1,1,74,81,0.0082692,"\int \log ^4(c (d+e x)) \, dx","Integrate[Log[c*(d + e*x)]^4,x]","\frac{(d+e x) \log ^4(c (d+e x))-4 (d+e x) \log ^3(c (d+e x))+12 (d+e x) \log ^2(c (d+e x))-24 (d+e x) \log (c (d+e x))+24 e x}{e}","\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*e*x - 24*(d + e*x)*Log[c*(d + e*x)] + 12*(d + e*x)*Log[c*(d + e*x)]^2 - 4*(d + e*x)*Log[c*(d + e*x)]^3 + (d + e*x)*Log[c*(d + e*x)]^4)/e","A",1
2,1,57,61,0.0060087,"\int \log ^3(c (d+e x)) \, dx","Integrate[Log[c*(d + e*x)]^3,x]","\frac{(d+e x) \log ^3(c (d+e x))-3 (d+e x) \log ^2(c (d+e x))+6 (d+e x) \log (c (d+e x))-6 e x}{e}","\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*e*x + 6*(d + e*x)*Log[c*(d + e*x)] - 3*(d + e*x)*Log[c*(d + e*x)]^2 + (d + e*x)*Log[c*(d + e*x)]^3)/e","A",1
3,1,40,41,0.0046907,"\int \log ^2(c (d+e x)) \, dx","Integrate[Log[c*(d + e*x)]^2,x]","\frac{(d+e x) \log ^2(c (d+e x))-2 (d+e x) \log (c (d+e x))+2 e x}{e}","\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*e*x - 2*(d + e*x)*Log[c*(d + e*x)] + (d + e*x)*Log[c*(d + e*x)]^2)/e","A",1
4,1,21,21,0.0046593,"\int \log (c (d+e x)) \, dx","Integrate[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",1
5,1,15,15,0.0085762,"\int \frac{1}{\log (c (d+e x))} \, dx","Integrate[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",1
6,1,36,36,0.0147201,"\int \frac{1}{\log ^2(c (d+e x))} \, dx","Integrate[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",1
7,1,47,63,0.0162928,"\int \frac{1}{\log ^3(c (d+e x))} \, dx","Integrate[Log[c*(d + e*x)]^(-3),x]","\frac{\frac{\text{li}(c (d+e x))}{c}-\frac{(d+e x) (\log (c (d+e x))+1)}{\log ^2(c (d+e x))}}{2 e}","\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)*(1 + Log[c*(d + e*x)]))/Log[c*(d + e*x)]^2) + LogIntegral[c*(d + e*x)]/c)/(2*e)","A",1
8,1,57,85,0.0193543,"\int \frac{1}{\log ^4(c (d+e x))} \, dx","Integrate[Log[c*(d + e*x)]^(-4),x]","\frac{\frac{\text{li}(c (d+e x))}{c}-\frac{(d+e x) \left(\log ^2(c (d+e x))+\log (c (d+e x))+2\right)}{\log ^3(c (d+e x))}}{6 e}","\frac{\text{li}(c (d+e x))}{6 c e}-\frac{d+e x}{3 e \log ^3(c (d+e x))}-\frac{d+e x}{6 e \log ^2(c (d+e x))}-\frac{d+e x}{6 e \log (c (d+e x))}",1,"(-(((d + e*x)*(2 + Log[c*(d + e*x)] + Log[c*(d + e*x)]^2))/Log[c*(d + e*x)]^3) + LogIntegral[c*(d + e*x)]/c)/(6*e)","A",1
9,1,75,98,0.0131124,"\int \log ^{\frac{5}{2}}(c (d+e x)) \, dx","Integrate[Log[c*(d + e*x)]^(5/2),x]","\frac{2 c (d+e x) \sqrt{\log (c (d+e x))} \left(4 \log ^2(c (d+e x))-10 \log (c (d+e x))+15\right)-15 \sqrt{\pi } \text{erfi}\left(\sqrt{\log (c (d+e x))}\right)}{8 c 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)]]] + 2*c*(d + e*x)*Sqrt[Log[c*(d + e*x)]]*(15 - 10*Log[c*(d + e*x)] + 4*Log[c*(d + e*x)]^2))/(8*c*e)","A",1
10,1,63,74,0.0102153,"\int \log ^{\frac{3}{2}}(c (d+e x)) \, dx","Integrate[Log[c*(d + e*x)]^(3/2),x]","\frac{3 \sqrt{\pi } \text{erfi}\left(\sqrt{\log (c (d+e x))}\right)+2 c (d+e x) \sqrt{\log (c (d+e x))} (2 \log (c (d+e x))-3)}{4 c 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)]]] + 2*c*(d + e*x)*Sqrt[Log[c*(d + e*x)]]*(-3 + 2*Log[c*(d + e*x)]))/(4*c*e)","A",1
11,1,50,50,0.0088441,"\int \sqrt{\log (c (d+e x))} \, dx","Integrate[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,"-1/2*(Sqrt[Pi]*Erfi[Sqrt[Log[c*(d + e*x)]]])/(c*e) + ((d + e*x)*Sqrt[Log[c*(d + e*x)]])/e","A",1
12,1,25,25,0.0021075,"\int \frac{1}{\sqrt{\log (c (d+e x))}} \, dx","Integrate[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",1
13,1,58,49,0.0246446,"\int \frac{1}{\log ^{\frac{3}{2}}(c (d+e x))} \, dx","Integrate[Log[c*(d + e*x)]^(-3/2),x]","\frac{2 \sqrt{-\log (c (d+e x))} \Gamma \left(\frac{1}{2},-\log (c (d+e x))\right)-2 c (d+e x)}{c 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*c*(d + e*x) + 2*Gamma[1/2, -Log[c*(d + e*x)]]*Sqrt[-Log[c*(d + e*x)]])/(c*e*Sqrt[Log[c*(d + e*x)]])","A",1
14,1,72,77,0.0286307,"\int \frac{1}{\log ^{\frac{5}{2}}(c (d+e x))} \, dx","Integrate[Log[c*(d + e*x)]^(-5/2),x]","-\frac{2 \left(c (d+e x) (2 \log (c (d+e x))+1)+2 (-\log (c (d+e x)))^{3/2} \Gamma \left(\frac{1}{2},-\log (c (d+e x))\right)\right)}{3 c e \log ^{\frac{3}{2}}(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,"(-2*(2*Gamma[1/2, -Log[c*(d + e*x)]]*(-Log[c*(d + e*x)])^(3/2) + c*(d + e*x)*(1 + 2*Log[c*(d + e*x)])))/(3*c*e*Log[c*(d + e*x)]^(3/2))","A",1
15,1,85,101,0.0359026,"\int \frac{1}{\log ^{\frac{7}{2}}(c (d+e x))} \, dx","Integrate[Log[c*(d + e*x)]^(-7/2),x]","\frac{8 (-\log (c (d+e x)))^{5/2} \Gamma \left(\frac{1}{2},-\log (c (d+e x))\right)-2 c (d+e x) \left(4 \log ^2(c (d+e x))+2 \log (c (d+e x))+3\right)}{15 c e \log ^{\frac{5}{2}}(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*Gamma[1/2, -Log[c*(d + e*x)]]*(-Log[c*(d + e*x)])^(5/2) - 2*c*(d + e*x)*(3 + 2*Log[c*(d + e*x)] + 4*Log[c*(d + e*x)]^2))/(15*c*e*Log[c*(d + e*x)]^(5/2))","A",1
16,1,45,45,0.016609,"\int \log ^p(c (d+e x)) \, dx","Integrate[Log[c*(d + e*x)]^p,x]","\frac{(-\log (c (d+e x)))^{-p} \log ^p(c (d+e x)) \Gamma (p+1,-\log (c (d+e x)))}{c e}","\frac{(-\log (c (d+e x)))^{-p} \log ^p(c (d+e x)) \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",1
17,1,112,131,0.0580482,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^4 \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^4,x]","\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^4-4 b n \left((d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3-3 b n \left((d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2-2 b n \left(e x (a-b n)+b (d+e x) \log \left(c (d+e x)^n\right)\right)\right)\right)}{e}","-24 a b^3 n^3 x+\frac{12 b^2 n^2 (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-\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,"((d + e*x)*(a + b*Log[c*(d + e*x)^n])^4 - 4*b*n*((d + e*x)*(a + b*Log[c*(d + e*x)^n])^3 - 3*b*n*((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2 - 2*b*n*(e*(a - b*n)*x + b*(d + e*x)*Log[c*(d + e*x)^n]))))/e","A",1
18,1,85,99,0.012125,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^3,x]","\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3-3 b n \left((d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2-2 b n \left(e x (a-b n)+b (d+e x) \log \left(c (d+e x)^n\right)\right)\right)}{e}","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,"((d + e*x)*(a + b*Log[c*(d + e*x)^n])^3 - 3*b*n*((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2 - 2*b*n*(e*(a - b*n)*x + b*(d + e*x)*Log[c*(d + e*x)^n])))/e","A",1
19,1,59,65,0.0096667,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Integrate[(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 b n \left(a x+\frac{b (d+e x) \log \left(c (d+e x)^n\right)}{e}-b n x\right)","\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,"((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e - 2*b*n*(a*x - b*n*x + (b*(d + e*x)*Log[c*(d + e*x)^n])/e)","A",1
20,1,29,29,0.0067428,"\int \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Integrate[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",1
21,1,63,63,0.0678184,"\int \frac{1}{a+b \log \left(c (d+e x)^n\right)} \, dx","Integrate[(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",1
22,1,123,96,0.0689299,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Integrate[(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} \left(b n e^{\frac{a}{b n}} \left(c (d+e x)^n\right)^{\frac{1}{n}}-\left(a+b \log \left(c (d+e x)^n\right)\right) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)\right)}{b^2 e n^2 \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)*(b*E^(a/(b*n))*n*(c*(d + e*x)^n)^n^(-1) - ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)]*(a + b*Log[c*(d + e*x)^n])))/(b^2*e*E^(a/(b*n))*n^2*(c*(d + e*x)^n)^n^(-1)*(a + b*Log[c*(d + e*x)^n])))","A",1
23,1,144,135,0.0985405,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^3} \, dx","Integrate[(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} \left(b n e^{\frac{a}{b n}} \left(c (d+e x)^n\right)^{\frac{1}{n}} \left(a+b \log \left(c (d+e x)^n\right)+b n\right)-\left(a+b \log \left(c (d+e x)^n\right)\right)^2 \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)\right)}{2 b^3 e n^3 \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,"-1/2*((d + e*x)*(-(ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)]*(a + b*Log[c*(d + e*x)^n])^2) + b*E^(a/(b*n))*n*(c*(d + e*x)^n)^n^(-1)*(a + b*n + b*Log[c*(d + e*x)^n])))/(b^3*e*E^(a/(b*n))*n^3*(c*(d + e*x)^n)^n^(-1)*(a + b*Log[c*(d + e*x)^n])^2)","A",1
24,1,152,179,0.2675589,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^(5/2),x]","\frac{(d+e x) \left(8 \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}-5 b n \left(3 \sqrt{\pi } b^{3/2} n^{3/2} e^{-\frac{a}{b n}} \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 \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(2 a+2 b \log \left(c (d+e x)^n\right)-3 b n\right)\right)\right)}{8 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,"((d + e*x)*(8*(a + b*Log[c*(d + e*x)^n])^(5/2) - 5*b*n*((3*b^(3/2)*n^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + 2*Sqrt[a + b*Log[c*(d + e*x)^n]]*(2*a - 3*b*n + 2*b*Log[c*(d + e*x)^n]))))/(8*e)","A",1
25,1,127,143,0.0735292,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^(3/2),x]","\frac{(d+e x) \left(3 \sqrt{\pi } b^{3/2} n^{3/2} e^{-\frac{a}{b n}} \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 \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(2 a+2 b \log \left(c (d+e x)^n\right)-3 b n\right)\right)}{4 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,"((d + e*x)*((3*b^(3/2)*n^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + 2*Sqrt[a + b*Log[c*(d + e*x)^n]]*(2*a - 3*b*n + 2*b*Log[c*(d + e*x)^n])))/(4*e)","A",1
26,1,106,111,0.0518431,"\int \sqrt{a+b \log \left(c (d+e x)^n\right)} \, dx","Integrate[Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\frac{(d+e x) \left(2 \sqrt{a+b \log \left(c (d+e x)^n\right)}-\sqrt{\pi } \sqrt{b} \sqrt{n} e^{-\frac{a}{b n}} \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)\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,"((d + e*x)*(-((Sqrt[b]*Sqrt[n]*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1))) + 2*Sqrt[a + b*Log[c*(d + e*x)^n]]))/(2*e)","A",1
27,1,80,80,0.0160336,"\int \frac{1}{\sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Integrate[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",1
28,1,139,116,0.1243361,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^(-3/2),x]","-\frac{2 e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \left(e^{\frac{a}{b n}} \left(c (d+e x)^n\right)^{\frac{1}{n}}-\sqrt{-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}} \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)\right)}{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*(d + e*x)*(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1) - Gamma[1/2, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*Sqrt[-((a + b*Log[c*(d + e*x)^n])/(b*n))]))/(b*e*E^(a/(b*n))*n*(c*(d + e*x)^n)^n^(-1)*Sqrt[a + b*Log[c*(d + e*x)^n]])","A",1
29,1,163,156,0.1853257,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^(-5/2),x]","-\frac{2 e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \left(e^{\frac{a}{b n}} \left(c (d+e x)^n\right)^{\frac{1}{n}} \left(2 a+2 b \log \left(c (d+e x)^n\right)+b n\right)+2 b n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)\right)}{3 b^2 e n^2 \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,"(-2*(d + e*x)*(2*b*n*Gamma[1/2, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^(3/2) + E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)*(2*a + b*n + 2*b*Log[c*(d + e*x)^n])))/(3*b^2*e*E^(a/(b*n))*n^2*(c*(d + e*x)^n)^n^(-1)*(a + b*Log[c*(d + e*x)^n])^(3/2))","A",1
30,1,203,192,0.2213577,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{7/2}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^(-7/2),x]","-\frac{2 e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \left(e^{\frac{a}{b n}} \left(c (d+e x)^n\right)^{\frac{1}{n}} \left(4 a^2+2 b (4 a+b n) \log \left(c (d+e x)^n\right)+2 a b n+4 b^2 \log ^2\left(c (d+e x)^n\right)+3 b^2 n^2\right)-4 b^2 n^2 \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{5/2} \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)\right)}{15 b^3 e n^3 \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,"(-2*(d + e*x)*(-4*b^2*n^2*Gamma[1/2, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^(5/2) + E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)*(4*a^2 + 2*a*b*n + 3*b^2*n^2 + 2*b*(4*a + b*n)*Log[c*(d + e*x)^n] + 4*b^2*Log[c*(d + e*x)^n]^2)))/(15*b^3*e*E^(a/(b*n))*n^3*(c*(d + e*x)^n)^n^(-1)*(a + b*Log[c*(d + e*x)^n])^(5/2))","A",1
31,1,103,103,0.0967437,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^p \, dx","Integrate[(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} \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} \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",1
32,1,88,88,0.05177,"\int \left(a+b \log \left(c \sqrt{d+e x}\right)\right)^p \, dx","Integrate[(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} \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} \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",1
33,1,20,20,0.028242,"\int \frac{(e+f x)^{-1+p}}{\log \left(d (e+f x)^p\right)} \, dx","Integrate[(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",1
34,1,42,42,0.0269171,"\int \frac{(e g+f g x)^{-1+p}}{\log \left(d (e+f x)^p\right)} \, dx","Integrate[(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",1
35,1,315,178,0.3123864,"\int (f+g x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Integrate[(f + g*x)^4*(a + b*Log[c*(d + e*x)^n]),x]","\frac{e x \left(60 a e^4 \left(5 f^4+10 f^3 g x+10 f^2 g^2 x^2+5 f g^3 x^3+g^4 x^4\right)-b n \left(60 d^4 g^4-30 d^3 e g^3 (10 f+g x)+10 d^2 e^2 g^2 \left(60 f^2+15 f g x+2 g^2 x^2\right)-5 d e^3 g \left(120 f^3+60 f^2 g x+20 f g^2 x^2+3 g^3 x^3\right)+e^4 \left(300 f^4+300 f^3 g x+200 f^2 g^2 x^2+75 f g^3 x^3+12 g^4 x^4\right)\right)\right)+60 b e^4 \left(5 d f^4+e x \left(5 f^4+10 f^3 g x+10 f^2 g^2 x^2+5 f g^3 x^3+g^4 x^4\right)\right) \log \left(c (d+e x)^n\right)+60 b d^2 g n \left(d^3 g^3-5 d^2 e f g^2+10 d e^2 f^2 g-10 e^3 f^3\right) \log (d+e x)}{300 e^5}","\frac{(f+g x)^5 \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 g}-\frac{b n (e f-d g)^5 \log (d+e x)}{5 e^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 (f+g x)^4 (e f-d g)}{20 e g}-\frac{b n (f+g x)^5}{25 g}",1,"(e*x*(60*a*e^4*(5*f^4 + 10*f^3*g*x + 10*f^2*g^2*x^2 + 5*f*g^3*x^3 + g^4*x^4) - b*n*(60*d^4*g^4 - 30*d^3*e*g^3*(10*f + g*x) + 10*d^2*e^2*g^2*(60*f^2 + 15*f*g*x + 2*g^2*x^2) - 5*d*e^3*g*(120*f^3 + 60*f^2*g*x + 20*f*g^2*x^2 + 3*g^3*x^3) + e^4*(300*f^4 + 300*f^3*g*x + 200*f^2*g^2*x^2 + 75*f*g^3*x^3 + 12*g^4*x^4))) + 60*b*d^2*g*(-10*e^3*f^3 + 10*d*e^2*f^2*g - 5*d^2*e*f*g^2 + d^3*g^3)*n*Log[d + e*x] + 60*b*e^4*(5*d*f^4 + e*x*(5*f^4 + 10*f^3*g*x + 10*f^2*g^2*x^2 + 5*f*g^3*x^3 + g^4*x^4))*Log[c*(d + e*x)^n])/(300*e^5)","A",1
36,1,226,149,0.2261183,"\int (f+g x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Integrate[(f + g*x)^3*(a + b*Log[c*(d + e*x)^n]),x]","\frac{e x \left(12 a e^3 \left(4 f^3+6 f^2 g x+4 f g^2 x^2+g^3 x^3\right)-b n \left(-12 d^3 g^3+6 d^2 e g^2 (8 f+g x)-4 d e^2 g \left(18 f^2+6 f g x+g^2 x^2\right)+e^3 \left(48 f^3+36 f^2 g x+16 f g^2 x^2+3 g^3 x^3\right)\right)\right)+12 b e^3 \left(4 d f^3+e x \left(4 f^3+6 f^2 g x+4 f g^2 x^2+g^3 x^3\right)\right) \log \left(c (d+e x)^n\right)-12 b d^2 g n \left(d^2 g^2-4 d e f g+6 e^2 f^2\right) \log (d+e x)}{48 e^4}","\frac{(f+g x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 g}-\frac{b n (e f-d g)^4 \log (d+e x)}{4 e^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 (f+g x)^3 (e f-d g)}{12 e g}-\frac{b n (f+g x)^4}{16 g}",1,"(e*x*(12*a*e^3*(4*f^3 + 6*f^2*g*x + 4*f*g^2*x^2 + g^3*x^3) - b*n*(-12*d^3*g^3 + 6*d^2*e*g^2*(8*f + g*x) - 4*d*e^2*g*(18*f^2 + 6*f*g*x + g^2*x^2) + e^3*(48*f^3 + 36*f^2*g*x + 16*f*g^2*x^2 + 3*g^3*x^3))) - 12*b*d^2*g*(6*e^2*f^2 - 4*d*e*f*g + d^2*g^2)*n*Log[d + e*x] + 12*b*e^3*(4*d*f^3 + e*x*(4*f^3 + 6*f^2*g*x + 4*f*g^2*x^2 + g^3*x^3))*Log[c*(d + e*x)^n])/(48*e^4)","A",1
37,1,150,120,0.1467122,"\int (f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Integrate[(f + g*x)^2*(a + b*Log[c*(d + e*x)^n]),x]","\frac{e \left(x \left(6 a e^2 \left(3 f^2+3 f g x+g^2 x^2\right)-b n \left(6 d^2 g^2-3 d e g (6 f+g x)+e^2 \left(18 f^2+9 f g x+2 g^2 x^2\right)\right)\right)+6 b e \left(3 d f^2+e x \left(3 f^2+3 f g x+g^2 x^2\right)\right) \log \left(c (d+e x)^n\right)\right)+6 b d^2 g n (d g-3 e f) \log (d+e x)}{18 e^3}","\frac{(f+g x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 g}-\frac{b n (e f-d g)^3 \log (d+e x)}{3 e^3 g}-\frac{b n x (e f-d g)^2}{3 e^2}-\frac{b n (f+g x)^2 (e f-d g)}{6 e g}-\frac{b n (f+g x)^3}{9 g}",1,"(6*b*d^2*g*(-3*e*f + d*g)*n*Log[d + e*x] + e*(x*(6*a*e^2*(3*f^2 + 3*f*g*x + g^2*x^2) - b*n*(6*d^2*g^2 - 3*d*e*g*(6*f + g*x) + e^2*(18*f^2 + 9*f*g*x + 2*g^2*x^2))) + 6*b*e*(3*d*f^2 + e*x*(3*f^2 + 3*f*g*x + g^2*x^2))*Log[c*(d + e*x)^n]))/(18*e^3)","A",1
38,1,101,91,0.0526258,"\int (f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Integrate[(f + g*x)*(a + b*Log[c*(d + e*x)^n]),x]","a f x+\frac{1}{2} a g x^2+\frac{b f (d+e x) \log \left(c (d+e x)^n\right)}{e}+\frac{1}{2} b g x^2 \log \left(c (d+e x)^n\right)-\frac{b d^2 g n \log (d+e x)}{2 e^2}+\frac{b d g n x}{2 e}-b f n x-\frac{1}{4} b g n x^2","\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,"a*f*x - b*f*n*x + (b*d*g*n*x)/(2*e) + (a*g*x^2)/2 - (b*g*n*x^2)/4 - (b*d^2*g*n*Log[d + e*x])/(2*e^2) + (b*g*x^2*Log[c*(d + e*x)^n])/2 + (b*f*(d + e*x)*Log[c*(d + e*x)^n])/e","A",1
39,1,29,29,0.0080266,"\int \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Integrate[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",1
40,1,62,63,0.0139421,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{f+g x} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(f + g*x),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}+\frac{b n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\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{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\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",1
41,1,57,74,0.0642537,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(f + g*x)^2,x]","\frac{\frac{b e n (\log (d+e x)-\log (f+g x))}{e f-d g}-\frac{a+b \log \left(c (d+e x)^n\right)}{f+g x}}{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,"(-((a + b*Log[c*(d + e*x)^n])/(f + g*x)) + (b*e*n*(Log[d + e*x] - Log[f + g*x]))/(e*f - d*g))/g","A",1
42,1,83,112,0.1130294,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x)^3} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(f + g*x)^3,x]","-\frac{a+b \log \left(c (d+e x)^n\right)-\frac{b e n (f+g x) (e (f+g x) \log (d+e x)-d g-e (f+g x) \log (f+g x)+e f)}{(e f-d g)^2}}{2 g (f+g x)^2}","-\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,"-1/2*(a + b*Log[c*(d + e*x)^n] - (b*e*n*(f + g*x)*(e*f - d*g + e*(f + g*x)*Log[d + e*x] - e*(f + g*x)*Log[f + g*x]))/(e*f - d*g)^2)/(g*(f + g*x)^2)","A",1
43,1,110,141,0.1770574,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x)^4} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(f + g*x)^4,x]","\frac{\frac{b e n (f+g x) \left(2 e^2 (f+g x)^2 \log (d+e x)+(e f-d g) (-d g+3 e f+2 e g x)-2 e^2 (f+g x)^2 \log (f+g x)\right)}{(e f-d g)^3}-2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{6 g (f+g x)^3}","-\frac{a+b \log \left(c (d+e x)^n\right)}{3 g (f+g x)^3}+\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^2 n}{3 g (f+g x) (e f-d g)^2}+\frac{b e n}{6 g (f+g x)^2 (e f-d g)}",1,"(-2*(a + b*Log[c*(d + e*x)^n]) + (b*e*n*(f + g*x)*((e*f - d*g)*(3*e*f - d*g + 2*e*g*x) + 2*e^2*(f + g*x)^2*Log[d + e*x] - 2*e^2*(f + g*x)^2*Log[f + g*x]))/(e*f - d*g)^3)/(6*g*(f + g*x)^3)","A",1
44,1,360,365,0.3022486,"\int (f+g x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Integrate[(f + g*x)^3*(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{64 b g^2 n (e f-d g) \left(b e n x \left(3 d^2+3 d e x+e^2 x^2\right)-3 (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)\right)+9 b g^3 n \left(b e n x \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)-4 (d+e x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)\right)+288 g^2 (d+e x)^3 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^2+432 g (d+e x)^2 (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2+288 (d+e x) (e f-d g)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2-576 b n (e f-d g)^3 \left(e x (a-b n)+b (d+e x) \log \left(c (d+e x)^n\right)\right)+216 b g n (e f-d g)^2 \left(b e n x (2 d+e x)-2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)\right)+72 g^3 (d+e x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{288 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{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^2 n^2 x (e f-d g)^3}{e^3}",1,"(288*(e*f - d*g)^3*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2 + 432*g*(e*f - d*g)^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2 + 288*g^2*(e*f - d*g)*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])^2 + 72*g^3*(d + e*x)^4*(a + b*Log[c*(d + e*x)^n])^2 - 576*b*(e*f - d*g)^3*n*(e*(a - b*n)*x + b*(d + e*x)*Log[c*(d + e*x)^n]) + 216*b*g*(e*f - d*g)^2*n*(b*e*n*x*(2*d + e*x) - 2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])) + 64*b*g^2*(e*f - d*g)*n*(b*e*n*x*(3*d^2 + 3*d*e*x + e^2*x^2) - 3*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])) + 9*b*g^3*n*(b*e*n*x*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3) - 4*(d + e*x)^4*(a + b*Log[c*(d + e*x)^n])))/(288*e^4)","A",1
45,1,247,287,0.157019,"\int (f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Integrate[(f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{4 b g^2 n \left(b e n x \left(3 d^2+3 d e x+e^2 x^2\right)-3 (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)\right)+54 g (d+e x)^2 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^2+54 (d+e x) (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2-108 b n (e f-d g)^2 \left(e x (a-b n)+b (d+e x) \log \left(c (d+e x)^n\right)\right)+27 b g n (e f-d g) \left(b e n x (2 d+e x)-2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)\right)+18 g^2 (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{54 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{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^2 n^2 x (e f-d g)^2}{e^2}",1,"(54*(e*f - d*g)^2*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2 + 54*g*(e*f - d*g)*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2 + 18*g^2*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])^2 - 108*b*(e*f - d*g)^2*n*(e*(a - b*n)*x + b*(d + e*x)*Log[c*(d + e*x)^n]) + 27*b*g*(e*f - d*g)*n*(b*e*n*x*(2*d + e*x) - 2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])) + 4*b*g^2*n*(b*e*n*x*(3*d^2 + 3*d*e*x + e^2*x^2) - 3*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])))/(54*e^3)","A",1
46,1,144,186,0.0791211,"\int (f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Integrate[(f + g*x)*(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{4 (d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^2-8 b n (e f-d g) \left(e x (a-b n)+b (d+e x) \log \left(c (d+e x)^n\right)\right)+2 g (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2+b g n \left(b e n x (2 d+e x)-2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)\right)}{4 e^2}","\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,"(4*(e*f - d*g)*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2 + 2*g*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2 - 8*b*(e*f - d*g)*n*(e*(a - b*n)*x + b*(d + e*x)*Log[c*(d + e*x)^n]) + b*g*n*(b*e*n*x*(2*d + e*x) - 2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])))/(4*e^2)","A",1
47,1,59,65,0.0049791,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Integrate[(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 b n \left(a x+\frac{b (d+e x) \log \left(c (d+e x)^n\right)}{e}-b n x\right)","\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,"((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e - 2*b*n*(a*x - b*n*x + (b*(d + e*x)*Log[c*(d + e*x)^n])/e)","A",1
48,1,194,111,0.1322572,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x),x]","\frac{2 b n \left(\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)+\log (f+g x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+b^2 n^2 \left(-2 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log ^2(d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)}{g}","\frac{2 b n \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\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^2 n^2 \text{Li}_3\left(-\frac{g (d+e x)}{e f-d g}\right)}{g}",1,"((a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x] + 2*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + b^2*n^2*(Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)] + 2*Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)]))/g","A",1
49,1,126,132,0.0867976,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x)^2,x]","\frac{2 b^2 e n^2 (f+g x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-\left(a+b \log \left(c (d+e x)^n\right)\right) \left(a g (d+e x)+b g (d+e x) \log \left(c (d+e x)^n\right)-2 b e n (f+g x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)}{g (f+g x) (d g-e f)}","-\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{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{g (e f-d g)}",1,"(-((a + b*Log[c*(d + e*x)^n])*(a*g*(d + e*x) + b*g*(d + e*x)*Log[c*(d + e*x)^n] - 2*b*e*n*(f + g*x)*Log[(e*(f + g*x))/(e*f - d*g)])) + 2*b^2*e*n^2*(f + g*x)*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)])/(g*(-(e*f) + d*g)*(f + g*x))","A",1
50,1,204,202,0.1991224,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x)^3} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x)^3,x]","\frac{\frac{e (f+g x) \left(2 b n (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)-2 b e n (f+g x) \log \left(\frac{e (f+g x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+e (f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2-2 b^2 e n^2 (f+g x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-2 b^2 e n^2 (f+g x) (\log (d+e x)-\log (f+g x))\right)}{(e f-d g)^2}-\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{2 g (f+g x)^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 \text{Li}_2\left(-\frac{e f-d g}{g (d+e x)}\right)}{g (e f-d g)^2}+\frac{b^2 e^2 n^2 \log (f+g x)}{g (e f-d g)^2}",1,"(-(a + b*Log[c*(d + e*x)^n])^2 + (e*(f + g*x)*(2*b*(e*f - d*g)*n*(a + b*Log[c*(d + e*x)^n]) + e*(f + g*x)*(a + b*Log[c*(d + e*x)^n])^2 - 2*b^2*e*n^2*(f + g*x)*(Log[d + e*x] - Log[f + g*x]) - 2*b*e*n*(f + g*x)*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)] - 2*b^2*e*n^2*(f + g*x)*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]))/(e*f - d*g)^2)/(2*g*(f + g*x)^2)","A",1
51,1,302,317,0.3434933,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x)^4} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x)^4,x]","\frac{\frac{e (f+g x) \left(e^2 (f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2-2 b e^2 n (f+g x)^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)+b n (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)+2 b e n (f+g x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)-2 b^2 e^2 n^2 (f+g x)^2 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-2 b^2 e^2 n^2 (f+g x)^2 (\log (d+e x)-\log (f+g x))-b^2 e n^2 (f+g x) (e (f+g x) \log (d+e x)-d g-e (f+g x) \log (f+g x)+e f)\right)}{(e f-d g)^3}-\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 g (f+g x)^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{2 b^2 e^3 n^2 \text{Li}_2\left(-\frac{e f-d g}{g (d+e x)}\right)}{3 g (e f-d g)^3}-\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{b^2 e^2 n^2}{3 g (f+g x) (e f-d g)^2}",1,"(-(a + b*Log[c*(d + e*x)^n])^2 + (e*(f + g*x)*(b*(e*f - d*g)^2*n*(a + b*Log[c*(d + e*x)^n]) + 2*b*e*(e*f - d*g)*n*(f + g*x)*(a + b*Log[c*(d + e*x)^n]) + e^2*(f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^2 - 2*b^2*e^2*n^2*(f + g*x)^2*(Log[d + e*x] - Log[f + g*x]) - b^2*e*n^2*(f + g*x)*(e*f - d*g + e*(f + g*x)*Log[d + e*x] - e*(f + g*x)*Log[f + g*x]) - 2*b*e^2*n*(f + g*x)^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)] - 2*b^2*e^2*n^2*(f + g*x)^2*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]))/(e*f - d*g)^3)/(3*g*(f + g*x)^3)","A",1
52,1,475,598,0.4253522,"\int (f+g x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \, dx","Integrate[(f + g*x)^3*(a + b*Log[c*(d + e*x)^n])^3,x]","\frac{-128 b g^2 n (e f-d g) \left(2 b n \left(b e n x \left(3 d^2+3 d e x+e^2 x^2\right)-3 (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)\right)+9 (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2\right)-27 b g^3 n \left(b n \left(b e n x \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)-4 (d+e x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)\right)+8 (d+e x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)^2\right)+1152 g^2 (d+e x)^3 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^3+1728 g (d+e x)^2 (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3+1152 (d+e x) (e f-d g)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^3-3456 b n (e f-d g)^3 \left((d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2-2 b n \left(e x (a-b n)+b (d+e x) \log \left(c (d+e x)^n\right)\right)\right)-1296 b g n (e f-d g)^2 \left(2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2+b n \left(b e n x (2 d+e x)-2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)\right)\right)+288 g^3 (d+e x)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{1152 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{3 b^3 g^3 n^3 (d+e x)^4}{128 e^4}-\frac{6 b^3 n^3 x (e f-d g)^3}{e^3}",1,"(1152*(e*f - d*g)^3*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3 + 1728*g*(e*f - d*g)^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^3 + 1152*g^2*(e*f - d*g)*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])^3 + 288*g^3*(d + e*x)^4*(a + b*Log[c*(d + e*x)^n])^3 - 3456*b*(e*f - d*g)^3*n*((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2 - 2*b*n*(e*(a - b*n)*x + b*(d + e*x)*Log[c*(d + e*x)^n])) - 1296*b*g*(e*f - d*g)^2*n*(2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2 + b*n*(b*e*n*x*(2*d + e*x) - 2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))) - 128*b*g^2*(e*f - d*g)*n*(9*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])^2 + 2*b*n*(b*e*n*x*(3*d^2 + 3*d*e*x + e^2*x^2) - 3*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n]))) - 27*b*g^3*n*(8*(d + e*x)^4*(a + b*Log[c*(d + e*x)^n])^2 + b*n*(b*e*n*x*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3) - 4*(d + e*x)^4*(a + b*Log[c*(d + e*x)^n]))))/(1152*e^4)","A",1
53,1,333,432,0.2281647,"\int (f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \, dx","Integrate[(f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^3,x]","\frac{-4 b g^2 n \left(2 b n \left(b e n x \left(3 d^2+3 d e x+e^2 x^2\right)-3 (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)\right)+9 (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2\right)+108 g (d+e x)^2 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^3+108 (d+e x) (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3-324 b n (e f-d g)^2 \left((d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2-2 b n \left(e x (a-b n)+b (d+e x) \log \left(c (d+e x)^n\right)\right)\right)-81 b g n (e f-d g) \left(2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2+b n \left(b e n x (2 d+e x)-2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)\right)\right)+36 g^2 (d+e x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{108 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{2 b^3 g^2 n^3 (d+e x)^3}{27 e^3}-\frac{6 b^3 n^3 x (e f-d g)^2}{e^2}",1,"(108*(e*f - d*g)^2*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3 + 108*g*(e*f - d*g)*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^3 + 36*g^2*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])^3 - 324*b*(e*f - d*g)^2*n*((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2 - 2*b*n*(e*(a - b*n)*x + b*(d + e*x)*Log[c*(d + e*x)^n])) - 81*b*g*(e*f - d*g)*n*(2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2 + b*n*(b*e*n*x*(2*d + e*x) - 2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))) - 4*b*g^2*n*(9*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])^2 + 2*b*n*(b*e*n*x*(3*d^2 + 3*d*e*x + e^2*x^2) - 3*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n]))))/(108*e^3)","A",1
54,1,201,265,0.1371031,"\int (f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \, dx","Integrate[(f + g*x)*(a + b*Log[c*(d + e*x)^n])^3,x]","\frac{8 (d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^3-24 b n (e f-d g) \left((d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2-2 b n \left(e x (a-b n)+b (d+e x) \log \left(c (d+e x)^n\right)\right)\right)+4 g (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3-3 b g n \left(2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2+b n \left(b e n x (2 d+e x)-2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)\right)\right)}{8 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)}{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,"(8*(e*f - d*g)*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3 + 4*g*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^3 - 24*b*(e*f - d*g)*n*((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2 - 2*b*n*(e*(a - b*n)*x + b*(d + e*x)*Log[c*(d + e*x)^n])) - 3*b*g*n*(2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2 + b*n*(b*e*n*x*(2*d + e*x) - 2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))))/(8*e^2)","A",1
55,1,85,99,0.0225193,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^3,x]","\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3-3 b n \left((d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2-2 b n \left(e x (a-b n)+b (d+e x) \log \left(c (d+e x)^n\right)\right)\right)}{e}","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,"((d + e*x)*(a + b*Log[c*(d + e*x)^n])^3 - 3*b*n*((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2 - 2*b*n*(e*(a - b*n)*x + b*(d + e*x)*Log[c*(d + e*x)^n])))/e","A",1
56,1,335,158,0.2537638,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{f+g x} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^3/(f + g*x),x]","\frac{6 b^2 n^2 \left(-\text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)+\log (d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\frac{1}{2} \log ^2(d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)+3 b n \left(\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+\log (f+g x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^3+b^3 n^3 \left(6 \text{Li}_4\left(\frac{g (d+e x)}{d g-e f}\right)+3 \log ^2(d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-6 \log (d+e x) \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)+\log ^3(d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)}{g}","-\frac{6 b^2 n^2 \text{Li}_3\left(-\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{Li}_2\left(-\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{\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^3 n^3 \text{Li}_4\left(-\frac{g (d+e x)}{e f-d g}\right)}{g}",1,"((a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3*Log[f + g*x] + 3*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + 6*b^2*n^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)])/2 + Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)]) + b^3*n^3*(Log[d + e*x]^3*Log[(e*(f + g*x))/(e*f - d*g)] + 3*Log[d + e*x]^2*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 6*Log[d + e*x]*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)] + 6*PolyLog[4, (g*(d + e*x))/(-(e*f) + d*g)]))/g","B",1
57,1,410,190,0.3898112,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(f+g x)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^3/(f + g*x)^2,x]","\frac{3 b^2 n^2 \left(\log (d+e x) \left(g (d+e x) \log (d+e x)-2 e (f+g x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)-2 e (f+g x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)-3 b n (e f-d g) \log (d+e x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+3 b e n (f+g x) \log (d+e x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2-3 b e n (f+g x) \log (f+g x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2-(e f-d g) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^3+b^3 n^3 \left(6 e (f+g x) \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)-6 e (f+g x) \log (d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log ^2(d+e x) \left(g (d+e x) \log (d+e x)-3 e (f+g x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)\right)}{g (f+g x) (e f-d g)}","-\frac{6 b^2 e n^2 \text{Li}_2\left(-\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{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^3 e n^3 \text{Li}_3\left(-\frac{g (d+e x)}{e f-d g}\right)}{g (e f-d g)}",1,"(-3*b*(e*f - d*g)*n*Log[d + e*x]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 3*b*e*n*(f + g*x)*Log[d + e*x]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 - (e*f - d*g)*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3 - 3*b*e*n*(f + g*x)*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x] + 3*b^2*n^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(Log[d + e*x]*(g*(d + e*x)*Log[d + e*x] - 2*e*(f + g*x)*Log[(e*(f + g*x))/(e*f - d*g)]) - 2*e*(f + g*x)*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + b^3*n^3*(Log[d + e*x]^2*(g*(d + e*x)*Log[d + e*x] - 3*e*(f + g*x)*Log[(e*(f + g*x))/(e*f - d*g)]) - 6*e*(f + g*x)*Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] + 6*e*(f + g*x)*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)]))/(g*(e*f - d*g)*(f + g*x))","B",1
58,1,620,342,0.7454421,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(f+g x)^3} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^3/(f + g*x)^3,x]","-\frac{3 b^2 n^2 \left(2 e^2 (f+g x)^2 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-2 e^2 (f+g x)^2 \log \left(\frac{e (f+g x)}{e f-d g}\right)+g (d+e x) \log ^2(d+e x) (d g-e (2 f+g x))+2 e (f+g x) \log (d+e x) \left(e (f+g x) \log \left(\frac{e (f+g x)}{e f-d g}\right)+g (d+e x)\right)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)-3 b e^2 n (f+g x)^2 \log (d+e x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+3 b e^2 n (f+g x)^2 \log (f+g x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2-3 b e n (f+g x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+3 b n (e f-d g)^2 \log (d+e x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+(e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^3+b^3 n^3 \left(-6 e^2 (f+g x)^2 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-6 e^2 (f+g x)^2 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)-6 e^2 (f+g x)^2 \log (d+e x) \left(\log \left(\frac{e (f+g x)}{e f-d g}\right)-\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)\right)+g (d+e x) \log ^3(d+e x) (d g-e (2 f+g x))+3 e (f+g x) \log ^2(d+e x) \left(e (f+g x) \log \left(\frac{e (f+g x)}{e f-d g}\right)+g (d+e x)\right)\right)}{2 g (f+g x)^2 (e f-d g)^2}","\frac{3 b^2 e^2 n^2 \text{Li}_2\left(-\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^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}+\frac{3 b^3 e^2 n^3 \text{Li}_2\left(-\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{Li}_3\left(-\frac{e f-d g}{g (d+e x)}\right)}{g (e f-d g)^2}",1,"-1/2*(-3*b*e*(e*f - d*g)*n*(f + g*x)*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 3*b*(e*f - d*g)^2*n*Log[d + e*x]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 - 3*b*e^2*n*(f + g*x)^2*Log[d + e*x]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + (e*f - d*g)^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3 + 3*b*e^2*n*(f + g*x)^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x] + 3*b^2*n^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(g*(d + e*x)*(d*g - e*(2*f + g*x))*Log[d + e*x]^2 - 2*e^2*(f + g*x)^2*Log[(e*(f + g*x))/(e*f - d*g)] + 2*e*(f + g*x)*Log[d + e*x]*(g*(d + e*x) + e*(f + g*x)*Log[(e*(f + g*x))/(e*f - d*g)]) + 2*e^2*(f + g*x)^2*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + b^3*n^3*(g*(d + e*x)*(d*g - e*(2*f + g*x))*Log[d + e*x]^3 + 3*e*(f + g*x)*Log[d + e*x]^2*(g*(d + e*x) + e*(f + g*x)*Log[(e*(f + g*x))/(e*f - d*g)]) - 6*e^2*(f + g*x)^2*Log[d + e*x]*(Log[(e*(f + g*x))/(e*f - d*g)] - PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) - 6*e^2*(f + g*x)^2*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 6*e^2*(f + g*x)^2*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)]))/(g*(e*f - d*g)^2*(f + g*x)^2)","A",1
59,1,843,564,1.1261041,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(f+g x)^4} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^3/(f + g*x)^4,x]","\frac{-2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^3 (e f-d g)^3-6 b n \log (d+e x) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 (e f-d g)^3+3 b e n (f+g x) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 (e f-d g)^2+6 b e^2 n (f+g x)^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 (e f-d g)+6 b e^3 n (f+g x)^3 \log (d+e x) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2-6 b e^3 n (f+g x)^3 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 \log (f+g x)+6 b^2 n^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(3 e^3 \log \left(\frac{e (f+g x)}{e f-d g}\right) (f+g x)^3-2 e^3 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) (f+g x)^3+e^2 g (d+e x) (f+g x)^2+e \log (d+e x) \left(g^2 (d+e x)^2-4 e g (f+g x) (d+e x)-2 e^2 (f+g x)^2 \log \left(\frac{e (f+g x)}{e f-d g}\right)\right) (f+g x)+g \left(g^2 d^3-3 e f g d^2+3 e^2 f^2 d+e^3 x \left(3 f^2+3 g x f+g^2 x^2\right)\right) \log ^2(d+e x)\right)+b^3 n^3 \left(-6 e^3 \log \left(\frac{e (f+g x)}{e f-d g}\right) (f+g x)^3+18 e^3 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) (f+g x)^3+12 e^3 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right) (f+g x)^3+6 e^2 \log (d+e x) \left(g (d+e x)+3 e (f+g x) \log \left(\frac{e (f+g x)}{e f-d g}\right)-2 e (f+g x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)\right) (f+g x)^2+3 e \log ^2(d+e x) \left(g^2 (d+e x)^2-4 e g (f+g x) (d+e x)-2 e^2 (f+g x)^2 \log \left(\frac{e (f+g x)}{e f-d g}\right)\right) (f+g x)+2 g \left(g^2 d^3-3 e f g d^2+3 e^2 f^2 d+e^3 x \left(3 f^2+3 g x f+g^2 x^2\right)\right) \log ^3(d+e x)\right)}{6 g (e f-d g)^3 (f+g x)^3}","\frac{2 b^2 e^3 n^2 \text{Li}_2\left(-\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{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 \text{Li}_2\left(-\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{Li}_2\left(-\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{Li}_3\left(-\frac{e f-d g}{g (d+e x)}\right)}{g (e f-d g)^3}-\frac{b^3 e^3 n^3 \log (f+g x)}{g (e f-d g)^3}",1,"(3*b*e*(e*f - d*g)^2*n*(f + g*x)*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 6*b*e^2*(e*f - d*g)*n*(f + g*x)^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 - 6*b*(e*f - d*g)^3*n*Log[d + e*x]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 6*b*e^3*n*(f + g*x)^3*Log[d + e*x]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 - 2*(e*f - d*g)^3*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3 - 6*b*e^3*n*(f + g*x)^3*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x] + 6*b^2*n^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(e^2*g*(d + e*x)*(f + g*x)^2 + g*(3*d*e^2*f^2 - 3*d^2*e*f*g + d^3*g^2 + e^3*x*(3*f^2 + 3*f*g*x + g^2*x^2))*Log[d + e*x]^2 + 3*e^3*(f + g*x)^3*Log[(e*(f + g*x))/(e*f - d*g)] + e*(f + g*x)*Log[d + e*x]*(g^2*(d + e*x)^2 - 4*e*g*(d + e*x)*(f + g*x) - 2*e^2*(f + g*x)^2*Log[(e*(f + g*x))/(e*f - d*g)]) - 2*e^3*(f + g*x)^3*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + b^3*n^3*(2*g*(3*d*e^2*f^2 - 3*d^2*e*f*g + d^3*g^2 + e^3*x*(3*f^2 + 3*f*g*x + g^2*x^2))*Log[d + e*x]^3 - 6*e^3*(f + g*x)^3*Log[(e*(f + g*x))/(e*f - d*g)] + 3*e*(f + g*x)*Log[d + e*x]^2*(g^2*(d + e*x)^2 - 4*e*g*(d + e*x)*(f + g*x) - 2*e^2*(f + g*x)^2*Log[(e*(f + g*x))/(e*f - d*g)]) + 18*e^3*(f + g*x)^3*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] + 6*e^2*(f + g*x)^2*Log[d + e*x]*(g*(d + e*x) + 3*e*(f + g*x)*Log[(e*(f + g*x))/(e*f - d*g)] - 2*e*(f + g*x)*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + 12*e^3*(f + g*x)^3*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)]))/(6*g*(e*f - d*g)^3*(f + g*x)^3)","A",1
60,1,258,340,0.2236641,"\int (f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^4 \, dx","Integrate[(f + g*x)*(a + b*Log[c*(d + e*x)^n])^4,x]","\frac{4 (d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^4-16 b n (e f-d g) \left((d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3-3 b n \left((d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2-2 b n \left(e x (a-b n)+b (d+e x) \log \left(c (d+e x)^n\right)\right)\right)\right)+2 g (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^4-b g n \left(4 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3-3 b n \left(2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2+b n \left(b e n x (2 d+e x)-2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)\right)\right)\right)}{4 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{24 a b^3 n^3 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^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{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,"(4*(e*f - d*g)*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^4 + 2*g*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^4 - 16*b*(e*f - d*g)*n*((d + e*x)*(a + b*Log[c*(d + e*x)^n])^3 - 3*b*n*((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2 - 2*b*n*(e*(a - b*n)*x + b*(d + e*x)*Log[c*(d + e*x)^n]))) - b*g*n*(4*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^3 - 3*b*n*(2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2 + b*n*(b*e*n*x*(2*d + e*x) - 2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])))))/(4*e^2)","A",1
61,1,112,131,0.0311598,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^4 \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^4,x]","\frac{(d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^4-4 b n \left((d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3-3 b n \left((d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2-2 b n \left(e x (a-b n)+b (d+e x) \log \left(c (d+e x)^n\right)\right)\right)\right)}{e}","-24 a b^3 n^3 x+\frac{12 b^2 n^2 (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e}-\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,"((d + e*x)*(a + b*Log[c*(d + e*x)^n])^4 - 4*b*n*((d + e*x)*(a + b*Log[c*(d + e*x)^n])^3 - 3*b*n*((d + e*x)*(a + b*Log[c*(d + e*x)^n])^2 - 2*b*n*(e*(a - b*n)*x + b*(d + e*x)*Log[c*(d + e*x)^n]))))/e","A",1
62,1,503,205,0.2304582,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^4}{f+g x} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^4/(f + g*x),x]","\frac{-4 b^3 n^3 \left(6 \text{Li}_4\left(\frac{g (d+e x)}{d g-e f}\right)+3 \log ^2(d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-6 \log (d+e x) \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)+\log ^3(d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right) \left(-a-b \log \left(c (d+e x)^n\right)+b n \log (d+e x)\right)+6 b^2 n^2 \left(-2 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log ^2(d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+4 b n \left(\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^3+\log (f+g x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^4+b^4 n^4 \left(-24 \text{Li}_5\left(\frac{g (d+e x)}{d g-e f}\right)+4 \log ^3(d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-12 \log ^2(d+e x) \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)+24 \log (d+e x) \text{Li}_4\left(\frac{g (d+e x)}{d g-e f}\right)+\log ^4(d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)}{g}","\frac{24 b^3 n^3 \text{Li}_4\left(-\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{Li}_3\left(-\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{Li}_2\left(-\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{\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^4 n^4 \text{Li}_5\left(-\frac{g (d+e x)}{e f-d g}\right)}{g}",1,"((a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^4*Log[f + g*x] + 4*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + 6*b^2*n^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*(Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)] + 2*Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)]) - 4*b^3*n^3*(-a + b*n*Log[d + e*x] - b*Log[c*(d + e*x)^n])*(Log[d + e*x]^3*Log[(e*(f + g*x))/(e*f - d*g)] + 3*Log[d + e*x]^2*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 6*Log[d + e*x]*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)] + 6*PolyLog[4, (g*(d + e*x))/(-(e*f) + d*g)]) + b^4*n^4*(Log[d + e*x]^4*Log[(e*(f + g*x))/(e*f - d*g)] + 4*Log[d + e*x]^3*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 12*Log[d + e*x]^2*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)] + 24*Log[d + e*x]*PolyLog[4, (g*(d + e*x))/(-(e*f) + d*g)] - 24*PolyLog[5, (g*(d + e*x))/(-(e*f) + d*g)]))/g","B",1
63,1,531,248,0.7391297,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^4}{(f+g x)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^4/(f + g*x)^2,x]","\frac{4 b^3 n^3 \left(6 e (f+g x) \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)-6 e (f+g x) \log (d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log ^2(d+e x) \left(g (d+e x) \log (d+e x)-3 e (f+g x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)+6 b^2 n^2 \left(\log (d+e x) \left(g (d+e x) \log (d+e x)-2 e (f+g x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)-2 e (f+g x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+4 b n \left(g (d+e x) \log (d+e x)-e (f+g x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^3-(e f-d g) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^4+b^4 n^4 \left(-24 e (f+g x) \text{Li}_4\left(\frac{g (d+e x)}{d g-e f}\right)-12 e (f+g x) \log ^2(d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+24 e (f+g x) \log (d+e x) \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)-4 e (f+g x) \log ^3(d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)+g (d+e x) \log ^4(d+e x)\right)}{g (f+g x) (e f-d g)}","\frac{24 b^3 e n^3 \text{Li}_3\left(-\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{Li}_2\left(-\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{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^4 e n^4 \text{Li}_4\left(-\frac{g (d+e x)}{e f-d g}\right)}{g (e f-d g)}",1,"(-((e*f - d*g)*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^4) + 4*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3*(g*(d + e*x)*Log[d + e*x] - e*(f + g*x)*Log[(e*(f + g*x))/(e*f - d*g)]) + 6*b^2*n^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*(Log[d + e*x]*(g*(d + e*x)*Log[d + e*x] - 2*e*(f + g*x)*Log[(e*(f + g*x))/(e*f - d*g)]) - 2*e*(f + g*x)*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + 4*b^3*n^3*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(Log[d + e*x]^2*(g*(d + e*x)*Log[d + e*x] - 3*e*(f + g*x)*Log[(e*(f + g*x))/(e*f - d*g)]) - 6*e*(f + g*x)*Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] + 6*e*(f + g*x)*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)]) + b^4*n^4*(g*(d + e*x)*Log[d + e*x]^4 - 4*e*(f + g*x)*Log[d + e*x]^3*Log[(e*(f + g*x))/(e*f - d*g)] - 12*e*(f + g*x)*Log[d + e*x]^2*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] + 24*e*(f + g*x)*Log[d + e*x]*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)] - 24*e*(f + g*x)*PolyLog[4, (g*(d + e*x))/(-(e*f) + d*g)]))/(g*(e*f - d*g)*(f + g*x))","B",1
64,1,19,19,0.004703,"\int \log (a+b x) \, dx","Integrate[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",1
65,1,36,37,0.0044428,"\int \log ^2(a+b x) \, dx","Integrate[Log[a + b*x]^2,x]","\frac{(a+b x) \log ^2(a+b x)-2 (a+b x) \log (a+b x)+2 b x}{b}","\frac{(a+b x) \log ^2(a+b x)}{b}-\frac{2 (a+b x) \log (a+b x)}{b}+2 x",1,"(2*b*x - 2*(a + b*x)*Log[a + b*x] + (a + b*x)*Log[a + b*x]^2)/b","A",1
66,1,51,55,0.006209,"\int \log ^3(a+b x) \, dx","Integrate[Log[a + b*x]^3,x]","\frac{(a+b x) \log ^3(a+b x)-3 (a+b x) \log ^2(a+b x)+6 (a+b x) \log (a+b x)-6 b x}{b}","\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*b*x + 6*(a + b*x)*Log[a + b*x] - 3*(a + b*x)*Log[a + b*x]^2 + (a + b*x)*Log[a + b*x]^3)/b","A",1
67,1,25,25,0.0071553,"\int \log (a+b x+c x) \, dx","Integrate[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",1
68,1,48,49,0.006429,"\int \log ^2(a+b x+c x) \, dx","Integrate[Log[a + b*x + c*x]^2,x]","\frac{(a+x (b+c)) \log ^2(a+x (b+c))-2 (a+x (b+c)) \log (a+x (b+c))+2 x (b+c)}{b+c}","\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*(b + c)*x - 2*(a + (b + c)*x)*Log[a + (b + c)*x] + (a + (b + c)*x)*Log[a + (b + c)*x]^2)/(b + c)","A",1
69,1,67,73,0.0091369,"\int \log ^3(a+b x+c x) \, dx","Integrate[Log[a + b*x + c*x]^3,x]","\frac{(a+x (b+c)) \log ^3(a+x (b+c))-3 (a+x (b+c)) \log ^2(a+x (b+c))+6 (a+x (b+c)) \log (a+x (b+c))-6 x (b+c)}{b+c}","\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*(b + c)*x + 6*(a + (b + c)*x)*Log[a + (b + c)*x] - 3*(a + (b + c)*x)*Log[a + (b + c)*x]^2 + (a + (b + c)*x)*Log[a + (b + c)*x]^3)/(b + c)","A",1
70,1,24,24,0.0069045,"\int \log \left(c (d+e x)^n\right) \, dx","Integrate[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",1
71,1,24,24,0.0068791,"\int \frac{\log \left(-\frac{g (d+e x)}{e f-d g}\right)}{f+g x} \, dx","Integrate[Log[-((g*(d + e*x))/(e*f - d*g))]/(f + g*x),x]","-\frac{\text{Li}_2\left(\frac{e (f+g x)}{e f-d g}\right)}{g}","-\frac{\text{Li}_2\left(\frac{e (f+g x)}{e f-d g}\right)}{g}",1,"-(PolyLog[2, (e*(f + g*x))/(e*f - d*g)]/g)","A",1
72,1,15,15,0.0030476,"\int \frac{a+b \log \left(c \left(\frac{1}{c}+e x\right)\right)}{x} \, dx","Integrate[(a + b*Log[c*(c^(-1) + e*x)])/x,x]","a \log (x)-b \text{Li}_2(-c e x)","a \log (x)-b \text{Li}_2(-c e x)",1,"a*Log[x] - b*PolyLog[2, -(c*e*x)]","A",1
73,1,16,16,0.0018497,"\int \frac{\log (3+e x)}{x} \, dx","Integrate[Log[3 + e*x]/x,x]","\log (3) \log (x)-\text{Li}_2\left(-\frac{e x}{3}\right)","\log (3) \log (x)-\text{Li}_2\left(-\frac{e x}{3}\right)",1,"Log[3]*Log[x] - PolyLog[2, -1/3*(e*x)]","A",1
74,1,16,16,0.0020347,"\int \frac{\log (2+e x)}{x} \, dx","Integrate[Log[2 + e*x]/x,x]","\log (2) \log (x)-\text{Li}_2\left(-\frac{e x}{2}\right)","\log (2) \log (x)-\text{Li}_2\left(-\frac{e x}{2}\right)",1,"Log[2]*Log[x] - PolyLog[2, -1/2*(e*x)]","A",1
75,1,8,8,0.0014212,"\int \frac{\log (1+e x)}{x} \, dx","Integrate[Log[1 + e*x]/x,x]","-\text{Li}_2(-e x)","-\text{Li}_2(-e x)",1,"-PolyLog[2, -(e*x)]","A",1
76,1,10,10,0.0011243,"\int \frac{\log (e x)}{x} \, dx","Integrate[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
77,1,20,20,0.0019803,"\int \frac{\log (-1+e x)}{x} \, dx","Integrate[Log[-1 + e*x]/x,x]","\text{Li}_2(1-e x)+\log (e x) \log (e x-1)","\text{Li}_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",1
78,1,27,25,0.002082,"\int \frac{\log (-2+e x)}{x} \, dx","Integrate[Log[-2 + e*x]/x,x]","\text{Li}_2\left(\frac{1}{2} (2-e x)\right)+\log \left(\frac{e x}{2}\right) \log (e x-2)","\text{Li}_2\left(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, (2 - e*x)/2]","A",1
79,1,22,21,0.002605,"\int \frac{a+b \log (3+e x)}{x} \, dx","Integrate[(a + b*Log[3 + e*x])/x,x]","a \log (x)-b \text{Li}_2\left(-\frac{e x}{3}\right)+b \log (3) \log (x)","\log (x) (a+b \log (3))-b \text{Li}_2\left(-\frac{e x}{3}\right)",1,"a*Log[x] + b*Log[3]*Log[x] - b*PolyLog[2, -1/3*(e*x)]","A",1
80,1,22,21,0.0021313,"\int \frac{a+b \log (2+e x)}{x} \, dx","Integrate[(a + b*Log[2 + e*x])/x,x]","a \log (x)-b \text{Li}_2\left(-\frac{e x}{2}\right)+b \log (2) \log (x)","\log (x) (a+b \log (2))-b \text{Li}_2\left(-\frac{e x}{2}\right)",1,"a*Log[x] + b*Log[2]*Log[x] - b*PolyLog[2, -1/2*(e*x)]","A",1
81,1,14,14,0.0016812,"\int \frac{a+b \log (1+e x)}{x} \, dx","Integrate[(a + b*Log[1 + e*x])/x,x]","a \log (x)-b \text{Li}_2(-e x)","a \log (x)-b \text{Li}_2(-e x)",1,"a*Log[x] - b*PolyLog[2, -(e*x)]","A",1
82,1,16,17,0.0016072,"\int \frac{a+b \log (e x)}{x} \, dx","Integrate[(a + b*Log[e*x])/x,x]","a \log (x)+\frac{1}{2} b \log ^2(e x)","\frac{(a+b \log (e x))^2}{2 b}",1,"a*Log[x] + (b*Log[e*x]^2)/2","A",1
83,1,27,26,0.0022421,"\int \frac{a+b \log (-1+e x)}{x} \, dx","Integrate[(a + b*Log[-1 + e*x])/x,x]","a \log (x)+b \text{Li}_2(1-e x)+b \log (e x) \log (e x-1)","\log (e x) (a+b \log (e x-1))+b \text{Li}_2(1-e x)",1,"a*Log[x] + b*Log[e*x]*Log[-1 + e*x] + b*PolyLog[2, 1 - e*x]","A",1
84,1,34,31,0.0023695,"\int \frac{a+b \log (-2+e x)}{x} \, dx","Integrate[(a + b*Log[-2 + e*x])/x,x]","a \log (x)+b \text{Li}_2\left(\frac{1}{2} (2-e x)\right)+b \log \left(\frac{e x}{2}\right) \log (e x-2)","\log \left(\frac{e x}{2}\right) (a+b \log (e x-2))+b \text{Li}_2\left(1-\frac{e x}{2}\right)",1,"a*Log[x] + b*Log[(e*x)/2]*Log[-2 + e*x] + b*PolyLog[2, (2 - e*x)/2]","A",1
85,1,163,187,0.0508773,"\int x^2 \log ^2\left(c (a+b x)^n\right) \, dx","Integrate[x^2*Log[c*(a + b*x)^n]^2,x]","\frac{a^3 \log ^2\left(c (a+b x)^n\right)}{3 b^3}-\frac{11 a^3 n \log \left(c (a+b x)^n\right)}{9 b^3}-\frac{2 a^2 n x \log \left(c (a+b x)^n\right)}{3 b^2}+\frac{11 a^2 n^2 x}{9 b^2}+\frac{1}{3} x^3 \log ^2\left(c (a+b x)^n\right)-\frac{2}{9} n x^3 \log \left(c (a+b x)^n\right)+\frac{a n x^2 \log \left(c (a+b x)^n\right)}{3 b}-\frac{5 a n^2 x^2}{18 b}+\frac{2 n^2 x^3}{27}","\frac{2 a^3 n \log (a+b x) \log \left(c (a+b x)^n\right)}{3 b^3}-\frac{a^3 n^2 \log ^2(a+b x)}{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 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,"(11*a^2*n^2*x)/(9*b^2) - (5*a*n^2*x^2)/(18*b) + (2*n^2*x^3)/27 - (11*a^3*n*Log[c*(a + b*x)^n])/(9*b^3) - (2*a^2*n*x*Log[c*(a + b*x)^n])/(3*b^2) + (a*n*x^2*Log[c*(a + b*x)^n])/(3*b) - (2*n*x^3*Log[c*(a + b*x)^n])/9 + (a^3*Log[c*(a + b*x)^n]^2)/(3*b^3) + (x^3*Log[c*(a + b*x)^n]^2)/3","A",1
86,1,186,177,0.0594915,"\int \frac{\log ^2\left(c (a+b x)^n\right)}{x^4} \, dx","Integrate[Log[c*(a + b*x)^n]^2/x^4,x]","-\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^3 n^2 \text{Li}_2\left(\frac{a+b x}{a}\right)}{3 a^3}-\frac{b^3 n^2 \log (x)}{a^3}+\frac{b^3 n^2 \log (a+b x)}{a^3}+\frac{2 b^2 n \log \left(c (a+b x)^n\right)}{3 a^2 x}-\frac{b^2 n^2}{3 a^2 x}-\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 \log \left(1-\frac{a}{a+b x}\right) \log \left(c (a+b x)^n\right)}{3 a^3}-\frac{2 b^3 n^2 \text{Li}_2\left(\frac{a}{a+b x}\right)}{3 a^3}-\frac{b^3 n^2 \log (x)}{a^3}+\frac{b^3 n^2 \log (a+b x)}{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{\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,"-1/3*(b^2*n^2)/(a^2*x) - (b^3*n^2*Log[x])/a^3 + (b^3*n^2*Log[a + b*x])/a^3 - (b*n*Log[c*(a + b*x)^n])/(3*a*x^2) + (2*b^2*n*Log[c*(a + b*x)^n])/(3*a^2*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, (a + b*x)/a])/(3*a^3)","A",1
87,1,260,285,0.099821,"\int x^2 \log ^3\left(c (a+b x)^n\right) \, dx","Integrate[x^2*Log[c*(a + b*x)^n]^3,x]","\frac{85 a^3 n^2 \log \left(c (a+b x)^n\right)}{18 b^3}+\frac{a^3 \log ^3\left(c (a+b x)^n\right)}{3 b^3}-\frac{11 a^3 n \log ^2\left(c (a+b x)^n\right)}{6 b^3}+\frac{11 a^2 n^2 x \log \left(c (a+b x)^n\right)}{3 b^2}-\frac{a^2 n x \log ^2\left(c (a+b x)^n\right)}{b^2}-\frac{85 a^2 n^3 x}{18 b^2}+\frac{2}{9} n^2 x^3 \log \left(c (a+b x)^n\right)-\frac{5 a n^2 x^2 \log \left(c (a+b x)^n\right)}{6 b}+\frac{1}{3} x^3 \log ^3\left(c (a+b x)^n\right)-\frac{1}{3} n x^3 \log ^2\left(c (a+b x)^n\right)+\frac{a n x^2 \log ^2\left(c (a+b x)^n\right)}{2 b}+\frac{19 a n^3 x^2}{36 b}-\frac{2 n^3 x^3}{27}","\frac{6 a^2 n^2 (a+b x) \log \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{3 a^2 n (a+b x) \log ^2\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{(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{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{2 n^3 (a+b x)^3}{27 b^3}+\frac{3 a n^3 (a+b x)^2}{4 b^3}",1,"(-85*a^2*n^3*x)/(18*b^2) + (19*a*n^3*x^2)/(36*b) - (2*n^3*x^3)/27 + (85*a^3*n^2*Log[c*(a + b*x)^n])/(18*b^3) + (11*a^2*n^2*x*Log[c*(a + b*x)^n])/(3*b^2) - (5*a*n^2*x^2*Log[c*(a + b*x)^n])/(6*b) + (2*n^2*x^3*Log[c*(a + b*x)^n])/9 - (11*a^3*n*Log[c*(a + b*x)^n]^2)/(6*b^3) - (a^2*n*x*Log[c*(a + b*x)^n]^2)/b^2 + (a*n*x^2*Log[c*(a + b*x)^n]^2)/(2*b) - (n*x^3*Log[c*(a + b*x)^n]^2)/3 + (a^3*Log[c*(a + b*x)^n]^3)/(3*b^3) + (x^3*Log[c*(a + b*x)^n]^3)/3","A",1
88,1,266,299,1.0354115,"\int \frac{(f+g x)^3}{a+b \log \left(c (d+e x)^n\right)} \, dx","Integrate[(f + g*x)^3/(a + b*Log[c*(d + e*x)^n]),x]","\frac{e^{-\frac{4 a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-4/n} \left(e^{\frac{3 a}{b n}} (e f-d g)^3 \left(c (d+e x)^n\right)^{3/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)+g (d+e x) \left(3 e^{\frac{2 a}{b n}} (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)-g (d+e x) \left(-3 e^{\frac{a}{b n}} (e f-d g) \left(c (d+e x)^n\right)^{\frac{1}{n}} \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)-g (d+e x) \text{Ei}\left(\frac{4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)\right)\right)\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,"((d + e*x)*(E^((3*a)/(b*n))*(e*f - d*g)^3*(c*(d + e*x)^n)^(3/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)] + g*(d + e*x)*(3*E^((2*a)/(b*n))*(e*f - d*g)^2*(c*(d + e*x)^n)^(2/n)*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)] - g*(d + e*x)*(-3*E^(a/(b*n))*(e*f - d*g)*(c*(d + e*x)^n)^n^(-1)*ExpIntegralEi[(3*(a + b*Log[c*(d + e*x)^n]))/(b*n)] - g*(d + e*x)*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",1
89,1,197,219,0.4105975,"\int \frac{(f+g x)^2}{a+b \log \left(c (d+e x)^n\right)} \, dx","Integrate[(f + g*x)^2/(a + b*Log[c*(d + e*x)^n]),x]","\frac{e^{-\frac{3 a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-3/n} \left(e^{\frac{2 a}{b n}} (e f-d g)^2 \left(c (d+e x)^n\right)^{2/n} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)-g (d+e x) \left(-2 e^{\frac{a}{b n}} (e f-d g) \left(c (d+e x)^n\right)^{\frac{1}{n}} \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)-g (d+e x) \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)\right)\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,"((d + e*x)*(E^((2*a)/(b*n))*(e*f - d*g)^2*(c*(d + e*x)^n)^(2/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)] - g*(d + e*x)*(-2*E^(a/(b*n))*(e*f - d*g)*(c*(d + e*x)^n)^n^(-1)*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)] - g*(d + e*x)*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",1
90,1,126,139,0.1694835,"\int \frac{f+g x}{a+b \log \left(c (d+e x)^n\right)} \, dx","Integrate[(f + g*x)/(a + b*Log[c*(d + e*x)^n]),x]","\frac{e^{-\frac{2 a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-2/n} \left(e^{\frac{a}{b n}} (e f-d g) \left(c (d+e x)^n\right)^{\frac{1}{n}} \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)+g (d+e x) \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)\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,"((d + e*x)*(E^(a/(b*n))*(e*f - d*g)*(c*(d + e*x)^n)^n^(-1)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)] + g*(d + e*x)*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",1
91,1,63,63,0.0187666,"\int \frac{1}{a+b \log \left(c (d+e x)^n\right)} \, dx","Integrate[(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",1
92,0,0,27,0.2047444,"\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","Integrate[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,"Integrate[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])), x]","A",-1
93,0,0,27,0.6071677,"\int \frac{1}{(f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","Integrate[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,"Integrate[1/((f + g*x)^2*(a + b*Log[c*(d + e*x)^n])), x]","A",-1
