2 h}","\frac{i b p q \text{PolyLog}\left(2,-\frac{2 f e^{i \sin ^{-1}\left(\frac{h x}{2}\right)}}{-\sqrt{4 f^2-e^2 h^2}+i e h}\right)}{h}+\frac{i b p q \text{PolyLog}\left(2,-\frac{2 f e^{i \sin ^{-1}\left(\frac{h x}{2}\right)}}{\sqrt{4 f^2-e^2 h^2}+i e h}\right)}{h}+\frac{\sin ^{-1}\left(\frac{h x}{2}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}-\frac{b p q \sin ^{-1}\left(\frac{h x}{2}\right) \log \left(1+\frac{2 f e^{i \sin ^{-1}\left(\frac{h x}{2}\right)}}{-\sqrt{4 f^2-e^2 h^2}+i e h}\right)}{h}-\frac{b p q \sin ^{-1}\left(\frac{h x}{2}\right) \log \left(1+\frac{2 f e^{i \sin ^{-1}\left(\frac{h x}{2}\right)}}{\sqrt{4 f^2-e^2 h^2}+i e h}\right)}{h}+\frac{i b p q \sin ^{-1}\left(\frac{h x}{2}\right)^2}{2 h}",1,"((I/2)*b*p*q*ArcSin[(h*x)/2]^2)/h - (b*p*q*ArcSin[(h*x)/2]*Log[1 + (2*E^(I*ArcSin[(h*x)/2])*f)/(I*e*h - Sqrt[4*f^2 - e^2*h^2])])/h - (b*p*q*ArcSin[(h*x)/2]*Log[1 + (2*E^(I*ArcSin[(h*x)/2])*f)/(I*e*h + Sqrt[4*f^2 - e^2*h^2])])/h + (ArcSin[(h*x)/2]*(a + b*Log[c*(d*(e + f*x)^p)^q]))/h + (I*b*p*q*PolyLog[2, (-2*E^(I*ArcSin[(h*x)/2])*f)/(I*e*h - Sqrt[4*f^2 - e^2*h^2])])/h + (I*b*p*q*PolyLog[2, (-2*E^(I*ArcSin[(h*x)/2])*f)/(I*e*h + Sqrt[4*f^2 - e^2*h^2])])/h","A",10,8,38,0.2105,1,"{216, 2405, 4741, 4521, 2190, 2279, 2391, 2445}"
522,1,519,0,1.4112023,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{\sqrt{g-h x} \sqrt{g+h x}} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/(Sqrt[g - h*x]*Sqrt[g + h*x]),x]","\frac{i b g p q \sqrt{1-\frac{h^2 x^2}{g^2}} \text{PolyLog}\left(2,-\frac{f g e^{i \sin ^{-1}\left(\frac{h x}{g}\right)}}{-\sqrt{f^2 g^2-e^2 h^2}+i e h}\right)}{h \sqrt{g-h x} \sqrt{g+h x}}+\frac{i b g p q \sqrt{1-\frac{h^2 x^2}{g^2}} \text{PolyLog}\left(2,-\frac{f g e^{i \sin ^{-1}\left(\frac{h x}{g}\right)}}{\sqrt{f^2 g^2-e^2 h^2}+i e h}\right)}{h \sqrt{g-h x} \sqrt{g+h x}}+\frac{g \sqrt{1-\frac{h^2 x^2}{g^2}} \sin ^{-1}\left(\frac{h x}{g}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h \sqrt{g-h x} \sqrt{g+h x}}-\frac{b g p q \sqrt{1-\frac{h^2 x^2}{g^2}} \sin ^{-1}\left(\frac{h x}{g}\right) \log \left(1+\frac{f g e^{i \sin ^{-1}\left(\frac{h x}{g}\right)}}{-\sqrt{f^2 g^2-e^2 h^2}+i e h}\right)}{h \sqrt{g-h x} \sqrt{g+h x}}-\frac{b g p q \sqrt{1-\frac{h^2 x^2}{g^2}} \sin ^{-1}\left(\frac{h x}{g}\right) \log \left(1+\frac{f g e^{i \sin ^{-1}\left(\frac{h x}{g}\right)}}{\sqrt{f^2 g^2-e^2 h^2}+i e h}\right)}{h \sqrt{g-h x} \sqrt{g+h x}}+\frac{i b g p q \sqrt{1-\frac{h^2 x^2}{g^2}} \sin ^{-1}\left(\frac{h x}{g}\right)^2}{2 h \sqrt{g-h x} \sqrt{g+h x}}","\frac{i b g p q \sqrt{1-\frac{h^2 x^2}{g^2}} \text{PolyLog}\left(2,-\frac{f g e^{i \sin ^{-1}\left(\frac{h x}{g}\right)}}{-\sqrt{f^2 g^2-e^2 h^2}+i e h}\right)}{h \sqrt{g-h x} \sqrt{g+h x}}+\frac{i b g p q \sqrt{1-\frac{h^2 x^2}{g^2}} \text{PolyLog}\left(2,-\frac{f g e^{i \sin ^{-1}\left(\frac{h x}{g}\right)}}{\sqrt{f^2 g^2-e^2 h^2}+i e h}\right)}{h \sqrt{g-h x} \sqrt{g+h x}}+\frac{g \sqrt{1-\frac{h^2 x^2}{g^2}} \sin ^{-1}\left(\frac{h x}{g}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h \sqrt{g-h x} \sqrt{g+h x}}-\frac{b g p q \sqrt{1-\frac{h^2 x^2}{g^2}} \sin ^{-1}\left(\frac{h x}{g}\right) \log \left(1+\frac{f g e^{i \sin ^{-1}\left(\frac{h x}{g}\right)}}{-\sqrt{f^2 g^2-e^2 h^2}+i e h}\right)}{h \sqrt{g-h x} \sqrt{g+h x}}-\frac{b g p q \sqrt{1-\frac{h^2 x^2}{g^2}} \sin ^{-1}\left(\frac{h x}{g}\right) \log \left(1+\frac{f g e^{i \sin ^{-1}\left(\frac{h x}{g}\right)}}{\sqrt{f^2 g^2-e^2 h^2}+i e h}\right)}{h \sqrt{g-h x} \sqrt{g+h x}}+\frac{i b g p q \sqrt{1-\frac{h^2 x^2}{g^2}} \sin ^{-1}\left(\frac{h x}{g}\right)^2}{2 h \sqrt{g-h x} \sqrt{g+h x}}",1,"((I/2)*b*g*p*q*Sqrt[1 - (h^2*x^2)/g^2]*ArcSin[(h*x)/g]^2)/(h*Sqrt[g - h*x]*Sqrt[g + h*x]) - (b*g*p*q*Sqrt[1 - (h^2*x^2)/g^2]*ArcSin[(h*x)/g]*Log[1 + (E^(I*ArcSin[(h*x)/g])*f*g)/(I*e*h - Sqrt[f^2*g^2 - e^2*h^2])])/(h*Sqrt[g - h*x]*Sqrt[g + h*x]) - (b*g*p*q*Sqrt[1 - (h^2*x^2)/g^2]*ArcSin[(h*x)/g]*Log[1 + (E^(I*ArcSin[(h*x)/g])*f*g)/(I*e*h + Sqrt[f^2*g^2 - e^2*h^2])])/(h*Sqrt[g - h*x]*Sqrt[g + h*x]) + (g*Sqrt[1 - (h^2*x^2)/g^2]*ArcSin[(h*x)/g]*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(h*Sqrt[g - h*x]*Sqrt[g + h*x]) + (I*b*g*p*q*Sqrt[1 - (h^2*x^2)/g^2]*PolyLog[2, -((E^(I*ArcSin[(h*x)/g])*f*g)/(I*e*h - Sqrt[f^2*g^2 - e^2*h^2]))])/(h*Sqrt[g - h*x]*Sqrt[g + h*x]) + (I*b*g*p*q*Sqrt[1 - (h^2*x^2)/g^2]*PolyLog[2, -((E^(I*ArcSin[(h*x)/g])*f*g)/(I*e*h + Sqrt[f^2*g^2 - e^2*h^2]))])/(h*Sqrt[g - h*x]*Sqrt[g + h*x])","A",12,10,38,0.2632,1,"{2407, 216, 2404, 12, 4741, 4521, 2190, 2279, 2391, 2445}"
523,1,427,0,0.8167065,"\int \frac{(i+j x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{g+h x} \, dx","Int[((i + j*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(g + h*x),x]","\frac{b p q (h i-g j)^3 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h^4}+\frac{(i+j x)^2 (h i-g j) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 h^2}+\frac{(h i-g j)^3 \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h^4}+\frac{(i+j x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 h}+\frac{a j x (h i-g j)^2}{h^3}+\frac{b j (e+f x) (h i-g j)^2 \log \left(c \left(d (e+f x)^p\right)^q\right)}{f h^3}-\frac{b p q (f i-e j)^2 \log (e+f x) (h i-g j)}{2 f^2 h^2}-\frac{b j p q x (f i-e j)^2}{3 f^2 h}-\frac{b p q (f i-e j)^3 \log (e+f x)}{3 f^3 h}-\frac{b j p q x (f i-e j) (h i-g j)}{2 f h^2}-\frac{b p q (i+j