94,1,1674,339,1.1340516,"\int \frac{(f+g x)^3}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Integrate[(f + g*x)^3/(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{e^{-\frac{4 a}{b n}} \left(c (d+e x)^n\right)^{-4/n} \left(6 a d^2 e^{\frac{2 a}{b n}} g^3 (d+e x)^2 \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right) \left(c (d+e x)^n\right)^{2/n}-12 a d e e^{\frac{2 a}{b n}} f g^2 (d+e x)^2 \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right) \left(c (d+e x)^n\right)^{2/n}+6 a e^2 e^{\frac{2 a}{b n}} f^2 g (d+e x)^2 \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right) \left(c (d+e x)^n\right)^{2/n}+6 b d^2 e^{\frac{2 a}{b n}} g^3 (d+e x)^2 \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right) \log \left(c (d+e x)^n\right) \left(c (d+e x)^n\right)^{2/n}-12 b d e e^{\frac{2 a}{b n}} f g^2 (d+e x)^2 \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right) \log \left(c (d+e x)^n\right) \left(c (d+e x)^n\right)^{2/n}+6 b e^2 e^{\frac{2 a}{b n}} f^2 g (d+e x)^2 \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right) \log \left(c (d+e x)^n\right) \left(c (d+e x)^n\right)^{2/n}+a e^3 e^{\frac{3 a}{b n}} f^3 (d+e x) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \left(c (d+e x)^n\right)^{3/n}-a d^3 e^{\frac{3 a}{b n}} g^3 (d+e x) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \left(c (d+e x)^n\right)^{3/n}+3 a d^2 e e^{\frac{3 a}{b n}} f g^2 (d+e x) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \left(c (d+e x)^n\right)^{3/n}-3 a d e^2 e^{\frac{3 a}{b n}} f^2 g (d+e x) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \left(c (d+e x)^n\right)^{3/n}+b e^3 e^{\frac{3 a}{b n}} f^3 (d+e x) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \log \left(c (d+e x)^n\right) \left(c (d+e x)^n\right)^{3/n}-b d^3 e^{\frac{3 a}{b n}} g^3 (d+e x) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \log \left(c (d+e x)^n\right) \left(c (d+e x)^n\right)^{3/n}+3 b d^2 e e^{\frac{3 a}{b n}} f g^2 (d+e x) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \log \left(c (d+e x)^n\right) \left(c (d+e x)^n\right)^{3/n}-3 b d e^2 e^{\frac{3 a}{b n}} f^2 g (d+e x) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \log \left(c (d+e x)^n\right) \left(c (d+e x)^n\right)^{3/n}-b e^4 e^{\frac{4 a}{b n}} g^3 n x^4 \left(c (d+e x)^n\right)^{4/n}-b d e^3 e^{\frac{4 a}{b n}} g^3 n x^3 \left(c (d+e x)^n\right)^{4/n}-3 b e^4 e^{\frac{4 a}{b n}} f g^2 n x^3 \left(c (d+e x)^n\right)^{4/n}-3 b d e^3 e^{\frac{4 a}{b n}} f g^2 n x^2 \left(c (d+e x)^n\right)^{4/n}-3 b e^4 e^{\frac{4 a}{b n}} f^2 g n x^2 \left(c (d+e x)^n\right)^{4/n}-b d e^3 e^{\frac{4 a}{b n}} f^3 n \left(c (d+e x)^n\right)^{4/n}-b e^4 e^{\frac{4 a}{b n}} f^3 n x \left(c (d+e x)^n\right)^{4/n}-3 b d e^3 e^{\frac{4 a}{b n}} f^2 g n x \left(c (d+e x)^n\right)^{4/n}-9 a d e^{\frac{a}{b n}} g^3 (d+e x)^3 \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right) \left(c (d+e x)^n\right)^{\frac{1}{n}}+9 a e e^{\frac{a}{b n}} f g^2 (d+e x)^3 \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right) \left(c (d+e x)^n\right)^{\frac{1}{n}}-9 b d e^{\frac{a}{b n}} g^3 (d+e x)^3 \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right) \log \left(c (d+e x)^n\right) \left(c (d+e x)^n\right)^{\frac{1}{n}}+9 b e e^{\frac{a}{b n}} f g^2 (d+e x)^3 \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right) \log \left(c (d+e x)^n\right) \left(c (d+e x)^n\right)^{\frac{1}{n}}+4 a g^3 (d+e x)^4 \text{Ei}\left(\frac{4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)+4 b g^3 (d+e x)^4 \text{Ei}\left(\frac{4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right) \log \left(c (d+e x)^n\right)\right)}{b^2 e^4 n^2 \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,"(-(b*d*e^3*E^((4*a)/(b*n))*f^3*n*(c*(d + e*x)^n)^(4/n)) - b*e^4*E^((4*a)/(b*n))*f^3*n*x*(c*(d + e*x)^n)^(4/n) - 3*b*d*e^3*E^((4*a)/(b*n))*f^2*g*n*x*(c*(d + e*x)^n)^(4/n) - 3*b*e^4*E^((4*a)/(b*n))*f^2*g*n*x^2*(c*(d + e*x)^n)^(4/n) - 3*b*d*e^3*E^((4*a)/(b*n))*f*g^2*n*x^2*(c*(d + e*x)^n)^(4/n) - 3*b*e^4*E^((4*a)/(b*n))*f*g^2*n*x^3*(c*(d + e*x)^n)^(4/n) - b*d*e^3*E^((4*a)/(b*n))*g^3*n*x^3*(c*(d + e*x)^n)^(4/n) - b*e^4*E^((4*a)/(b*n))*g^3*n*x^4*(c*(d + e*x)^n)^(4/n) + a*e^3*E^((3*a)/(b*n))*f^3*(d + e*x)*(c*(d + e*x)^n)^(3/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)] - 3*a*d*e^2*E^((3*a)/(b*n))*f^2*g*(d + e*x)*(c*(d + e*x)^n)^(3/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)] + 3*a*d^2*e*E^((3*a)/(b*n))*f*g^2*(d + e*x)*(c*(d + e*x)^n)^(3/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)] - a*d^3*E^((3*a)/(b*n))*g^3*(d + e*x)*(c*(d + e*x)^n)^(3/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)] + 6*a*e^2*E^((2*a)/(b*n))*f^2*g*(d + e*x)^2*(c*(d + e*x)^n)^(2/n)*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)] - 12*a*d*e*E^((2*a)/(b*n))*f*g^2*(d + e*x)^2*(c*(d + e*x)^n)^(2/n)*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)] + 6*a*d^2*E^((2*a)/(b*n))*g^3*(d + e*x)^2*(c*(d + e*x)^n)^(2/n)*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)] + 9*a*e*E^(a/(b*n))*f*g^2*(d + e*x)^3*(c*(d + e*x)^n)^n^(-1)*ExpIntegralEi[(3*(a + b*Log[c*(d + e*x)^n]))/(b*n)] - 9*a*d*E^(a/(b*n))*g^3*(d + e*x)^3*(c*(d + e*x)^n)^n^(-1)*ExpIntegralEi[(3*(a + b*Log[c*(d + e*x)^n]))/(b*n)] + 4*a*g^3*(d + e*x)^4*ExpIntegralEi[(4*(a + b*Log[c*(d + e*x)^n]))/(b*n)] + b*e^3*E^((3*a)/(b*n))*f^3*(d + e*x)*(c*(d + e*x)^n)^(3/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)]*Log[c*(d + e*x)^n] - 3*b*d*e^2*E^((3*a)/(b*n))*f^2*g*(d + e*x)*(c*(d + e*x)^n)^(3/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)]*Log[c*(d + e*x)^n] + 3*b*d^2*e*E^((3*a)/(b*n))*f*g^2*(d + e*x)*(c*(d + e*x)^n)^(3/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)]*Log[c*(d + e*x)^n] - b*d^3*E^((3*a)/(b*n))*g^3*(d + e*x)*(c*(d + e*x)^n)^(3/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)]*Log[c*(d + e*x)^n] + 6*b*e^2*E^((2*a)/(b*n))*f^2*g*(d + e*x)^2*(c*(d + e*x)^n)^(2/n)*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*Log[c*(d + e*x)^n] - 12*b*d*e*E^((2*a)/(b*n))*f*g^2*(d + e*x)^2*(c*(d + e*x)^n)^(2/n)*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*Log[c*(d + e*x)^n] + 6*b*d^2*E^((2*a)/(b*n))*g^3*(d + e*x)^2*(c*(d + e*x)^n)^(2/n)*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*Log[c*(d + e*x)^n] + 9*b*e*E^(a/(b*n))*f*g^2*(d + e*x)^3*(c*(d + e*x)^n)^n^(-1)*ExpIntegralEi[(3*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*Log[c*(d + e*x)^n] - 9*b*d*E^(a/(b*n))*g^3*(d + e*x)^3*(c*(d + e*x)^n)^n^(-1)*ExpIntegralEi[(3*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*Log[c*(d + e*x)^n] + 4*b*g^3*(d + e*x)^4*ExpIntegralEi[(4*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*Log[c*(d + e*x)^n])/(b^2*e^4*E^((4*a)/(b*n))*n^2*(c*(d + e*x)^n)^(4/n)*(a + b*Log[c*(d + e*x)^n]))","B",1
95,1,1015,259,0.6240922,"\int \frac{(f+g x)^2}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Integrate[(f + g*x)^2/(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{e^{-\frac{3 a}{b n}} \left(c (d+e x)^n\right)^{-3/n} \left(a e^2 e^{\frac{2 a}{b n}} f^2 (d+e x) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \left(c (d+e x)^n\right)^{2/n}+a d^2 e^{\frac{2 a}{b n}} g^2 (d+e x) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \left(c (d+e x)^n\right)^{2/n}-2 a d e e^{\frac{2 a}{b n}} f g (d+e x) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \left(c (d+e x)^n\right)^{2/n}+b e^2 e^{\frac{2 a}{b n}} f^2 (d+e x) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \log \left(c (d+e x)^n\right) \left(c (d+e x)^n\right)^{2/n}+b d^2 e^{\frac{2 a}{b n}} g^2 (d+e x) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \log \left(c (d+e x)^n\right) \left(c (d+e x)^n\right)^{2/n}-2 b d e e^{\frac{2 a}{b n}} f g (d+e x) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \log \left(c (d+e x)^n\right) \left(c (d+e x)^n\right)^{2/n}-b e^3 e^{\frac{3 a}{b n}} g^2 n x^3 \left(c (d+e x)^n\right)^{3/n}-b d e^2 e^{\frac{3 a}{b n}} g^2 n x^2 \left(c (d+e x)^n\right)^{3/n}-2 b e^3 e^{\frac{3 a}{b n}} f g n x^2 \left(c (d+e x)^n\right)^{3/n}-b d e^2 e^{\frac{3 a}{b n}} f^2 n \left(c (d+e x)^n\right)^{3/n}-b e^3 e^{\frac{3 a}{b n}} f^2 n x \left(c (d+e x)^n\right)^{3/n}-2 b d e^2 e^{\frac{3 a}{b n}} f g n x \left(c (d+e x)^n\right)^{3/n}-4 a d e^{\frac{a}{b n}} g^2 (d+e x)^2 \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right) \left(c (d+e x)^n\right)^{\frac{1}{n}}+4 a e e^{\frac{a}{b n}} f g (d+e x)^2 \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right) \left(c (d+e x)^n\right)^{\frac{1}{n}}-4 b d e^{\frac{a}{b n}} g^2 (d+e x)^2 \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right) \log \left(c (d+e x)^n\right) \left(c (d+e x)^n\right)^{\frac{1}{n}}+4 b e e^{\frac{a}{b n}} f g (d+e x)^2 \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right) \log \left(c (d+e x)^n\right) \left(c (d+e x)^n\right)^{\frac{1}{n}}+3 a g^2 (d+e x)^3 \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)+3 b g^2 (d+e x)^3 \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right) \log \left(c (d+e x)^n\right)\right)}{b^2 e^3 n^2 \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,"(-(b*d*e^2*E^((3*a)/(b*n))*f^2*n*(c*(d + e*x)^n)^(3/n)) - b*e^3*E^((3*a)/(b*n))*f^2*n*x*(c*(d + e*x)^n)^(3/n) - 2*b*d*e^2*E^((3*a)/(b*n))*f*g*n*x*(c*(d + e*x)^n)^(3/n) - 2*b*e^3*E^((3*a)/(b*n))*f*g*n*x^2*(c*(d + e*x)^n)^(3/n) - b*d*e^2*E^((3*a)/(b*n))*g^2*n*x^2*(c*(d + e*x)^n)^(3/n) - b*e^3*E^((3*a)/(b*n))*g^2*n*x^3*(c*(d + e*x)^n)^(3/n) + a*e^2*E^((2*a)/(b*n))*f^2*(d + e*x)*(c*(d + e*x)^n)^(2/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)] - 2*a*d*e*E^((2*a)/(b*n))*f*g*(d + e*x)*(c*(d + e*x)^n)^(2/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)] + a*d^2*E^((2*a)/(b*n))*g^2*(d + e*x)*(c*(d + e*x)^n)^(2/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)] + 4*a*e*E^(a/(b*n))*f*g*(d + e*x)^2*(c*(d + e*x)^n)^n^(-1)*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)] - 4*a*d*E^(a/(b*n))*g^2*(d + e*x)^2*(c*(d + e*x)^n)^n^(-1)*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)] + 3*a*g^2*(d + e*x)^3*ExpIntegralEi[(3*(a + b*Log[c*(d + e*x)^n]))/(b*n)] + b*e^2*E^((2*a)/(b*n))*f^2*(d + e*x)*(c*(d + e*x)^n)^(2/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)]*Log[c*(d + e*x)^n] - 2*b*d*e*E^((2*a)/(b*n))*f*g*(d + e*x)*(c*(d + e*x)^n)^(2/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)]*Log[c*(d + e*x)^n] + b*d^2*E^((2*a)/(b*n))*g^2*(d + e*x)*(c*(d + e*x)^n)^(2/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)]*Log[c*(d + e*x)^n] + 4*b*e*E^(a/(b*n))*f*g*(d + e*x)^2*(c*(d + e*x)^n)^n^(-1)*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*Log[c*(d + e*x)^n] - 4*b*d*E^(a/(b*n))*g^2*(d + e*x)^2*(c*(d + e*x)^n)^n^(-1)*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*Log[c*(d + e*x)^n] + 3*b*g^2*(d + e*x)^3*ExpIntegralEi[(3*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*Log[c*(d + e*x)^n])/(b^2*e^3*E^((3*a)/(b*n))*n^2*(c*(d + e*x)^n)^(3/n)*(a + b*Log[c*(d + e*x)^n]))","B",1
96,1,208,177,0.2888286,"\int \frac{f+g x}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Integrate[(f + g*x)/(a + b*Log[c*(d + e*x)^n])^2,x]","-\frac{e^{-\frac{2 a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-2/n} \left(-e^{\frac{a}{b n}} (e f-d g) \left(c (d+e x)^n\right)^{\frac{1}{n}} \left(a+b \log \left(c (d+e x)^n\right)\right) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)-2 g (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right) \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)+b e n e^{\frac{2 a}{b n}} (f+g x) \left(c (d+e x)^n\right)^{2/n}\right)}{b^2 e^2 n^2 \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,"-(((d + e*x)*(b*e*E^((2*a)/(b*n))*n*(c*(d + e*x)^n)^(2/n)*(f + g*x) - E^(a/(b*n))*(e*f - d*g)*(c*(d + e*x)^n)^n^(-1)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)]*(a + b*Log[c*(d + e*x)^n]) - 2*g*(d + e*x)*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*(a + b*Log[c*(d + e*x)^n])))/(b^2*e^2*E^((2*a)/(b*n))*n^2*(c*(d + e*x)^n)^(2/n)*(a + b*Log[c*(d + e*x)^n])))","A",1
97,1,123,96,0.0477881,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Integrate[(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} \left(b n e^{\frac{a}{b n}} \left(c (d+e x)^n\right)^{\frac{1}{n}}-\left(a+b \log \left(c (d+e x)^n\right)\right) \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)\right)}{b^2 e n^2 \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)*(b*E^(a/(b*n))*n*(c*(d + e*x)^n)^n^(-1) - ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)]*(a + b*Log[c*(d + e*x)^n])))/(b^2*e*E^(a/(b*n))*n^2*(c*(d + e*x)^n)^n^(-1)*(a + b*Log[c*(d + e*x)^n])))","A",1
98,0,0,27,0.5888924,"\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Integrate[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,"Integrate[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^2), x]","A",-1
99,0,0,27,5.0273203,"\int \frac{1}{(f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Integrate[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,"Integrate[1/((f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^2), x]","A",-1
100,1,351,351,1.6015499,"\int \frac{(f+g x)^2}{\left(a+b \log \left(c (d+e x)^n\right)\right)^3} \, dx","Integrate[(f + g*x)^2/(a + b*Log[c*(d + e*x)^n])^3,x]","\frac{e^{-\frac{3 a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-3/n} \left(e^{\frac{2 a}{b n}} (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)^2 \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)-8 g e^{\frac{a}{b n}} (d+e x) (d g-e f) \left(c (d+e x)^n\right)^{\frac{1}{n}} \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)+9 g^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \text{Ei}\left(\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)-b e n e^{\frac{3 a}{b n}} (f+g x) \left(c (d+e x)^n\right)^{3/n} \left(a (2 d g+e f+3 e g x)+b (2 d g+e (f+3 g x)) \log \left(c (d+e x)^n\right)+b e n (f+g x)\right)\right)}{2 b^3 e^3 n^3 \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,"((d + e*x)*(E^((2*a)/(b*n))*(e*f - d*g)^2*(c*(d + e*x)^n)^(2/n)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)]*(a + b*Log[c*(d + e*x)^n])^2 - 8*E^(a/(b*n))*g*(-(e*f) + d*g)*(d + e*x)*(c*(d + e*x)^n)^n^(-1)*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*(a + b*Log[c*(d + e*x)^n])^2 + 9*g^2*(d + e*x)^2*ExpIntegralEi[(3*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*(a + b*Log[c*(d + e*x)^n])^2 - b*e*E^((3*a)/(b*n))*n*(c*(d + e*x)^n)^(3/n)*(f + g*x)*(b*e*n*(f + g*x) + a*(e*f + 2*d*g + 3*e*g*x) + b*(2*d*g + e*(f + 3*g*x))*Log[c*(d + e*x)^n])))/(2*b^3*e^3*E^((3*a)/(b*n))*n^3*(c*(d + e*x)^n)^(3/n)*(a + b*Log[c*(d + e*x)^n])^2)","A",1
101,1,256,261,0.413579,"\int \frac{f+g x}{\left(a+b \log \left(c (d+e x)^n\right)\right)^3} \, dx","Integrate[(f + g*x)/(a + b*Log[c*(d + e*x)^n])^3,x]","-\frac{e^{-\frac{2 a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-2/n} \left(-e^{\frac{a}{b n}} (e f-d g) \left(c (d+e x)^n\right)^{\frac{1}{n}} \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \text{Ei}\left(\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)-4 g (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \text{Ei}\left(\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)+b n e^{\frac{2 a}{b n}} \left(c (d+e x)^n\right)^{2/n} \left(a (d g+e f+2 e g x)+b (d g+e (f+2 g x)) \log \left(c (d+e x)^n\right)+b e n (f+g x)\right)\right)}{2 b^3 e^2 n^3 \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,"-1/2*((d + e*x)*(-(E^(a/(b*n))*(e*f - d*g)*(c*(d + e*x)^n)^n^(-1)*ExpIntegralEi[(a + b*Log[c*(d + e*x)^n])/(b*n)]*(a + b*Log[c*(d + e*x)^n])^2) - 4*g*(d + e*x)*ExpIntegralEi[(2*(a + b*Log[c*(d + e*x)^n]))/(b*n)]*(a + b*Log[c*(d + e*x)^n])^2 + b*E^((2*a)/(b*n))*n*(c*(d + e*x)^n)^(2/n)*(b*e*n*(f + g*x) + a*(e*f + d*g + 2*e*g*x) + b*(d*g + e*(f + 2*g*x))*Log[c*(d + e*x)^n])))/(b^3*e^2*E^((2*a)/(b*n))*n^3*(c*(d + e*x)^n)^(2/n)*(a + b*Log[c*(d + e*x)^n])^2)","A",1
102,1,118,135,0.077179,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^3} \, dx","Integrate[(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) \left(a+b \log \left(c (d+e x)^n\right)+b n\right)}{2 b^2 e n^2 \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)*(a + b*n + b*Log[c*(d + e*x)^n]))/(2*b^2*e*n^2*(a + b*Log[c*(d + e*x)^n])^2)","A",1
103,0,0,27,1.3394021,"\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3} \, dx","Integrate[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,"Integrate[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^3), x]","A",-1
104,0,0,27,5.0843509,"\int \frac{1}{(f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3} \, dx","Integrate[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,"Integrate[1/((f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^3), x]","A",-1
105,1,374,404,0.5112587,"\int (f+g x)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)} \, dx","Integrate[(f + g*x)^2*Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\frac{(d+e x) \left(9 \sqrt{2 \pi } \sqrt{b} g \sqrt{n} e^{-\frac{2 a}{b n}} (d+e x) (d g-e f) \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)-18 \sqrt{\pi } \sqrt{b} \sqrt{n} e^{-\frac{a}{b n}} (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 \sqrt{3 \pi } \sqrt{b} g^2 \sqrt{n} e^{-\frac{3 a}{b n}} (d+e x)^2 \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)+36 (e f-d g)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}+36 g (d+e x) (e f-d g) \sqrt{a+b \log \left(c (d+e x)^n\right)}+12 g^2 (d+e x)^2 \sqrt{a+b \log \left(c (d+e x)^n\right)}\right)}{36 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,"((d + e*x)*((-18*Sqrt[b]*(e*f - d*g)^2*Sqrt[n]*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + (9*Sqrt[b]*g*(-(e*f) + d*g)*Sqrt[n]*Sqrt[2*Pi]*(d + e*x)*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)) - (2*Sqrt[b]*g^2*Sqrt[n]*Sqrt[3*Pi]*(d + e*x)^2*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(E^((3*a)/(b*n))*(c*(d + e*x)^n)^(3/n)) + 36*(e*f - d*g)^2*Sqrt[a + b*Log[c*(d + e*x)^n]] + 36*g*(e*f - d*g)*(d + e*x)*Sqrt[a + b*Log[c*(d + e*x)^n]] + 12*g^2*(d + e*x)^2*Sqrt[a + b*Log[c*(d + e*x)^n]]))/(36*e^3)","A",1
106,1,235,255,0.2866773,"\int (f+g x) \sqrt{a+b \log \left(c (d+e x)^n\right)} \, dx","Integrate[(f + g*x)*Sqrt[a + b*Log[c*(d + e*x)^n]],x]","-\frac{e^{-\frac{2 a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-2/n} \left(4 \sqrt{\pi } \sqrt{b} \sqrt{n} e^{\frac{a}{b n}} (e f-d g) \left(c (d+e x)^n\right)^{\frac{1}{n}} \text{erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)+\sqrt{2 \pi } \sqrt{b} g \sqrt{n} (d+e x) \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)-4 e^{\frac{2 a}{b n}} \left(c (d+e x)^n\right)^{2/n} (-d g+2 e f+e g x) \sqrt{a+b \log \left(c (d+e x)^n\right)}\right)}{8 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,"-1/8*((d + e*x)*(4*Sqrt[b]*E^(a/(b*n))*(e*f - d*g)*Sqrt[n]*Sqrt[Pi]*(c*(d + e*x)^n)^n^(-1)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])] + Sqrt[b]*g*Sqrt[n]*Sqrt[2*Pi]*(d + e*x)*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])] - 4*E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)*(2*e*f - d*g + e*g*x)*Sqrt[a + b*Log[c*(d + e*x)^n]]))/(e^2*E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n))","A",1
107,1,106,111,0.0469439,"\int \sqrt{a+b \log \left(c (d+e x)^n\right)} \, dx","Integrate[Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\frac{(d+e x) \left(2 \sqrt{a+b \log \left(c (d+e x)^n\right)}-\sqrt{\pi } \sqrt{b} \sqrt{n} e^{-\frac{a}{b n}} \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)\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,"((d + e*x)*(-((Sqrt[b]*Sqrt[n]*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1))) + 2*Sqrt[a + b*Log[c*(d + e*x)^n]]))/(2*e)","A",1
108,0,0,29,1.1762492,"\int \frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{f+g x} \, dx","Integrate[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,"Integrate[Sqrt[a + b*Log[c*(d + e*x)^n]]/(f + g*x), x]","A",-1
109,0,0,88,0.331316,"\int \frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{(f+g x)^2} \, dx","Integrate[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,"Integrate[Sqrt[a + b*Log[c*(d + e*x)^n]]/(f + g*x)^2, x]","A",-1
110,0,0,79,0.4088975,"\int \frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{(f+g x)^3} \, dx","Integrate[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,"Integrate[Sqrt[a + b*Log[c*(d + e*x)^n]]/(f + g*x)^3, x]","A",-1
111,1,446,526,1.0911121,"\int (f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2} \, dx","Integrate[(f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^(3/2),x]","\frac{(d+e x) \left(108 b n (e f-d g)^2 \left(\sqrt{\pi } \sqrt{b} \sqrt{n} e^{-\frac{a}{b n}} \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 \sqrt{a+b \log \left(c (d+e x)^n\right)}\right)+27 b g n (d+e x) (e f-d g) \left(\sqrt{2 \pi } \sqrt{b} \sqrt{n} e^{-\frac{2 a}{b n}} \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 \sqrt{a+b \log \left(c (d+e x)^n\right)}\right)+4 b g^2 n (d+e x)^2 \left(\sqrt{3 \pi } \sqrt{b} \sqrt{n} e^{-\frac{3 a}{b n}} \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 \sqrt{a+b \log \left(c (d+e x)^n\right)}\right)+144 (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}+144 g (d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}+48 g^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}\right)}{144 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,"((d + e*x)*(144*(e*f - d*g)^2*(a + b*Log[c*(d + e*x)^n])^(3/2) + 144*g*(e*f - d*g)*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^(3/2) + 48*g^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^(3/2) + 4*b*g^2*n*(d + e*x)^2*((Sqrt[b]*Sqrt[n]*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(E^((3*a)/(b*n))*(c*(d + e*x)^n)^(3/n)) - 6*Sqrt[a + b*Log[c*(d + e*x)^n]]) + 27*b*g*(e*f - d*g)*n*(d + e*x)*((Sqrt[b]*Sqrt[n]*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)) - 4*Sqrt[a + b*Log[c*(d + e*x)^n]]) + 108*b*(e*f - d*g)^2*n*((Sqrt[b]*Sqrt[n]*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) - 2*Sqrt[a + b*Log[c*(d + e*x)^n]])))/(144*e^3)","A",1
112,1,282,330,0.4150705,"\int (f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2} \, dx","Integrate[(f + g*x)*(a + b*Log[c*(d + e*x)^n])^(3/2),x]","\frac{(d+e x) \left(24 b n (e f-d g) \left(\sqrt{\pi } \sqrt{b} \sqrt{n} e^{-\frac{a}{b n}} \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 \sqrt{a+b \log \left(c (d+e x)^n\right)}\right)+3 b g n (d+e x) \left(\sqrt{2 \pi } \sqrt{b} \sqrt{n} e^{-\frac{2 a}{b n}} \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 \sqrt{a+b \log \left(c (d+e x)^n\right)}\right)+32 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}+16 g (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}\right)}{32 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,"((d + e*x)*(32*(e*f - d*g)*(a + b*Log[c*(d + e*x)^n])^(3/2) + 16*g*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^(3/2) + 3*b*g*n*(d + e*x)*((Sqrt[b]*Sqrt[n]*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)) - 4*Sqrt[a + b*Log[c*(d + e*x)^n]]) + 24*b*(e*f - d*g)*n*((Sqrt[b]*Sqrt[n]*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) - 2*Sqrt[a + b*Log[c*(d + e*x)^n]])))/(32*e^2)","A",1
113,1,127,143,0.0060674,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^(3/2),x]","\frac{(d+e x) \left(3 \sqrt{\pi } b^{3/2} n^{3/2} e^{-\frac{a}{b n}} \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 \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(2 a+2 b \log \left(c (d+e x)^n\right)-3 b n\right)\right)}{4 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,"((d + e*x)*((3*b^(3/2)*n^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + 2*Sqrt[a + b*Log[c*(d + e*x)^n]]*(2*a - 3*b*n + 2*b*Log[c*(d + e*x)^n])))/(4*e)","A",1
114,0,0,29,2.1292703,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{f+g x} \, dx","Integrate[(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,"Integrate[(a + b*Log[c*(d + e*x)^n])^(3/2)/(f + g*x), x]","A",-1
115,0,0,88,0.8456273,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{(f+g x)^2} \, dx","Integrate[(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,"Integrate[(a + b*Log[c*(d + e*x)^n])^(3/2)/(f + g*x)^2, x]","A",-1
116,0,0,79,0.8080572,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}{(f+g x)^3} \, dx","Integrate[(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,"Integrate[(a + b*Log[c*(d + e*x)^n])^(3/2)/(f + g*x)^3, x]","A",-1
117,1,511,660,1.816067,"\int (f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2} \, dx","Integrate[(f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^(5/2),x]","\frac{(d+e x) \left(-1080 b n (e f-d g)^2 \left(3 \sqrt{\pi } b^{3/2} n^{3/2} e^{-\frac{a}{b n}} \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 \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(2 a+2 b \log \left(c (d+e x)^n\right)-3 b n\right)\right)-135 b g n (d+e x) (e f-d g) \left(3 \sqrt{2 \pi } b^{3/2} n^{3/2} e^{-\frac{2 a}{b n}} \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 \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(4 a+4 b \log \left(c (d+e x)^n\right)-3 b n\right)\right)-40 b g^2 n (d+e x)^2 \left(\sqrt{3 \pi } b^{3/2} n^{3/2} e^{-\frac{3 a}{b n}} \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 \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(2 a+2 b \log \left(c (d+e x)^n\right)-b n\right)\right)+1728 (e f-d g)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}+1728 g (d+e x) (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}+576 g^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}\right)}{1728 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,"((d + e*x)*(1728*(e*f - d*g)^2*(a + b*Log[c*(d + e*x)^n])^(5/2) + 1728*g*(e*f - d*g)*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^(5/2) + 576*g^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^(5/2) - 1080*b*(e*f - d*g)^2*n*((3*b^(3/2)*n^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + 2*Sqrt[a + b*Log[c*(d + e*x)^n]]*(2*a - 3*b*n + 2*b*Log[c*(d + e*x)^n])) - 40*b*g^2*n*(d + e*x)^2*((b^(3/2)*n^(3/2)*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(E^((3*a)/(b*n))*(c*(d + e*x)^n)^(3/n)) + 6*Sqrt[a + b*Log[c*(d + e*x)^n]]*(2*a - b*n + 2*b*Log[c*(d + e*x)^n])) - 135*b*g*(e*f - d*g)*n*(d + e*x)*((3*b^(3/2)*n^(3/2)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)) + 4*Sqrt[a + b*Log[c*(d + e*x)^n]]*(4*a - 3*b*n + 4*b*Log[c*(d + e*x)^n]))))/(1728*e^3)","A",1
118,1,326,413,0.6725381,"\int (f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2} \, dx","Integrate[(f + g*x)*(a + b*Log[c*(d + e*x)^n])^(5/2),x]","\frac{(d+e x) \left(-80 b n (e f-d g) \left(3 \sqrt{\pi } b^{3/2} n^{3/2} e^{-\frac{a}{b n}} \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 \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(2 a+2 b \log \left(c (d+e x)^n\right)-3 b n\right)\right)-5 b g n (d+e x) \left(3 \sqrt{2 \pi } b^{3/2} n^{3/2} e^{-\frac{2 a}{b n}} \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 \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(4 a+4 b \log \left(c (d+e x)^n\right)-3 b n\right)\right)+128 (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}+64 g (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}\right)}{128 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,"((d + e*x)*(128*(e*f - d*g)*(a + b*Log[c*(d + e*x)^n])^(5/2) + 64*g*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^(5/2) - 80*b*(e*f - d*g)*n*((3*b^(3/2)*n^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + 2*Sqrt[a + b*Log[c*(d + e*x)^n]]*(2*a - 3*b*n + 2*b*Log[c*(d + e*x)^n])) - 5*b*g*n*(d + e*x)*((3*b^(3/2)*n^(3/2)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])])/(E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)) + 4*Sqrt[a + b*Log[c*(d + e*x)^n]]*(4*a - 3*b*n + 4*b*Log[c*(d + e*x)^n]))))/(128*e^2)","A",1
119,1,152,179,0.1724033,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^(5/2),x]","\frac{(d+e x) \left(8 \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}-5 b n \left(3 \sqrt{\pi } b^{3/2} n^{3/2} e^{-\frac{a}{b n}} \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 \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(2 a+2 b \log \left(c (d+e x)^n\right)-3 b n\right)\right)\right)}{8 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,"((d + e*x)*(8*(a + b*Log[c*(d + e*x)^n])^(5/2) - 5*b*n*((3*b^(3/2)*n^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + 2*Sqrt[a + b*Log[c*(d + e*x)^n]]*(2*a - 3*b*n + 2*b*Log[c*(d + e*x)^n]))))/(8*e)","A",1
120,0,0,29,2.1516449,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{f+g x} \, dx","Integrate[(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,"Integrate[(a + b*Log[c*(d + e*x)^n])^(5/2)/(f + g*x), x]","A",-1
121,0,0,88,7.0551814,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{(f+g x)^2} \, dx","Integrate[(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,"Integrate[(a + b*Log[c*(d + e*x)^n])^(5/2)/(f + g*x)^2, x]","A",-1
122,0,0,79,6.4771029,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}}{(f+g x)^3} \, dx","Integrate[(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,"Integrate[(a + b*Log[c*(d + e*x)^n])^(5/2)/(f + g*x)^3, x]","A",-1
123,1,331,383,0.4495807,"\int \frac{(f+g x)^3}{\sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Integrate[(f + g*x)^3/Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\frac{\sqrt{\pi } e^{-\frac{4 a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-4/n} \left(2 \sqrt{3} g^2 e^{\frac{a}{b n}} (d+e x)^2 (e f-d g) \left(c (d+e x)^n\right)^{\frac{1}{n}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)+3 \sqrt{2} g e^{\frac{2 a}{b n}} (d+e x) (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)+2 e^{\frac{3 a}{b n}} (e f-d g)^3 \left(c (d+e x)^n\right)^{3/n} \text{erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)+g^3 (d+e x)^3 \text{erfi}\left(\frac{2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)\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,"(Sqrt[Pi]*(d + e*x)*(2*E^((3*a)/(b*n))*(e*f - d*g)^3*(c*(d + e*x)^n)^(3/n)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])] + g^3*(d + e*x)^3*Erfi[(2*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])] + 3*Sqrt[2]*E^((2*a)/(b*n))*g*(e*f - d*g)^2*(d + e*x)*(c*(d + e*x)^n)^(2/n)*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])] + 2*Sqrt[3]*E^(a/(b*n))*g^2*(e*f - d*g)*(d + e*x)^2*(c*(d + e*x)^n)^n^(-1)*Erfi[(Sqrt[3]*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))","A",1
124,1,252,283,0.2765202,"\int \frac{(f+g x)^2}{\sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Integrate[(f + g*x)^2/Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\frac{\sqrt{\pi } e^{-\frac{3 a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-3/n} \left(3 e^{\frac{2 a}{b n}} (e f-d g)^2 \left(c (d+e x)^n\right)^{2/n} \text{erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)+3 \sqrt{2} g e^{\frac{a}{b n}} (d+e x) (e f-d g) \left(c (d+e x)^n\right)^{\frac{1}{n}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)+\sqrt{3} g^2 (d+e x)^2 \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)\right)}{3 \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,"(Sqrt[Pi]*(d + e*x)*(3*E^((2*a)/(b*n))*(e*f - d*g)^2*(c*(d + e*x)^n)^(2/n)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])] + 3*Sqrt[2]*E^(a/(b*n))*g*(e*f - d*g)*(d + e*x)*(c*(d + e*x)^n)^n^(-1)*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])] + Sqrt[3]*g^2*(d + e*x)^2*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])]))/(3*Sqrt[b]*e^3*E^((3*a)/(b*n))*Sqrt[n]*(c*(d + e*x)^n)^(3/n))","A",1
125,1,164,181,0.1550924,"\int \frac{f+g x}{\sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Integrate[(f + g*x)/Sqrt[a + b*Log[c*(d + e*x)^n]],x]","\frac{\sqrt{\pi } e^{-\frac{2 a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-2/n} \left(2 e^{\frac{a}{b n}} (e f-d g) \left(c (d+e x)^n\right)^{\frac{1}{n}} \text{erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)+\sqrt{2} g (d+e x) \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)\right)}{2 \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,"(Sqrt[Pi]*(d + e*x)*(2*E^(a/(b*n))*(e*f - d*g)*(c*(d + e*x)^n)^n^(-1)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])] + Sqrt[2]*g*(d + e*x)*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])]))/(2*Sqrt[b]*e^2*E^((2*a)/(b*n))*Sqrt[n]*(c*(d + e*x)^n)^(2/n))","A",1
126,1,80,80,0.0168063,"\int \frac{1}{\sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Integrate[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",1
127,0,0,29,0.0833641,"\int \frac{1}{(f+g x) \sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Integrate[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,"Integrate[1/((f + g*x)*Sqrt[a + b*Log[c*(d + e*x)^n]]), x]","A",-1
128,1,1281,422,2.8393952,"\int \frac{(f+g x)^3}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}} \, dx","Integrate[(f + g*x)^3/(a + b*Log[c*(d + e*x)^n])^(3/2),x]","\frac{2 \left(2 e^{-\frac{4 a}{b n}} g^3 \sqrt{\pi } (d+e x)^4 \text{erfi}\left(\frac{2 \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right) \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(c (d+e x)^n\right)^{-4/n}-3 d e^{-\frac{3 a}{b n}} g^3 \sqrt{3 \pi } (d+e x)^3 \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right) \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(c (d+e x)^n\right)^{-3/n}+3 e e^{-\frac{3 a}{b n}} f g^2 \sqrt{3 \pi } (d+e x)^3 \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right) \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(c (d+e x)^n\right)^{-3/n}+3 d^2 e^{-\frac{2 a}{b n}} g^3 \sqrt{2 \pi } (d+e x)^2 \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right) \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(c (d+e x)^n\right)^{-2/n}-6 d e e^{-\frac{2 a}{b n}} f g^2 \sqrt{2 \pi } (d+e x)^2 \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right) \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(c (d+e x)^n\right)^{-2/n}+3 e^2 e^{-\frac{2 a}{b n}} f^2 g \sqrt{2 \pi } (d+e x)^2 \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right) \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(c (d+e x)^n\right)^{-2/n}-d^3 e^{-\frac{a}{b n}} g^3 \sqrt{\pi } (d+e x) \text{erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right) \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(c (d+e x)^n\right)^{-1/n}+3 d^2 e e^{-\frac{a}{b n}} f g^2 \sqrt{\pi } (d+e x) \text{erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right) \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(c (d+e x)^n\right)^{-1/n}-6 d e^2 e^{-\frac{a}{b n}} f^2 g \sqrt{\pi } (d+e x) \text{erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right) \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(c (d+e x)^n\right)^{-1/n}+\sqrt{b} e^3 e^{-\frac{a}{b n}} f^3 \sqrt{n} (d+e x) \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \sqrt{-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}} \left(c (d+e x)^n\right)^{-1/n}+3 \sqrt{b} d e^2 e^{-\frac{a}{b n}} f^2 g \sqrt{n} (d+e x) \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \sqrt{-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}} \left(c (d+e x)^n\right)^{-1/n}-\sqrt{b} e^4 g^3 \sqrt{n} x^4-\sqrt{b} d e^3 g^3 \sqrt{n} x^3-3 \sqrt{b} e^4 f g^2 \sqrt{n} x^3-3 \sqrt{b} d e^3 f g^2 \sqrt{n} x^2-3 \sqrt{b} e^4 f^2 g \sqrt{n} x^2-\sqrt{b} e^4 f^3 \sqrt{n} x-3 \sqrt{b} d e^3 f^2 g \sqrt{n} x-\sqrt{b} d e^3 f^3 \sqrt{n}\right)}{b^{3/2} e^4 n^{3/2} \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*(-(Sqrt[b]*d*e^3*f^3*Sqrt[n]) - Sqrt[b]*e^4*f^3*Sqrt[n]*x - 3*Sqrt[b]*d*e^3*f^2*g*Sqrt[n]*x - 3*Sqrt[b]*e^4*f^2*g*Sqrt[n]*x^2 - 3*Sqrt[b]*d*e^3*f*g^2*Sqrt[n]*x^2 - 3*Sqrt[b]*e^4*f*g^2*Sqrt[n]*x^3 - Sqrt[b]*d*e^3*g^3*Sqrt[n]*x^3 - Sqrt[b]*e^4*g^3*Sqrt[n]*x^4 - (6*d*e^2*f^2*g*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + (3*d^2*e*f*g^2*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) - (d^3*g^3*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + (2*g^3*Sqrt[Pi]*(d + e*x)^4*Erfi[(2*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(E^((4*a)/(b*n))*(c*(d + e*x)^n)^(4/n)) + (3*e^2*f^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])]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)) - (6*d*e*f*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])]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)) + (3*d^2*g^3*Sqrt[2*Pi]*(d + e*x)^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)) + (3*e*f*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])]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(E^((3*a)/(b*n))*(c*(d + e*x)^n)^(3/n)) - (3*d*g^3*Sqrt[3*Pi]*(d + e*x)^3*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(E^((3*a)/(b*n))*(c*(d + e*x)^n)^(3/n)) + (Sqrt[b]*e^3*f^3*Sqrt[n]*(d + e*x)*Gamma[1/2, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*Sqrt[-((a + b*Log[c*(d + e*x)^n])/(b*n))])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + (3*Sqrt[b]*d*e^2*f^2*g*Sqrt[n]*(d + e*x)*Gamma[1/2, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*Sqrt[-((a + b*Log[c*(d + e*x)^n])/(b*n))])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1))))/(b^(3/2)*e^4*n^(3/2)*Sqrt[a + b*Log[c*(d + e*x)^n]])","B",1
129,1,828,325,1.4333671,"\int \frac{(f+g x)^2}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}} \, dx","Integrate[(f + g*x)^2/(a + b*Log[c*(d + e*x)^n])^(3/2),x]","\frac{2 \left(e^{-\frac{3 a}{b n}} g^2 \sqrt{3 \pi } (d+e x)^3 \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right) \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(c (d+e x)^n\right)^{-3/n}-2 d e^{-\frac{2 a}{b n}} g^2 \sqrt{2 \pi } (d+e x)^2 \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right) \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(c (d+e x)^n\right)^{-2/n}+2 e e^{-\frac{2 a}{b n}} f g \sqrt{2 \pi } (d+e x)^2 \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right) \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(c (d+e x)^n\right)^{-2/n}+d^2 e^{-\frac{a}{b n}} g^2 \sqrt{\pi } (d+e x) \text{erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right) \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(c (d+e x)^n\right)^{-1/n}-4 d e e^{-\frac{a}{b n}} f g \sqrt{\pi } (d+e x) \text{erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right) \sqrt{a+b \log \left(c (d+e x)^n\right)} \left(c (d+e x)^n\right)^{-1/n}+\sqrt{b} e^2 e^{-\frac{a}{b n}} f^2 \sqrt{n} (d+e x) \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \sqrt{-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}} \left(c (d+e x)^n\right)^{-1/n}+2 \sqrt{b} d e e^{-\frac{a}{b n}} f g \sqrt{n} (d+e x) \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right) \sqrt{-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}} \left(c (d+e x)^n\right)^{-1/n}-\sqrt{b} e^3 g^2 \sqrt{n} x^3-\sqrt{b} d e^2 g^2 \sqrt{n} x^2-2 \sqrt{b} e^3 f g \sqrt{n} x^2-\sqrt{b} e^3 f^2 \sqrt{n} x-2 \sqrt{b} d e^2 f g \sqrt{n} x-\sqrt{b} d e^2 f^2 \sqrt{n}\right)}{b^{3/2} e^3 n^{3/2} \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*(-(Sqrt[b]*d*e^2*f^2*Sqrt[n]) - Sqrt[b]*e^3*f^2*Sqrt[n]*x - 2*Sqrt[b]*d*e^2*f*g*Sqrt[n]*x - 2*Sqrt[b]*e^3*f*g*Sqrt[n]*x^2 - Sqrt[b]*d*e^2*g^2*Sqrt[n]*x^2 - Sqrt[b]*e^3*g^2*Sqrt[n]*x^3 - (4*d*e*f*g*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + (d^2*g^2*Sqrt[Pi]*(d + e*x)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + (2*e*f*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[a + b*Log[c*(d + e*x)^n]])/(E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)) - (2*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])]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(E^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)) + (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])]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(E^((3*a)/(b*n))*(c*(d + e*x)^n)^(3/n)) + (Sqrt[b]*e^2*f^2*Sqrt[n]*(d + e*x)*Gamma[1/2, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*Sqrt[-((a + b*Log[c*(d + e*x)^n])/(b*n))])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)) + (2*Sqrt[b]*d*e*f*g*Sqrt[n]*(d + e*x)*Gamma[1/2, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*Sqrt[-((a + b*Log[c*(d + e*x)^n])/(b*n))])/(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1))))/(b^(3/2)*e^3*n^(3/2)*Sqrt[a + b*Log[c*(d + e*x)^n]])","B",1
130,1,338,220,0.8364331,"\int \frac{f+g x}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}} \, dx","Integrate[(f + g*x)/(a + b*Log[c*(d + e*x)^n])^(3/2),x]","\frac{2 e^{-\frac{2 a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-2/n} \left(-2 \sqrt{\pi } d g e^{\frac{a}{b n}} \left(c (d+e x)^n\right)^{\frac{1}{n}} \sqrt{a+b \log \left(c (d+e x)^n\right)} \text{erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)+\sqrt{2 \pi } g (d+e x) \sqrt{a+b \log \left(c (d+e x)^n\right)} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)+\sqrt{b} \sqrt{n} e^{\frac{a}{b n}} \left(c (d+e x)^n\right)^{\frac{1}{n}} \left((d g+e f) \sqrt{-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}} \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)-e e^{\frac{a}{b n}} (f+g x) \left(c (d+e x)^n\right)^{\frac{1}{n}}\right)\right)}{b^{3/2} e^2 n^{3/2} \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*(d + e*x)*(-2*d*E^(a/(b*n))*g*Sqrt[Pi]*(c*(d + e*x)^n)^n^(-1)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])]*Sqrt[a + b*Log[c*(d + e*x)^n]] + g*Sqrt[2*Pi]*(d + e*x)*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])]*Sqrt[a + b*Log[c*(d + e*x)^n]] + Sqrt[b]*E^(a/(b*n))*Sqrt[n]*(c*(d + e*x)^n)^n^(-1)*(-(e*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)*(f + g*x)) + (e*f + d*g)*Gamma[1/2, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*Sqrt[-((a + b*Log[c*(d + e*x)^n])/(b*n))])))/(b^(3/2)*e^2*E^((2*a)/(b*n))*n^(3/2)*(c*(d + e*x)^n)^(2/n)*Sqrt[a + b*Log[c*(d + e*x)^n]])","A",1
131,1,139,116,0.1288323,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^(-3/2),x]","-\frac{2 e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \left(e^{\frac{a}{b n}} \left(c (d+e x)^n\right)^{\frac{1}{n}}-\sqrt{-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}} \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)\right)}{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*(d + e*x)*(E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1) - Gamma[1/2, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*Sqrt[-((a + b*Log[c*(d + e*x)^n])/(b*n))]))/(b*e*E^(a/(b*n))*n*(c*(d + e*x)^n)^n^(-1)*Sqrt[a + b*Log[c*(d + e*x)^n]])","A",1
132,0,0,29,0.2553288,"\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}} \, dx","Integrate[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,"Integrate[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^(3/2)), x]","A",-1
133,1,2647,520,7.0752978,"\int \frac{(f+g x)^3}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}} \, dx","Integrate[(f + g*x)^3/(a + b*Log[c*(d + e*x)^n])^(5/2),x]","\text{Result too large to show}","\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,"(8*f^2*g*Sqrt[Pi]*(-2*d*E^((a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))/(b*n))*Erfi[Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])]/(Sqrt[b]*Sqrt[n])] + Sqrt[2]*Erfi[(Sqrt[2]*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])])/(Sqrt[b]*Sqrt[n])])*Sqrt[a + b*Log[c*(d + e*x)^n]])/(b^(5/2)*e^2*E^((2*(a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])))/(b*n))*n^(5/2)*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])]) + (20*d*f*g^2*Sqrt[Pi]*(-2*d*E^((a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))/(b*n))*Erfi[Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])]/(Sqrt[b]*Sqrt[n])] + Sqrt[2]*Erfi[(Sqrt[2]*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])])/(Sqrt[b]*Sqrt[n])])*Sqrt[a + b*Log[c*(d + e*x)^n]])/(b^(5/2)*e^3*E^((2*(a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])))/(b*n))*n^(5/2)*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])]) + (4*d^2*g^3*Sqrt[Pi]*(-2*d*E^((a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))/(b*n))*Erfi[Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])]/(Sqrt[b]*Sqrt[n])] + Sqrt[2]*Erfi[(Sqrt[2]*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])])/(Sqrt[b]*Sqrt[n])])*Sqrt[a + b*Log[c*(d + e*x)^n]])/(b^(5/2)*e^4*E^((2*(a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])))/(b*n))*n^(5/2)*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])]) + (12*f*g^2*Sqrt[Pi]*(3*d^2*E^((2*(a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])))/(b*n))*Erfi[Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])]/(Sqrt[b]*Sqrt[n])] - 3*Sqrt[2]*d*E^((a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))/(b*n))*Erfi[(Sqrt[2]*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])])/(Sqrt[b]*Sqrt[n])] + Sqrt[3]*Erfi[(Sqrt[3]*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])])/(Sqrt[b]*Sqrt[n])])*Sqrt[a + b*Log[c*(d + e*x)^n]])/(b^(5/2)*e^3*E^((3*(a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])))/(b*n))*n^(5/2)*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])]) + (28*d*g^3*Sqrt[Pi]*(3*d^2*E^((2*(a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])))/(b*n))*Erfi[Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])]/(Sqrt[b]*Sqrt[n])] - 3*Sqrt[2]*d*E^((a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))/(b*n))*Erfi[(Sqrt[2]*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])])/(Sqrt[b]*Sqrt[n])] + Sqrt[3]*Erfi[(Sqrt[3]*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])])/(Sqrt[b]*Sqrt[n])])*Sqrt[a + b*Log[c*(d + e*x)^n]])/(3*b^(5/2)*e^4*E^((3*(a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])))/(b*n))*n^(5/2)*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])]) + (32*g^3*Sqrt[Pi]*(-2*d^3*E^((3*(a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])))/(b*n))*Erfi[Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])]/(Sqrt[b]*Sqrt[n])] + Erfi[(2*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])])/(Sqrt[b]*Sqrt[n])] + d*E^((a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))/(b*n))*(3*Sqrt[2]*d*E^((a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))/(b*n))*Erfi[(Sqrt[2]*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])])/(Sqrt[b]*Sqrt[n])] - 2*Sqrt[3]*Erfi[(Sqrt[3]*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])])/(Sqrt[b]*Sqrt[n])]))*Sqrt[a + b*Log[c*(d + e*x)^n]])/(3*b^(5/2)*e^4*E^((4*(a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])))/(b*n))*n^(5/2)*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])]) + (4*f^3*Gamma[1/2, -((a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))/(b*n))]*Sqrt[-((a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))/(b*n))])/(3*b^2*e*E^((a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))/(b*n))*n^2*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])]) + (12*d*f^2*g*Gamma[1/2, -((a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))/(b*n))]*Sqrt[-((a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))/(b*n))])/(b^2*e^2*E^((a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))/(b*n))*n^2*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])]) + (8*d^2*f*g^2*Gamma[1/2, -((a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))/(b*n))]*Sqrt[-((a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))/(b*n))])/(b^2*e^3*E^((a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))/(b*n))*n^2*Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])]) + Sqrt[a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])]*((-2*(d + e*x)*(f + g*x)^3)/(3*b*e*n*(a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))^2) - (4*(d + e*x)*(f + g*x)^2*(e*f + 3*d*g + 4*e*g*x))/(3*b^2*e^2*n^2*(a + b*n*Log[d + e*x] + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))))","B",1
134,1,527,421,4.5818189,"\int \frac{(f+g x)^2}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}} \, dx","Integrate[(f + g*x)^2/(a + b*Log[c*(d + e*x)^n])^(5/2),x]","-\frac{2 e^{-\frac{3 a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-3/n} \left(\sqrt{b} \sqrt{n} e^{\frac{2 a}{b n}} \left(c (d+e x)^n\right)^{2/n} \left(2 b n \left(2 d^2 g^2+6 d e f g+e^2 f^2\right) \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)+e e^{\frac{a}{b n}} (f+g x) \left(c (d+e x)^n\right)^{\frac{1}{n}} \left(2 a (2 d g+e f+3 e g x)+2 b (2 d g+e (f+3 g x)) \log \left(c (d+e x)^n\right)+b e n (f+g x)\right)\right)+2 \sqrt{\pi } d g e^{\frac{2 a}{b n}} (d g+8 e f) \left(c (d+e x)^n\right)^{2/n} \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2} \text{erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)+8 \sqrt{2 \pi } g e^{\frac{a}{b n}} (d+e x) (d g-e f) \left(c (d+e x)^n\right)^{\frac{1}{n}} \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)-6 \sqrt{3 \pi } g^2 (d+e x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)\right)}{3 b^{5/2} e^3 n^{5/2} \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,"(-2*(d + e*x)*(2*d*E^((2*a)/(b*n))*g*(8*e*f + d*g)*Sqrt[Pi]*(c*(d + e*x)^n)^(2/n)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])]*(a + b*Log[c*(d + e*x)^n])^(3/2) + 8*E^(a/(b*n))*g*(-(e*f) + d*g)*Sqrt[2*Pi]*(d + e*x)*(c*(d + e*x)^n)^n^(-1)*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])]*(a + b*Log[c*(d + e*x)^n])^(3/2) - 6*g^2*Sqrt[3*Pi]*(d + e*x)^2*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])]*(a + b*Log[c*(d + e*x)^n])^(3/2) + Sqrt[b]*E^((2*a)/(b*n))*Sqrt[n]*(c*(d + e*x)^n)^(2/n)*(2*b*(e^2*f^2 + 6*d*e*f*g + 2*d^2*g^2)*n*Gamma[1/2, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^(3/2) + e*E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)*(f + g*x)*(b*e*n*(f + g*x) + 2*a*(e*f + 2*d*g + 3*e*g*x) + 2*b*(2*d*g + e*(f + 3*g*x))*Log[c*(d + e*x)^n]))))/(3*b^(5/2)*e^3*E^((3*a)/(b*n))*n^(5/2)*(c*(d + e*x)^n)^(3/n)*(a + b*Log[c*(d + e*x)^n])^(3/2))","A",1
135,1,353,311,1.9619326,"\int \frac{f+g x}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}} \, dx","Integrate[(f + g*x)/(a + b*Log[c*(d + e*x)^n])^(5/2),x]","\frac{2 e^{-\frac{2 a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-2/n} \left(-8 \sqrt{\pi } d g e^{\frac{a}{b n}} \left(c (d+e x)^n\right)^{\frac{1}{n}} \text{erfi}\left(\frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)+4 \sqrt{2 \pi } g (d+e x) \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{b} \sqrt{n}}\right)-\frac{\sqrt{b} \sqrt{n} e^{\frac{a}{b n}} \left(c (d+e x)^n\right)^{\frac{1}{n}} \left(e^{\frac{a}{b n}} \left(c (d+e x)^n\right)^{\frac{1}{n}} \left(2 a (d g+e f+2 e g x)+2 b (d g+e (f+2 g x)) \log \left(c (d+e x)^n\right)+b e n (f+g x)\right)+2 b n (3 d g+e f) \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)\right)}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}}\right)}{3 b^{5/2} e^2 n^{5/2}}","\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,"(2*(d + e*x)*(-8*d*E^(a/(b*n))*g*Sqrt[Pi]*(c*(d + e*x)^n)^n^(-1)*Erfi[Sqrt[a + b*Log[c*(d + e*x)^n]]/(Sqrt[b]*Sqrt[n])] + 4*g*Sqrt[2*Pi]*(d + e*x)*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d + e*x)^n]])/(Sqrt[b]*Sqrt[n])] - (Sqrt[b]*E^(a/(b*n))*Sqrt[n]*(c*(d + e*x)^n)^n^(-1)*(2*b*(e*f + 3*d*g)*n*Gamma[1/2, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^(3/2) + E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)*(b*e*n*(f + g*x) + 2*a*(e*f + d*g + 2*e*g*x) + 2*b*(d*g + e*(f + 2*g*x))*Log[c*(d + e*x)^n])))/(a + b*Log[c*(d + e*x)^n])^(3/2)))/(3*b^(5/2)*e^2*E^((2*a)/(b*n))*n^(5/2)*(c*(d + e*x)^n)^(2/n))","A",1
136,1,163,156,0.1626779,"\int \frac{1}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^(-5/2),x]","-\frac{2 e^{-\frac{a}{b n}} (d+e x) \left(c (d+e x)^n\right)^{-1/n} \left(e^{\frac{a}{b n}} \left(c (d+e x)^n\right)^{\frac{1}{n}} \left(2 a+2 b \log \left(c (d+e x)^n\right)+b n\right)+2 b n \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)\right)}{3 b^2 e n^2 \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,"(-2*(d + e*x)*(2*b*n*Gamma[1/2, -((a + b*Log[c*(d + e*x)^n])/(b*n))]*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^(3/2) + E^(a/(b*n))*(c*(d + e*x)^n)^n^(-1)*(2*a + b*n + 2*b*Log[c*(d + e*x)^n])))/(3*b^2*e*E^(a/(b*n))*n^2*(c*(d + e*x)^n)^n^(-1)*(a + b*Log[c*(d + e*x)^n])^(3/2))","A",1
137,0,0,29,0.5586211,"\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^{5/2}} \, dx","Integrate[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,"Integrate[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^(5/2)), x]","A",-1
138,1,137,163,0.2276972,"\int (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Integrate[(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n]),x]","\frac{2 \left((f+g x)^{5/2} \left(a+b \log \left(c (d+e x)^n\right)\right)-\frac{2 b n (e f-d g) \left(\sqrt{e} \sqrt{f+g x} (-3 d g+4 e f+e g x)-3 (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)\right)}{3 e^{5/2}}-\frac{2}{5} b n (f+g x)^{5/2}\right)}{5 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 (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 \sqrt{f+g x} (e f-d g)^2}{5 e^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,"(2*((-2*b*n*(f + g*x)^(5/2))/5 - (2*b*(e*f - d*g)*n*(Sqrt[e]*Sqrt[f + g*x]*(4*e*f - 3*d*g + e*g*x) - 3*(e*f - d*g)^(3/2)*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]))/(3*e^(5/2)) + (f + g*x)^(5/2)*(a + b*Log[c*(d + e*x)^n])))/(5*g)","A",1
139,1,118,132,0.1364086,"\int \sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Integrate[Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n]),x]","\frac{2 \left(\sqrt{e} \sqrt{f+g x} \left(3 a e (f+g x)+3 b e (f+g x) \log \left(c (d+e x)^n\right)-2 b n (-3 d g+4 e f+e g x)\right)+6 b n (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)\right)}{9 e^{3/2} 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,"(2*(6*b*(e*f - d*g)^(3/2)*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]] + Sqrt[e]*Sqrt[f + g*x]*(3*a*e*(f + g*x) - 2*b*n*(4*e*f - 3*d*g + e*g*x) + 3*b*e*(f + g*x)*Log[c*(d + e*x)^n])))/(9*e^(3/2)*g)","A",1
140,1,83,97,0.0827817,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\sqrt{f+g x}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/Sqrt[f + g*x],x]","\frac{2 \left(\sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)-2 b n\right)+\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)}{\sqrt{e}}\right)}{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,"(2*((2*b*Sqrt[e*f - d*g]*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/Sqrt[e] + Sqrt[f + g*x]*(a - 2*b*n + b*Log[c*(d + e*x)^n])))/g","A",1
141,1,80,81,0.1699679,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x)^{3/2}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(f + g*x)^(3/2),x]","\frac{2 \left(-\frac{a+b \log \left(c (d+e x)^n\right)}{\sqrt{f+g x}}-\frac{2 b \sqrt{e} n \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{\sqrt{e f-d g}}\right)}{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,"(2*((-2*b*Sqrt[e]*n*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/Sqrt[e*f - d*g] - (a + b*Log[c*(d + e*x)^n])/Sqrt[f + g*x]))/g","A",1
142,1,85,114,0.0362657,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x)^{5/2}} \, dx","Integrate[(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 n \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{e (f+g x)}{e f-d g}\right)}{3 g \sqrt{f+g x} (d g-e f)}","-\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*Hypergeometric2F1[-1/2, 1, 1/2, (e*(f + g*x))/(e*f - d*g)])/(3*g*(-(e*f) + d*g)*Sqrt[f + g*x]) - (2*(a + b*Log[c*(d + e*x)^n]))/(3*g*(f + g*x)^(3/2))","C",1
143,1,78,145,0.0462877,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x)^{7/2}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(f + g*x)^(7/2),x]","\frac{2 \left(\frac{2 b e n (f+g x) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{e (f+g x)}{e f-d g}\right)}{e f-d g}-3 \left(a+b \log \left(c (d+e x)^n\right)\right)\right)}{15 g (f+g x)^{5/2}}","-\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^{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^2 n}{5 g \sqrt{f+g x} (e f-d g)^2}+\frac{4 b e n}{15 g (f+g x)^{3/2} (e f-d g)}",1,"(2*((2*b*e*n*(f + g*x)*Hypergeometric2F1[-3/2, 1, -1/2, (e*(f + g*x))/(e*f - d*g)])/(e*f - d*g) - 3*(a + b*Log[c*(d + e*x)^n])))/(15*g*(f + g*x)^(5/2))","C",1
144,1,78,176,0.0510058,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x)^{9/2}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(f + g*x)^(9/2),x]","\frac{2 \left(\frac{2 b e n (f+g x) \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\frac{e (f+g x)}{e f-d g}\right)}{e f-d g}-5 \left(a+b \log \left(c (d+e x)^n\right)\right)\right)}{35 g (f+g x)^{7/2}}","-\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^{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^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 n}{35 g (f+g x)^{5/2} (e f-d g)}",1,"(2*((2*b*e*n*(f + g*x)*Hypergeometric2F1[-5/2, 1, -3/2, (e*(f + g*x))/(e*f - d*g)])/(e*f - d*g) - 5*(a + b*Log[c*(d + e*x)^n])))/(35*g*(f + g*x)^(7/2))","C",1
145,1,854,590,1.9426263,"\int (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Integrate[(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{2 \left((f+g x)^{5/2} \left(a+b \log \left(c (d+e x)^n\right)\right)^2-\frac{b n \left(450 \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) (e f-d g)^{5/2}-450 \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) (e f-d g)^{5/2}-225 b n \left(\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)\right)+2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)\right) (e f-d g)^{5/2}+225 b n \left(\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)\right)+2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)\right) (e f-d g)^{5/2}-1800 b n \left(\sqrt{e} \sqrt{f+g x}-\sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)\right) (e f-d g)^2+900 b \sqrt{e} \sqrt{f+g x} \log \left(c (d+e x)^n\right) (e f-d g)^2+900 a \sqrt{e} \sqrt{f+g x} (e f-d g)^2-200 b n \left(\sqrt{e} \sqrt{f+g x} (4 e f-3 d g+e g x)-3 (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)\right) (e f-d g)+300 e^{3/2} (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right) (e f-d g)-24 b n \left(3 e^{5/2} (f+g x)^{5/2}+5 (e f-d g) \left(\sqrt{e} \sqrt{f+g x} (4 e f-3 d g+e g x)-3 (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)\right)\right)+180 e^{5/2} (f+g x)^{5/2} \left(a+b \log \left(c (d+e x)^n\right)\right)\right)}{225 e^{5/2}}\right)}{5 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 \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 (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{8 b^2 n^2 (e f-d g)^{5/2} \text{Li}_2\left(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^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{368 b^2 n^2 \sqrt{f+g x} (e f-d g)^2}{75 e^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,"(2*((f + g*x)^(5/2)*(a + b*Log[c*(d + e*x)^n])^2 - (b*n*(900*a*Sqrt[e]*(e*f - d*g)^2*Sqrt[f + g*x] - 1800*b*(e*f - d*g)^2*n*(Sqrt[e]*Sqrt[f + g*x] - Sqrt[e*f - d*g]*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]) - 200*b*(e*f - d*g)*n*(Sqrt[e]*Sqrt[f + g*x]*(4*e*f - 3*d*g + e*g*x) - 3*(e*f - d*g)^(3/2)*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]) - 24*b*n*(3*e^(5/2)*(f + g*x)^(5/2) + 5*(e*f - d*g)*(Sqrt[e]*Sqrt[f + g*x]*(4*e*f - 3*d*g + e*g*x) - 3*(e*f - d*g)^(3/2)*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])) + 900*b*Sqrt[e]*(e*f - d*g)^2*Sqrt[f + g*x]*Log[c*(d + e*x)^n] + 300*e^(3/2)*(e*f - d*g)*(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n]) + 180*e^(5/2)*(f + g*x)^(5/2)*(a + b*Log[c*(d + e*x)^n]) + 450*(e*f - d*g)^(5/2)*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] - 450*(e*f - d*g)^(5/2)*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] - 225*b*(e*f - d*g)^(5/2)*n*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] + 2*Log[(1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]) + 2*PolyLog[2, 1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 225*b*(e*f - d*g)^(5/2)*n*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] + 2*Log[1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 2*PolyLog[2, (1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2])))/(225*e^(5/2))))/(5*g)","A",1
146,1,643,510,1.1692473,"\int \sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Integrate[Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{2 \left((f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)^2-\frac{b n \left(12 e^{3/2} (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)+18 (e f-d g)^{3/2} \log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-18 (e f-d g)^{3/2} \log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+36 a \sqrt{e} \sqrt{f+g x} (e f-d g)+36 b \sqrt{e} \sqrt{f+g x} (e f-d g) \log \left(c (d+e x)^n\right)-9 b n (e f-d g)^{3/2} \left(2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)+\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)\right)\right)+9 b n (e f-d g)^{3/2} \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)+\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)\right)\right)-96 b n (e f-d g) \left(\sqrt{e} \sqrt{f+g x}-\sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)\right)-8 b e^{3/2} n (f+g x)^{3/2}\right)}{9 e^{3/2}}\right)}{3 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} \text{Li}_2\left(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^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,"(2*((f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n])^2 - (b*n*(36*a*Sqrt[e]*(e*f - d*g)*Sqrt[f + g*x] - 8*b*e^(3/2)*n*(f + g*x)^(3/2) - 96*b*(e*f - d*g)*n*(Sqrt[e]*Sqrt[f + g*x] - Sqrt[e*f - d*g]*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]) + 36*b*Sqrt[e]*(e*f - d*g)*Sqrt[f + g*x]*Log[c*(d + e*x)^n] + 12*e^(3/2)*(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n]) + 18*(e*f - d*g)^(3/2)*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] - 18*(e*f - d*g)^(3/2)*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] - 9*b*(e*f - d*g)^(3/2)*n*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] + 2*Log[(1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]) + 2*PolyLog[2, 1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 9*b*(e*f - d*g)^(3/2)*n*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] + 2*Log[1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 2*PolyLog[2, (1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2])))/(9*e^(3/2))))/(3*g)","A",1
147,1,566,418,1.0899482,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{\sqrt{f+g x}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/Sqrt[f + g*x],x]","\frac{2 \left(\sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)^2-\frac{b n \left(2 \sqrt{e f-d g} \log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-2 \sqrt{e f-d g} \log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+4 a \sqrt{e} \sqrt{f+g x}+4 b \sqrt{e} \sqrt{f+g x} \log \left(c (d+e x)^n\right)-b n \sqrt{e f-d g} \left(2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)+\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)\right)\right)+b n \sqrt{e f-d g} \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)+\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)\right)\right)-8 b n \left(\sqrt{e} \sqrt{f+g x}-\sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)\right)\right)}{\sqrt{e}}\right)}{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} \text{Li}_2\left(1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\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,"(2*(Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n])^2 - (b*n*(4*a*Sqrt[e]*Sqrt[f + g*x] - 8*b*n*(Sqrt[e]*Sqrt[f + g*x] - Sqrt[e*f - d*g]*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]) + 4*b*Sqrt[e]*Sqrt[f + g*x]*Log[c*(d + e*x)^n] + 2*Sqrt[e*f - d*g]*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] - 2*Sqrt[e*f - d*g]*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] - b*Sqrt[e*f - d*g]*n*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] + 2*Log[(1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]) + 2*PolyLog[2, 1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + b*Sqrt[e*f - d*g]*n*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] + 2*Log[1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 2*PolyLog[2, (1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2])))/Sqrt[e]))/g","A",1
148,1,424,312,0.6701675,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x)^{3/2}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x)^(3/2),x]","\frac{2 \left(\frac{b \sqrt{e} n \left(2 \log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-2 \log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-b n \left(2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)+\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)\right)\right)+b n \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)+\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)\right)\right)\right)}{\sqrt{e f-d g}}-\frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{\sqrt{f+g x}}\right)}{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 \text{Li}_2\left(1-\frac{2}{1-\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 \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,"(2*(-((a + b*Log[c*(d + e*x)^n])^2/Sqrt[f + g*x]) + (b*Sqrt[e]*n*(2*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] - 2*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] - b*n*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] + 2*Log[(1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]) + 2*PolyLog[2, 1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + b*n*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] + 2*Log[1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 2*PolyLog[2, (1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2])))/Sqrt[e*f - d*g]))/g","A",1
149,1,557,423,1.332499,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x)^{5/2}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x)^(5/2),x]","\frac{2 \left(\frac{b e n (f+g x) \left(4 \sqrt{e f-d g} \left(a+b \log \left(c (d+e x)^n\right)\right)+2 \sqrt{e} \sqrt{f+g x} \log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-2 \sqrt{e} \sqrt{f+g x} \log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-b \sqrt{e} n \sqrt{f+g x} \left(2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)+\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)\right)\right)+b \sqrt{e} n \sqrt{f+g x} \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)+\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)\right)\right)+8 b \sqrt{e} n \sqrt{f+g x} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)\right)}{(e f-d g)^{3/2}}-\left(a+b \log \left(c (d+e x)^n\right)\right)^2\right)}{3 g (f+g x)^{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 \text{Li}_2\left(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^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,"(2*(-(a + b*Log[c*(d + e*x)^n])^2 + (b*e*n*(f + g*x)*(8*b*Sqrt[e]*n*Sqrt[f + g*x]*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]] + 4*Sqrt[e*f - d*g]*(a + b*Log[c*(d + e*x)^n]) + 2*Sqrt[e]*Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] - 2*Sqrt[e]*Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] - b*Sqrt[e]*n*Sqrt[f + g*x]*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] + 2*Log[(1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]) + 2*PolyLog[2, 1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + b*Sqrt[e]*n*Sqrt[f + g*x]*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] + 2*Log[1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 2*PolyLog[2, (1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2])))/(e*f - d*g)^(3/2)))/(3*g*(f + g*x)^(3/2))","A",1
150,1,639,503,2.1956882,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x)^{7/2}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x)^(7/2),x]","\frac{2 \left(\frac{b e n (f+g x) \left(6 e^{3/2} (f+g x)^{3/2} \log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-6 e^{3/2} (f+g x)^{3/2} \log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+4 (e f-d g)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)+12 e (f+g x) \sqrt{e f-d g} \left(a+b \log \left(c (d+e x)^n\right)\right)-3 b e^{3/2} n (f+g x)^{3/2} \left(2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)+\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)\right)\right)+3 b e^{3/2} n (f+g x)^{3/2} \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)+\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)\right)\right)+24 b e^{3/2} n (f+g x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)-8 b e n (f+g x) \sqrt{e f-d g} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{e (f+g x)}{e f-d g}\right)\right)}{(e f-d g)^{5/2}}-3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2\right)}{15 g (f+g x)^{5/2}}","-\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^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 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{8 b^2 e^{5/2} n^2 \text{Li}_2\left(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^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{16 b^2 e^2 n^2}{15 g \sqrt{f+g x} (e f-d g)^2}",1,"(2*(-3*(a + b*Log[c*(d + e*x)^n])^2 + (b*e*n*(f + g*x)*(24*b*e^(3/2)*n*(f + g*x)^(3/2)*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]] - 8*b*e*Sqrt[e*f - d*g]*n*(f + g*x)*Hypergeometric2F1[-1/2, 1, 1/2, (e*(f + g*x))/(e*f - d*g)] + 4*(e*f - d*g)^(3/2)*(a + b*Log[c*(d + e*x)^n]) + 12*e*Sqrt[e*f - d*g]*(f + g*x)*(a + b*Log[c*(d + e*x)^n]) + 6*e^(3/2)*(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] - 6*e^(3/2)*(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] - 3*b*e^(3/2)*n*(f + g*x)^(3/2)*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] + 2*Log[(1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]) + 2*PolyLog[2, 1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 3*b*e^(3/2)*n*(f + g*x)^(3/2)*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] + 2*Log[1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 2*PolyLog[2, (1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2])))/(e*f - d*g)^(5/2)))/(15*g*(f + g*x)^(5/2))","C",1
151,1,728,583,3.9452996,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x)^{9/2}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x)^(9/2),x]","\frac{2 \left(\frac{b e n (f+g x) \left(30 e^{5/2} (f+g x)^{5/2} \log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-30 e^{5/2} (f+g x)^{5/2} \log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+60 e^2 (f+g x)^2 \sqrt{e f-d g} \left(a+b \log \left(c (d+e x)^n\right)\right)+12 (e f-d g)^{5/2} \left(a+b \log \left(c (d+e x)^n\right)\right)+20 e (f+g x) (e f-d g)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)-15 b e^{5/2} n (f+g x)^{5/2} \left(2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)+\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)\right)\right)+15 b e^{5/2} n (f+g x)^{5/2} \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)+\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)\right)\right)+120 b e^{5/2} n (f+g x)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)-40 b e^2 n (f+g x)^2 \sqrt{e f-d g} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{e (f+g x)}{e f-d g}\right)-8 b e n (f+g x) (e f-d g)^{3/2} \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{e (f+g x)}{e f-d g}\right)\right)}{(e f-d g)^{7/2}}-15 \left(a+b \log \left(c (d+e x)^n\right)\right)^2\right)}{105 g (f+g x)^{7/2}}","-\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^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 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{8 b^2 e^{7/2} n^2 \text{Li}_2\left(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^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{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}",1,"(2*(-15*(a + b*Log[c*(d + e*x)^n])^2 + (b*e*n*(f + g*x)*(120*b*e^(5/2)*n*(f + g*x)^(5/2)*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]] - 8*b*e*(e*f - d*g)^(3/2)*n*(f + g*x)*Hypergeometric2F1[-3/2, 1, -1/2, (e*(f + g*x))/(e*f - d*g)] - 40*b*e^2*Sqrt[e*f - d*g]*n*(f + g*x)^2*Hypergeometric2F1[-1/2, 1, 1/2, (e*(f + g*x))/(e*f - d*g)] + 12*(e*f - d*g)^(5/2)*(a + b*Log[c*(d + e*x)^n]) + 20*e*(e*f - d*g)^(3/2)*(f + g*x)*(a + b*Log[c*(d + e*x)^n]) + 60*e^2*Sqrt[e*f - d*g]*(f + g*x)^2*(a + b*Log[c*(d + e*x)^n]) + 30*e^(5/2)*(f + g*x)^(5/2)*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] - 30*e^(5/2)*(f + g*x)^(5/2)*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] - 15*b*e^(5/2)*n*(f + g*x)^(5/2)*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] + 2*Log[(1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]) + 2*PolyLog[2, 1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 15*b*e^(5/2)*n*(f + g*x)^(5/2)*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] + 2*Log[1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 2*PolyLog[2, (1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2])))/(e*f - d*g)^(7/2)))/(105*g*(f + g*x)^(7/2))","C",1
152,0,0,29,1.0884376,"\int \frac{(f+g x)^{3/2}}{a+b \log \left(c (d+e x)^n\right)} \, dx","Integrate[(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,"Integrate[(f + g*x)^(3/2)/(a + b*Log[c*(d + e*x)^n]), x]","A",-1
153,0,0,29,0.9448258,"\int \frac{\sqrt{f+g x}}{a+b \log \left(c (d+e x)^n\right)} \, dx","Integrate[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,"Integrate[Sqrt[f + g*x]/(a + b*Log[c*(d + e*x)^n]), x]","A",-1
154,0,0,29,1.35497,"\int \frac{1}{\sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","Integrate[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,"Integrate[1/(Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n])), x]","A",-1
155,0,0,29,1.4500525,"\int \frac{1}{(f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","Integrate[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,"Integrate[1/((f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n])), x]","A",-1
156,0,0,83,1.4168564,"\int \sqrt{f+g x} \sqrt{a+b \log \left(c (d+e x)^n\right)} \, dx","Integrate[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,"Integrate[Sqrt[f + g*x]*Sqrt[a + b*Log[c*(d + e*x)^n]], x]","A",-1
157,0,0,79,1.6556961,"\int \frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{\sqrt{f+g x}} \, dx","Integrate[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,"Integrate[Sqrt[a + b*Log[c*(d + e*x)^n]]/Sqrt[f + g*x], x]","A",-1
158,0,0,78,1.3207371,"\int \frac{\sqrt{a+b \log \left(c (d+e x)^n\right)}}{(f+g x)^{3/2}} \, dx","Integrate[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,"Integrate[Sqrt[a + b*Log[c*(d + e*x)^n]]/(f + g*x)^(3/2), x]","A",-1
159,0,0,31,5.3299965,"\int \frac{\sqrt{f+g x}}{\sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Integrate[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,"Integrate[Sqrt[f + g*x]/Sqrt[a + b*Log[c*(d + e*x)^n]], x]","A",-1
160,0,0,31,3.0781181,"\int \frac{1}{\sqrt{f+g x} \sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Integrate[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,"Integrate[1/(Sqrt[f + g*x]*Sqrt[a + b*Log[c*(d + e*x)^n]]), x]","A",-1
161,0,0,31,0.7809455,"\int \frac{1}{(f+g x)^{3/2} \sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Integrate[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,"Integrate[1/((f + g*x)^(3/2)*Sqrt[a + b*Log[c*(d + e*x)^n]]), x]","A",-1
162,1,81,94,0.0726858,"\int (f+g x)^m \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Integrate[(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)+\frac{b e n (f+g x) \, _2F_1\left(1,m+2;m+3;\frac{e (f+g x)}{e f-d g}\right)}{(m+2) (e f-d g)}\right)}{g (m+1)}","\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,"((f + g*x)^(1 + m)*(a + (b*e*n*(f + g*x)*Hypergeometric2F1[1, 2 + m, 3 + m, (e*(f + g*x))/(e*f - d*g)])/((e*f - d*g)*(2 + m)) + b*Log[c*(d + e*x)^n]))/(g*(1 + m))","A",1
163,0,0,27,0.3436055,"\int \frac{(f+g x)^m}{a+b \log \left(c (d+e x)^n\right)} \, dx","Integrate[(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,"Integrate[(f + g*x)^m/(a + b*Log[c*(d + e*x)^n]), x]","A",-1
164,0,0,27,2.9072816,"\int \frac{(f+g x)^m}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Integrate[(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,"Integrate[(f + g*x)^m/(a + b*Log[c*(d + e*x)^n])^2, x]","A",-1
165,0,0,29,6.2490357,"\int (f+g x)^m \left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2} \, dx","Integrate[(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,"Integrate[(f + g*x)^m*(a + b*Log[c*(d + e*x)^n])^(3/2), x]","A",-1
166,0,0,29,0.0695574,"\int (f+g x)^m \sqrt{a+b \log \left(c (d+e x)^n\right)} \, dx","Integrate[(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,"Integrate[(f + g*x)^m*Sqrt[a + b*Log[c*(d + e*x)^n]], x]","A",-1
167,0,0,29,3.2152243,"\int \frac{(f+g x)^m}{\sqrt{a+b \log \left(c (d+e x)^n\right)}} \, dx","Integrate[(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,"Integrate[(f + g*x)^m/Sqrt[a + b*Log[c*(d + e*x)^n]], x]","A",-1
168,0,0,29,2.8734449,"\int \frac{(f+g x)^m}{\left(a+b \log \left(c (d+e x)^n\right)\right)^{3/2}} \, dx","Integrate[(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,"Integrate[(f + g*x)^m/(a + b*Log[c*(d + e*x)^n])^(3/2), x]","A",-1
169,0,0,27,0.4689349,"\int (f+g x)^m \left(a+b \log \left(c (d+e x)^n\right)\right)^n \, dx","Integrate[(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,"Integrate[(f + g*x)^m*(a + b*Log[c*(d + e*x)^n])^n, x]","A",-1
170,1,343,474,1.8515329,"\int (f+g x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^n \, dx","Integrate[(f + g*x)^3*(a + b*Log[c*(d + e*x)^n])^n,x]","\frac{3^{-n} 4^{-n-1} e^{-\frac{4 a}{b n}} (d+e x) \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} \left(2^{n+1} e^{\frac{a}{b n}} (e f-d g) \left(c (d+e x)^n\right)^{\frac{1}{n}} \left(3^n e^{\frac{a}{b n}} (e f-d g) \left(c (d+e x)^n\right)^{\frac{1}{n}} \left(2^{n+1} e^{\frac{a}{b n}} (e f-d g) \left(c (d+e x)^n\right)^{\frac{1}{n}} \Gamma \left(n+1,-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)+3 g (d+e x) \Gamma \left(n+1,-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)\right)+g^2 2^{n+1} (d+e x)^2 \Gamma \left(n+1,-\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)\right)+g^3 3^n (d+e x)^3 \Gamma \left(n+1,-\frac{4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)\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} \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} \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} \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} \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)*(d + e*x)*(3^n*g^3*(d + e*x)^3*Gamma[1 + n, (-4*(a + b*Log[c*(d + e*x)^n]))/(b*n)] + 2^(1 + n)*E^(a/(b*n))*(e*f - d*g)*(c*(d + e*x)^n)^n^(-1)*(2^(1 + n)*g^2*(d + e*x)^2*Gamma[1 + n, (-3*(a + b*Log[c*(d + e*x)^n]))/(b*n)] + 3^n*E^(a/(b*n))*(e*f - d*g)*(c*(d + e*x)^n)^n^(-1)*(3*g*(d + e*x)*Gamma[1 + n, (-2*(a + b*Log[c*(d + e*x)^n]))/(b*n)] + 2^(1 + n)*E^(a/(b*n))*(e*f - d*g)*(c*(d + e*x)^n)^n^(-1)*Gamma[1 + n, -((a + b*Log[c*(d + e*x)^n])/(b*n))])))*(a + b*Log[c*(d + e*x)^n])^n)/(3^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)","A",1
171,1,262,348,0.6152099,"\int (f+g x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^n \, dx","Integrate[(f + g*x)^2*(a + b*Log[c*(d + e*x)^n])^n,x]","\frac{2^{-n} 3^{-n-1} e^{-\frac{3 a}{b n}} (d+e x) \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} \left(3^{n+1} e^{\frac{a}{b n}} (e f-d g) \left(c (d+e x)^n\right)^{\frac{1}{n}} \left(2^n e^{\frac{a}{b n}} (e f-d g) \left(c (d+e x)^n\right)^{\frac{1}{n}} \Gamma \left(n+1,-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)+g (d+e x) \Gamma \left(n+1,-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)\right)+g^2 2^n (d+e x)^2 \Gamma \left(n+1,-\frac{3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)\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} \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} \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} \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)*(d + e*x)*(2^n*g^2*(d + e*x)^2*Gamma[1 + n, (-3*(a + b*Log[c*(d + e*x)^n]))/(b*n)] + 3^(1 + n)*E^(a/(b*n))*(e*f - d*g)*(c*(d + e*x)^n)^n^(-1)*(g*(d + e*x)*Gamma[1 + n, (-2*(a + b*Log[c*(d + e*x)^n]))/(b*n)] + 2^n*E^(a/(b*n))*(e*f - d*g)*(c*(d + e*x)^n)^n^(-1)*Gamma[1 + n, -((a + b*Log[c*(d + e*x)^n])/(b*n))]))*(a + b*Log[c*(d + e*x)^n])^n)/(2^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)","A",1
172,1,181,225,0.221876,"\int (f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^n \, dx","Integrate[(f + g*x)*(a + b*Log[c*(d + e*x)^n])^n,x]","\frac{2^{-n-1} e^{-\frac{2 a}{b n}} (d+e x) \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} \left(2^{n+1} e^{\frac{a}{b n}} (e f-d g) \left(c (d+e x)^n\right)^{\frac{1}{n}} \Gamma \left(n+1,-\frac{a+b \log \left(c (d+e x)^n\right)}{b n}\right)+g (d+e x) \Gamma \left(n+1,-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{b n}\right)\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} \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} \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)*(d + e*x)*(g*(d + e*x)*Gamma[1 + n, (-2*(a + b*Log[c*(d + e*x)^n]))/(b*n)] + 2^(1 + n)*E^(a/(b*n))*(e*f - d*g)*(c*(d + e*x)^n)^n^(-1)*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^((2*a)/(b*n))*(c*(d + e*x)^n)^(2/n)*(-((a + b*Log[c*(d + e*x)^n])/(b*n)))^n)","A",1
173,1,103,103,0.0622871,"\int \left(a+b \log \left(c (d+e x)^n\right)\right)^n \, dx","Integrate[(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} \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} \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",1
174,0,0,27,0.3155995,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^n}{f+g x} \, dx","Integrate[(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,"Integrate[(a + b*Log[c*(d + e*x)^n])^n/(f + g*x), x]","A",-1
175,1,589,315,0.6375059,"\int \frac{(h+i x)^4 (a+b \log (c (e+f x)))}{d e+d f x} \, dx","Integrate[((h + i*x)^4*(a + b*Log[c*(e + f*x)]))/(d*e + d*f*x),x]","\frac{72 a^2 e^4 i^4-288 a^2 e^3 f h i^3+432 a^2 e^2 f^2 h^2 i^2-288 a^2 e f^3 h^3 i+72 a^2 f^4 h^4+12 b \log (c (e+f x)) \left(12 a (f h-e i)^4+b i \left(-12 e^4 i^3-12 e^3 f i^2 (i x-4 h)+6 e^2 f^2 i \left(-12 h^2+8 h i x+i^2 x^2\right)+4 e f^3 \left(12 h^3-18 h^2 i x-6 h i^2 x^2-i^3 x^3\right)+f^4 x \left(48 h^3+36 h^2 i x+16 h i^2 x^2+3 i^3 x^3\right)\right)\right)-144 a b e^3 f i^4 x+576 a b e^2 f^2 h i^3 x+72 a b e^2 f^2 i^4 x^2-864 a b e f^3 h^2 i^2 x-288 a b e f^3 h i^3 x^2-48 a b e f^3 i^4 x^3+576 a b f^4 h^3 i x+432 a b f^4 h^2 i^2 x^2+192 a b f^4 h i^3 x^3+36 a b f^4 i^4 x^4+72 b^2 (f h-e i)^4 \log ^2(c (e+f x))+300 b^2 e^3 f i^4 x-12 b^2 e^2 i^2 \left(13 e^2 i^2-40 e f h i+36 f^2 h^2\right) \log (e+f x)-1056 b^2 e^2 f^2 h i^3 x-78 b^2 e^2 f^2 i^4 x^2+1296 b^2 e f^3 h^2 i^2 x+240 b^2 e f^3 h i^3 x^2+28 b^2 e f^3 i^4 x^3-576 b^2 f^4 h^3 i x-216 b^2 f^4 h^2 i^2 x^2-64 b^2 f^4 h i^3 x^3-9 b^2 f^4 i^4 x^4}{144 b 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{3 i^2 (e+f x)^2 (f h-e i)^2 (a+b \log (c (e+f x)))}{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{4 b i^3 (e+f x)^3 (f h-e i)}{9 d f^5}-\frac{3 b i^2 (e+f x)^2 (f h-e i)^2}{2 d f^5}-\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{4 b i x (f h-e i)^3}{d f^4}",1,"(72*a^2*f^4*h^4 - 288*a^2*e*f^3*h^3*i + 432*a^2*e^2*f^2*h^2*i^2 - 288*a^2*e^3*f*h*i^3 + 72*a^2*e^4*i^4 + 576*a*b*f^4*h^3*i*x - 576*b^2*f^4*h^3*i*x - 864*a*b*e*f^3*h^2*i^2*x + 1296*b^2*e*f^3*h^2*i^2*x + 576*a*b*e^2*f^2*h*i^3*x - 1056*b^2*e^2*f^2*h*i^3*x - 144*a*b*e^3*f*i^4*x + 300*b^2*e^3*f*i^4*x + 432*a*b*f^4*h^2*i^2*x^2 - 216*b^2*f^4*h^2*i^2*x^2 - 288*a*b*e*f^3*h*i^3*x^2 + 240*b^2*e*f^3*h*i^3*x^2 + 72*a*b*e^2*f^2*i^4*x^2 - 78*b^2*e^2*f^2*i^4*x^2 + 192*a*b*f^4*h*i^3*x^3 - 64*b^2*f^4*h*i^3*x^3 - 48*a*b*e*f^3*i^4*x^3 + 28*b^2*e*f^3*i^4*x^3 + 36*a*b*f^4*i^4*x^4 - 9*b^2*f^4*i^4*x^4 - 12*b^2*e^2*i^2*(36*f^2*h^2 - 40*e*f*h*i + 13*e^2*i^2)*Log[e + f*x] + 12*b*(12*a*(f*h - e*i)^4 + b*i*(-12*e^4*i^3 - 12*e^3*f*i^2*(-4*h + i*x) + 6*e^2*f^2*i*(-12*h^2 + 8*h*i*x + i^2*x^2) + 4*e*f^3*(12*h^3 - 18*h^2*i*x - 6*h*i^2*x^2 - i^3*x^3) + f^4*x*(48*h^3 + 36*h^2*i*x + 16*h*i^2*x^2 + 3*i^3*x^3)))*Log[c*(e + f*x)] + 72*b^2*(f*h - e*i)^4*Log[c*(e + f*x)]^2)/(144*b*d*f^5)","A",1
176,1,375,244,0.3623622,"\int \frac{(h+i x)^3 (a+b \log (c (e+f x)))}{d e+d f x} \, dx","Integrate[((h + i*x)^3*(a + b*Log[c*(e + f*x)]))/(d*e + d*f*x),x]","\frac{-18 a^2 e^3 i^3+54 a^2 e^2 f h i^2-54 a^2 e f^2 h^2 i+18 a^2 f^3 h^3+6 b \log (c (e+f x)) \left(6 a (f h-e i)^3+b i \left(6 e^3 i^2+6 e^2 f i (i x-3 h)+3 e f^2 \left(6 h^2-6 h i x-i^2 x^2\right)+f^3 x \left(18 h^2+9 h i x+2 i^2 x^2\right)\right)\right)+36 a b e^2 f i^3 x-108 a b e f^2 h i^2 x-18 a b e f^2 i^3 x^2+108 a b f^3 h^2 i x+54 a b f^3 h i^2 x^2+12 a b f^3 i^3 x^3+18 b^2 (f h-e i)^3 \log ^2(c (e+f x))+6 b^2 e^2 i^2 (5 e i-9 f h) \log (e+f x)-66 b^2 e^2 f i^3 x+162 b^2 e f^2 h i^2 x+15 b^2 e f^2 i^3 x^2-108 b^2 f^3 h^2 i x-27 b^2 f^3 h i^2 x^2-4 b^2 f^3 i^3 x^3}{36 b 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{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 b i x (f h-e i)^2}{d f^3}",1,"(18*a^2*f^3*h^3 - 54*a^2*e*f^2*h^2*i + 54*a^2*e^2*f*h*i^2 - 18*a^2*e^3*i^3 + 108*a*b*f^3*h^2*i*x - 108*b^2*f^3*h^2*i*x - 108*a*b*e*f^2*h*i^2*x + 162*b^2*e*f^2*h*i^2*x + 36*a*b*e^2*f*i^3*x - 66*b^2*e^2*f*i^3*x + 54*a*b*f^3*h*i^2*x^2 - 27*b^2*f^3*h*i^2*x^2 - 18*a*b*e*f^2*i^3*x^2 + 15*b^2*e*f^2*i^3*x^2 + 12*a*b*f^3*i^3*x^3 - 4*b^2*f^3*i^3*x^3 + 6*b^2*e^2*i^2*(-9*f*h + 5*e*i)*Log[e + f*x] + 6*b*(6*a*(f*h - e*i)^3 + b*i*(6*e^3*i^2 + 6*e^2*f*i*(-3*h + i*x) + 3*e*f^2*(6*h^2 - 6*h*i*x - i^2*x^2) + f^3*x*(18*h^2 + 9*h*i*x + 2*i^2*x^2)))*Log[c*(e + f*x)] + 18*b^2*(f*h - e*i)^3*Log[c*(e + f*x)]^2)/(36*b*d*f^4)","A",1
177,1,214,157,0.1536232,"\int \frac{(h+i x)^2 (a+b \log (c (e+f x)))}{d e+d f x} \, dx","Integrate[((h + i*x)^2*(a + b*Log[c*(e + f*x)]))/(d*e + d*f*x),x]","\frac{2 a^2 e^2 i^2-4 a^2 e f h i+2 a^2 f^2 h^2+2 b \log (c (e+f x)) \left(2 a (f h-e i)^2+b i \left(-2 e^2 i+e f (4 h-2 i x)+f^2 x (4 h+i x)\right)\right)-4 a b e f i^2 x+8 a b f^2 h i x+2 a b f^2 i^2 x^2+2 b^2 (f h-e i)^2 \log ^2(c (e+f x))-2 b^2 e^2 i^2 \log (e+f x)+6 b^2 e f i^2 x-8 b^2 f^2 h i x-b^2 f^2 i^2 x^2}{4 b 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,"(2*a^2*f^2*h^2 - 4*a^2*e*f*h*i + 2*a^2*e^2*i^2 + 8*a*b*f^2*h*i*x - 8*b^2*f^2*h*i*x - 4*a*b*e*f*i^2*x + 6*b^2*e*f*i^2*x + 2*a*b*f^2*i^2*x^2 - b^2*f^2*i^2*x^2 - 2*b^2*e^2*i^2*Log[e + f*x] + 2*b*(2*a*(f*h - e*i)^2 + b*i*(-2*e^2*i + e*f*(4*h - 2*i*x) + f^2*x*(4*h + i*x)))*Log[c*(e + f*x)] + 2*b^2*(f*h - e*i)^2*Log[c*(e + f*x)]^2)/(4*b*d*f^3)","A",1
178,1,66,79,0.0541936,"\int \frac{(h+i x) (a+b \log (c (e+f x)))}{d e+d f x} \, dx","Integrate[((h + i*x)*(a + b*Log[c*(e + f*x)]))/(d*e + d*f*x),x]","\frac{\frac{(f h-e i) (a+b \log (c (e+f x)))^2}{b}+2 a f i x+2 b i (e+f x) \log (c (e+f x))-2 b f i x}{2 d f^2}","\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,"(2*a*f*i*x - 2*b*f*i*x + 2*b*i*(e + f*x)*Log[c*(e + f*x)] + ((f*h - e*i)*(a + b*Log[c*(e + f*x)])^2)/b)/(2*d*f^2)","A",1
179,1,27,27,0.0041547,"\int \frac{a+b \log (c (e+f x))}{d e+d f x} \, dx","Integrate[(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",1
180,1,91,87,0.0879426,"\int \frac{a+b \log (c (e+f x))}{(d e+d f x) (h+i x)} \, dx","Integrate[(a + b*Log[c*(e + f*x)])/((d*e + d*f*x)*(h + i*x)),x]","\frac{(a+b \log (c (e+f x))) \left(a+b \log (c (e+f x))-2 b \log \left(\frac{f (h+i x)}{f h-e i}\right)\right)-2 b^2 \text{Li}_2\left(\frac{i (e+f x)}{e i-f h}\right)}{2 b d (f h-e i)}","\frac{b \text{Li}_2\left(-\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)])*(a + b*Log[c*(e + f*x)] - 2*b*Log[(f*(h + i*x))/(f*h - e*i)]) - 2*b^2*PolyLog[2, (i*(e + f*x))/(-(f*h) + e*i)])/(2*b*d*(f*h - e*i))","A",1
181,1,141,151,0.1704062,"\int \frac{a+b \log (c (e+f x))}{(d e+d f x) (h+i x)^2} \, dx","Integrate[(a + b*Log[c*(e + f*x)])/((d*e + d*f*x)*(h + i*x)^2),x]","\frac{-2 f \log \left(\frac{f (h+i x)}{f h-e i}\right) (a+b \log (c (e+f x)))+\frac{2 (f h-e i) (a+b \log (c (e+f x)))}{h+i x}+\frac{f (a+b \log (c (e+f x)))^2}{b}-2 b f \text{Li}_2\left(\frac{i (e+f x)}{e i-f h}\right)-2 b f (\log (e+f x)-\log (h+i x))}{2 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 \text{Li}_2\left(-\frac{f h-e i}{i (e+f x)}\right)}{d (f h-e i)^2}+\frac{b f \log (h+i x)}{d (f h-e i)^2}",1,"((2*(f*h - e*i)*(a + b*Log[c*(e + f*x)]))/(h + i*x) + (f*(a + b*Log[c*(e + f*x)])^2)/b - 2*b*f*(Log[e + f*x] - Log[h + i*x]) - 2*f*(a + b*Log[c*(e + f*x)])*Log[(f*(h + i*x))/(f*h - e*i)] - 2*b*f*PolyLog[2, (i*(e + f*x))/(-(f*h) + e*i)])/(2*d*(f*h - e*i)^2)","A",1
182,1,226,250,0.2352886,"\int \frac{a+b \log (c (e+f x))}{(d e+d f x) (h+i x)^3} \, dx","Integrate[(a + b*Log[c*(e + f*x)])/((d*e + d*f*x)*(h + i*x)^3),x]","\frac{-2 f^2 \log \left(\frac{f (h+i x)}{f h-e i}\right) (a+b \log (c (e+f x)))+\frac{f^2 (a+b \log (c (e+f x)))^2}{b}+\frac{2 f (f h-e i) (a+b \log (c (e+f x)))}{h+i x}+\frac{(f h-e i)^2 (a+b \log (c (e+f x)))}{(h+i x)^2}-2 b f^2 \text{Li}_2\left(\frac{i (e+f x)}{e i-f h}\right)-2 b f^2 (\log (e+f x)-\log (h+i x))-\frac{b f (f (h+i x) \log (e+f x)-e i-f (h+i x) \log (h+i x)+f h)}{h+i x}}{2 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 \text{Li}_2\left(-\frac{f h-e i}{i (e+f x)}\right)}{d (f h-e i)^3}-\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,"(((f*h - e*i)^2*(a + b*Log[c*(e + f*x)]))/(h + i*x)^2 + (2*f*(f*h - e*i)*(a + b*Log[c*(e + f*x)]))/(h + i*x) + (f^2*(a + b*Log[c*(e + f*x)])^2)/b - 2*b*f^2*(Log[e + f*x] - Log[h + i*x]) - (b*f*(f*h - e*i + f*(h + i*x)*Log[e + f*x] - f*(h + i*x)*Log[h + i*x]))/(h + i*x) - 2*f^2*(a + b*Log[c*(e + f*x)])*Log[(f*(h + i*x))/(f*h - e*i)] - 2*b*f^2*PolyLog[2, (i*(e + f*x))/(-(f*h) + e*i)])/(2*d*(f*h - e*i)^3)","A",1
183,1,374,579,0.5955021,"\int \frac{(h+i x)^4 (a+b \log (c (e+f x)))^2}{d e+d f x} \, dx","Integrate[((h + i*x)^4*(a + b*Log[c*(e + f*x)])^2)/(d*e + d*f*x),x]","\frac{256 b i^3 (f h-e i) \left(b f x \left(3 e^2+3 e f x+f^2 x^2\right)-3 (e+f x)^3 (a+b \log (c (e+f x)))\right)+27 b i^4 \left(b f x \left(4 e^3+6 e^2 f x+4 e f^2 x^2+f^3 x^3\right)-4 (e+f x)^4 (a+b \log (c (e+f x)))\right)+1152 i^3 (e+f x)^3 (f h-e i) (a+b \log (c (e+f x)))^2+2592 i^2 (e+f x)^2 (f h-e i)^2 (a+b \log (c (e+f x)))^2+1296 b i^2 (f h-e i)^2 \left(b f x (2 e+f x)-2 (e+f x)^2 (a+b \log (c (e+f x)))\right)+3456 i (e+f x) (f h-e i)^3 (a+b \log (c (e+f x)))^2-6912 b i (f h-e i)^3 (f x (a-b)+b (e+f x) \log (c (e+f x)))+\frac{288 (f h-e i)^4 (a+b \log (c (e+f x)))^3}{b}+216 i^4 (e+f x)^4 (a+b \log (c (e+f x)))^2}{864 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{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{(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{b i^4 (e+f x)^4 (a+b \log (c (e+f x)))}{8 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{8 b^2 i^3 (e+f x)^3 (f h-e i)}{27 d f^5}+\frac{3 b^2 i^2 (e+f x)^2 (f h-e i)^2}{2 d f^5}+\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{8 b^2 i x (f h-e i)^3}{d f^4}",1,"(3456*i*(f*h - e*i)^3*(e + f*x)*(a + b*Log[c*(e + f*x)])^2 + 2592*i^2*(f*h - e*i)^2*(e + f*x)^2*(a + b*Log[c*(e + f*x)])^2 + 1152*i^3*(f*h - e*i)*(e + f*x)^3*(a + b*Log[c*(e + f*x)])^2 + 216*i^4*(e + f*x)^4*(a + b*Log[c*(e + f*x)])^2 + (288*(f*h - e*i)^4*(a + b*Log[c*(e + f*x)])^3)/b - 6912*b*i*(f*h - e*i)^3*((a - b)*f*x + b*(e + f*x)*Log[c*(e + f*x)]) + 1296*b*i^2*(f*h - e*i)^2*(b*f*x*(2*e + f*x) - 2*(e + f*x)^2*(a + b*Log[c*(e + f*x)])) + 256*b*i^3*(f*h - e*i)*(b*f*x*(3*e^2 + 3*e*f*x + f^2*x^2) - 3*(e + f*x)^3*(a + b*Log[c*(e + f*x)])) + 27*b*i^4*(b*f*x*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3) - 4*(e + f*x)^4*(a + b*Log[c*(e + f*x)])))/(864*d*f^5)","A",1
184,1,267,464,0.3585567,"\int \frac{(h+i x)^3 (a+b \log (c (e+f x)))^2}{d e+d f x} \, dx","Integrate[((h + i*x)^3*(a + b*Log[c*(e + f*x)])^2)/(d*e + d*f*x),x]","\frac{8 b i^3 \left(b f x \left(3 e^2+3 e f x+f^2 x^2\right)-3 (e+f x)^3 (a+b \log (c (e+f x)))\right)+162 i^2 (e+f x)^2 (f h-e i) (a+b \log (c (e+f x)))^2+81 b i^2 (f h-e i) \left(b f x (2 e+f x)-2 (e+f x)^2 (a+b \log (c (e+f x)))\right)+324 i (e+f x) (f h-e i)^2 (a+b \log (c (e+f x)))^2-648 b i (f h-e i)^2 (f x (a-b)+b (e+f x) \log (c (e+f x)))+\frac{36 (f h-e i)^3 (a+b \log (c (e+f x)))^3}{b}+36 i^3 (e+f x)^3 (a+b \log (c (e+f x)))^2}{108 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{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{6 b^2 i x (f h-e i)^2}{d f^3}",1,"(324*i*(f*h - e*i)^2*(e + f*x)*(a + b*Log[c*(e + f*x)])^2 + 162*i^2*(f*h - e*i)*(e + f*x)^2*(a + b*Log[c*(e + f*x)])^2 + 36*i^3*(e + f*x)^3*(a + b*Log[c*(e + f*x)])^2 + (36*(f*h - e*i)^3*(a + b*Log[c*(e + f*x)])^3)/b - 648*b*i*(f*h - e*i)^2*((a - b)*f*x + b*(e + f*x)*Log[c*(e + f*x)]) + 81*b*i^2*(f*h - e*i)*(b*f*x*(2*e + f*x) - 2*(e + f*x)^2*(a + b*Log[c*(e + f*x)])) + 8*b*i^3*(b*f*x*(3*e^2 + 3*e*f*x + f^2*x^2) - 3*(e + f*x)^3*(a + b*Log[c*(e + f*x)])))/(108*d*f^4)","A",1
185,1,171,238,0.2153151,"\int \frac{(h+i x)^2 (a+b \log (c (e+f x)))^2}{d e+d f x} \, dx","Integrate[((h + i*x)^2*(a + b*Log[c*(e + f*x)])^2)/(d*e + d*f*x),x]","\frac{\frac{4 (f h-e i)^2 (a+b \log (c (e+f x)))^3}{b}+24 i (e+f x) (f h-e i) (a+b \log (c (e+f x)))^2-48 b i (f h-e i) (f x (a-b)+b (e+f x) \log (c (e+f x)))+6 i^2 (e+f x)^2 (a+b \log (c (e+f x)))^2+3 b i^2 \left(b f x (2 e+f x)-2 (e+f x)^2 (a+b \log (c (e+f x)))\right)}{12 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{b^2 i^2 (e+f x)^2}{4 d f^3}+\frac{4 b^2 i x (f h-e i)}{d f^2}",1,"(24*i*(f*h - e*i)*(e + f*x)*(a + b*Log[c*(e + f*x)])^2 + 6*i^2*(e + f*x)^2*(a + b*Log[c*(e + f*x)])^2 + (4*(f*h - e*i)^2*(a + b*Log[c*(e + f*x)])^3)/b - 48*b*i*(f*h - e*i)*((a - b)*f*x + b*(e + f*x)*Log[c*(e + f*x)]) + 3*b*i^2*(b*f*x*(2*e + f*x) - 2*(e + f*x)^2*(a + b*Log[c*(e + f*x)])))/(12*d*f^3)","A",1
186,1,89,113,0.0622481,"\int \frac{(h+i x) (a+b \log (c (e+f x)))^2}{d e+d f x} \, dx","Integrate[((h + i*x)*(a + b*Log[c*(e + f*x)])^2)/(d*e + d*f*x),x]","\frac{\frac{(f h-e i) (a+b \log (c (e+f x)))^3}{b}+3 i (e+f x) (a+b \log (c (e+f x)))^2-6 b f i x (a-b)-6 b^2 i (e+f x) \log (c (e+f x))}{3 d f^2}","\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,"(-6*(a - b)*b*f*i*x - 6*b^2*i*(e + f*x)*Log[c*(e + f*x)] + 3*i*(e + f*x)*(a + b*Log[c*(e + f*x)])^2 + ((f*h - e*i)*(a + b*Log[c*(e + f*x)])^3)/b)/(3*d*f^2)","A",1
187,1,27,27,0.0049562,"\int \frac{(a+b \log (c (e+f x)))^2}{d e+d f x} \, dx","Integrate[(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",1
188,1,189,142,0.2378884,"\int \frac{(a+b \log (c (e+f x)))^2}{(d e+d f x) (h+i x)} \, dx","Integrate[(a + b*Log[c*(e + f*x)])^2/((d*e + d*f*x)*(h + i*x)),x]","\frac{3 a^2 \log (e+f x)-3 a^2 \log (h+i x)-6 b \text{Li}_2\left(\frac{i (e+f x)}{e i-f h}\right) (a+b \log (c (e+f x)))-6 a b \log (c (e+f x)) \log \left(\frac{f (h+i x)}{f h-e i}\right)+3 a b \log ^2(c (e+f x))-3 b^2 \log ^2(c (e+f x)) \log \left(\frac{f (h+i x)}{f h-e i}\right)+b^2 \log ^3(c (e+f x))+6 b^2 \text{Li}_3\left(\frac{i (e+f x)}{e i-f h}\right)}{3 d (f h-e i)}","\frac{2 b \text{Li}_2\left(-\frac{f h-e i}{i (e+f x)}\right) (a+b \log (c (e+f x)))}{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)}+\frac{2 b^2 \text{Li}_3\left(-\frac{f h-e i}{i (e+f x)}\right)}{d (f h-e i)}",1,"(3*a^2*Log[e + f*x] + 3*a*b*Log[c*(e + f*x)]^2 + b^2*Log[c*(e + f*x)]^3 - 3*a^2*Log[h + i*x] - 6*a*b*Log[c*(e + f*x)]*Log[(f*(h + i*x))/(f*h - e*i)] - 3*b^2*Log[c*(e + f*x)]^2*Log[(f*(h + i*x))/(f*h - e*i)] - 6*b*(a + b*Log[c*(e + f*x)])*PolyLog[2, (i*(e + f*x))/(-(f*h) + e*i)] + 6*b^2*PolyLog[3, (i*(e + f*x))/(-(f*h) + e*i)])/(3*d*(f*h - e*i))","A",1
189,1,360,273,0.5400681,"\int \frac{(a+b \log (c (e+f x)))^2}{(d e+d f x) (h+i x)^2} \, dx","Integrate[(a + b*Log[c*(e + f*x)])^2/((d*e + d*f*x)*(h + i*x)^2),x]","\frac{3 a^2 f (h+i x) \log (e+f x)+3 a^2 (f h-e i)-3 a^2 f (h+i x) \log (h+i x)+3 a b \left(-2 f (h+i x) \left(\log (c (e+f x)) \log \left(\frac{f (h+i x)}{f h-e i}\right)+\text{Li}_2\left(\frac{i (e+f x)}{e i-f h}\right)\right)+f (h+i x) \log ^2(c (e+f x))+2 (f h-e i) \log (c (e+f x))-2 f (h+i x) \log (e+f x)+2 f (h+i x) \log (h+i x)\right)+b^2 \left(-6 f (h+i x) (\log (c (e+f x))-1) \text{Li}_2\left(\frac{i (e+f x)}{e i-f h}\right)+\log (c (e+f x)) \left(f (h+i x) \log ^2(c (e+f x))-3 \log (c (e+f x)) \left(f (h+i x) \log \left(\frac{f (h+i x)}{f h-e i}\right)+i (e+f x)\right)+6 f (h+i x) \log \left(\frac{f (h+i x)}{f h-e i}\right)\right)+6 f (h+i x) \text{Li}_3\left(\frac{i (e+f x)}{e i-f h}\right)\right)}{3 d (h+i x) (f h-e i)^2}","\frac{2 b f \text{Li}_2\left(-\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 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}+\frac{2 b^2 f \text{Li}_2\left(-\frac{i (e+f x)}{f h-e i}\right)}{d (f h-e i)^2}+\frac{2 b^2 f \text{Li}_3\left(-\frac{f h-e i}{i (e+f x)}\right)}{d (f h-e i)^2}",1,"(3*a^2*(f*h - e*i) + 3*a^2*f*(h + i*x)*Log[e + f*x] - 3*a^2*f*(h + i*x)*Log[h + i*x] + 3*a*b*(-2*f*(h + i*x)*Log[e + f*x] + 2*(f*h - e*i)*Log[c*(e + f*x)] + f*(h + i*x)*Log[c*(e + f*x)]^2 + 2*f*(h + i*x)*Log[h + i*x] - 2*f*(h + i*x)*(Log[c*(e + f*x)]*Log[(f*(h + i*x))/(f*h - e*i)] + PolyLog[2, (i*(e + f*x))/(-(f*h) + e*i)])) + b^2*(Log[c*(e + f*x)]*(f*(h + i*x)*Log[c*(e + f*x)]^2 + 6*f*(h + i*x)*Log[(f*(h + i*x))/(f*h - e*i)] - 3*Log[c*(e + f*x)]*(i*(e + f*x) + f*(h + i*x)*Log[(f*(h + i*x))/(f*h - e*i)])) - 6*f*(h + i*x)*(-1 + Log[c*(e + f*x)])*PolyLog[2, (i*(e + f*x))/(-(f*h) + e*i)] + 6*f*(h + i*x)*PolyLog[3, (i*(e + f*x))/(-(f*h) + e*i)]))/(3*d*(f*h - e*i)^2*(h + i*x))","A",1
190,1,680,485,0.9516274,"\int \frac{(a+b \log (c (e+f x)))^2}{(d e+d f x) (h+i x)^3} \, dx","Integrate[(a + b*Log[c*(e + f*x)])^2/((d*e + d*f*x)*(h + i*x)^3),x]","\frac{6 a^2 f^2 (h+i x)^2 \log (e+f x)+6 a^2 f (h+i x) (f h-e i)+3 a^2 (f h-e i)^2-6 a^2 f^2 (h+i x)^2 \log (h+i x)+6 a b \left(-2 f^2 (h+i x)^2 \left(\log (c (e+f x)) \log \left(\frac{f (h+i x)}{f h-e i}\right)+\text{Li}_2\left(\frac{i (e+f x)}{e i-f h}\right)\right)+f^2 (h+i x)^2 \log ^2(c (e+f x))+(f h-e i)^2 \log (c (e+f x))-2 f (h+i x) ((e i-f h) \log (c (e+f x))+f (h+i x) \log (e+f x)-f (h+i x) \log (h+i x))-f (h+i x) (f (h+i x) \log (e+f x)-e i-f (h+i x) \log (h+i x)+f h)\right)+b^2 \left(-6 f^2 (h+i x)^2 \left(2 \log (c (e+f x)) \text{Li}_2\left(\frac{i (e+f x)}{e i-f h}\right)+\log ^2(c (e+f x)) \log \left(\frac{f (h+i x)}{f h-e i}\right)-2 \text{Li}_3\left(\frac{i (e+f x)}{e i-f h}\right)\right)+2 f^2 (h+i x)^2 \log ^3(c (e+f x))-3 f^2 (h+i x)^2 \log ^2(c (e+f x))+6 f^2 (h+i x)^2 \log (c (e+f x)) \log \left(\frac{f (h+i x)}{f h-e i}\right)-6 f (h+i x) \left(\log (c (e+f x)) \left(i (e+f x) \log (c (e+f x))-2 f (h+i x) \log \left(\frac{f (h+i x)}{f h-e i}\right)\right)-2 f (h+i x) \text{Li}_2\left(\frac{i (e+f x)}{e i-f h}\right)\right)+3 (f h-e i)^2 \log ^2(c (e+f x))-6 f (h+i x) (f h-e i) \log (c (e+f x))+6 f^2 (h+i x)^2 \text{Li}_2\left(\frac{i (e+f x)}{e i-f h}\right)+6 f^2 (h+i x)^2 \log (e+f x)-6 f^2 (h+i x)^2 \log (h+i x)\right)}{6 d (h+i x)^2 (f h-e i)^3}","\frac{2 b f^2 \text{Li}_2\left(-\frac{f h-e i}{i (e+f x)}\right) (a+b \log (c (e+f x)))}{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 \text{Li}_2\left(-\frac{f h-e i}{i (e+f x)}\right)}{d (f h-e i)^3}+\frac{2 b^2 f^2 \text{Li}_2\left(-\frac{i (e+f x)}{f h-e i}\right)}{d (f h-e i)^3}+\frac{2 b^2 f^2 \text{Li}_3\left(-\frac{f h-e i}{i (e+f x)}\right)}{d (f h-e i)^3}-\frac{b^2 f^2 \log (h+i x)}{d (f h-e i)^3}",1,"(3*a^2*(f*h - e*i)^2 + 6*a^2*f*(f*h - e*i)*(h + i*x) + 6*a^2*f^2*(h + i*x)^2*Log[e + f*x] - 6*a^2*f^2*(h + i*x)^2*Log[h + i*x] + 6*a*b*((f*h - e*i)^2*Log[c*(e + f*x)] + f^2*(h + i*x)^2*Log[c*(e + f*x)]^2 - f*(h + i*x)*(f*h - e*i + f*(h + i*x)*Log[e + f*x] - f*(h + i*x)*Log[h + i*x]) - 2*f*(h + i*x)*(f*(h + i*x)*Log[e + f*x] + (-(f*h) + e*i)*Log[c*(e + f*x)] - f*(h + i*x)*Log[h + i*x]) - 2*f^2*(h + i*x)^2*(Log[c*(e + f*x)]*Log[(f*(h + i*x))/(f*h - e*i)] + PolyLog[2, (i*(e + f*x))/(-(f*h) + e*i)])) + b^2*(6*f^2*(h + i*x)^2*Log[e + f*x] - 6*f*(f*h - e*i)*(h + i*x)*Log[c*(e + f*x)] + 3*(f*h - e*i)^2*Log[c*(e + f*x)]^2 - 3*f^2*(h + i*x)^2*Log[c*(e + f*x)]^2 + 2*f^2*(h + i*x)^2*Log[c*(e + f*x)]^3 - 6*f^2*(h + i*x)^2*Log[h + i*x] + 6*f^2*(h + i*x)^2*Log[c*(e + f*x)]*Log[(f*(h + i*x))/(f*h - e*i)] + 6*f^2*(h + i*x)^2*PolyLog[2, (i*(e + f*x))/(-(f*h) + e*i)] - 6*f*(h + i*x)*(Log[c*(e + f*x)]*(i*(e + f*x)*Log[c*(e + f*x)] - 2*f*(h + i*x)*Log[(f*(h + i*x))/(f*h - e*i)]) - 2*f*(h + i*x)*PolyLog[2, (i*(e + f*x))/(-(f*h) + e*i)]) - 6*f^2*(h + i*x)^2*(Log[c*(e + f*x)]^2*Log[(f*(h + i*x))/(f*h - e*i)] + 2*Log[c*(e + f*x)]*PolyLog[2, (i*(e + f*x))/(-(f*h) + e*i)] - 2*PolyLog[3, (i*(e + f*x))/(-(f*h) + e*i)])))/(6*d*(f*h - e*i)^3*(h + i*x)^2)","A",1
191,1,397,230,0.9667507,"\int \frac{(h+i x)^4}{(d e+d f x) (a+b \log (c (e+f x)))} \, dx","Integrate[(h + i*x)^4/((d*e + d*f*x)*(a + b*Log[c*(e + f*x)])),x]","\frac{e^{-\frac{4 a}{b}} \left(c^4 e^4 i^4 e^{\frac{4 a}{b}} \log (a+b \log (c (e+f x)))-4 c^4 e^3 f h i^3 e^{\frac{4 a}{b}} \log (a+b \log (c (e+f x)))+6 c^4 e^2 f^2 h^2 i^2 e^{\frac{4 a}{b}} \log (a+b \log (c (e+f x)))+c^4 f^4 h^4 e^{\frac{4 a}{b}} \log (f (a+b \log (c (e+f x))))-4 c^4 e f^3 h^3 i e^{\frac{4 a}{b}} \log (a+b \log (c (e+f x)))+4 c^3 i e^{\frac{3 a}{b}} (f h-e i)^3 \text{Ei}\left(\frac{a}{b}+\log (c (e+f x))\right)+6 c^2 f^2 h^2 i^2 e^{\frac{2 a}{b}} \text{Ei}\left(\frac{2 (a+b \log (c (e+f x)))}{b}\right)+6 c^2 e i^3 e^{\frac{2 a}{b}} (e i-2 f h) \text{Ei}\left(2 \left(\frac{a}{b}+\log (c (e+f x))\right)\right)+4 c f h i^3 e^{a/b} \text{Ei}\left(3 \left(\frac{a}{b}+\log (c (e+f x))\right)\right)-4 c e i^4 e^{a/b} \text{Ei}\left(3 \left(\frac{a}{b}+\log (c (e+f x))\right)\right)+i^4 \text{Ei}\left(4 \left(\frac{a}{b}+\log (c (e+f x))\right)\right)\right)}{b c^4 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^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{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*c^3*E^((3*a)/b)*i*(f*h - e*i)^3*ExpIntegralEi[a/b + Log[c*(e + f*x)]] + 6*c^2*e*E^((2*a)/b)*i^3*(-2*f*h + e*i)*ExpIntegralEi[2*(a/b + Log[c*(e + f*x)])] + 4*c*E^(a/b)*f*h*i^3*ExpIntegralEi[3*(a/b + Log[c*(e + f*x)])] - 4*c*e*E^(a/b)*i^4*ExpIntegralEi[3*(a/b + Log[c*(e + f*x)])] + i^4*ExpIntegralEi[4*(a/b + Log[c*(e + f*x)])] + 6*c^2*E^((2*a)/b)*f^2*h^2*i^2*ExpIntegralEi[(2*(a + b*Log[c*(e + f*x)]))/b] - 4*c^4*e*E^((4*a)/b)*f^3*h^3*i*Log[a + b*Log[c*(e + f*x)]] + 6*c^4*e^2*E^((4*a)/b)*f^2*h^2*i^2*Log[a + b*Log[c*(e + f*x)]] - 4*c^4*e^3*E^((4*a)/b)*f*h*i^3*Log[a + b*Log[c*(e + f*x)]] + c^4*e^4*E^((4*a)/b)*i^4*Log[a + b*Log[c*(e + f*x)]] + c^4*E^((4*a)/b)*f^4*h^4*Log[f*(a + b*Log[c*(e + f*x)])])/(b*c^4*d*E^((4*a)/b)*f^5)","A",1
192,1,279,177,0.6509039,"\int \frac{(h+i x)^3}{(d e+d f x) (a+b \log (c (e+f x)))} \, dx","Integrate[(h + i*x)^3/((d*e + d*f*x)*(a + b*Log[c*(e + f*x)])),x]","\frac{e^{-\frac{3 a}{b}} \left(c^3 \left(-e^3\right) i^3 e^{\frac{3 a}{b}} \log (a+b \log (c (e+f x)))+3 c^3 e^2 f h i^2 e^{\frac{3 a}{b}} \log (a+b \log (c (e+f x)))+c^3 f^3 h^3 e^{\frac{3 a}{b}} \log (f (a+b \log (c (e+f x))))-3 c^3 e f^2 h^2 i e^{\frac{3 a}{b}} \log (a+b \log (c (e+f x)))+3 c^2 i e^{\frac{2 a}{b}} (f h-e i)^2 \text{Ei}\left(\frac{a}{b}+\log (c (e+f x))\right)+3 c f h i^2 e^{a/b} \text{Ei}\left(\frac{2 (a+b \log (c (e+f x)))}{b}\right)-3 c e i^3 e^{a/b} \text{Ei}\left(2 \left(\frac{a}{b}+\log (c (e+f x))\right)\right)+i^3 \text{Ei}\left(3 \left(\frac{a}{b}+\log (c (e+f x))\right)\right)\right)}{b c^3 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^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{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*c^2*E^((2*a)/b)*i*(f*h - e*i)^2*ExpIntegralEi[a/b + Log[c*(e + f*x)]] - 3*c*e*E^(a/b)*i^3*ExpIntegralEi[2*(a/b + Log[c*(e + f*x)])] + i^3*ExpIntegralEi[3*(a/b + Log[c*(e + f*x)])] + 3*c*E^(a/b)*f*h*i^2*ExpIntegralEi[(2*(a + b*Log[c*(e + f*x)]))/b] - 3*c^3*e*E^((3*a)/b)*f^2*h^2*i*Log[a + b*Log[c*(e + f*x)]] + 3*c^3*e^2*E^((3*a)/b)*f*h*i^2*Log[a + b*Log[c*(e + f*x)]] - c^3*e^3*E^((3*a)/b)*i^3*Log[a + b*Log[c*(e + f*x)]] + c^3*E^((3*a)/b)*f^3*h^3*Log[f*(a + b*Log[c*(e + f*x)])])/(b*c^3*d*E^((3*a)/b)*f^4)","A",1
193,1,137,124,0.3392118,"\int \frac{(h+i x)^2}{(d e+d f x) (a+b \log (c (e+f x)))} \, dx","Integrate[(h + i*x)^2/((d*e + d*f*x)*(a + b*Log[c*(e + f*x)])),x]","\frac{e^{-\frac{2 a}{b}} \left(c^2 e^{\frac{2 a}{b}} \left(f^2 h^2 \log (f (a+b \log (c (e+f x))))+e i (e i-2 f h) \log (a+b \log (c (e+f x)))\right)+2 c i e^{a/b} (f h-e i) \text{Ei}\left(\frac{a}{b}+\log (c (e+f x))\right)+i^2 \text{Ei}\left(\frac{2 (a+b \log (c (e+f x)))}{b}\right)\right)}{b c^2 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*c*E^(a/b)*i*(f*h - e*i)*ExpIntegralEi[a/b + Log[c*(e + f*x)]] + i^2*ExpIntegralEi[(2*(a + b*Log[c*(e + f*x)]))/b] + c^2*E^((2*a)/b)*(e*i*(-2*f*h + e*i)*Log[a + b*Log[c*(e + f*x)]] + f^2*h^2*Log[f*(a + b*Log[c*(e + f*x)])]))/(b*c^2*d*E^((2*a)/b)*f^3)","A",1
194,1,76,71,0.2343563,"\int \frac{h+i x}{(d e+d f x) (a+b \log (c (e+f x)))} \, dx","Integrate[(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))\right)+c f h \log (f (a+b \log (c (e+f x))))-c e i \log (a+b \log (c (e+f x)))}{b c 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)]])/E^(a/b) - c*e*i*Log[a + b*Log[c*(e + f*x)]] + c*f*h*Log[f*(a + b*Log[c*(e + f*x)])])/(b*c*d*f^2)","A",1
195,1,23,23,0.0203998,"\int \frac{1}{(d e+d f x) (a+b \log (c (e+f x)))} \, dx","Integrate[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",1
196,0,0,72,0.433398,"\int \frac{1}{(d e+d f x) (h+i x) (a+b \log (c (e+f x)))} \, dx","Integrate[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,"Integrate[1/((d*e + d*f*x)*(h + i*x)*(a + b*Log[c*(e + f*x)])), x]","A",-1
197,0,0,115,4.4953037,"\int \frac{1}{(d e+d f x) (h+i x)^2 (a+b \log (c (e+f x)))} \, dx","Integrate[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,"Integrate[1/((d*e + d*f*x)*(h + i*x)^2*(a + b*Log[c*(e + f*x)])), x]","A",-1
198,1,818,485,1.3151793,"\int \frac{(f+g x)^{5/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{d+e x} \, dx","Integrate[((f + g*x)^(5/2)*(a + b*Log[c*(d + e*x)^n]))/(d + e*x),x]","\frac{450 \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) (e f-d g)^{5/2}-450 \left(a+b \log \left(c (d+e x)^n\right)\right) \log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) (e f-d g)^{5/2}-225 b n \left(\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)\right)+2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)\right) (e f-d g)^{5/2}+225 b n \left(\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)\right)+2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)\right) (e f-d g)^{5/2}-1800 b n \left(\sqrt{e} \sqrt{f+g x}-\sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)\right) (e f-d g)^2+900 b \sqrt{e} \sqrt{f+g x} \log \left(c (d+e x)^n\right) (e f-d g)^2+900 a \sqrt{e} \sqrt{f+g x} (e f-d g)^2-200 b n \left(\sqrt{e} \sqrt{f+g x} (4 e f-3 d g+e g x)-3 (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)\right) (e f-d g)+300 e^{3/2} (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right) (e f-d g)-24 b n \left(3 e^{5/2} (f+g x)^{5/2}+5 (e f-d g) \left(\sqrt{e} \sqrt{f+g x} (4 e f-3 d g+e g x)-3 (e f-d g)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)\right)\right)+180 e^{5/2} (f+g x)^{5/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{450 e^{7/2}}","-\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 \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 (f+g x)^{5/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{5 e}-\frac{2 b n (e f-d g)^{5/2} \text{Li}_2\left(1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{e^{7/2}}+\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{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{4 b n (f+g x)^{5/2}}{25 e}",1,"(900*a*Sqrt[e]*(e*f - d*g)^2*Sqrt[f + g*x] - 1800*b*(e*f - d*g)^2*n*(Sqrt[e]*Sqrt[f + g*x] - Sqrt[e*f - d*g]*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]) - 200*b*(e*f - d*g)*n*(Sqrt[e]*Sqrt[f + g*x]*(4*e*f - 3*d*g + e*g*x) - 3*(e*f - d*g)^(3/2)*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]) - 24*b*n*(3*e^(5/2)*(f + g*x)^(5/2) + 5*(e*f - d*g)*(Sqrt[e]*Sqrt[f + g*x]*(4*e*f - 3*d*g + e*g*x) - 3*(e*f - d*g)^(3/2)*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])) + 900*b*Sqrt[e]*(e*f - d*g)^2*Sqrt[f + g*x]*Log[c*(d + e*x)^n] + 300*e^(3/2)*(e*f - d*g)*(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n]) + 180*e^(5/2)*(f + g*x)^(5/2)*(a + b*Log[c*(d + e*x)^n]) + 450*(e*f - d*g)^(5/2)*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] - 450*(e*f - d*g)^(5/2)*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] - 225*b*(e*f - d*g)^(5/2)*n*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] + 2*Log[(1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]) + 2*PolyLog[2, 1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 225*b*(e*f - d*g)^(5/2)*n*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] + 2*Log[1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 2*PolyLog[2, (1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]))/(450*e^(7/2))","A",1
199,1,607,417,1.1427893,"\int \frac{(f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{d+e x} \, dx","Integrate[((f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n]))/(d + e*x),x]","\frac{12 e^{3/2} (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)+18 (e f-d g)^{3/2} \log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-18 (e f-d g)^{3/2} \log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+36 a \sqrt{e} \sqrt{f+g x} (e f-d g)+36 b \sqrt{e} \sqrt{f+g x} (e f-d g) \log \left(c (d+e x)^n\right)-9 b n (e f-d g)^{3/2} \left(2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)+\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)\right)\right)+9 b n (e f-d g)^{3/2} \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)+\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)\right)\right)-96 b n (e f-d g) \left(\sqrt{e} \sqrt{f+g x}-\sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)\right)-8 b e^{3/2} n (f+g x)^{3/2}}{18 e^{5/2}}","-\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 \sqrt{f+g x} (e f-d g) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e^2}+\frac{2 (f+g x)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 e}-\frac{2 b n (e f-d g)^{3/2} \text{Li}_2\left(1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{e^{5/2}}+\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{16 b n \sqrt{f+g x} (e f-d g)}{3 e^2}-\frac{4 b n (f+g x)^{3/2}}{9 e}",1,"(36*a*Sqrt[e]*(e*f - d*g)*Sqrt[f + g*x] - 8*b*e^(3/2)*n*(f + g*x)^(3/2) - 96*b*(e*f - d*g)*n*(Sqrt[e]*Sqrt[f + g*x] - Sqrt[e*f - d*g]*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]) + 36*b*Sqrt[e]*(e*f - d*g)*Sqrt[f + g*x]*Log[c*(d + e*x)^n] + 12*e^(3/2)*(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n]) + 18*(e*f - d*g)^(3/2)*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] - 18*(e*f - d*g)^(3/2)*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] - 9*b*(e*f - d*g)^(3/2)*n*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] + 2*Log[(1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]) + 2*PolyLog[2, 1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 9*b*(e*f - d*g)^(3/2)*n*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] + 2*Log[1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 2*PolyLog[2, (1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]))/(18*e^(5/2))","A",1
200,1,534,349,0.5738779,"\int \frac{\sqrt{f+g x} \left(a+b \log \left(c (d+e x)^n\right)\right)}{d+e x} \, dx","Integrate[(Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n]))/(d + e*x),x]","\frac{2 \sqrt{e f-d g} \log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-2 \sqrt{e f-d g} \log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+4 a \sqrt{e} \sqrt{f+g x}+4 b \sqrt{e} \sqrt{f+g x} \log \left(c (d+e x)^n\right)-b n \sqrt{e f-d g} \left(2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)+\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)\right)\right)+b n \sqrt{e f-d g} \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)+\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)\right)\right)-8 b n \left(\sqrt{e} \sqrt{f+g x}-\sqrt{e f-d g} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)\right)}{2 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} \text{Li}_2\left(1-\frac{2}{1-\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}}\right)}{e^{3/2}}+\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*a*Sqrt[e]*Sqrt[f + g*x] - 8*b*n*(Sqrt[e]*Sqrt[f + g*x] - Sqrt[e*f - d*g]*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]]) + 4*b*Sqrt[e]*Sqrt[f + g*x]*Log[c*(d + e*x)^n] + 2*Sqrt[e*f - d*g]*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] - 2*Sqrt[e*f - d*g]*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] - b*Sqrt[e*f - d*g]*n*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] + 2*Log[(1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]) + 2*PolyLog[2, 1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + b*Sqrt[e*f - d*g]*n*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] + 2*Log[1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 2*PolyLog[2, (1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]))/(2*e^(3/2))","A",1
201,1,457,256,0.2359034,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(d+e x) \sqrt{f+g x}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/((d + e*x)*Sqrt[f + g*x]),x]","\frac{2 a \log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right)-2 a \log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right)+2 b \log \left(c (d+e x)^n\right) \log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right)-2 b \log \left(c (d+e x)^n\right) \log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right)-2 b n \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)+2 b n \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)-b n \log ^2\left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right)+b n \log ^2\left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right)-2 b n \log \left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right) \log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right)+2 b n \log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \log \left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)}{2 \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 \text{Li}_2\left(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 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*a*Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] + 2*b*Log[c*(d + e*x)^n]*Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] - b*n*Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]]^2 - 2*a*Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] - 2*b*Log[c*(d + e*x)^n]*Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] + b*n*Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]]^2 + 2*b*n*Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]]*Log[1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])] - 2*b*n*Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]]*Log[(1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2] - 2*b*n*PolyLog[2, 1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])] + 2*b*n*PolyLog[2, (1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2])/(2*Sqrt[e]*Sqrt[e*f - d*g])","A",1
202,1,526,340,0.5344623,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(d+e x) (f+g x)^{3/2}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/((d + e*x)*(f + g*x)^(3/2)),x]","\frac{4 \sqrt{e f-d g} \left(a+b \log \left(c (d+e x)^n\right)\right)+2 \sqrt{e} \sqrt{f+g x} \log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-2 \sqrt{e} \sqrt{f+g x} \log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-b \sqrt{e} n \sqrt{f+g x} \left(2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)+\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)\right)\right)+b \sqrt{e} n \sqrt{f+g x} \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)+\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)\right)\right)+8 b \sqrt{e} n \sqrt{f+g x} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{2 \sqrt{f+g x} (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 \text{Li}_2\left(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 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,"(8*b*Sqrt[e]*n*Sqrt[f + g*x]*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]] + 4*Sqrt[e*f - d*g]*(a + b*Log[c*(d + e*x)^n]) + 2*Sqrt[e]*Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] - 2*Sqrt[e]*Sqrt[f + g*x]*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] - b*Sqrt[e]*n*Sqrt[f + g*x]*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] + 2*Log[(1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]) + 2*PolyLog[2, 1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + b*Sqrt[e]*n*Sqrt[f + g*x]*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] + 2*Log[1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 2*PolyLog[2, (1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]))/(2*(e*f - d*g)^(3/2)*Sqrt[f + g*x])","A",1
203,1,608,406,0.8112852,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(d+e x) (f+g x)^{5/2}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/((d + e*x)*(f + g*x)^(5/2)),x]","\frac{6 e^{3/2} (f+g x)^{3/2} \log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-6 e^{3/2} (f+g x)^{3/2} \log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+4 (e f-d g)^{3/2} \left(a+b \log \left(c (d+e x)^n\right)\right)+12 e (f+g x) \sqrt{e f-d g} \left(a+b \log \left(c (d+e x)^n\right)\right)-3 b e^{3/2} n (f+g x)^{3/2} \left(2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)+\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}-\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)\right)\right)+3 b e^{3/2} n (f+g x)^{3/2} \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}+1\right)\right)+\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right) \left(\log \left(\sqrt{e f-d g}+\sqrt{e} \sqrt{f+g x}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{e} \sqrt{f+g x}}{2 \sqrt{e f-d g}}\right)\right)\right)+24 b e^{3/2} n (f+g x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)-8 b e n (f+g x) \sqrt{e f-d g} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{e (f+g x)}{e f-d g}\right)}{6 (f+g x)^{3/2} (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 \text{Li}_2\left(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 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,"(24*b*e^(3/2)*n*(f + g*x)^(3/2)*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]] - 8*b*e*Sqrt[e*f - d*g]*n*(f + g*x)*Hypergeometric2F1[-1/2, 1, 1/2, (e*(f + g*x))/(e*f - d*g)] + 4*(e*f - d*g)^(3/2)*(a + b*Log[c*(d + e*x)^n]) + 12*e*Sqrt[e*f - d*g]*(f + g*x)*(a + b*Log[c*(d + e*x)^n]) + 6*e^(3/2)*(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] - 6*e^(3/2)*(f + g*x)^(3/2)*(a + b*Log[c*(d + e*x)^n])*Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] - 3*b*e^(3/2)*n*(f + g*x)^(3/2)*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] - Sqrt[e]*Sqrt[f + g*x]] + 2*Log[(1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]) + 2*PolyLog[2, 1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 3*b*e^(3/2)*n*(f + g*x)^(3/2)*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]]*(Log[Sqrt[e*f - d*g] + Sqrt[e]*Sqrt[f + g*x]] + 2*Log[1/2 - (Sqrt[e]*Sqrt[f + g*x])/(2*Sqrt[e*f - d*g])]) + 2*PolyLog[2, (1 + (Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g])/2]))/(6*(e*f - d*g)^(5/2)*(f + g*x)^(3/2))","C",1
204,1,663,381,1.0991038,"\int \frac{(d+e x)^{3/2} \log (a+b x)}{a+b x} \, dx","Integrate[((d + e*x)^(3/2)*Log[a + b*x])/(a + b*x),x]","\frac{12 b^{3/2} (d+e x)^{3/2} \log (a+b x)+36 b^{3/2} d \sqrt{d+e x} \log (a+b x)-18 (b d-a e)^{3/2} \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{b} \sqrt{d+e x}}{2 \sqrt{b d-a e}}\right)+18 (b d-a e)^{3/2} \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}+1\right)\right)+96 a \sqrt{b} e \sqrt{d+e x}-9 (b d-a e)^{3/2} \log ^2\left(\sqrt{b d-a e}-\sqrt{b} \sqrt{d+e x}\right)+9 (b d-a e)^{3/2} \log ^2\left(\sqrt{b d-a e}+\sqrt{b} \sqrt{d+e x}\right)+18 (b d-a e)^{3/2} \log (a+b x) \log \left(\sqrt{b d-a e}-\sqrt{b} \sqrt{d+e x}\right)-18 (b d-a e)^{3/2} \log \left(\frac{1}{2} \left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}+1\right)\right) \log \left(\sqrt{b d-a e}-\sqrt{b} \sqrt{d+e x}\right)-36 a \sqrt{b} e \sqrt{d+e x} \log (a+b x)-18 (b d-a e)^{3/2} \log (a+b x) \log \left(\sqrt{b d-a e}+\sqrt{b} \sqrt{d+e x}\right)+18 (b d-a e)^{3/2} \log \left(\sqrt{b d-a e}+\sqrt{b} \sqrt{d+e x}\right) \log \left(\frac{1}{2}-\frac{\sqrt{b} \sqrt{d+e x}}{2 \sqrt{b d-a e}}\right)+96 b d \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)-96 a e \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)-8 b^{3/2} (d+e x)^{3/2}-96 b^{3/2} d \sqrt{d+e x}}{18 b^{5/2}}","-\frac{2 (b d-a e)^{3/2} \text{Li}_2\left(1-\frac{2}{1-\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}}\right)}{b^{5/2}}+\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{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 (d+e x)^{3/2} \log (a+b x)}{3 b}-\frac{4 (d+e x)^{3/2}}{9 b}",1,"(-96*b^(3/2)*d*Sqrt[d + e*x] + 96*a*Sqrt[b]*e*Sqrt[d + e*x] - 8*b^(3/2)*(d + e*x)^(3/2) + 96*b*d*Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]] - 96*a*e*Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]] + 36*b^(3/2)*d*Sqrt[d + e*x]*Log[a + b*x] - 36*a*Sqrt[b]*e*Sqrt[d + e*x]*Log[a + b*x] + 12*b^(3/2)*(d + e*x)^(3/2)*Log[a + b*x] + 18*(b*d - a*e)^(3/2)*Log[a + b*x]*Log[Sqrt[b*d - a*e] - Sqrt[b]*Sqrt[d + e*x]] - 9*(b*d - a*e)^(3/2)*Log[Sqrt[b*d - a*e] - Sqrt[b]*Sqrt[d + e*x]]^2 - 18*(b*d - a*e)^(3/2)*Log[a + b*x]*Log[Sqrt[b*d - a*e] + Sqrt[b]*Sqrt[d + e*x]] + 9*(b*d - a*e)^(3/2)*Log[Sqrt[b*d - a*e] + Sqrt[b]*Sqrt[d + e*x]]^2 + 18*(b*d - a*e)^(3/2)*Log[Sqrt[b*d - a*e] + Sqrt[b]*Sqrt[d + e*x]]*Log[1/2 - (Sqrt[b]*Sqrt[d + e*x])/(2*Sqrt[b*d - a*e])] - 18*(b*d - a*e)^(3/2)*Log[Sqrt[b*d - a*e] - Sqrt[b]*Sqrt[d + e*x]]*Log[(1 + (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])/2] - 18*(b*d - a*e)^(3/2)*PolyLog[2, 1/2 - (Sqrt[b]*Sqrt[d + e*x])/(2*Sqrt[b*d - a*e])] + 18*(b*d - a*e)^(3/2)*PolyLog[2, (1 + (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])/2])/(18*b^(5/2))","A",1
205,1,534,323,0.4084443,"\int \frac{\sqrt{d+e x} \log (a+b x)}{a+b x} \, dx","Integrate[(Sqrt[d + e*x]*Log[a + b*x])/(a + b*x),x]","\frac{-2 \sqrt{b d-a e} \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{b} \sqrt{d+e x}}{2 \sqrt{b d-a e}}\right)+2 \sqrt{b d-a e} \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}+1\right)\right)-\sqrt{b d-a e} \log ^2\left(\sqrt{b d-a e}-\sqrt{b} \sqrt{d+e x}\right)+\sqrt{b d-a e} \log ^2\left(\sqrt{b d-a e}+\sqrt{b} \sqrt{d+e x}\right)+2 \sqrt{b d-a e} \log (a+b x) \log \left(\sqrt{b d-a e}-\sqrt{b} \sqrt{d+e x}\right)-2 \sqrt{b d-a e} \log \left(\frac{1}{2} \left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}+1\right)\right) \log \left(\sqrt{b d-a e}-\sqrt{b} \sqrt{d+e x}\right)+4 \sqrt{b} \sqrt{d+e x} \log (a+b x)-2 \sqrt{b d-a e} \log (a+b x) \log \left(\sqrt{b d-a e}+\sqrt{b} \sqrt{d+e x}\right)+2 \sqrt{b d-a e} \log \left(\sqrt{b d-a e}+\sqrt{b} \sqrt{d+e x}\right) \log \left(\frac{1}{2}-\frac{\sqrt{b} \sqrt{d+e x}}{2 \sqrt{b d-a e}}\right)+8 \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)-8 \sqrt{b} \sqrt{d+e x}}{2 b^{3/2}}","-\frac{2 \sqrt{b d-a e} \text{Li}_2\left(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,"(-8*Sqrt[b]*Sqrt[d + e*x] + 8*Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]] + 4*Sqrt[b]*Sqrt[d + e*x]*Log[a + b*x] + 2*Sqrt[b*d - a*e]*Log[a + b*x]*Log[Sqrt[b*d - a*e] - Sqrt[b]*Sqrt[d + e*x]] - Sqrt[b*d - a*e]*Log[Sqrt[b*d - a*e] - Sqrt[b]*Sqrt[d + e*x]]^2 - 2*Sqrt[b*d - a*e]*Log[a + b*x]*Log[Sqrt[b*d - a*e] + Sqrt[b]*Sqrt[d + e*x]] + Sqrt[b*d - a*e]*Log[Sqrt[b*d - a*e] + Sqrt[b]*Sqrt[d + e*x]]^2 + 2*Sqrt[b*d - a*e]*Log[Sqrt[b*d - a*e] + Sqrt[b]*Sqrt[d + e*x]]*Log[1/2 - (Sqrt[b]*Sqrt[d + e*x])/(2*Sqrt[b*d - a*e])] - 2*Sqrt[b*d - a*e]*Log[Sqrt[b*d - a*e] - Sqrt[b]*Sqrt[d + e*x]]*Log[(1 + (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])/2] - 2*Sqrt[b*d - a*e]*PolyLog[2, 1/2 - (Sqrt[b]*Sqrt[d + e*x])/(2*Sqrt[b*d - a*e])] + 2*Sqrt[b*d - a*e]*PolyLog[2, (1 + (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])/2])/(2*b^(3/2))","A",1
206,1,239,242,2.8943727,"\int \frac{\log (a+b x)}{(a+b x) \sqrt{d+e x}} \, dx","Integrate[Log[a + b*x]/((a + b*x)*Sqrt[d + e*x]),x]","\frac{\frac{\sqrt{\frac{b (d+e x)}{b d-a e}} \left(-4 \text{Li}_2\left(\frac{1}{2}-\frac{1}{2} \sqrt{\frac{b (d+e x)}{b d-a e}}\right)+\log ^2\left(\frac{e (a+b x)}{a e-b d}\right)+2 \log ^2\left(\frac{1}{2} \left(\sqrt{\frac{b (d+e x)}{b d-a e}}+1\right)\right)-4 \log \left(\frac{1}{2} \left(\sqrt{\frac{b (d+e x)}{b d-a e}}+1\right)\right) \log \left(\frac{e (a+b x)}{a e-b d}\right)\right)}{2 \sqrt{d+e x}}-\frac{2 \left(\log (a+b x)-\log \left(\frac{e (a+b x)}{a e-b d}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d-\frac{a e}{b}}}\right)}{\sqrt{d-\frac{a e}{b}}}}{b}","-\frac{2 \text{Li}_2\left(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[d + e*x]/Sqrt[d - (a*e)/b]]*(Log[a + b*x] - Log[(e*(a + b*x))/(-(b*d) + a*e)]))/Sqrt[d - (a*e)/b] + (Sqrt[(b*(d + e*x))/(b*d - a*e)]*(Log[(e*(a + b*x))/(-(b*d) + a*e)]^2 - 4*Log[(e*(a + b*x))/(-(b*d) + a*e)]*Log[(1 + Sqrt[(b*(d + e*x))/(b*d - a*e)])/2] + 2*Log[(1 + Sqrt[(b*(d + e*x))/(b*d - a*e)])/2]^2 - 4*PolyLog[2, 1/2 - Sqrt[(b*(d + e*x))/(b*d - a*e)]/2]))/(2*Sqrt[d + e*x]))/b","A",1
207,1,550,316,0.4707769,"\int \frac{\log (a+b x)}{(a+b x) (d+e x)^{3/2}} \, dx","Integrate[Log[a + b*x]/((a + b*x)*(d + e*x)^(3/2)),x]","\frac{-2 \sqrt{b} \sqrt{d+e x} \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{b} \sqrt{d+e x}}{2 \sqrt{b d-a e}}\right)+2 \sqrt{b} \sqrt{d+e x} \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}+1\right)\right)-\sqrt{b} \sqrt{d+e x} \log ^2\left(\sqrt{b d-a e}-\sqrt{b} \sqrt{d+e x}\right)+\sqrt{b} \sqrt{d+e x} \log ^2\left(\sqrt{b d-a e}+\sqrt{b} \sqrt{d+e x}\right)+2 \sqrt{b} \sqrt{d+e x} \log (a+b x) \log \left(\sqrt{b d-a e}-\sqrt{b} \sqrt{d+e x}\right)-2 \sqrt{b} \sqrt{d+e x} \log \left(\frac{1}{2} \left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}+1\right)\right) \log \left(\sqrt{b d-a e}-\sqrt{b} \sqrt{d+e x}\right)+4 \sqrt{b d-a e} \log (a+b x)-2 \sqrt{b} \sqrt{d+e x} \log (a+b x) \log \left(\sqrt{b d-a e}+\sqrt{b} \sqrt{d+e x}\right)+2 \sqrt{b} \sqrt{d+e x} \log \left(\sqrt{b d-a e}+\sqrt{b} \sqrt{d+e x}\right) \log \left(\frac{1}{2}-\frac{\sqrt{b} \sqrt{d+e x}}{2 \sqrt{b d-a e}}\right)+8 \sqrt{b} \sqrt{d+e x} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{2 \sqrt{d+e x} (b d-a e)^{3/2}}","-\frac{2 \sqrt{b} \text{Li}_2\left(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,"(8*Sqrt[b]*Sqrt[d + e*x]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]] + 4*Sqrt[b*d - a*e]*Log[a + b*x] + 2*Sqrt[b]*Sqrt[d + e*x]*Log[a + b*x]*Log[Sqrt[b*d - a*e] - Sqrt[b]*Sqrt[d + e*x]] - Sqrt[b]*Sqrt[d + e*x]*Log[Sqrt[b*d - a*e] - Sqrt[b]*Sqrt[d + e*x]]^2 - 2*Sqrt[b]*Sqrt[d + e*x]*Log[a + b*x]*Log[Sqrt[b*d - a*e] + Sqrt[b]*Sqrt[d + e*x]] + Sqrt[b]*Sqrt[d + e*x]*Log[Sqrt[b*d - a*e] + Sqrt[b]*Sqrt[d + e*x]]^2 + 2*Sqrt[b]*Sqrt[d + e*x]*Log[Sqrt[b*d - a*e] + Sqrt[b]*Sqrt[d + e*x]]*Log[1/2 - (Sqrt[b]*Sqrt[d + e*x])/(2*Sqrt[b*d - a*e])] - 2*Sqrt[b]*Sqrt[d + e*x]*Log[Sqrt[b*d - a*e] - Sqrt[b]*Sqrt[d + e*x]]*Log[(1 + (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])/2] - 2*Sqrt[b]*Sqrt[d + e*x]*PolyLog[2, 1/2 - (Sqrt[b]*Sqrt[d + e*x])/(2*Sqrt[b*d - a*e])] + 2*Sqrt[b]*Sqrt[d + e*x]*PolyLog[2, (1 + (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])/2])/(2*(b*d - a*e)^(3/2)*Sqrt[d + e*x])","A",1
208,1,568,372,0.9728293,"\int \frac{\log (a+b x)}{(a+b x) (d+e x)^{5/2}} \, dx","Integrate[Log[a + b*x]/((a + b*x)*(d + e*x)^(5/2)),x]","\frac{-3 b^{3/2} (d+e x)^{3/2} \left(2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{b} \sqrt{d+e x}}{2 \sqrt{b d-a e}}\right)+\log \left(\sqrt{b d-a e}-\sqrt{b} \sqrt{d+e x}\right) \left(\log \left(\sqrt{b d-a e}-\sqrt{b} \sqrt{d+e x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}+1\right)\right)\right)\right)+3 b^{3/2} (d+e x)^{3/2} \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}+1\right)\right)+\log \left(\sqrt{b d-a e}+\sqrt{b} \sqrt{d+e x}\right) \left(\log \left(\sqrt{b d-a e}+\sqrt{b} \sqrt{d+e x}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{b} \sqrt{d+e x}}{2 \sqrt{b d-a e}}\right)\right)\right)+6 b^{3/2} (d+e x)^{3/2} \log (a+b x) \log \left(\sqrt{b d-a e}-\sqrt{b} \sqrt{d+e x}\right)-6 b^{3/2} (d+e x)^{3/2} \log (a+b x) \log \left(\sqrt{b d-a e}+\sqrt{b} \sqrt{d+e x}\right)+24 b^{3/2} (d+e x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)-8 b (d+e x) \sqrt{b d-a e} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)+4 (b d-a e)^{3/2} \log (a+b x)+12 b (d+e x) \sqrt{b d-a e} \log (a+b x)}{6 (d+e x)^{3/2} (b d-a e)^{5/2}}","-\frac{2 b^{3/2} \text{Li}_2\left(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,"(24*b^(3/2)*(d + e*x)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]] - 8*b*Sqrt[b*d - a*e]*(d + e*x)*Hypergeometric2F1[-1/2, 1, 1/2, (b*(d + e*x))/(b*d - a*e)] + 4*(b*d - a*e)^(3/2)*Log[a + b*x] + 12*b*Sqrt[b*d - a*e]*(d + e*x)*Log[a + b*x] + 6*b^(3/2)*(d + e*x)^(3/2)*Log[a + b*x]*Log[Sqrt[b*d - a*e] - Sqrt[b]*Sqrt[d + e*x]] - 6*b^(3/2)*(d + e*x)^(3/2)*Log[a + b*x]*Log[Sqrt[b*d - a*e] + Sqrt[b]*Sqrt[d + e*x]] - 3*b^(3/2)*(d + e*x)^(3/2)*(Log[Sqrt[b*d - a*e] - Sqrt[b]*Sqrt[d + e*x]]*(Log[Sqrt[b*d - a*e] - Sqrt[b]*Sqrt[d + e*x]] + 2*Log[(1 + (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])/2]) + 2*PolyLog[2, 1/2 - (Sqrt[b]*Sqrt[d + e*x])/(2*Sqrt[b*d - a*e])]) + 3*b^(3/2)*(d + e*x)^(3/2)*(Log[Sqrt[b*d - a*e] + Sqrt[b]*Sqrt[d + e*x]]*(Log[Sqrt[b*d - a*e] + Sqrt[b]*Sqrt[d + e*x]] + 2*Log[1/2 - (Sqrt[b]*Sqrt[d + e*x])/(2*Sqrt[b*d - a*e])]) + 2*PolyLog[2, (1 + (Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e])/2]))/(6*(b*d - a*e)^(5/2)*(d + e*x)^(3/2))","C",1
209,0,0,35,0.6233787,"\int \frac{(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx","Integrate[((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,"Integrate[((h + i*x)^q*(a + b*Log[c*(e + f*x)])^p)/(d*e + d*f*x), x]","A",-1
210,1,247,305,1.3803356,"\int \frac{(h+i x)^3 (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx","Integrate[((h + i*x)^3*(a + b*Log[c*(e + f*x)])^p)/(d*e + d*f*x),x]","\frac{6^{-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} \left(c 3^{p+1} e^{a/b} (f h-e i) \left(c 2^{p+1} e^{a/b} (f h-e i) \left(3 b i (p+1) \Gamma \left(p+1,-\frac{a+b \log (c (e+f x))}{b}\right)-b c e^{a/b} (f h-e i) \left(-\frac{a+b \log (c (e+f x))}{b}\right)^{p+1}\right)+3 b i^2 (p+1) \Gamma \left(p+1,-\frac{2 (a+b \log (c (e+f x)))}{b}\right)\right)+b i^3 2^{p+1} (p+1) \Gamma \left(p+1,-\frac{3 (a+b \log (c (e+f x)))}{b}\right)\right)}{b c^3 d f^4 (p+1)}","\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} \Gamma \left(p+1,-\frac{3 (a+b \log (c (e+f x)))}{b}\right)}{c^3 d f^4}+\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} \Gamma \left(p+1,-\frac{2 (a+b \log (c (e+f x)))}{b}\right)}{c^2 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 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} \Gamma \left(p+1,-\frac{a+b \log (c (e+f x))}{b}\right)}{c d f^4}",1,"(6^(-1 - p)*(a + b*Log[c*(e + f*x)])^p*(2^(1 + p)*b*i^3*(1 + p)*Gamma[1 + p, (-3*(a + b*Log[c*(e + f*x)]))/b] + 3^(1 + p)*c*E^(a/b)*(f*h - e*i)*(3*b*i^2*(1 + p)*Gamma[1 + p, (-2*(a + b*Log[c*(e + f*x)]))/b] + 2^(1 + p)*c*E^(a/b)*(f*h - e*i)*(3*b*i*(1 + p)*Gamma[1 + p, -((a + b*Log[c*(e + f*x)])/b)] - b*c*E^(a/b)*(f*h - e*i)*(-((a + b*Log[c*(e + f*x)])/b))^(1 + p)))))/(b*c^3*d*E^((3*a)/b)*f^4*(1 + p)*(-((a + b*Log[c*(e + f*x)])/b))^p)","A",1
211,1,189,210,0.6508242,"\int \frac{(h+i x)^2 (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx","Integrate[((h + i*x)^2*(a + b*Log[c*(e + f*x)])^p)/(d*e + d*f*x),x]","\frac{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} \left(c 2^{p+1} e^{a/b} (f h-e i) \left(2 b i (p+1) \Gamma \left(p+1,-\frac{a+b \log (c (e+f x))}{b}\right)-b c e^{a/b} (f h-e i) \left(-\frac{a+b \log (c (e+f x))}{b}\right)^{p+1}\right)+b i^2 (p+1) \Gamma \left(p+1,-\frac{2 (a+b \log (c (e+f x)))}{b}\right)\right)}{b c^2 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} \Gamma \left(p+1,-\frac{2 (a+b \log (c (e+f x)))}{b}\right)}{c^2 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{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} \Gamma \left(p+1,-\frac{a+b \log (c (e+f x))}{b}\right)}{c d f^3}",1,"(2^(-1 - p)*(a + b*Log[c*(e + f*x)])^p*(b*i^2*(1 + p)*Gamma[1 + p, (-2*(a + b*Log[c*(e + f*x)]))/b] + 2^(1 + p)*c*E^(a/b)*(f*h - e*i)*(2*b*i*(1 + p)*Gamma[1 + p, -((a + b*Log[c*(e + f*x)])/b)] - b*c*E^(a/b)*(f*h - e*i)*(-((a + b*Log[c*(e + f*x)])/b))^(1 + p))))/(b*c^2*d*E^((2*a)/b)*f^3*(1 + p)*(-((a + b*Log[c*(e + f*x)])/b))^p)","A",1
212,1,106,115,0.2715929,"\int \frac{(h+i x) (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx","Integrate[((h + i*x)*(a + b*Log[c*(e + f*x)])^p)/(d*e + d*f*x),x]","\frac{(a+b \log (c (e+f x)))^p \left(\frac{(f h-e i) (a+b \log (c (e+f x)))}{b (p+1)}+\frac{i e^{-\frac{a}{b}} \left(-\frac{a+b \log (c (e+f x))}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log (c (e+f x))}{b}\right)}{c}\right)}{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} \Gamma \left(p+1,-\frac{a+b \log (c (e+f x))}{b}\right)}{c d f^2}",1,"((a + b*Log[c*(e + f*x)])^p*(((f*h - e*i)*(a + b*Log[c*(e + f*x)]))/(b*(1 + p)) + (i*Gamma[1 + p, -((a + b*Log[c*(e + f*x)])/b)])/(c*E^(a/b)*(-((a + b*Log[c*(e + f*x)])/b))^p)))/(d*f^2)","A",1
213,1,31,31,0.0140535,"\int \frac{(a+b \log (c (e+f x)))^p}{d e+d f x} \, dx","Integrate[(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",1
214,0,0,35,0.6458395,"\int \frac{(a+b \log (c (e+f x)))^p}{(d e+d f x) (h+i x)} \, dx","Integrate[(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,"Integrate[(a + b*Log[c*(e + f*x)])^p/((d*e + d*f*x)*(h + i*x)), x]","A",-1
215,0,0,35,1.6811604,"\int \frac{(a+b \log (c (e+f x)))^p}{(d e+d f x) (h+i x)^2} \, dx","Integrate[(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,"Integrate[(a + b*Log[c*(e + f*x)])^p/((d*e + d*f*x)*(h + i*x)^2), x]","A",-1
216,0,0,35,3.852614,"\int \frac{(a+b \log (c (e+f x)))^p}{(d e+d f x) (h+i x)^3} \, dx","Integrate[(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,"Integrate[(a + b*Log[c*(e + f*x)])^p/((d*e + d*f*x)*(h + i*x)^3), x]","A",-1
217,1,379,402,0.616702,"\int \frac{(h+i x)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x} \, dx","Integrate[((h + i*x)^3*(a + b*Log[c*(d + e*x)^n]))/(f + g*x),x]","\frac{e \left(g i x \left(6 a e^2 \left(6 f^2 i^2-3 f g i (6 h+i x)+g^2 \left(18 h^2+9 h i x+2 i^2 x^2\right)\right)-b n \left(12 d^2 g^2 i^2-6 d e g i (-3 f i+9 g h+g i x)+e^2 \left(36 f^2 i^2-9 f g i (12 h+i x)+g^2 \left(108 h^2+27 h i x+4 i^2 x^2\right)\right)\right)\right)+36 a e^2 (g h-f i)^3 \log \left(\frac{e (f+g x)}{e f-d g}\right)+6 b e \log \left(c (d+e x)^n\right) \left(g i \left(6 d \left(f^2 i^2-3 f g h i+3 g^2 h^2\right)+e x \left(6 f^2 i^2-3 f g i (6 h+i x)+g^2 \left(18 h^2+9 h i x+2 i^2 x^2\right)\right)\right)+6 e (g h-f i)^3 \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)\right)+6 b d^2 g^2 i^2 n \log (d+e x) (2 d g i+3 e f i-9 e g h)+36 b e^3 n (g h-f i)^3 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)}{36 e^3 g^4}","\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)^2 (g h-f i) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 g^2}+\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)^3 \log (d+e x)}{3 e^3 g}-\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 (g h-f i)^3 \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{g^4}-\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 i n x (g h-f i)^2}{g^3}-\frac{b n (h+i x)^2 (g h-f i)}{4 g^2}-\frac{b n (h+i x)^3}{9 g}",1,"(6*b*d^2*g^2*i^2*(-9*e*g*h + 3*e*f*i + 2*d*g*i)*n*Log[d + e*x] + e*(g*i*x*(6*a*e^2*(6*f^2*i^2 - 3*f*g*i*(6*h + i*x) + g^2*(18*h^2 + 9*h*i*x + 2*i^2*x^2)) - b*n*(12*d^2*g^2*i^2 - 6*d*e*g*i*(9*g*h - 3*f*i + g*i*x) + e^2*(36*f^2*i^2 - 9*f*g*i*(12*h + i*x) + g^2*(108*h^2 + 27*h*i*x + 4*i^2*x^2)))) + 36*a*e^2*(g*h - f*i)^3*Log[(e*(f + g*x))/(e*f - d*g)] + 6*b*e*Log[c*(d + e*x)^n]*(g*i*(6*d*(3*g^2*h^2 - 3*f*g*h*i + f^2*i^2) + e*x*(6*f^2*i^2 - 3*f*g*i*(6*h + i*x) + g^2*(18*h^2 + 9*h*i*x + 2*i^2*x^2))) + 6*e*(g*h - f*i)^3*Log[(e*(f + g*x))/(e*f - d*g)])) + 36*b*e^3*(g*h - f*i)^3*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)])/(36*e^3*g^4)","A",1