x)^2 (f i-e j)}{6 f h}-\frac{b p q (i+j x)^2 (h i-g j)}{4 h^2}-\frac{b j p q x (h i-g j)^2}{h^3}-\frac{b p q (i+j x)^3}{9 h}","\frac{b p q (h i-g j)^3 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h^4}+\frac{(i+j x)^2 (h i-g j) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 h^2}+\frac{(h i-g j)^3 \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h^4}+\frac{(i+j x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{3 h}+\frac{a j x (h i-g j)^2}{h^3}+\frac{b j (e+f x) (h i-g j)^2 \log \left(c \left(d (e+f x)^p\right)^q\right)}{f h^3}-\frac{b p q (f i-e j)^2 \log (e+f x) (h i-g j)}{2 f^2 h^2}-\frac{b j p q x (f i-e j)^2}{3 f^2 h}-\frac{b p q (f i-e j)^3 \log (e+f x)}{3 f^3 h}-\frac{b j p q x (f i-e j) (h i-g j)}{2 f h^2}-\frac{b p q (i+j x)^2 (f i-e j)}{6 f h}-\frac{b p q (i+j x)^2 (h i-g j)}{4 h^2}-\frac{b j p q x (h i-g j)^2}{h^3}-\frac{b p q (i+j x)^3}{9 h}",1,"(a*j*(h*i - g*j)^2*x)/h^3 - (b*j*(f*i - e*j)^2*p*q*x)/(3*f^2*h) - (b*j*(f*i - e*j)*(h*i - g*j)*p*q*x)/(2*f*h^2) - (b*j*(h*i - g*j)^2*p*q*x)/h^3 - (b*(f*i - e*j)*p*q*(i + j*x)^2)/(6*f*h) - (b*(h*i - g*j)*p*q*(i + j*x)^2)/(4*h^2) - (b*p*q*(i + j*x)^3)/(9*h) - (b*(f*i - e*j)^3*p*q*Log[e + f*x])/(3*f^3*h) - (b*(f*i - e*j)^2*(h*i - g*j)*p*q*Log[e + f*x])/(2*f^2*h^2) + (b*j*(h*i - g*j)^2*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/(f*h^3) + ((h*i - g*j)*(i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(2*h^2) + ((i + j*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(3*h) + ((h*i - g*j)^3*(a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(g + h*x))/(f*g - e*h)])/h^4 + (b*(h*i - g*j)^3*p*q*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/h^4","A",15,9,33,0.2727,1,"{2418, 2389, 2295, 2394, 2393, 2391, 2395, 43, 2445}"
524,1,258,0,0.5445842,"\int \frac{(i+j x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{g+h x} \, dx","Int[((i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(g + h*x),x]","\frac{b p q (h i-g j)^2 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h^3}+\frac{(h i-g j)^2 \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h^3}+\frac{(i+j x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 h}+\frac{a j x (h i-g j)}{h^2}+\frac{b j (e+f x) (h i-g j) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f h^2}-\frac{b p q (f i-e j)^2 \log (e+f x)}{2 f^2 h}-\frac{b j p q x (f i-e j)}{2 f h}-\frac{b j p q x (h i-g j)}{h^2}-\frac{b p q (i+j x)^2}{4 h}","\frac{b p q (h i-g j)^2 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h^3}+\frac{(h i-g j)^2 \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h^3}+\frac{(i+j x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 h}+\frac{a j x (h i-g j)}{h^2}+\frac{b j (e+f x) (h i-g j) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f h^2}-\frac{b p q (f i-e j)^2 \log (e+f x)}{2 f^2 h}-\frac{b j p q x (f i-e j)}{2 f h}-\frac{b j p q x (h i-g j)}{h^2}-\frac{b p q (i+j x)^2}{4 h}",1,"(a*j*(h*i - g*j)*x)/h^2 - (b*j*(f*i - e*j)*p*q*x)/(2*f*h) - (b*j*(h*i - g*j)*p*q*x)/h^2 - (b*p*q*(i + j*x)^2)/(4*h) - (b*(f*i - e*j)^2*p*q*Log[e + f*x])/(2*f^2*h) + (b*j*(h*i - g*j)*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/(f*h^2) + ((i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(2*h) + ((h*i - g*j)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(g + h*x))/(f*g - e*h)])/h^3 + (b*(h*i - g*j)^2*p*q*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/h^3","A",12,9,33,0.2727,1,"{2418, 2389, 2295, 2394, 2393, 2391, 2395, 43, 2445}"
525,1,129,0,0.3323616,"\int \frac{(i+j x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{g+h x} \, dx","Int[((i + j*x)*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(g + h*x),x]","\frac{b p q (h i-g j) \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h^2}+\frac{(h i-g j) \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h^2}+\frac{a j x}{h}+\frac{b j (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f h}-\frac{b j p q x}{h}","\frac{b p q (h i-g j) \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h^2}+\frac{(h i-g j) \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h^2}+\frac{a j x}{h}+\frac{b j (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f h}-\frac{b j p q x}{h}",1,"(a*j*x)/h - (b*j*p*q*x)/h + (b*j*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/(f*h) + ((h*i - g*j)*(a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(g + h*x))/(f*g - e*h)])/h^2 + (b*(h*i - g*j)*p*q*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/h^2","A",9,7,31,0.2258,1,"{2418, 2389, 2295, 2394, 2393, 2391, 2445}"
526,1,68,0,0.1123727,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{g+h x} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x),x]","\frac{b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}","\frac{b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}",1,"((a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(g + h*x))/(f*g - e*h)])/h + (b*p*q*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/h","A",4,4,26,0.1538,1,"{2394, 2393, 2391, 2445}"