218,1,224,241,0.3142334,"\int \frac{(h+i x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x} \, dx","Integrate[((h + i*x)^2*(a + b*Log[c*(d + e*x)^n]))/(f + g*x),x]","\frac{e \left(g i x (2 a e (-2 f i+4 g h+g i x)+b n (2 d g i-e (-4 f i+8 g h+g i x)))+4 a e (g h-f i)^2 \log \left(\frac{e (f+g x)}{e f-d g}\right)+2 b \log \left(c (d+e x)^n\right) \left(g i (d (4 g h-2 f i)+e x (-2 f i+4 g h+g i x))+2 e (g h-f i)^2 \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)\right)-2 b d^2 g^2 i^2 n \log (d+e x)+4 b e^2 n (g h-f i)^2 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)}{4 e^2 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 n (g h-f i)^2 \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{g^3}-\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,"(-2*b*d^2*g^2*i^2*n*Log[d + e*x] + e*(g*i*x*(2*a*e*(4*g*h - 2*f*i + g*i*x) + b*n*(2*d*g*i - e*(8*g*h - 4*f*i + g*i*x))) + 4*a*e*(g*h - f*i)^2*Log[(e*(f + g*x))/(e*f - d*g)] + 2*b*Log[c*(d + e*x)^n]*(g*i*(d*(4*g*h - 2*f*i) + e*x*(4*g*h - 2*f*i + g*i*x)) + 2*e*(g*h - f*i)^2*Log[(e*(f + g*x))/(e*f - d*g)])) + 4*b*e^2*(g*h - f*i)^2*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)])/(4*e^2*g^3)","A",1
219,1,110,119,0.1164754,"\int \frac{(h+i x) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x} \, dx","Integrate[((h + i*x)*(a + b*Log[c*(d + e*x)^n]))/(f + g*x),x]","\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)+a g i x+\frac{b g i (d+e x) \log \left(c (d+e x)^n\right)}{e}+b n (g h-f i) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-b g i n x}{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 n (g h-f i) \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{g^2}-\frac{b i n x}{g}",1,"(a*g*i*x - b*g*i*n*x + (b*g*i*(d + e*x)*Log[c*(d + e*x)^n])/e + (g*h - f*i)*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)] + b*(g*h - f*i)*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)])/g^2","A",1
220,1,62,63,0.0074198,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{f+g x} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(f + g*x),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}+\frac{b n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\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{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\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",1
221,1,111,155,0.0694619,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x) (h+i x)} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/((f + g*x)*(h + i*x)),x]","\frac{\left(a+b \log \left(c (d+e x)^n\right)\right) \left(\log \left(\frac{e (f+g x)}{e f-d g}\right)-\log \left(\frac{e (h+i x)}{e h-d i}\right)\right)+b n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-b n \text{Li}_2\left(\frac{i (d+e x)}{d i-e h}\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{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{g h-f i}-\frac{b n \text{Li}_2\left(-\frac{i (d+e x)}{e h-d i}\right)}{g h-f i}",1,"((a + b*Log[c*(d + e*x)^n])*(Log[(e*(f + g*x))/(e*f - d*g)] - Log[(e*(h + i*x))/(e*h - d*i)]) + b*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - b*n*PolyLog[2, (i*(d + e*x))/(-(e*h) + d*i)])/(g*h - f*i)","A",1
222,1,196,252,0.1945373,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x) (h+i x)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/((f + g*x)*(h + i*x)^2),x]","\frac{\frac{(g h-f i) \left(a+b \log \left(c (d+e x)^n\right)\right)}{h+i x}+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 \log \left(\frac{e (h+i x)}{e h-d i}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-\frac{b e n (g h-f i) (\log (d+e x)-\log (h+i x))}{e h-d i}+b g n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-b g n \text{Li}_2\left(\frac{i (d+e x)}{d i-e h}\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 g n \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{(g h-f i)^2}-\frac{b g n \text{Li}_2\left(-\frac{i (d+e x)}{e h-d i}\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,"(((g*h - f*i)*(a + b*Log[c*(d + e*x)^n]))/(h + i*x) + g*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)] - (b*e*(g*h - f*i)*n*(Log[d + e*x] - Log[h + i*x]))/(e*h - d*i) - g*(a + b*Log[c*(d + e*x)^n])*Log[(e*(h + i*x))/(e*h - d*i)] + b*g*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - b*g*n*PolyLog[2, (i*(d + e*x))/(-(e*h) + d*i)])/(g*h - f*i)^2","A",1
223,1,311,402,0.3996362,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x) (h+i x)^3} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/((f + g*x)*(h + i*x)^3),x]","\frac{2 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)+\frac{2 g (g h-f i) \left(a+b \log \left(c (d+e x)^n\right)\right)}{h+i x}+\frac{(g h-f i)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{(h+i x)^2}-2 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)+2 b g^2 n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-\frac{2 b e g n (g h-f i) (\log (d+e x)-\log (h+i x))}{e h-d i}-\frac{b e n (g h-f i)^2 (e (h+i x) \log (d+e x)-d i-e (h+i x) \log (h+i x)+e h)}{(h+i x) (e h-d i)^2}-2 b g^2 n \text{Li}_2\left(\frac{i (d+e x)}{d i-e h}\right)}{2 (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 g^2 n \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{(g h-f i)^3}-\frac{b g^2 n \text{Li}_2\left(-\frac{i (d+e x)}{e h-d i}\right)}{(g h-f i)^3}-\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,"(((g*h - f*i)^2*(a + b*Log[c*(d + e*x)^n]))/(h + i*x)^2 + (2*g*(g*h - f*i)*(a + b*Log[c*(d + e*x)^n]))/(h + i*x) + 2*g^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)] - (2*b*e*g*(g*h - f*i)*n*(Log[d + e*x] - Log[h + i*x]))/(e*h - d*i) - (b*e*(g*h - f*i)^2*n*(e*h - d*i + e*(h + i*x)*Log[d + e*x] - e*(h + i*x)*Log[h + i*x]))/((e*h - d*i)^2*(h + i*x)) - 2*g^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(h + i*x))/(e*h - d*i)] + 2*b*g^2*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*b*g^2*n*PolyLog[2, (i*(d + e*x))/(-(e*h) + d*i)])/(2*(g*h - f*i)^3)","A",1
224,1,876,469,0.6409989,"\int \frac{(h+i x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x} \, dx","Integrate[((h + i*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x),x]","\frac{8 b e^2 g^2 n \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)+\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)\right) h^2+4 b^2 e^2 g^2 n^2 \left(\log \left(\frac{e (f+g x)}{e f-d g}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)\right) h^2-16 b e g i n \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(e f \left(\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)+\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)\right)-g (d+e x) (\log (d+e x)-1)\right) h+8 b^2 e g i n^2 \left(g \left((d+e x) \log ^2(d+e x)-2 (d+e x) \log (d+e x)+2 e x\right)-e f \left(\log \left(\frac{e (f+g x)}{e f-d g}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)\right)\right) h+2 e^2 g^2 i^2 x^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2+4 e^2 g i (2 g h-f i) x \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2+4 e^2 (g h-f i)^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 \log (f+g x)+2 b i^2 n \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(4 e^2 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) f^2+e g (e x (4 f-g x)+2 d (2 f+g x))-2 \log (d+e x) \left(g (d+e x) (2 e f+d g-e g x)-2 e^2 f^2 \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)\right)-b^2 i^2 n^2 \left(-4 e^2 \left(\log \left(\frac{e (f+g x)}{e f-d g}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)\right) f^2+4 e g \left((d+e x) \log ^2(d+e x)-2 (d+e x) \log (d+e x)+2 e x\right) f+g^2 \left(2 \left(d^2-e^2 x^2\right) \log ^2(d+e x)+\left(-6 d^2-4 e x d+2 e^2 x^2\right) \log (d+e x)+e x (6 d-e x)\right)\right)}{4 e^2 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{2 b n (g h-f i)^2 \text{Li}_2\left(-\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{(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{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{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 n^2 (g h-f i)^2 \text{Li}_3\left(-\frac{g (d+e x)}{e f-d g}\right)}{g^3}+\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,"(4*e^2*g*i*(2*g*h - f*i)*x*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 2*e^2*g^2*i^2*x^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 4*e^2*(g*h - f*i)^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x] + 8*b*e^2*g^2*h^2*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + 2*b*i^2*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(e*g*(e*x*(4*f - g*x) + 2*d*(2*f + g*x)) - 2*Log[d + e*x]*(g*(d + e*x)*(2*e*f + d*g - e*g*x) - 2*e^2*f^2*Log[(e*(f + g*x))/(e*f - d*g)]) + 4*e^2*f^2*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) - 16*b*e*g*h*i*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(-(g*(d + e*x)*(-1 + Log[d + e*x])) + e*f*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)])) + 8*b^2*e*g*h*i*n^2*(g*(2*e*x - 2*(d + e*x)*Log[d + e*x] + (d + e*x)*Log[d + e*x]^2) - e*f*(Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)] + 2*Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)])) - b^2*i^2*n^2*(4*e*f*g*(2*e*x - 2*(d + e*x)*Log[d + e*x] + (d + e*x)*Log[d + e*x]^2) + g^2*(e*x*(6*d - e*x) + (-6*d^2 - 4*d*e*x + 2*e^2*x^2)*Log[d + e*x] + 2*(d^2 - e^2*x^2)*Log[d + e*x]^2) - 4*e^2*f^2*(Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)] + 2*Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)])) + 4*b^2*e^2*g^2*h^2*n^2*(Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)] + 2*Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)]))/(4*e^2*g^3)","A",1
225,1,460,215,0.3423498,"\int \frac{(h+i x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x} \, dx","Integrate[((h + i*x)*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x),x]","\frac{e (g h-f i) \log (f+g x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+2 b e g h n \left(\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)-2 b i n \left(e f \left(\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)-g (d+e x) (\log (d+e x)-1)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)+e g i x \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+b^2 e g h n^2 \left(-2 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log ^2(d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)+b^2 i n^2 \left(g \left((d+e x) \log ^2(d+e x)-2 (d+e x) \log (d+e x)+2 e x\right)-e f \left(-2 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log ^2(d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)\right)}{e g^2}","\frac{2 b n (g h-f i) \text{Li}_2\left(-\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{(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 n^2 (g h-f i) \text{Li}_3\left(-\frac{g (d+e x)}{e f-d g}\right)}{g^2}+\frac{2 b^2 i n^2 x}{g}",1,"(e*g*i*x*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + e*(g*h - f*i)*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x] + 2*b*e*g*h*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) - 2*b*i*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(-(g*(d + e*x)*(-1 + Log[d + e*x])) + e*f*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)])) + b^2*i*n^2*(g*(2*e*x - 2*(d + e*x)*Log[d + e*x] + (d + e*x)*Log[d + e*x]^2) - e*f*(Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)] + 2*Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)])) + b^2*e*g*h*n^2*(Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)] + 2*Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)]))/(e*g^2)","B",1
226,1,242,111,0.119121,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x),x]","\frac{\log (f+g x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+2 a b n \left(\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)+2 b^2 n \left(\log \left(c (d+e x)^n\right)-n \log (d+e x)\right) \left(\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)+b^2 n^2 \left(-2 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log ^2(d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)}{g}","\frac{2 b n \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right) \left(a+b \log \left(c (d+e x)^n\right)\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^2 n^2 \text{Li}_3\left(-\frac{g (d+e x)}{e f-d g}\right)}{g}",1,"((a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x] + 2*a*b*n*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + 2*b^2*n*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + b^2*n^2*(Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)] + 2*Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)]))/g","B",1
227,1,353,264,0.3153547,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x) (h+i x)} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/((f + g*x)*(h + i*x)),x]","\frac{2 b n \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right) \left(\log (d+e x) \left(\log \left(\frac{e (f+g x)}{e f-d g}\right)-\log \left(\frac{e (h+i x)}{e h-d i}\right)\right)+\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-\text{Li}_2\left(\frac{i (d+e x)}{d i-e h}\right)\right)+\log (f+g x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2-\log (h+i x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+b^2 n^2 \left(-2 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log ^2(d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)+2 \text{Li}_3\left(\frac{i (d+e x)}{d i-e h}\right)-2 \log (d+e x) \text{Li}_2\left(\frac{i (d+e x)}{d i-e h}\right)-\log ^2(d+e x) \log \left(\frac{e (h+i x)}{e h-d i}\right)\right)}{g h-f i}","\frac{2 b n \text{Li}_2\left(-\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{Li}_2\left(-\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{\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^2 n^2 \text{Li}_3\left(-\frac{g (d+e x)}{e f-d g}\right)}{g h-f i}+\frac{2 b^2 n^2 \text{Li}_3\left(-\frac{i (d+e x)}{e h-d i}\right)}{g h-f i}",1,"((a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x] - (a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[h + i*x] + 2*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(Log[d + e*x]*(Log[(e*(f + g*x))/(e*f - d*g)] - Log[(e*(h + i*x))/(e*h - d*i)]) + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - PolyLog[2, (i*(d + e*x))/(-(e*h) + d*i)]) + b^2*n^2*(Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)] - Log[d + e*x]^2*Log[(e*(h + i*x))/(e*h - d*i)] + 2*Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*Log[d + e*x]*PolyLog[2, (i*(d + e*x))/(-(e*h) + d*i)] - 2*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)] + 2*PolyLog[3, (i*(d + e*x))/(-(e*h) + d*i)]))/(g*h - f*i)","A",1
228,1,630,427,0.7296517,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{(f+g x) (h+i x)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/((f + g*x)*(h + i*x)^2),x]","\frac{-2 b n \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right) \left(-g (h+i x) (e h-d i) \left(\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)+(g h-f i) (i (d+e x) \log (d+e x)-e (h+i x) \log (h+i x))+g (h+i x) (e h-d i) \left(\text{Li}_2\left(\frac{i (d+e x)}{d i-e h}\right)+\log (d+e x) \log \left(\frac{e (h+i x)}{e h-d i}\right)\right)\right)+(e h-d i) (g h-f i) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+g (h+i x) (e h-d i) \log (f+g x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2-g (h+i x) (e h-d i) \log (h+i x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2-b^2 n^2 \left(-g (h+i x) (e h-d i) \left(-2 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log ^2(d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)+(g h-f i) \left(\log (d+e x) \left(i (d+e x) \log (d+e x)-2 e (h+i x) \log \left(\frac{e (h+i x)}{e h-d i}\right)\right)-2 e (h+i x) \text{Li}_2\left(\frac{i (d+e x)}{d i-e h}\right)\right)+g (h+i x) (e h-d i) \left(-2 \text{Li}_3\left(\frac{i (d+e x)}{d i-e h}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{i (d+e x)}{d i-e h}\right)+\log ^2(d+e x) \log \left(\frac{e (h+i x)}{e h-d i}\right)\right)\right)}{(h+i x) (e h-d i) (g h-f i)^2}","\frac{2 b g n \text{Li}_2\left(-\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{Li}_2\left(-\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 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^2 e n^2 \text{Li}_2\left(-\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{Li}_3\left(-\frac{g (d+e x)}{e f-d g}\right)}{(g h-f i)^2}+\frac{2 b^2 g n^2 \text{Li}_3\left(-\frac{i (d+e x)}{e h-d i}\right)}{(g h-f i)^2}",1,"((e*h - d*i)*(g*h - f*i)*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + g*(e*h - d*i)*(h + i*x)*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x] - g*(e*h - d*i)*(h + i*x)*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[h + i*x] - 2*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((g*h - f*i)*(i*(d + e*x)*Log[d + e*x] - e*(h + i*x)*Log[h + i*x]) - g*(e*h - d*i)*(h + i*x)*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + g*(e*h - d*i)*(h + i*x)*(Log[d + e*x]*Log[(e*(h + i*x))/(e*h - d*i)] + PolyLog[2, (i*(d + e*x))/(-(e*h) + d*i)])) - b^2*n^2*((g*h - f*i)*(Log[d + e*x]*(i*(d + e*x)*Log[d + e*x] - 2*e*(h + i*x)*Log[(e*(h + i*x))/(e*h - d*i)]) - 2*e*(h + i*x)*PolyLog[2, (i*(d + e*x))/(-(e*h) + d*i)]) - g*(e*h - d*i)*(h + i*x)*(Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)] + 2*Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)]) + g*(e*h - d*i)*(h + i*x)*(Log[d + e*x]^2*Log[(e*(h + i*x))/(e*h - d*i)] + 2*Log[d + e*x]*PolyLog[2, (i*(d + e*x))/(-(e*h) + d*i)] - 2*PolyLog[3, (i*(d + e*x))/(-(e*h) + d*i)])))/((e*h - d*i)*(g*h - f*i)^2*(h + i*x))","A",1
229,1,1521,660,1.0306113,"\int \frac{(h+i x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{f+g x} \, dx","Integrate[((h + i*x)^2*(a + b*Log[c*(d + e*x)^n])^3)/(f + g*x),x]","\frac{8 b^3 e^2 g^2 h^2 \left(\log \left(\frac{e (f+g x)}{e f-d g}\right) \log ^3(d+e x)+3 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) \log ^2(d+e x)-6 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right) \log (d+e x)+6 \text{Li}_4\left(\frac{g (d+e x)}{d g-e f}\right)\right) n^3-16 b^3 e g h i \left(g \left(-\left((d+e x) \log ^3(d+e x)\right)+3 (d+e x) \log ^2(d+e x)-6 (d+e x) \log (d+e x)+6 e x\right)+e f \left(\log \left(\frac{e (f+g x)}{e f-d g}\right) \log ^3(d+e x)+3 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) \log ^2(d+e x)-6 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right) \log (d+e x)+6 \text{Li}_4\left(\frac{g (d+e x)}{d g-e f}\right)\right)\right) n^3+b^3 i^2 \left(8 e^2 \left(\log \left(\frac{e (f+g x)}{e f-d g}\right) \log ^3(d+e x)+3 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) \log ^2(d+e x)-6 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right) \log (d+e x)+6 \text{Li}_4\left(\frac{g (d+e x)}{d g-e f}\right)\right) f^2+8 e g \left(-\left((d+e x) \log ^3(d+e x)\right)+3 (d+e x) \log ^2(d+e x)-6 (d+e x) \log (d+e x)+6 e x\right) f-g^2 \left(4 \left(d^2-e^2 x^2\right) \log ^3(d+e x)-6 \left(3 d^2+2 e x d-e^2 x^2\right) \log ^2(d+e x)+6 \left(7 d^2+6 e x d-e^2 x^2\right) \log (d+e x)+3 e x (e x-14 d)\right)\right) n^3+48 b^2 e g h i \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(g \left((d+e x) \log ^2(d+e x)-2 (d+e x) \log (d+e x)+2 e x\right)-e f \left(\log \left(\frac{e (f+g x)}{e f-d g}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)\right)\right) n^2-6 b^2 i^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(-4 e^2 \left(\log \left(\frac{e (f+g x)}{e f-d g}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)\right) f^2+4 e g \left((d+e x) \log ^2(d+e x)-2 (d+e x) \log (d+e x)+2 e x\right) f+g^2 \left(2 \left(d^2-e^2 x^2\right) \log ^2(d+e x)+\left(-6 d^2-4 e x d+2 e^2 x^2\right) \log (d+e x)+e x (6 d-e x)\right)\right) n^2+48 b^2 e^2 g^2 h^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(\frac{1}{2} \log \left(\frac{e (f+g x)}{e f-d g}\right) \log ^2(d+e x)+\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) \log (d+e x)-\text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)\right) n^2+24 b e^2 g^2 h^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 \left(\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)+\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)\right) n+6 b i^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 \left(4 e^2 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) f^2+e g (e x (4 f-g x)+2 d (2 f+g x))-2 \log (d+e x) \left(g (d+e x) (2 e f+d g-e g x)-2 e^2 f^2 \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)\right) n-48 b e g h i \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 \left(e f \left(\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)+\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)\right)-g (d+e x) (\log (d+e x)-1)\right) n+4 e^2 g^2 i^2 x^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^3+8 e^2 g i (2 g h-f i) x \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^3+8 e^2 (g h-f i)^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^3 \log (f+g x)}{8 e^2 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 b^2 n^2 (g h-f i)^2 \text{Li}_3\left(-\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{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 n (g h-f i)^2 \text{Li}_2\left(-\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{(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{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{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 n^3 (g h-f i)^2 \text{Li}_4\left(-\frac{g (d+e x)}{e f-d g}\right)}{g^3}-\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,"(8*e^2*g*i*(2*g*h - f*i)*x*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3 + 4*e^2*g^2*i^2*x^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3 + 8*e^2*(g*h - f*i)^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3*Log[f + g*x] + 24*b*e^2*g^2*h^2*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + 6*b*i^2*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*(e*g*(e*x*(4*f - g*x) + 2*d*(2*f + g*x)) - 2*Log[d + e*x]*(g*(d + e*x)*(2*e*f + d*g - e*g*x) - 2*e^2*f^2*Log[(e*(f + g*x))/(e*f - d*g)]) + 4*e^2*f^2*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) - 48*b*e*g*h*i*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*(-(g*(d + e*x)*(-1 + Log[d + e*x])) + e*f*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)])) + 48*b^2*e*g*h*i*n^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(g*(2*e*x - 2*(d + e*x)*Log[d + e*x] + (d + e*x)*Log[d + e*x]^2) - e*f*(Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)] + 2*Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)])) - 6*b^2*i^2*n^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(4*e*f*g*(2*e*x - 2*(d + e*x)*Log[d + e*x] + (d + e*x)*Log[d + e*x]^2) + g^2*(e*x*(6*d - e*x) + (-6*d^2 - 4*d*e*x + 2*e^2*x^2)*Log[d + e*x] + 2*(d^2 - e^2*x^2)*Log[d + e*x]^2) - 4*e^2*f^2*(Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)] + 2*Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)])) + 48*b^2*e^2*g^2*h^2*n^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)])/2 + Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)]) + 8*b^3*e^2*g^2*h^2*n^3*(Log[d + e*x]^3*Log[(e*(f + g*x))/(e*f - d*g)] + 3*Log[d + e*x]^2*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 6*Log[d + e*x]*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)] + 6*PolyLog[4, (g*(d + e*x))/(-(e*f) + d*g)]) - 16*b^3*e*g*h*i*n^3*(g*(6*e*x - 6*(d + e*x)*Log[d + e*x] + 3*(d + e*x)*Log[d + e*x]^2 - (d + e*x)*Log[d + e*x]^3) + e*f*(Log[d + e*x]^3*Log[(e*(f + g*x))/(e*f - d*g)] + 3*Log[d + e*x]^2*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 6*Log[d + e*x]*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)] + 6*PolyLog[4, (g*(d + e*x))/(-(e*f) + d*g)])) + b^3*i^2*n^3*(8*e*f*g*(6*e*x - 6*(d + e*x)*Log[d + e*x] + 3*(d + e*x)*Log[d + e*x]^2 - (d + e*x)*Log[d + e*x]^3) - g^2*(3*e*x*(-14*d + e*x) + 6*(7*d^2 + 6*d*e*x - e^2*x^2)*Log[d + e*x] - 6*(3*d^2 + 2*d*e*x - e^2*x^2)*Log[d + e*x]^2 + 4*(d^2 - e^2*x^2)*Log[d + e*x]^3) + 8*e^2*f^2*(Log[d + e*x]^3*Log[(e*(f + g*x))/(e*f - d*g)] + 3*Log[d + e*x]^2*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 6*Log[d + e*x]*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)] + 6*PolyLog[4, (g*(d + e*x))/(-(e*f) + d*g)])))/(8*e^2*g^3)","B",1
230,1,799,308,0.4397211,"\int \frac{(h+i x) \left(a+b \log \left(c (d+e x)^n\right)\right)^3}{f+g x} \, dx","Integrate[((h + i*x)*(a + b*Log[c*(d + e*x)^n])^3)/(f + g*x),x]","\frac{b^3 e g h \left(\log \left(\frac{e (f+g x)}{e f-d g}\right) \log ^3(d+e x)+3 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) \log ^2(d+e x)-6 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right) \log (d+e x)+6 \text{Li}_4\left(\frac{g (d+e x)}{d g-e f}\right)\right) n^3-b^3 i \left(g \left(-\left((d+e x) \log ^3(d+e x)\right)+3 (d+e x) \log ^2(d+e x)-6 (d+e x) \log (d+e x)+6 e x\right)+e f \left(\log \left(\frac{e (f+g x)}{e f-d g}\right) \log ^3(d+e x)+3 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) \log ^2(d+e x)-6 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right) \log (d+e x)+6 \text{Li}_4\left(\frac{g (d+e x)}{d g-e f}\right)\right)\right) n^3+3 b^2 i \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(g \left((d+e x) \log ^2(d+e x)-2 (d+e x) \log (d+e x)+2 e x\right)-e f \left(\log \left(\frac{e (f+g x)}{e f-d g}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)\right)\right) n^2+6 b^2 e g h \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(\frac{1}{2} \log \left(\frac{e (f+g x)}{e f-d g}\right) \log ^2(d+e x)+\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) \log (d+e x)-\text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)\right) n^2+3 b e g h \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 \left(\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)+\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)\right) n-3 b i \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 \left(e f \left(\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)+\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)\right)-g (d+e x) (\log (d+e x)-1)\right) n+e g i x \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^3+e (g h-f i) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^3 \log (f+g x)}{e g^2}","-\frac{6 b^2 n^2 (g h-f i) \text{Li}_3\left(-\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{6 a b^2 i n^2 x}{g}+\frac{3 b n (g h-f i) \text{Li}_2\left(-\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{(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 n^3 (g h-f i) \text{Li}_4\left(-\frac{g (d+e x)}{e f-d g}\right)}{g^2}-\frac{6 b^3 i n^3 x}{g}",1,"(e*g*i*x*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3 + e*(g*h - f*i)*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3*Log[f + g*x] + 3*b*e*g*h*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) - 3*b*i*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*(-(g*(d + e*x)*(-1 + Log[d + e*x])) + e*f*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)])) + 3*b^2*i*n^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(g*(2*e*x - 2*(d + e*x)*Log[d + e*x] + (d + e*x)*Log[d + e*x]^2) - e*f*(Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)] + 2*Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)])) + 6*b^2*e*g*h*n^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)])/2 + Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)]) + b^3*e*g*h*n^3*(Log[d + e*x]^3*Log[(e*(f + g*x))/(e*f - d*g)] + 3*Log[d + e*x]^2*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 6*Log[d + e*x]*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)] + 6*PolyLog[4, (g*(d + e*x))/(-(e*f) + d*g)]) - b^3*i*n^3*(g*(6*e*x - 6*(d + e*x)*Log[d + e*x] + 3*(d + e*x)*Log[d + e*x]^2 - (d + e*x)*Log[d + e*x]^3) + e*f*(Log[d + e*x]^3*Log[(e*(f + g*x))/(e*f - d*g)] + 3*Log[d + e*x]^2*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 6*Log[d + e*x]*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)] + 6*PolyLog[4, (g*(d + e*x))/(-(e*f) + d*g)])))/(e*g^2)","B",1
231,1,457,158,0.2201738,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{f+g x} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^3/(f + g*x),x]","\frac{3 a^2 b n \left(\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)+6 b^2 n^2 \left(-\text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)+\log (d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\frac{1}{2} \log ^2(d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)+6 a b^2 n \left(\log \left(c (d+e x)^n\right)-n \log (d+e x)\right) \left(\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)+\log (f+g x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^3+3 b^3 n \left(\log \left(c (d+e x)^n\right)-n \log (d+e x)\right)^2 \left(\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)+b^3 n^3 \left(6 \text{Li}_4\left(\frac{g (d+e x)}{d g-e f}\right)+3 \log ^2(d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-6 \log (d+e x) \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)+\log ^3(d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)\right)}{g}","-\frac{6 b^2 n^2 \text{Li}_3\left(-\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{Li}_2\left(-\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{\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^3 n^3 \text{Li}_4\left(-\frac{g (d+e x)}{e f-d g}\right)}{g}",1,"((a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3*Log[f + g*x] + 3*a^2*b*n*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + 6*a*b^2*n*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + 3*b^3*n*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])^2*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + 6*b^2*n^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)])/2 + Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)]) + b^3*n^3*(Log[d + e*x]^3*Log[(e*(f + g*x))/(e*f - d*g)] + 3*Log[d + e*x]^2*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 6*Log[d + e*x]*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)] + 6*PolyLog[4, (g*(d + e*x))/(-(e*f) + d*g)]))/g","B",1
232,1,599,372,0.5524447,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(f+g x) (h+i x)} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^3/((f + g*x)*(h + i*x)),x]","\frac{6 b^2 n^2 \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right) \left(-\text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)+\log (d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\frac{1}{2} \log ^2(d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)+\text{Li}_3\left(\frac{i (d+e x)}{d i-e h}\right)-\log (d+e x) \text{Li}_2\left(\frac{i (d+e x)}{d i-e h}\right)-\frac{1}{2} \log ^2(d+e x) \log \left(\frac{e (h+i x)}{e h-d i}\right)\right)+3 b n \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2 \left(\log (d+e x) \left(\log \left(\frac{e (f+g x)}{e f-d g}\right)-\log \left(\frac{e (h+i x)}{e h-d i}\right)\right)+\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-\text{Li}_2\left(\frac{i (d+e x)}{d i-e h}\right)\right)+\log (f+g x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^3-\log (h+i x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^3+b^3 n^3 \left(6 \text{Li}_4\left(\frac{g (d+e x)}{d g-e f}\right)+3 \log ^2(d+e x) \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-6 \log (d+e x) \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)+\log ^3(d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)-6 \text{Li}_4\left(\frac{i (d+e x)}{d i-e h}\right)-3 \log ^2(d+e x) \text{Li}_2\left(\frac{i (d+e x)}{d i-e h}\right)+6 \log (d+e x) \text{Li}_3\left(\frac{i (d+e x)}{d i-e h}\right)-\log ^3(d+e x) \log \left(\frac{e (h+i x)}{e h-d i}\right)\right)}{g h-f i}","-\frac{6 b^2 n^2 \text{Li}_3\left(-\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{Li}_3\left(-\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{Li}_2\left(-\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{Li}_2\left(-\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{\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^3 n^3 \text{Li}_4\left(-\frac{g (d+e x)}{e f-d g}\right)}{g h-f i}-\frac{6 b^3 n^3 \text{Li}_4\left(-\frac{i (d+e x)}{e h-d i}\right)}{g h-f i}",1,"((a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3*Log[f + g*x] - (a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3*Log[h + i*x] + 3*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*(Log[d + e*x]*(Log[(e*(f + g*x))/(e*f - d*g)] - Log[(e*(h + i*x))/(e*h - d*i)]) + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - PolyLog[2, (i*(d + e*x))/(-(e*h) + d*i)]) + 6*b^2*n^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)])/2 - (Log[d + e*x]^2*Log[(e*(h + i*x))/(e*h - d*i)])/2 + Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - Log[d + e*x]*PolyLog[2, (i*(d + e*x))/(-(e*h) + d*i)] - PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)] + PolyLog[3, (i*(d + e*x))/(-(e*h) + d*i)]) + b^3*n^3*(Log[d + e*x]^3*Log[(e*(f + g*x))/(e*f - d*g)] - Log[d + e*x]^3*Log[(e*(h + i*x))/(e*h - d*i)] + 3*Log[d + e*x]^2*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 3*Log[d + e*x]^2*PolyLog[2, (i*(d + e*x))/(-(e*h) + d*i)] - 6*Log[d + e*x]*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)] + 6*Log[d + e*x]*PolyLog[3, (i*(d + e*x))/(-(e*h) + d*i)] + 6*PolyLog[4, (g*(d + e*x))/(-(e*f) + d*g)] - 6*PolyLog[4, (i*(d + e*x))/(-(e*h) + d*i)]))/(g*h - f*i)","A",1
233,1,1025,602,1.3262121,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^3}{(f+g x) (h+i x)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^3/((f + g*x)*(h + i*x)^2),x]","\frac{-b^3 \left((g h-f i) \left(\left(i (d+e x) \log (d+e x)-3 e (h+i x) \log \left(\frac{e (h+i x)}{e h-d i}\right)\right) \log ^2(d+e x)-6 e (h+i x) \text{Li}_2\left(\frac{i (d+e x)}{d i-e h}\right) \log (d+e x)+6 e (h+i x) \text{Li}_3\left(\frac{i (d+e x)}{d i-e h}\right)\right)-g (e h-d i) (h+i x) \left(\log \left(\frac{e (f+g x)}{e f-d g}\right) \log ^3(d+e x)+3 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) \log ^2(d+e x)-6 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right) \log (d+e x)+6 \text{Li}_4\left(\frac{g (d+e x)}{d g-e f}\right)\right)+g (e h-d i) (h+i x) \left(\log \left(\frac{e (h+i x)}{e h-d i}\right) \log ^3(d+e x)+3 \text{Li}_2\left(\frac{i (d+e x)}{d i-e h}\right) \log ^2(d+e x)-6 \text{Li}_3\left(\frac{i (d+e x)}{d i-e h}\right) \log (d+e x)+6 \text{Li}_4\left(\frac{i (d+e x)}{d i-e h}\right)\right)\right) n^3-3 b^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left((g h-f i) \left(\log (d+e x) \left(i (d+e x) \log (d+e x)-2 e (h+i x) \log \left(\frac{e (h+i x)}{e h-d i}\right)\right)-2 e (h+i x) \text{Li}_2\left(\frac{i (d+e x)}{d i-e h}\right)\right)-g (e h-d i) (h+i x) \left(\log \left(\frac{e (f+g x)}{e f-d g}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)\right)+g (e h-d i) (h+i x) \left(\log \left(\frac{e (h+i x)}{e h-d i}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{i (d+e x)}{d i-e h}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{i (d+e x)}{d i-e h}\right)\right)\right) n^2-3 b \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 \left((g h-f i) (i (d+e x) \log (d+e x)-e (h+i x) \log (h+i x))-g (e h-d i) (h+i x) \left(\log (d+e x) \log \left(\frac{e (f+g x)}{e f-d g}\right)+\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)\right)+g (e h-d i) (h+i x) \left(\log (d+e x) \log \left(\frac{e (h+i x)}{e h-d i}\right)+\text{Li}_2\left(\frac{i (d+e x)}{d i-e h}\right)\right)\right) n+(e h-d i) (g h-f i) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^3+g (e h-d i) (h+i x) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^3 \log (f+g x)-g (e h-d i) (h+i x) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^3 \log (h+i x)}{(e h-d i) (g h-f i)^2 (h+i x)}","\frac{6 b^2 e n^2 \text{Li}_2\left(-\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{Li}_3\left(-\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{Li}_3\left(-\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{Li}_2\left(-\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{Li}_2\left(-\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{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^3 e n^3 \text{Li}_3\left(-\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{Li}_4\left(-\frac{g (d+e x)}{e f-d g}\right)}{(g h-f i)^2}-\frac{6 b^3 g n^3 \text{Li}_4\left(-\frac{i (d+e x)}{e h-d i}\right)}{(g h-f i)^2}",1,"((e*h - d*i)*(g*h - f*i)*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3 + g*(e*h - d*i)*(h + i*x)*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3*Log[f + g*x] - g*(e*h - d*i)*(h + i*x)*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^3*Log[h + i*x] - 3*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*((g*h - f*i)*(i*(d + e*x)*Log[d + e*x] - e*(h + i*x)*Log[h + i*x]) - g*(e*h - d*i)*(h + i*x)*(Log[d + e*x]*Log[(e*(f + g*x))/(e*f - d*g)] + PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)]) + g*(e*h - d*i)*(h + i*x)*(Log[d + e*x]*Log[(e*(h + i*x))/(e*h - d*i)] + PolyLog[2, (i*(d + e*x))/(-(e*h) + d*i)])) - 3*b^2*n^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((g*h - f*i)*(Log[d + e*x]*(i*(d + e*x)*Log[d + e*x] - 2*e*(h + i*x)*Log[(e*(h + i*x))/(e*h - d*i)]) - 2*e*(h + i*x)*PolyLog[2, (i*(d + e*x))/(-(e*h) + d*i)]) - g*(e*h - d*i)*(h + i*x)*(Log[d + e*x]^2*Log[(e*(f + g*x))/(e*f - d*g)] + 2*Log[d + e*x]*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)]) + g*(e*h - d*i)*(h + i*x)*(Log[d + e*x]^2*Log[(e*(h + i*x))/(e*h - d*i)] + 2*Log[d + e*x]*PolyLog[2, (i*(d + e*x))/(-(e*h) + d*i)] - 2*PolyLog[3, (i*(d + e*x))/(-(e*h) + d*i)])) - b^3*n^3*((g*h - f*i)*(Log[d + e*x]^2*(i*(d + e*x)*Log[d + e*x] - 3*e*(h + i*x)*Log[(e*(h + i*x))/(e*h - d*i)]) - 6*e*(h + i*x)*Log[d + e*x]*PolyLog[2, (i*(d + e*x))/(-(e*h) + d*i)] + 6*e*(h + i*x)*PolyLog[3, (i*(d + e*x))/(-(e*h) + d*i)]) - g*(e*h - d*i)*(h + i*x)*(Log[d + e*x]^3*Log[(e*(f + g*x))/(e*f - d*g)] + 3*Log[d + e*x]^2*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 6*Log[d + e*x]*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)] + 6*PolyLog[4, (g*(d + e*x))/(-(e*f) + d*g)]) + g*(e*h - d*i)*(h + i*x)*(Log[d + e*x]^3*Log[(e*(h + i*x))/(e*h - d*i)] + 3*Log[d + e*x]^2*PolyLog[2, (i*(d + e*x))/(-(e*h) + d*i)] - 6*Log[d + e*x]*PolyLog[3, (i*(d + e*x))/(-(e*h) + d*i)] + 6*PolyLog[4, (i*(d + e*x))/(-(e*h) + d*i)])))/((e*h - d*i)*(g*h - f*i)^2*(h + i*x))","A",1
234,0,0,107,0.3063605,"\int \frac{h+i x}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","Integrate[(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,"Integrate[(h + i*x)/((f + g*x)*(a + b*Log[c*(d + e*x)^n])), x]","A",-1
235,0,0,27,0.0261002,"\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","Integrate[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,"Integrate[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])), x]","A",-1
236,0,0,80,0.9821148,"\int \frac{1}{(f+g x) (h+i x) \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","Integrate[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,"Integrate[1/((f + g*x)*(h + i*x)*(a + b*Log[c*(d + e*x)^n])), x]","A",-1
237,0,0,123,3.2767119,"\int \frac{1}{(f+g x) (h+i x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)} \, dx","Integrate[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,"Integrate[1/((f + g*x)*(h + i*x)^2*(a + b*Log[c*(d + e*x)^n])), x]","A",-1
238,0,0,143,1.4234841,"\int \frac{h+i x}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Integrate[(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,"Integrate[(h + i*x)/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^2), x]","A",-1
239,0,0,27,0.1355577,"\int \frac{1}{(f+g x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Integrate[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,"Integrate[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^2), x]","A",-1
240,0,0,80,13.2536361,"\int \frac{1}{(f+g x) (h+i x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Integrate[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,"Integrate[1/((f + g*x)*(h + i*x)*(a + b*Log[c*(d + e*x)^n])^2), x]","A",-1
241,0,0,123,26.94218,"\int \frac{1}{(f+g x) (h+i x)^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Integrate[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,"Integrate[1/((f + g*x)*(h + i*x)^2*(a + b*Log[c*(d + e*x)^n])^2), x]","A",-1
242,1,241,281,0.2867866,"\int \frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x} \, dx","Integrate[(x^3*(a + b*Log[c*(d + e*x)^n]))/(f + g*x),x]","\frac{e \left(g x \left(6 a e^2 \left(6 f^2-3 f g x+2 g^2 x^2\right)-b n \left(12 d^2 g^2-6 d e g (g x-3 f)+e^2 \left(36 f^2-9 f g x+4 g^2 x^2\right)\right)\right)-36 a e^2 f^3 \log \left(\frac{e (f+g x)}{e f-d g}\right)+6 b e \log \left(c (d+e x)^n\right) \left(-6 e f^3 \log \left(\frac{e (f+g x)}{e f-d g}\right)+6 d f^2 g+e g x \left(6 f^2-3 f g x+2 g^2 x^2\right)\right)\right)+6 b d^2 g^2 n (2 d g+3 e f) \log (d+e x)-36 b e^3 f^3 n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)}{36 e^3 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^3 n \log (d+e x)}{3 e^3 g}+\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 f^3 n \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{g^4}-\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,"(6*b*d^2*g^2*(3*e*f + 2*d*g)*n*Log[d + e*x] + e*(g*x*(6*a*e^2*(6*f^2 - 3*f*g*x + 2*g^2*x^2) - b*n*(12*d^2*g^2 - 6*d*e*g*(-3*f + g*x) + e^2*(36*f^2 - 9*f*g*x + 4*g^2*x^2))) - 36*a*e^2*f^3*Log[(e*(f + g*x))/(e*f - d*g)] + 6*b*e*Log[c*(d + e*x)^n]*(6*d*f^2*g + e*g*x*(6*f^2 - 3*f*g*x + 2*g^2*x^2) - 6*e*f^3*Log[(e*(f + g*x))/(e*f - d*g)])) - 36*b*e^3*f^3*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)])/(36*e^3*g^4)","A",1
243,1,170,181,0.1613204,"\int \frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x} \, dx","Integrate[(x^2*(a + b*Log[c*(d + e*x)^n]))/(f + g*x),x]","\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 n \left(-\frac{2 d^2 \log (d+e x)}{e^2}+\frac{2 d x}{e}-x^2\right)}{4 g}+\frac{b f^2 n \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{g^3}+\frac{b f n x}{g^2}","\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 f^2 n \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{g^3}+\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*n*((2*d*x)/e - x^2 - (2*d^2*Log[d + e*x])/e^2))/(4*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",1
244,1,95,104,0.0787953,"\int \frac{x \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x} \, dx","Integrate[(x*(a + b*Log[c*(d + e*x)^n]))/(f + g*x),x]","\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)+a g x+\frac{b g (d+e x) \log \left(c (d+e x)^n\right)}{e}-b f n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-b g n x}{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 f n \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{g^2}-\frac{b n x}{g}",1,"(a*g*x - b*g*n*x + (b*g*(d + e*x)*Log[c*(d + e*x)^n])/e - f*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)] - b*f*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)])/g^2","A",1
245,1,62,63,0.0163042,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{f+g x} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(f + g*x),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}+\frac{b n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\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{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\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",1
246,1,85,107,0.0416506,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x (f+g x)} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(x*(f + g*x)),x]","\frac{\left(\log \left(-\frac{e x}{d}\right)-\log \left(\frac{e (f+g x)}{e f-d g}\right)\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-b n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+b n \text{Li}_2\left(\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{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{f}+\frac{b n \text{Li}_2\left(\frac{e x}{d}+1\right)}{f}",1,"((a + b*Log[c*(d + e*x)^n])*(Log[-((e*x)/d)] - Log[(e*(f + g*x))/(e*f - d*g)]) - b*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] + b*n*PolyLog[2, 1 + (e*x)/d])/f","A",1
247,1,141,162,0.0955266,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^2 (f+g x)} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(x^2*(f + g*x)),x]","\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)-\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)}{x}-g \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+b g n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\frac{b e f n (\log (x)-\log (d+e x))}{d}-b g n \text{Li}_2\left(\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 g n \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{f^2}-\frac{b g n \text{Li}_2\left(\frac{e x}{d}+1\right)}{f^2}+\frac{b e n \log (x)}{d f}-\frac{b e n \log (d+e x)}{d f}",1,"((b*e*f*n*(Log[x] - Log[d + e*x]))/d - (f*(a + b*Log[c*(d + e*x)^n]))/x - g*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]) + g*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)] + b*g*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - b*g*n*PolyLog[2, 1 + (e*x)/d])/f^2","A",1
248,1,208,250,0.2408762,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^3 (f+g x)} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(x^3*(f + g*x)),x]","-\frac{\frac{f^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{x^2}+2 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)-\frac{2 f g \left(a+b \log \left(c (d+e x)^n\right)\right)}{x}-2 g^2 \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{b e f^2 n (-e x \log (d+e x)+d+e x \log (x))}{d^2 x}+2 b g^2 n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\frac{2 b e f g n (\log (x)-\log (d+e x))}{d}-2 b g^2 n \text{Li}_2\left(\frac{e x}{d}+1\right)}{2 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 g^2 n \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{f^3}+\frac{b g^2 n \text{Li}_2\left(\frac{e x}{d}+1\right)}{f^3}-\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,"-1/2*((2*b*e*f*g*n*(Log[x] - Log[d + e*x]))/d + (b*e*f^2*n*(d + e*x*Log[x] - e*x*Log[d + e*x]))/(d^2*x) + (f^2*(a + b*Log[c*(d + e*x)^n]))/x^2 - (2*f*g*(a + b*Log[c*(d + e*x)^n]))/x - 2*g^2*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]) + 2*g^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)] + 2*b*g^2*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*b*g^2*n*PolyLog[2, 1 + (e*x)/d])/f^3","A",1
249,1,220,265,0.3298586,"\int \frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{(f+g x)^2} \, dx","Integrate[(x^3*(a + b*Log[c*(d + e*x)^n]))/(f + g*x)^2,x]","\frac{\frac{4 f^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x}+12 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)+2 g^2 x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)-8 a f g x-\frac{8 b f g (d+e x) \log \left(c (d+e x)^n\right)}{e}-\frac{b g^2 n \left(2 d^2 \log (d+e x)+e x (e x-2 d)\right)}{e^2}-\frac{4 b e f^3 n (\log (d+e x)-\log (f+g x))}{e f-d g}+12 b f^2 n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+8 b f g n x}{4 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{3 b f^2 n \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{g^4}+\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,"(-8*a*f*g*x + 8*b*f*g*n*x - (b*g^2*n*(e*x*(-2*d + e*x) + 2*d^2*Log[d + e*x]))/e^2 - (8*b*f*g*(d + e*x)*Log[c*(d + e*x)^n])/e + 2*g^2*x^2*(a + b*Log[c*(d + e*x)^n]) + (4*f^3*(a + b*Log[c*(d + e*x)^n]))/(f + g*x) - (4*b*e*f^3*n*(Log[d + e*x] - Log[f + g*x]))/(e*f - d*g) + 12*f^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)] + 12*b*f^2*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)])/(4*g^4)","A",1
250,1,153,186,0.1784108,"\int \frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{(f+g x)^2} \, dx","Integrate[(x^2*(a + b*Log[c*(d + e*x)^n]))/(f + g*x)^2,x]","\frac{-\frac{f^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x}-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)+a g x+\frac{b g (d+e x) \log \left(c (d+e x)^n\right)}{e}+\frac{b e f^2 n (\log (d+e x)-\log (f+g x))}{e f-d g}-2 b f n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-b g n x}{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{2 b f n \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{g^3}-\frac{b n x}{g^2}",1,"(a*g*x - b*g*n*x + (b*g*(d + e*x)*Log[c*(d + e*x)^n])/e - (f^2*(a + b*Log[c*(d + e*x)^n]))/(f + g*x) + (b*e*f^2*n*(Log[d + e*x] - Log[f + g*x]))/(e*f - d*g) - 2*f*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)] - 2*b*f*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)])/g^3","A",1
251,1,114,138,0.1051582,"\int \frac{x \left(a+b \log \left(c (d+e x)^n\right)\right)}{(f+g x)^2} \, dx","Integrate[(x*(a + b*Log[c*(d + e*x)^n]))/(f + g*x)^2,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)+\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x}+b n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-\frac{b e f n (\log (d+e x)-\log (f+g x))}{e f-d g}}{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 n \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\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,"((f*(a + b*Log[c*(d + e*x)^n]))/(f + g*x) - (b*e*f*n*(Log[d + e*x] - Log[f + g*x]))/(e*f - d*g) + (a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)] + b*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)])/g^2","A",1
252,1,57,74,0.0876757,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{(f+g x)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(f + g*x)^2,x]","\frac{\frac{b e n (\log (d+e x)-\log (f+g x))}{e f-d g}-\frac{a+b \log \left(c (d+e x)^n\right)}{f+g x}}{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,"(-((a + b*Log[c*(d + e*x)^n])/(f + g*x)) + (b*e*n*(Log[d + e*x] - Log[f + g*x]))/(e*f - d*g))/g","A",1
253,1,152,179,0.1308809,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x (f+g x)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(x*(f + g*x)^2),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)+\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x}+\log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-b n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)-\frac{b e f n (\log (d+e x)-\log (f+g x))}{e f-d g}+b n \text{Li}_2\left(\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 n \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{f^2}+\frac{b n \text{Li}_2\left(\frac{e x}{d}+1\right)}{f^2}-\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,"((f*(a + b*Log[c*(d + e*x)^n]))/(f + g*x) + Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]) - (b*e*f*n*(Log[d + e*x] - Log[f + g*x]))/(e*f - d*g) - (a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)] - b*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] + b*n*PolyLog[2, 1 + (e*x)/d])/f^2","A",1
254,1,199,240,0.2116123,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^2 (f+g x)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(x^2*(f + g*x)^2),x]","\frac{-\frac{f g \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x}+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)-\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)}{x}-2 g \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+2 b g n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\frac{b e f g n (\log (d+e x)-\log (f+g x))}{e f-d g}+\frac{b e f n (\log (x)-\log (d+e x))}{d}-2 b g n \text{Li}_2\left(\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{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{g \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2 (f+g x)}-\frac{a+b \log \left(c (d+e x)^n\right)}{f^2 x}+\frac{2 b g n \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{f^3}-\frac{2 b g n \text{Li}_2\left(\frac{e x}{d}+1\right)}{f^3}+\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*f*n*(Log[x] - Log[d + e*x]))/d - (f*(a + b*Log[c*(d + e*x)^n]))/x - (f*g*(a + b*Log[c*(d + e*x)^n]))/(f + g*x) - 2*g*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]) + (b*e*f*g*n*(Log[d + e*x] - Log[f + g*x]))/(e*f - d*g) + 2*g*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)] + 2*b*g*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 2*b*g*n*PolyLog[2, 1 + (e*x)/d])/f^3","A",1
255,1,269,335,0.4952824,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^3 (f+g x)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(x^3*(f + g*x)^2),x]","-\frac{\frac{f^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{x^2}-\frac{2 f g^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x}+6 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)-\frac{4 f g \left(a+b \log \left(c (d+e x)^n\right)\right)}{x}-6 g^2 \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{b e f^2 n (-e x \log (d+e x)+d+e x \log (x))}{d^2 x}+6 b g^2 n \text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right)+\frac{2 b e f g^2 n (\log (d+e x)-\log (f+g x))}{e f-d g}+\frac{4 b e f g n (\log (x)-\log (d+e x))}{d}-6 b g^2 n \text{Li}_2\left(\frac{e x}{d}+1\right)}{2 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{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{g^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^3 (f+g x)}+\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{3 b g^2 n \text{Li}_2\left(-\frac{g (d+e x)}{e f-d g}\right)}{f^4}+\frac{3 b g^2 n \text{Li}_2\left(\frac{e x}{d}+1\right)}{f^4}-\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,"-1/2*((4*b*e*f*g*n*(Log[x] - Log[d + e*x]))/d + (b*e*f^2*n*(d + e*x*Log[x] - e*x*Log[d + e*x]))/(d^2*x) + (f^2*(a + b*Log[c*(d + e*x)^n]))/x^2 - (4*f*g*(a + b*Log[c*(d + e*x)^n]))/x - (2*f*g^2*(a + b*Log[c*(d + e*x)^n]))/(f + g*x) - 6*g^2*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]) + (2*b*e*f*g^2*n*(Log[d + e*x] - Log[f + g*x]))/(e*f - d*g) + 6*g^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(f + g*x))/(e*f - d*g)] + 6*b*g^2*n*PolyLog[2, (g*(d + e*x))/(-(e*f) + d*g)] - 6*b*g^2*n*PolyLog[2, 1 + (e*x)/d])/f^4","A",1
256,1,331,397,0.3153231,"\int \frac{x^5 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x^2} \, dx","Integrate[(x^5*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2),x]","\frac{24 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)+24 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)-24 f g x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)+12 g^2 x^4 \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{12 b f g n \left(2 d^2 \log (d+e x)+e x (e x-2 d)\right)}{e^2}-\frac{b g^2 n \left(12 d^4 \log (d+e x)+e x \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)\right)}{e^4}+24 b f^2 n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)+24 b f^2 n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{48 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^4 n \log (d+e x)}{4 e^4 g}+\frac{b d^3 n x}{4 e^3 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 f^2 n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^3}+\frac{b f^2 n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 g^3}-\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,"((12*b*f*g*n*(e*x*(-2*d + e*x) + 2*d^2*Log[d + e*x]))/e^2 - (b*g^2*n*(e*x*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3) + 12*d^4*Log[d + e*x]))/e^4 - 24*f*g*x^2*(a + b*Log[c*(d + e*x)^n]) + 12*g^2*x^4*(a + b*Log[c*(d + e*x)^n]) + 24*f^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])] + 24*f^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])] + 24*b*f^2*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))] + 24*b*f^2*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(48*g^3)","A",1
257,1,243,278,0.1797553,"\int \frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x^2} \, dx","Integrate[(x^3*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2),x]","-\frac{2 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 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 x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)+\frac{b g n \left(2 d^2 \log (d+e x)+e x (e x-2 d)\right)}{e^2}+2 b f n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)+2 b f n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{4 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 f n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^2}-\frac{b f n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 g^2}+\frac{b d n x}{2 e g}-\frac{b n x^2}{4 g}",1,"-1/4*((b*g*n*(e*x*(-2*d + e*x) + 2*d^2*Log[d + e*x]))/e^2 - 2*g*x^2*(a + b*Log[c*(d + e*x)^n]) + 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*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])] + 2*b*f*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))] + 2*b*f*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/g^2","A",1
258,1,172,203,0.0456077,"\int \frac{x \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x^2} \, dx","Integrate[(x*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2),x]","\frac{\left(\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right)+\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right)\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+b n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)+b n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+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{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g}+\frac{b n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\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])] + Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])]) + b*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))] + b*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g)","A",1
259,1,224,245,0.1041295,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x \left(f+g x^2\right)} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(x*(f + g*x^2)),x]","-\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)+\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 \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)+b n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)+b n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)-2 b n \text{Li}_2\left(\frac{e x}{d}+1\right)}{2 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{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f}-\frac{b n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 f}+\frac{b n \text{Li}_2\left(\frac{e x}{d}+1\right)}{f}",1,"-1/2*(-2*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]) + (a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])] + (a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])] + b*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))] + b*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])] - 2*b*n*PolyLog[2, 1 + (e*x)/d])/f","A",1
260,1,279,331,0.1875014,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^3 \left(f+g x^2\right)} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(x^3*(f + g*x^2)),x]","\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)+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)-\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)}{x^2}-2 g \log \left(-\frac{e x}{d}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-\frac{b e f n (-e x \log (d+e x)+d+e x \log (x))}{d^2 x}+b g n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)+b g n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)-2 b g n \text{Li}_2\left(\frac{e x}{d}+1\right)}{2 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 g n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f^2}+\frac{b g n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 f^2}-\frac{b g n \text{Li}_2\left(\frac{e x}{d}+1\right)}{f^2}-\frac{b e n}{2 d f x}",1,"(-((b*e*f*n*(d + e*x*Log[x] - e*x*Log[d + e*x]))/(d^2*x)) - (f*(a + b*Log[c*(d + e*x)^n]))/x^2 - 2*g*Log[-((e*x)/d)]*(a + b*Log[c*(d + e*x)^n]) + g*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])] + g*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])] + b*g*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))] + b*g*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])] - 2*b*g*n*PolyLog[2, 1 + (e*x)/d])/(2*f^2)","A",1
261,1,339,369,0.3543071,"\int \frac{x^4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x^2} \, dx","Integrate[(x^4*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2),x]","\frac{9 (-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)+9 \sqrt{-f} 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)+6 g^{3/2} x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)-18 a f \sqrt{g} x-\frac{18 b f \sqrt{g} (d+e x) \log \left(c (d+e x)^n\right)}{e}-\frac{b g^{3/2} n \left(e x \left(6 d^2-3 d e x+2 e^2 x^2\right)-6 d^3 \log (d+e x)\right)}{e^3}-9 b (-f)^{3/2} n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)+9 b (-f)^{3/2} n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)+18 b f \sqrt{g} n x}{18 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^3 n \log (d+e x)}{3 e^3 g}-\frac{b d^2 n x}{3 e^2 g}-\frac{b (-f)^{3/2} n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^{5/2}}+\frac{b (-f)^{3/2} n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 g^{5/2}}+\frac{b d n x^2}{6 e g}+\frac{b f n x}{g^2}-\frac{b n x^3}{9 g}",1,"(-18*a*f*Sqrt[g]*x + 18*b*f*Sqrt[g]*n*x - (b*g^(3/2)*n*(e*x*(6*d^2 - 3*d*e*x + 2*e^2*x^2) - 6*d^3*Log[d + e*x]))/e^3 - (18*b*f*Sqrt[g]*(d + e*x)*Log[c*(d + e*x)^n])/e + 6*g^(3/2)*x^3*(a + b*Log[c*(d + e*x)^n]) + 9*(-f)^(3/2)*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])] + 9*Sqrt[-f]*f*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])] - 9*b*(-f)^(3/2)*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))] + 9*b*(-f)^(3/2)*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(18*g^(5/2))","A",1
262,1,263,276,0.1547246,"\int \frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f+g x^2} \, dx","Integrate[(x^2*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2),x]","\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)-\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 a \sqrt{g} x+\frac{2 b \sqrt{g} (d+e x) \log \left(c (d+e x)^n\right)}{e}-b \sqrt{-f} n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)+b \sqrt{-f} n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)-2 b \sqrt{g} n x}{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 \sqrt{-f} n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^{3/2}}+\frac{b \sqrt{-f} n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 g^{3/2}}-\frac{b n x}{g}",1,"(2*a*Sqrt[g]*x - 2*b*Sqrt[g]*n*x + (2*b*Sqrt[g]*(d + e*x)*Log[c*(d + e*x)^n])/e + Sqrt[-f]*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])] - Sqrt[-f]*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])] - b*Sqrt[-f]*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))] + b*Sqrt[-f]*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*g^(3/2))","A",1
263,1,184,239,0.0573599,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{f+g x^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(f + g*x^2),x]","\frac{\left(\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right)-\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right)\right) \left(a+b \log \left(c (d+e x)^n\right)\right)-b n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)+b n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 \sqrt{-f} \sqrt{g}}","\frac{\log \left(\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{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{b n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\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])] - Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])]) - b*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))] + b*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*Sqrt[-f]*Sqrt[g])","A",1
264,1,280,290,0.2292363,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^2 \left(f+g x^2\right)} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(x^2*(f + g*x^2)),x]","\frac{f \left(d f \sqrt{g} x \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)-d f \sqrt{g} x \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 d f \sqrt{-f} \left(a+b \log \left(c (d+e x)^n\right)\right)-b d f \sqrt{g} n x \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)+b d f \sqrt{g} n x \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)+2 b e (-f)^{3/2} n x (\log (x)-\log (d+e x))\right)}{2 d (-f)^{7/2} x}","\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 \sqrt{g} n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 (-f)^{3/2}}+\frac{b \sqrt{g} n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 (-f)^{3/2}}+\frac{b e n \log (x)}{d f}-\frac{b e n \log (d+e x)}{d f}",1,"(f*(2*b*e*(-f)^(3/2)*n*x*(Log[x] - Log[d + e*x]) + 2*d*Sqrt[-f]*f*(a + b*Log[c*(d + e*x)^n]) + d*f*Sqrt[g]*x*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])] - d*f*Sqrt[g]*x*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])] - b*d*f*Sqrt[g]*n*x*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))] + b*d*f*Sqrt[g]*n*x*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])]))/(2*d*(-f)^(7/2)*x)","A",1
265,1,350,388,0.4754646,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^4 \left(f+g x^2\right)} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(x^4*(f + g*x^2)),x]","\frac{1}{6} \left(\frac{6 g \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2 x}+\frac{3 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)}{(-f)^{5/2}}-\frac{3 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)}{(-f)^{5/2}}-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{f x^3}-\frac{b e n \left(2 e^2 x^2 \log (d+e x)+d (d-2 e x)-2 e^2 x^2 \log (x)\right)}{d^3 f x^2}-\frac{6 b e g n (\log (x)-\log (d+e x))}{d f^2}-\frac{3 b g^{3/2} n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{(-f)^{5/2}}+\frac{3 b g^{3/2} n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{(-f)^{5/2}}\right)","\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^3 n \log (x)}{3 d^3 f}-\frac{b e^3 n \log (d+e x)}{3 d^3 f}+\frac{b e^2 n}{3 d^2 f x}-\frac{b e g n \log (x)}{d f^2}+\frac{b e g n \log (d+e x)}{d f^2}-\frac{b g^{3/2} n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 (-f)^{5/2}}+\frac{b g^{3/2} n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 (-f)^{5/2}}-\frac{b e n}{6 d f x^2}",1,"((-6*b*e*g*n*(Log[x] - Log[d + e*x]))/(d*f^2) - (b*e*n*(d*(d - 2*e*x) - 2*e^2*x^2*Log[x] + 2*e^2*x^2*Log[d + e*x]))/(d^3*f*x^2) - (2*(a + b*Log[c*(d + e*x)^n]))/(f*x^3) + (6*g*(a + b*Log[c*(d + e*x)^n]))/(f^2*x) + (3*g^(3/2)*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(-f)^(5/2) - (3*g^(3/2)*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(-f)^(5/2) - (3*b*g^(3/2)*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(-f)^(5/2) + (3*b*g^(3/2)*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(-f)^(5/2))/6","A",1