527,1,165,0,0.4678891,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x) (i+j x)} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/((g + h*x)*(i + j*x)),x]","\frac{b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h i-g j}-\frac{b p q \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right)}{h i-g j}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h i-g j}-\frac{\log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h i-g j}","\frac{b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{h i-g j}-\frac{b p q \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right)}{h i-g j}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h i-g j}-\frac{\log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h i-g j}",1,"((a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(g + h*x))/(f*g - e*h)])/(h*i - g*j) - ((a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(i + j*x))/(f*i - e*j)])/(h*i - g*j) + (b*p*q*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/(h*i - g*j) - (b*p*q*PolyLog[2, -((j*(e + f*x))/(f*i - e*j))])/(h*i - g*j)","A",9,5,33,0.1515,1,"{2418, 2394, 2393, 2391, 2445}"
528,1,268,0,0.5953511,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x) (i+j x)^2} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/((g + h*x)*(i + j*x)^2),x]","\frac{b h p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{(h i-g j)^2}-\frac{b h p q \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right)}{(h i-g j)^2}+\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(i+j x) (h i-g j)}+\frac{h \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(h i-g j)^2}-\frac{h \log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(h i-g j)^2}-\frac{b f p q \log (e+f x)}{(f i-e j) (h i-g j)}+\frac{b f p q \log (i+j x)}{(f i-e j) (h i-g j)}","\frac{b h p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{(h i-g j)^2}-\frac{b h p q \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right)}{(h i-g j)^2}+\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(i+j x) (h i-g j)}+\frac{h \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(h i-g j)^2}-\frac{h \log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(h i-g j)^2}-\frac{b f p q \log (e+f x)}{(f i-e j) (h i-g j)}+\frac{b f p q \log (i+j x)}{(f i-e j) (h i-g j)}",1,"-((b*f*p*q*Log[e + f*x])/((f*i - e*j)*(h*i - g*j))) + (a + b*Log[c*(d*(e + f*x)^p)^q])/((h*i - g*j)*(i + j*x)) + (h*(a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(g + h*x))/(f*g - e*h)])/(h*i - g*j)^2 + (b*f*p*q*Log[i + j*x])/((f*i - e*j)*(h*i - g*j)) - (h*(a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(i + j*x))/(f*i - e*j)])/(h*i - g*j)^2 + (b*h*p*q*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/(h*i - g*j)^2 - (b*h*p*q*PolyLog[2, -((j*(e + f*x))/(f*i - e*j))])/(h*i - g*j)^2","A",13,8,33,0.2424,1,"{2418, 2394, 2393, 2391, 2395, 36, 31, 2445}"
529,1,425,0,0.8350424,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x) (i+j x)^3} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])/((g + h*x)*(i + j*x)^3),x]","\frac{b h^2 p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{(h i-g j)^3}-\frac{b h^2 p q \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right)}{(h i-g j)^3}+\frac{h^2 \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(h i-g j)^3}-\frac{h^2 \log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(h i-g j)^3}+\frac{h \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(i+j x) (h i-g j)^2}+\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{2 (i+j x)^2 (h i-g j)}-\frac{b f^2 p q \log (e+f x)}{2 (f i-e j)^2 (h i-g j)}+\frac{b f^2 p q \log (i+j x)}{2 (f i-e j)^2 (h i-g j)}-\frac{b f p q}{2 (i+j x) (f i-e j) (h i-g j)}-\frac{b f h p q \log (e+f x)}{(f i-e j) (h i-g j)^2}+\frac{b f h p q \log (i+j x)}{(f i-e j) (h i-g j)^2}","\frac{b h^2 p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right)}{(h i-g j)^3}-\frac{b h^2 p q \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right)}{(h i-g j)^3}+\frac{h^2 \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(h i-g j)^3}-\frac{h^2 \log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(h i-g j)^3}+\frac{h \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(i+j x) (h i-g j)^2}+\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{2 (i+j x)^2 (h i-g j)}-\frac{b f^2 p q \log (e+f x)}{2 (f i-e j)^2 (h i-g j)}+\frac{b f^2 p q \log (i+j x)}{2 (f i-e j)^2 (h i-g j)}-\frac{b f p q}{2 (i+j x) (f i-e j) (h i-g j)}-\frac{b f h p q \log (e+f x)}{(f i-e j) (h i-g j)^2}+\frac{b f h p q \log (i+j x)}{(f i-e j) (h i-g j)^2}",1,"-(b*f*p*q)/(2*(f*i - e*j)*(h*i - g*j)*(i + j*x)) - (b*f*h*p*q*Log[e + f*x])/((f*i - e*j)*(h*i - g*j)^2) - (b*f^2*p*q*Log[e + f*x])/(2*(f*i - e*j)^2*(h*i - g*j)) + (a + b*Log[c*(d*(e + f*x)^p)^q])/(2*(h*i - g*j)*(i + j*x)^2) + (h*(a + b*Log[c*(d*(e + f*x)^p)^q]))/((h*i - g*j)^2*(i + j*x)) + (h^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(g + h*x))/(f*g - e*h)])/(h*i - g*j)^3 + (b*f*h*p*q*Log[i + j*x])/((f*i - e*j)*(h*i - g*j)^2) + (b*f^2*p*q*Log[i + j*x])/(2*(f*i - e*j)^2*(h*i - g*j)) - (h^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(i + j*x))/(f*i - e*j)])/(h*i - g*j)^3 + (b*h^2*p*q*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/(h*i - g*j)^3 - (b*h^2*p*q*PolyLog[2, -((j*(e + f*x))/(f*i - e*j))])/(h*i - g*j)^3","A",16,9,33,0.2727,1,"{2418, 2394, 2393, 2391, 2395, 44, 36, 31, 2445}"