266,1,530,417,1.4778105,"\int \frac{x^5 \left(a+b \log \left(c (d+e x)^n\right)\right)}{\left(f+g x^2\right)^2} \, dx","Integrate[(x^5*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2)^2,x]","\frac{-\frac{2 f^2 \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)}{f+g x^2}-4 f \log \left(f+g x^2\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)+2 g x^2 \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)+b n \left(\frac{g \left(e x (2 d-e x)-2 \left(d^2-e^2 x^2\right) \log (d+e x)\right)}{e^2}+\frac{f^{3/2} \left(i \sqrt{g} (d+e x) \log (d+e x)-e \left(\sqrt{f}+i \sqrt{g} x\right) \log \left(-\sqrt{g} x+i \sqrt{f}\right)\right)}{\left(\sqrt{f}+i \sqrt{g} x\right) \left(e \sqrt{f}-i d \sqrt{g}\right)}+\frac{i f^{3/2} \left(-\sqrt{g} (d+e x) \log (d+e x)+e \left(\sqrt{g} x+i \sqrt{f}\right) \log \left(\sqrt{g} x+i \sqrt{f}\right)\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(e \sqrt{f}+i d \sqrt{g}\right)}-4 f \left(\text{Li}_2\left(-\frac{i \sqrt{g} (d+e x)}{e \sqrt{f}-i d \sqrt{g}}\right)+\log (d+e x) \log \left(\frac{e \left(\sqrt{f}+i \sqrt{g} x\right)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)-4 f \left(\text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)+\log (d+e x) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{e \sqrt{f}+i d \sqrt{g}}\right)\right)\right)}{4 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 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 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^2 n \log (d+e x)}{2 e^2 g^2}-\frac{b f n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^3}-\frac{b f n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{g^3}+\frac{b d n x}{2 e g^2}-\frac{b n x^2}{4 g^2}",1,"(2*g*x^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n]) - (2*f^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n]))/(f + g*x^2) - 4*f*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*Log[f + g*x^2] + b*n*((g*(e*x*(2*d - e*x) - 2*(d^2 - e^2*x^2)*Log[d + e*x]))/e^2 + (f^(3/2)*(I*Sqrt[g]*(d + e*x)*Log[d + e*x] - e*(Sqrt[f] + I*Sqrt[g]*x)*Log[I*Sqrt[f] - Sqrt[g]*x]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) + (I*f^(3/2)*(-(Sqrt[g]*(d + e*x)*Log[d + e*x]) + e*(I*Sqrt[f] + Sqrt[g]*x)*Log[I*Sqrt[f] + Sqrt[g]*x]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) - 4*f*(Log[d + e*x]*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])] + PolyLog[2, ((-I)*Sqrt[g]*(d + e*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) - 4*f*(Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])])))/(4*g^3)","C",1
267,1,455,344,1.1591615,"\int \frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{\left(f+g x^2\right)^2} \, dx","Integrate[(x^3*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2)^2,x]","\frac{2 \log \left(f+g x^2\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)+\frac{2 f \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)}{f+g x^2}+b n \left(2 \left(\text{Li}_2\left(-\frac{i \sqrt{g} (d+e x)}{e \sqrt{f}-i d \sqrt{g}}\right)+\log (d+e x) \log \left(\frac{e \left(\sqrt{f}+i \sqrt{g} x\right)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)+2 \left(\text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)+\log (d+e x) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{e \sqrt{f}+i d \sqrt{g}}\right)\right)+\frac{\sqrt{f} \left(e \left(\sqrt{f}+i \sqrt{g} x\right) \log \left(-\sqrt{g} x+i \sqrt{f}\right)-i \sqrt{g} (d+e x) \log (d+e x)\right)}{\left(\sqrt{f}+i \sqrt{g} x\right) \left(e \sqrt{f}-i d \sqrt{g}\right)}+\frac{\sqrt{f} \left(i \sqrt{g} (d+e x) \log (d+e x)+e \left(\sqrt{f}-i \sqrt{g} x\right) \log \left(\sqrt{g} x+i \sqrt{f}\right)\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(e \sqrt{f}+i d \sqrt{g}\right)}\right)}{4 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 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 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 n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 g^2}+\frac{b n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 g^2}",1,"((2*f*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n]))/(f + g*x^2) + 2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*Log[f + g*x^2] + b*n*((Sqrt[f]*((-I)*Sqrt[g]*(d + e*x)*Log[d + e*x] + e*(Sqrt[f] + I*Sqrt[g]*x)*Log[I*Sqrt[f] - Sqrt[g]*x]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) + (Sqrt[f]*(I*Sqrt[g]*(d + e*x)*Log[d + e*x] + e*(Sqrt[f] - I*Sqrt[g]*x)*Log[I*Sqrt[f] + Sqrt[g]*x]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) + 2*(Log[d + e*x]*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])] + PolyLog[2, ((-I)*Sqrt[g]*(d + e*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) + 2*(Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])])))/(4*g^2)","C",1
268,1,165,139,0.1969517,"\int \frac{x \left(a+b \log \left(c (d+e x)^n\right)\right)}{\left(f+g x^2\right)^2} \, dx","Integrate[(x*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2)^2,x]","\frac{2 b d e \sqrt{g} n \left(f+g x^2\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)-\sqrt{f} \left(2 a d^2 g+2 a e^2 f+2 b \left(d^2 g+e^2 f\right) \log \left(c (d+e x)^n\right)-2 b e^2 n \left(f+g x^2\right) \log (d+e x)+b e^2 g n x^2 \log \left(f+g x^2\right)+b e^2 f n \log \left(f+g x^2\right)\right)}{4 \sqrt{f} g \left(f+g x^2\right) \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,"(2*b*d*e*Sqrt[g]*n*(f + g*x^2)*ArcTan[(Sqrt[g]*x)/Sqrt[f]] - Sqrt[f]*(2*a*e^2*f + 2*a*d^2*g - 2*b*e^2*n*(f + g*x^2)*Log[d + e*x] + 2*b*(e^2*f + d^2*g)*Log[c*(d + e*x)^n] + b*e^2*f*n*Log[f + g*x^2] + b*e^2*g*n*x^2*Log[f + g*x^2]))/(4*Sqrt[f]*g*(e^2*f + d^2*g)*(f + g*x^2))","A",1
269,1,521,383,1.4130144,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x \left(f+g x^2\right)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(x*(f + g*x^2)^2),x]","-\frac{\log \left(f+g x^2\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)}{2 f^2}+\frac{a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)}{2 f^2+2 f g x^2}+\frac{\log (x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)}{f^2}+\frac{b n \left(-2 \left(\text{Li}_2\left(-\frac{i \sqrt{g} (d+e x)}{e \sqrt{f}-i d \sqrt{g}}\right)+\log (d+e x) \log \left(\frac{e \left(\sqrt{f}+i \sqrt{g} x\right)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)-2 \left(\text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)+\log (d+e x) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{e \sqrt{f}+i d \sqrt{g}}\right)\right)+\frac{\sqrt{f} \left(e \left(\sqrt{f}+i \sqrt{g} x\right) \log \left(-\sqrt{g} x+i \sqrt{f}\right)-i \sqrt{g} (d+e x) \log (d+e x)\right)}{\left(\sqrt{f}+i \sqrt{g} x\right) \left(e \sqrt{f}-i d \sqrt{g}\right)}+\frac{\sqrt{f} \left(i \sqrt{g} (d+e x) \log (d+e x)+e \left(\sqrt{f}-i \sqrt{g} x\right) \log \left(\sqrt{g} x+i \sqrt{f}\right)\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(e \sqrt{f}+i d \sqrt{g}\right)}+4 \left(\text{Li}_2\left(\frac{e x}{d}+1\right)+\log \left(-\frac{e x}{d}\right) \log (d+e x)\right)\right)}{4 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{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f^2}-\frac{b n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 f^2}+\frac{b n \text{Li}_2\left(\frac{e x}{d}+1\right)}{f^2}",1,"(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])/(2*f^2 + 2*f*g*x^2) + (Log[x]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n]))/f^2 - ((a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*Log[f + g*x^2])/(2*f^2) + (b*n*((Sqrt[f]*((-I)*Sqrt[g]*(d + e*x)*Log[d + e*x] + e*(Sqrt[f] + I*Sqrt[g]*x)*Log[I*Sqrt[f] - Sqrt[g]*x]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) + (Sqrt[f]*(I*Sqrt[g]*(d + e*x)*Log[d + e*x] + e*(Sqrt[f] - I*Sqrt[g]*x)*Log[I*Sqrt[f] + Sqrt[g]*x]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) - 2*(Log[d + e*x]*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])] + PolyLog[2, ((-I)*Sqrt[g]*(d + e*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) - 2*(Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])]) + 4*(Log[-((e*x)/d)]*Log[d + e*x] + PolyLog[2, 1 + (e*x)/d])))/(4*f^2)","C",1
270,1,596,460,1.5442588,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^3 \left(f+g x^2\right)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(x^3*(f + g*x^2)^2),x]","\frac{4 g \log \left(f+g x^2\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)-\frac{2 f g \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)}{f+g x^2}-\frac{2 f \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)}{x^2}-8 g \log (x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)+b n \left(-\frac{2 f \left(\left(d^2-e^2 x^2\right) \log (d+e x)+d e x+e^2 x^2 \log (x)\right)}{d^2 x^2}+4 g \left(\text{Li}_2\left(-\frac{i \sqrt{g} (d+e x)}{e \sqrt{f}-i d \sqrt{g}}\right)+\log (d+e x) \log \left(\frac{e \left(\sqrt{f}+i \sqrt{g} x\right)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)+4 g \left(\text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)+\log (d+e x) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{e \sqrt{f}+i d \sqrt{g}}\right)\right)+\frac{i \sqrt{f} g \left(\sqrt{g} (d+e x) \log (d+e x)+i e \left(\sqrt{f}+i \sqrt{g} x\right) \log \left(-\sqrt{g} x+i \sqrt{f}\right)\right)}{\left(\sqrt{f}+i \sqrt{g} x\right) \left(e \sqrt{f}-i d \sqrt{g}\right)}+\frac{i \sqrt{f} g \left(-\sqrt{g} (d+e x) \log (d+e x)+e \left(\sqrt{g} x+i \sqrt{f}\right) \log \left(\sqrt{g} x+i \sqrt{f}\right)\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(e \sqrt{f}+i d \sqrt{g}\right)}-8 g \left(\text{Li}_2\left(\frac{e x}{d}+1\right)+\log \left(-\frac{e x}{d}\right) \log (d+e x)\right)\right)}{4 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 \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{g \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 f^2 \left(f+g x^2\right)}-\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 g n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{f^3}+\frac{b g n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{f^3}-\frac{2 b g n \text{Li}_2\left(\frac{e x}{d}+1\right)}{f^3}-\frac{b e n}{2 d f^2 x}",1,"((-2*f*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n]))/x^2 - (2*f*g*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n]))/(f + g*x^2) - 8*g*Log[x]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n]) + 4*g*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*Log[f + g*x^2] + b*n*((-2*f*(d*e*x + e^2*x^2*Log[x] + (d^2 - e^2*x^2)*Log[d + e*x]))/(d^2*x^2) + (I*Sqrt[f]*g*(Sqrt[g]*(d + e*x)*Log[d + e*x] + I*e*(Sqrt[f] + I*Sqrt[g]*x)*Log[I*Sqrt[f] - Sqrt[g]*x]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) + (I*Sqrt[f]*g*(-(Sqrt[g]*(d + e*x)*Log[d + e*x]) + e*(I*Sqrt[f] + Sqrt[g]*x)*Log[I*Sqrt[f] + Sqrt[g]*x]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) + 4*g*(Log[d + e*x]*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])] + PolyLog[2, ((-I)*Sqrt[g]*(d + e*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) + 4*g*(Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])]) - 8*g*(Log[-((e*x)/d)]*Log[d + e*x] + PolyLog[2, 1 + (e*x)/d])))/(4*f^3)","C",1
271,1,434,534,0.7760096,"\int \frac{x^4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{\left(f+g x^2\right)^2} \, dx","Integrate[(x^4*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2)^2,x]","\frac{-\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{-f}-\sqrt{g} x}+\frac{f \left(a+b \log \left(c (d+e x)^n\right)\right)}{\sqrt{-f}+\sqrt{g} x}+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)-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 a \sqrt{g} x+\frac{4 b \sqrt{g} (d+e x) \log \left(c (d+e x)^n\right)}{e}-3 b \sqrt{-f} n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)+3 b \sqrt{-f} n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)+\frac{b e f n \left(\log (d+e x)-\log \left(\sqrt{-f}-\sqrt{g} x\right)\right)}{d \sqrt{g}+e \sqrt{-f}}-\frac{b e f n \left(\log (d+e x)-\log \left(\sqrt{-f}+\sqrt{g} x\right)\right)}{e \sqrt{-f}-d \sqrt{g}}-4 b \sqrt{g} n x}{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{3 b \sqrt{-f} n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 g^{5/2}}+\frac{3 b \sqrt{-f} n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{4 g^{5/2}}-\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,"(4*a*Sqrt[g]*x - 4*b*Sqrt[g]*n*x + (4*b*Sqrt[g]*(d + e*x)*Log[c*(d + e*x)^n])/e - (f*(a + b*Log[c*(d + e*x)^n]))/(Sqrt[-f] - Sqrt[g]*x) + (f*(a + b*Log[c*(d + e*x)^n]))/(Sqrt[-f] + Sqrt[g]*x) + (b*e*f*n*(Log[d + e*x] - Log[Sqrt[-f] - Sqrt[g]*x]))/(e*Sqrt[-f] + d*Sqrt[g]) + 3*Sqrt[-f]*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])] - (b*e*f*n*(Log[d + e*x] - Log[Sqrt[-f] + Sqrt[g]*x]))/(e*Sqrt[-f] - d*Sqrt[g]) - 3*Sqrt[-f]*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])] - 3*b*Sqrt[-f]*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))] + 3*b*Sqrt[-f]*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(4*g^(5/2))","A",1
272,1,383,491,0.6692683,"\int \frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{\left(f+g x^2\right)^2} \, dx","Integrate[(x^2*(a + b*Log[c*(d + e*x)^n]))/(f + g*x^2)^2,x]","\frac{\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)}{\sqrt{-f}}+\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)}{(-f)^{3/2}}+\frac{a+b \log \left(c (d+e x)^n\right)}{\sqrt{-f}-\sqrt{g} x}-\frac{a+b \log \left(c (d+e x)^n\right)}{\sqrt{-f}+\sqrt{g} x}+\frac{b f n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{(-f)^{3/2}}+\frac{b n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{\sqrt{-f}}-\frac{b e n \left(\log (d+e x)-\log \left(\sqrt{-f}-\sqrt{g} x\right)\right)}{d \sqrt{g}+e \sqrt{-f}}+\frac{b e n \left(\log (d+e x)-\log \left(\sqrt{-f}+\sqrt{g} x\right)\right)}{e \sqrt{-f}-d \sqrt{g}}}{4 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 n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 \sqrt{-f} g^{3/2}}+\frac{b n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\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,"((a + b*Log[c*(d + e*x)^n])/(Sqrt[-f] - Sqrt[g]*x) - (a + b*Log[c*(d + e*x)^n])/(Sqrt[-f] + Sqrt[g]*x) - (b*e*n*(Log[d + e*x] - Log[Sqrt[-f] - Sqrt[g]*x]))/(e*Sqrt[-f] + d*Sqrt[g]) + ((a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/Sqrt[-f] + (b*e*n*(Log[d + e*x] - Log[Sqrt[-f] + Sqrt[g]*x]))/(e*Sqrt[-f] - d*Sqrt[g]) + (f*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(-f)^(3/2) + (b*f*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(-f)^(3/2) + (b*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/Sqrt[-f])/(4*g^(3/2))","A",1
273,1,407,503,1.058356,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\left(f+g x^2\right)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(f + g*x^2)^2,x]","\frac{1}{4} \left(\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)}{(-f)^{5/2} \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)}{(-f)^{3/2} \sqrt{g}}+\frac{a+b \log \left(c (d+e x)^n\right)}{f \left(\sqrt{-f} \sqrt{g}+g x\right)}+\frac{a+b \log \left(c (d+e x)^n\right)}{f g x+(-f)^{3/2} \sqrt{g}}+\frac{b n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{(-f)^{3/2} \sqrt{g}}+\frac{b f n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{(-f)^{5/2} \sqrt{g}}+\frac{b e n \left(\log (d+e x)-\log \left(\sqrt{-f}-\sqrt{g} x\right)\right)}{d f g+e \sqrt{-f} f \sqrt{g}}+\frac{b e n \left(\log (d+e x)-\log \left(\sqrt{-f}+\sqrt{g} x\right)\right)}{d f g+e (-f)^{3/2} \sqrt{g}}\right)","-\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 n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 (-f)^{3/2} \sqrt{g}}-\frac{b n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\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,"((a + b*Log[c*(d + e*x)^n])/(f*(Sqrt[-f]*Sqrt[g] + g*x)) + (a + b*Log[c*(d + e*x)^n])/((-f)^(3/2)*Sqrt[g] + f*g*x) + (b*e*n*(Log[d + e*x] - Log[Sqrt[-f] - Sqrt[g]*x]))/(e*Sqrt[-f]*f*Sqrt[g] + d*f*g) + (f*(a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/((-f)^(5/2)*Sqrt[g]) + (b*e*n*(Log[d + e*x] - Log[Sqrt[-f] + Sqrt[g]*x]))/(e*(-f)^(3/2)*Sqrt[g] + d*f*g) + ((a + b*Log[c*(d + e*x)^n])*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/((-f)^(3/2)*Sqrt[g]) + (b*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/((-f)^(3/2)*Sqrt[g]) + (b*f*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/((-f)^(5/2)*Sqrt[g]))/4","A",1
274,1,476,560,0.8175009,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{x^2 \left(f+g x^2\right)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(x^2*(f + g*x^2)^2),x]","\frac{1}{4} \left(\frac{\sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2 \left(\sqrt{-f}-\sqrt{g} x\right)}-\frac{\sqrt{g} \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2 \left(\sqrt{-f}+\sqrt{g} x\right)}-\frac{4 \left(a+b \log \left(c (d+e x)^n\right)\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)}{(-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)}{(-f)^{5/2}}-\frac{b e \sqrt{g} n \left(\log (d+e x)-\log \left(\sqrt{-f}-\sqrt{g} x\right)\right)}{f^2 \left(d \sqrt{g}+e \sqrt{-f}\right)}+\frac{b e \sqrt{g} n \left(\log (d+e x)-\log \left(\sqrt{-f}+\sqrt{g} x\right)\right)}{f^2 \left(e \sqrt{-f}-d \sqrt{g}\right)}+\frac{4 b e n (\log (x)-\log (d+e x))}{d f^2}+\frac{3 b \sqrt{g} n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{(-f)^{5/2}}-\frac{3 b \sqrt{g} n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{(-f)^{5/2}}\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{\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{3 b \sqrt{g} n \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{4 (-f)^{5/2}}-\frac{3 b \sqrt{g} n \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{4 (-f)^{5/2}}-\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,"((4*b*e*n*(Log[x] - Log[d + e*x]))/(d*f^2) - (4*(a + b*Log[c*(d + e*x)^n]))/(f^2*x) + (Sqrt[g]*(a + b*Log[c*(d + e*x)^n]))/(f^2*(Sqrt[-f] - Sqrt[g]*x)) - (Sqrt[g]*(a + b*Log[c*(d + e*x)^n]))/(f^2*(Sqrt[-f] + Sqrt[g]*x)) - (b*e*Sqrt[g]*n*(Log[d + e*x] - Log[Sqrt[-f] - Sqrt[g]*x]))/(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])])/(-f)^(5/2) + (b*e*Sqrt[g]*n*(Log[d + e*x] - Log[Sqrt[-f] + Sqrt[g]*x]))/(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])])/(-f)^(5/2) + (3*b*Sqrt[g]*n*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(-f)^(5/2) - (3*b*Sqrt[g]*n*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(-f)^(5/2))/4","A",1
275,1,275,326,0.2455872,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\sqrt{2+g x^2}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/Sqrt[2 + g*x^2],x]","\frac{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right) \left(2 a+2 b \log \left(c (d+e x)^n\right)-2 b n \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)-2 b n \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)+b n \sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right)\right)-2 b n \text{Li}_2\left(\frac{\sqrt{2} e e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right)}}{\sqrt{g d^2+2 e^2}-d \sqrt{g}}\right)-2 b n \text{Li}_2\left(-\frac{\sqrt{2} e e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right)}}{\sqrt{g} d+\sqrt{g d^2+2 e^2}}\right)}{2 \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 \text{Li}_2\left(-\frac{\sqrt{2} e e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right)}}{d \sqrt{g}-\sqrt{g d^2+2 e^2}}\right)}{\sqrt{g}}-\frac{b n \text{Li}_2\left(-\frac{\sqrt{2} e e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{2}}\right)}}{\sqrt{g} d+\sqrt{g d^2+2 e^2}}\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,"(ArcSinh[(Sqrt[g]*x)/Sqrt[2]]*(2*a + b*n*ArcSinh[(Sqrt[g]*x)/Sqrt[2]] - 2*b*n*Log[1 + (Sqrt[2]*e*E^ArcSinh[(Sqrt[g]*x)/Sqrt[2]])/(d*Sqrt[g] - Sqrt[2*e^2 + d^2*g])] - 2*b*n*Log[1 + (Sqrt[2]*e*E^ArcSinh[(Sqrt[g]*x)/Sqrt[2]])/(d*Sqrt[g] + Sqrt[2*e^2 + d^2*g])] + 2*b*Log[c*(d + e*x)^n]) - 2*b*n*PolyLog[2, (Sqrt[2]*e*E^ArcSinh[(Sqrt[g]*x)/Sqrt[2]])/(-(d*Sqrt[g]) + Sqrt[2*e^2 + d^2*g])] - 2*b*n*PolyLog[2, -((Sqrt[2]*e*E^ArcSinh[(Sqrt[g]*x)/Sqrt[2]])/(d*Sqrt[g] + Sqrt[2*e^2 + d^2*g]))])/(2*Sqrt[g])","A",1
276,0,0,506,3.7712974,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\sqrt{f+g x^2}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/Sqrt[f + g*x^2],x]","\int \frac{a+b \log \left(c (d+e x)^n\right)}{\sqrt{f+g x^2}} \, dx","\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} \text{Li}_2\left(-\frac{e e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)} \sqrt{f}}{d \sqrt{g}-\sqrt{g d^2+e^2 f}}\right)}{\sqrt{g} \sqrt{f+g x^2}}-\frac{b \sqrt{f} n \sqrt{\frac{g x^2}{f}+1} \text{Li}_2\left(-\frac{e e^{\sinh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)} \sqrt{f}}{\sqrt{g} d+\sqrt{g d^2+e^2 f}}\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,"Integrate[(a + b*Log[c*(d + e*x)^n])/Sqrt[f + g*x^2], x]","F",-1
277,1,307,278,0.0294879,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\sqrt{2-g x} \sqrt{2+g x}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(Sqrt[2 - g*x]*Sqrt[2 + g*x]),x]","\frac{a \sin ^{-1}\left(\frac{g x}{2}\right)}{g}+\frac{b \sin ^{-1}\left(\frac{g x}{2}\right) \log \left(c (d+e x)^n\right)}{g}+\frac{i b n \text{Li}_2\left(\frac{2 i e e^{i \sin ^{-1}\left(\frac{g x}{2}\right)}}{d g-i \sqrt{4 e^2-d^2 g^2}}\right)}{g}+\frac{i b n \text{Li}_2\left(\frac{2 i e e^{i \sin ^{-1}\left(\frac{g x}{2}\right)}}{d g+i \sqrt{4 e^2-d^2 g^2}}\right)}{g}-\frac{b n \sin ^{-1}\left(\frac{g x}{2}\right) \log \left(1+\frac{e g e^{i \sin ^{-1}\left(\frac{g x}{2}\right)}}{-\frac{1}{2} g \sqrt{4 e^2-d^2 g^2}+\frac{1}{2} i d g^2}\right)}{g}-\frac{b n \sin ^{-1}\left(\frac{g x}{2}\right) \log \left(1+\frac{e g e^{i \sin ^{-1}\left(\frac{g x}{2}\right)}}{\frac{1}{2} g \sqrt{4 e^2-d^2 g^2}+\frac{1}{2} i d g^2}\right)}{g}+\frac{i b n \sin ^{-1}\left(\frac{g x}{2}\right)^2}{2 g}","\frac{\sin ^{-1}\left(\frac{g x}{2}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g}+\frac{i b n \text{Li}_2\left(-\frac{2 e e^{i \sin ^{-1}\left(\frac{g x}{2}\right)}}{i d g-\sqrt{4 e^2-d^2 g^2}}\right)}{g}+\frac{i b n \text{Li}_2\left(-\frac{2 e e^{i \sin ^{-1}\left(\frac{g x}{2}\right)}}{i d g+\sqrt{4 e^2-d^2 g^2}}\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,"(a*ArcSin[(g*x)/2])/g + ((I/2)*b*n*ArcSin[(g*x)/2]^2)/g - (b*n*ArcSin[(g*x)/2]*Log[1 + (e*E^(I*ArcSin[(g*x)/2])*g)/((I/2)*d*g^2 - (g*Sqrt[4*e^2 - d^2*g^2])/2)])/g - (b*n*ArcSin[(g*x)/2]*Log[1 + (e*E^(I*ArcSin[(g*x)/2])*g)/((I/2)*d*g^2 + (g*Sqrt[4*e^2 - d^2*g^2])/2)])/g + (b*ArcSin[(g*x)/2]*Log[c*(d + e*x)^n])/g + (I*b*n*PolyLog[2, ((2*I)*e*E^(I*ArcSin[(g*x)/2]))/(d*g - I*Sqrt[4*e^2 - d^2*g^2])])/g + (I*b*n*PolyLog[2, ((2*I)*e*E^(I*ArcSin[(g*x)/2]))/(d*g + I*Sqrt[4*e^2 - d^2*g^2])])/g","A",1
278,1,1077,510,4.784513,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\sqrt{f-g x} \sqrt{f+g x}} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/(Sqrt[f - g*x]*Sqrt[f + g*x]),x]","\frac{\tan ^{-1}\left(\frac{g x}{\sqrt{f-g x} \sqrt{f+g x}}\right) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)}{g}-\frac{i b n \sqrt{f-g x} \sqrt{\frac{f+g x}{f-g x}} \left(\log ^2\left(i-\sqrt{\frac{f+g x}{f-g x}}\right)+2 \log (d+e x) \log \left(i-\sqrt{\frac{f+g x}{f-g x}}\right)+2 \log \left(\frac{1}{2} \left(1-i \sqrt{\frac{f+g x}{f-g x}}\right)\right) \log \left(i-\sqrt{\frac{f+g x}{f-g x}}\right)-2 \log \left(\frac{\sqrt{e f-d g}-\sqrt{e f+d g} \sqrt{\frac{f+g x}{f-g x}}}{\sqrt{e f-d g}-i \sqrt{e f+d g}}\right) \log \left(i-\sqrt{\frac{f+g x}{f-g x}}\right)-2 \log \left(\frac{\sqrt{e f-d g}+\sqrt{e f+d g} \sqrt{\frac{f+g x}{f-g x}}}{\sqrt{e f-d g}+i \sqrt{e f+d g}}\right) \log \left(i-\sqrt{\frac{f+g x}{f-g x}}\right)-\log ^2\left(\sqrt{\frac{f+g x}{f-g x}}+i\right)-2 \log (d+e x) \log \left(\sqrt{\frac{f+g x}{f-g x}}+i\right)-2 \log \left(\frac{1}{2} \left(i \sqrt{\frac{f+g x}{f-g x}}+1\right)\right) \log \left(\sqrt{\frac{f+g x}{f-g x}}+i\right)+2 \log \left(\sqrt{\frac{f+g x}{f-g x}}+i\right) \log \left(\frac{\sqrt{e f-d g}-\sqrt{e f+d g} \sqrt{\frac{f+g x}{f-g x}}}{\sqrt{e f-d g}+i \sqrt{e f+d g}}\right)+2 \log \left(\sqrt{\frac{f+g x}{f-g x}}+i\right) \log \left(\frac{\sqrt{e f-d g}+\sqrt{e f+d g} \sqrt{\frac{f+g x}{f-g x}}}{\sqrt{e f-d g}-i \sqrt{e f+d g}}\right)-2 \text{Li}_2\left(\frac{1}{2}-\frac{1}{2} i \sqrt{\frac{f+g x}{f-g x}}\right)+2 \text{Li}_2\left(\frac{1}{2} i \sqrt{\frac{f+g x}{f-g x}}+\frac{1}{2}\right)+2 \text{Li}_2\left(\frac{\sqrt{e f+d g} \left(1-i \sqrt{\frac{f+g x}{f-g x}}\right)}{i \sqrt{e f-d g}+\sqrt{e f+d g}}\right)-2 \text{Li}_2\left(\frac{\sqrt{e f+d g} \left(i \sqrt{\frac{f+g x}{f-g x}}+1\right)}{\sqrt{e f+d g}-i \sqrt{e f-d g}}\right)-2 \text{Li}_2\left(\frac{\sqrt{e f+d g} \left(i \sqrt{\frac{f+g x}{f-g x}}+1\right)}{i \sqrt{e f-d g}+\sqrt{e f+d g}}\right)+2 \text{Li}_2\left(\frac{\sqrt{e f+d g} \left(\sqrt{\frac{f+g x}{f-g x}}+i\right)}{\sqrt{e f-d g}+i \sqrt{e f+d g}}\right)\right)}{2 g \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{i b f n \sqrt{1-\frac{g^2 x^2}{f^2}} \text{Li}_2\left(-\frac{e e^{i \sin ^{-1}\left(\frac{g x}{f}\right)} f}{i d g-\sqrt{e^2 f^2-d^2 g^2}}\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{Li}_2\left(-\frac{e e^{i \sin ^{-1}\left(\frac{g x}{f}\right)} f}{i d g+\sqrt{e^2 f^2-d^2 g^2}}\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,"(ArcTan[(g*x)/(Sqrt[f - g*x]*Sqrt[f + g*x])]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n]))/g - ((I/2)*b*n*Sqrt[f - g*x]*Sqrt[(f + g*x)/(f - g*x)]*(2*Log[d + e*x]*Log[I - Sqrt[(f + g*x)/(f - g*x)]] + Log[I - Sqrt[(f + g*x)/(f - g*x)]]^2 + 2*Log[I - Sqrt[(f + g*x)/(f - g*x)]]*Log[(1 - I*Sqrt[(f + g*x)/(f - g*x)])/2] - 2*Log[d + e*x]*Log[I + Sqrt[(f + g*x)/(f - g*x)]] - 2*Log[(1 + I*Sqrt[(f + g*x)/(f - g*x)])/2]*Log[I + Sqrt[(f + g*x)/(f - g*x)]] - Log[I + Sqrt[(f + g*x)/(f - g*x)]]^2 - 2*Log[I - Sqrt[(f + g*x)/(f - g*x)]]*Log[(Sqrt[e*f - d*g] - Sqrt[e*f + d*g]*Sqrt[(f + g*x)/(f - g*x)])/(Sqrt[e*f - d*g] - I*Sqrt[e*f + d*g])] + 2*Log[I + Sqrt[(f + g*x)/(f - g*x)]]*Log[(Sqrt[e*f - d*g] - Sqrt[e*f + d*g]*Sqrt[(f + g*x)/(f - g*x)])/(Sqrt[e*f - d*g] + I*Sqrt[e*f + d*g])] + 2*Log[I + Sqrt[(f + g*x)/(f - g*x)]]*Log[(Sqrt[e*f - d*g] + Sqrt[e*f + d*g]*Sqrt[(f + g*x)/(f - g*x)])/(Sqrt[e*f - d*g] - I*Sqrt[e*f + d*g])] - 2*Log[I - Sqrt[(f + g*x)/(f - g*x)]]*Log[(Sqrt[e*f - d*g] + Sqrt[e*f + d*g]*Sqrt[(f + g*x)/(f - g*x)])/(Sqrt[e*f - d*g] + I*Sqrt[e*f + d*g])] - 2*PolyLog[2, 1/2 - (I/2)*Sqrt[(f + g*x)/(f - g*x)]] + 2*PolyLog[2, 1/2 + (I/2)*Sqrt[(f + g*x)/(f - g*x)]] + 2*PolyLog[2, (Sqrt[e*f + d*g]*(1 - I*Sqrt[(f + g*x)/(f - g*x)]))/(I*Sqrt[e*f - d*g] + Sqrt[e*f + d*g])] - 2*PolyLog[2, (Sqrt[e*f + d*g]*(1 + I*Sqrt[(f + g*x)/(f - g*x)]))/((-I)*Sqrt[e*f - d*g] + Sqrt[e*f + d*g])] - 2*PolyLog[2, (Sqrt[e*f + d*g]*(1 + I*Sqrt[(f + g*x)/(f - g*x)]))/(I*Sqrt[e*f - d*g] + Sqrt[e*f + d*g])] + 2*PolyLog[2, (Sqrt[e*f + d*g]*(I + Sqrt[(f + g*x)/(f - g*x)]))/(Sqrt[e*f - d*g] + I*Sqrt[e*f + d*g])]))/(g*Sqrt[f + g*x])","B",1
279,1,27,24,0.0057425,"\int \frac{\log \left(\frac{2 e}{e+f x}\right)}{e^2-f^2 x^2} \, dx","Integrate[Log[(2*e)/(e + f*x)]/(e^2 - f^2*x^2),x]","\frac{\text{Li}_2\left(\frac{f x-e}{e+f x}\right)}{2 e f}","\frac{\text{Li}_2\left(1-\frac{2 e}{e+f x}\right)}{2 e f}",1,"PolyLog[2, (-e + f*x)/(e + f*x)]/(2*e*f)","A",1
280,1,81,42,0.0164281,"\int \frac{\log \left(\frac{e}{e+f x}\right)}{e^2-f^2 x^2} \, dx","Integrate[Log[e/(e + f*x)]/(e^2 - f^2*x^2),x]","\frac{\text{Li}_2\left(\frac{e+f x}{2 e}\right)}{2 e f}-\frac{\log ^2\left(\frac{e}{e+f x}\right)}{4 e f}-\frac{\log \left(\frac{e-f x}{2 e}\right) \log \left(\frac{e}{e+f x}\right)}{2 e f}","\frac{\text{Li}_2\left(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,"-1/2*(Log[(e - f*x)/(2*e)]*Log[e/(e + f*x)])/(e*f) - Log[e/(e + f*x)]^2/(4*e*f) + PolyLog[2, (e + f*x)/(2*e)]/(2*e*f)","A",1
281,1,82,41,0.033661,"\int \frac{a+b \log \left(\frac{2 e}{e+f x}\right)}{e^2-f^2 x^2} \, dx","Integrate[(a + b*Log[(2*e)/(e + f*x)])/(e^2 - f^2*x^2),x]","\frac{2 b^2 \text{Li}_2\left(\frac{e+f x}{2 e}\right)-\left(a+b \log \left(\frac{2 e}{e+f x}\right)\right) \left(a+2 b \log \left(\frac{e-f x}{2 e}\right)+b \log \left(\frac{2 e}{e+f x}\right)\right)}{4 b e f}","\frac{a \tanh ^{-1}\left(\frac{f x}{e}\right)}{e f}+\frac{b \text{Li}_2\left(1-\frac{2 e}{e+f x}\right)}{2 e f}",1,"(-((a + b*Log[(2*e)/(e + f*x)])*(a + 2*b*Log[(e - f*x)/(2*e)] + b*Log[(2*e)/(e + f*x)])) + 2*b^2*PolyLog[2, (e + f*x)/(2*e)])/(4*b*e*f)","A",1
282,1,80,47,0.0266469,"\int \frac{a+b \log \left(\frac{e}{e+f x}\right)}{e^2-f^2 x^2} \, dx","Integrate[(a + b*Log[e/(e + f*x)])/(e^2 - f^2*x^2),x]","\frac{2 b^2 \text{Li}_2\left(\frac{e+f x}{2 e}\right)-\left(a+b \log \left(\frac{e}{e+f x}\right)\right) \left(a+2 b \log \left(\frac{e-f x}{2 e}\right)+b \log \left(\frac{e}{e+f x}\right)\right)}{4 b e f}","\frac{(a-b \log (2)) \tanh ^{-1}\left(\frac{f x}{e}\right)}{e f}+\frac{b \text{Li}_2\left(1-\frac{2 e}{e+f x}\right)}{2 e f}",1,"(-((a + b*Log[e/(e + f*x)])*(a + 2*b*Log[(e - f*x)/(2*e)] + b*Log[e/(e + f*x)])) + 2*b^2*PolyLog[2, (e + f*x)/(2*e)])/(4*b*e*f)","A",1
283,1,345,371,0.3460635,"\int \frac{x^5 \log (c+d x)}{a+b x^3} \, dx","Integrate[(x^5*Log[c + d*x])/(a + b*x^3),x]","-\frac{6 a d^3 \text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)+6 a d^3 \text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c+\sqrt[3]{-1} \sqrt[3]{a} d}\right)+6 a d^3 \text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)+6 a d^3 \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{-1} \sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c}\right)+6 a d^3 \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a} d-\sqrt[3]{b} c}\right)+6 a d^3 \log (c+d x) \log \left(\frac{d \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{a} d-\sqrt[3]{b} c}\right)-6 b c^3 \log (c+d x)+6 b c^2 d x-6 b d^3 x^3 \log (c+d x)-3 b c d^2 x^2+2 b d^3 x^3}{18 b^2 d^3}","-\frac{a \text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^2}-\frac{a \text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c+\sqrt[3]{-1} \sqrt[3]{a} d}\right)}{3 b^2}-\frac{a \text{Li}_2\left(\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^3 \log (c+d x)}{3 b d^3}-\frac{c^2 x}{3 b d^2}+\frac{x^3 \log (c+d x)}{3 b}+\frac{c x^2}{6 b d}-\frac{x^3}{9 b}",1,"-1/18*(6*b*c^2*d*x - 3*b*c*d^2*x^2 + 2*b*d^3*x^3 - 6*b*c^3*Log[c + d*x] - 6*b*d^3*x^3*Log[c + d*x] + 6*a*d^3*Log[(d*((-1)^(1/3)*a^(1/3) - b^(1/3)*x))/(b^(1/3)*c + (-1)^(1/3)*a^(1/3)*d)]*Log[c + d*x] + 6*a*d^3*Log[(d*(a^(1/3) + b^(1/3)*x))/(-(b^(1/3)*c) + a^(1/3)*d)]*Log[c + d*x] + 6*a*d^3*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] + 6*a*d^3*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)] + 6*a*d^3*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c + (-1)^(1/3)*a^(1/3)*d)] + 6*a*d^3*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - (-1)^(2/3)*a^(1/3)*d)])/(b^2*d^3)","A",1
284,1,297,292,0.0551557,"\int \frac{x^2 \log (c+d x)}{a+b x^3} \, dx","Integrate[(x^2*Log[c + d*x])/(a + b*x^3),x]","\frac{\text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b}+\frac{\text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c+\sqrt[3]{-1} \sqrt[3]{a} d}\right)}{3 b}+\frac{\text{Li}_2\left(\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{(-1)^{2/3} d \left(\sqrt[3]{a}-\sqrt[3]{-1} \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{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b}+\frac{\text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c+\sqrt[3]{-1} \sqrt[3]{a} d}\right)}{3 b}+\frac{\text{Li}_2\left(\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[-(((-1)^(2/3)*d*(a^(1/3) - (-1)^(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",1
285,1,330,324,0.107864,"\int \frac{\log (c+d x)}{x \left(a+b x^3\right)} \, dx","Integrate[Log[c + d*x]/(x*(a + b*x^3)),x]","-\frac{\text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a}-\frac{\text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c+\sqrt[3]{-1} \sqrt[3]{a} d}\right)}{3 a}-\frac{\text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 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{(-1)^{2/3} d \left(\sqrt[3]{a}-\sqrt[3]{-1} \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{\text{Li}_2\left(\frac{c+d x}{c}\right)}{a}+\frac{\log \left(-\frac{d x}{c}\right) \log (c+d x)}{a}","-\frac{\text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a}-\frac{\text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c+\sqrt[3]{-1} \sqrt[3]{a} d}\right)}{3 a}-\frac{\text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 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{\text{Li}_2\left(\frac{d x}{c}+1\right)}{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[-(((-1)^(2/3)*d*(a^(1/3) - (-1)^(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, (c + d*x)/c]/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)","A",1
286,1,405,414,0.1643591,"\int \frac{\log (c+d x)}{x^4 \left(a+b x^3\right)} \, dx","Integrate[Log[c + d*x]/(x^4*(a + b*x^3)),x]","-\frac{b \text{Li}_2\left(\frac{c+d x}{c}\right)}{a^2}+\frac{b \text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^2}+\frac{b \text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c+\sqrt[3]{-1} \sqrt[3]{a} d}\right)}{3 a^2}+\frac{b \text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 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{(-1)^{2/3} d \left(\sqrt[3]{a}-\sqrt[3]{-1} \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 \left(-\frac{2 d^2 \log (x)}{c^3}+\frac{2 d^2 \log (c+d x)}{c^3}-\frac{2 d}{c^2 x}+\frac{1}{c x^2}\right)}{6 a}-\frac{\log (c+d x)}{3 a x^3}","\frac{b \text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 a^2}+\frac{b \text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c+\sqrt[3]{-1} \sqrt[3]{a} d}\right)}{3 a^2}+\frac{b \text{Li}_2\left(\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{Li}_2\left(\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^3 \log (x)}{3 a c^3}-\frac{d^3 \log (c+d x)}{3 a c^3}+\frac{d^2}{3 a c^2 x}-\frac{\log (c+d x)}{3 a x^3}-\frac{d}{6 a c x^2}",1,"-1/3*Log[c + d*x]/(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[-(((-1)^(2/3)*d*(a^(1/3) - (-1)^(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) - (d*(1/(c*x^2) - (2*d)/(c^2*x) - (2*d^2*Log[x])/c^3 + (2*d^2*Log[c + d*x])/c^3))/(6*a) - (b*PolyLog[2, (c + d*x)/c])/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)","A",1
287,1,403,416,0.3305648,"\int \frac{x^4 \log (c+d x)}{a+b x^3} \, dx","Integrate[(x^4*Log[c + d*x])/(a + b*x^3),x]","\frac{4 a^{2/3} d^2 \text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)+4 (-1)^{2/3} a^{2/3} d^2 \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)-4 \sqrt[3]{-1} a^{2/3} d^2 \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{b} c+\sqrt[3]{a} d}\right)+4 a^{2/3} d^2 \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a} d-\sqrt[3]{b} c}\right)-4 \sqrt[3]{-1} a^{2/3} d^2 \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)+4 (-1)^{2/3} a^{2/3} d^2 \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} c}\right)-6 b^{2/3} c^2 \log (c+d x)+6 b^{2/3} d^2 x^2 \log (c+d x)+6 b^{2/3} c d x-3 b^{2/3} d^2 x^2}{12 b^{5/3} d^2}","\frac{a^{2/3} \text{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{b} c+\sqrt[3]{a} d}\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,"(6*b^(2/3)*c*d*x - 3*b^(2/3)*d^2*x^2 - 6*b^(2/3)*c^2*Log[c + d*x] + 6*b^(2/3)*d^2*x^2*Log[c + d*x] + 4*a^(2/3)*d^2*Log[(d*(a^(1/3) + b^(1/3)*x))/(-(b^(1/3)*c) + a^(1/3)*d)]*Log[c + d*x] - 4*(-1)^(1/3)*a^(2/3)*d^2*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] + 4*(-1)^(2/3)*a^(2/3)*d^2*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] + 4*a^(2/3)*d^2*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)] + 4*(-1)^(2/3)*a^(2/3)*d^2*PolyLog[2, ((-1)^(2/3)*b^(1/3)*(c + d*x))/((-1)^(2/3)*b^(1/3)*c - a^(1/3)*d)] - 4*(-1)^(1/3)*a^(2/3)*d^2*PolyLog[2, ((-1)^(1/3)*b^(1/3)*(c + d*x))/((-1)^(1/3)*b^(1/3)*c + a^(1/3)*d)])/(12*b^(5/3)*d^2)","A",1
288,1,369,383,0.1388154,"\int \frac{x^3 \log (c+d x)}{a+b x^3} \, dx","Integrate[(x^3*Log[c + d*x])/(a + b*x^3),x]","\frac{-\sqrt[3]{a} d \text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)+\sqrt[3]{-1} \sqrt[3]{a} d \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)-(-1)^{2/3} \sqrt[3]{a} d \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{b} c+\sqrt[3]{a} d}\right)-\sqrt[3]{a} d \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a} d-\sqrt[3]{b} c}\right)-(-1)^{2/3} \sqrt[3]{a} d \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)+\sqrt[3]{-1} \sqrt[3]{a} d \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} c}\right)+3 \sqrt[3]{b} d x \log (c+d x)+3 \sqrt[3]{b} c \log (c+d x)-3 \sqrt[3]{b} d x}{3 b^{4/3} d}","-\frac{\sqrt[3]{a} \text{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{b} c+\sqrt[3]{a} d}\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,"(-3*b^(1/3)*d*x + 3*b^(1/3)*c*Log[c + d*x] + 3*b^(1/3)*d*x*Log[c + d*x] - a^(1/3)*d*Log[(d*(a^(1/3) + b^(1/3)*x))/(-(b^(1/3)*c) + a^(1/3)*d)]*Log[c + d*x] - (-1)^(2/3)*a^(1/3)*d*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] + (-1)^(1/3)*a^(1/3)*d*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] - a^(1/3)*d*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)] + (-1)^(1/3)*a^(1/3)*d*PolyLog[2, ((-1)^(2/3)*b^(1/3)*(c + d*x))/((-1)^(2/3)*b^(1/3)*c - a^(1/3)*d)] - (-1)^(2/3)*a^(1/3)*d*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)*d)","A",1
289,1,297,359,0.0881473,"\int \frac{x \log (c+d x)}{a+b x^3} \, dx","Integrate[(x*Log[c + d*x])/(a + b*x^3),x]","\frac{-\text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)-(-1)^{2/3} \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)+\sqrt[3]{-1} \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{b} c+\sqrt[3]{a} d}\right)+\log (c+d x) \left(-\log \left(\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a} d-\sqrt[3]{b} c}\right)\right)+\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)-(-1)^{2/3} \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} c}\right)}{3 \sqrt[3]{a} b^{2/3}}","-\frac{\text{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{b} c+\sqrt[3]{a} d}\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]) + (-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] - (-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] - PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)] - (-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)] + (-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",1
290,1,294,359,0.0717372,"\int \frac{\log (c+d x)}{a+b x^3} \, dx","Integrate[Log[c + d*x]/(a + b*x^3),x]","\frac{\text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)-\sqrt[3]{-1} \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)+(-1)^{2/3} \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{b} c+\sqrt[3]{a} d}\right)+\log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a} d-\sqrt[3]{b} c}\right)+(-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)-\sqrt[3]{-1} \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} c}\right)}{3 a^{2/3} \sqrt[3]{b}}","\frac{\text{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{b} c+\sqrt[3]{a} d}\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] + (-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] - (-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] + PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)] - (-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)] + (-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",1
291,1,378,398,0.1416115,"\int \frac{\log (c+d x)}{x^2 \left(a+b x^3\right)} \, dx","Integrate[Log[c + d*x]/(x^2*(a + b*x^3)),x]","\frac{\sqrt[3]{b} c x \text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)+(-1)^{2/3} \sqrt[3]{b} c x \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)-\sqrt[3]{-1} \sqrt[3]{b} c x \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{b} c+\sqrt[3]{a} d}\right)+\sqrt[3]{b} c x \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a} d-\sqrt[3]{b} c}\right)-\sqrt[3]{-1} \sqrt[3]{b} c x \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)+(-1)^{2/3} \sqrt[3]{b} c x \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} c}\right)-3 \sqrt[3]{a} c \log (c+d x)-3 \sqrt[3]{a} d x \log (c+d x)+3 \sqrt[3]{a} d x \log (x)}{3 a^{4/3} c x}","\frac{\sqrt[3]{b} \text{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{b} c+\sqrt[3]{a} d}\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,"(3*a^(1/3)*d*x*Log[x] - 3*a^(1/3)*c*Log[c + d*x] - 3*a^(1/3)*d*x*Log[c + d*x] + b^(1/3)*c*x*Log[(d*(a^(1/3) + b^(1/3)*x))/(-(b^(1/3)*c) + a^(1/3)*d)]*Log[c + d*x] - (-1)^(1/3)*b^(1/3)*c*x*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] + (-1)^(2/3)*b^(1/3)*c*x*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] + b^(1/3)*c*x*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)] + (-1)^(2/3)*b^(1/3)*c*x*PolyLog[2, ((-1)^(2/3)*b^(1/3)*(c + d*x))/((-1)^(2/3)*b^(1/3)*c - a^(1/3)*d)] - (-1)^(1/3)*b^(1/3)*c*x*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)*c*x)","A",1
292,1,371,423,0.2344982,"\int \frac{\log (c+d x)}{x^3 \left(a+b x^3\right)} \, dx","Integrate[Log[c + d*x]/(x^3*(a + b*x^3)),x]","\frac{-\frac{3 a^{2/3} d (-d x \log (c+d x)+c+d x \log (x))}{c^2 x}-\frac{3 a^{2/3} \log (c+d x)}{x^2}-2 b^{2/3} \text{Li}_2\left(\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)+2 \sqrt[3]{-1} b^{2/3} \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{b} (c+d x)}{(-1)^{2/3} \sqrt[3]{b} c-\sqrt[3]{a} d}\right)-2 (-1)^{2/3} b^{2/3} \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{b} c+\sqrt[3]{a} d}\right)-2 b^{2/3} \log (c+d x) \log \left(\frac{d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a} d-\sqrt[3]{b} c}\right)-2 (-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)+2 \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)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} c}\right)}{6 a^{5/3}}","-\frac{b^{2/3} \text{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{b} (c+d x)}{\sqrt[3]{-1} \sqrt[3]{b} c+\sqrt[3]{a} d}\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,"((-3*a^(2/3)*Log[c + d*x])/x^2 - 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] - 2*(-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] + 2*(-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^(2/3)*d*(c + d*x*Log[x] - d*x*Log[c + d*x]))/(c^2*x) - 2*b^(2/3)*PolyLog[2, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)] + 2*(-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)] - 2*(-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)])/(6*a^(5/3))","A",1
293,1,446,498,0.3394714,"\int \frac{x^7 \log (c+d x)}{a+b x^4} \, dx","Integrate[(x^7*Log[c + d*x])/(a + b*x^4),x]","-\frac{12 a d^4 \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)+12 a d^4 \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-i \sqrt[4]{-a} d}\right)+12 a d^4 \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+i \sqrt[4]{-a} d}\right)+12 a d^4 \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\right)+12 a d^4 \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)+12 a d^4 \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-i \sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+i \sqrt[4]{b} c}\right)+12 a d^4 \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}+i \sqrt[4]{b} x\right)}{\sqrt[4]{-a} d-i \sqrt[4]{b} c}\right)+12 a d^4 \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)+12 b c^4 \log (c+d x)-12 b c^3 d x+6 b c^2 d^2 x^2-12 b d^4 x^4 \log (c+d x)-4 b c d^3 x^3+3 b d^4 x^4}{48 b^2 d^4}","-\frac{a \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^2}-\frac{a \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt{-\sqrt{-a}} d}\right)}{4 b^2}-\frac{a \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^2}-\frac{a \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\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^4 \log (c+d x)}{4 b d^4}+\frac{c^3 x}{4 b d^3}-\frac{c^2 x^2}{8 b d^2}+\frac{x^4 \log (c+d x)}{4 b}+\frac{c x^3}{12 b d}-\frac{x^4}{16 b}",1,"-1/48*(-12*b*c^3*d*x + 6*b*c^2*d^2*x^2 - 4*b*c*d^3*x^3 + 3*b*d^4*x^4 + 12*b*c^4*Log[c + d*x] - 12*b*d^4*x^4*Log[c + d*x] + 12*a*d^4*Log[(d*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x] + 12*a*d^4*Log[(d*((-a)^(1/4) - I*b^(1/4)*x))/(I*b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x] + 12*a*d^4*Log[(d*((-a)^(1/4) + I*b^(1/4)*x))/((-I)*b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x] + 12*a*d^4*Log[(d*((-a)^(1/4) + b^(1/4)*x))/(-(b^(1/4)*c) + (-a)^(1/4)*d)]*Log[c + d*x] + 12*a*d^4*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)] + 12*a*d^4*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - I*(-a)^(1/4)*d)] + 12*a*d^4*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + I*(-a)^(1/4)*d)] + 12*a*d^4*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)])/(b^2*d^4)","C",1
294,1,383,401,0.0674216,"\int \frac{x^3 \log (c+d x)}{a+b x^4} \, dx","Integrate[(x^3*Log[c + d*x])/(a + b*x^4),x]","\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b}+\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-i \sqrt[4]{-a} d}\right)}{4 b}+\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+i \sqrt[4]{-a} d}\right)}{4 b}+\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\right)}{4 b}+\frac{\log (c+d x) \log \left(\frac{d \left(-\sqrt[4]{b} x+i \sqrt[4]{-a}\right)}{\sqrt[4]{b} c+i \sqrt[4]{-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]{-a} d+\sqrt[4]{b} c}\right)}{4 b}+\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{b} x+i \sqrt[4]{-a}\right)}{\sqrt[4]{b} c-i \sqrt[4]{-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{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b}+\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt{-\sqrt{-a}} d}\right)}{4 b}+\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b}+\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\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*(I*(-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + I*(-a)^(1/4)*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*(I*(-a)^(1/4) + b^(1/4)*x))/(b^(1/4)*c - I*(-a)^(1/4)*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 - (-a)^(1/4)*d)]/(4*b) + PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - I*(-a)^(1/4)*d)]/(4*b) + PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + I*(-a)^(1/4)*d)]/(4*b) + PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)]/(4*b)","C",1
295,1,416,433,0.110463,"\int \frac{\log (c+d x)}{x \left(a+b x^4\right)} \, dx","Integrate[Log[c + d*x]/(x*(a + b*x^4)),x]","-\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 a}-\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-i \sqrt[4]{-a} d}\right)}{4 a}-\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+i \sqrt[4]{-a} d}\right)}{4 a}-\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\right)}{4 a}-\frac{\log (c+d x) \log \left(\frac{d \left(-\sqrt[4]{b} x+i \sqrt[4]{-a}\right)}{\sqrt[4]{b} c+i \sqrt[4]{-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]{-a} d+\sqrt[4]{b} c}\right)}{4 a}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt[4]{b} x+i \sqrt[4]{-a}\right)}{\sqrt[4]{b} c-i \sqrt[4]{-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{\text{Li}_2\left(\frac{c+d x}{c}\right)}{a}+\frac{\log \left(-\frac{d x}{c}\right) \log (c+d x)}{a}","-\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 a}-\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt{-\sqrt{-a}} d}\right)}{4 a}-\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 a}-\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\right)}{4 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{\text{Li}_2\left(\frac{d x}{c}+1\right)}{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*(I*(-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + I*(-a)^(1/4)*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*(I*(-a)^(1/4) + b^(1/4)*x))/(b^(1/4)*c - I*(-a)^(1/4)*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, (c + d*x)/c]/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 - I*(-a)^(1/4)*d)]/(4*a) - PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + I*(-a)^(1/4)*d)]/(4*a) - PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)]/(4*a)","C",1
296,1,484,530,0.2298439,"\int \frac{x^5 \log (c+d x)}{a+b x^4} \, dx","Integrate[(x^5*Log[c + d*x])/(a + b*x^4),x]","\frac{\sqrt{-a} d^2 \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)-\sqrt{-a} d^2 \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-i \sqrt[4]{-a} d}\right)-\sqrt{-a} d^2 \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+i \sqrt[4]{-a} d}\right)+\sqrt{-a} d^2 \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\right)+\sqrt{-a} d^2 \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)-\sqrt{-a} d^2 \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-i \sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+i \sqrt[4]{b} c}\right)-\sqrt{-a} d^2 \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}+i \sqrt[4]{b} x\right)}{\sqrt[4]{-a} d-i \sqrt[4]{b} c}\right)+\sqrt{-a} d^2 \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)-2 \sqrt{b} c^2 \log (c+d x)+2 \sqrt{b} d^2 x^2 \log (c+d x)+2 \sqrt{b} c d x-\sqrt{b} d^2 x^2}{4 b^{3/2} d^2}","-\frac{\sqrt{-a} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^{3/2}}-\frac{\sqrt{-a} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt{-\sqrt{-a}} d}\right)}{4 b^{3/2}}+\frac{\sqrt{-a} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^{3/2}}+\frac{\sqrt{-a} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\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,"(2*Sqrt[b]*c*d*x - Sqrt[b]*d^2*x^2 - 2*Sqrt[b]*c^2*Log[c + d*x] + 2*Sqrt[b]*d^2*x^2*Log[c + d*x] + Sqrt[-a]*d^2*Log[(d*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x] - Sqrt[-a]*d^2*Log[(d*((-a)^(1/4) - I*b^(1/4)*x))/(I*b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x] - Sqrt[-a]*d^2*Log[(d*((-a)^(1/4) + I*b^(1/4)*x))/((-I)*b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x] + Sqrt[-a]*d^2*Log[(d*((-a)^(1/4) + b^(1/4)*x))/(-(b^(1/4)*c) + (-a)^(1/4)*d)]*Log[c + d*x] + Sqrt[-a]*d^2*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)] - Sqrt[-a]*d^2*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - I*(-a)^(1/4)*d)] - Sqrt[-a]*d^2*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + I*(-a)^(1/4)*d)] + Sqrt[-a]*d^2*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)])/(4*b^(3/2)*d^2)","C",1
297,1,348,473,0.1204571,"\int \frac{x \log (c+d x)}{a+b x^4} \, dx","Integrate[(x*Log[c + d*x])/(a + b*x^4),x]","\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)-\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-i \sqrt[4]{-a} d}\right)-\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+i \sqrt[4]{-a} d}\right)+\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\right)+\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)-\log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-i \sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+i \sqrt[4]{b} c}\right)-\log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}+i \sqrt[4]{b} x\right)}{\sqrt[4]{-a} d-i \sqrt[4]{b} c}\right)+\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{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt{-\sqrt{-a}} d}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\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*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x] - Log[(d*((-a)^(1/4) - I*b^(1/4)*x))/(I*b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x] - Log[(d*((-a)^(1/4) + I*b^(1/4)*x))/((-I)*b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x] + Log[(d*((-a)^(1/4) + b^(1/4)*x))/(-(b^(1/4)*c) + (-a)^(1/4)*d)]*Log[c + d*x] + PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)] - PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - I*(-a)^(1/4)*d)] - PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + I*(-a)^(1/4)*d)] + PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)])/(4*Sqrt[-a]*Sqrt[b])","C",1
298,1,506,537,0.2156852,"\int \frac{\log (c+d x)}{x^3 \left(a+b x^4\right)} \, dx","Integrate[Log[c + d*x]/(x^3*(a + b*x^4)),x]","\frac{\sqrt{b} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 (-a)^{3/2}}-\frac{\sqrt{b} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-i \sqrt[4]{-a} d}\right)}{4 (-a)^{3/2}}-\frac{\sqrt{b} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+i \sqrt[4]{-a} d}\right)}{4 (-a)^{3/2}}+\frac{\sqrt{b} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\right)}{4 (-a)^{3/2}}-\frac{\sqrt{b} \log (c+d x) \log \left(\frac{d \left(-\sqrt[4]{b} x+i \sqrt[4]{-a}\right)}{\sqrt[4]{b} c+i \sqrt[4]{-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]{-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]{b} x+i \sqrt[4]{-a}\right)}{\sqrt[4]{b} c-i \sqrt[4]{-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 \left(\frac{d \log (x)}{c^2}-\frac{d \log (c+d x)}{c^2}+\frac{1}{c x}\right)}{2 a}-\frac{\log (c+d x)}{2 a x^2}","-\frac{\sqrt{b} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 (-a)^{3/2}}-\frac{\sqrt{b} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt{-\sqrt{-a}} d}\right)}{4 (-a)^{3/2}}+\frac{\sqrt{b} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 (-a)^{3/2}}+\frac{\sqrt{b} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\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,"-1/2*Log[c + d*x]/(a*x^2) - (Sqrt[b]*Log[(d*(I*(-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + I*(-a)^(1/4)*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*(I*(-a)^(1/4) + b^(1/4)*x))/(b^(1/4)*c - I*(-a)^(1/4)*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)) - (d*(1/(c*x) + (d*Log[x])/c^2 - (d*Log[c + d*x])/c^2))/(2*a) + (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 - I*(-a)^(1/4)*d)])/(4*(-a)^(3/2)) - (Sqrt[b]*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + I*(-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))","C",1
299,1,458,521,0.2449238,"\int \frac{x^4 \log (c+d x)}{a+b x^4} \, dx","Integrate[(x^4*Log[c + d*x])/(a + b*x^4),x]","\frac{-\sqrt[4]{-a} d \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)-i \sqrt[4]{-a} d \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-i \sqrt[4]{-a} d}\right)+i \sqrt[4]{-a} d \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+i \sqrt[4]{-a} d}\right)+\sqrt[4]{-a} d \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\right)+\sqrt[4]{-a} d \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)-i \sqrt[4]{-a} d \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-i \sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+i \sqrt[4]{b} c}\right)+i \sqrt[4]{-a} d \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}+i \sqrt[4]{b} x\right)}{\sqrt[4]{-a} d-i \sqrt[4]{b} c}\right)-\sqrt[4]{-a} d \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]{b} d x \log (c+d x)+4 \sqrt[4]{b} c \log (c+d x)-4 \sqrt[4]{b} d x}{4 b^{5/4} d}","-\frac{\sqrt{-\sqrt{-a}} \text{Li}_2\left(\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{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt{-\sqrt{-a}} d}\right)}{4 b^{5/4}}-\frac{\sqrt[4]{-a} \text{Li}_2\left(\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{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\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,"(-4*b^(1/4)*d*x + 4*b^(1/4)*c*Log[c + d*x] + 4*b^(1/4)*d*x*Log[c + d*x] + (-a)^(1/4)*d*Log[(d*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x] - I*(-a)^(1/4)*d*Log[(d*((-a)^(1/4) - I*b^(1/4)*x))/(I*b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x] + I*(-a)^(1/4)*d*Log[(d*((-a)^(1/4) + I*b^(1/4)*x))/((-I)*b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x] - (-a)^(1/4)*d*Log[(d*((-a)^(1/4) + b^(1/4)*x))/(-(b^(1/4)*c) + (-a)^(1/4)*d)]*Log[c + d*x] - (-a)^(1/4)*d*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)] - I*(-a)^(1/4)*d*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - I*(-a)^(1/4)*d)] + I*(-a)^(1/4)*d*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + I*(-a)^(1/4)*d)] + (-a)^(1/4)*d*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)])/(4*b^(5/4)*d)","C",1
300,1,464,497,0.2884839,"\int \frac{x^2 \log (c+d x)}{a+b x^4} \, dx","Integrate[(x^2*Log[c + d*x])/(a + b*x^4),x]","\frac{-\sqrt[4]{-a} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)+\sqrt[4]{-a} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt{-\sqrt{-a}} d}\right)-\sqrt{-\sqrt{-a}} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)+\sqrt{-\sqrt{-a}} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\right)+\sqrt[4]{-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)+\sqrt{-\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)-\sqrt[4]{-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)-\sqrt{-\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 \sqrt{-\sqrt{-a}} \sqrt[4]{-a} b^{3/4}}","-\frac{\text{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\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,"((-a)^(1/4)*Log[(d*(Sqrt[-Sqrt[-a]] - b^(1/4)*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)]*Log[c + d*x] + Sqrt[-Sqrt[-a]]*Log[(d*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x] - (-a)^(1/4)*Log[(d*(Sqrt[-Sqrt[-a]] + b^(1/4)*x))/(-(b^(1/4)*c) + Sqrt[-Sqrt[-a]]*d)]*Log[c + d*x] - Sqrt[-Sqrt[-a]]*Log[(d*((-a)^(1/4) + b^(1/4)*x))/(-(b^(1/4)*c) + (-a)^(1/4)*d)]*Log[c + d*x] - (-a)^(1/4)*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d)] + (-a)^(1/4)*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)] - Sqrt[-Sqrt[-a]]*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)] + Sqrt[-Sqrt[-a]]*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)])/(4*Sqrt[-Sqrt[-a]]*(-a)^(1/4)*b^(3/4))","A",1
301,1,359,497,0.1172369,"\int \frac{\log (c+d x)}{a+b x^4} \, dx","Integrate[Log[c + d*x]/(a + b*x^4),x]","\frac{-\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)-i \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-i \sqrt[4]{-a} d}\right)+i \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+i \sqrt[4]{-a} d}\right)+\text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\right)+\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)-i \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}-i \sqrt[4]{b} x\right)}{\sqrt[4]{-a} d+i \sqrt[4]{b} c}\right)+i \log (c+d x) \log \left(\frac{d \left(\sqrt[4]{-a}+i \sqrt[4]{b} x\right)}{\sqrt[4]{-a} d-i \sqrt[4]{b} c}\right)-\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{\text{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\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*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x] - I*Log[(d*((-a)^(1/4) - I*b^(1/4)*x))/(I*b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x] + I*Log[(d*((-a)^(1/4) + I*b^(1/4)*x))/((-I)*b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x] - Log[(d*((-a)^(1/4) + b^(1/4)*x))/(-(b^(1/4)*c) + (-a)^(1/4)*d)]*Log[c + d*x] - PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)] - I*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - I*(-a)^(1/4)*d)] + I*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + I*(-a)^(1/4)*d)] + PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)])/(4*(-a)^(3/4)*b^(1/4))","C",1
302,1,525,536,0.625396,"\int \frac{\log (c+d x)}{x^2 \left(a+b x^4\right)} \, dx","Integrate[Log[c + d*x]/(x^2*(a + b*x^4)),x]","\frac{1}{4} \left(\frac{\sqrt[4]{b} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{\sqrt{-\sqrt{-a}} a}-\frac{\sqrt[4]{b} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt{-\sqrt{-a}} d}\right)}{\sqrt{-\sqrt{-a}} a}+\frac{a \sqrt[4]{b} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{(-a)^{9/4}}+\frac{\sqrt[4]{b} \text{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\right)}{(-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)}{\sqrt{-\sqrt{-a}} a}+\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)}{(-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)}{\sqrt{-\sqrt{-a}} a}+\frac{a \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)}{(-a)^{9/4}}+\frac{4 d (\log (x)-\log (c+d x))}{a c}-\frac{4 \log (c+d x)}{a x}\right)","-\frac{\sqrt[4]{b} \text{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\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,"((4*d*(Log[x] - Log[c + d*x]))/(a*c) - (4*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])/(Sqrt[-Sqrt[-a]]*a) + (b^(1/4)*Log[(d*((-a)^(1/4) - b^(1/4)*x))/(b^(1/4)*c + (-a)^(1/4)*d)]*Log[c + d*x])/(-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])/(Sqrt[-Sqrt[-a]]*a) + (a*b^(1/4)*Log[(d*((-a)^(1/4) + b^(1/4)*x))/(-(b^(1/4)*c) + (-a)^(1/4)*d)]*Log[c + d*x])/(-a)^(9/4) + (b^(1/4)*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d)])/(Sqrt[-Sqrt[-a]]*a) - (b^(1/4)*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)])/(Sqrt[-Sqrt[-a]]*a) + (a*b^(1/4)*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)])/(-a)^(9/4) + (b^(1/4)*PolyLog[2, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)])/(-a)^(5/4))/4","A",1
303,1,101,91,0.0579392,"\int \left(f+\frac{g}{x}\right) x \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Integrate[(f + g/x)*x*(a + b*Log[c*(d + e*x)^n]),x]","\frac{1}{2} a f x^2+a g x+\frac{1}{2} b f x^2 \log \left(c (d+e x)^n\right)+\frac{b g (d+e x) \log \left(c (d+e x)^n\right)}{e}-\frac{b d^2 f n \log (d+e x)}{2 e^2}+\frac{b d f n x}{2 e}-\frac{1}{4} b f n x^2-b g 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}",1,"a*g*x + (b*d*f*n*x)/(2*e) - b*g*n*x + (a*f*x^2)/2 - (b*f*n*x^2)/4 - (b*d^2*f*n*Log[d + e*x])/(2*e^2) + (b*f*x^2*Log[c*(d + e*x)^n])/2 + (b*g*(d + e*x)*Log[c*(d + e*x)^n])/e","A",1
304,1,150,120,0.1476122,"\int \left(f+\frac{g}{x}\right)^2 x^2 \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Integrate[(f + g/x)^2*x^2*(a + b*Log[c*(d + e*x)^n]),x]","\frac{e \left(x \left(6 a e^2 \left(f^2 x^2+3 f g x+3 g^2\right)-b n \left(6 d^2 f^2-3 d e f (f x+6 g)+e^2 \left(2 f^2 x^2+9 f g x+18 g^2\right)\right)\right)+6 b e \left(3 d g^2+e x \left(f^2 x^2+3 f g x+3 g^2\right)\right) \log \left(c (d+e x)^n\right)\right)+6 b d^2 f n (d f-3 e g) \log (d+e x)}{18 e^3}","\frac{(f x+g)^3 \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 f}+\frac{b n (d f-e g)^3 \log (d+e x)}{3 e^3 f}-\frac{b n x (d f-e g)^2}{3 e^2}+\frac{b n (f x+g)^2 (d f-e g)}{6 e f}-\frac{b n (f x+g)^3}{9 f}",1,"(6*b*d^2*f*(d*f - 3*e*g)*n*Log[d + e*x] + e*(x*(6*a*e^2*(3*g^2 + 3*f*g*x + f^2*x^2) - b*n*(6*d^2*f^2 - 3*d*e*f*(6*g + f*x) + e^2*(18*g^2 + 9*f*g*x + 2*f^2*x^2))) + 6*b*e*(3*d*g^2 + e*x*(3*g^2 + 3*f*g*x + f^2*x^2))*Log[c*(d + e*x)^n]))/(18*e^3)","A",1
305,1,226,149,0.219084,"\int \left(f+\frac{g}{x}\right)^3 x^3 \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Integrate[(f + g/x)^3*x^3*(a + b*Log[c*(d + e*x)^n]),x]","\frac{e x \left(12 a e^3 \left(f^3 x^3+4 f^2 g x^2+6 f g^2 x+4 g^3\right)+b n \left(12 d^3 f^3-6 d^2 e f^2 (f x+8 g)+4 d e^2 f \left(f^2 x^2+6 f g x+18 g^2\right)-\left(e^3 \left(3 f^3 x^3+16 f^2 g x^2+36 f g^2 x+48 g^3\right)\right)\right)\right)+12 b e^3 \left(4 d g^3+e x \left(f^3 x^3+4 f^2 g x^2+6 f g^2 x+4 g^3\right)\right) \log \left(c (d+e x)^n\right)-12 b d^2 f n \left(d^2 f^2-4 d e f g+6 e^2 g^2\right) \log (d+e x)}{48 e^4}","\frac{(f x+g)^4 \left(a+b \log \left(c (d+e x)^n\right)\right)}{4 f}-\frac{b n (d f-e g)^4 \log (d+e x)}{4 e^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 (f x+g)^3 (d f-e g)}{12 e f}-\frac{b n (f x+g)^4}{16 f}",1,"(e*x*(12*a*e^3*(4*g^3 + 6*f*g^2*x + 4*f^2*g*x^2 + f^3*x^3) + b*n*(12*d^3*f^3 - 6*d^2*e*f^2*(8*g + f*x) + 4*d*e^2*f*(18*g^2 + 6*f*g*x + f^2*x^2) - e^3*(48*g^3 + 36*f*g^2*x + 16*f^2*g*x^2 + 3*f^3*x^3))) - 12*b*d^2*f*(d^2*f^2 - 4*d*e*f*g + 6*e^2*g^2)*n*Log[d + e*x] + 12*b*e^3*(4*d*g^3 + e*x*(4*g^3 + 6*f*g^2*x + 4*f^2*g*x^2 + f^3*x^3))*Log[c*(d + e*x)^n])/(48*e^4)","A",1
306,1,62,63,0.0138995,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\left(f+\frac{g}{x}\right) x} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/((f + g/x)*x),x]","\frac{\log \left(\frac{e (f x+g)}{e g-d f}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f}+\frac{b n \text{Li}_2\left(\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{Li}_2\left(\frac{f (d+e x)}{d f-e g}\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",1
307,1,57,74,0.0654762,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\left(f+\frac{g}{x}\right)^2 x^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])/((f + g/x)^2*x^2),x]","\frac{\frac{b e n (\log (d+e x)-\log (f x+g))}{e g-d f}-\frac{a+b \log \left(c (d+e x)^n\right)}{f x+g}}{f}","-\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,"(-((a + b*Log[c*(d + e*x)^n])/(g + f*x)) + (b*e*n*(Log[d + e*x] - Log[g + f*x]))/(-(d*f) + e*g))/f","A",1
308,1,83,112,0.1143694,"\int \frac{a+b \log \left(c (d+e x)^n\right)}{\left(f+\frac{g}{x}\right)^3 x^3} \, dx","Integrate[(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)-\frac{b e n (f x+g) (e (f x+g) \log (d+e x)-d f-e (f x+g) \log (f x+g)+e g)}{(d f-e g)^2}}{2 f (f x+g)^2}","-\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,"-1/2*(a + b*Log[c*(d + e*x)^n] - (b*e*n*(g + f*x)*(-(d*f) + e*g + e*(g + f*x)*Log[d + e*x] - e*(g + f*x)*Log[g + f*x]))/(d*f - e*g)^2)/(f*(g + f*x)^2)","A",1
309,1,247,247,0.182082,"\int \frac{\log (a+b x)}{c+\frac{d}{x^2}} \, dx","Integrate[Log[a + b*x]/(c + d/x^2),x]","\frac{\sqrt{d} \text{Li}_2\left(\frac{\sqrt{-c} (a+b x)}{a \sqrt{-c}-b \sqrt{d}}\right)}{2 (-c)^{3/2}}-\frac{\sqrt{d} \text{Li}_2\left(\frac{\sqrt{-c} (a+b x)}{\sqrt{-c} a+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{Li}_2\left(\frac{\sqrt{-c} (a+b x)}{a \sqrt{-c}-b \sqrt{d}}\right)}{2 (-c)^{3/2}}-\frac{\sqrt{d} \text{Li}_2\left(\frac{\sqrt{-c} (a+b x)}{\sqrt{-c} a+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",1