530,1,519,0,1.3437062,"\int \frac{(i+j x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{g+h x} \, dx","Int[((i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(g + h*x),x]","\frac{2 b p q (h i-g j)^2 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h^3}-\frac{2 b^2 p^2 q^2 (h i-g j)^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right)}{h^3}+\frac{j (e+f x) (f i-e j) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f^2 h}-\frac{b j^2 p q (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 f^2 h}+\frac{j^2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{2 f^2 h}+\frac{j (e+f x) (h i-g j) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f h^2}+\frac{(h i-g j)^2 \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h^3}-\frac{2 a b j p q x (f i-e j)}{f h}-\frac{2 a b j p q x (h i-g j)}{h^2}-\frac{2 b^2 j p q (e+f x) (f i-e j) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f^2 h}-\frac{2 b^2 j p q (e+f x) (h i-g j) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f h^2}+\frac{b^2 j^2 p^2 q^2 (e+f x)^2}{4 f^2 h}+\frac{2 b^2 j p^2 q^2 x (f i-e j)}{f h}+\frac{2 b^2 j p^2 q^2 x (h i-g j)}{h^2}","\frac{2 b p q (h i-g j)^2 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h^3}-\frac{2 b^2 p^2 q^2 (h i-g j)^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right)}{h^3}+\frac{j (e+f x) (f i-e j) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f^2 h}-\frac{b j^2 p q (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{2 f^2 h}+\frac{j^2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{2 f^2 h}+\frac{j (e+f x) (h i-g j) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f h^2}+\frac{(h i-g j)^2 \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h^3}-\frac{2 a b j p q x (f i-e j)}{f h}-\frac{2 a b j p q x (h i-g j)}{h^2}-\frac{2 b^2 j p q (e+f x) (f i-e j) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f^2 h}-\frac{2 b^2 j p q (e+f x) (h i-g j) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f h^2}+\frac{b^2 j^2 p^2 q^2 (e+f x)^2}{4 f^2 h}+\frac{2 b^2 j p^2 q^2 x (f i-e j)}{f h}+\frac{2 b^2 j p^2 q^2 x (h i-g j)}{h^2}",1,"(-2*a*b*j*(f*i - e*j)*p*q*x)/(f*h) - (2*a*b*j*(h*i - g*j)*p*q*x)/h^2 + (2*b^2*j*(f*i - e*j)*p^2*q^2*x)/(f*h) + (2*b^2*j*(h*i - g*j)*p^2*q^2*x)/h^2 + (b^2*j^2*p^2*q^2*(e + f*x)^2)/(4*f^2*h) - (2*b^2*j*(f*i - e*j)*p*q*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/(f^2*h) - (2*b^2*j*(h*i - g*j)*p*q*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/(f*h^2) - (b*j^2*p*q*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(2*f^2*h) + (j*(f*i - e*j)*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(f^2*h) + (j*(h*i - g*j)*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(f*h^2) + (j^2*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(2*f^2*h) + ((h*i - g*j)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*Log[(f*(g + h*x))/(f*g - e*h)])/h^3 + (2*b*(h*i - g*j)^2*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/h^3 - (2*b^2*(h*i - g*j)^2*p^2*q^2*PolyLog[3, -((h*(e + f*x))/(f*g - e*h))])/h^3","A",20,13,35,0.3714,1,"{2418, 2389, 2296, 2295, 2396, 2433, 2374, 6589, 2401, 2390, 2305, 2304, 2445}"
531,1,240,0,0.6471816,"\int \frac{(i+j x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{g+h x} \, dx","Int[((i + j*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(g + h*x),x]","\frac{2 b p q (h i-g j) \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h^2}-\frac{2 b^2 p^2 q^2 (h i-g j) \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right)}{h^2}+\frac{(h i-g j) \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h^2}+\frac{j (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f h}-\frac{2 a b j p q x}{h}-\frac{2 b^2 j p q (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f h}+\frac{2 b^2 j p^2 q^2 x}{h}","\frac{2 b p q (h i-g j) \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h^2}-\frac{2 b^2 p^2 q^2 (h i-g j) \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right)}{h^2}+\frac{(h i-g j) \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h^2}+\frac{j (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f h}-\frac{2 a b j p q x}{h}-\frac{2 b^2 j p q (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f h}+\frac{2 b^2 j p^2 q^2 x}{h}",1,"(-2*a*b*j*p*q*x)/h + (2*b^2*j*p^2*q^2*x)/h - (2*b^2*j*p*q*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/(f*h) + (j*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(f*h) + ((h*i - g*j)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*Log[(f*(g + h*x))/(f*g - e*h)])/h^2 + (2*b*(h*i - g*j)*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/h^2 - (2*b^2*(h*i - g*j)*p^2*q^2*PolyLog[3, -((h*(e + f*x))/(f*g - e*h))])/h^2","A",11,9,33,0.2727,1,"{2418, 2389, 2296, 2295, 2396, 2433, 2374, 6589, 2445}"
532,1,123,0,0.2751492,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{g+h x} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/(g + h*x),x]","\frac{2 b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}-\frac{2 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right)}{h}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h}","\frac{2 b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}-\frac{2 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right)}{h}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h}",1,"((a + b*Log[c*(d*(e + f*x)^p)^q])^2*Log[(f*(g + h*x))/(f*g - e*h)])/h + (2*b*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/h - (2*b^2*p^2*q^2*PolyLog[3, -((h*(e + f*x))/(f*g - e*h))])/h","A",5,5,28,0.1786,1,"{2396, 2433, 2374, 6589, 2445}"
533,1,288,0,0.8988046,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(g+h x) (i+j x)} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/((g + h*x)*(i + j*x)),x]","\frac{2 b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h i-g j}-\frac{2 b p q \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h i-g j}-\frac{2 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right)}{h i-g j}+\frac{2 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{j (e+f x)}{f i-e j}\right)}{h i-g j}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h i-g j}-\frac{\log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h i-g j}","\frac{2 b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h i-g j}-\frac{2 b p q \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h i-g j}-\frac{2 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right)}{h i-g j}+\frac{2 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{j (e+f x)}{f i-e j}\right)}{h i-g j}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h i-g j}-\frac{\log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h i-g j}",1,"((a + b*Log[c*(d*(e + f*x)^p)^q])^2*Log[(f*(g + h*x))/(f*g - e*h)])/(h*i - g*j) - ((a + b*Log[c*(d*(e + f*x)^p)^q])^2*Log[(f*(i + j*x))/(f*i - e*j)])/(h*i - g*j) + (2*b*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/(h*i - g*j) - (2*b*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[2, -((j*(e + f*x))/(f*i - e*j))])/(h*i - g*j) - (2*b^2*p^2*q^2*PolyLog[3, -((h*(e + f*x))/(f*g - e*h))])/(h*i - g*j) + (2*b^2*p^2*q^2*PolyLog[3, -((j*(e + f*x))/(f*i - e*j))])/(h*i - g*j)","A",11,6,35,0.1714,1,"{2418, 2396, 2433, 2374, 6589, 2445}"
534,1,463,0,1.1828655,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(g+h x) (i+j x)^2} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/((g + h*x)*(i + j*x)^2),x]","\frac{2 b h p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(h i-g j)^2}-\frac{2 b h p q \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(h i-g j)^2}+\frac{2 b^2 f p^2 q^2 \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right)}{(f i-e j) (h i-g j)}-\frac{2 b^2 h p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right)}{(h i-g j)^2}+\frac{2 b^2 h p^2 q^2 \text{PolyLog}\left(3,-\frac{j (e+f x)}{f i-e j}\right)}{(h i-g j)^2}+\frac{2 b f p q \log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(f i-e j) (h i-g j)}-\frac{j (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(i+j x) (f i-e j) (h i-g j)}+\frac{h \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(h i-g j)^2}-\frac{h \log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(h i-g j)^2}","\frac{2 b h p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(h i-g j)^2}-\frac{2 b h p q \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(h i-g j)^2}+\frac{2 b^2 f p^2 q^2 \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right)}{(f i-e j) (h i-g j)}-\frac{2 b^2 h p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right)}{(h i-g j)^2}+\frac{2 b^2 h p^2 q^2 \text{PolyLog}\left(3,-\frac{j (e+f x)}{f i-e j}\right)}{(h i-g j)^2}+\frac{2 b f p q \log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(f i-e j) (h i-g j)}-\frac{j (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(i+j x) (f i-e j) (h i-g j)}+\frac{h \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(h i-g j)^2}-\frac{h \log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(h i-g j)^2}",1,"-((j*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/((f*i - e*j)*(h*i - g*j)*(i + j*x))) + (h*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*Log[(f*(g + h*x))/(f*g - e*h)])/(h*i - g*j)^2 + (2*b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(i + j*x))/(f*i - e*j)])/((f*i - e*j)*(h*i - g*j)) - (h*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*Log[(f*(i + j*x))/(f*i - e*j)])/(h*i - g*j)^2 + (2*b*h*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/(h*i - g*j)^2 + (2*b^2*f*p^2*q^2*PolyLog[2, -((j*(e + f*x))/(f*i - e*j))])/((f*i - e*j)*(h*i - g*j)) - (2*b*h*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[2, -((j*(e + f*x))/(f*i - e*j))])/(h*i - g*j)^2 - (2*b^2*h*p^2*q^2*PolyLog[3, -((h*(e + f*x))/(f*g - e*h))])/(h*i - g*j)^2 + (2*b^2*h*p^2*q^2*PolyLog[3, -((j*(e + f*x))/(f*i - e*j))])/(h*i - g*j)^2","A",15,10,35,0.2857,1,"{2418, 2396, 2433, 2374, 6589, 2397, 2394, 2393, 2391, 2445}"
535,1,742,0,1.8312445,"\int \frac{(i+j x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{g+h x} \, dx","Int[((i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/(g + h*x),x]","-\frac{6 b^2 p^2 q^2 (h i-g j)^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h^3}+\frac{3 b p q (h i-g j)^2 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h^3}+\frac{6 b^3 p^3 q^3 (h i-g j)^2 \text{PolyLog}\left(4,-\frac{h (e+f x)}{f g-e h}\right)}{h^3}+\frac{3 b^2 j^2 p^2 q^2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{4 f^2 h}+\frac{6 a b^2 j p^2 q^2 x (f i-e j)}{f h}+\frac{6 a b^2 j p^2 q^2 x (h i-g j)}{h^2}-\frac{3 b j p q (e+f x) (f i-e j) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f^2 h}+\frac{j (e+f x) (f i-e j) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{f^2 h}-\frac{3 b j^2 p q (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{4 f^2 h}+\frac{j^2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{2 f^2 h}-\frac{3 b j p q (e+f x) (h i-g j) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f h^2}+\frac{j (e+f x) (h i-g j) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{f