310,1,862,831,1.0973804,"\int \frac{x^5 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x^2} \, dx","Integrate[(x^5*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2),x]","\frac{72 g^2 x^4 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 e^4-144 f g x^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 e^4+144 f^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(g x^2+f\right) e^4-12 b n \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(-24 f^2 \left(\log (d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+\text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right) e^4-24 f^2 \left(\log (d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+\text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right) e^4+12 f g \left(e x (2 d-e x)-2 \left(d^2-e^2 x^2\right) \log (d+e x)\right) e^2+g^2 \left(e x \left(-12 d^3+6 e x d^2-4 e^2 x^2 d+3 e^3 x^3\right)+12 \left(d^4-e^4 x^4\right) \log (d+e x)\right)\right)+b^2 n^2 \left(144 f^2 \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right) e^4+144 f^2 \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right) e^4-72 f g \left(-2 \left(d^2-e^2 x^2\right) \log ^2(d+e x)+\left(6 d^2+4 e x d-2 e^2 x^2\right) \log (d+e x)+e x (e x-6 d)\right) e^2-g^2 \left(72 \left(d^4-e^4 x^4\right) \log ^2(d+e x)-12 \left(25 d^4+12 e x d^3-6 e^2 x^2 d^2+4 e^3 x^3 d-3 e^4 x^4\right) \log (d+e x)+e x \left(300 d^3-78 e x d^2+28 e^2 x^2 d-9 e^3 x^3\right)\right)\right)}{288 e^4 g^3}","\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{Li}_2\left(-\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{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{g^3}-\frac{b^2 f^2 n^2 \text{Li}_3\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^3}-\frac{b^2 f^2 n^2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{g^3}",1,"(-144*e^4*f*g*x^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 72*e^4*g^2*x^4*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 144*e^4*f^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x^2] - 12*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(12*e^2*f*g*(e*x*(2*d - e*x) - 2*(d^2 - e^2*x^2)*Log[d + e*x]) + g^2*(e*x*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3) + 12*(d^4 - e^4*x^4)*Log[d + e*x]) - 24*e^4*f^2*(Log[d + e*x]*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]) - 24*e^4*f^2*(Log[d + e*x]*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])])) + b^2*n^2*(-72*e^2*f*g*(e*x*(-6*d + e*x) + (6*d^2 + 4*d*e*x - 2*e^2*x^2)*Log[d + e*x] - 2*(d^2 - e^2*x^2)*Log[d + e*x]^2) - g^2*(e*x*(300*d^3 - 78*d^2*e*x + 28*d*e^2*x^2 - 9*e^3*x^3) - 12*(25*d^4 + 12*d^3*e*x - 6*d^2*e^2*x^2 + 4*d*e^3*x^3 - 3*e^4*x^4)*Log[d + e*x] + 72*(d^4 - e^4*x^4)*Log[d + e*x]^2) + 144*e^4*f^2*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]) + 144*e^4*f^2*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])])))/(288*e^4*g^3)","C",1
311,1,637,499,0.5387992,"\int \frac{x^3 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x^2} \, dx","Integrate[(x^3*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2),x]","\frac{2 b n \left(-2 g \left(d^2-e^2 x^2\right) \log (d+e x)-2 e^2 f \left(\text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+\log (d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right)-2 e^2 f \left(\text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+\log (d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+i e \sqrt{f}}\right)\right)+e g x (2 d-e x)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)-2 e^2 f \log \left(f+g x^2\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+2 e^2 g x^2 \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2-b^2 n^2 \left(g \left(2 \left(d^2-e^2 x^2\right) \log ^2(d+e x)+\left(-6 d^2-4 d e x+2 e^2 x^2\right) \log (d+e x)+e x (6 d-e x)\right)+2 e^2 f \left(-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+\log ^2(d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right)+2 e^2 f \left(-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+\log ^2(d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+i e \sqrt{f}}\right)\right)\right)}{4 e^2 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{b f n \text{Li}_2\left(-\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{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{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}{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{b^2 f n^2 \text{Li}_3\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^2}+\frac{b^2 f n^2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{g^2}-\frac{2 b^2 d n^2 x}{e g}",1,"(2*e^2*g*x^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 - 2*e^2*f*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x^2] + 2*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(e*g*x*(2*d - e*x) - 2*g*(d^2 - e^2*x^2)*Log[d + e*x] - 2*e^2*f*(Log[d + e*x]*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]) - 2*e^2*f*(Log[d + e*x]*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])])) - b^2*n^2*(g*(e*x*(6*d - e*x) + (-6*d^2 - 4*d*e*x + 2*e^2*x^2)*Log[d + e*x] + 2*(d^2 - e^2*x^2)*Log[d + e*x]^2) + 2*e^2*f*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]) + 2*e^2*f*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])])))/(4*e^2*g^2)","C",1
312,1,464,317,0.2798577,"\int \frac{x \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x^2} \, dx","Integrate[(x*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2),x]","\frac{2 b n \left(\text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+\text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+\log (d+e x) \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+\log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+i e \sqrt{f}}\right)\right)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)+\log \left(f+g x^2\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+b^2 n^2 \left(-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+\log ^2(d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+\log ^2(d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+i e \sqrt{f}}\right)\right)}{2 g}","\frac{b n \text{Li}_2\left(-\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{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\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^2 n^2 \text{Li}_3\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g}-\frac{b^2 n^2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{g}",1,"((a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x^2] + 2*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(Log[d + e*x]*(Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]) + PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]) + b^2*n^2*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]))/(2*g)","C",1
313,1,576,397,0.4081377,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x \left(f+g x^2\right)} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(x*(f + g*x^2)),x]","-\frac{2 b n \left(\text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+\text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+\log (d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+\log (d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+i e \sqrt{f}}\right)-2 \left(\text{Li}_2\left(\frac{e x}{d}+1\right)+\log \left(-\frac{e x}{d}\right) \log (d+e x)\right)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)+\log \left(f+g x^2\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2-2 \log (x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+b^2 n^2 \left(-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+\log ^2(d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+\log ^2(d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+i e \sqrt{f}}\right)+4 \text{Li}_3\left(\frac{e x}{d}+1\right)-4 \text{Li}_2\left(\frac{e x}{d}+1\right) \log (d+e x)-2 \log \left(-\frac{e x}{d}\right) \log ^2(d+e x)\right)}{2 f}","-\frac{b n \text{Li}_2\left(-\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{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\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{2 b n \text{Li}_2\left(\frac{e x}{d}+1\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)^2}{f}+\frac{b^2 n^2 \text{Li}_3\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{f}+\frac{b^2 n^2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{f}-\frac{2 b^2 n^2 \text{Li}_3\left(\frac{e x}{d}+1\right)}{f}",1,"-1/2*(-2*Log[x]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + (a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x^2] + 2*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(Log[d + e*x]*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + Log[d + e*x]*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 2*(Log[-((e*x)/d)]*Log[d + e*x] + PolyLog[2, 1 + (e*x)/d])) + b^2*n^2*(-2*Log[-((e*x)/d)]*Log[d + e*x]^2 + Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 4*Log[d + e*x]*PolyLog[2, 1 + (e*x)/d] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 4*PolyLog[3, 1 + (e*x)/d]))/f","C",1
314,1,811,551,0.7671665,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x^3 \left(f+g x^2\right)} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(x^3*(f + g*x^2)),x]","\frac{b^2 \left(d^2 g \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right) x^2+d^2 g \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right) x^2-2 d^2 g \left(\log \left(-\frac{e x}{d}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{e x}{d}+1\right) \log (d+e x)-2 \text{Li}_3\left(\frac{e x}{d}+1\right)\right) x^2+f \left(2 e^2 \log (x) x^2-2 e^2 \text{Li}_2\left(\frac{e x}{d}+1\right) x^2-\log (d+e x) \left(2 e^2 \log \left(-\frac{e x}{d}\right) x^2+(d+e x) (2 e x+(d-e x) \log (d+e x))\right)\right)\right) n^2-2 b \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(-d^2 g \left(\log (d+e x) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)+\text{Li}_2\left(-\frac{i \sqrt{g} (d+e x)}{e \sqrt{f}-i d \sqrt{g}}\right)\right) x^2-d^2 g \left(\log (d+e x) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right)+\text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right) x^2+2 d^2 g \left(\log \left(-\frac{e x}{d}\right) \log (d+e x)+\text{Li}_2\left(\frac{e x}{d}+1\right)\right) x^2+f \left(e^2 \log (x) x^2+d e x+\left(d^2-e^2 x^2\right) \log (d+e x)\right)\right) n-d^2 f \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2-2 d^2 g x^2 \log (x) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2+d^2 g x^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(g x^2+f\right)}{2 d^2 f^2 x^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{b g n \text{Li}_2\left(-\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{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}-\frac{2 b g n \text{Li}_2\left(\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{f^2}-\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 \text{Li}_2\left(\frac{d}{d+e x}\right)}{d^2 f}+\frac{b^2 e^2 n^2 \log (x)}{d^2 f}-\frac{b^2 g n^2 \text{Li}_3\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{f^2}-\frac{b^2 g n^2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{f^2}+\frac{2 b^2 g n^2 \text{Li}_3\left(\frac{e x}{d}+1\right)}{f^2}",1,"(-(d^2*f*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2) - 2*d^2*g*x^2*Log[x]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + d^2*g*x^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x^2] - 2*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(f*(d*e*x + e^2*x^2*Log[x] + (d^2 - e^2*x^2)*Log[d + e*x]) - d^2*g*x^2*(Log[d + e*x]*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])] + PolyLog[2, ((-I)*Sqrt[g]*(d + e*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) - d^2*g*x^2*(Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])]) + 2*d^2*g*x^2*(Log[-((e*x)/d)]*Log[d + e*x] + PolyLog[2, 1 + (e*x)/d])) + b^2*n^2*(f*(2*e^2*x^2*Log[x] - Log[d + e*x]*(2*e^2*x^2*Log[-((e*x)/d)] + (d + e*x)*(2*e*x + (d - e*x)*Log[d + e*x])) - 2*e^2*x^2*PolyLog[2, 1 + (e*x)/d]) + d^2*g*x^2*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]) + d^2*g*x^2*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]) - 2*d^2*g*x^2*(Log[-((e*x)/d)]*Log[d + e*x]^2 + 2*Log[d + e*x]*PolyLog[2, 1 + (e*x)/d] - 2*PolyLog[3, 1 + (e*x)/d])))/(2*d^2*f^2*x^2)","C",1
315,1,821,701,0.9981957,"\int \frac{x^4 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x^2} \, dx","Integrate[(x^4*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2),x]","\frac{18 g^{3/2} x^3 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 e^3-54 f \sqrt{g} x \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 e^3+54 f^{3/2} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 e^3+6 b n \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(9 i f^{3/2} \left(\log (d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+\text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right) e^3-9 i f^{3/2} \left(\log (d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+\text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right) e^3-18 f \sqrt{g} (d+e x) (\log (d+e x)-1) e^2+g^{3/2} \left(e x \left(-6 d^2+3 e x d-2 e^2 x^2\right)+6 \left(d^3+e^3 x^3\right) \log (d+e x)\right)\right)+b^2 n^2 \left(27 i f^{3/2} \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right) e^3-27 i f^{3/2} \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right) e^3-54 f \sqrt{g} \left((d+e x) \log ^2(d+e x)-2 (d+e x) \log (d+e x)+2 e x\right) e^2+g^{3/2} \left(18 \left(d^3+e^3 x^3\right) \log ^2(d+e x)-6 \left(11 d^3+6 e x d^2-3 e^2 x^2 d+2 e^3 x^3\right) \log (d+e x)+e x \left(66 d^2-15 e x d+4 e^2 x^2\right)\right)\right)}{54 e^3 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{b (-f)^{3/2} n \text{Li}_2\left(-\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{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{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}{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{f (d+e x) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{e g^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{b^2 d^3 n^2 \log ^2(d+e x)}{3 e^3 g}+\frac{2 b^2 d^2 n^2 x}{e^2 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{b^2 (-f)^{3/2} n^2 \text{Li}_3\left(-\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{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{g^{5/2}}-\frac{2 b^2 f n^2 x}{g^2}",1,"(-54*e^3*f*Sqrt[g]*x*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 18*e^3*g^(3/2)*x^3*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 54*e^3*f^(3/2)*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 6*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(-18*e^2*f*Sqrt[g]*(d + e*x)*(-1 + Log[d + e*x]) + g^(3/2)*(e*x*(-6*d^2 + 3*d*e*x - 2*e^2*x^2) + 6*(d^3 + e^3*x^3)*Log[d + e*x]) + (9*I)*e^3*f^(3/2)*(Log[d + e*x]*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]) - (9*I)*e^3*f^(3/2)*(Log[d + e*x]*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])])) + b^2*n^2*(-54*e^2*f*Sqrt[g]*(2*e*x - 2*(d + e*x)*Log[d + e*x] + (d + e*x)*Log[d + e*x]^2) + g^(3/2)*(e*x*(66*d^2 - 15*d*e*x + 4*e^2*x^2) - 6*(11*d^3 + 6*d^2*e*x - 3*d*e^2*x^2 + 2*e^3*x^3)*Log[d + e*x] + 18*(d^3 + e^3*x^3)*Log[d + e*x]^2) + (27*I)*e^3*f^(3/2)*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]) - (27*I)*e^3*f^(3/2)*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])])))/(54*e^3*g^(5/2))","C",1
316,1,623,447,0.6187363,"\int \frac{x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x^2} \, dx","Integrate[(x^2*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2),x]","\frac{i b n \left(-e \sqrt{f} \left(\text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+\log (d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right)+e \sqrt{f} \left(\text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+\log (d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+i e \sqrt{f}}\right)\right)-2 i \sqrt{g} (d+e x) (\log (d+e x)-1)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)-e \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+e \sqrt{g} x \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+b^2 n^2 \left(-\frac{1}{2} i e \sqrt{f} \left(-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+\log ^2(d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right)+\frac{1}{2} i e \sqrt{f} \left(-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+\log ^2(d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+i e \sqrt{f}}\right)\right)+\sqrt{g} \left((d+e x) \log ^2(d+e x)-2 (d+e x) \log (d+e x)+2 e x\right)\right)}{e g^{3/2}}","-\frac{b \sqrt{-f} n \text{Li}_2\left(-\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{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\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{b^2 \sqrt{-f} n^2 \text{Li}_3\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^{3/2}}-\frac{b^2 \sqrt{-f} n^2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{g^{3/2}}+\frac{2 b^2 n^2 x}{g}",1,"(e*Sqrt[g]*x*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 - e*Sqrt[f]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + I*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((-2*I)*Sqrt[g]*(d + e*x)*(-1 + Log[d + e*x]) - e*Sqrt[f]*(Log[d + e*x]*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]) + e*Sqrt[f]*(Log[d + e*x]*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])])) + b^2*n^2*(Sqrt[g]*(2*e*x - 2*(d + e*x)*Log[d + e*x] + (d + e*x)*Log[d + e*x]^2) - (I/2)*e*Sqrt[f]*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]) + (I/2)*e*Sqrt[f]*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])])))/(e*g^(3/2))","C",1
317,1,485,371,0.3392075,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{f+g x^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x^2),x]","\frac{i b n \left(\text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)-\text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+\log (d+e x) \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)-\log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+i e \sqrt{f}}\right)\right)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)+\tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+\frac{1}{2} i b^2 n^2 \left(-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)-2 \log (d+e x) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+\log ^2(d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)-\log ^2(d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+i e \sqrt{f}}\right)\right)}{\sqrt{f} \sqrt{g}}","-\frac{b n \text{Li}_2\left(-\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{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\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^2 n^2 \text{Li}_3\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{\sqrt{-f} \sqrt{g}}-\frac{b^2 n^2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{\sqrt{-f} \sqrt{g}}",1,"(ArcTan[(Sqrt[g]*x)/Sqrt[f]]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + I*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(Log[d + e*x]*(Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]) + PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]) + (I/2)*b^2*n^2*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]))/(Sqrt[f]*Sqrt[g])","C",1
318,1,668,461,0.5219907,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x^2 \left(f+g x^2\right)} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(x^2*(f + g*x^2)),x]","\frac{2 b n \left(i d \sqrt{g} x \left(\text{Li}_2\left(-\frac{i \sqrt{g} (d+e x)}{e \sqrt{f}-i d \sqrt{g}}\right)+\log (d+e x) \log \left(\frac{e \left(\sqrt{f}+i \sqrt{g} x\right)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)-i d \sqrt{g} x \left(\text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)+\log (d+e x) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{e \sqrt{f}+i d \sqrt{g}}\right)\right)+2 \sqrt{f} (e x \log (x)-(d+e x) \log (d+e x))\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)-2 d \sqrt{g} x \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2-2 d \sqrt{f} \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+b^2 n^2 \left(-i d \sqrt{g} x \left(-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+\log ^2(d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right)+i d \sqrt{g} x \left(-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+2 \log (d+e x) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+\log ^2(d+e x) \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}+i e \sqrt{f}}\right)\right)+2 \sqrt{f} \left(2 e x \text{Li}_2\left(\frac{e x}{d}+1\right)-\left((d+e x) \log ^2(d+e x)\right)+2 e x \log \left(-\frac{e x}{d}\right) \log (d+e x)\right)\right)}{2 d f^{3/2} x}","-\frac{b \sqrt{g} n \text{Li}_2\left(-\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{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(-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}{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^2 \sqrt{g} n^2 \text{Li}_3\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{(-f)^{3/2}}-\frac{b^2 \sqrt{g} n^2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{(-f)^{3/2}}+\frac{2 b^2 e n^2 \text{Li}_2\left(\frac{e x}{d}+1\right)}{d f}",1,"(-2*d*Sqrt[f]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 - 2*d*Sqrt[g]*x*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 2*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(2*Sqrt[f]*(e*x*Log[x] - (d + e*x)*Log[d + e*x]) + I*d*Sqrt[g]*x*(Log[d + e*x]*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])] + PolyLog[2, ((-I)*Sqrt[g]*(d + e*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) - I*d*Sqrt[g]*x*(Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])])) + b^2*n^2*(2*Sqrt[f]*(2*e*x*Log[-((e*x)/d)]*Log[d + e*x] - (d + e*x)*Log[d + e*x]^2 + 2*e*x*PolyLog[2, 1 + (e*x)/d]) - I*d*Sqrt[g]*x*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]) + I*d*Sqrt[g]*x*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])])))/(2*d*f^(3/2)*x)","C",1
319,1,930,694,0.8454856,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x^4 \left(f+g x^2\right)} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(x^4*(f + g*x^2)),x]","\frac{6 \sqrt{f} g x^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 d^3-2 f^{3/2} \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 d^3+6 g^{3/2} x^3 \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 d^3+2 i b n \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(-3 d^3 g^{3/2} \left(\log (d+e x) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)+\text{Li}_2\left(-\frac{i \sqrt{g} (d+e x)}{e \sqrt{f}-i d \sqrt{g}}\right)\right) x^3+3 d^3 g^{3/2} \left(\log (d+e x) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right)+\text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right) x^3+6 i d^2 \sqrt{f} g (e x \log (x)-(d+e x) \log (d+e x)) x^2+i f^{3/2} \left(-2 e^3 \log (x) x^3+d e (d-2 e x) x+2 \left(d^3+e^3 x^3\right) \log (d+e x)\right)\right)+i b^2 n^2 \left(3 d^3 g^{3/2} \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right) x^3-3 d^3 g^{3/2} \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right) x^3+6 i d^2 \sqrt{f} g \left(-\left((d+e x) \log ^2(d+e x)\right)+2 e x \log \left(-\frac{e x}{d}\right) \log (d+e x)+2 e x \text{Li}_2\left(\frac{e x}{d}+1\right)\right) x^2+2 i f^{3/2} \left(\log ^2(d+e x) d^3+e x \log (d+e x) d^2+e^2 x^2 d-2 e^2 x^2 \log (d+e x) d+e^3 x^3 \log ^2(d+e x)+3 e^3 x^3 \log (x)-3 e^3 x^3 \log (d+e x)-2 e^3 x^3 \log \left(-\frac{e x}{d}\right) \log (d+e x)-2 e^3 x^3 \text{Li}_2\left(\frac{e x}{d}+1\right)\right)\right)}{6 d^3 f^{5/2} x^3}","\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{b g^{3/2} n \text{Li}_2\left(-\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{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{(-f)^{5/2}}+\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{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{3 f x^3}-\frac{b e n \left(a+b \log \left(c (d+e x)^n\right)\right)}{3 d f x^2}-\frac{2 b^2 e^3 n^2 \text{Li}_2\left(\frac{d}{d+e x}\right)}{3 d^3 f}-\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^2 e^2 n^2}{3 d^2 f x}-\frac{2 b^2 e g n^2 \text{Li}_2\left(\frac{e x}{d}+1\right)}{d f^2}+\frac{b^2 g^{3/2} n^2 \text{Li}_3\left(-\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{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{(-f)^{5/2}}",1,"(-2*d^3*f^(3/2)*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 6*d^3*Sqrt[f]*g*x^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 6*d^3*g^(3/2)*x^3*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + (2*I)*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((6*I)*d^2*Sqrt[f]*g*x^2*(e*x*Log[x] - (d + e*x)*Log[d + e*x]) + I*f^(3/2)*(d*e*x*(d - 2*e*x) - 2*e^3*x^3*Log[x] + 2*(d^3 + e^3*x^3)*Log[d + e*x]) - 3*d^3*g^(3/2)*x^3*(Log[d + e*x]*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])] + PolyLog[2, ((-I)*Sqrt[g]*(d + e*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) + 3*d^3*g^(3/2)*x^3*(Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])])) + I*b^2*n^2*((6*I)*d^2*Sqrt[f]*g*x^2*(2*e*x*Log[-((e*x)/d)]*Log[d + e*x] - (d + e*x)*Log[d + e*x]^2 + 2*e*x*PolyLog[2, 1 + (e*x)/d]) + (2*I)*f^(3/2)*(d*e^2*x^2 + 3*e^3*x^3*Log[x] + d^2*e*x*Log[d + e*x] - 2*d*e^2*x^2*Log[d + e*x] - 3*e^3*x^3*Log[d + e*x] - 2*e^3*x^3*Log[-((e*x)/d)]*Log[d + e*x] + d^3*Log[d + e*x]^2 + e^3*x^3*Log[d + e*x]^2 - 2*e^3*x^3*PolyLog[2, 1 + (e*x)/d]) + 3*d^3*g^(3/2)*x^3*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]) - 3*d^3*g^(3/2)*x^3*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])])))/(6*d^3*f^(5/2)*x^3)","C",1
320,1,1254,936,3.3111088,"\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","Integrate[(x^5*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2)^2,x]","\frac{b^2 \left(\frac{i \left(-\sqrt{g} (d+e x) \log ^2(d+e x)+2 e \left(\sqrt{g} x+i \sqrt{f}\right) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right) \log (d+e x)+2 e \left(\sqrt{g} x+i \sqrt{f}\right) \text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right) f^{3/2}}{\left(i \sqrt{g} d+e \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}-\frac{\left(\log (d+e x) \left(2 e \left(i \sqrt{g} x+\sqrt{f}\right) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)-i \sqrt{g} (d+e x) \log (d+e x)\right)+2 e \left(i \sqrt{g} x+\sqrt{f}\right) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right) f^{3/2}}{\left(e \sqrt{f}-i d \sqrt{g}\right) \left(i \sqrt{g} x+\sqrt{f}\right)}-4 \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right) f-4 \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right) f+\frac{g \left(-2 \left(d^2-e^2 x^2\right) \log ^2(d+e x)+\left(6 d^2+4 e x d-2 e^2 x^2\right) \log (d+e x)+e x (e x-6 d)\right)}{e^2}\right) n^2+2 b \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(\frac{\left(i \sqrt{g} (d+e x) \log (d+e x)-e \left(i \sqrt{g} x+\sqrt{f}\right) \log \left(i \sqrt{f}-\sqrt{g} x\right)\right) f^{3/2}}{\left(e \sqrt{f}-i d \sqrt{g}\right) \left(i \sqrt{g} x+\sqrt{f}\right)}+\frac{i \left(e \left(\sqrt{g} x+i \sqrt{f}\right) \log \left(\sqrt{g} x+i \sqrt{f}\right)-\sqrt{g} (d+e x) \log (d+e x)\right) f^{3/2}}{\left(i \sqrt{g} d+e \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}-4 \left(\log (d+e x) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)+\text{Li}_2\left(-\frac{i \sqrt{g} (d+e x)}{e \sqrt{f}-i d \sqrt{g}}\right)\right) f-4 \left(\log (d+e x) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right)+\text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right) f+\frac{g \left(e x (2 d-e x)-2 \left(d^2-e^2 x^2\right) \log (d+e x)\right)}{e^2}\right) n+2 g x^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2-\frac{2 f^2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2}{g x^2+f}-4 f \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(g x^2+f\right)}{4 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{Li}_2\left(-\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{Li}_2\left(\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{Li}_3\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) b^2}{g^3}+\frac{2 f n^2 \text{Li}_3\left(\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{Li}_2\left(-\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{Li}_2\left(\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*g*x^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 - (2*f^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2) - 4*f*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x^2] + 2*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((g*(e*x*(2*d - e*x) - 2*(d^2 - e^2*x^2)*Log[d + e*x]))/e^2 + (f^(3/2)*(I*Sqrt[g]*(d + e*x)*Log[d + e*x] - e*(Sqrt[f] + I*Sqrt[g]*x)*Log[I*Sqrt[f] - Sqrt[g]*x]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) + (I*f^(3/2)*(-(Sqrt[g]*(d + e*x)*Log[d + e*x]) + e*(I*Sqrt[f] + Sqrt[g]*x)*Log[I*Sqrt[f] + Sqrt[g]*x]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) - 4*f*(Log[d + e*x]*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])] + PolyLog[2, ((-I)*Sqrt[g]*(d + e*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) - 4*f*(Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])])) + b^2*n^2*((g*(e*x*(-6*d + e*x) + (6*d^2 + 4*d*e*x - 2*e^2*x^2)*Log[d + e*x] - 2*(d^2 - e^2*x^2)*Log[d + e*x]^2))/e^2 + (I*f^(3/2)*(-(Sqrt[g]*(d + e*x)*Log[d + e*x]^2) + 2*e*(I*Sqrt[f] + Sqrt[g]*x)*Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + 2*e*(I*Sqrt[f] + Sqrt[g]*x)*PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) - (f^(3/2)*(Log[d + e*x]*((-I)*Sqrt[g]*(d + e*x)*Log[d + e*x] + 2*e*(Sqrt[f] + I*Sqrt[g]*x)*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) + 2*e*(Sqrt[f] + I*Sqrt[g]*x)*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) - 4*f*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]) - 4*f*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])])))/(4*g^3)","C",1
321,1,1103,739,2.654985,"\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","Integrate[(x^3*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2)^2,x]","\frac{b^2 \left(2 \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log ^2(d+e x)+2 \log \left(1-\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log ^2(d+e x)+4 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log (d+e x)+4 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log (d+e x)+\frac{\sqrt{f} \left(\log (d+e x) \left(i \sqrt{g} (d+e x) \log (d+e x)+2 e \left(\sqrt{f}-i \sqrt{g} x\right) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right)\right)+2 e \left(\sqrt{f}-i \sqrt{g} x\right) \text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right)}{\left(i \sqrt{g} d+e \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+\frac{\sqrt{f} \left(\log (d+e x) \left(2 e \left(i \sqrt{g} x+\sqrt{f}\right) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)-i \sqrt{g} (d+e x) \log (d+e x)\right)+2 e \left(i \sqrt{g} x+\sqrt{f}\right) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right)}{\left(e \sqrt{f}-i d \sqrt{g}\right) \left(i \sqrt{g} x+\sqrt{f}\right)}-4 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)-4 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right) n^2+2 b \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(\frac{\sqrt{f} \left(e \left(i \sqrt{g} x+\sqrt{f}\right) \log \left(i \sqrt{f}-\sqrt{g} x\right)-i \sqrt{g} (d+e x) \log (d+e x)\right)}{\left(e \sqrt{f}-i d \sqrt{g}\right) \left(i \sqrt{g} x+\sqrt{f}\right)}+\frac{\sqrt{f} \left(i \sqrt{g} (d+e x) \log (d+e x)+e \left(\sqrt{f}-i \sqrt{g} x\right) \log \left(\sqrt{g} x+i \sqrt{f}\right)\right)}{\left(i \sqrt{g} d+e \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+2 \left(\log (d+e x) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)+\text{Li}_2\left(-\frac{i \sqrt{g} (d+e x)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)+2 \left(\log (d+e x) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right)+\text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right)\right) n+\frac{2 f \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2}{g x^2+f}+2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(g x^2+f\right)}{4 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{b n \text{Li}_2\left(-\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{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{g^2}+\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^2 e \sqrt{-f} n^2 \left(d \sqrt{g}+e \sqrt{-f}\right) \text{Li}_2\left(-\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{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 g^2 \left(d^2 g+e^2 f\right)}-\frac{b^2 n^2 \text{Li}_3\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{g^2}-\frac{b^2 n^2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{g^2}",1,"((2*f*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2) + 2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x^2] + 2*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((Sqrt[f]*((-I)*Sqrt[g]*(d + e*x)*Log[d + e*x] + e*(Sqrt[f] + I*Sqrt[g]*x)*Log[I*Sqrt[f] - Sqrt[g]*x]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) + (Sqrt[f]*(I*Sqrt[g]*(d + e*x)*Log[d + e*x] + e*(Sqrt[f] - I*Sqrt[g]*x)*Log[I*Sqrt[f] + Sqrt[g]*x]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) + 2*(Log[d + e*x]*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])] + PolyLog[2, ((-I)*Sqrt[g]*(d + e*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) + 2*(Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])])) + b^2*n^2*(2*Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + (Sqrt[f]*(Log[d + e*x]*(I*Sqrt[g]*(d + e*x)*Log[d + e*x] + 2*e*(Sqrt[f] - I*Sqrt[g]*x)*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])]) + 2*e*(Sqrt[f] - I*Sqrt[g]*x)*PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) + 4*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 4*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + (Sqrt[f]*(Log[d + e*x]*((-I)*Sqrt[g]*(d + e*x)*Log[d + e*x] + 2*e*(Sqrt[f] + I*Sqrt[g]*x)*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) + 2*e*(Sqrt[f] + I*Sqrt[g]*x)*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) - 4*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 4*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]))/(4*g^2)","C",1
322,1,590,430,0.6897154,"\int \frac{x \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{\left(f+g x^2\right)^2} \, dx","Integrate[(x*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2)^2,x]","\frac{\frac{2 b n \left(2 \sqrt{f} g \left(d^2-e^2 x^2\right) \log (d+e x)+e \left(f+g x^2\right) \left(\left(e \sqrt{f}+i d \sqrt{g}\right) \log \left(-\sqrt{g} x+i \sqrt{f}\right)+\left(e \sqrt{f}-i d \sqrt{g}\right) \log \left(\sqrt{g} x+i \sqrt{f}\right)\right)\right) \left(-a-b \log \left(c (d+e x)^n\right)+b n \log (d+e x)\right)}{\sqrt{f} \left(f+g x^2\right) \left(d^2 g+e^2 f\right)}-\frac{2 \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2}{f+g x^2}+\frac{i b^2 n^2 \left(\frac{2 e \left(\sqrt{g} x+i \sqrt{f}\right) \text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)+2 e \left(\sqrt{g} x+i \sqrt{f}\right) \log (d+e x) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{e \sqrt{f}+i d \sqrt{g}}\right)-\sqrt{g} (d+e x) \log ^2(d+e x)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(e \sqrt{f}+i d \sqrt{g}\right)}+\frac{2 i e \left(\sqrt{f}+i \sqrt{g} x\right) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)+\log (d+e x) \left(\sqrt{g} (d+e x) \log (d+e x)+2 i e \left(\sqrt{f}+i \sqrt{g} x\right) \log \left(\frac{e \left(\sqrt{f}+i \sqrt{g} x\right)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)}{\left(\sqrt{f}+i \sqrt{g} x\right) \left(e \sqrt{f}-i d \sqrt{g}\right)}\right)}{\sqrt{f}}}{4 g}","-\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{Li}_2\left(-\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{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 f g \left(d^2 g+e^2 f\right)}",1,"((-2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2) + (2*b*n*(-a + b*n*Log[d + e*x] - b*Log[c*(d + e*x)^n])*(2*Sqrt[f]*g*(d^2 - e^2*x^2)*Log[d + e*x] + e*(f + g*x^2)*((e*Sqrt[f] + I*d*Sqrt[g])*Log[I*Sqrt[f] - Sqrt[g]*x] + (e*Sqrt[f] - I*d*Sqrt[g])*Log[I*Sqrt[f] + Sqrt[g]*x])))/(Sqrt[f]*(e^2*f + d^2*g)*(f + g*x^2)) + (I*b^2*n^2*((-(Sqrt[g]*(d + e*x)*Log[d + e*x]^2) + 2*e*(I*Sqrt[f] + Sqrt[g]*x)*Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + 2*e*(I*Sqrt[f] + Sqrt[g]*x)*PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])])/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) + (Log[d + e*x]*(Sqrt[g]*(d + e*x)*Log[d + e*x] + (2*I)*e*(Sqrt[f] + I*Sqrt[g]*x)*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) + (2*I)*e*(Sqrt[f] + I*Sqrt[g]*x)*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])])/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x))))/Sqrt[f])/(4*g)","C",1
323,1,1209,814,2.3620331,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x \left(f+g x^2\right)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(x*(f + g*x^2)^2),x]","\frac{b^2 \left(4 \log \left(-\frac{e x}{d}\right) \log ^2(d+e x)-2 \log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log ^2(d+e x)-2 \log \left(1-\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log ^2(d+e x)-4 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log (d+e x)-4 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log (d+e x)+8 \text{Li}_2\left(\frac{e x}{d}+1\right) \log (d+e x)+\frac{\sqrt{f} \left(\log (d+e x) \left(i \sqrt{g} (d+e x) \log (d+e x)+2 e \left(\sqrt{f}-i \sqrt{g} x\right) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right)\right)+2 e \left(\sqrt{f}-i \sqrt{g} x\right) \text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right)}{\left(i \sqrt{g} d+e \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+\frac{\sqrt{f} \left(\log (d+e x) \left(2 e \left(i \sqrt{g} x+\sqrt{f}\right) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)-i \sqrt{g} (d+e x) \log (d+e x)\right)+2 e \left(i \sqrt{g} x+\sqrt{f}\right) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right)}{\left(e \sqrt{f}-i d \sqrt{g}\right) \left(i \sqrt{g} x+\sqrt{f}\right)}+4 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)+4 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)-8 \text{Li}_3\left(\frac{e x}{d}+1\right)\right) n^2+2 b \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(\frac{\sqrt{f} \left(e \left(i \sqrt{g} x+\sqrt{f}\right) \log \left(i \sqrt{f}-\sqrt{g} x\right)-i \sqrt{g} (d+e x) \log (d+e x)\right)}{\left(e \sqrt{f}-i d \sqrt{g}\right) \left(i \sqrt{g} x+\sqrt{f}\right)}+\frac{\sqrt{f} \left(i \sqrt{g} (d+e x) \log (d+e x)+e \left(\sqrt{f}-i \sqrt{g} x\right) \log \left(\sqrt{g} x+i \sqrt{f}\right)\right)}{\left(i \sqrt{g} d+e \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}-2 \left(\log (d+e x) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)+\text{Li}_2\left(-\frac{i \sqrt{g} (d+e x)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)-2 \left(\log (d+e x) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right)+\text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right)+4 \left(\log \left(-\frac{e x}{d}\right) \log (d+e x)+\text{Li}_2\left(\frac{e x}{d}+1\right)\right)\right) n+4 \log (x) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2+\frac{2 f \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2}{g x^2+f}-2 \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(g x^2+f\right)}{4 f^2}","-\frac{b^2 e \left(\sqrt{g} d+e \sqrt{-f}\right) \text{Li}_2\left(-\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{Li}_2\left(\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{Li}_3\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right) n^2}{f^2}+\frac{b^2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right) n^2}{f^2}-\frac{2 b^2 \text{Li}_3\left(\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{Li}_2\left(-\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{Li}_2\left(\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{Li}_2\left(\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,"((2*f*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2) + 4*Log[x]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 - 2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x^2] + 2*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((Sqrt[f]*((-I)*Sqrt[g]*(d + e*x)*Log[d + e*x] + e*(Sqrt[f] + I*Sqrt[g]*x)*Log[I*Sqrt[f] - Sqrt[g]*x]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) + (Sqrt[f]*(I*Sqrt[g]*(d + e*x)*Log[d + e*x] + e*(Sqrt[f] - I*Sqrt[g]*x)*Log[I*Sqrt[f] + Sqrt[g]*x]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) - 2*(Log[d + e*x]*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])] + PolyLog[2, ((-I)*Sqrt[g]*(d + e*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) - 2*(Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])]) + 4*(Log[-((e*x)/d)]*Log[d + e*x] + PolyLog[2, 1 + (e*x)/d])) + b^2*n^2*(4*Log[-((e*x)/d)]*Log[d + e*x]^2 - 2*Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + (Sqrt[f]*(Log[d + e*x]*(I*Sqrt[g]*(d + e*x)*Log[d + e*x] + 2*e*(Sqrt[f] - I*Sqrt[g]*x)*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])]) + 2*e*(Sqrt[f] - I*Sqrt[g]*x)*PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) - 4*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 4*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + (Sqrt[f]*(Log[d + e*x]*((-I)*Sqrt[g]*(d + e*x)*Log[d + e*x] + 2*e*(Sqrt[f] + I*Sqrt[g]*x)*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) + 2*e*(Sqrt[f] + I*Sqrt[g]*x)*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) + 8*Log[d + e*x]*PolyLog[2, 1 + (e*x)/d] + 4*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 4*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 8*PolyLog[3, 1 + (e*x)/d]))/(4*f^2)","C",1
324,1,1391,970,3.3079428,"\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","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(x^3*(f + g*x^2)^2),x]","\frac{b^2 \left(\frac{i \sqrt{f} g \left(-\sqrt{g} (d+e x) \log ^2(d+e x)+2 e \left(\sqrt{g} x+i \sqrt{f}\right) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right) \log (d+e x)+2 e \left(\sqrt{g} x+i \sqrt{f}\right) \text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right)}{\left(i \sqrt{g} d+e \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}-\frac{\sqrt{f} g \left(\log (d+e x) \left(2 e \left(i \sqrt{g} x+\sqrt{f}\right) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)-i \sqrt{g} (d+e x) \log (d+e x)\right)+2 e \left(i \sqrt{g} x+\sqrt{f}\right) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right)}{\left(e \sqrt{f}-i d \sqrt{g}\right) \left(i \sqrt{g} x+\sqrt{f}\right)}-\frac{2 f \left(-2 \log (x) e^2+2 \text{Li}_2\left(\frac{e x}{d}+1\right) e^2+\frac{\log (d+e x) \left(2 e^2 \log \left(-\frac{e x}{d}\right) x^2+(d+e x) (2 e x+(d-e x) \log (d+e x))\right)}{x^2}\right)}{d^2}+4 g \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right)+4 g \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right)-8 g \left(\log \left(-\frac{e x}{d}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{e x}{d}+1\right) \log (d+e x)-2 \text{Li}_3\left(\frac{e x}{d}+1\right)\right)\right) n^2+2 b \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(-\frac{2 f \left(e^2 \log (x) x^2+d e x+\left(d^2-e^2 x^2\right) \log (d+e x)\right)}{d^2 x^2}+\frac{i \sqrt{f} g \left(\sqrt{g} (d+e x) \log (d+e x)+i e \left(i \sqrt{g} x+\sqrt{f}\right) \log \left(i \sqrt{f}-\sqrt{g} x\right)\right)}{\left(e \sqrt{f}-i d \sqrt{g}\right) \left(i \sqrt{g} x+\sqrt{f}\right)}+\frac{i \sqrt{f} g \left(e \left(\sqrt{g} x+i \sqrt{f}\right) \log \left(\sqrt{g} x+i \sqrt{f}\right)-\sqrt{g} (d+e x) \log (d+e x)\right)}{\left(i \sqrt{g} d+e \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+4 g \left(\log (d+e x) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)+\text{Li}_2\left(-\frac{i \sqrt{g} (d+e x)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)+4 g \left(\log (d+e x) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right)+\text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right)-8 g \left(\log \left(-\frac{e x}{d}\right) \log (d+e x)+\text{Li}_2\left(\frac{e x}{d}+1\right)\right)\right) n-8 g \log (x) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2-\frac{2 f g \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2}{g x^2+f}-\frac{2 f \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2}{x^2}+4 g \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2 \log \left(g x^2+f\right)}{4 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{Li}_2\left(\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{Li}_2\left(-\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{Li}_2\left(\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{Li}_2\left(-\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{Li}_2\left(\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{Li}_2\left(\frac{e x}{d}+1\right)}{f^3}-\frac{2 b^2 g n^2 \text{Li}_3\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{f^3}-\frac{2 b^2 g n^2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{f^3}+\frac{4 b^2 g n^2 \text{Li}_3\left(\frac{e x}{d}+1\right)}{f^3}",1,"((-2*f*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2)/x^2 - (2*f*g*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2) - 8*g*Log[x]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 4*g*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2*Log[f + g*x^2] + 2*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((-2*f*(d*e*x + e^2*x^2*Log[x] + (d^2 - e^2*x^2)*Log[d + e*x]))/(d^2*x^2) + (I*Sqrt[f]*g*(Sqrt[g]*(d + e*x)*Log[d + e*x] + I*e*(Sqrt[f] + I*Sqrt[g]*x)*Log[I*Sqrt[f] - Sqrt[g]*x]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) + (I*Sqrt[f]*g*(-(Sqrt[g]*(d + e*x)*Log[d + e*x]) + e*(I*Sqrt[f] + Sqrt[g]*x)*Log[I*Sqrt[f] + Sqrt[g]*x]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) + 4*g*(Log[d + e*x]*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])] + PolyLog[2, ((-I)*Sqrt[g]*(d + e*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) + 4*g*(Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])]) - 8*g*(Log[-((e*x)/d)]*Log[d + e*x] + PolyLog[2, 1 + (e*x)/d])) + b^2*n^2*((I*Sqrt[f]*g*(-(Sqrt[g]*(d + e*x)*Log[d + e*x]^2) + 2*e*(I*Sqrt[f] + Sqrt[g]*x)*Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + 2*e*(I*Sqrt[f] + Sqrt[g]*x)*PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) - (Sqrt[f]*g*(Log[d + e*x]*((-I)*Sqrt[g]*(d + e*x)*Log[d + e*x] + 2*e*(Sqrt[f] + I*Sqrt[g]*x)*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) + 2*e*(Sqrt[f] + I*Sqrt[g]*x)*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) - (2*f*(-2*e^2*Log[x] + (Log[d + e*x]*(2*e^2*x^2*Log[-((e*x)/d)] + (d + e*x)*(2*e*x + (d - e*x)*Log[d + e*x])))/x^2 + 2*e^2*PolyLog[2, 1 + (e*x)/d]))/d^2 + 4*g*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]) + 4*g*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]) - 8*g*(Log[-((e*x)/d)]*Log[d + e*x]^2 + 2*Log[d + e*x]*PolyLog[2, 1 + (e*x)/d] - 2*PolyLog[3, 1 + (e*x)/d])))/(4*f^3)","C",1
325,1,1237,897,3.4981247,"\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","Integrate[(x^4*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2)^2,x]","\frac{b^2 \left(\frac{4 \sqrt{g} \left((d+e x) \log ^2(d+e x)-2 (d+e x) \log (d+e x)+2 e x\right)}{e}-\frac{f \left(-\sqrt{g} (d+e x) \log ^2(d+e x)+2 e \left(\sqrt{g} x+i \sqrt{f}\right) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right) \log (d+e x)+2 e \left(\sqrt{g} x+i \sqrt{f}\right) \text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right)}{\left(i \sqrt{g} d+e \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+\frac{f \left(\log (d+e x) \left(\sqrt{g} (d+e x) \log (d+e x)+2 i e \left(i \sqrt{g} x+\sqrt{f}\right) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)+2 i e \left(i \sqrt{g} x+\sqrt{f}\right) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right)}{\left(e \sqrt{f}-i d \sqrt{g}\right) \left(i \sqrt{g} x+\sqrt{f}\right)}-3 i \sqrt{f} \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right)+3 i \sqrt{f} \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right)\right) n^2+2 b \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(\frac{4 \sqrt{g} (d+e x) (\log (d+e x)-1)}{e}+\frac{f \left(\sqrt{g} (d+e x) \log (d+e x)+i e \left(i \sqrt{g} x+\sqrt{f}\right) \log \left(i \sqrt{f}-\sqrt{g} x\right)\right)}{\left(e \sqrt{f}-i d \sqrt{g}\right) \left(i \sqrt{g} x+\sqrt{f}\right)}+\frac{f \left(\sqrt{g} (d+e x) \log (d+e x)+e \left(-\sqrt{g} x-i \sqrt{f}\right) \log \left(\sqrt{g} x+i \sqrt{f}\right)\right)}{\left(i \sqrt{g} d+e \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+3 i \sqrt{f} \left(\log (d+e x) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)+\text{Li}_2\left(-\frac{i \sqrt{g} (d+e x)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)-3 i \sqrt{f} \left(\log (d+e x) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right)+\text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right)\right) n+4 \sqrt{g} x \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2-6 \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2+\frac{2 f \sqrt{g} x \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2}{g x^2+f}}{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{Li}_2\left(-\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{Li}_2\left(\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{Li}_3\left(-\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{Li}_3\left(\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{Li}_2\left(-\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{Li}_2\left(\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,"(4*Sqrt[g]*x*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + (2*f*Sqrt[g]*x*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2) - 6*Sqrt[f]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 2*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((4*Sqrt[g]*(d + e*x)*(-1 + Log[d + e*x]))/e + (f*(Sqrt[g]*(d + e*x)*Log[d + e*x] + I*e*(Sqrt[f] + I*Sqrt[g]*x)*Log[I*Sqrt[f] - Sqrt[g]*x]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) + (f*(Sqrt[g]*(d + e*x)*Log[d + e*x] + e*((-I)*Sqrt[f] - Sqrt[g]*x)*Log[I*Sqrt[f] + Sqrt[g]*x]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) + (3*I)*Sqrt[f]*(Log[d + e*x]*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])] + PolyLog[2, ((-I)*Sqrt[g]*(d + e*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) - (3*I)*Sqrt[f]*(Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])])) + b^2*n^2*((4*Sqrt[g]*(2*e*x - 2*(d + e*x)*Log[d + e*x] + (d + e*x)*Log[d + e*x]^2))/e - (f*(-(Sqrt[g]*(d + e*x)*Log[d + e*x]^2) + 2*e*(I*Sqrt[f] + Sqrt[g]*x)*Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + 2*e*(I*Sqrt[f] + Sqrt[g]*x)*PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) + (f*(Log[d + e*x]*(Sqrt[g]*(d + e*x)*Log[d + e*x] + (2*I)*e*(Sqrt[f] + I*Sqrt[g]*x)*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) + (2*I)*e*(Sqrt[f] + I*Sqrt[g]*x)*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) - (3*I)*Sqrt[f]*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]) + (3*I)*Sqrt[f]*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])])))/(4*g^(5/2))","C",1
326,1,1132,815,2.8227831,"\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","Integrate[(x^2*(a + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2)^2,x]","\frac{b^2 \left(\frac{-\sqrt{g} (d+e x) \log ^2(d+e x)+2 e \left(\sqrt{g} x+i \sqrt{f}\right) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right) \log (d+e x)+2 e \left(\sqrt{g} x+i \sqrt{f}\right) \text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)}{\left(i \sqrt{g} d+e \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}-\frac{\log (d+e x) \left(\sqrt{g} (d+e x) \log (d+e x)+2 i e \left(i \sqrt{g} x+\sqrt{f}\right) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)+2 i e \left(i \sqrt{g} x+\sqrt{f}\right) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)}{\left(e \sqrt{f}-i d \sqrt{g}\right) \left(i \sqrt{g} x+\sqrt{f}\right)}+\frac{i \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right)}{\sqrt{f}}-\frac{i \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right)}{\sqrt{f}}\right) n^2+2 b \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(\frac{e \left(\sqrt{g} x-i \sqrt{f}\right) \log \left(i \sqrt{f}-\sqrt{g} x\right)-\sqrt{g} (d+e x) \log (d+e x)}{\left(e \sqrt{f}-i d \sqrt{g}\right) \left(i \sqrt{g} x+\sqrt{f}\right)}+\frac{e \left(\sqrt{g} x+i \sqrt{f}\right) \log \left(\sqrt{g} x+i \sqrt{f}\right)-\sqrt{g} (d+e x) \log (d+e x)}{\left(i \sqrt{g} d+e \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}-\frac{i \left(\log (d+e x) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)+\text{Li}_2\left(-\frac{i \sqrt{g} (d+e x)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)}{\sqrt{f}}+\frac{i \left(\log (d+e x) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right)+\text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right)}{\sqrt{f}}\right) n+\frac{2 \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2}{\sqrt{f}}-\frac{2 \sqrt{g} x \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2}{g x^2+f}}{4 g^{3/2}}","-\frac{b^2 e \text{Li}_2\left(-\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{Li}_2\left(\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{Li}_3\left(-\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{Li}_3\left(\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{Li}_2\left(-\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{Li}_2\left(\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,"((-2*Sqrt[g]*x*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2) + (2*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2)/Sqrt[f] + 2*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((-(Sqrt[g]*(d + e*x)*Log[d + e*x]) + e*((-I)*Sqrt[f] + Sqrt[g]*x)*Log[I*Sqrt[f] - Sqrt[g]*x])/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) + (-(Sqrt[g]*(d + e*x)*Log[d + e*x]) + e*(I*Sqrt[f] + Sqrt[g]*x)*Log[I*Sqrt[f] + Sqrt[g]*x])/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) - (I*(Log[d + e*x]*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])] + PolyLog[2, ((-I)*Sqrt[g]*(d + e*x))/(e*Sqrt[f] - I*d*Sqrt[g])]))/Sqrt[f] + (I*(Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])]))/Sqrt[f]) + b^2*n^2*((-(Sqrt[g]*(d + e*x)*Log[d + e*x]^2) + 2*e*(I*Sqrt[f] + Sqrt[g]*x)*Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + 2*e*(I*Sqrt[f] + Sqrt[g]*x)*PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])])/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) - (Log[d + e*x]*(Sqrt[g]*(d + e*x)*Log[d + e*x] + (2*I)*e*(Sqrt[f] + I*Sqrt[g]*x)*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) + (2*I)*e*(Sqrt[f] + I*Sqrt[g]*x)*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])])/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) + (I*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]))/Sqrt[f] - (I*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]))/Sqrt[f]))/(4*g^(3/2))","C",1
327,1,1143,821,3.0785673,"\int \frac{\left(a+b \log \left(c (d+e x)^n\right)\right)^2}{\left(f+g x^2\right)^2} \, dx","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(f + g*x^2)^2,x]","\frac{\frac{b^2 \left(-\frac{\sqrt{f} \left(-\sqrt{g} (d+e x) \log ^2(d+e x)+2 e \left(\sqrt{g} x+i \sqrt{f}\right) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right) \log (d+e x)+2 e \left(\sqrt{g} x+i \sqrt{f}\right) \text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right)}{\left(i \sqrt{g} d+e \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+\frac{\sqrt{f} \left(\log (d+e x) \left(\sqrt{g} (d+e x) \log (d+e x)+2 i e \left(i \sqrt{g} x+\sqrt{f}\right) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)+2 i e \left(i \sqrt{g} x+\sqrt{f}\right) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right)}{\left(e \sqrt{f}-i d \sqrt{g}\right) \left(i \sqrt{g} x+\sqrt{f}\right)}+i \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right)-i \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right)\right) n^2}{\sqrt{g}}+\frac{2 b \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(\frac{\sqrt{f} \left(\sqrt{g} (d+e x) \log (d+e x)+i e \left(i \sqrt{g} x+\sqrt{f}\right) \log \left(i \sqrt{f}-\sqrt{g} x\right)\right)}{\left(e \sqrt{f}-i d \sqrt{g}\right) \left(i \sqrt{g} x+\sqrt{f}\right)}+\frac{\sqrt{f} \left(\sqrt{g} (d+e x) \log (d+e x)+e \left(-\sqrt{g} x-i \sqrt{f}\right) \log \left(\sqrt{g} x+i \sqrt{f}\right)\right)}{\left(i \sqrt{g} d+e \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}-i \left(\log (d+e x) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)+\text{Li}_2\left(-\frac{i \sqrt{g} (d+e x)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)+i \left(\log (d+e x) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right)+\text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right)\right) n}{\sqrt{g}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2}{\sqrt{g}}+\frac{2 \sqrt{f} x \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2}{g x^2+f}}{4 f^{3/2}}","-\frac{b^2 e \text{Li}_2\left(-\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{Li}_2\left(\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{Li}_3\left(-\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{Li}_3\left(\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{Li}_2\left(-\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{Li}_2\left(\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,"((2*Sqrt[f]*x*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2) + (2*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2)/Sqrt[g] + (2*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((Sqrt[f]*(Sqrt[g]*(d + e*x)*Log[d + e*x] + I*e*(Sqrt[f] + I*Sqrt[g]*x)*Log[I*Sqrt[f] - Sqrt[g]*x]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) + (Sqrt[f]*(Sqrt[g]*(d + e*x)*Log[d + e*x] + e*((-I)*Sqrt[f] - Sqrt[g]*x)*Log[I*Sqrt[f] + Sqrt[g]*x]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) - I*(Log[d + e*x]*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])] + PolyLog[2, ((-I)*Sqrt[g]*(d + e*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) + I*(Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])])))/Sqrt[g] + (b^2*n^2*(-((Sqrt[f]*(-(Sqrt[g]*(d + e*x)*Log[d + e*x]^2) + 2*e*(I*Sqrt[f] + Sqrt[g]*x)*Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + 2*e*(I*Sqrt[f] + Sqrt[g]*x)*PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))) + (Sqrt[f]*(Log[d + e*x]*(Sqrt[g]*(d + e*x)*Log[d + e*x] + (2*I)*e*(Sqrt[f] + I*Sqrt[g]*x)*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) + (2*I)*e*(Sqrt[f] + I*Sqrt[g]*x)*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) + I*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]) - I*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])])))/Sqrt[g])/(4*f^(3/2))","C",1
328,1,1304,919,3.6902036,"\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","Integrate[(a + b*Log[c*(d + e*x)^n])^2/(x^2*(f + g*x^2)^2),x]","\frac{b^2 \left(\frac{\sqrt{f} \sqrt{g} \left(-\sqrt{g} (d+e x) \log ^2(d+e x)+2 e \left(\sqrt{g} x+i \sqrt{f}\right) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right) \log (d+e x)+2 e \left(\sqrt{g} x+i \sqrt{f}\right) \text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right)}{\left(i \sqrt{g} d+e \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}-\frac{\sqrt{f} \sqrt{g} \left(\log (d+e x) \left(\sqrt{g} (d+e x) \log (d+e x)+2 i e \left(i \sqrt{g} x+\sqrt{f}\right) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)+2 i e \left(i \sqrt{g} x+\sqrt{f}\right) \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right)}{\left(e \sqrt{f}-i d \sqrt{g}\right) \left(i \sqrt{g} x+\sqrt{f}\right)}+\frac{4 \sqrt{f} \left(-\left((d+e x) \log ^2(d+e x)\right)+2 e x \log \left(-\frac{e x}{d}\right) \log (d+e x)+2 e x \text{Li}_2\left(\frac{e x}{d}+1\right)\right)}{d x}-3 i \sqrt{g} \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{d \sqrt{g}-i e \sqrt{f}}\right)\right)+3 i \sqrt{g} \left(\log \left(1-\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log ^2(d+e x)+2 \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right) \log (d+e x)-2 \text{Li}_3\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+i e \sqrt{f}}\right)\right)\right) n^2+2 b \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right) \left(\frac{4 \sqrt{f} (e x \log (x)-(d+e x) \log (d+e x))}{d x}-\frac{\sqrt{f} \sqrt{g} \left(\sqrt{g} (d+e x) \log (d+e x)+i e \left(i \sqrt{g} x+\sqrt{f}\right) \log \left(i \sqrt{f}-\sqrt{g} x\right)\right)}{\left(e \sqrt{f}-i d \sqrt{g}\right) \left(i \sqrt{g} x+\sqrt{f}\right)}+\frac{\sqrt{f} \sqrt{g} \left(e \left(\sqrt{g} x+i \sqrt{f}\right) \log \left(\sqrt{g} x+i \sqrt{f}\right)-\sqrt{g} (d+e x) \log (d+e x)\right)}{\left(i \sqrt{g} d+e \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+3 i \sqrt{g} \left(\log (d+e x) \log \left(\frac{e \left(i \sqrt{g} x+\sqrt{f}\right)}{e \sqrt{f}-i d \sqrt{g}}\right)+\text{Li}_2\left(-\frac{i \sqrt{g} (d+e x)}{e \sqrt{f}-i d \sqrt{g}}\right)\right)-3 i \sqrt{g} \left(\log (d+e x) \log \left(\frac{e \left(\sqrt{f}-i \sqrt{g} x\right)}{i \sqrt{g} d+e \sqrt{f}}\right)+\text{Li}_2\left(\frac{i \sqrt{g} (d+e x)}{i \sqrt{g} d+e \sqrt{f}}\right)\right)\right) n-6 \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2-\frac{4 \sqrt{f} \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2}{x}-\frac{2 \sqrt{f} g x \left(a-b n \log (d+e x)+b \log \left(c (d+e x)^n\right)\right)^2}{g x^2+f}}{4 f^{5/2}}","\frac{b^2 e \sqrt{g} \text{Li}_2\left(-\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{Li}_2\left(\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{Li}_2\left(\frac{e x}{d}+1\right) n^2}{d f^2}-\frac{3 b^2 \sqrt{g} \text{Li}_3\left(-\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{Li}_3\left(\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{Li}_2\left(-\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{Li}_2\left(\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,"((-4*Sqrt[f]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2)/x - (2*Sqrt[f]*g*x*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2)/(f + g*x^2) - 6*Sqrt[g]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 2*b*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((4*Sqrt[f]*(e*x*Log[x] - (d + e*x)*Log[d + e*x]))/(d*x) - (Sqrt[f]*Sqrt[g]*(Sqrt[g]*(d + e*x)*Log[d + e*x] + I*e*(Sqrt[f] + I*Sqrt[g]*x)*Log[I*Sqrt[f] - Sqrt[g]*x]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) + (Sqrt[f]*Sqrt[g]*(-(Sqrt[g]*(d + e*x)*Log[d + e*x]) + e*(I*Sqrt[f] + Sqrt[g]*x)*Log[I*Sqrt[f] + Sqrt[g]*x]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) + (3*I)*Sqrt[g]*(Log[d + e*x]*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])] + PolyLog[2, ((-I)*Sqrt[g]*(d + e*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) - (3*I)*Sqrt[g]*(Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])])) + b^2*n^2*((Sqrt[f]*Sqrt[g]*(-(Sqrt[g]*(d + e*x)*Log[d + e*x]^2) + 2*e*(I*Sqrt[f] + Sqrt[g]*x)*Log[d + e*x]*Log[(e*(Sqrt[f] - I*Sqrt[g]*x))/(e*Sqrt[f] + I*d*Sqrt[g])] + 2*e*(I*Sqrt[f] + Sqrt[g]*x)*PolyLog[2, (I*Sqrt[g]*(d + e*x))/(e*Sqrt[f] + I*d*Sqrt[g])]))/((e*Sqrt[f] + I*d*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x)) - (Sqrt[f]*Sqrt[g]*(Log[d + e*x]*(Sqrt[g]*(d + e*x)*Log[d + e*x] + (2*I)*e*(Sqrt[f] + I*Sqrt[g]*x)*Log[(e*(Sqrt[f] + I*Sqrt[g]*x))/(e*Sqrt[f] - I*d*Sqrt[g])]) + (2*I)*e*(Sqrt[f] + I*Sqrt[g]*x)*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])]))/((e*Sqrt[f] - I*d*Sqrt[g])*(Sqrt[f] + I*Sqrt[g]*x)) + (4*Sqrt[f]*(2*e*x*Log[-((e*x)/d)]*Log[d + e*x] - (d + e*x)*Log[d + e*x]^2 + 2*e*x*PolyLog[2, 1 + (e*x)/d]))/(d*x) - (3*I)*Sqrt[g]*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/((-I)*e*Sqrt[f] + d*Sqrt[g])]) + (3*I)*Sqrt[g]*(Log[d + e*x]^2*Log[1 - (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] + 2*Log[d + e*x]*PolyLog[2, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])] - 2*PolyLog[3, (Sqrt[g]*(d + e*x))/(I*e*Sqrt[f] + d*Sqrt[g])])))/(4*f^(5/2))","C",1
329,1,754,477,0.3256898,"\int \frac{\log ^3\left(c (a+b x)^n\right)}{d+e x^2} \, dx","Integrate[Log[c*(a + b*x)^n]^3/(d + e*x^2),x]","\frac{-6 i n^2 \log \left(c (a+b x)^n\right) \text{Li}_3\left(\frac{\sqrt{e} (a+b x)}{a \sqrt{e}-i b \sqrt{d}}\right)+6 i n^2 \log \left(c (a+b x)^n\right) \text{Li}_3\left(\frac{\sqrt{e} (a+b x)}{\sqrt{e} a+i b \sqrt{d}}\right)-3 i n^2 \log ^2(a+b x) \log \left(c (a+b x)^n\right) \log \left(1-\frac{\sqrt{e} (a+b x)}{a \sqrt{e}-i b \sqrt{d}}\right)+3 i n^2 \log ^2(a+b x) \log \left(c (a+b x)^n\right) \log \left(1-\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+i b \sqrt{d}}\right)+6 n^2 \log ^2(a+b x) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c (a+b x)^n\right)+3 i n \log ^2\left(c (a+b x)^n\right) \text{Li}_2\left(\frac{\sqrt{e} (a+b x)}{a \sqrt{e}-i b \sqrt{d}}\right)-3 i n \log ^2\left(c (a+b x)^n\right) \text{Li}_2\left(\frac{\sqrt{e} (a+b x)}{\sqrt{e} a+i b \sqrt{d}}\right)+3 i n \log (a+b x) \log ^2\left(c (a+b x)^n\right) \log \left(1-\frac{\sqrt{e} (a+b x)}{a \sqrt{e}-i b \sqrt{d}}\right)-3 i n \log (a+b x) \log ^2\left(c (a+b x)^n\right) \log \left(1-\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+i b \sqrt{d}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log ^3\left(c (a+b x)^n\right)-6 n \log (a+b x) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log ^2\left(c (a+b x)^n\right)+6 i n^3 \text{Li}_4\left(\frac{\sqrt{e} (a+b x)}{a \sqrt{e}-i b \sqrt{d}}\right)-6 i n^3 \text{Li}_4\left(\frac{\sqrt{e} (a+b x)}{\sqrt{e} a+i b \sqrt{d}}\right)+i n^3 \log ^3(a+b x) \log \left(1-\frac{\sqrt{e} (a+b x)}{a \sqrt{e}-i b \sqrt{d}}\right)-i n^3 \log ^3(a+b x) \log \left(1-\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+i b \sqrt{d}}\right)-2 n^3 \log ^3(a+b x) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 \sqrt{d} \sqrt{e}}","\frac{3 n^2 \log \left(c (a+b x)^n\right) \text{Li}_3\left(-\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{Li}_3\left(\frac{\sqrt{e} (a+b x)}{\sqrt{e} a+b \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{3 n \log ^2\left(c (a+b x)^n\right) \text{Li}_2\left(-\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{Li}_2\left(\frac{\sqrt{e} (a+b x)}{\sqrt{e} a+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)}{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^3 \text{Li}_4\left(-\frac{\sqrt{e} (a+b x)}{b \sqrt{-d}-a \sqrt{e}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{3 n^3 \text{Li}_4\left(\frac{\sqrt{e} (a+b x)}{\sqrt{e} a+b \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}",1,"(-2*n^3*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[a + b*x]^3 + 6*n^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[a + b*x]^2*Log[c*(a + b*x)^n] - 6*n*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[a + b*x]*Log[c*(a + b*x)^n]^2 + 2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(a + b*x)^n]^3 + I*n^3*Log[a + b*x]^3*Log[1 - (Sqrt[e]*(a + b*x))/((-I)*b*Sqrt[d] + a*Sqrt[e])] - (3*I)*n^2*Log[a + b*x]^2*Log[c*(a + b*x)^n]*Log[1 - (Sqrt[e]*(a + b*x))/((-I)*b*Sqrt[d] + a*Sqrt[e])] + (3*I)*n*Log[a + b*x]*Log[c*(a + b*x)^n]^2*Log[1 - (Sqrt[e]*(a + b*x))/((-I)*b*Sqrt[d] + a*Sqrt[e])] - I*n^3*Log[a + b*x]^3*Log[1 - (Sqrt[e]*(a + b*x))/(I*b*Sqrt[d] + a*Sqrt[e])] + (3*I)*n^2*Log[a + b*x]^2*Log[c*(a + b*x)^n]*Log[1 - (Sqrt[e]*(a + b*x))/(I*b*Sqrt[d] + a*Sqrt[e])] - (3*I)*n*Log[a + b*x]*Log[c*(a + b*x)^n]^2*Log[1 - (Sqrt[e]*(a + b*x))/(I*b*Sqrt[d] + a*Sqrt[e])] + (3*I)*n*Log[c*(a + b*x)^n]^2*PolyLog[2, (Sqrt[e]*(a + b*x))/((-I)*b*Sqrt[d] + a*Sqrt[e])] - (3*I)*n*Log[c*(a + b*x)^n]^2*PolyLog[2, (Sqrt[e]*(a + b*x))/(I*b*Sqrt[d] + a*Sqrt[e])] - (6*I)*n^2*Log[c*(a + b*x)^n]*PolyLog[3, (Sqrt[e]*(a + b*x))/((-I)*b*Sqrt[d] + a*Sqrt[e])] + (6*I)*n^2*Log[c*(a + b*x)^n]*PolyLog[3, (Sqrt[e]*(a + b*x))/(I*b*Sqrt[d] + a*Sqrt[e])] + (6*I)*n^3*PolyLog[4, (Sqrt[e]*(a + b*x))/((-I)*b*Sqrt[d] + a*Sqrt[e])] - (6*I)*n^3*PolyLog[4, (Sqrt[e]*(a + b*x))/(I*b*Sqrt[d] + a*Sqrt[e])])/(2*Sqrt[d]*Sqrt[e])","C",1