h^2}+\frac{(h i-g j)^2 \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{h^3}+\frac{6 b^3 j p^2 q^2 (e+f x) (f i-e j) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f^2 h}+\frac{6 b^3 j p^2 q^2 (e+f x) (h i-g j) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f h^2}-\frac{3 b^3 j^2 p^3 q^3 (e+f x)^2}{8 f^2 h}-\frac{6 b^3 j p^3 q^3 x (f i-e j)}{f h}-\frac{6 b^3 j p^3 q^3 x (h i-g j)}{h^2}","-\frac{6 b^2 p^2 q^2 (h i-g j)^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h^3}+\frac{3 b p q (h i-g j)^2 \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h^3}+\frac{6 b^3 p^3 q^3 (h i-g j)^2 \text{PolyLog}\left(4,-\frac{h (e+f x)}{f g-e h}\right)}{h^3}+\frac{3 b^2 j^2 p^2 q^2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{4 f^2 h}+\frac{6 a b^2 j p^2 q^2 x (f i-e j)}{f h}+\frac{6 a b^2 j p^2 q^2 x (h i-g j)}{h^2}-\frac{3 b j p q (e+f x) (f i-e j) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f^2 h}+\frac{j (e+f x) (f i-e j) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{f^2 h}-\frac{3 b j^2 p q (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{4 f^2 h}+\frac{j^2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{2 f^2 h}-\frac{3 b j p q (e+f x) (h i-g j) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f h^2}+\frac{j (e+f x) (h i-g j) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{f h^2}+\frac{(h i-g j)^2 \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{h^3}+\frac{6 b^3 j p^2 q^2 (e+f x) (f i-e j) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f^2 h}+\frac{6 b^3 j p^2 q^2 (e+f x) (h i-g j) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f h^2}-\frac{3 b^3 j^2 p^3 q^3 (e+f x)^2}{8 f^2 h}-\frac{6 b^3 j p^3 q^3 x (f i-e j)}{f h}-\frac{6 b^3 j p^3 q^3 x (h i-g j)}{h^2}",1,"(6*a*b^2*j*(f*i - e*j)*p^2*q^2*x)/(f*h) + (6*a*b^2*j*(h*i - g*j)*p^2*q^2*x)/h^2 - (6*b^3*j*(f*i - e*j)*p^3*q^3*x)/(f*h) - (6*b^3*j*(h*i - g*j)*p^3*q^3*x)/h^2 - (3*b^3*j^2*p^3*q^3*(e + f*x)^2)/(8*f^2*h) + (6*b^3*j*(f*i - e*j)*p^2*q^2*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/(f^2*h) + (6*b^3*j*(h*i - g*j)*p^2*q^2*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/(f*h^2) + (3*b^2*j^2*p^2*q^2*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(4*f^2*h) - (3*b*j*(f*i - e*j)*p*q*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(f^2*h) - (3*b*j*(h*i - g*j)*p*q*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(f*h^2) - (3*b*j^2*p*q*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(4*f^2*h) + (j*(f*i - e*j)*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/(f^2*h) + (j*(h*i - g*j)*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/(f*h^2) + (j^2*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/(2*f^2*h) + ((h*i - g*j)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^3*Log[(f*(g + h*x))/(f*g - e*h)])/h^3 + (3*b*(h*i - g*j)^2*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/h^3 - (6*b^2*(h*i - g*j)^2*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[3, -((h*(e + f*x))/(f*g - e*h))])/h^3 + (6*b^3*(h*i - g*j)^2*p^3*q^3*PolyLog[4, -((h*(e + f*x))/(f*g - e*h))])/h^3","A",24,14,35,0.4000,1,"{2418, 2389, 2296, 2295, 2396, 2433, 2374, 2383, 6589, 2401, 2390, 2305, 2304, 2445}"
536,1,349,0,0.8933406,"\int \frac{(i+j x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{g+h x} \, dx","Int[((i + j*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/(g + h*x),x]","-\frac{6 b^2 p^2 q^2 (h i-g j) \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h^2}+\frac{3 b p q (h i-g j) \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h^2}+\frac{6 b^3 p^3 q^3 (h i-g j) \text{PolyLog}\left(4,-\frac{h (e+f x)}{f g-e h}\right)}{h^2}+\frac{6 a b^2 j p^2 q^2 x}{h}+\frac{(h i-g j) \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{h^2}-\frac{3 b j p q (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f h}+\frac{j (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{f h}+\frac{6 b^3 j p^2 q^2 (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f h}-\frac{6 b^3 j p^3 q^3 x}{h}","-\frac{6 b^2 p^2 q^2 (h i-g j) \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h^2}+\frac{3 b p q (h i-g j) \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h^2}+\frac{6 b^3 p^3 q^3 (h i-g j) \text{PolyLog}\left(4,-\frac{h (e+f x)}{f g-e h}\right)}{h^2}+\frac{6 a b^2 j p^2 q^2 x}{h}+\frac{(h i-g j) \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{h^2}-\frac{3 b j p q (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{f h}+\frac{j (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{f h}+\frac{6 b^3 j p^2 q^2 (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f h}-\frac{6 b^3 j p^3 q^3 x}{h}",1,"(6*a*b^2*j*p^2*q^2*x)/h - (6*b^3*j*p^3*q^3*x)/h + (6*b^3*j*p^2*q^2*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/(f*h) - (3*b*j*p*q*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(f*h) + (j*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/(f*h) + ((h*i - g*j)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3*Log[(f*(g + h*x))/(f*g - e*h)])/h^2 + (3*b*(h*i - g*j)*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/h^2 - (6*b^2*(h*i - g*j)*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[3, -((h*(e + f*x))/(f*g - e*h))])/h^2 + (6*b^3*(h*i - g*j)*p^3*q^3*PolyLog[4, -((h*(e + f*x))/(f*g - e*h))])/h^2","A",13,10,33,0.3030,1,"{2418, 2389, 2296, 2295, 2396, 2433, 2374, 2383, 6589, 2445}"