330,1,488,347,0.1822412,"\int \frac{\log ^2\left(c (a+b x)^n\right)}{d+e x^2} \, dx","Integrate[Log[c*(a + b*x)^n]^2/(d + e*x^2),x]","\frac{2 i n \log \left(c (a+b x)^n\right) \text{Li}_2\left(\frac{\sqrt{e} (a+b x)}{a \sqrt{e}-i b \sqrt{d}}\right)-2 i n \log \left(c (a+b x)^n\right) \text{Li}_2\left(\frac{\sqrt{e} (a+b x)}{\sqrt{e} a+i b \sqrt{d}}\right)+2 i n \log (a+b x) \log \left(c (a+b x)^n\right) \log \left(1-\frac{\sqrt{e} (a+b x)}{a \sqrt{e}-i b \sqrt{d}}\right)-2 i n \log (a+b x) \log \left(c (a+b x)^n\right) \log \left(1-\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+i b \sqrt{d}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log ^2\left(c (a+b x)^n\right)-4 n \log (a+b x) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c (a+b x)^n\right)-2 i n^2 \text{Li}_3\left(\frac{\sqrt{e} (a+b x)}{a \sqrt{e}-i b \sqrt{d}}\right)+2 i n^2 \text{Li}_3\left(\frac{\sqrt{e} (a+b x)}{\sqrt{e} a+i b \sqrt{d}}\right)-i n^2 \log ^2(a+b x) \log \left(1-\frac{\sqrt{e} (a+b x)}{a \sqrt{e}-i b \sqrt{d}}\right)+i n^2 \log ^2(a+b x) \log \left(1-\frac{\sqrt{e} (a+b x)}{a \sqrt{e}+i b \sqrt{d}}\right)+2 n^2 \log ^2(a+b x) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 \sqrt{d} \sqrt{e}}","-\frac{n \log \left(c (a+b x)^n\right) \text{Li}_2\left(-\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{Li}_2\left(\frac{\sqrt{e} (a+b x)}{\sqrt{e} a+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^2 \text{Li}_3\left(-\frac{\sqrt{e} (a+b x)}{b \sqrt{-d}-a \sqrt{e}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{n^2 \text{Li}_3\left(\frac{\sqrt{e} (a+b x)}{\sqrt{e} a+b \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}",1,"(2*n^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[a + b*x]^2 - 4*n*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[a + b*x]*Log[c*(a + b*x)^n] + 2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(a + b*x)^n]^2 - I*n^2*Log[a + b*x]^2*Log[1 - (Sqrt[e]*(a + b*x))/((-I)*b*Sqrt[d] + a*Sqrt[e])] + (2*I)*n*Log[a + b*x]*Log[c*(a + b*x)^n]*Log[1 - (Sqrt[e]*(a + b*x))/((-I)*b*Sqrt[d] + a*Sqrt[e])] + I*n^2*Log[a + b*x]^2*Log[1 - (Sqrt[e]*(a + b*x))/(I*b*Sqrt[d] + a*Sqrt[e])] - (2*I)*n*Log[a + b*x]*Log[c*(a + b*x)^n]*Log[1 - (Sqrt[e]*(a + b*x))/(I*b*Sqrt[d] + a*Sqrt[e])] + (2*I)*n*Log[c*(a + b*x)^n]*PolyLog[2, (Sqrt[e]*(a + b*x))/((-I)*b*Sqrt[d] + a*Sqrt[e])] - (2*I)*n*Log[c*(a + b*x)^n]*PolyLog[2, (Sqrt[e]*(a + b*x))/(I*b*Sqrt[d] + a*Sqrt[e])] - (2*I)*n^2*PolyLog[3, (Sqrt[e]*(a + b*x))/((-I)*b*Sqrt[d] + a*Sqrt[e])] + (2*I)*n^2*PolyLog[3, (Sqrt[e]*(a + b*x))/(I*b*Sqrt[d] + a*Sqrt[e])])/(2*Sqrt[d]*Sqrt[e])","C",1
331,1,178,229,0.1123735,"\int \frac{\log \left(c (a+b x)^n\right)}{d+e x^2} \, dx","Integrate[Log[c*(a + b*x)^n]/(d + e*x^2),x]","\frac{\log \left(c (a+b x)^n\right) \left(\log \left(\frac{b \left(\sqrt{-d}-\sqrt{e} x\right)}{a \sqrt{e}+b \sqrt{-d}}\right)-\log \left(\frac{b \left(\sqrt{-d}+\sqrt{e} x\right)}{b \sqrt{-d}-a \sqrt{e}}\right)\right)-n \text{Li}_2\left(-\frac{\sqrt{e} (a+b x)}{b \sqrt{-d}-a \sqrt{e}}\right)+n \text{Li}_2\left(\frac{\sqrt{e} (a+b x)}{\sqrt{e} a+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{Li}_2\left(-\frac{\sqrt{e} (a+b x)}{b \sqrt{-d}-a \sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{n \text{Li}_2\left(\frac{\sqrt{e} (a+b x)}{\sqrt{e} a+b \sqrt{-d}}\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])] - Log[(b*(Sqrt[-d] + Sqrt[e]*x))/(b*Sqrt[-d] - a*Sqrt[e])]) - n*PolyLog[2, -((Sqrt[e]*(a + b*x))/(b*Sqrt[-d] - a*Sqrt[e]))] + n*PolyLog[2, (Sqrt[e]*(a + b*x))/(b*Sqrt[-d] + a*Sqrt[e])])/(2*Sqrt[-d]*Sqrt[e])","A",1
332,0,0,90,0.4234795,"\int \frac{1}{\left(d+e x^2\right) \log \left(c (a+b x)^n\right)} \, dx","Integrate[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,"Integrate[1/((d + e*x^2)*Log[c*(a + b*x)^n]), x]","A",-1
333,1,29,27,0.0219599,"\int \frac{\log \left(c-\frac{a (1-c) x^{-m}}{b}\right)}{x \left(a+b x^m\right)} \, dx","Integrate[Log[c - (a*(1 - c))/(b*x^m)]/(x*(a + b*x^m)),x]","\frac{\text{Li}_2\left(-\frac{(c-1) x^{-m} \left(b x^m+a\right)}{b}\right)}{a m}","\frac{\text{Li}_2\left(\frac{(1-c) \left(a x^{-m}+b\right)}{b}\right)}{a m}",1,"PolyLog[2, -(((-1 + c)*(a + b*x^m))/(b*x^m))]/(a*m)","A",1
334,1,29,27,0.0079782,"\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","Integrate[Log[(-a + a*c + b*c*x^m)/(b*x^m)]/(x*(a + b*x^m)),x]","\frac{\text{Li}_2\left(-\frac{(c-1) x^{-m} \left(b x^m+a\right)}{b}\right)}{a m}","\frac{\text{Li}_2\left(\frac{(1-c) \left(a x^{-m}+b\right)}{b}\right)}{a m}",1,"PolyLog[2, -(((-1 + c)*(a + b*x^m))/(b*x^m))]/(a*m)","A",1
335,1,31,28,0.0233331,"\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","Integrate[Log[c*(a - (d - a*c*d)/(c*e*x^m))]/(x*(d + e*x^m)),x]","\frac{\text{Li}_2\left(-\frac{(a c-1) x^{-m} \left(e x^m+d\right)}{e}\right)}{d m}","\frac{\text{Li}_2\left(\frac{(1-a c) \left(d x^{-m}+e\right)}{e}\right)}{d m}",1,"PolyLog[2, -(((-1 + a*c)*(d + e*x^m))/(e*x^m))]/(d*m)","A",1
336,1,31,28,0.0077349,"\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","Integrate[Log[(-d + a*c*d + a*c*e*x^m)/(e*x^m)]/(x*(d + e*x^m)),x]","\frac{\text{Li}_2\left(-\frac{(a c-1) x^{-m} \left(e x^m+d\right)}{e}\right)}{d m}","\frac{\text{Li}_2\left(\frac{(1-a c) \left(d x^{-m}+e\right)}{e}\right)}{d m}",1,"PolyLog[2, -(((-1 + a*c)*(d + e*x^m))/(e*x^m))]/(d*m)","A",1
337,1,27,24,0.0056231,"\int \frac{\log \left(\frac{2 a}{a+b x}\right)}{a^2-b^2 x^2} \, dx","Integrate[Log[(2*a)/(a + b*x)]/(a^2 - b^2*x^2),x]","\frac{\text{Li}_2\left(\frac{b x-a}{a+b x}\right)}{2 a b}","\frac{\text{Li}_2\left(1-\frac{2 a}{a+b x}\right)}{2 a b}",1,"PolyLog[2, (-a + b*x)/(a + b*x)]/(2*a*b)","A",1
338,1,27,24,0.0040113,"\int \frac{\log \left(\frac{2 a}{a+b x}\right)}{(a-b x) (a+b x)} \, dx","Integrate[Log[(2*a)/(a + b*x)]/((a - b*x)*(a + b*x)),x]","\frac{\text{Li}_2\left(\frac{b x-a}{a+b x}\right)}{2 a b}","\frac{\text{Li}_2\left(1-\frac{2 a}{a+b x}\right)}{2 a b}",1,"PolyLog[2, (-a + b*x)/(a + b*x)]/(2*a*b)","A",1
339,1,252,37,0.1973792,"\int \frac{\log \left(\frac{a (1-c)+b (1+c) x}{a+b x}\right)}{a^2-b^2 x^2} \, dx","Integrate[Log[(a*(1 - c) + b*(1 + c)*x)/(a + b*x)]/(a^2 - b^2*x^2),x]","\frac{2 \text{Li}_2\left(\frac{(c+1) (a-b x)}{2 a}\right)-2 \text{Li}_2\left(\frac{(c+1) (a+b x)}{2 a c}\right)+\log ^2\left(\frac{2 a c}{(c+1) (a+b x)}\right)+2 \log \left(-\frac{a (-c)+a+b (c+1) x}{2 a c}\right) \log \left(\frac{2 a c}{(c+1) (a+b x)}\right)-2 \log \left(\frac{a (-c)+a+b (c+1) x}{a+b x}\right) \log \left(\frac{2 a c}{(c+1) (a+b x)}\right)+2 \log (a-b x) \log \left(\frac{a (-c)+a+b (c+1) x}{2 a}\right)-2 \log (a-b x) \log \left(\frac{a (-c)+a+b (c+1) x}{a+b x}\right)-2 \text{Li}_2\left(\frac{a-b x}{2 a}\right)-2 \log (a-b x) \log \left(\frac{a+b x}{2 a}\right)}{4 a b}","\frac{\text{Li}_2\left(1-\frac{a (1-c)+b (c+1) x}{a+b x}\right)}{2 a b}",1,"(Log[(2*a*c)/((1 + c)*(a + b*x))]^2 - 2*Log[a - b*x]*Log[(a + b*x)/(2*a)] + 2*Log[a - b*x]*Log[(a - a*c + b*(1 + c)*x)/(2*a)] + 2*Log[(2*a*c)/((1 + c)*(a + b*x))]*Log[-1/2*(a - a*c + b*(1 + c)*x)/(a*c)] - 2*Log[a - b*x]*Log[(a - a*c + b*(1 + c)*x)/(a + b*x)] - 2*Log[(2*a*c)/((1 + c)*(a + b*x))]*Log[(a - a*c + b*(1 + c)*x)/(a + b*x)] - 2*PolyLog[2, (a - b*x)/(2*a)] + 2*PolyLog[2, ((1 + c)*(a - b*x))/(2*a)] - 2*PolyLog[2, ((1 + c)*(a + b*x))/(2*a*c)])/(4*a*b)","B",1
340,1,252,27,0.1622343,"\int \frac{\log \left(\frac{a (1-c)+b (1+c) x}{a+b x}\right)}{(a-b x) (a+b x)} \, dx","Integrate[Log[(a*(1 - c) + b*(1 + c)*x)/(a + b*x)]/((a - b*x)*(a + b*x)),x]","\frac{2 \text{Li}_2\left(\frac{(c+1) (a-b x)}{2 a}\right)-2 \text{Li}_2\left(\frac{(c+1) (a+b x)}{2 a c}\right)+\log ^2\left(\frac{2 a c}{(c+1) (a+b x)}\right)+2 \log \left(-\frac{a (-c)+a+b (c+1) x}{2 a c}\right) \log \left(\frac{2 a c}{(c+1) (a+b x)}\right)-2 \log \left(\frac{a (-c)+a+b (c+1) x}{a+b x}\right) \log \left(\frac{2 a c}{(c+1) (a+b x)}\right)+2 \log (a-b x) \log \left(\frac{a (-c)+a+b (c+1) x}{2 a}\right)-2 \log (a-b x) \log \left(\frac{a (-c)+a+b (c+1) x}{a+b x}\right)-2 \text{Li}_2\left(\frac{a-b x}{2 a}\right)-2 \log (a-b x) \log \left(\frac{a+b x}{2 a}\right)}{4 a b}","\frac{\text{Li}_2\left(\frac{c (a-b x)}{a+b x}\right)}{2 a b}",1,"(Log[(2*a*c)/((1 + c)*(a + b*x))]^2 - 2*Log[a - b*x]*Log[(a + b*x)/(2*a)] + 2*Log[a - b*x]*Log[(a - a*c + b*(1 + c)*x)/(2*a)] + 2*Log[(2*a*c)/((1 + c)*(a + b*x))]*Log[-1/2*(a - a*c + b*(1 + c)*x)/(a*c)] - 2*Log[a - b*x]*Log[(a - a*c + b*(1 + c)*x)/(a + b*x)] - 2*Log[(2*a*c)/((1 + c)*(a + b*x))]*Log[(a - a*c + b*(1 + c)*x)/(a + b*x)] - 2*PolyLog[2, (a - b*x)/(2*a)] + 2*PolyLog[2, ((1 + c)*(a - b*x))/(2*a)] - 2*PolyLog[2, ((1 + c)*(a + b*x))/(2*a*c)])/(4*a*b)","B",1
341,1,252,27,0.1456636,"\int \frac{\log \left(1-\frac{c (a-b x)}{a+b x}\right)}{a^2-b^2 x^2} \, dx","Integrate[Log[1 - (c*(a - b*x))/(a + b*x)]/(a^2 - b^2*x^2),x]","\frac{2 \text{Li}_2\left(\frac{(c+1) (a-b x)}{2 a}\right)-2 \text{Li}_2\left(\frac{(c+1) (a+b x)}{2 a c}\right)+\log ^2\left(\frac{2 a c}{(c+1) (a+b x)}\right)+2 \log \left(-\frac{a (-c)+a+b (c+1) x}{2 a c}\right) \log \left(\frac{2 a c}{(c+1) (a+b x)}\right)-2 \log \left(\frac{a (-c)+a+b (c+1) x}{a+b x}\right) \log \left(\frac{2 a c}{(c+1) (a+b x)}\right)+2 \log (a-b x) \log \left(\frac{a (-c)+a+b (c+1) x}{2 a}\right)-2 \log (a-b x) \log \left(\frac{a (-c)+a+b (c+1) x}{a+b x}\right)-2 \text{Li}_2\left(\frac{a-b x}{2 a}\right)-2 \log (a-b x) \log \left(\frac{a+b x}{2 a}\right)}{4 a b}","\frac{\text{Li}_2\left(\frac{c (a-b x)}{a+b x}\right)}{2 a b}",1,"(Log[(2*a*c)/((1 + c)*(a + b*x))]^2 - 2*Log[a - b*x]*Log[(a + b*x)/(2*a)] + 2*Log[a - b*x]*Log[(a - a*c + b*(1 + c)*x)/(2*a)] + 2*Log[(2*a*c)/((1 + c)*(a + b*x))]*Log[-1/2*(a - a*c + b*(1 + c)*x)/(a*c)] - 2*Log[a - b*x]*Log[(a - a*c + b*(1 + c)*x)/(a + b*x)] - 2*Log[(2*a*c)/((1 + c)*(a + b*x))]*Log[(a - a*c + b*(1 + c)*x)/(a + b*x)] - 2*PolyLog[2, (a - b*x)/(2*a)] + 2*PolyLog[2, ((1 + c)*(a - b*x))/(2*a)] - 2*PolyLog[2, ((1 + c)*(a + b*x))/(2*a*c)])/(4*a*b)","B",1
342,1,252,27,0.1597065,"\int \frac{\log \left(1-\frac{c (a-b x)}{a+b x}\right)}{(a-b x) (a+b x)} \, dx","Integrate[Log[1 - (c*(a - b*x))/(a + b*x)]/((a - b*x)*(a + b*x)),x]","\frac{2 \text{Li}_2\left(\frac{(c+1) (a-b x)}{2 a}\right)-2 \text{Li}_2\left(\frac{(c+1) (a+b x)}{2 a c}\right)+\log ^2\left(\frac{2 a c}{(c+1) (a+b x)}\right)+2 \log \left(-\frac{a (-c)+a+b (c+1) x}{2 a c}\right) \log \left(\frac{2 a c}{(c+1) (a+b x)}\right)-2 \log \left(\frac{a (-c)+a+b (c+1) x}{a+b x}\right) \log \left(\frac{2 a c}{(c+1) (a+b x)}\right)+2 \log (a-b x) \log \left(\frac{a (-c)+a+b (c+1) x}{2 a}\right)-2 \log (a-b x) \log \left(\frac{a (-c)+a+b (c+1) x}{a+b x}\right)-2 \text{Li}_2\left(\frac{a-b x}{2 a}\right)-2 \log (a-b x) \log \left(\frac{a+b x}{2 a}\right)}{4 a b}","\frac{\text{Li}_2\left(\frac{c (a-b x)}{a+b x}\right)}{2 a b}",1,"(Log[(2*a*c)/((1 + c)*(a + b*x))]^2 - 2*Log[a - b*x]*Log[(a + b*x)/(2*a)] + 2*Log[a - b*x]*Log[(a - a*c + b*(1 + c)*x)/(2*a)] + 2*Log[(2*a*c)/((1 + c)*(a + b*x))]*Log[-1/2*(a - a*c + b*(1 + c)*x)/(a*c)] - 2*Log[a - b*x]*Log[(a - a*c + b*(1 + c)*x)/(a + b*x)] - 2*Log[(2*a*c)/((1 + c)*(a + b*x))]*Log[(a - a*c + b*(1 + c)*x)/(a + b*x)] - 2*PolyLog[2, (a - b*x)/(2*a)] + 2*PolyLog[2, ((1 + c)*(a - b*x))/(2*a)] - 2*PolyLog[2, ((1 + c)*(a + b*x))/(2*a*c)])/(4*a*b)","B",1
343,1,494,238,0.2247425,"\int \frac{\log ^3\left(c (a+b x)^n\right)}{d x+e x^2} \, dx","Integrate[Log[c*(a + b*x)^n]^3/(d*x + e*x^2),x]","\frac{-3 n^2 \left(n \log (a+b x)-\log \left(c (a+b x)^n\right)\right) \left(2 \text{Li}_3\left(\frac{e (a+b x)}{a e-b d}\right)-2 \log (a+b x) \text{Li}_2\left(\frac{e (a+b x)}{a e-b d}\right)-\log ^2(a+b x) \log \left(\frac{b (d+e x)}{b d-a e}\right)-2 \text{Li}_3\left(\frac{b x}{a}+1\right)+2 \text{Li}_2\left(\frac{b x}{a}+1\right) \log (a+b x)+\log \left(-\frac{b x}{a}\right) \log ^2(a+b x)\right)+3 n \left(\log \left(c (a+b x)^n\right)-n \log (a+b x)\right)^2 \left(-\text{Li}_2\left(\frac{e (a+b x)}{a e-b d}\right)-\log (a+b x) \log \left(\frac{b (d+e x)}{b d-a e}\right)-\text{Li}_2\left(-\frac{b x}{a}\right)+\log (x) \left(\log (a+b x)-\log \left(\frac{b x}{a}+1\right)\right)\right)+\log (d+e x) \left(n \log (a+b x)-\log \left(c (a+b x)^n\right)\right)^3-\log (x) \left(n \log (a+b x)-\log \left(c (a+b x)^n\right)\right)^3+n^3 \left(-6 \text{Li}_4\left(\frac{e (a+b x)}{a e-b d}\right)-3 \log ^2(a+b x) \text{Li}_2\left(\frac{e (a+b x)}{a e-b d}\right)+6 \log (a+b x) \text{Li}_3\left(\frac{e (a+b x)}{a e-b d}\right)-\log ^3(a+b x) \log \left(\frac{b (d+e x)}{b d-a e}\right)+6 \text{Li}_4\left(\frac{b x}{a}+1\right)+3 \text{Li}_2\left(\frac{b x}{a}+1\right) \log ^2(a+b x)-6 \text{Li}_3\left(\frac{b x}{a}+1\right) \log (a+b x)+\log \left(-\frac{b x}{a}\right) \log ^3(a+b x)\right)}{d}","\frac{6 n^2 \log \left(c (a+b x)^n\right) \text{Li}_3\left(-\frac{e (a+b x)}{b d-a e}\right)}{d}-\frac{3 n \log ^2\left(c (a+b x)^n\right) \text{Li}_2\left(-\frac{e (a+b x)}{b d-a e}\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{6 n^2 \text{Li}_3\left(\frac{b x}{a}+1\right) \log \left(c (a+b x)^n\right)}{d}+\frac{3 n \text{Li}_2\left(\frac{b x}{a}+1\right) \log ^2\left(c (a+b x)^n\right)}{d}+\frac{\log \left(-\frac{b x}{a}\right) \log ^3\left(c (a+b x)^n\right)}{d}-\frac{6 n^3 \text{Li}_4\left(-\frac{e (a+b x)}{b d-a e}\right)}{d}+\frac{6 n^3 \text{Li}_4\left(\frac{b x}{a}+1\right)}{d}",1,"(-(Log[x]*(n*Log[a + b*x] - Log[c*(a + b*x)^n])^3) + (n*Log[a + b*x] - Log[c*(a + b*x)^n])^3*Log[d + e*x] + 3*n*(-(n*Log[a + b*x]) + Log[c*(a + b*x)^n])^2*(Log[x]*(Log[a + b*x] - Log[1 + (b*x)/a]) - Log[a + b*x]*Log[(b*(d + e*x))/(b*d - a*e)] - PolyLog[2, -((b*x)/a)] - PolyLog[2, (e*(a + b*x))/(-(b*d) + a*e)]) - 3*n^2*(n*Log[a + b*x] - Log[c*(a + b*x)^n])*(Log[-((b*x)/a)]*Log[a + b*x]^2 - Log[a + b*x]^2*Log[(b*(d + e*x))/(b*d - a*e)] - 2*Log[a + b*x]*PolyLog[2, (e*(a + b*x))/(-(b*d) + a*e)] + 2*Log[a + b*x]*PolyLog[2, 1 + (b*x)/a] + 2*PolyLog[3, (e*(a + b*x))/(-(b*d) + a*e)] - 2*PolyLog[3, 1 + (b*x)/a]) + n^3*(Log[-((b*x)/a)]*Log[a + b*x]^3 - Log[a + b*x]^3*Log[(b*(d + e*x))/(b*d - a*e)] - 3*Log[a + b*x]^2*PolyLog[2, (e*(a + b*x))/(-(b*d) + a*e)] + 3*Log[a + b*x]^2*PolyLog[2, 1 + (b*x)/a] + 6*Log[a + b*x]*PolyLog[3, (e*(a + b*x))/(-(b*d) + a*e)] - 6*Log[a + b*x]*PolyLog[3, 1 + (b*x)/a] - 6*PolyLog[4, (e*(a + b*x))/(-(b*d) + a*e)] + 6*PolyLog[4, 1 + (b*x)/a]))/d","B",1
344,1,292,168,0.1413776,"\int \frac{\log ^2\left(c (a+b x)^n\right)}{d x+e x^2} \, dx","Integrate[Log[c*(a + b*x)^n]^2/(d*x + e*x^2),x]","\frac{-2 n \left(n \log (a+b x)-\log \left(c (a+b x)^n\right)\right) \left(-\text{Li}_2\left(\frac{e (a+b x)}{a e-b d}\right)-\log (a+b x) \log \left(\frac{b (d+e x)}{b d-a e}\right)-\text{Li}_2\left(-\frac{b x}{a}\right)+\log (x) \left(\log (a+b x)-\log \left(\frac{b x}{a}+1\right)\right)\right)-\log (d+e x) \left(\log \left(c (a+b x)^n\right)-n \log (a+b x)\right)^2+\log (x) \left(\log \left(c (a+b x)^n\right)-n \log (a+b x)\right)^2+n^2 \left(2 \text{Li}_3\left(\frac{e (a+b x)}{a e-b d}\right)-2 \log (a+b x) \text{Li}_2\left(\frac{e (a+b x)}{a e-b d}\right)-\log ^2(a+b x) \log \left(\frac{b (d+e x)}{b d-a e}\right)-2 \text{Li}_3\left(\frac{b x}{a}+1\right)+2 \text{Li}_2\left(\frac{b x}{a}+1\right) \log (a+b x)+\log \left(-\frac{b x}{a}\right) \log ^2(a+b x)\right)}{d}","-\frac{2 n \log \left(c (a+b x)^n\right) \text{Li}_2\left(-\frac{e (a+b x)}{b d-a e}\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{2 n \text{Li}_2\left(\frac{b x}{a}+1\right) \log \left(c (a+b x)^n\right)}{d}+\frac{\log \left(-\frac{b x}{a}\right) \log ^2\left(c (a+b x)^n\right)}{d}+\frac{2 n^2 \text{Li}_3\left(-\frac{e (a+b x)}{b d-a e}\right)}{d}-\frac{2 n^2 \text{Li}_3\left(\frac{b x}{a}+1\right)}{d}",1,"(Log[x]*(-(n*Log[a + b*x]) + Log[c*(a + b*x)^n])^2 - (-(n*Log[a + b*x]) + Log[c*(a + b*x)^n])^2*Log[d + e*x] - 2*n*(n*Log[a + b*x] - Log[c*(a + b*x)^n])*(Log[x]*(Log[a + b*x] - Log[1 + (b*x)/a]) - Log[a + b*x]*Log[(b*(d + e*x))/(b*d - a*e)] - PolyLog[2, -((b*x)/a)] - PolyLog[2, (e*(a + b*x))/(-(b*d) + a*e)]) + n^2*(Log[-((b*x)/a)]*Log[a + b*x]^2 - Log[a + b*x]^2*Log[(b*(d + e*x))/(b*d - a*e)] - 2*Log[a + b*x]*PolyLog[2, (e*(a + b*x))/(-(b*d) + a*e)] + 2*Log[a + b*x]*PolyLog[2, 1 + (b*x)/a] + 2*PolyLog[3, (e*(a + b*x))/(-(b*d) + a*e)] - 2*PolyLog[3, 1 + (b*x)/a]))/d","A",1
345,1,98,97,0.0233942,"\int \frac{\log \left(c (a+b x)^n\right)}{d x+e x^2} \, dx","Integrate[Log[c*(a + b*x)^n]/(d*x + e*x^2),x]","-\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{Li}_2\left(-\frac{e (a+b x)}{b d-a e}\right)}{d}+\frac{n \text{Li}_2\left(\frac{a+b x}{a}\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{Li}_2\left(-\frac{e (a+b x)}{b d-a e}\right)}{d}+\frac{n \text{Li}_2\left(\frac{b x}{a}+1\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, (a + b*x)/a])/d - (n*PolyLog[2, -((e*(a + b*x))/(b*d - a*e))])/d","A",1
346,0,0,53,0.6983011,"\int \frac{1}{\left(d x+e x^2\right) \log \left(c (a+b x)^n\right)} \, dx","Integrate[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,"Integrate[1/((d*x + e*x^2)*Log[c*(a + b*x)^n]), x]","A",-1
347,1,993,500,0.8074085,"\int \frac{\log ^3\left(c (a+b x)^n\right)}{d+e x+f x^2} \, dx","Integrate[Log[c*(a + b*x)^n]^3/(d + e*x + f*x^2),x]","\frac{-2 \sqrt{e^2-4 d f} \tan ^{-1}\left(\frac{e+2 f x}{\sqrt{4 d f-e^2}}\right) \log ^3(a+b x) n^3+\sqrt{4 d f-e^2} \log ^3(a+b x) \log \left(1-\frac{2 f (a+b x)}{-e b+\sqrt{e^2-4 d f} b+2 a f}\right) n^3-\sqrt{4 d f-e^2} \log ^3(a+b x) \log \left(\frac{2 f (a+b x)}{b \left(e+\sqrt{e^2-4 d f}\right)-2 a f}+1\right) n^3+6 \sqrt{4 d f-e^2} \text{Li}_4\left(\frac{2 f (a+b x)}{-e b+\sqrt{e^2-4 d f} b+2 a f}\right) n^3-6 \sqrt{4 d f-e^2} \text{Li}_4\left(\frac{2 f (a+b x)}{2 a f-b \left(e+\sqrt{e^2-4 d f}\right)}\right) n^3+6 \sqrt{e^2-4 d f} \tan ^{-1}\left(\frac{e+2 f x}{\sqrt{4 d f-e^2}}\right) \log ^2(a+b x) \log \left(c (a+b x)^n\right) n^2-3 \sqrt{4 d f-e^2} \log ^2(a+b x) \log \left(c (a+b x)^n\right) \log \left(1-\frac{2 f (a+b x)}{-e b+\sqrt{e^2-4 d f} b+2 a f}\right) n^2+3 \sqrt{4 d f-e^2} \log ^2(a+b x) \log \left(c (a+b x)^n\right) \log \left(\frac{2 f (a+b x)}{b \left(e+\sqrt{e^2-4 d f}\right)-2 a f}+1\right) n^2-6 \sqrt{4 d f-e^2} \log \left(c (a+b x)^n\right) \text{Li}_3\left(\frac{2 f (a+b x)}{-e b+\sqrt{e^2-4 d f} b+2 a f}\right) n^2+6 \sqrt{4 d f-e^2} \log \left(c (a+b x)^n\right) \text{Li}_3\left(\frac{2 f (a+b x)}{2 a f-b \left(e+\sqrt{e^2-4 d f}\right)}\right) n^2-6 \sqrt{e^2-4 d f} \tan ^{-1}\left(\frac{e+2 f x}{\sqrt{4 d f-e^2}}\right) \log (a+b x) \log ^2\left(c (a+b x)^n\right) n+3 \sqrt{4 d f-e^2} \log (a+b x) \log ^2\left(c (a+b x)^n\right) \log \left(1-\frac{2 f (a+b x)}{-e b+\sqrt{e^2-4 d f} b+2 a f}\right) n-3 \sqrt{4 d f-e^2} \log (a+b x) \log ^2\left(c (a+b x)^n\right) \log \left(\frac{2 f (a+b x)}{b \left(e+\sqrt{e^2-4 d f}\right)-2 a f}+1\right) n+3 \sqrt{4 d f-e^2} \log ^2\left(c (a+b x)^n\right) \text{Li}_2\left(\frac{2 f (a+b x)}{2 a f+b \left(\sqrt{e^2-4 d f}-e\right)}\right) n-3 \sqrt{4 d f-e^2} \log ^2\left(c (a+b x)^n\right) \text{Li}_2\left(\frac{2 f (a+b x)}{2 a f-b \left(e+\sqrt{e^2-4 d f}\right)}\right) n+2 \sqrt{e^2-4 d f} \tan ^{-1}\left(\frac{e+2 f x}{\sqrt{4 d f-e^2}}\right) \log ^3\left(c (a+b x)^n\right)}{\sqrt{-\left(e^2-4 d f\right)^2}}","-\frac{6 n^2 \log \left(c (a+b x)^n\right) \text{Li}_3\left(\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{Li}_3\left(\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{Li}_2\left(\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{Li}_2\left(\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{\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^3 \text{Li}_4\left(\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{Li}_4\left(\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}}",1,"(-2*Sqrt[e^2 - 4*d*f]*n^3*ArcTan[(e + 2*f*x)/Sqrt[-e^2 + 4*d*f]]*Log[a + b*x]^3 + 6*Sqrt[e^2 - 4*d*f]*n^2*ArcTan[(e + 2*f*x)/Sqrt[-e^2 + 4*d*f]]*Log[a + b*x]^2*Log[c*(a + b*x)^n] - 6*Sqrt[e^2 - 4*d*f]*n*ArcTan[(e + 2*f*x)/Sqrt[-e^2 + 4*d*f]]*Log[a + b*x]*Log[c*(a + b*x)^n]^2 + 2*Sqrt[e^2 - 4*d*f]*ArcTan[(e + 2*f*x)/Sqrt[-e^2 + 4*d*f]]*Log[c*(a + b*x)^n]^3 + Sqrt[-e^2 + 4*d*f]*n^3*Log[a + b*x]^3*Log[1 - (2*f*(a + b*x))/(-(b*e) + 2*a*f + b*Sqrt[e^2 - 4*d*f])] - 3*Sqrt[-e^2 + 4*d*f]*n^2*Log[a + b*x]^2*Log[c*(a + b*x)^n]*Log[1 - (2*f*(a + b*x))/(-(b*e) + 2*a*f + b*Sqrt[e^2 - 4*d*f])] + 3*Sqrt[-e^2 + 4*d*f]*n*Log[a + b*x]*Log[c*(a + b*x)^n]^2*Log[1 - (2*f*(a + b*x))/(-(b*e) + 2*a*f + b*Sqrt[e^2 - 4*d*f])] - Sqrt[-e^2 + 4*d*f]*n^3*Log[a + b*x]^3*Log[1 + (2*f*(a + b*x))/(-2*a*f + b*(e + Sqrt[e^2 - 4*d*f]))] + 3*Sqrt[-e^2 + 4*d*f]*n^2*Log[a + b*x]^2*Log[c*(a + b*x)^n]*Log[1 + (2*f*(a + b*x))/(-2*a*f + b*(e + Sqrt[e^2 - 4*d*f]))] - 3*Sqrt[-e^2 + 4*d*f]*n*Log[a + b*x]*Log[c*(a + b*x)^n]^2*Log[1 + (2*f*(a + b*x))/(-2*a*f + b*(e + Sqrt[e^2 - 4*d*f]))] + 3*Sqrt[-e^2 + 4*d*f]*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]))] - 3*Sqrt[-e^2 + 4*d*f]*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]))] - 6*Sqrt[-e^2 + 4*d*f]*n^2*Log[c*(a + b*x)^n]*PolyLog[3, (2*f*(a + b*x))/(-(b*e) + 2*a*f + b*Sqrt[e^2 - 4*d*f])] + 6*Sqrt[-e^2 + 4*d*f]*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]))] + 6*Sqrt[-e^2 + 4*d*f]*n^3*PolyLog[4, (2*f*(a + b*x))/(-(b*e) + 2*a*f + b*Sqrt[e^2 - 4*d*f])] - 6*Sqrt[-e^2 + 4*d*f]*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)^2]","A",1
348,1,655,372,0.4536012,"\int \frac{\log ^2\left(c (a+b x)^n\right)}{d+e x+f x^2} \, dx","Integrate[Log[c*(a + b*x)^n]^2/(d + e*x + f*x^2),x]","\frac{2 n \sqrt{4 d f-e^2} \log \left(c (a+b x)^n\right) \text{Li}_2\left(\frac{2 f (a+b x)}{2 a f+b \left(\sqrt{e^2-4 d f}-e\right)}\right)-2 n \sqrt{4 d f-e^2} \log \left(c (a+b x)^n\right) \text{Li}_2\left(\frac{2 f (a+b x)}{2 a f-b \left(e+\sqrt{e^2-4 d f}\right)}\right)+2 n \sqrt{4 d f-e^2} \log (a+b x) \log \left(c (a+b x)^n\right) \log \left(1-\frac{2 f (a+b x)}{2 a f+b \sqrt{e^2-4 d f}+b (-e)}\right)-2 n \sqrt{4 d f-e^2} \log (a+b x) \log \left(c (a+b x)^n\right) \log \left(\frac{2 f (a+b x)}{b \left(\sqrt{e^2-4 d f}+e\right)-2 a f}+1\right)+2 \sqrt{e^2-4 d f} \tan ^{-1}\left(\frac{e+2 f x}{\sqrt{4 d f-e^2}}\right) \log ^2\left(c (a+b x)^n\right)-4 n \sqrt{e^2-4 d f} \log (a+b x) \tan ^{-1}\left(\frac{e+2 f x}{\sqrt{4 d f-e^2}}\right) \log \left(c (a+b x)^n\right)-2 n^2 \sqrt{4 d f-e^2} \text{Li}_3\left(\frac{2 f (a+b x)}{-e b+\sqrt{e^2-4 d f} b+2 a f}\right)+2 n^2 \sqrt{4 d f-e^2} \text{Li}_3\left(\frac{2 f (a+b x)}{2 a f-b \left(e+\sqrt{e^2-4 d f}\right)}\right)-n^2 \sqrt{4 d f-e^2} \log ^2(a+b x) \log \left(1-\frac{2 f (a+b x)}{2 a f+b \sqrt{e^2-4 d f}+b (-e)}\right)+n^2 \sqrt{4 d f-e^2} \log ^2(a+b x) \log \left(\frac{2 f (a+b x)}{b \left(\sqrt{e^2-4 d f}+e\right)-2 a f}+1\right)+2 n^2 \sqrt{e^2-4 d f} \log ^2(a+b x) \tan ^{-1}\left(\frac{e+2 f x}{\sqrt{4 d f-e^2}}\right)}{\sqrt{-\left(e^2-4 d f\right)^2}}","\frac{2 n \log \left(c (a+b x)^n\right) \text{Li}_2\left(\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{Li}_2\left(\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{\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^2 \text{Li}_3\left(\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{Li}_3\left(\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}}",1,"(2*Sqrt[e^2 - 4*d*f]*n^2*ArcTan[(e + 2*f*x)/Sqrt[-e^2 + 4*d*f]]*Log[a + b*x]^2 - 4*Sqrt[e^2 - 4*d*f]*n*ArcTan[(e + 2*f*x)/Sqrt[-e^2 + 4*d*f]]*Log[a + b*x]*Log[c*(a + b*x)^n] + 2*Sqrt[e^2 - 4*d*f]*ArcTan[(e + 2*f*x)/Sqrt[-e^2 + 4*d*f]]*Log[c*(a + b*x)^n]^2 - Sqrt[-e^2 + 4*d*f]*n^2*Log[a + b*x]^2*Log[1 - (2*f*(a + b*x))/(-(b*e) + 2*a*f + b*Sqrt[e^2 - 4*d*f])] + 2*Sqrt[-e^2 + 4*d*f]*n*Log[a + b*x]*Log[c*(a + b*x)^n]*Log[1 - (2*f*(a + b*x))/(-(b*e) + 2*a*f + b*Sqrt[e^2 - 4*d*f])] + Sqrt[-e^2 + 4*d*f]*n^2*Log[a + b*x]^2*Log[1 + (2*f*(a + b*x))/(-2*a*f + b*(e + Sqrt[e^2 - 4*d*f]))] - 2*Sqrt[-e^2 + 4*d*f]*n*Log[a + b*x]*Log[c*(a + b*x)^n]*Log[1 + (2*f*(a + b*x))/(-2*a*f + b*(e + Sqrt[e^2 - 4*d*f]))] + 2*Sqrt[-e^2 + 4*d*f]*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]))] - 2*Sqrt[-e^2 + 4*d*f]*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]))] - 2*Sqrt[-e^2 + 4*d*f]*n^2*PolyLog[3, (2*f*(a + b*x))/(-(b*e) + 2*a*f + b*Sqrt[e^2 - 4*d*f])] + 2*Sqrt[-e^2 + 4*d*f]*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]","A",1
349,1,194,243,0.1821037,"\int \frac{\log \left(c (a+b x)^n\right)}{d+e x+f x^2} \, dx","Integrate[Log[c*(a + b*x)^n]/(d + e*x + f*x^2),x]","\frac{\log \left(c (a+b x)^n\right) \left(\log \left(\frac{b \left(\sqrt{e^2-4 d f}-e-2 f x\right)}{2 a f+b \sqrt{e^2-4 d f}+b (-e)}\right)-\log \left(\frac{b \left(\sqrt{e^2-4 d f}+e+2 f x\right)}{b \left(\sqrt{e^2-4 d f}+e\right)-2 a f}\right)\right)+n \text{Li}_2\left(\frac{2 f (a+b x)}{2 a f+b \left(\sqrt{e^2-4 d f}-e\right)}\right)-n \text{Li}_2\left(\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{\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{Li}_2\left(\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{Li}_2\left(\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}}",1,"(Log[c*(a + b*x)^n]*(Log[(b*(-e + Sqrt[e^2 - 4*d*f] - 2*f*x))/(-(b*e) + 2*a*f + b*Sqrt[e^2 - 4*d*f])] - Log[(b*(e + Sqrt[e^2 - 4*d*f] + 2*f*x))/(-2*a*f + b*(e + 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]))] - 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",1
350,0,0,105,0.5986457,"\int \frac{1}{\left(d+e x+f x^2\right) \log \left(c (a+b x)^n\right)} \, dx","Integrate[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,"Integrate[1/((d + e*x + f*x^2)*Log[c*(a + b*x)^n]), x]","A",-1
351,1,464,286,0.6866455,"\int \frac{x^3 \log (x)}{a+b x+c x^2} \, dx","Integrate[(x^3*Log[x])/(a + b*x + c*x^2),x]","\frac{2 \left(b^2-a c\right) \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \text{Li}_2\left(\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)+\frac{4 a b c \text{Li}_2\left(\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)}{\sqrt{b^2-4 a c}}+2 \left(b^2-a c\right) \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \text{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)-\frac{4 a b c \text{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}+2 \log (x) \left(b^2-a c\right) \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \log \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}\right)+\frac{4 a b c \log (x) \log \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}+2 \log (x) \left(b^2-a c\right) \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \log \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}\right)-\frac{4 a b c \log (x) \log \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}\right)}{\sqrt{b^2-4 a c}}+4 b c x-4 b c x \log (x)-c^2 x^2+2 c^2 x^2 \log (x)}{4 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{Li}_2\left(-\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{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\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,"(4*b*c*x - c^2*x^2 - 4*b*c*x*Log[x] + 2*c^2*x^2*Log[x] + (4*a*b*c*Log[x]*Log[(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/Sqrt[b^2 - 4*a*c] + 2*(b^2 - a*c)*(1 - b/Sqrt[b^2 - 4*a*c])*Log[x]*Log[(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c])] - (4*a*b*c*Log[x]*Log[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[b^2 - 4*a*c] + 2*(b^2 - a*c)*(1 + b/Sqrt[b^2 - 4*a*c])*Log[x]*Log[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c])] + (4*a*b*c*PolyLog[2, (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])])/Sqrt[b^2 - 4*a*c] + 2*(b^2 - a*c)*(1 - b/Sqrt[b^2 - 4*a*c])*PolyLog[2, (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])] - (4*a*b*c*PolyLog[2, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[b^2 - 4*a*c] + 2*(b^2 - a*c)*(1 + b/Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(4*c^3)","A",1
352,1,434,234,0.2772148,"\int \frac{x^2 \log (x)}{a+b x+c x^2} \, dx","Integrate[(x^2*Log[x])/(a + b*x + c*x^2),x]","-\frac{b \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \text{Li}_2\left(-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{2 c^2}-\frac{b \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \text{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{2 c^2}-\frac{b \log (x) \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \log \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}\right)}{2 c^2}-\frac{b \log (x) \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \log \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}\right)}{2 c^2}-\frac{a \text{Li}_2\left(-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c}}+\frac{a \text{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c}}-\frac{a \log (x) \log \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c}}+\frac{a \log (x) \log \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}\right)}{c \sqrt{b^2-4 a c}}-\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{Li}_2\left(-\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{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\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 - (a*Log[x]*Log[(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(c*Sqrt[b^2 - 4*a*c]) - (b*(1 - b/Sqrt[b^2 - 4*a*c])*Log[x]*Log[(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(2*c^2) + (a*Log[x]*Log[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(c*Sqrt[b^2 - 4*a*c]) - (b*(1 + b/Sqrt[b^2 - 4*a*c])*Log[x]*Log[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(2*c^2) - (a*PolyLog[2, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(c*Sqrt[b^2 - 4*a*c]) - (b*(1 - b/Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(2*c^2) + (a*PolyLog[2, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(c*Sqrt[b^2 - 4*a*c]) - (b*(1 + b/Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(2*c^2)","A",1
353,1,210,193,0.1458295,"\int \frac{x \log (x)}{a+b x+c x^2} \, dx","Integrate[(x*Log[x])/(a + b*x + c*x^2),x]","\frac{\left(\sqrt{b^2-4 a c}-b\right) \text{Li}_2\left(\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)+\left(\sqrt{b^2-4 a c}+b\right) \text{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)+\log (x) \left(\left(\sqrt{b^2-4 a c}-b\right) \log \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}\right)+\left(\sqrt{b^2-4 a c}+b\right) \log \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}\right)\right)}{2 c \sqrt{b^2-4 a c}}","\frac{\left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \text{Li}_2\left(-\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{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\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,"(Log[x]*((-b + Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c])] + (b + Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c])]) + (-b + Sqrt[b^2 - 4*a*c])*PolyLog[2, (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])] + (b + Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(2*c*Sqrt[b^2 - 4*a*c])","A",1
354,1,144,153,0.0648725,"\int \frac{\log (x)}{a+b x+c x^2} \, dx","Integrate[Log[x]/(a + b*x + c*x^2),x]","\frac{\text{Li}_2\left(\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)-\text{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)+\log (x) \left(\log \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}\right)-\log \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}\right)\right)}{\sqrt{b^2-4 a c}}","\frac{\text{Li}_2\left(-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}-\frac{\text{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\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[(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c])] - Log[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c])]) + PolyLog[2, (2*c*x)/(-b + 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",1
355,1,227,204,0.2177051,"\int \frac{\log (x)}{x \left(a+b x+c x^2\right)} \, dx","Integrate[Log[x]/(x*(a + b*x + c*x^2)),x]","\frac{-\left(\sqrt{b^2-4 a c}+b\right) \text{Li}_2\left(\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)+\left(b-\sqrt{b^2-4 a c}\right) \text{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)+\log (x) \left(\log (x) \sqrt{b^2-4 a c}-\left(\sqrt{b^2-4 a c}+b\right) \log \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}\right)+\left(b-\sqrt{b^2-4 a c}\right) \log \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}\right)\right)}{2 a \sqrt{b^2-4 a c}}","-\frac{\left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \text{Li}_2\left(-\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{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\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]*(Sqrt[b^2 - 4*a*c]*Log[x] - (b + Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c])] + (b - Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c])]) - (b + Sqrt[b^2 - 4*a*c])*PolyLog[2, (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])] + (b - Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(2*a*Sqrt[b^2 - 4*a*c])","A",1
356,1,255,251,0.3861136,"\int \frac{\log (x)}{x^2 \left(a+b x+c x^2\right)} \, dx","Integrate[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{Li}_2\left(\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)+\left(\frac{2 a c-b^2}{\sqrt{b^2-4 a c}}+b\right) \text{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)+\log (x) \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}\right)+\log (x) \left(\frac{2 a c-b^2}{\sqrt{b^2-4 a c}}+b\right) \log \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}\right)-\frac{2 a}{x}-\frac{2 a \log (x)}{x}-b \log ^2(x)}{2 a^2}","\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \text{Li}_2\left(-\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{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\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,"((-2*a)/x - (2*a*Log[x])/x - b*Log[x]^2 + (b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[x]*Log[(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c])] + (b + (-b^2 + 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[x]*Log[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c])] + (b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*PolyLog[2, (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])] + (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",1
357,1,311,308,0.4683089,"\int \frac{\log (x)}{x^3 \left(a+b x+c x^2\right)} \, dx","Integrate[Log[x]/(x^3*(a + b*x + c*x^2)),x]","-\frac{\frac{a^2}{x^2}+\frac{2 a^2 \log (x)}{x^2}+2 \left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \text{Li}_2\left(\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)+2 \left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \text{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)-2 \log ^2(x) \left(b^2-a c\right)+2 \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{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}\right)+2 \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{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}\right)-\frac{4 a b}{x}-\frac{4 a b \log (x)}{x}}{4 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{Li}_2\left(-\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{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\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^2/x^2 - (4*a*b)/x + (2*a^2*Log[x])/x^2 - (4*a*b*Log[x])/x - 2*(b^2 - a*c)*Log[x]^2 + 2*(b^2 - a*c + (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*Log[x]*Log[(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c])] + 2*(b^2 - a*c - (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*Log[x]*Log[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c])] + 2*(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*(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])])/a^3","A",1
358,1,221,232,0.1921848,"\int x^3 \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Integrate[x^3*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]),x]","\frac{-6 \log \left(f x^m\right) \left(-12 a e^4 x^4-12 b e^4 x^4 \log \left(c (d+e x)^n\right)+12 b d^4 n \log (d+e x)+b e n x \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)\right)+m \left(-18 a e^4 x^4-18 b e^4 x^4 \log \left(c (d+e x)^n\right)+18 b d^4 n (4 \log (x)+1) \log (d+e x)-72 b d^4 n \log (x) \log \left(\frac{e x}{d}+1\right)-90 b d^3 e n x+27 b d^2 e^2 n x^2-14 b d e^3 n x^3+9 b e^4 n x^4\right)-72 b d^4 m n \text{Li}_2\left(-\frac{e x}{d}\right)}{288 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^4 m n \text{Li}_2\left(-\frac{e x}{d}\right)}{4 e^4}+\frac{b d^4 m n \log (d+e x)}{16 e^4}+\frac{b d^3 n x \log \left(f x^m\right)}{4 e^3}-\frac{5 b d^3 m n x}{16 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{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,"(-6*Log[f*x^m]*(-12*a*e^4*x^4 + b*e*n*x*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3) + 12*b*d^4*n*Log[d + e*x] - 12*b*e^4*x^4*Log[c*(d + e*x)^n]) + m*(-90*b*d^3*e*n*x + 27*b*d^2*e^2*n*x^2 - 14*b*d*e^3*n*x^3 - 18*a*e^4*x^4 + 9*b*e^4*n*x^4 + 18*b*d^4*n*(1 + 4*Log[x])*Log[d + e*x] - 18*b*e^4*x^4*Log[c*(d + e*x)^n] - 72*b*d^4*n*Log[x]*Log[1 + (e*x)/d]) - 72*b*d^4*m*n*PolyLog[2, -((e*x)/d)])/(288*e^4)","A",1
359,1,197,195,0.1837596,"\int x^2 \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Integrate[x^2*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]),x]","\frac{6 \log \left(f x^m\right) \left(6 a e^3 x^3+6 b e^3 x^3 \log \left(c (d+e x)^n\right)+6 b d^3 n \log (d+e x)+b e n x \left(-6 d^2+3 d e x-2 e^2 x^2\right)\right)+m \left(-12 a e^3 x^3-12 b e^3 x^3 \log \left(c (d+e x)^n\right)-12 b d^3 n (3 \log (x)+1) \log (d+e x)+36 b d^3 n \log (x) \log \left(\frac{e x}{d}+1\right)+48 b d^2 e n x-15 b d e^2 n x^2+8 b e^3 n x^3\right)+36 b d^3 m n \text{Li}_2\left(-\frac{e x}{d}\right)}{108 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^3 m n \text{Li}_2\left(-\frac{e x}{d}\right)}{3 e^3}-\frac{b d^3 m n \log (d+e x)}{9 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 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,"(6*Log[f*x^m]*(6*a*e^3*x^3 + b*e*n*x*(-6*d^2 + 3*d*e*x - 2*e^2*x^2) + 6*b*d^3*n*Log[d + e*x] + 6*b*e^3*x^3*Log[c*(d + e*x)^n]) + m*(48*b*d^2*e*n*x - 15*b*d*e^2*n*x^2 - 12*a*e^3*x^3 + 8*b*e^3*n*x^3 - 12*b*d^3*n*(1 + 3*Log[x])*Log[d + e*x] - 12*b*e^3*x^3*Log[c*(d + e*x)^n] + 36*b*d^3*n*Log[x]*Log[1 + (e*x)/d]) + 36*b*d^3*m*n*PolyLog[2, -((e*x)/d)])/(108*e^3)","A",1
360,1,164,158,0.1291423,"\int x \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Integrate[x*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]),x]","\frac{m \left(-a e^2 x^2-b e^2 x^2 \log \left(c (d+e x)^n\right)+b d^2 n (2 \log (x)+1) \log (d+e x)-2 b d^2 n \log (x) \log \left(\frac{e x}{d}+1\right)-3 b d e n x+b e^2 n x^2\right)+\log \left(f x^m\right) \left(e x \left(2 a e x+2 b e x \log \left(c (d+e x)^n\right)+2 b d n-b e n x\right)-2 b d^2 n \log (d+e x)\right)-2 b d^2 m n \text{Li}_2\left(-\frac{e x}{d}\right)}{4 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 \text{Li}_2\left(-\frac{e x}{d}\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,"(Log[f*x^m]*(-2*b*d^2*n*Log[d + e*x] + e*x*(2*b*d*n + 2*a*e*x - b*e*n*x + 2*b*e*x*Log[c*(d + e*x)^n])) + m*(-3*b*d*e*n*x - a*e^2*x^2 + b*e^2*n*x^2 + b*d^2*n*(1 + 2*Log[x])*Log[d + e*x] - b*e^2*x^2*Log[c*(d + e*x)^n] - 2*b*d^2*n*Log[x]*Log[1 + (e*x)/d]) - 2*b*d^2*m*n*PolyLog[2, -((e*x)/d)])/(4*e^2)","A",1
361,1,116,99,0.0823777,"\int \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right) \, dx","Integrate[Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]),x]","\frac{\log \left(f x^m\right) \left(e x \left(a+b \log \left(c (d+e x)^n\right)-b n\right)+b d n \log (d+e x)\right)-m \left(a e x+b e x \log \left(c (d+e x)^n\right)+b d n (\log (x)+1) \log (d+e x)-b d n \log (x) \log \left(\frac{e x}{d}+1\right)-2 b e n x\right)+b d m n \text{Li}_2\left(-\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 \text{Li}_2\left(-\frac{e x}{d}\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,"(Log[f*x^m]*(b*d*n*Log[d + e*x] + e*x*(a - b*n + b*Log[c*(d + e*x)^n])) - m*(a*e*x - 2*b*e*n*x + b*d*n*(1 + Log[x])*Log[d + e*x] + b*e*x*Log[c*(d + e*x)^n] - b*d*n*Log[x]*Log[1 + (e*x)/d]) + b*d*m*n*PolyLog[2, -((e*x)/d)])/e","A",1
362,1,128,88,0.074815,"\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{x} \, dx","Integrate[(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]))/x,x]","\frac{1}{2} \left(\frac{a \log ^2\left(f x^m\right)}{m}+2 b \log (x) \log \left(f x^m\right) \log \left(c (d+e x)^n\right)-b m \log ^2(x) \log \left(c (d+e x)^n\right)-2 b n \text{Li}_2\left(-\frac{e x}{d}\right) \log \left(f x^m\right)-2 b n \log (x) \log \left(\frac{e x}{d}+1\right) \log \left(f x^m\right)+2 b m n \text{Li}_3\left(-\frac{e x}{d}\right)+b m n \log ^2(x) \log \left(\frac{e x}{d}+1\right)\right)","\frac{\log ^2\left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{2 m}-b n \text{Li}_2\left(-\frac{e x}{d}\right) \log \left(f x^m\right)-\frac{b n \log \left(\frac{e x}{d}+1\right) \log ^2\left(f x^m\right)}{2 m}+b m n \text{Li}_3\left(-\frac{e x}{d}\right)",1,"((a*Log[f*x^m]^2)/m - b*m*Log[x]^2*Log[c*(d + e*x)^n] + 2*b*Log[x]*Log[f*x^m]*Log[c*(d + e*x)^n] + b*m*n*Log[x]^2*Log[1 + (e*x)/d] - 2*b*n*Log[x]*Log[f*x^m]*Log[1 + (e*x)/d] - 2*b*n*Log[f*x^m]*PolyLog[2, -((e*x)/d)] + 2*b*m*n*PolyLog[3, -((e*x)/d)])/2","A",1
363,1,111,102,0.1154281,"\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{x^2} \, dx","Integrate[(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]))/x^2,x]","-\frac{2 \left(\log \left(f x^m\right)+m\right) \left(a d+b d \log \left(c (d+e x)^n\right)+b e n x \log (d+e x)\right)-2 b e n x \log (x) \left(m \log (d+e x)-m \log \left(\frac{e x}{d}+1\right)+\log \left(f x^m\right)+m\right)+2 b e m n x \text{Li}_2\left(-\frac{e x}{d}\right)+b e m n x \log ^2(x)}{2 d x}","-\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 \text{Li}_2\left(-\frac{d}{e x}\right)}{d}+\frac{b e m n \log (x)}{d}-\frac{b e m n \log (d+e x)}{d}",1,"-1/2*(b*e*m*n*x*Log[x]^2 + 2*(m + Log[f*x^m])*(a*d + b*e*n*x*Log[d + e*x] + b*d*Log[c*(d + e*x)^n]) - 2*b*e*n*x*Log[x]*(m + Log[f*x^m] + m*Log[d + e*x] - m*Log[1 + (e*x)/d]) + 2*b*e*m*n*x*PolyLog[2, -((e*x)/d)])/(d*x)","A",1
364,1,204,156,0.1275035,"\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{x^3} \, dx","Integrate[(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]))/x^3,x]","-\frac{2 a d^2 \log \left(f x^m\right)+a d^2 m+2 b d^2 \log \left(f x^m\right) \log \left(c (d+e x)^n\right)+b d^2 m \log \left(c (d+e x)^n\right)-2 b e^2 n x^2 \log (d+e x) \log \left(f x^m\right)+b e^2 n x^2 \log (x) \left(2 m \log (d+e x)-2 m \log \left(\frac{e x}{d}+1\right)+2 \log \left(f x^m\right)+m\right)-2 b e^2 m n x^2 \text{Li}_2\left(-\frac{e x}{d}\right)-b e^2 m n x^2 \log (d+e x)+2 b d e n x \log \left(f x^m\right)+3 b d e m n x-b e^2 m n x^2 \log ^2(x)}{4 d^2 x^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 \text{Li}_2\left(-\frac{d}{e x}\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,"-1/4*(a*d^2*m + 3*b*d*e*m*n*x - b*e^2*m*n*x^2*Log[x]^2 + 2*a*d^2*Log[f*x^m] + 2*b*d*e*n*x*Log[f*x^m] - b*e^2*m*n*x^2*Log[d + e*x] - 2*b*e^2*n*x^2*Log[f*x^m]*Log[d + e*x] + b*d^2*m*Log[c*(d + e*x)^n] + 2*b*d^2*Log[f*x^m]*Log[c*(d + e*x)^n] + b*e^2*n*x^2*Log[x]*(m + 2*Log[f*x^m] + 2*m*Log[d + e*x] - 2*m*Log[1 + (e*x)/d]) - 2*b*e^2*m*n*x^2*PolyLog[2, -((e*x)/d)])/(d^2*x^2)","A",1
365,1,240,193,0.1439212,"\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{x^4} \, dx","Integrate[(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]))/x^4,x]","-\frac{12 a d^3 \log \left(f x^m\right)+4 a d^3 m+12 b d^3 \log \left(f x^m\right) \log \left(c (d+e x)^n\right)+4 b d^3 m \log \left(c (d+e x)^n\right)+6 b d^2 e n x \log \left(f x^m\right)+5 b d^2 e m n x+12 b e^3 n x^3 \log (d+e x) \log \left(f x^m\right)-4 b e^3 n x^3 \log (x) \left(3 m \log (d+e x)-3 m \log \left(\frac{e x}{d}+1\right)+3 \log \left(f x^m\right)+m\right)+12 b e^3 m n x^3 \text{Li}_2\left(-\frac{e x}{d}\right)+4 b e^3 m n x^3 \log (d+e x)-12 b d e^2 n x^2 \log \left(f x^m\right)-16 b d e^2 m n x^2+6 b e^3 m n x^3 \log ^2(x)}{36 d^3 x^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^3 m n \text{Li}_2\left(-\frac{d}{e x}\right)}{3 d^3}+\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^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 n \log \left(f x^m\right)}{6 d x^2}-\frac{5 b e m n}{36 d x^2}",1,"-1/36*(4*a*d^3*m + 5*b*d^2*e*m*n*x - 16*b*d*e^2*m*n*x^2 + 6*b*e^3*m*n*x^3*Log[x]^2 + 12*a*d^3*Log[f*x^m] + 6*b*d^2*e*n*x*Log[f*x^m] - 12*b*d*e^2*n*x^2*Log[f*x^m] + 4*b*e^3*m*n*x^3*Log[d + e*x] + 12*b*e^3*n*x^3*Log[f*x^m]*Log[d + e*x] + 4*b*d^3*m*Log[c*(d + e*x)^n] + 12*b*d^3*Log[f*x^m]*Log[c*(d + e*x)^n] - 4*b*e^3*n*x^3*Log[x]*(m + 3*Log[f*x^m] + 3*m*Log[d + e*x] - 3*m*Log[1 + (e*x)/d]) + 12*b*e^3*m*n*x^3*PolyLog[2, -((e*x)/d)])/(d^3*x^3)","A",1
366,1,273,230,0.1536307,"\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{x^5} \, dx","Integrate[(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n]))/x^5,x]","-\frac{72 a d^4 \log \left(f x^m\right)+18 a d^4 m+72 b d^4 \log \left(f x^m\right) \log \left(c (d+e x)^n\right)+18 b d^4 m \log \left(c (d+e x)^n\right)+24 b d^3 e n x \log \left(f x^m\right)+14 b d^3 e m n x-36 b d^2 e^2 n x^2 \log \left(f x^m\right)-27 b d^2 e^2 m n x^2-72 b e^4 n x^4 \log (d+e x) \log \left(f x^m\right)+18 b e^4 n x^4 \log (x) \left(4 m \log (d+e x)-4 m \log \left(\frac{e x}{d}+1\right)+4 \log \left(f x^m\right)+m\right)-72 b e^4 m n x^4 \text{Li}_2\left(-\frac{e x}{d}\right)-18 b e^4 m n x^4 \log (d+e x)+72 b d e^3 n x^3 \log \left(f x^m\right)+90 b d e^3 m n x^3-36 b e^4 m n x^4 \log ^2(x)}{288 d^4 x^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^4 m n \text{Li}_2\left(-\frac{d}{e x}\right)}{4 d^4}-\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^3 n \log \left(f x^m\right)}{4 d^3 x}-\frac{5 b e^3 m n}{16 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{b e n \log \left(f x^m\right)}{12 d x^3}-\frac{7 b e m n}{144 d x^3}",1,"-1/288*(18*a*d^4*m + 14*b*d^3*e*m*n*x - 27*b*d^2*e^2*m*n*x^2 + 90*b*d*e^3*m*n*x^3 - 36*b*e^4*m*n*x^4*Log[x]^2 + 72*a*d^4*Log[f*x^m] + 24*b*d^3*e*n*x*Log[f*x^m] - 36*b*d^2*e^2*n*x^2*Log[f*x^m] + 72*b*d*e^3*n*x^3*Log[f*x^m] - 18*b*e^4*m*n*x^4*Log[d + e*x] - 72*b*e^4*n*x^4*Log[f*x^m]*Log[d + e*x] + 18*b*d^4*m*Log[c*(d + e*x)^n] + 72*b*d^4*Log[f*x^m]*Log[c*(d + e*x)^n] + 18*b*e^4*n*x^4*Log[x]*(m + 4*Log[f*x^m] + 4*m*Log[d + e*x] - 4*m*Log[1 + (e*x)/d]) - 72*b*e^4*m*n*x^4*PolyLog[2, -((e*x)/d)])/(d^4*x^4)","A",1
367,1,735,705,1.8014303,"\int x^2 \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Integrate[x^2*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2,x]","\frac{6 b n \left(e x \left(6 d^2-3 d e x+2 e^2 x^2\right)-6 \left(d^3+e^3 x^3\right) \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)+b m n \left(-36 d^3 \text{Li}_2\left(-\frac{e x}{d}\right)+12 d^3 \log (d+e x)-48 d^2 e x-6 \log (x) \left(6 d^3 \log \left(\frac{e x}{d}+1\right)+e x \left(-6 d^2+3 d e x-2 e^2 x^2\right)+6 e^3 x^3 \log (d+e x)\right)+12 e^3 x^3 \log (d+e x)+15 d e^2 x^2-8 e^3 x^3\right) \left(-a-b \log \left(c (d+e x)^n\right)+b n \log (d+e x)\right)-6 e^3 x^3 \left(-3 \log \left(f x^m\right)+3 m \log (x)+m\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+18 e^3 m x^3 \log (x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2-b^2 n^2 \left(-18 d^3 \log ^2(d+e x) \log \left(f x^m\right)+66 d^3 \log (d+e x) \log \left(f x^m\right)+66 d^3 m \text{Li}_2\left(-\frac{e x}{d}\right)-36 d^3 m \text{Li}_3\left(\frac{e x}{d}+1\right)+36 d^3 m \text{Li}_2\left(\frac{e x}{d}+1\right) \log (d+e x)+6 d^3 m \log ^2(d+e x)+18 d^3 m \log \left(-\frac{e x}{d}\right) \log ^2(d+e x)-71 d^3 m \log (d+e x)-66 d^3 m \log (x) \log (d+e x)+66 d^3 m \log (x) \log \left(\frac{e x}{d}+1\right)-36 d^3 \log \left(f x^m\right)+36 d^3 m \log (x)-66 d^2 e x \log \left(f x^m\right)+36 d^2 e x \log (d+e x) \log \left(f x^m\right)+137 d^2 e m x-48 d^2 e m x \log (d+e x)-18 e^3 x^3 \log ^2(d+e x) \log \left(f x^m\right)+12 e^3 x^3 \log (d+e x) \log \left(f x^m\right)+6 e^3 m x^3 \log ^2(d+e x)-8 e^3 m x^3 \log (d+e x)+15 d e^2 x^2 \log \left(f x^m\right)-18 d e^2 x^2 \log (d+e x) \log \left(f x^m\right)-19 d e^2 m x^2+15 d e^2 m x^2 \log (d+e x)-4 e^3 x^3 \log \left(f x^m\right)+4 e^3 m x^3\right)}{54 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{2 b d^3 m n \text{Li}_2\left(\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{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{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{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}{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{5 b d m n x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{18 e}-\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^3 m n \log \left(-\frac{e x}{d}\right) \log \left(c (d+e x)^n\right)}{3 e^3}-\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{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^3 m n^2 \text{Li}_2\left(\frac{e x}{d}+1\right)}{9 e^3}+\frac{2 b^2 d^3 m n^2 \text{Li}_3\left(\frac{e x}{d}+1\right)}{3 e^3}+\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{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{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,"(6*b*n*(m*Log[x] - Log[f*x^m])*(e*x*(6*d^2 - 3*d*e*x + 2*e^2*x^2) - 6*(d^3 + e^3*x^3)*Log[d + e*x])*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n]) + 18*e^3*m*x^3*Log[x]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 - 6*e^3*x^3*(m + 3*m*Log[x] - 3*Log[f*x^m])*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + b*m*n*(-a + b*n*Log[d + e*x] - b*Log[c*(d + e*x)^n])*(-48*d^2*e*x + 15*d*e^2*x^2 - 8*e^3*x^3 + 12*d^3*Log[d + e*x] + 12*e^3*x^3*Log[d + e*x] - 6*Log[x]*(e*x*(-6*d^2 + 3*d*e*x - 2*e^2*x^2) + 6*e^3*x^3*Log[d + e*x] + 6*d^3*Log[1 + (e*x)/d]) - 36*d^3*PolyLog[2, -((e*x)/d)]) - b^2*n^2*(137*d^2*e*m*x - 19*d*e^2*m*x^2 + 4*e^3*m*x^3 + 36*d^3*m*Log[x] - 36*d^3*Log[f*x^m] - 66*d^2*e*x*Log[f*x^m] + 15*d*e^2*x^2*Log[f*x^m] - 4*e^3*x^3*Log[f*x^m] - 71*d^3*m*Log[d + e*x] - 48*d^2*e*m*x*Log[d + e*x] + 15*d*e^2*m*x^2*Log[d + e*x] - 8*e^3*m*x^3*Log[d + e*x] - 66*d^3*m*Log[x]*Log[d + e*x] + 66*d^3*Log[f*x^m]*Log[d + e*x] + 36*d^2*e*x*Log[f*x^m]*Log[d + e*x] - 18*d*e^2*x^2*Log[f*x^m]*Log[d + e*x] + 12*e^3*x^3*Log[f*x^m]*Log[d + e*x] + 6*d^3*m*Log[d + e*x]^2 + 6*e^3*m*x^3*Log[d + e*x]^2 + 18*d^3*m*Log[-((e*x)/d)]*Log[d + e*x]^2 - 18*d^3*Log[f*x^m]*Log[d + e*x]^2 - 18*e^3*x^3*Log[f*x^m]*Log[d + e*x]^2 + 66*d^3*m*Log[x]*Log[1 + (e*x)/d] + 66*d^3*m*PolyLog[2, -((e*x)/d)] + 36*d^3*m*Log[d + e*x]*PolyLog[2, 1 + (e*x)/d] - 36*d^3*m*PolyLog[3, 1 + (e*x)/d]))/(54*e^3)","A",1
368,0,0,602,0.4066846,"\int x \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Integrate[x*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2,x]","\int x \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","\frac{b d^2 m n \text{Li}_2\left(\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\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{3 b^2 d^2 m n^2 \text{Li}_2\left(\frac{e x}{d}+1\right)}{2 e^2}-\frac{b^2 d^2 m n^2 \text{Li}_3\left(\frac{e x}{d}+1\right)}{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,"Integrate[x*Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2, x]","F",-1
369,1,549,309,0.4873564,"\int \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2 \, dx","Integrate[Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2,x]","-2 b n x \left(\log \left(f x^m\right)+m (-\log (x))-m\right) \left(a+b \left(\log \left(c (d+e x)^n\right)-n \log (d+e x)\right)\right)+2 b n x \log (d+e x) \left(\log \left(f x^m\right)-m\right) \left(a+b \left(\log \left(c (d+e x)^n\right)-n \log (d+e x)\right)\right)+\frac{2 b d n \log (d+e x) \left(\log \left(f x^m\right)+m (-\log (x))-m\right) \left(a+b \left(\log \left(c (d+e x)^n\right)-n \log (d+e x)\right)\right)}{e}-x \left(m-\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)^2-2 b e m n \left(\frac{x (\log (x)-1)}{e}-\frac{d \left(\frac{\text{Li}_2\left(-\frac{e x}{d}\right)}{e}+\frac{\log (x) \log \left(\frac{d+e x}{d}\right)}{e}\right)}{e}\right) \left(a+b \left(\log \left(c (d+e x)^n\right)-n \log (d+e x)\right)\right)+b^2 n^2 \left(x \log ^2(d+e x)-2 e \left(-\frac{d \log ^2(d+e x)}{2 e^2}+\frac{d \log (d+e x)}{e^2}+\frac{x \log (d+e x)}{e}-\frac{x}{e}\right)\right) \left(\log \left(f x^m\right)-m \log (x)\right)+b^2 m n^2 \left(-2 e \left(\frac{d \text{Li}_2\left(-\frac{e x}{d}\right)-e x \log (d+e x)-d \log (d+e x)+\log (x) \left(e x \log (d+e x)+d \log \left(\frac{e x}{d}+1\right)-e x\right)+2 e x}{e^2}-\frac{d \left(\text{Li}_3\left(\frac{d+e x}{d}\right)-\text{Li}_2\left(\frac{d+e x}{d}\right) \log (d+e x)+\frac{1}{2} \left(\log (x)-\log \left(-\frac{e x}{d}\right)\right) \log ^2(d+e x)\right)}{e^2}\right)+2 e \left(-\frac{d \log ^2(d+e x)}{2 e^2}+\frac{d \log (d+e x)}{e^2}+\frac{x \log (d+e x)}{e}-\frac{x}{e}\right)-x \log ^2(d+e x)+x \log (x) \log ^2(d+e x)\right)","\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{2 b d m n \text{Li}_2\left(\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{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}+\frac{2 b^2 d m n^2 \text{Li}_2\left(\frac{e x}{d}+1\right)}{e}+\frac{2 b^2 d m n^2 \text{Li}_3\left(\frac{e x}{d}+1\right)}{e}+2 b^2 n^2 x \log \left(f x^m\right)-4 b^2 m n^2 x",1,"b^2*n^2*(-(m*Log[x]) + Log[f*x^m])*(x*Log[d + e*x]^2 - 2*e*(-(x/e) + (d*Log[d + e*x])/e^2 + (x*Log[d + e*x])/e - (d*Log[d + e*x]^2)/(2*e^2))) - x*(m - Log[f*x^m])*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 - 2*b*n*x*(-m - m*Log[x] + Log[f*x^m])*(a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])) + 2*b*n*x*(-m + Log[f*x^m])*Log[d + e*x]*(a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])) + (2*b*d*n*(-m - m*Log[x] + Log[f*x^m])*Log[d + e*x]*(a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])))/e - 2*b*e*m*n*(a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))*((x*(-1 + Log[x]))/e - (d*((Log[x]*Log[(d + e*x)/d])/e + PolyLog[2, -((e*x)/d)]/e))/e) + b^2*m*n^2*(-(x*Log[d + e*x]^2) + x*Log[x]*Log[d + e*x]^2 + 2*e*(-(x/e) + (d*Log[d + e*x])/e^2 + (x*Log[d + e*x])/e - (d*Log[d + e*x]^2)/(2*e^2)) - 2*e*((2*e*x - d*Log[d + e*x] - e*x*Log[d + e*x] + Log[x]*(-(e*x) + e*x*Log[d + e*x] + d*Log[1 + (e*x)/d]) + d*PolyLog[2, -((e*x)/d)])/e^2 - (d*(((Log[x] - Log[-((e*x)/d)])*Log[d + e*x]^2)/2 - Log[d + e*x]*PolyLog[2, (d + e*x)/d] + PolyLog[3, (d + e*x)/d]))/e^2))","A",1
370,1,823,823,0.3974978,"\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x} \, dx","Integrate[(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2)/x,x]","-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{Li}_2\left(\frac{e x}{d}+1\right) \log (d+e x)-2 \text{Li}_3\left(\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{Li}_2\left(-\frac{e x}{d}\right)-12 \log ^2\left(-\frac{e x}{d+e x}\right) \text{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\frac{e x}{d}+1\right)+24 \left(\log \left(-\frac{e x}{d+e x}\right)+\log (d+e x)\right) \text{Li}_3\left(-\frac{e x}{d}\right)+24 \log \left(-\frac{e x}{d+e x}\right) \text{Li}_3\left(\frac{e x}{d+e x}\right)+24 \left(\log \left(-\frac{e x}{d+e x}\right)-\log (x)\right) \text{Li}_3\left(\frac{e x}{d}+1\right)-24 \left(\text{Li}_4\left(-\frac{e x}{d}\right)+\text{Li}_4\left(\frac{e x}{d+e x}\right)-\text{Li}_4\left(\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{Li}_2\left(-\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{Li}_2\left(-\frac{e x}{d}\right) \log (x)+\text{Li}_3\left(-\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","-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{Li}_2\left(\frac{e x}{d}+1\right) \log (d+e x)-2 \text{Li}_3\left(\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{Li}_2\left(-\frac{e x}{d}\right)-12 \log ^2\left(-\frac{e x}{d+e x}\right) \text{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\frac{e x}{d}+1\right)+24 \left(\log \left(-\frac{e x}{d+e x}\right)+\log (d+e x)\right) \text{Li}_3\left(-\frac{e x}{d}\right)+24 \log \left(-\frac{e x}{d+e x}\right) \text{Li}_3\left(\frac{e x}{d+e x}\right)+24 \left(\log \left(-\frac{e x}{d+e x}\right)-\log (x)\right) \text{Li}_3\left(\frac{e x}{d}+1\right)-24 \left(\text{Li}_4\left(-\frac{e x}{d}\right)+\text{Li}_4\left(\frac{e x}{d+e x}\right)-\text{Li}_4\left(\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{Li}_2\left(-\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{Li}_2\left(-\frac{e x}{d}\right) \log (x)+\text{Li}_3\left(-\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,"(m*Log[x]^2*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2)/2 + Log[x]*(-(m*Log[x]) + Log[f*x^m])*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + 2*b*n*(-(m*Log[x]) + Log[f*x^m])*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(Log[x]*(Log[d + e*x] - Log[1 + (e*x)/d]) - PolyLog[2, -((e*x)/d)]) + 2*b*m*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*((Log[x]^2*(Log[d + e*x] - Log[1 + (e*x)/d]))/2 - Log[x]*PolyLog[2, -((e*x)/d)] + PolyLog[3, -((e*x)/d)]) - b^2*n^2*(m*Log[x] - Log[f*x^m])*(Log[-((e*x)/d)]*Log[d + e*x]^2 + 2*Log[d + e*x]*PolyLog[2, 1 + (e*x)/d] - 2*PolyLog[3, 1 + (e*x)/d]) + (b^2*m*n^2*(Log[-((e*x)/d)]^4 + 6*Log[-((e*x)/d)]^2*Log[-((e*x)/(d + e*x))]^2 - 4*(Log[-((e*x)/d)] + Log[d/(d + e*x)])*Log[-((e*x)/(d + e*x))]^3 + Log[-((e*x)/(d + e*x))]^4 + 6*Log[x]^2*Log[d + e*x]^2 + 4*(2*Log[-((e*x)/d)]^3 - 3*Log[x]^2*Log[d + e*x])*Log[1 + (e*x)/d] + 6*(Log[x] - Log[-((e*x)/d)])*(Log[x] + 3*Log[-((e*x)/d)])*Log[1 + (e*x)/d]^2 - 4*Log[-((e*x)/d)]^2*Log[-((e*x)/(d + e*x))]*(Log[-((e*x)/d)] + 3*Log[1 + (e*x)/d]) + 12*(Log[-((e*x)/d)]^2 - 2*Log[-((e*x)/d)]*(Log[-((e*x)/(d + e*x))] + Log[1 + (e*x)/d]) + 2*Log[x]*(-Log[d + e*x] + Log[1 + (e*x)/d]))*PolyLog[2, -((e*x)/d)] - 12*Log[-((e*x)/(d + e*x))]^2*PolyLog[2, (e*x)/(d + e*x)] + 12*(Log[-((e*x)/d)] - Log[-((e*x)/(d + e*x))])^2*PolyLog[2, 1 + (e*x)/d] + 24*(Log[x] - Log[-((e*x)/d)])*Log[1 + (e*x)/d]*PolyLog[2, 1 + (e*x)/d] + 24*(Log[-((e*x)/(d + e*x))] + Log[d + e*x])*PolyLog[3, -((e*x)/d)] + 24*Log[-((e*x)/(d + e*x))]*PolyLog[3, (e*x)/(d + e*x)] + 24*(-Log[x] + Log[-((e*x)/(d + e*x))])*PolyLog[3, 1 + (e*x)/d] - 24*(PolyLog[4, -((e*x)/d)] + PolyLog[4, (e*x)/(d + e*x)] - PolyLog[4, 1 + (e*x)/d])))/12","A",1
371,1,513,607,0.7090427,"\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x^2} \, dx","Integrate[(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2)/x^2,x]","\frac{2 b n \left((d+e x) \log (d+e x)-e x \log \left(-\frac{e x}{d}\right)\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 \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-b m n \left(-e x \left(\log ^2(x)-2 \left(\text{Li}_2\left(-\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 m \log (x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+b^2 n^2 \left(2 e x \text{Li}_2\left(\frac{e x}{d}+1\right) \left(m \log (d+e x)+\log \left(f x^m\right)+m (-\log (x))+m\right)-d \log ^2(d+e x) \log \left(f x^m\right)-e x \log ^2(d+e x) \log \left(f x^m\right)+2 e x \log \left(-\frac{e x}{d}\right) \log (d+e x) \log \left(f x^m\right)+2 e m x \text{Li}_3\left(-\frac{e x}{d}\right)-2 e m x \text{Li}_3\left(\frac{e x}{d}+1\right)-2 e m x \log (x) \text{Li}_2\left(-\frac{e x}{d}\right)+e m x \log ^2(x) \log (d+e x)-e m x \log ^2(x) \log \left(\frac{e x}{d}+1\right)-d m \log ^2(d+e x)-e m x \log ^2(d+e x)+e m x \log \left(-\frac{e x}{d}\right) \log ^2(d+e x)-2 e m x \log (x) \log \left(-\frac{e x}{d}\right) \log (d+e x)+2 e m x \log \left(-\frac{e x}{d}\right) \log (d+e x)\right)}{d x}","-\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{b m n \left(e x \left(\log ^2(x)-2 \left(\text{Li}_2\left(-\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{m \log (x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2}{x}-\frac{2 b^2 e n^2 \text{Li}_2\left(-\frac{e x}{d}\right) \log \left(f x^m\right)}{d}-\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{2 b^2 e m n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{d}-\frac{2 b^2 e m n^2 \text{Li}_3\left(\frac{e x}{d}+1\right)}{d}+\frac{2 b^2 e m n^2 \text{Li}_2\left(\frac{e x}{d}+1\right) (\log (d+e x)+1)}{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,"(2*b*n*(m*Log[x] - Log[f*x^m])*(-(e*x*Log[-((e*x)/d)]) + (d + e*x)*Log[d + e*x])*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n]) - d*m*Log[x]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + d*(-m + m*Log[x] - Log[f*x^m])*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 - b*m*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(-2*e*x*Log[-((e*x)/d)] + 2*(d + e*x)*Log[d + e*x] + 2*d*Log[x]*Log[d + e*x] - e*x*(Log[x]^2 - 2*(Log[x]*Log[1 + (e*x)/d] + PolyLog[2, -((e*x)/d)]))) + b^2*n^2*(e*m*x*Log[x]^2*Log[d + e*x] + 2*e*m*x*Log[-((e*x)/d)]*Log[d + e*x] - 2*e*m*x*Log[x]*Log[-((e*x)/d)]*Log[d + e*x] + 2*e*x*Log[-((e*x)/d)]*Log[f*x^m]*Log[d + e*x] - d*m*Log[d + e*x]^2 - e*m*x*Log[d + e*x]^2 + e*m*x*Log[-((e*x)/d)]*Log[d + e*x]^2 - d*Log[f*x^m]*Log[d + e*x]^2 - e*x*Log[f*x^m]*Log[d + e*x]^2 - e*m*x*Log[x]^2*Log[1 + (e*x)/d] - 2*e*m*x*Log[x]*PolyLog[2, -((e*x)/d)] + 2*e*x*(m - m*Log[x] + Log[f*x^m] + m*Log[d + e*x])*PolyLog[2, 1 + (e*x)/d] + 2*e*m*x*PolyLog[3, -((e*x)/d)] - 2*e*m*x*PolyLog[3, 1 + (e*x)/d]))/(d*x)","A",1
372,1,781,939,1.0106177,"\int \frac{\log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{x^3} \, dx","Integrate[(Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^2)/x^3,x]","\frac{-2 b m n \left(\left(d^2-e^2 x^2\right) \log (d+e x)+2 d^2 \log (x) \log (d+e x)+e^2 x^2 \log \left(-\frac{e x}{d}\right)+e x \left(-2 e x \left(\text{Li}_2\left(-\frac{e x}{d}\right)+\log (x) \log \left(\frac{e x}{d}+1\right)\right)+2 d (\log (x)+1)+e x \log ^2(x)\right)+e x (d+e x)\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)+d^2 \left(-2 \log \left(f x^m\right)+2 m \log (x)-m\right) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2-2 d^2 m \log (x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right)^2+4 b n \left(e^2 x^2 \log \left(-\frac{e x}{d}\right)+(d+e x) ((d-e x) \log (d+e x)+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)+b^2 n^2 \left(-2 d^2 \log ^2(d+e x) \log \left(f x^m\right)-d^2 m \log ^2(d+e x)-2 e^2 x^2 \text{Li}_2\left(\frac{e x}{d}+1\right) \left(2 m \log (d+e x)+2 \log \left(f x^m\right)-2 m \log (x)+m\right)+2 e^2 x^2 \log ^2(d+e x) \log \left(f x^m\right)-4 e^2 x^2 \log (d+e x) \log \left(f x^m\right)-4 e^2 x^2 \log \left(-\frac{e x}{d}\right) \log (d+e x) \log \left(f x^m\right)-4 e^2 m x^2 \text{Li}_3\left(-\frac{e x}{d}\right)+4 e^2 m x^2 \text{Li}_3\left(\frac{e x}{d}+1\right)+4 e^2 m x^2 (\log (x)-1) \text{Li}_2\left(-\frac{e x}{d}\right)+e^2 m x^2 \log ^2(d+e x)-2 e^2 m x^2 \log \left(-\frac{e x}{d}\right) \log ^2(d+e x)-2 e^2 m x^2 \log ^2(x) \log (d+e x)+2 e^2 m x^2 \log ^2(x) \log \left(\frac{e x}{d}+1\right)+2 e^2 m x^2 \log \left(-\frac{e x}{d}\right)-6 e^2 m x^2 \log (d+e x)+4 e^2 m x^2 \log (x) \log (d+e x)-2 e^2 m x^2 \log \left(-\frac{e x}{d}\right) \log (d+e x)+4 e^2 m x^2 \log (x) \log \left(-\frac{e x}{d}\right) \log (d+e x)-4 e^2 m x^2 \log (x) \log \left(\frac{e x}{d}+1\right)-4 d e x \log (d+e x) \log \left(f x^m\right)-6 d e m x \log (d+e x)+4 e^2 x^2 \log (x) \log \left(f x^m\right)-2 e^2 m x^2 \log ^2(x)+4 e^2 m x^2 \log (x)\right)}{4 d^2 x^2}","-\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{Li}_2\left(-\frac{e x}{d}\right) n^2}{d^2}-\frac{b^2 e^2 m (2 \log (d+e x)+1) \text{Li}_2\left(\frac{e x}{d}+1\right) n^2}{2 d^2}-\frac{b^2 e^2 m \text{Li}_3\left(-\frac{e x}{d}\right) n^2}{d^2}+\frac{b^2 e^2 m \text{Li}_3\left(\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{Li}_2\left(-\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,"(4*b*n*(m*Log[x] - Log[f*x^m])*(e^2*x^2*Log[-((e*x)/d)] + (d + e*x)*(e*x + (d - e*x)*Log[d + e*x]))*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n]) - 2*d^2*m*Log[x]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 + d^2*(-m + 2*m*Log[x] - 2*Log[f*x^m])*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])^2 - 2*b*m*n*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(e*x*(d + e*x) + e^2*x^2*Log[-((e*x)/d)] + (d^2 - e^2*x^2)*Log[d + e*x] + 2*d^2*Log[x]*Log[d + e*x] + e*x*(e*x*Log[x]^2 + 2*d*(1 + Log[x]) - 2*e*x*(Log[x]*Log[1 + (e*x)/d] + PolyLog[2, -((e*x)/d)]))) + b^2*n^2*(4*e^2*m*x^2*Log[x] - 2*e^2*m*x^2*Log[x]^2 + 2*e^2*m*x^2*Log[-((e*x)/d)] + 4*e^2*x^2*Log[x]*Log[f*x^m] - 6*d*e*m*x*Log[d + e*x] - 6*e^2*m*x^2*Log[d + e*x] + 4*e^2*m*x^2*Log[x]*Log[d + e*x] - 2*e^2*m*x^2*Log[x]^2*Log[d + e*x] - 2*e^2*m*x^2*Log[-((e*x)/d)]*Log[d + e*x] + 4*e^2*m*x^2*Log[x]*Log[-((e*x)/d)]*Log[d + e*x] - 4*d*e*x*Log[f*x^m]*Log[d + e*x] - 4*e^2*x^2*Log[f*x^m]*Log[d + e*x] - 4*e^2*x^2*Log[-((e*x)/d)]*Log[f*x^m]*Log[d + e*x] - d^2*m*Log[d + e*x]^2 + e^2*m*x^2*Log[d + e*x]^2 - 2*e^2*m*x^2*Log[-((e*x)/d)]*Log[d + e*x]^2 - 2*d^2*Log[f*x^m]*Log[d + e*x]^2 + 2*e^2*x^2*Log[f*x^m]*Log[d + e*x]^2 - 4*e^2*m*x^2*Log[x]*Log[1 + (e*x)/d] + 2*e^2*m*x^2*Log[x]^2*Log[1 + (e*x)/d] + 4*e^2*m*x^2*(-1 + Log[x])*PolyLog[2, -((e*x)/d)] - 2*e^2*x^2*(m - 2*m*Log[x] + 2*Log[f*x^m] + 2*m*Log[d + e*x])*PolyLog[2, 1 + (e*x)/d] - 4*e^2*m*x^2*PolyLog[3, -((e*x)/d)] + 4*e^2*m*x^2*PolyLog[3, 1 + (e*x)/d]))/(4*d^2*x^2)","A",1
373,0,0,522,0.5422507,"\int \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \, dx","Integrate[Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^3,x]","\int \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^3 \, dx","\frac{6 b^2 d m n^2 \text{Li}_2\left(\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{Li}_3\left(\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\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{3 b d m n \text{Li}_2\left(\frac{e x}{d}+1\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^2}{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}-\frac{6 b^3 d m n^3 \text{Li}_2\left(\frac{e x}{d}+1\right)}{e}-\frac{6 b^3 d m n^3 \text{Li}_3\left(\frac{e x}{d}+1\right)}{e}-\frac{6 b^3 d m n^3 \text{Li}_4\left(\frac{e x}{d}+1\right)}{e}-6 b^3 n^3 x \log \left(f x^m\right)+18 b^3 m n^3 x",1,"Integrate[Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^3, x]","F",-1