537,1,177,0,0.4267364,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{g+h x} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^3/(g + h*x),x]","-\frac{6 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}+\frac{3 b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h}+\frac{6 b^3 p^3 q^3 \text{PolyLog}\left(4,-\frac{h (e+f x)}{f g-e h}\right)}{h}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{h}","-\frac{6 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}+\frac{3 b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h}+\frac{6 b^3 p^3 q^3 \text{PolyLog}\left(4,-\frac{h (e+f x)}{f g-e h}\right)}{h}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{h}",1,"((a + b*Log[c*(d*(e + f*x)^p)^q])^3*Log[(f*(g + h*x))/(f*g - e*h)])/h + (3*b*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/h - (6*b^2*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[3, -((h*(e + f*x))/(f*g - e*h))])/h + (6*b^3*p^3*q^3*PolyLog[4, -((h*(e + f*x))/(f*g - e*h))])/h","A",6,6,28,0.2143,1,"{2396, 2433, 2374, 2383, 6589, 2445}"
538,1,410,0,1.2576474,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{(g+h x) (i+j x)} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^3/((g + h*x)*(i + j*x)),x]","-\frac{6 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h i-g j}+\frac{6 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{j (e+f x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h i-g j}+\frac{3 b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h i-g j}-\frac{3 b p q \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h i-g j}+\frac{6 b^3 p^3 q^3 \text{PolyLog}\left(4,-\frac{h (e+f x)}{f g-e h}\right)}{h i-g j}-\frac{6 b^3 p^3 q^3 \text{PolyLog}\left(4,-\frac{j (e+f x)}{f i-e j}\right)}{h i-g j}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{h i-g j}-\frac{\log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{h i-g j}","-\frac{6 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h i-g j}+\frac{6 b^2 p^2 q^2 \text{PolyLog}\left(3,-\frac{j (e+f x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h i-g j}+\frac{3 b p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h i-g j}-\frac{3 b p q \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{h i-g j}+\frac{6 b^3 p^3 q^3 \text{PolyLog}\left(4,-\frac{h (e+f x)}{f g-e h}\right)}{h i-g j}-\frac{6 b^3 p^3 q^3 \text{PolyLog}\left(4,-\frac{j (e+f x)}{f i-e j}\right)}{h i-g j}+\frac{\log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{h i-g j}-\frac{\log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{h i-g j}",1,"((a + b*Log[c*(d*(e + f*x)^p)^q])^3*Log[(f*(g + h*x))/(f*g - e*h)])/(h*i - g*j) - ((a + b*Log[c*(d*(e + f*x)^p)^q])^3*Log[(f*(i + j*x))/(f*i - e*j)])/(h*i - g*j) + (3*b*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/(h*i - g*j) - (3*b*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*PolyLog[2, -((j*(e + f*x))/(f*i - e*j))])/(h*i - g*j) - (6*b^2*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[3, -((h*(e + f*x))/(f*g - e*h))])/(h*i - g*j) + (6*b^2*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[3, -((j*(e + f*x))/(f*i - e*j))])/(h*i - g*j) + (6*b^3*p^3*q^3*PolyLog[4, -((h*(e + f*x))/(f*g - e*h))])/(h*i - g*j) - (6*b^3*p^3*q^3*PolyLog[4, -((j*(e + f*x))/(f*i - e*j))])/(h*i - g*j)","A",13,7,35,0.2000,1,"{2418, 2396, 2433, 2374, 2383, 6589, 2445}"
539,1,659,0,1.7156614,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{(g+h x) (i+j x)^2} \, dx","Int[(a + b*Log[c*(d*(e + f*x)^p)^q])^3/((g + h*x)*(i + j*x)^2),x]","\frac{6 b^2 f p^2 q^2 \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(f i-e j) (h i-g j)}-\frac{6 b^2 h p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(h i-g j)^2}+\frac{6 b^2 h p^2 q^2 \text{PolyLog}\left(3,-\frac{j (e+f x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(h i-g j)^2}+\frac{3 b h p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(h i-g j)^2}-\frac{3 b h p q \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(h i-g j)^2}-\frac{6 b^3 f p^3 q^3 \text{PolyLog}\left(3,-\frac{j (e+f x)}{f i-e j}\right)}{(f i-e j) (h i-g j)}+\frac{6 b^3 h p^3 q^3 \text{PolyLog}\left(4,-\frac{h (e+f x)}{f g-e h}\right)}{(h i-g j)^2}-\frac{6 b^3 h p^3 q^3 \text{PolyLog}\left(4,-\frac{j (e+f x)}{f i-e j}\right)}{(h i-g j)^2}+\frac{3 b f p q \log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(f i-e j) (h i-g j)}-\frac{j (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{(i+j x) (f i-e j) (h i-g j)}+\frac{h \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{(h i-g j)^2}-\frac{h \log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{(h i-g j)^2}","\frac{6 b^2 f p^2 q^2 \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(f i-e j) (h i-g j)}-\frac{6 b^2 h p^2 q^2 \text{PolyLog}\left(3,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(h i-g j)^2}+\frac{6 b^2 h p^2 q^2 \text{PolyLog}\left(3,-\frac{j (e+f x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{(h i-g j)^2}+\frac{3 b h p q \text{PolyLog}\left(2,-\frac{h (e+f x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(h i-g j)^2}-\frac{3 b h p q \text{PolyLog}\left(2,-\frac{j (e+f x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(h i-g j)^2}-\frac{6 b^3 f p^3 q^3 \text{PolyLog}\left(3,-\frac{j (e+f x)}{f i-e j}\right)}{(f i-e j) (h i-g j)}+\frac{6 b^3 h p^3 q^3 \text{PolyLog}\left(4,-\frac{h (e+f x)}{f g-e h}\right)}{(h i-g j)^2}-\frac{6 b^3 h p^3 q^3 \text{PolyLog}\left(4,-\frac{j (e+f x)}{f i-e j}\right)}{(h i-g j)^2}+\frac{3 b f p q \log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(f i-e j) (h i-g j)}-\frac{j (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{(i+j x) (f i-e j) (h i-g j)}+\frac{h \log \left(\frac{f (g+h x)}{f g-e h}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{(h i-g j)^2}-\frac{h \log \left(\frac{f (i+j x)}{f i-e j}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{(h i-g j)^2}",1,"-((j*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/((f*i - e*j)*(h*i - g*j)*(i + j*x))) + (h*(a + b*Log[c*(d*(e + f*x)^p)^q])^3*Log[(f*(g + h*x))/(f*g - e*h)])/(h*i - g*j)^2 + (3*b*f*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*Log[(f*(i + j*x))/(f*i - e*j)])/((f*i - e*j)*(h*i - g*j)) - (h*(a + b*Log[c*(d*(e + f*x)^p)^q])^3*Log[(f*(i + j*x))/(f*i - e*j)])/(h*i - g*j)^2 + (3*b*h*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*PolyLog[2, -((h*(e + f*x))/(f*g - e*h))])/(h*i - g*j)^2 + (6*b^2*f*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[2, -((j*(e + f*x))/(f*i - e*j))])/((f*i - e*j)*(h*i - g*j)) - (3*b*h*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*PolyLog[2, -((j*(e + f*x))/(f*i - e*j))])/(h*i - g*j)^2 - (6*b^2*h*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[3, -((h*(e + f*x))/(f*g - e*h))])/(h*i - g*j)^2 - (6*b^3*f*p^3*q^3*PolyLog[3, -((j*(e + f*x))/(f*i - e*j))])/((f*i - e*j)*(h*i - g*j)) + (6*b^2*h*p^2*q^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[3, -((j*(e + f*x))/(f*i - e*j))])/(h*i - g*j)^2 + (6*b^3*h*p^3*q^3*PolyLog[4, -((h*(e + f*x))/(f*g - e*h))])/(h*i - g*j)^2 - (6*b^3*h*p^3*q^3*PolyLog[4, -((j*(e + f*x))/(f*i - e*j))])/(h*i - g*j)^2","A",18,8,35,0.2286,1,"{2418, 2396, 2433, 2374, 2383, 6589, 2397, 2445}"
540,0,0,0,0.2598178,"\int \frac{i+j x}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","Int[(i + j*x)/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])),x]","\int \frac{i+j x}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","\text{Int}\left(\frac{i+j x}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)},x\right)",0,"Defer[Int][(i + j*x)/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])), x]","A",0,0,0,0,-1,"{}"
541,0,0,0,0.0706707,"\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","Int[1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])),x]","\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","\text{Int}\left(\frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)},x\right)",0,"Defer[Int][1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])), x]","A",0,0,0,0,-1,"{}"
542,0,0,0,0.3020492,"\int \frac{1}{(g+h x) (i+j x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","Int[1/((g + h*x)*(i + j*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])),x]","\int \frac{1}{(g+h x) (i+j x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","\text{Int}\left(\frac{1}{(g+h x) (i+j x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)},x\right)",0,"Defer[Int][1/((g + h*x)*(i + j*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])), x]","A",0,0,0,0,-1,"{}"
543,0,0,0,0.3405096,"\int \frac{1}{(g+h x) (i+j x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","Int[1/((g + h*x)*(i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])),x]","\int \frac{1}{(g+h x) (i+j x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","\text{Int}\left(\frac{1}{(g+h x) (i+j x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)},x\right)",0,"Defer[Int][1/((g + h*x)*(i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])), x]","A",0,0,0,0,-1,"{}"
544,0,0,0,0.2989961,"\int \frac{i+j x}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","Int[(i + j*x)/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2),x]","\int \frac{i+j x}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","\text{Int}\left(\frac{i+j x}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2},x\right)",0,"Defer[Int][(i + j*x)/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2), x]","A",0,0,0,0,-1,"{}"
545,0,0,0,0.0670413,"\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","Int[1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2),x]","\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2},x\right)",0,"Defer[Int][1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2), x]","A",0,0,0,0,-1,"{}"
546,0,0,0,0.2941827,"\int \frac{1}{(g+h x) (i+j x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","Int[1/((g + h*x)*(i + j*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2),x]","\int \frac{1}{(g+h x) (i+j x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(g+h x) (i+j x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2},x\right)",0,"Defer[Int][1/((g + h*x)*(i + j*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2), x]","A",0,0,0,0,-1,"{}"
547,0,0,0,0.3347123,"\int \frac{1}{(g+h x) (i+j x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","Int[1/((g + h*x)*(i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2),x]","\int \frac{1}{(g+h x) (i+j x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(g+h x) (i+j x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2},x\right)",0,"Defer[Int][1/((g + h*x)*(i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2), x]","A",0,0,0,0,-1,"{}"