374,1,519,519,0.1006702,"\int \frac{\log (x) \log ^2(a+b x)}{x} \, dx","Integrate[(Log[x]*Log[a + b*x]^2)/x,x]","\frac{1}{12} \left(-24 \left(\text{Li}_4\left(-\frac{b x}{a}\right)+\text{Li}_4\left(\frac{b x}{a+b x}\right)-\text{Li}_4\left(\frac{b x}{a}+1\right)\right)+12 \text{Li}_2\left(-\frac{b x}{a}\right) \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)-12 \text{Li}_2\left(\frac{b x}{a+b x}\right) \log ^2\left(-\frac{b x}{a+b x}\right)+12 \text{Li}_2\left(\frac{b x}{a}+1\right) \left(\log \left(-\frac{b x}{a}\right)-\log \left(-\frac{b x}{a+b x}\right)\right)^2+24 \text{Li}_2\left(\frac{b x}{a}+1\right) \left(\log (x)-\log \left(-\frac{b x}{a}\right)\right) \log \left(\frac{b x}{a}+1\right)+24 \text{Li}_3\left(-\frac{b x}{a}\right) \left(\log \left(-\frac{b x}{a+b x}\right)+\log (a+b x)\right)+24 \text{Li}_3\left(\frac{b x}{a+b x}\right) \log \left(-\frac{b x}{a+b x}\right)+24 \text{Li}_3\left(\frac{b x}{a}+1\right) \left(\log \left(-\frac{b x}{a+b x}\right)-\log (x)\right)+\log ^4\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\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)+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)","\frac{1}{12} \left(-24 \left(\text{Li}_4\left(-\frac{b x}{a}\right)+\text{Li}_4\left(\frac{b x}{a+b x}\right)-\text{Li}_4\left(\frac{b x}{a}+1\right)\right)+12 \text{Li}_2\left(-\frac{b x}{a}\right) \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)-12 \text{Li}_2\left(\frac{b x}{a+b x}\right) \log ^2\left(-\frac{b x}{a+b x}\right)+12 \text{Li}_2\left(\frac{b x}{a}+1\right) \left(\log \left(-\frac{b x}{a}\right)-\log \left(-\frac{b x}{a+b x}\right)\right)^2+24 \text{Li}_2\left(\frac{b x}{a}+1\right) \left(\log (x)-\log \left(-\frac{b x}{a}\right)\right) \log \left(\frac{b x}{a}+1\right)+24 \text{Li}_3\left(-\frac{b x}{a}\right) \left(\log \left(-\frac{b x}{a+b x}\right)+\log (a+b x)\right)+24 \text{Li}_3\left(\frac{b x}{a+b x}\right) \log \left(-\frac{b x}{a+b x}\right)+24 \text{Li}_3\left(\frac{b x}{a}+1\right) \left(\log \left(-\frac{b x}{a+b x}\right)-\log (x)\right)+\log ^4\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\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)+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[-((b*x)/a)]^4 + 6*Log[-((b*x)/a)]^2*Log[-((b*x)/(a + b*x))]^2 - 4*(Log[-((b*x)/a)] + Log[a/(a + b*x)])*Log[-((b*x)/(a + b*x))]^3 + Log[-((b*x)/(a + b*x))]^4 + 6*Log[x]^2*Log[a + b*x]^2 + 4*(2*Log[-((b*x)/a)]^3 - 3*Log[x]^2*Log[a + b*x])*Log[1 + (b*x)/a] + 6*(Log[x] - Log[-((b*x)/a)])*(Log[x] + 3*Log[-((b*x)/a)])*Log[1 + (b*x)/a]^2 - 4*Log[-((b*x)/a)]^2*Log[-((b*x)/(a + b*x))]*(Log[-((b*x)/a)] + 3*Log[1 + (b*x)/a]) + 12*(Log[-((b*x)/a)]^2 - 2*Log[-((b*x)/a)]*(Log[-((b*x)/(a + b*x))] + Log[1 + (b*x)/a]) + 2*Log[x]*(-Log[a + b*x] + Log[1 + (b*x)/a]))*PolyLog[2, -((b*x)/a)] - 12*Log[-((b*x)/(a + b*x))]^2*PolyLog[2, (b*x)/(a + b*x)] + 12*(Log[-((b*x)/a)] - Log[-((b*x)/(a + b*x))])^2*PolyLog[2, 1 + (b*x)/a] + 24*(Log[x] - Log[-((b*x)/a)])*Log[1 + (b*x)/a]*PolyLog[2, 1 + (b*x)/a] + 24*(Log[-((b*x)/(a + b*x))] + Log[a + b*x])*PolyLog[3, -((b*x)/a)] + 24*Log[-((b*x)/(a + b*x))]*PolyLog[3, (b*x)/(a + b*x)] + 24*(-Log[x] + Log[-((b*x)/(a + b*x))])*PolyLog[3, 1 + (b*x)/a] - 24*(PolyLog[4, -((b*x)/a)] + PolyLog[4, (b*x)/(a + b*x)] - PolyLog[4, 1 + (b*x)/a]))/12","A",1
375,0,0,26,0.0450649,"\int \frac{\log \left(f x^m\right)}{a+b \log \left(c (d+e x)^n\right)} \, dx","Integrate[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,"Integrate[Log[f*x^m]/(a + b*Log[c*(d + e*x)^n]), x]","A",-1
376,0,0,26,0.4943773,"\int \frac{\log \left(f x^m\right)}{\left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Integrate[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,"Integrate[Log[f*x^m]/(a + b*Log[c*(d + e*x)^n])^2, x]","A",-1
377,0,0,26,0.0964237,"\int \log \left(f x^m\right) \left(a+b \log \left(c (d+e x)^n\right)\right)^p \, dx","Integrate[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,"Integrate[Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^p, x]","A",-1
378,1,394,364,0.0629594,"\int \frac{\log (a+b x) \log (c+d x)}{x} \, dx","Integrate[(Log[a + b*x]*Log[c + d*x])/x,x]","\text{Li}_3\left(\frac{a (c+d x)}{c (a+b x)}\right)-\text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)+\left(\text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)-\text{Li}_2\left(\frac{a (c+d x)}{c (a+b x)}\right)\right) \log \left(\frac{a (c+d x)}{c (a+b x)}\right)+\text{Li}_2\left(\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{Li}_2\left(\frac{d x}{c}+1\right) \left(\log \left(\frac{a (c+d x)}{c (a+b x)}\right)+\log (a+b x)\right)+\frac{1}{2} \left(\log \left(\frac{a d-b c}{d (a+b x)}\right)-\log \left(\frac{b c x-a d x}{a c+b c x}\right)+\log \left(-\frac{b x}{a}\right)\right) \log ^2\left(\frac{a (c+d x)}{c (a+b x)}\right)+\log \left(\frac{d x}{c}+1\right) \left(\log \left(-\frac{d x}{c}\right)-\log \left(-\frac{b x}{a}\right)\right) \log \left(\frac{a (c+d x)}{c (a+b x)}\right)+\log \left(-\frac{b x}{a}\right) \log (a+b x) \log (c+d x)+\frac{1}{2} \log \left(\frac{d x}{c}+1\right) \left(\log \left(-\frac{b x}{a}\right)-\log \left(-\frac{d x}{c}\right)\right) \left(\log \left(\frac{d x}{c}+1\right)-2 \log (a+b x)\right)-\text{Li}_3\left(\frac{b x}{a}+1\right)-\text{Li}_3\left(\frac{d x}{c}+1\right)","\text{Li}_3\left(\frac{c (a+b x)}{a (c+d x)}\right)-\text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)+\text{Li}_2\left(\frac{c (a+b x)}{a (c+d x)}\right) \log \left(\frac{a (c+d x)}{c (a+b x)}\right)-\text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right) \log \left(\frac{a (c+d x)}{c (a+b x)}\right)+\text{Li}_2\left(\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{Li}_2\left(\frac{d x}{c}+1\right) \left(\log \left(\frac{a (c+d x)}{c (a+b x)}\right)+\log (a+b x)\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{Li}_3\left(\frac{b x}{a}+1\right)-\text{Li}_3\left(\frac{d x}{c}+1\right)",1,"Log[-((b*x)/a)]*Log[a + b*x]*Log[c + d*x] + (Log[(a*(c + d*x))/(c*(a + b*x))]^2*(Log[-((b*x)/a)] + Log[(-(b*c) + a*d)/(d*(a + b*x))] - Log[(b*c*x - a*d*x)/(a*c + b*c*x)]))/2 + (-Log[-((b*x)/a)] + Log[-((d*x)/c)])*Log[(a*(c + d*x))/(c*(a + b*x))]*Log[1 + (d*x)/c] + ((Log[-((b*x)/a)] - Log[-((d*x)/c)])*Log[1 + (d*x)/c]*(-2*Log[a + b*x] + Log[1 + (d*x)/c]))/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, (a*(c + d*x))/(c*(a + b*x))] + PolyLog[2, (b*(c + d*x))/(d*(a + b*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, (a*(c + d*x))/(c*(a + b*x))] - PolyLog[3, (b*(c + d*x))/(d*(a + b*x))] - PolyLog[3, 1 + (d*x)/c]","A",1
379,1,342,258,0.0908777,"\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","Integrate[x^2*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]),x]","\frac{1}{3} a g x^3 \log \left(c (d+e x)^n\right)+\frac{a d^3 g n \log (d+e x)}{3 e^3}-\frac{a d^2 g n x}{3 e^2}+\frac{a d g n x^2}{6 e}+\frac{1}{3} a f x^3-\frac{1}{9} a g n x^3+\frac{b d^3 g \log ^2\left(c (d+e x)^n\right)}{3 e^3}-\frac{11 b d^3 g n \log \left(c (d+e x)^n\right)}{9 e^3}-\frac{2 b d^2 g n x \log \left(c (d+e x)^n\right)}{3 e^2}+\frac{1}{3} b f x^3 \log \left(c (d+e x)^n\right)+\frac{1}{3} b g x^3 \log ^2\left(c (d+e x)^n\right)-\frac{2}{9} b g n x^3 \log \left(c (d+e x)^n\right)+\frac{b d g n x^2 \log \left(c (d+e x)^n\right)}{3 e}+\frac{b d^3 f n \log (d+e x)}{3 e^3}-\frac{b d^2 f n x}{3 e^2}+\frac{11 b d^2 g n^2 x}{9 e^2}+\frac{b d f n x^2}{6 e}-\frac{5 b d g n^2 x^2}{18 e}-\frac{1}{9} b f n x^3+\frac{2}{27} b g n^2 x^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{b d^3 g n^2 \log ^2(d+e x)}{3 e^3}+\frac{2 b d^2 g n^2 x}{e^2}-\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,"-1/3*(b*d^2*f*n*x)/e^2 - (a*d^2*g*n*x)/(3*e^2) + (11*b*d^2*g*n^2*x)/(9*e^2) + (b*d*f*n*x^2)/(6*e) + (a*d*g*n*x^2)/(6*e) - (5*b*d*g*n^2*x^2)/(18*e) + (a*f*x^3)/3 - (b*f*n*x^3)/9 - (a*g*n*x^3)/9 + (2*b*g*n^2*x^3)/27 + (b*d^3*f*n*Log[d + e*x])/(3*e^3) + (a*d^3*g*n*Log[d + e*x])/(3*e^3) - (11*b*d^3*g*n*Log[c*(d + e*x)^n])/(9*e^3) - (2*b*d^2*g*n*x*Log[c*(d + e*x)^n])/(3*e^2) + (b*d*g*n*x^2*Log[c*(d + e*x)^n])/(3*e) + (b*f*x^3*Log[c*(d + e*x)^n])/3 + (a*g*x^3*Log[c*(d + e*x)^n])/3 - (2*b*g*n*x^3*Log[c*(d + e*x)^n])/9 + (b*d^3*g*Log[c*(d + e*x)^n]^2)/(3*e^3) + (b*g*x^3*Log[c*(d + e*x)^n]^2)/3","A",1
380,1,263,196,0.0506747,"\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","Integrate[x*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]),x]","\frac{1}{2} a g x^2 \log \left(c (d+e x)^n\right)-\frac{a d^2 g n \log (d+e x)}{2 e^2}+\frac{a d g n x}{2 e}+\frac{1}{2} a f x^2-\frac{1}{4} a g n x^2-\frac{b d^2 g \log ^2\left(c (d+e x)^n\right)}{2 e^2}+\frac{3 b d^2 g n \log \left(c (d+e x)^n\right)}{2 e^2}+\frac{1}{2} b f x^2 \log \left(c (d+e x)^n\right)+\frac{1}{2} b g x^2 \log ^2\left(c (d+e x)^n\right)-\frac{1}{2} b g n x^2 \log \left(c (d+e x)^n\right)+\frac{b d g n x \log \left(c (d+e x)^n\right)}{e}-\frac{b d^2 f n \log (d+e x)}{2 e^2}+\frac{b d f n x}{2 e}-\frac{3 b d g n^2 x}{2 e}-\frac{1}{4} b f n x^2+\frac{1}{4} b g n^2 x^2","-\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,"(b*d*f*n*x)/(2*e) + (a*d*g*n*x)/(2*e) - (3*b*d*g*n^2*x)/(2*e) + (a*f*x^2)/2 - (b*f*n*x^2)/4 - (a*g*n*x^2)/4 + (b*g*n^2*x^2)/4 - (b*d^2*f*n*Log[d + e*x])/(2*e^2) - (a*d^2*g*n*Log[d + e*x])/(2*e^2) + (3*b*d^2*g*n*Log[c*(d + e*x)^n])/(2*e^2) + (b*d*g*n*x*Log[c*(d + e*x)^n])/e + (b*f*x^2*Log[c*(d + e*x)^n])/2 + (a*g*x^2*Log[c*(d + e*x)^n])/2 - (b*g*n*x^2*Log[c*(d + e*x)^n])/2 - (b*d^2*g*Log[c*(d + e*x)^n]^2)/(2*e^2) + (b*g*x^2*Log[c*(d + e*x)^n]^2)/2","A",1
381,1,76,110,0.0288568,"\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","Integrate[(a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]),x]","\frac{(d+e x) (a g+b (f-2 g n)) \log \left(c (d+e x)^n\right)+e x (a (f-g n)+b n (2 g n-f))+b g (d+e x) \log ^2\left(c (d+e x)^n\right)}{e}","\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,"(e*(a*(f - g*n) + b*n*(-f + 2*g*n))*x + (a*g + b*(f - 2*g*n))*(d + e*x)*Log[c*(d + e*x)^n] + b*g*(d + e*x)*Log[c*(d + e*x)^n]^2)/e","A",1
382,1,227,158,0.0620441,"\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","Integrate[((a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]))/x,x]","a g \log \left(-\frac{e x}{d}\right) \log \left(c (d+e x)^n\right)+a g n \text{Li}_2\left(\frac{d+e x}{d}\right)+a f \log (x)+b f \log \left(-\frac{e x}{d}\right) \log \left(c (d+e x)^n\right)+2 b g n \left(\log (x) \left(\log (d+e x)-\log \left(\frac{e x}{d}+1\right)\right)-\text{Li}_2\left(-\frac{e x}{d}\right)\right) \left(\log \left(c (d+e x)^n\right)-n \log (d+e x)\right)+b g \log (x) \left(\log \left(c (d+e x)^n\right)-n \log (d+e x)\right)^2+b f n \text{Li}_2\left(\frac{d+e x}{d}\right)+2 b g n^2 \left(-\text{Li}_3\left(\frac{d+e x}{d}\right)+\text{Li}_2\left(\frac{d+e x}{d}\right) \log (d+e x)+\frac{1}{2} \log \left(1-\frac{d+e x}{d}\right) \log ^2(d+e x)\right)","n \text{Li}_2\left(\frac{e x}{d}+1\right) \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\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)-2 b g n^2 \text{Li}_3\left(\frac{e x}{d}+1\right)",1,"a*f*Log[x] + b*f*Log[-((e*x)/d)]*Log[c*(d + e*x)^n] + a*g*Log[-((e*x)/d)]*Log[c*(d + e*x)^n] + b*g*Log[x]*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])^2 + 2*b*g*n*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])*(Log[x]*(Log[d + e*x] - Log[1 + (e*x)/d]) - PolyLog[2, -((e*x)/d)]) + b*f*n*PolyLog[2, (d + e*x)/d] + a*g*n*PolyLog[2, (d + e*x)/d] + 2*b*g*n^2*((Log[d + e*x]^2*Log[1 - (d + e*x)/d])/2 + Log[d + e*x]*PolyLog[2, (d + e*x)/d] - PolyLog[3, (d + e*x)/d])","A",1
383,1,180,96,0.0296458,"\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","Integrate[((a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]))/x^2,x]","-\frac{a g \log \left(c (d+e x)^n\right)}{x}+\frac{a e g n \log (x)}{d}-\frac{a e g n \log (d+e x)}{d}-\frac{a f}{x}-\frac{b f \log \left(c (d+e x)^n\right)}{x}-\frac{b e g \log ^2\left(c (d+e x)^n\right)}{d}-\frac{b g \log ^2\left(c (d+e x)^n\right)}{x}+\frac{2 b e g n \log \left(-\frac{e x}{d}\right) \log \left(c (d+e x)^n\right)}{d}+\frac{b e f n \log (x)}{d}-\frac{b e f n \log (d+e x)}{d}+\frac{2 b e g n^2 \text{Li}_2\left(\frac{d+e x}{d}\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}-\frac{2 b e g n^2 \text{Li}_2\left(\frac{d}{d+e x}\right)}{d}",1,"-((a*f)/x) + (b*e*f*n*Log[x])/d + (a*e*g*n*Log[x])/d - (b*e*f*n*Log[d + e*x])/d - (a*e*g*n*Log[d + e*x])/d - (b*f*Log[c*(d + e*x)^n])/x - (a*g*Log[c*(d + e*x)^n])/x + (2*b*e*g*n*Log[-((e*x)/d)]*Log[c*(d + e*x)^n])/d - (b*e*g*Log[c*(d + e*x)^n]^2)/d - (b*g*Log[c*(d + e*x)^n]^2)/x + (2*b*e*g*n^2*PolyLog[2, (d + e*x)/d])/d","A",1
384,1,254,156,0.1310291,"\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","Integrate[((a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]))/x^3,x]","-\frac{a g \log \left(c (d+e x)^n\right)}{2 x^2}+\frac{1}{2} a e g n \left(-\frac{e \log (x)}{d^2}+\frac{e \log (d+e x)}{d^2}-\frac{1}{d x}\right)-\frac{a f}{2 x^2}+b e g n \left(\frac{e \log ^2\left(c (d+e x)^n\right)}{2 d^2 n}-\frac{e \log \left(-\frac{e x}{d}\right) \log \left(c (d+e x)^n\right)}{d^2}-\frac{\log \left(c (d+e x)^n\right)}{d x}-\frac{e n \text{Li}_2\left(\frac{d+e x}{d}\right)}{d^2}+\frac{e n \left(\frac{\log (x)}{d}-\frac{\log (d+e x)}{d}\right)}{d}\right)-\frac{b f \log \left(c (d+e x)^n\right)}{2 x^2}-\frac{b g \log ^2\left(c (d+e x)^n\right)}{2 x^2}+\frac{1}{2} b e f n \left(-\frac{e \log (x)}{d^2}+\frac{e \log (d+e x)}{d^2}-\frac{1}{d x}\right)","-\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 \text{Li}_2\left(\frac{d}{d+e x}\right)}{d^2}+\frac{b e^2 g n^2 \log (x)}{d^2}",1,"-1/2*(a*f)/x^2 + (b*e*f*n*(-(1/(d*x)) - (e*Log[x])/d^2 + (e*Log[d + e*x])/d^2))/2 + (a*e*g*n*(-(1/(d*x)) - (e*Log[x])/d^2 + (e*Log[d + e*x])/d^2))/2 - (b*f*Log[c*(d + e*x)^n])/(2*x^2) - (a*g*Log[c*(d + e*x)^n])/(2*x^2) - (b*g*Log[c*(d + e*x)^n]^2)/(2*x^2) + b*e*g*n*((e*n*(Log[x]/d - Log[d + e*x]/d))/d - Log[c*(d + e*x)^n]/(d*x) - (e*Log[-((e*x)/d)]*Log[c*(d + e*x)^n])/d^2 + (e*Log[c*(d + e*x)^n]^2)/(2*d^2*n) - (e*n*PolyLog[2, (d + e*x)/d])/d^2)","A",1
385,1,351,234,0.1765637,"\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","Integrate[((a + b*Log[c*(d + e*x)^n])*(f + g*Log[c*(d + e*x)^n]))/x^4,x]","-\frac{a g \log \left(c (d+e x)^n\right)}{3 x^3}+\frac{1}{3} a e g n \left(\frac{e^2 \log (x)}{d^3}-\frac{e^2 \log (d+e x)}{d^3}+\frac{e}{d^2 x}-\frac{1}{2 d x^2}\right)-\frac{a f}{3 x^3}-\frac{b e^3 g \log ^2\left(c (d+e x)^n\right)}{3 d^3}+\frac{2 b e^3 g n \log \left(-\frac{e x}{d}\right) \log \left(c (d+e x)^n\right)}{3 d^3}+\frac{2 b e^2 g n \log \left(c (d+e x)^n\right)}{3 d^2 x}-\frac{b f \log \left(c (d+e x)^n\right)}{3 x^3}-\frac{b g \log ^2\left(c (d+e x)^n\right)}{3 x^3}-\frac{b e g n \log \left(c (d+e x)^n\right)}{3 d x^2}+\frac{2 b e^3 g n^2 \text{Li}_2\left(\frac{d+e x}{d}\right)}{3 d^3}-\frac{b e^3 g n^2 \log (x)}{d^3}+\frac{b e^3 g n^2 \log (d+e x)}{d^3}-\frac{b e^2 g n^2}{3 d^2 x}+\frac{1}{3} b e f n \left(\frac{e^2 \log (x)}{d^3}-\frac{e^2 \log (d+e x)}{d^3}+\frac{e}{d^2 x}-\frac{1}{2 d x^2}\right)","\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{\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 n \left(a g+2 b g \log \left(c (d+e x)^n\right)+b f\right)}{6 d x^2}-\frac{2 b e^3 g n^2 \text{Li}_2\left(\frac{d}{d+e x}\right)}{3 d^3}-\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{b e^2 g n^2}{3 d^2 x}",1,"-1/3*(a*f)/x^3 - (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])/d^3 + (b*e*f*n*(-1/2*1/(d*x^2) + e/(d^2*x) + (e^2*Log[x])/d^3 - (e^2*Log[d + e*x])/d^3))/3 + (a*e*g*n*(-1/2*1/(d*x^2) + e/(d^2*x) + (e^2*Log[x])/d^3 - (e^2*Log[d + e*x])/d^3))/3 - (b*f*Log[c*(d + e*x)^n])/(3*x^3) - (a*g*Log[c*(d + e*x)^n])/(3*x^3) - (b*e*g*n*Log[c*(d + e*x)^n])/(3*d*x^2) + (2*b*e^2*g*n*Log[c*(d + e*x)^n])/(3*d^2*x) + (2*b*e^3*g*n*Log[-((e*x)/d)]*Log[c*(d + e*x)^n])/(3*d^3) - (b*e^3*g*Log[c*(d + e*x)^n]^2)/(3*d^3) - (b*g*Log[c*(d + e*x)^n]^2)/(3*x^3) + (2*b*e^3*g*n^2*PolyLog[2, (d + e*x)/d])/(3*d^3)","A",1
386,1,605,742,1.2023707,"\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","Integrate[x^3*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]),x]","\frac{e \left(j \left(-6 g j^3 x \left(b n \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)-12 a e^3 x^3\right) \log \left(h (i+j x)^m\right)+6 a e^3 x \left(12 f j^3 x^3+g m \left(12 i^3-6 i^2 j x+4 i j^2 x^2-3 j^3 x^3\right)\right)-b n \left(18 d^3 j^3 x (5 g m-4 f)+3 d^2 e j^2 x (12 f j x+g m (20 i-9 j x))+2 d e^2 \left(g m \left(36 i^3+30 i^2 j x-12 i j^2 x^2+7 j^3 x^3\right)-12 f j^3 x^3\right)+e^3 x \left(18 f j^3 x^3+g m \left(90 i^3-27 i^2 j x+14 i j^2 x^2-9 j^3 x^3\right)\right)\right)\right)+6 g i m \log (i+j x) \left(b n \left(12 d^3 j^3+6 d^2 e i j^2+4 d e^2 i^2 j+3 e^3 i^3\right)-12 a e^3 i^3\right)-6 b e^3 \log \left(c (d+e x)^n\right) \left(-12 f j^4 x^4-12 g j^4 x^4 \log \left(h (i+j x)^m\right)+12 g i^4 m \log (i+j x)+g j m x \left(-12 i^3+6 i^2 j x-4 i j^2 x^2+3 j^3 x^3\right)\right)\right)-72 b g m n \left(e^4 i^4-d^4 j^4\right) \text{Li}_2\left(\frac{j (d+e x)}{d j-e i}\right)+6 b n \log (d+e x) \left(-12 g m \left(e^4 i^4-d^4 j^4\right) \log \left(\frac{e (i+j x)}{e i-d j}\right)+d j \left(3 d^3 j^3 (g m-4 f)-12 d^3 g j^3 \log \left(h (i+j x)^m\right)+4 d^2 e g i j^2 m+6 d e^2 g i^2 j m+12 e^3 g i^3 m\right)+12 e^4 g i^4 m \log (i+j x)\right)}{288 e^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^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^2 m x^2 \left(a+b \log \left(c (d+e x)^n\right)\right)}{8 j^2}+\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^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^4 g m n \text{Li}_2\left(\frac{e (i+j x)}{e i-d j}\right)}{4 e^4}+\frac{b d^4 g m n \log (d+e x)}{16 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^3 g i m n \log (d+e x)}{12 e^3 j}-\frac{5 b d^3 g m n x}{16 e^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^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{3 b d^2 g m n x^2}{32 e^2}+\frac{b d n x^3 \left(f+g \log \left(h (i+j x)^m\right)\right)}{12 e}-\frac{b g i^4 m n \text{Li}_2\left(-\frac{j (d+e x)}{e i-d j}\right)}{4 j^4}+\frac{b d g i^3 m n \log (i+j x)}{12 e j^3}-\frac{5 b d g i^2 m n x}{24 e j^2}+\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{b g i^4 m n \log (i+j x)}{16 j^4}-\frac{5 b g i^3 m n x}{16 j^3}+\frac{3 b g i^2 m n x^2}{32 j^2}-\frac{7 b g i m n x^3}{144 j}+\frac{1}{32} b g m n x^4",1,"(6*b*n*Log[d + e*x]*(12*e^4*g*i^4*m*Log[i + j*x] - 12*g*(e^4*i^4 - d^4*j^4)*m*Log[(e*(i + j*x))/(e*i - d*j)] + d*j*(12*e^3*g*i^3*m + 6*d*e^2*g*i^2*j*m + 4*d^2*e*g*i*j^2*m + 3*d^3*j^3*(-4*f + g*m) - 12*d^3*g*j^3*Log[h*(i + j*x)^m])) + e*(6*g*i*m*(-12*a*e^3*i^3 + b*(3*e^3*i^3 + 4*d*e^2*i^2*j + 6*d^2*e*i*j^2 + 12*d^3*j^3)*n)*Log[i + j*x] - 6*b*e^3*Log[c*(d + e*x)^n]*(-12*f*j^4*x^4 + g*j*m*x*(-12*i^3 + 6*i^2*j*x - 4*i*j^2*x^2 + 3*j^3*x^3) + 12*g*i^4*m*Log[i + j*x] - 12*g*j^4*x^4*Log[h*(i + j*x)^m]) + j*(6*a*e^3*x*(12*f*j^3*x^3 + g*m*(12*i^3 - 6*i^2*j*x + 4*i*j^2*x^2 - 3*j^3*x^3)) - b*n*(18*d^3*j^3*(-4*f + 5*g*m)*x + 3*d^2*e*j^2*x*(12*f*j*x + g*m*(20*i - 9*j*x)) + e^3*x*(18*f*j^3*x^3 + g*m*(90*i^3 - 27*i^2*j*x + 14*i*j^2*x^2 - 9*j^3*x^3)) + 2*d*e^2*(-12*f*j^3*x^3 + g*m*(36*i^3 + 30*i^2*j*x - 12*i*j^2*x^2 + 7*j^3*x^3))) - 6*g*j^3*x*(-12*a*e^3*x^3 + b*n*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3))*Log[h*(i + j*x)^m])) - 72*b*g*(e^4*i^4 - d^4*j^4)*m*n*PolyLog[2, (j*(d + e*x))/(-(e*i) + d*j)])/(288*e^4*j^4)","A",1
387,1,492,558,0.9482166,"\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","Integrate[x^2*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]),x]","\frac{e \left(j \left(-6 g j^2 x \left(b n \left(6 d^2-3 d e x+2 e^2 x^2\right)-6 a e^2 x^2\right) \log \left(h (i+j x)^m\right)+6 a e^2 x \left(6 f j^2 x^2+g m \left(-6 i^2+3 i j x-2 j^2 x^2\right)\right)+b n \left(12 d^2 j^2 x (4 g m-3 f)+3 d e \left(6 f j^2 x^2+g m \left(12 i^2+12 i j x-5 j^2 x^2\right)\right)+e^2 x \left(g m \left(48 i^2-15 i j x+8 j^2 x^2\right)-12 f j^2 x^2\right)\right)\right)+6 g i m \log (i+j x) \left(6 a e^2 i^2-b n \left(6 d^2 j^2+3 d e i j+2 e^2 i^2\right)\right)+6 b e^2 \log \left(c (d+e x)^n\right) \left(6 f j^3 x^3+6 g j^3 x^3 \log \left(h (i+j x)^m\right)+6 g i^3 m \log (i+j x)+g j m x \left(-6 i^2+3 i j x-2 j^2 x^2\right)\right)\right)+36 b g m n \left(e^3 i^3-d^3 j^3\right) \text{Li}_2\left(\frac{j (d+e x)}{d j-e i}\right)+6 b n \log (d+e x) \left(6 g m \left(e^3 i^3-d^3 j^3\right) \log \left(\frac{e (i+j x)}{e i-d j}\right)+d j \left(2 d^2 j^2 (3 f-g m)+6 d^2 g j^2 \log \left(h (i+j x)^m\right)-3 d e g i j m-6 e^2 g i^2 m\right)-6 e^3 g i^3 m \log (i+j x)\right)}{108 e^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^3 g m n \text{Li}_2\left(\frac{e (i+j x)}{e i-d j}\right)}{3 e^3}-\frac{b d^3 g m n \log (d+e x)}{9 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 n x^2 \left(f+g \log \left(h (i+j x)^m\right)\right)}{6 e}+\frac{b g i^3 m n \text{Li}_2\left(-\frac{j (d+e x)}{e i-d j}\right)}{3 j^3}-\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{b g i^3 m n \log (i+j x)}{9 j^3}+\frac{4 b g i^2 m n x}{9 j^2}-\frac{5 b g i m n x^2}{36 j}+\frac{2}{27} b g m n x^3",1,"(6*b*n*Log[d + e*x]*(-6*e^3*g*i^3*m*Log[i + j*x] + 6*g*(e^3*i^3 - d^3*j^3)*m*Log[(e*(i + j*x))/(e*i - d*j)] + d*j*(-6*e^2*g*i^2*m - 3*d*e*g*i*j*m + 2*d^2*j^2*(3*f - g*m) + 6*d^2*g*j^2*Log[h*(i + j*x)^m])) + e*(6*g*i*m*(6*a*e^2*i^2 - b*(2*e^2*i^2 + 3*d*e*i*j + 6*d^2*j^2)*n)*Log[i + j*x] + 6*b*e^2*Log[c*(d + e*x)^n]*(6*f*j^3*x^3 + g*j*m*x*(-6*i^2 + 3*i*j*x - 2*j^2*x^2) + 6*g*i^3*m*Log[i + j*x] + 6*g*j^3*x^3*Log[h*(i + j*x)^m]) + j*(6*a*e^2*x*(6*f*j^2*x^2 + g*m*(-6*i^2 + 3*i*j*x - 2*j^2*x^2)) + b*n*(12*d^2*j^2*(-3*f + 4*g*m)*x + 3*d*e*(6*f*j^2*x^2 + g*m*(12*i^2 + 12*i*j*x - 5*j^2*x^2)) + e^2*x*(-12*f*j^2*x^2 + g*m*(48*i^2 - 15*i*j*x + 8*j^2*x^2))) - 6*g*j^2*x*(-6*a*e^2*x^2 + b*n*(6*d^2 - 3*d*e*x + 2*e^2*x^2))*Log[h*(i + j*x)^m])) + 36*b*g*(e^3*i^3 - d^3*j^3)*m*n*PolyLog[2, (j*(d + e*x))/(-(e*i) + d*j)])/(108*e^3*j^3)","A",1
388,1,341,397,0.5973807,"\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","Integrate[x*(a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]),x]","\frac{e \left(j \left(g j x (2 a e x+b n (2 d-e x)) \log \left(h (i+j x)^m\right)+a e x (2 f j x+g m (2 i-j x))-b n (d (-2 f j x+2 g i m+3 g j m x)+e x (f j x+3 g i m-g j m x))\right)+g i m \log (i+j x) (b n (2 d j+e i)-2 a e i)+b e \log \left(c (d+e x)^n\right) \left(j x \left(2 f j x+2 g j x \log \left(h (i+j x)^m\right)+2 g i m-g j m x\right)-2 g i^2 m \log (i+j x)\right)\right)+b n \log (d+e x) \left(2 g m \left(d^2 j^2-e^2 i^2\right) \log \left(\frac{e (i+j x)}{e i-d j}\right)+d j \left(-2 d f j-2 d g j \log \left(h (i+j x)^m\right)+d g j m+2 e g i m\right)+2 e^2 g i^2 m \log (i+j x)\right)+2 b g m n \left(d^2 j^2-e^2 i^2\right) \text{Li}_2\left(\frac{j (d+e x)}{d j-e i}\right)}{4 e^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 \text{Li}_2\left(\frac{e (i+j x)}{e i-d j}\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{b g i^2 m n \text{Li}_2\left(-\frac{j (d+e x)}{e i-d j}\right)}{2 j^2}-\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,"(b*n*Log[d + e*x]*(2*e^2*g*i^2*m*Log[i + j*x] + 2*g*(-(e^2*i^2) + d^2*j^2)*m*Log[(e*(i + j*x))/(e*i - d*j)] + d*j*(-2*d*f*j + 2*e*g*i*m + d*g*j*m - 2*d*g*j*Log[h*(i + j*x)^m])) + e*(g*i*m*(-2*a*e*i + b*(e*i + 2*d*j)*n)*Log[i + j*x] + j*(a*e*x*(2*f*j*x + g*m*(2*i - j*x)) - b*n*(e*x*(3*g*i*m + f*j*x - g*j*m*x) + d*(2*g*i*m - 2*f*j*x + 3*g*j*m*x)) + g*j*x*(2*a*e*x + b*n*(2*d - e*x))*Log[h*(i + j*x)^m]) + b*e*Log[c*(d + e*x)^n]*(-2*g*i^2*m*Log[i + j*x] + j*x*(2*g*i*m + 2*f*j*x - g*j*m*x + 2*g*j*x*Log[h*(i + j*x)^m]))) + 2*b*g*(-(e^2*i^2) + d^2*j^2)*m*n*PolyLog[2, (j*(d + e*x))/(-(e*i) + d*j)])/(4*e^2*j^2)","A",1
389,1,329,232,0.2351704,"\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","Integrate[(a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]),x]","\frac{a e f j x+a e g j x \log \left(h (i+j x)^m\right)+a e g i m \log (i+j x)-a e g j m x+b e f j x \log \left(c (d+e x)^n\right)+b e g j x \log \left(c (d+e x)^n\right) \log \left(h (i+j x)^m\right)+b e g i m \log (i+j x) \log \left(c (d+e x)^n\right)-b e g j m x \log \left(c (d+e x)^n\right)+b n \log (d+e x) \left(g m (e i-d j) \log \left(\frac{e (i+j x)}{e i-d j}\right)+d j \left(f+g \log \left(h (i+j x)^m\right)-g m\right)-e g i m \log (i+j x)\right)+b g m n (e i-d j) \text{Li}_2\left(\frac{j (d+e x)}{d j-e i}\right)-b d f j n-b d g j n \log \left(h (i+j x)^m\right)+b d g j m n \log (i+j x)+b d g j m n-b e f j n x-b e g j n x \log \left(h (i+j x)^m\right)-b e g i m n \log (i+j x)+2 b e g j m n x}{e j}","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}+\frac{b g i m n \text{Li}_2\left(-\frac{j (d+e x)}{e i-d j}\right)}{j}+\frac{b d g m n \text{Li}_2\left(\frac{e (i+j x)}{e i-d j}\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,"(-(b*d*f*j*n) + b*d*g*j*m*n + a*e*f*j*x - a*e*g*j*m*x - b*e*f*j*n*x + 2*b*e*g*j*m*n*x + b*e*f*j*x*Log[c*(d + e*x)^n] - b*e*g*j*m*x*Log[c*(d + e*x)^n] + a*e*g*i*m*Log[i + j*x] - b*e*g*i*m*n*Log[i + j*x] + b*d*g*j*m*n*Log[i + j*x] + b*e*g*i*m*Log[c*(d + e*x)^n]*Log[i + j*x] - b*d*g*j*n*Log[h*(i + j*x)^m] + a*e*g*j*x*Log[h*(i + j*x)^m] - b*e*g*j*n*x*Log[h*(i + j*x)^m] + b*e*g*j*x*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] + b*n*Log[d + e*x]*(-(e*g*i*m*Log[i + j*x]) + g*(e*i - d*j)*m*Log[(e*(i + j*x))/(e*i - d*j)] + d*j*(f - g*m + g*Log[h*(i + j*x)^m])) + b*g*(e*i - d*j)*m*n*PolyLog[2, (j*(d + e*x))/(-(e*i) + d*j)])/(e*j)","A",1
390,1,605,637,0.2988158,"\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","Integrate[((a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]))/x,x]","\log (x) \left(a+b \log \left(c (d+e x)^n\right)-b n \log (d+e x)\right) \left(f+g \log \left(h (i+j x)^m\right)-g m \log (i+j x)\right)+a g m \left(\log (x) \left(\log (i+j x)-\log \left(\frac{j x}{i}+1\right)\right)-\text{Li}_2\left(-\frac{j x}{i}\right)\right)+b g m \left(\log (x) \left(\log (i+j x)-\log \left(\frac{j x}{i}+1\right)\right)-\text{Li}_2\left(-\frac{j x}{i}\right)\right) \left(\log \left(c (d+e x)^n\right)-n \log (d+e x)\right)+b n \left(\log (x) \left(\log (d+e x)-\log \left(\frac{e x}{d}+1\right)\right)-\text{Li}_2\left(-\frac{e x}{d}\right)\right) \left(f+g \log \left(h (i+j x)^m\right)-g m \log (i+j x)\right)+b g m n \left(\text{Li}_3\left(\frac{d (i+j x)}{i (d+e x)}\right)-\text{Li}_3\left(\frac{e (i+j x)}{j (d+e x)}\right)+\left(\text{Li}_2\left(\frac{e (i+j x)}{j (d+e x)}\right)-\text{Li}_2\left(\frac{d (i+j x)}{i (d+e x)}\right)\right) \log \left(\frac{d (i+j x)}{i (d+e x)}\right)+\text{Li}_2\left(\frac{e x}{d}+1\right) \left(\log (i+j x)-\log \left(\frac{d (i+j x)}{i (d+e x)}\right)\right)+\text{Li}_2\left(\frac{j x}{i}+1\right) \left(\log \left(\frac{d (i+j x)}{i (d+e x)}\right)+\log (d+e x)\right)+\frac{1}{2} \left(\log \left(\frac{d j-e i}{j (d+e x)}\right)-\log \left(\frac{e i x-d j x}{d i+e i x}\right)+\log \left(-\frac{e x}{d}\right)\right) \log ^2\left(\frac{d (i+j x)}{i (d+e x)}\right)+\log \left(\frac{j x}{i}+1\right) \left(\log \left(-\frac{j x}{i}\right)-\log \left(-\frac{e x}{d}\right)\right) \log \left(\frac{d (i+j x)}{i (d+e x)}\right)+\log \left(-\frac{e x}{d}\right) \log (d+e x) \log (i+j x)+\frac{1}{2} \log \left(\frac{j x}{i}+1\right) \left(\log \left(-\frac{e x}{d}\right)-\log \left(-\frac{j x}{i}\right)\right) \left(\log \left(\frac{j x}{i}+1\right)-2 \log (d+e x)\right)-\text{Li}_3\left(\frac{e x}{d}+1\right)-\text{Li}_3\left(\frac{j x}{i}+1\right)\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)+a g m \text{Li}_2\left(\frac{j x}{i}+1\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 \text{Li}_2\left(\frac{j x}{i}+1\right) \left(n \log (d+e x)-\log \left(c (d+e x)^n\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)+b f n \text{Li}_2\left(\frac{e x}{d}+1\right)-b g n \text{Li}_2\left(\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{Li}_3\left(\frac{i (d+e x)}{d (i+j x)}\right)-b g m n \text{Li}_3\left(\frac{j (d+e x)}{e (i+j x)}\right)+b g m n \text{Li}_2\left(\frac{i (d+e x)}{d (i+j x)}\right) \log \left(\frac{d (i+j x)}{i (d+e x)}\right)-b g m n \text{Li}_2\left(\frac{j (d+e x)}{e (i+j x)}\right) \log \left(\frac{d (i+j x)}{i (d+e x)}\right)+b g m n \text{Li}_2\left(\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{Li}_2\left(\frac{j x}{i}+1\right) \left(\log \left(\frac{d (i+j x)}{i (d+e x)}\right)+\log (d+e x)\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)-b g m n \text{Li}_3\left(\frac{e x}{d}+1\right)-b g m n \text{Li}_3\left(\frac{j x}{i}+1\right)",1,"Log[x]*(a - b*n*Log[d + e*x] + b*Log[c*(d + e*x)^n])*(f - g*m*Log[i + j*x] + g*Log[h*(i + j*x)^m]) + b*n*(f - g*m*Log[i + j*x] + g*Log[h*(i + j*x)^m])*(Log[x]*(Log[d + e*x] - Log[1 + (e*x)/d]) - PolyLog[2, -((e*x)/d)]) + a*g*m*(Log[x]*(Log[i + j*x] - Log[1 + (j*x)/i]) - PolyLog[2, -((j*x)/i)]) + b*g*m*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])*(Log[x]*(Log[i + j*x] - Log[1 + (j*x)/i]) - PolyLog[2, -((j*x)/i)]) + b*g*m*n*(Log[-((e*x)/d)]*Log[d + e*x]*Log[i + j*x] + (Log[(d*(i + j*x))/(i*(d + e*x))]^2*(Log[-((e*x)/d)] + Log[(-(e*i) + d*j)/(j*(d + e*x))] - Log[(e*i*x - d*j*x)/(d*i + e*i*x)]))/2 + (-Log[-((e*x)/d)] + Log[-((j*x)/i)])*Log[(d*(i + j*x))/(i*(d + e*x))]*Log[1 + (j*x)/i] + ((Log[-((e*x)/d)] - Log[-((j*x)/i)])*Log[1 + (j*x)/i]*(-2*Log[d + e*x] + Log[1 + (j*x)/i]))/2 + (Log[i + j*x] - Log[(d*(i + j*x))/(i*(d + e*x))])*PolyLog[2, 1 + (e*x)/d] + Log[(d*(i + j*x))/(i*(d + e*x))]*(-PolyLog[2, (d*(i + j*x))/(i*(d + e*x))] + PolyLog[2, (e*(i + j*x))/(j*(d + e*x))]) + (Log[d + e*x] + Log[(d*(i + j*x))/(i*(d + e*x))])*PolyLog[2, 1 + (j*x)/i] - PolyLog[3, 1 + (e*x)/d] + PolyLog[3, (d*(i + j*x))/(i*(d + e*x))] - PolyLog[3, (e*(i + j*x))/(j*(d + e*x))] - PolyLog[3, 1 + (j*x)/i])","A",1
391,1,476,270,0.2255478,"\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","Integrate[((a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]))/x^2,x]","-\frac{a d f i+a d g i \log \left(h (i+j x)^m\right)-a d g j m x \log \left(-\frac{j x}{i}\right)+a d g j m x \log (i+j x)+b d f i \log \left(c (d+e x)^n\right)+b d g i \log \left(c (d+e x)^n\right) \log \left(h (i+j x)^m\right)-b d g j m x \log \left(-\frac{j x}{i}\right) \log \left(c (d+e x)^n\right)+b d g j m x \log (i+j x) \log \left(c (d+e x)^n\right)+b e f i n x \log (d+e x)+b e g i n x \log (d+e x) \log \left(h (i+j x)^m\right)+b e g i m n x \text{Li}_2\left(\frac{e (i+j x)}{e i-d j}\right)+b d g j m n x \text{Li}_2\left(\frac{j (d+e x)}{d j-e i}\right)-b e g i m n x \log (d+e x) \log (i+j x)+b e g i m n x \log (i+j x) \log \left(\frac{j (d+e x)}{d j-e i}\right)+b d g j m n x \log (d+e x) \log \left(-\frac{j x}{i}\right)-b d g j m n x \log (d+e x) \log (i+j x)+b d g j m n x \log (d+e x) \log \left(\frac{e (i+j x)}{e i-d j}\right)-b d g j m n x \text{Li}_2\left(\frac{e x}{d}+1\right)-b d g j m n x \log \left(-\frac{e x}{d}\right) \log (d+e x)-b e f i n x \log (x)-b e g i n x \log (x) \log \left(h (i+j x)^m\right)+b e g i m n x \text{Li}_2\left(-\frac{j x}{i}\right)+b e g i m n x \log (x) \log \left(\frac{j x}{i}+1\right)}{d i x}","-\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{Li}_2\left(-\frac{j (d+e x)}{e i-d j}\right)}{i}+\frac{b g j m n \text{Li}_2\left(\frac{e x}{d}+1\right)}{i}-\frac{b e g m n \text{Li}_2\left(\frac{e (i+j x)}{e i-d j}\right)}{d}+\frac{b e g m n \text{Li}_2\left(\frac{j x}{i}+1\right)}{d}",1,"-((a*d*f*i - b*e*f*i*n*x*Log[x] - a*d*g*j*m*x*Log[-((j*x)/i)] + b*e*f*i*n*x*Log[d + e*x] - b*d*g*j*m*n*x*Log[-((e*x)/d)]*Log[d + e*x] + b*d*g*j*m*n*x*Log[-((j*x)/i)]*Log[d + e*x] + b*d*f*i*Log[c*(d + e*x)^n] - b*d*g*j*m*x*Log[-((j*x)/i)]*Log[c*(d + e*x)^n] + a*d*g*j*m*x*Log[i + j*x] - b*e*g*i*m*n*x*Log[d + e*x]*Log[i + j*x] - b*d*g*j*m*n*x*Log[d + e*x]*Log[i + j*x] + b*e*g*i*m*n*x*Log[(j*(d + e*x))/(-(e*i) + d*j)]*Log[i + j*x] + b*d*g*j*m*x*Log[c*(d + e*x)^n]*Log[i + j*x] + b*d*g*j*m*n*x*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] + a*d*g*i*Log[h*(i + j*x)^m] - b*e*g*i*n*x*Log[x]*Log[h*(i + j*x)^m] + b*e*g*i*n*x*Log[d + e*x]*Log[h*(i + j*x)^m] + b*d*g*i*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] + b*e*g*i*m*n*x*Log[x]*Log[1 + (j*x)/i] + b*e*g*i*m*n*x*PolyLog[2, -((j*x)/i)] + b*d*g*j*m*n*x*PolyLog[2, (j*(d + e*x))/(-(e*i) + d*j)] - b*d*g*j*m*n*x*PolyLog[2, 1 + (e*x)/d] + b*e*g*i*m*n*x*PolyLog[2, (e*(i + j*x))/(e*i - d*j)])/(d*i*x))","A",1
392,1,765,421,0.3466443,"\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","Integrate[((a + b*Log[c*(d + e*x)^n])*(f + g*Log[h*(i + j*x)^m]))/x^3,x]","-\frac{\left(a+b \left(\log \left(c (d+e x)^n\right)-n \log (d+e x)\right)\right) \left(f+g \left(\log \left(h (i+j x)^m\right)-m \log (i+j x)\right)\right)}{2 x^2}+\frac{1}{2} a g m \left(\frac{j^2 (i+j x)}{i^3 \left(1-\frac{i+j x}{i}\right)}-\frac{j^2 \log \left(1-\frac{i+j x}{i}\right)}{i^2}-\left(\frac{j^2 (i+j x)^2}{i^4 \left(1-\frac{i+j x}{i}\right)^2}+\frac{2 j^2 (i+j x)}{i^3 \left(1-\frac{i+j x}{i}\right)}\right) \log (i+j x)\right)+\frac{1}{2} b g m \left(\frac{j^2 (i+j x)}{i^3 \left(1-\frac{i+j x}{i}\right)}-\frac{j^2 \log \left(1-\frac{i+j x}{i}\right)}{i^2}-\left(\frac{j^2 (i+j x)^2}{i^4 \left(1-\frac{i+j x}{i}\right)^2}+\frac{2 j^2 (i+j x)}{i^3 \left(1-\frac{i+j x}{i}\right)}\right) \log (i+j x)\right) \left(\log \left(c (d+e x)^n\right)-n \log (d+e x)\right)-\frac{b e^2 n \log (x) \left(f+g \left(\log \left(h (i+j x)^m\right)-m \log (i+j x)\right)\right)}{2 d^2}+\frac{b e^2 n \log (d+e x) \left(f+g \left(\log \left(h (i+j x)^m\right)-m \log (i+j x)\right)\right)}{2 d^2}+\frac{1}{2} b g m n \left(e \left(\frac{e^2 \left(\frac{\text{Li}_2\left(\frac{e (i+j x)}{e i-d j}\right)}{e}+\frac{\log (i+j x) \log \left(\frac{j (d+e x)}{d j-e i}\right)}{e}\right)}{d^2}-\frac{e \left(\log (x) \left(\log (i+j x)-\log \left(\frac{j x}{i}+1\right)\right)-\text{Li}_2\left(-\frac{j x}{i}\right)\right)}{d^2}+\frac{\frac{j \log (x)}{i}-\frac{j \log (i+j x)}{i}-\frac{\log (i+j x)}{x}}{d}\right)+j \left(\frac{j^2 \left(\frac{\text{Li}_2\left(\frac{j (d+e x)}{d j-e i}\right)}{j}+\frac{\log (d+e x) \log \left(\frac{e (i+j x)}{e i-d j}\right)}{j}\right)}{i^2}-\frac{j \left(\text{Li}_2\left(\frac{d+e x}{d}\right)+\log \left(-\frac{e x}{d}\right) \log (d+e x)\right)}{i^2}+\frac{\frac{e \log (x)}{d}-\frac{e \log (d+e x)}{d}-\frac{\log (d+e x)}{x}}{i}\right)-\frac{\log (d+e x) \log (i+j x)}{x^2}\right)-\frac{b n \log (d+e x) \left(f+g \left(\log \left(h (i+j x)^m\right)-m \log (i+j x)\right)\right)}{2 x^2}-\frac{e \left(b f n+b g n \left(\log \left(h (i+j x)^m\right)-m \log (i+j x)\right)\right)}{2 d x}","-\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^2 g m n \text{Li}_2\left(\frac{e (i+j x)}{e i-d j}\right)}{2 d^2}-\frac{b e^2 g m n \text{Li}_2\left(\frac{j x}{i}+1\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 g j^2 m n \text{Li}_2\left(-\frac{j (d+e x)}{e i-d j}\right)}{2 i^2}-\frac{b g j^2 m n \text{Li}_2\left(\frac{e x}{d}+1\right)}{2 i^2}+\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,"-1/2*(b*e^2*n*Log[x]*(f + g*(-(m*Log[i + j*x]) + Log[h*(i + j*x)^m])))/d^2 + (b*e^2*n*Log[d + e*x]*(f + g*(-(m*Log[i + j*x]) + Log[h*(i + j*x)^m])))/(2*d^2) - (b*n*Log[d + e*x]*(f + g*(-(m*Log[i + j*x]) + Log[h*(i + j*x)^m])))/(2*x^2) - ((a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))*(f + g*(-(m*Log[i + j*x]) + Log[h*(i + j*x)^m])))/(2*x^2) - (e*(b*f*n + b*g*n*(-(m*Log[i + j*x]) + Log[h*(i + j*x)^m])))/(2*d*x) + (a*g*m*((j^2*(i + j*x))/(i^3*(1 - (i + j*x)/i)) - ((j^2*(i + j*x)^2)/(i^4*(1 - (i + j*x)/i)^2) + (2*j^2*(i + j*x))/(i^3*(1 - (i + j*x)/i)))*Log[i + j*x] - (j^2*Log[1 - (i + j*x)/i])/i^2))/2 + (b*g*m*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n])*((j^2*(i + j*x))/(i^3*(1 - (i + j*x)/i)) - ((j^2*(i + j*x)^2)/(i^4*(1 - (i + j*x)/i)^2) + (2*j^2*(i + j*x))/(i^3*(1 - (i + j*x)/i)))*Log[i + j*x] - (j^2*Log[1 - (i + j*x)/i])/i^2))/2 + (b*g*m*n*(-((Log[d + e*x]*Log[i + j*x])/x^2) + j*(((e*Log[x])/d - (e*Log[d + e*x])/d - Log[d + e*x]/x)/i - (j*(Log[-((e*x)/d)]*Log[d + e*x] + PolyLog[2, (d + e*x)/d]))/i^2 + (j^2*((Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)])/j + PolyLog[2, (j*(d + e*x))/(-(e*i) + d*j)]/j))/i^2) + e*(((j*Log[x])/i - (j*Log[i + j*x])/i - Log[i + j*x]/x)/d - (e*(Log[x]*(Log[i + j*x] - Log[1 + (j*x)/i]) - PolyLog[2, -((j*x)/i)]))/d^2 + (e^2*((Log[(j*(d + e*x))/(-(e*i) + d*j)]*Log[i + j*x])/e + PolyLog[2, (e*(i + j*x))/(e*i - d*j)]/e))/d^2)))/2","A",1
393,1,2067,1210,1.368624,"\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","Integrate[x*(a + b*Log[c*(d + e*x)^n])^2*(f + g*Log[h*(i + j*x)^m]),x]","\text{Result too large to show}","-\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{Li}_2\left(-\frac{j (d+e x)}{e i-d j}\right) b^2}{e j}+\frac{g i^2 m n^2 \text{Li}_2\left(-\frac{j (d+e x)}{e i-d j}\right) b^2}{2 j^2}+\frac{3 d^2 g m n^2 \text{Li}_2\left(\frac{e (i+j x)}{e i-d j}\right) b^2}{2 e^2}-\frac{d^2 g m n^2 \text{Li}_3\left(-\frac{j (d+e x)}{e i-d j}\right) b^2}{e^2}+\frac{g i^2 m n^2 \text{Li}_3\left(-\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{Li}_2\left(-\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{Li}_2\left(-\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,"(-8*a*b*d*e*g*i*j*m*n + 4*b^2*d*e*g*i*j*m*n^2 + 8*b^2*d^2*g*j^2*m*n^2 + 4*a^2*e^2*g*i*j*m*x + 8*a*b*d*e*f*j^2*n*x - 12*a*b*e^2*g*i*j*m*n*x - 12*a*b*d*e*g*j^2*m*n*x - 12*b^2*d*e*f*j^2*n^2*x + 14*b^2*e^2*g*i*j*m*n^2*x + 28*b^2*d*e*g*j^2*m*n^2*x + 4*a^2*e^2*f*j^2*x^2 - 2*a^2*e^2*g*j^2*m*x^2 - 4*a*b*e^2*f*j^2*n*x^2 + 4*a*b*e^2*g*j^2*m*n*x^2 + 2*b^2*e^2*f*j^2*n^2*x^2 - 3*b^2*e^2*g*j^2*m*n^2*x^2 - 8*a*b*d^2*f*j^2*n*Log[d + e*x] + 8*a*b*d*e*g*i*j*m*n*Log[d + e*x] + 4*a*b*d^2*g*j^2*m*n*Log[d + e*x] + 12*b^2*d^2*f*j^2*n^2*Log[d + e*x] - 4*b^2*d*e*g*i*j*m*n^2*Log[d + e*x] - 16*b^2*d^2*g*j^2*m*n^2*Log[d + e*x] + 4*b^2*d^2*f*j^2*n^2*Log[d + e*x]^2 - 4*b^2*d*e*g*i*j*m*n^2*Log[d + e*x]^2 - 2*b^2*d^2*g*j^2*m*n^2*Log[d + e*x]^2 - 8*b^2*d*e*g*i*j*m*n*Log[c*(d + e*x)^n] + 8*a*b*e^2*g*i*j*m*x*Log[c*(d + e*x)^n] + 8*b^2*d*e*f*j^2*n*x*Log[c*(d + e*x)^n] - 12*b^2*e^2*g*i*j*m*n*x*Log[c*(d + e*x)^n] - 12*b^2*d*e*g*j^2*m*n*x*Log[c*(d + e*x)^n] + 8*a*b*e^2*f*j^2*x^2*Log[c*(d + e*x)^n] - 4*a*b*e^2*g*j^2*m*x^2*Log[c*(d + e*x)^n] - 4*b^2*e^2*f*j^2*n*x^2*Log[c*(d + e*x)^n] + 4*b^2*e^2*g*j^2*m*n*x^2*Log[c*(d + e*x)^n] - 8*b^2*d^2*f*j^2*n*Log[d + e*x]*Log[c*(d + e*x)^n] + 8*b^2*d*e*g*i*j*m*n*Log[d + e*x]*Log[c*(d + e*x)^n] + 4*b^2*d^2*g*j^2*m*n*Log[d + e*x]*Log[c*(d + e*x)^n] + 4*b^2*e^2*g*i*j*m*x*Log[c*(d + e*x)^n]^2 + 4*b^2*e^2*f*j^2*x^2*Log[c*(d + e*x)^n]^2 - 2*b^2*e^2*g*j^2*m*x^2*Log[c*(d + e*x)^n]^2 - 4*a^2*e^2*g*i^2*m*Log[i + j*x] + 4*a*b*e^2*g*i^2*m*n*Log[i + j*x] + 8*a*b*d*e*g*i*j*m*n*Log[i + j*x] - 2*b^2*e^2*g*i^2*m*n^2*Log[i + j*x] - 12*b^2*d*e*g*i*j*m*n^2*Log[i + j*x] + 8*a*b*e^2*g*i^2*m*n*Log[d + e*x]*Log[i + j*x] - 4*b^2*e^2*g*i^2*m*n^2*Log[d + e*x]*Log[i + j*x] - 8*b^2*d*e*g*i*j*m*n^2*Log[d + e*x]*Log[i + j*x] - 4*b^2*e^2*g*i^2*m*n^2*Log[d + e*x]^2*Log[i + j*x] - 8*a*b*e^2*g*i^2*m*Log[c*(d + e*x)^n]*Log[i + j*x] + 4*b^2*e^2*g*i^2*m*n*Log[c*(d + e*x)^n]*Log[i + j*x] + 8*b^2*d*e*g*i*j*m*n*Log[c*(d + e*x)^n]*Log[i + j*x] + 8*b^2*e^2*g*i^2*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[i + j*x] - 4*b^2*e^2*g*i^2*m*Log[c*(d + e*x)^n]^2*Log[i + j*x] - 8*a*b*e^2*g*i^2*m*n*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] + 8*a*b*d^2*g*j^2*m*n*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] + 4*b^2*e^2*g*i^2*m*n^2*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] + 8*b^2*d*e*g*i*j*m*n^2*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] - 12*b^2*d^2*g*j^2*m*n^2*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] + 4*b^2*e^2*g*i^2*m*n^2*Log[d + e*x]^2*Log[(e*(i + j*x))/(e*i - d*j)] - 4*b^2*d^2*g*j^2*m*n^2*Log[d + e*x]^2*Log[(e*(i + j*x))/(e*i - d*j)] - 8*b^2*e^2*g*i^2*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] + 8*b^2*d^2*g*j^2*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] + 8*a*b*d*e*g*j^2*n*x*Log[h*(i + j*x)^m] - 12*b^2*d*e*g*j^2*n^2*x*Log[h*(i + j*x)^m] + 4*a^2*e^2*g*j^2*x^2*Log[h*(i + j*x)^m] - 4*a*b*e^2*g*j^2*n*x^2*Log[h*(i + j*x)^m] + 2*b^2*e^2*g*j^2*n^2*x^2*Log[h*(i + j*x)^m] - 8*a*b*d^2*g*j^2*n*Log[d + e*x]*Log[h*(i + j*x)^m] + 12*b^2*d^2*g*j^2*n^2*Log[d + e*x]*Log[h*(i + j*x)^m] + 4*b^2*d^2*g*j^2*n^2*Log[d + e*x]^2*Log[h*(i + j*x)^m] + 8*b^2*d*e*g*j^2*n*x*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] + 8*a*b*e^2*g*j^2*x^2*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] - 4*b^2*e^2*g*j^2*n*x^2*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] - 8*b^2*d^2*g*j^2*n*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] + 4*b^2*e^2*g*j^2*x^2*Log[c*(d + e*x)^n]^2*Log[h*(i + j*x)^m] - 4*b*g*(e*i - d*j)*m*n*(2*a*(e*i + d*j) - b*(e*i + 3*d*j)*n + 2*b*(e*i + d*j)*Log[c*(d + e*x)^n])*PolyLog[2, (j*(d + e*x))/(-(e*i) + d*j)] + 8*b^2*g*(e^2*i^2 - d^2*j^2)*m*n^2*PolyLog[3, (j*(d + e*x))/(-(e*i) + d*j)])/(8*e^2*j^2)","A",1
394,1,1355,649,0.5528081,"\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","Integrate[(a + b*Log[c*(d + e*x)^n])^2*(f + g*Log[h*(i + j*x)^m]),x]","\frac{e f j x a^2-e g j m x a^2+e g i m \log (i+j x) a^2+e g j x \log \left(h (i+j x)^m\right) a^2-2 b d f j n a+2 b d g j m n a-2 b e f j n x a+4 b e g j m n x a+2 b d f j n \log (d+e x) a-2 b d g j m n \log (d+e x) a+2 b e f j x \log \left(c (d+e x)^n\right) a-2 b e g j m x \log \left(c (d+e x)^n\right) a-2 b e g i m n \log (i+j x) a+2 b d g j m n \log (i+j x) a-2 b e g i m n \log (d+e x) \log (i+j x) a+2 b e g i m \log \left(c (d+e x)^n\right) \log (i+j x) a+2 b e g i m n \log (d+e x) \log \left(\frac{e (i+j x)}{e i-d j}\right) a-2 b d g j m n \log (d+e x) \log \left(\frac{e (i+j x)}{e i-d j}\right) a-2 b d g j n \log \left(h (i+j x)^m\right) a-2 b e g j n x \log \left(h (i+j x)^m\right) a+2 b d g j n \log (d+e x) \log \left(h (i+j x)^m\right) a+2 b e g j x \log \left(c (d+e x)^n\right) \log \left(h (i+j x)^m\right) a-2 b^2 d g j m n^2-b^2 d f j n^2 \log ^2(d+e x)+b^2 d g j m n^2 \log ^2(d+e x)+b^2 e f j x \log ^2\left(c (d+e x)^n\right)-b^2 e g j m x \log ^2\left(c (d+e x)^n\right)+2 b^2 e f j n^2 x-6 b^2 e g j m n^2 x+2 b^2 d g j m n^2 \log (d+e x)-2 b^2 d f j n \log \left(c (d+e x)^n\right)+2 b^2 d g j m n \log \left(c (d+e x)^n\right)-2 b^2 e f j n x \log \left(c (d+e x)^n\right)+4 b^2 e g j m n x \log \left(c (d+e x)^n\right)+2 b^2 d f j n \log (d+e x) \log \left(c (d+e x)^n\right)-2 b^2 d g j m n \log (d+e x) \log \left(c (d+e x)^n\right)+2 b^2 e g i m n^2 \log (i+j x)+b^2 e g i m n^2 \log ^2(d+e x) \log (i+j x)+b^2 e g i m \log ^2\left(c (d+e x)^n\right) \log (i+j x)+2 b^2 e g i m n^2 \log (d+e x) \log (i+j x)-2 b^2 d g j m n^2 \log (d+e x) \log (i+j x)-2 b^2 e g i m n \log \left(c (d+e x)^n\right) \log (i+j x)+2 b^2 d g j m n \log \left(c (d+e x)^n\right) \log (i+j x)-2 b^2 e g i m n \log (d+e x) \log \left(c (d+e x)^n\right) \log (i+j x)-b^2 e g i m n^2 \log ^2(d+e x) \log \left(\frac{e (i+j x)}{e i-d j}\right)+b^2 d g j m n^2 \log ^2(d+e x) \log \left(\frac{e (i+j x)}{e i-d j}\right)-2 b^2 e g i m n^2 \log (d+e x) \log \left(\frac{e (i+j x)}{e i-d j}\right)+2 b^2 d g j m n^2 \log (d+e x) \log \left(\frac{e (i+j x)}{e i-d j}\right)+2 b^2 e g i m n \log (d+e x) \log \left(c (d+e x)^n\right) \log \left(\frac{e (i+j x)}{e i-d j}\right)-2 b^2 d g j m n \log (d+e x) \log \left(c (d+e x)^n\right) \log \left(\frac{e (i+j x)}{e i-d j}\right)-b^2 d g j n^2 \log ^2(d+e x) \log \left(h (i+j x)^m\right)+b^2 e g j x \log ^2\left(c (d+e x)^n\right) \log \left(h (i+j x)^m\right)+2 b^2 e g j n^2 x \log \left(h (i+j x)^m\right)-2 b^2 d g j n \log \left(c (d+e x)^n\right) \log \left(h (i+j x)^m\right)-2 b^2 e g j n x \log \left(c (d+e x)^n\right) \log \left(h (i+j x)^m\right)+2 b^2 d g j n \log (d+e x) \log \left(c (d+e x)^n\right) \log \left(h (i+j x)^m\right)+2 b g (e i-d j) m n \left(a-b n+b \log \left(c (d+e x)^n\right)\right) \text{Li}_2\left(\frac{j (d+e x)}{d j-e i}\right)+2 b^2 g (d j-e i) m n^2 \text{Li}_3\left(\frac{j (d+e x)}{d j-e i}\right)}{e 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 d g m n \text{Li}_2\left(-\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{Li}_2\left(-\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 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}-\frac{2 b^2 g i m n^2 \text{Li}_2\left(-\frac{j (d+e x)}{e i-d j}\right)}{j}-\frac{2 b^2 d g m n^2 \text{Li}_2\left(\frac{e (i+j x)}{e i-d j}\right)}{e}+\frac{2 b^2 d g m n^2 \text{Li}_3\left(-\frac{j (d+e x)}{e i-d j}\right)}{e}-\frac{2 b^2 g i m n^2 \text{Li}_3\left(-\frac{j (d+e x)}{e i-d j}\right)}{j}+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*d*f*j*n + 2*a*b*d*g*j*m*n - 2*b^2*d*g*j*m*n^2 + a^2*e*f*j*x - a^2*e*g*j*m*x - 2*a*b*e*f*j*n*x + 4*a*b*e*g*j*m*n*x + 2*b^2*e*f*j*n^2*x - 6*b^2*e*g*j*m*n^2*x + 2*a*b*d*f*j*n*Log[d + e*x] - 2*a*b*d*g*j*m*n*Log[d + e*x] + 2*b^2*d*g*j*m*n^2*Log[d + e*x] - b^2*d*f*j*n^2*Log[d + e*x]^2 + b^2*d*g*j*m*n^2*Log[d + e*x]^2 - 2*b^2*d*f*j*n*Log[c*(d + e*x)^n] + 2*b^2*d*g*j*m*n*Log[c*(d + e*x)^n] + 2*a*b*e*f*j*x*Log[c*(d + e*x)^n] - 2*a*b*e*g*j*m*x*Log[c*(d + e*x)^n] - 2*b^2*e*f*j*n*x*Log[c*(d + e*x)^n] + 4*b^2*e*g*j*m*n*x*Log[c*(d + e*x)^n] + 2*b^2*d*f*j*n*Log[d + e*x]*Log[c*(d + e*x)^n] - 2*b^2*d*g*j*m*n*Log[d + e*x]*Log[c*(d + e*x)^n] + b^2*e*f*j*x*Log[c*(d + e*x)^n]^2 - b^2*e*g*j*m*x*Log[c*(d + e*x)^n]^2 + a^2*e*g*i*m*Log[i + j*x] - 2*a*b*e*g*i*m*n*Log[i + j*x] + 2*a*b*d*g*j*m*n*Log[i + j*x] + 2*b^2*e*g*i*m*n^2*Log[i + j*x] - 2*a*b*e*g*i*m*n*Log[d + e*x]*Log[i + j*x] + 2*b^2*e*g*i*m*n^2*Log[d + e*x]*Log[i + j*x] - 2*b^2*d*g*j*m*n^2*Log[d + e*x]*Log[i + j*x] + b^2*e*g*i*m*n^2*Log[d + e*x]^2*Log[i + j*x] + 2*a*b*e*g*i*m*Log[c*(d + e*x)^n]*Log[i + j*x] - 2*b^2*e*g*i*m*n*Log[c*(d + e*x)^n]*Log[i + j*x] + 2*b^2*d*g*j*m*n*Log[c*(d + e*x)^n]*Log[i + j*x] - 2*b^2*e*g*i*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[i + j*x] + b^2*e*g*i*m*Log[c*(d + e*x)^n]^2*Log[i + j*x] + 2*a*b*e*g*i*m*n*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] - 2*a*b*d*g*j*m*n*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] - 2*b^2*e*g*i*m*n^2*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] + 2*b^2*d*g*j*m*n^2*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] - b^2*e*g*i*m*n^2*Log[d + e*x]^2*Log[(e*(i + j*x))/(e*i - d*j)] + b^2*d*g*j*m*n^2*Log[d + e*x]^2*Log[(e*(i + j*x))/(e*i - d*j)] + 2*b^2*e*g*i*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] - 2*b^2*d*g*j*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] - 2*a*b*d*g*j*n*Log[h*(i + j*x)^m] + a^2*e*g*j*x*Log[h*(i + j*x)^m] - 2*a*b*e*g*j*n*x*Log[h*(i + j*x)^m] + 2*b^2*e*g*j*n^2*x*Log[h*(i + j*x)^m] + 2*a*b*d*g*j*n*Log[d + e*x]*Log[h*(i + j*x)^m] - b^2*d*g*j*n^2*Log[d + e*x]^2*Log[h*(i + j*x)^m] - 2*b^2*d*g*j*n*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] + 2*a*b*e*g*j*x*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] - 2*b^2*e*g*j*n*x*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] + 2*b^2*d*g*j*n*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] + b^2*e*g*j*x*Log[c*(d + e*x)^n]^2*Log[h*(i + j*x)^m] + 2*b*g*(e*i - d*j)*m*n*(a - b*n + b*Log[c*(d + e*x)^n])*PolyLog[2, (j*(d + e*x))/(-(e*i) + d*j)] + 2*b^2*g*(-(e*i) + d*j)*m*n^2*PolyLog[3, (j*(d + e*x))/(-(e*i) + d*j)])/(e*j)","B",1
395,0,0,37,0.7271159,"\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","Integrate[((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,"Integrate[((a + b*Log[c*(d + e*x)^n])^2*(f + g*Log[h*(i + j*x)^m]))/x, x]","A",-1
396,0,0,37,0.9127587,"\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","Integrate[((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,"Integrate[((a + b*Log[c*(d + e*x)^n])^2*(f + g*Log[h*(i + j*x)^m]))/x^2, x]","A",-1
397,1,4971,2050,3.7883689,"\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","Integrate[x*(a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]),x]","\text{Result too large to show}","\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{Li}_2\left(-\frac{j (d+e x)}{e i-d j}\right) b^3}{2 e j}-\frac{3 g i^2 m n^3 \text{Li}_2\left(-\frac{j (d+e x)}{e i-d j}\right) b^3}{4 j^2}-\frac{21 d^2 g m n^3 \text{Li}_2\left(\frac{e (i+j x)}{e i-d j}\right) b^3}{4 e^2}+\frac{9 d^2 g m n^3 \text{Li}_3\left(-\frac{j (d+e x)}{e i-d j}\right) b^3}{2 e^2}-\frac{3 d g i m n^3 \text{Li}_3\left(-\frac{j (d+e x)}{e i-d j}\right) b^3}{e j}-\frac{3 g i^2 m n^3 \text{Li}_3\left(-\frac{j (d+e x)}{e i-d j}\right) b^3}{2 j^2}+\frac{3 d^2 g m n^3 \text{Li}_4\left(-\frac{j (d+e x)}{e i-d j}\right) b^3}{e^2}-\frac{3 g i^2 m n^3 \text{Li}_4\left(-\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{Li}_2\left(-\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{Li}_2\left(-\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{Li}_2\left(-\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{Li}_3\left(-\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{Li}_3\left(-\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{Li}_2\left(-\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{Li}_2\left(-\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,"(-12*a^2*b*d*e*g*i*j*m*n + 12*a*b^2*d*e*g*i*j*m*n^2 + 24*a*b^2*d^2*g*j^2*m*n^2 - 6*b^3*d*e*g*i*j*m*n^3 - 36*b^3*d^2*g*j^2*m*n^3 + 4*a^3*e^2*g*i*j*m*x + 12*a^2*b*d*e*f*j^2*n*x - 18*a^2*b*e^2*g*i*j*m*n*x - 18*a^2*b*d*e*g*j^2*m*n*x - 36*a*b^2*d*e*f*j^2*n^2*x + 42*a*b^2*e^2*g*i*j*m*n^2*x + 84*a*b^2*d*e*g*j^2*m*n^2*x + 42*b^3*d*e*f*j^2*n^3*x - 45*b^3*e^2*g*i*j*m*n^3*x - 135*b^3*d*e*g*j^2*m*n^3*x + 4*a^3*e^2*f*j^2*x^2 - 2*a^3*e^2*g*j^2*m*x^2 - 6*a^2*b*e^2*f*j^2*n*x^2 + 6*a^2*b*e^2*g*j^2*m*n*x^2 + 6*a*b^2*e^2*f*j^2*n^2*x^2 - 9*a*b^2*e^2*g*j^2*m*n^2*x^2 - 3*b^3*e^2*f*j^2*n^3*x^2 + 6*b^3*e^2*g*j^2*m*n^3*x^2 - 12*a^2*b*d^2*f*j^2*n*Log[d + e*x] + 12*a^2*b*d*e*g*i*j*m*n*Log[d + e*x] + 6*a^2*b*d^2*g*j^2*m*n*Log[d + e*x] + 36*a*b^2*d^2*f*j^2*n^2*Log[d + e*x] - 12*a*b^2*d*e*g*i*j*m*n^2*Log[d + e*x] - 48*a*b^2*d^2*g*j^2*m*n^2*Log[d + e*x] - 42*b^3*d^2*f*j^2*n^3*Log[d + e*x] + 30*b^3*d*e*g*i*j*m*n^3*Log[d + e*x] + 69*b^3*d^2*g*j^2*m*n^3*Log[d + e*x] + 12*a*b^2*d^2*f*j^2*n^2*Log[d + e*x]^2 - 12*a*b^2*d*e*g*i*j*m*n^2*Log[d + e*x]^2 - 6*a*b^2*d^2*g*j^2*m*n^2*Log[d + e*x]^2 - 18*b^3*d^2*f*j^2*n^3*Log[d + e*x]^2 + 6*b^3*d*e*g*i*j*m*n^3*Log[d + e*x]^2 + 24*b^3*d^2*g*j^2*m*n^3*Log[d + e*x]^2 - 4*b^3*d^2*f*j^2*n^3*Log[d + e*x]^3 + 4*b^3*d*e*g*i*j*m*n^3*Log[d + e*x]^3 + 2*b^3*d^2*g*j^2*m*n^3*Log[d + e*x]^3 - 24*a*b^2*d*e*g*i*j*m*n*Log[c*(d + e*x)^n] + 12*b^3*d*e*g*i*j*m*n^2*Log[c*(d + e*x)^n] + 24*b^3*d^2*g*j^2*m*n^2*Log[c*(d + e*x)^n] + 12*a^2*b*e^2*g*i*j*m*x*Log[c*(d + e*x)^n] + 24*a*b^2*d*e*f*j^2*n*x*Log[c*(d + e*x)^n] - 36*a*b^2*e^2*g*i*j*m*n*x*Log[c*(d + e*x)^n] - 36*a*b^2*d*e*g*j^2*m*n*x*Log[c*(d + e*x)^n] - 36*b^3*d*e*f*j^2*n^2*x*Log[c*(d + e*x)^n] + 42*b^3*e^2*g*i*j*m*n^2*x*Log[c*(d + e*x)^n] + 84*b^3*d*e*g*j^2*m*n^2*x*Log[c*(d + e*x)^n] + 12*a^2*b*e^2*f*j^2*x^2*Log[c*(d + e*x)^n] - 6*a^2*b*e^2*g*j^2*m*x^2*Log[c*(d + e*x)^n] - 12*a*b^2*e^2*f*j^2*n*x^2*Log[c*(d + e*x)^n] + 12*a*b^2*e^2*g*j^2*m*n*x^2*Log[c*(d + e*x)^n] + 6*b^3*e^2*f*j^2*n^2*x^2*Log[c*(d + e*x)^n] - 9*b^3*e^2*g*j^2*m*n^2*x^2*Log[c*(d + e*x)^n] - 24*a*b^2*d^2*f*j^2*n*Log[d + e*x]*Log[c*(d + e*x)^n] + 24*a*b^2*d*e*g*i*j*m*n*Log[d + e*x]*Log[c*(d + e*x)^n] + 12*a*b^2*d^2*g*j^2*m*n*Log[d + e*x]*Log[c*(d + e*x)^n] + 36*b^3*d^2*f*j^2*n^2*Log[d + e*x]*Log[c*(d + e*x)^n] - 12*b^3*d*e*g*i*j*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n] - 48*b^3*d^2*g*j^2*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n] + 12*b^3*d^2*f*j^2*n^2*Log[d + e*x]^2*Log[c*(d + e*x)^n] - 12*b^3*d*e*g*i*j*m*n^2*Log[d + e*x]^2*Log[c*(d + e*x)^n] - 6*b^3*d^2*g*j^2*m*n^2*Log[d + e*x]^2*Log[c*(d + e*x)^n] - 12*b^3*d*e*g*i*j*m*n*Log[c*(d + e*x)^n]^2 + 12*a*b^2*e^2*g*i*j*m*x*Log[c*(d + e*x)^n]^2 + 12*b^3*d*e*f*j^2*n*x*Log[c*(d + e*x)^n]^2 - 18*b^3*e^2*g*i*j*m*n*x*Log[c*(d + e*x)^n]^2 - 18*b^3*d*e*g*j^2*m*n*x*Log[c*(d + e*x)^n]^2 + 12*a*b^2*e^2*f*j^2*x^2*Log[c*(d + e*x)^n]^2 - 6*a*b^2*e^2*g*j^2*m*x^2*Log[c*(d + e*x)^n]^2 - 6*b^3*e^2*f*j^2*n*x^2*Log[c*(d + e*x)^n]^2 + 6*b^3*e^2*g*j^2*m*n*x^2*Log[c*(d + e*x)^n]^2 - 12*b^3*d^2*f*j^2*n*Log[d + e*x]*Log[c*(d + e*x)^n]^2 + 12*b^3*d*e*g*i*j*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]^2 + 6*b^3*d^2*g*j^2*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]^2 + 4*b^3*e^2*g*i*j*m*x*Log[c*(d + e*x)^n]^3 + 4*b^3*e^2*f*j^2*x^2*Log[c*(d + e*x)^n]^3 - 2*b^3*e^2*g*j^2*m*x^2*Log[c*(d + e*x)^n]^3 - 4*a^3*e^2*g*i^2*m*Log[i + j*x] + 6*a^2*b*e^2*g*i^2*m*n*Log[i + j*x] + 12*a^2*b*d*e*g*i*j*m*n*Log[i + j*x] - 6*a*b^2*e^2*g*i^2*m*n^2*Log[i + j*x] - 36*a*b^2*d*e*g*i*j*m*n^2*Log[i + j*x] + 3*b^3*e^2*g*i^2*m*n^3*Log[i + j*x] + 42*b^3*d*e*g*i*j*m*n^3*Log[i + j*x] + 12*a^2*b*e^2*g*i^2*m*n*Log[d + e*x]*Log[i + j*x] - 12*a*b^2*e^2*g*i^2*m*n^2*Log[d + e*x]*Log[i + j*x] - 24*a*b^2*d*e*g*i*j*m*n^2*Log[d + e*x]*Log[i + j*x] + 6*b^3*e^2*g*i^2*m*n^3*Log[d + e*x]*Log[i + j*x] + 36*b^3*d*e*g*i*j*m*n^3*Log[d + e*x]*Log[i + j*x] - 12*a*b^2*e^2*g*i^2*m*n^2*Log[d + e*x]^2*Log[i + j*x] + 6*b^3*e^2*g*i^2*m*n^3*Log[d + e*x]^2*Log[i + j*x] + 12*b^3*d*e*g*i*j*m*n^3*Log[d + e*x]^2*Log[i + j*x] + 4*b^3*e^2*g*i^2*m*n^3*Log[d + e*x]^3*Log[i + j*x] - 12*a^2*b*e^2*g*i^2*m*Log[c*(d + e*x)^n]*Log[i + j*x] + 12*a*b^2*e^2*g*i^2*m*n*Log[c*(d + e*x)^n]*Log[i + j*x] + 24*a*b^2*d*e*g*i*j*m*n*Log[c*(d + e*x)^n]*Log[i + j*x] - 6*b^3*e^2*g*i^2*m*n^2*Log[c*(d + e*x)^n]*Log[i + j*x] - 36*b^3*d*e*g*i*j*m*n^2*Log[c*(d + e*x)^n]*Log[i + j*x] + 24*a*b^2*e^2*g*i^2*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[i + j*x] - 12*b^3*e^2*g*i^2*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[i + j*x] - 24*b^3*d*e*g*i*j*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[i + j*x] - 12*b^3*e^2*g*i^2*m*n^2*Log[d + e*x]^2*Log[c*(d + e*x)^n]*Log[i + j*x] - 12*a*b^2*e^2*g*i^2*m*Log[c*(d + e*x)^n]^2*Log[i + j*x] + 6*b^3*e^2*g*i^2*m*n*Log[c*(d + e*x)^n]^2*Log[i + j*x] + 12*b^3*d*e*g*i*j*m*n*Log[c*(d + e*x)^n]^2*Log[i + j*x] + 12*b^3*e^2*g*i^2*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]^2*Log[i + j*x] - 4*b^3*e^2*g*i^2*m*Log[c*(d + e*x)^n]^3*Log[i + j*x] - 12*a^2*b*e^2*g*i^2*m*n*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] + 12*a^2*b*d^2*g*j^2*m*n*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] + 12*a*b^2*e^2*g*i^2*m*n^2*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] + 24*a*b^2*d*e*g*i*j*m*n^2*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] - 36*a*b^2*d^2*g*j^2*m*n^2*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] - 6*b^3*e^2*g*i^2*m*n^3*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] - 36*b^3*d*e*g*i*j*m*n^3*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] + 42*b^3*d^2*g*j^2*m*n^3*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] + 12*a*b^2*e^2*g*i^2*m*n^2*Log[d + e*x]^2*Log[(e*(i + j*x))/(e*i - d*j)] - 12*a*b^2*d^2*g*j^2*m*n^2*Log[d + e*x]^2*Log[(e*(i + j*x))/(e*i - d*j)] - 6*b^3*e^2*g*i^2*m*n^3*Log[d + e*x]^2*Log[(e*(i + j*x))/(e*i - d*j)] - 12*b^3*d*e*g*i*j*m*n^3*Log[d + e*x]^2*Log[(e*(i + j*x))/(e*i - d*j)] + 18*b^3*d^2*g*j^2*m*n^3*Log[d + e*x]^2*Log[(e*(i + j*x))/(e*i - d*j)] - 4*b^3*e^2*g*i^2*m*n^3*Log[d + e*x]^3*Log[(e*(i + j*x))/(e*i - d*j)] + 4*b^3*d^2*g*j^2*m*n^3*Log[d + e*x]^3*Log[(e*(i + j*x))/(e*i - d*j)] - 24*a*b^2*e^2*g*i^2*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] + 24*a*b^2*d^2*g*j^2*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] + 12*b^3*e^2*g*i^2*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] + 24*b^3*d*e*g*i*j*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] - 36*b^3*d^2*g*j^2*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] + 12*b^3*e^2*g*i^2*m*n^2*Log[d + e*x]^2*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] - 12*b^3*d^2*g*j^2*m*n^2*Log[d + e*x]^2*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] - 12*b^3*e^2*g*i^2*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]^2*Log[(e*(i + j*x))/(e*i - d*j)] + 12*b^3*d^2*g*j^2*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]^2*Log[(e*(i + j*x))/(e*i - d*j)] + 12*a^2*b*d*e*g*j^2*n*x*Log[h*(i + j*x)^m] - 36*a*b^2*d*e*g*j^2*n^2*x*Log[h*(i + j*x)^m] + 42*b^3*d*e*g*j^2*n^3*x*Log[h*(i + j*x)^m] + 4*a^3*e^2*g*j^2*x^2*Log[h*(i + j*x)^m] - 6*a^2*b*e^2*g*j^2*n*x^2*Log[h*(i + j*x)^m] + 6*a*b^2*e^2*g*j^2*n^2*x^2*Log[h*(i + j*x)^m] - 3*b^3*e^2*g*j^2*n^3*x^2*Log[h*(i + j*x)^m] - 12*a^2*b*d^2*g*j^2*n*Log[d + e*x]*Log[h*(i + j*x)^m] + 36*a*b^2*d^2*g*j^2*n^2*Log[d + e*x]*Log[h*(i + j*x)^m] - 42*b^3*d^2*g*j^2*n^3*Log[d + e*x]*Log[h*(i + j*x)^m] + 12*a*b^2*d^2*g*j^2*n^2*Log[d + e*x]^2*Log[h*(i + j*x)^m] - 18*b^3*d^2*g*j^2*n^3*Log[d + e*x]^2*Log[h*(i + j*x)^m] - 4*b^3*d^2*g*j^2*n^3*Log[d + e*x]^3*Log[h*(i + j*x)^m] + 24*a*b^2*d*e*g*j^2*n*x*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] - 36*b^3*d*e*g*j^2*n^2*x*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] + 12*a^2*b*e^2*g*j^2*x^2*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] - 12*a*b^2*e^2*g*j^2*n*x^2*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] + 6*b^3*e^2*g*j^2*n^2*x^2*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] - 24*a*b^2*d^2*g*j^2*n*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] + 36*b^3*d^2*g*j^2*n^2*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] + 12*b^3*d^2*g*j^2*n^2*Log[d + e*x]^2*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] + 12*b^3*d*e*g*j^2*n*x*Log[c*(d + e*x)^n]^2*Log[h*(i + j*x)^m] + 12*a*b^2*e^2*g*j^2*x^2*Log[c*(d + e*x)^n]^2*Log[h*(i + j*x)^m] - 6*b^3*e^2*g*j^2*n*x^2*Log[c*(d + e*x)^n]^2*Log[h*(i + j*x)^m] - 12*b^3*d^2*g*j^2*n*Log[d + e*x]*Log[c*(d + e*x)^n]^2*Log[h*(i + j*x)^m] + 4*b^3*e^2*g*j^2*x^2*Log[c*(d + e*x)^n]^3*Log[h*(i + j*x)^m] - 6*b*g*(e*i - d*j)*m*n*(2*a^2*(e*i + d*j) - 2*a*b*(e*i + 3*d*j)*n + b^2*(e*i + 7*d*j)*n^2 - 2*b*(-2*a*(e*i + d*j) + b*(e*i + 3*d*j)*n)*Log[c*(d + e*x)^n] + 2*b^2*(e*i + d*j)*Log[c*(d + e*x)^n]^2)*PolyLog[2, (j*(d + e*x))/(-(e*i) + d*j)] + 12*b^2*g*(e*i - d*j)*m*n^2*(2*a*(e*i + d*j) - b*(e*i + 3*d*j)*n + 2*b*(e*i + d*j)*Log[c*(d + e*x)^n])*PolyLog[3, (j*(d + e*x))/(-(e*i) + d*j)] - 24*b^3*e^2*g*i^2*m*n^3*PolyLog[4, (j*(d + e*x))/(-(e*i) + d*j)] + 24*b^3*d^2*g*j^2*m*n^3*PolyLog[4, (j*(d + e*x))/(-(e*i) + d*j)])/(8*e^2*j^2)","B",1
398,1,3163,1147,1.1319294,"\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","Integrate[(a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]),x]","\text{Result too large to show}","-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{Li}_2\left(-\frac{j (d+e x)}{e i-d j}\right) b^3}{j}+\frac{6 d g m n^3 \text{Li}_2\left(\frac{e (i+j x)}{e i-d j}\right) b^3}{e}-\frac{6 d g m n^3 \text{Li}_3\left(-\frac{j (d+e x)}{e i-d j}\right) b^3}{e}+\frac{6 g i m n^3 \text{Li}_3\left(-\frac{j (d+e x)}{e i-d j}\right) b^3}{j}-\frac{6 d g m n^3 \text{Li}_4\left(-\frac{j (d+e x)}{e i-d j}\right) b^3}{e}+\frac{6 g i m n^3 \text{Li}_4\left(-\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{Li}_2\left(-\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{Li}_2\left(-\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{Li}_3\left(-\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{Li}_3\left(-\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{Li}_2\left(-\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{Li}_2\left(-\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,"(-3*a^2*b*d*f*j*n + 3*a^2*b*d*g*j*m*n - 6*a*b^2*d*g*j*m*n^2 + 6*b^3*d*g*j*m*n^3 + a^3*e*f*j*x - a^3*e*g*j*m*x - 3*a^2*b*e*f*j*n*x + 6*a^2*b*e*g*j*m*n*x + 6*a*b^2*e*f*j*n^2*x - 18*a*b^2*e*g*j*m*n^2*x - 6*b^3*e*f*j*n^3*x + 24*b^3*e*g*j*m*n^3*x + 3*a^2*b*d*f*j*n*Log[d + e*x] - 3*a^2*b*d*g*j*m*n*Log[d + e*x] + 6*a*b^2*d*g*j*m*n^2*Log[d + e*x] + 6*b^3*d*f*j*n^3*Log[d + e*x] - 12*b^3*d*g*j*m*n^3*Log[d + e*x] - 3*a*b^2*d*f*j*n^2*Log[d + e*x]^2 + 3*a*b^2*d*g*j*m*n^2*Log[d + e*x]^2 - 3*b^3*d*g*j*m*n^3*Log[d + e*x]^2 + b^3*d*f*j*n^3*Log[d + e*x]^3 - b^3*d*g*j*m*n^3*Log[d + e*x]^3 - 6*a*b^2*d*f*j*n*Log[c*(d + e*x)^n] + 6*a*b^2*d*g*j*m*n*Log[c*(d + e*x)^n] - 6*b^3*d*g*j*m*n^2*Log[c*(d + e*x)^n] + 3*a^2*b*e*f*j*x*Log[c*(d + e*x)^n] - 3*a^2*b*e*g*j*m*x*Log[c*(d + e*x)^n] - 6*a*b^2*e*f*j*n*x*Log[c*(d + e*x)^n] + 12*a*b^2*e*g*j*m*n*x*Log[c*(d + e*x)^n] + 6*b^3*e*f*j*n^2*x*Log[c*(d + e*x)^n] - 18*b^3*e*g*j*m*n^2*x*Log[c*(d + e*x)^n] + 6*a*b^2*d*f*j*n*Log[d + e*x]*Log[c*(d + e*x)^n] - 6*a*b^2*d*g*j*m*n*Log[d + e*x]*Log[c*(d + e*x)^n] + 6*b^3*d*g*j*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n] - 3*b^3*d*f*j*n^2*Log[d + e*x]^2*Log[c*(d + e*x)^n] + 3*b^3*d*g*j*m*n^2*Log[d + e*x]^2*Log[c*(d + e*x)^n] - 3*b^3*d*f*j*n*Log[c*(d + e*x)^n]^2 + 3*b^3*d*g*j*m*n*Log[c*(d + e*x)^n]^2 + 3*a*b^2*e*f*j*x*Log[c*(d + e*x)^n]^2 - 3*a*b^2*e*g*j*m*x*Log[c*(d + e*x)^n]^2 - 3*b^3*e*f*j*n*x*Log[c*(d + e*x)^n]^2 + 6*b^3*e*g*j*m*n*x*Log[c*(d + e*x)^n]^2 + 3*b^3*d*f*j*n*Log[d + e*x]*Log[c*(d + e*x)^n]^2 - 3*b^3*d*g*j*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]^2 + b^3*e*f*j*x*Log[c*(d + e*x)^n]^3 - b^3*e*g*j*m*x*Log[c*(d + e*x)^n]^3 + a^3*e*g*i*m*Log[i + j*x] - 3*a^2*b*e*g*i*m*n*Log[i + j*x] + 3*a^2*b*d*g*j*m*n*Log[i + j*x] + 6*a*b^2*e*g*i*m*n^2*Log[i + j*x] - 6*b^3*e*g*i*m*n^3*Log[i + j*x] - 3*a^2*b*e*g*i*m*n*Log[d + e*x]*Log[i + j*x] + 6*a*b^2*e*g*i*m*n^2*Log[d + e*x]*Log[i + j*x] - 6*a*b^2*d*g*j*m*n^2*Log[d + e*x]*Log[i + j*x] - 6*b^3*e*g*i*m*n^3*Log[d + e*x]*Log[i + j*x] + 3*a*b^2*e*g*i*m*n^2*Log[d + e*x]^2*Log[i + j*x] - 3*b^3*e*g*i*m*n^3*Log[d + e*x]^2*Log[i + j*x] + 3*b^3*d*g*j*m*n^3*Log[d + e*x]^2*Log[i + j*x] - b^3*e*g*i*m*n^3*Log[d + e*x]^3*Log[i + j*x] + 3*a^2*b*e*g*i*m*Log[c*(d + e*x)^n]*Log[i + j*x] - 6*a*b^2*e*g*i*m*n*Log[c*(d + e*x)^n]*Log[i + j*x] + 6*a*b^2*d*g*j*m*n*Log[c*(d + e*x)^n]*Log[i + j*x] + 6*b^3*e*g*i*m*n^2*Log[c*(d + e*x)^n]*Log[i + j*x] - 6*a*b^2*e*g*i*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[i + j*x] + 6*b^3*e*g*i*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[i + j*x] - 6*b^3*d*g*j*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[i + j*x] + 3*b^3*e*g*i*m*n^2*Log[d + e*x]^2*Log[c*(d + e*x)^n]*Log[i + j*x] + 3*a*b^2*e*g*i*m*Log[c*(d + e*x)^n]^2*Log[i + j*x] - 3*b^3*e*g*i*m*n*Log[c*(d + e*x)^n]^2*Log[i + j*x] + 3*b^3*d*g*j*m*n*Log[c*(d + e*x)^n]^2*Log[i + j*x] - 3*b^3*e*g*i*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]^2*Log[i + j*x] + b^3*e*g*i*m*Log[c*(d + e*x)^n]^3*Log[i + j*x] + 3*a^2*b*e*g*i*m*n*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] - 3*a^2*b*d*g*j*m*n*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] - 6*a*b^2*e*g*i*m*n^2*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] + 6*a*b^2*d*g*j*m*n^2*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] + 6*b^3*e*g*i*m*n^3*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] - 6*b^3*d*g*j*m*n^3*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] - 3*a*b^2*e*g*i*m*n^2*Log[d + e*x]^2*Log[(e*(i + j*x))/(e*i - d*j)] + 3*a*b^2*d*g*j*m*n^2*Log[d + e*x]^2*Log[(e*(i + j*x))/(e*i - d*j)] + 3*b^3*e*g*i*m*n^3*Log[d + e*x]^2*Log[(e*(i + j*x))/(e*i - d*j)] - 3*b^3*d*g*j*m*n^3*Log[d + e*x]^2*Log[(e*(i + j*x))/(e*i - d*j)] + b^3*e*g*i*m*n^3*Log[d + e*x]^3*Log[(e*(i + j*x))/(e*i - d*j)] - b^3*d*g*j*m*n^3*Log[d + e*x]^3*Log[(e*(i + j*x))/(e*i - d*j)] + 6*a*b^2*e*g*i*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] - 6*a*b^2*d*g*j*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] - 6*b^3*e*g*i*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] + 6*b^3*d*g*j*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] - 3*b^3*e*g*i*m*n^2*Log[d + e*x]^2*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] + 3*b^3*d*g*j*m*n^2*Log[d + e*x]^2*Log[c*(d + e*x)^n]*Log[(e*(i + j*x))/(e*i - d*j)] + 3*b^3*e*g*i*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]^2*Log[(e*(i + j*x))/(e*i - d*j)] - 3*b^3*d*g*j*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]^2*Log[(e*(i + j*x))/(e*i - d*j)] - 3*a^2*b*d*g*j*n*Log[h*(i + j*x)^m] + a^3*e*g*j*x*Log[h*(i + j*x)^m] - 3*a^2*b*e*g*j*n*x*Log[h*(i + j*x)^m] + 6*a*b^2*e*g*j*n^2*x*Log[h*(i + j*x)^m] - 6*b^3*e*g*j*n^3*x*Log[h*(i + j*x)^m] + 3*a^2*b*d*g*j*n*Log[d + e*x]*Log[h*(i + j*x)^m] + 6*b^3*d*g*j*n^3*Log[d + e*x]*Log[h*(i + j*x)^m] - 3*a*b^2*d*g*j*n^2*Log[d + e*x]^2*Log[h*(i + j*x)^m] + b^3*d*g*j*n^3*Log[d + e*x]^3*Log[h*(i + j*x)^m] - 6*a*b^2*d*g*j*n*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] + 3*a^2*b*e*g*j*x*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] - 6*a*b^2*e*g*j*n*x*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] + 6*b^3*e*g*j*n^2*x*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] + 6*a*b^2*d*g*j*n*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] - 3*b^3*d*g*j*n^2*Log[d + e*x]^2*Log[c*(d + e*x)^n]*Log[h*(i + j*x)^m] - 3*b^3*d*g*j*n*Log[c*(d + e*x)^n]^2*Log[h*(i + j*x)^m] + 3*a*b^2*e*g*j*x*Log[c*(d + e*x)^n]^2*Log[h*(i + j*x)^m] - 3*b^3*e*g*j*n*x*Log[c*(d + e*x)^n]^2*Log[h*(i + j*x)^m] + 3*b^3*d*g*j*n*Log[d + e*x]*Log[c*(d + e*x)^n]^2*Log[h*(i + j*x)^m] + b^3*e*g*j*x*Log[c*(d + e*x)^n]^3*Log[h*(i + j*x)^m] + 3*b*g*(e*i - d*j)*m*n*(a^2 - 2*a*b*n + 2*b^2*n^2 + 2*b*(a - b*n)*Log[c*(d + e*x)^n] + b^2*Log[c*(d + e*x)^n]^2)*PolyLog[2, (j*(d + e*x))/(-(e*i) + d*j)] - 6*b^2*g*(e*i - d*j)*m*n^2*(a - b*n + b*Log[c*(d + e*x)^n])*PolyLog[3, (j*(d + e*x))/(-(e*i) + d*j)] + 6*b^3*e*g*i*m*n^3*PolyLog[4, (j*(d + e*x))/(-(e*i) + d*j)] - 6*b^3*d*g*j*m*n^3*PolyLog[4, (j*(d + e*x))/(-(e*i) + d*j)])/(e*j)","B",1
399,0,0,37,1.3806719,"\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","Integrate[((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,"Integrate[((a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]))/x, x]","A",-1
400,0,0,37,1.9295743,"\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","Integrate[((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,"Integrate[((a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]))/x^2, x]","A",-1
401,1,62,66,0.1111922,"\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","Integrate[((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{Li}_3\left(\frac{g (d+e x)}{d g-e f}\right)-\text{Li}_2\left(\frac{g (d+e x)}{d g-e f}\right) \left(a+b \log \left(c (d+e x)^n\right)\right)}{e}","\frac{b n \text{Li}_3\left(-\frac{g (d+e x)}{e f-d g}\right)}{e}-\frac{\text{Li}_2\left(-\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)]) + b*n*PolyLog[3, (g*(d + e*x))/(-(e*f) + d*g)])/e","A",1
402,1,43,92,0.0704041,"\int \frac{\log (c (d+e x)) (a+b \log (c (d+e x)))}{(d+e x)^2} \, dx","Integrate[(Log[c*(d + e*x)]*(a + b*Log[c*(d + e*x)]))/(d + e*x)^2,x]","-\frac{(a+2 b) \log (c (d+e x))+a+b \log ^2(c (d+e x))+2 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,"-((a + 2*b + (a + 2*b)*Log[c*(d + e*x)] + b*Log[c*(d + e*x)]^2)/(e*(d + e*x)))","A",1
403,1,58,102,0.1124082,"\int \frac{(a+b \log (c (d+e x))) (f+g \log (c (d+e x)))}{(d+e x)^2} \, dx","Integrate[((a + b*Log[c*(d + e*x)])*(f + g*Log[c*(d + e*x)]))/(d + e*x)^2,x]","-\frac{(a g+b (f+2 g)) \log (c (d+e x))+a (f+g)+b g \log ^2(c (d+e x))+b (f+2 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,"-((a*(f + g) + b*(f + 2*g) + (a*g + b*(f + 2*g))*Log[c*(d + e*x)] + b*g*Log[c*(d + e*x)]^2)/(e*(d + e*x)))","A",1
404,1,132,160,0.0713844,"\int \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^4 \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^m)^n])^4,x]","\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^4-4 b m n \left((e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^3-3 b m n \left((e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^2-2 b m n \left(f x (a-b m n)+b (e+f x) \log \left(c \left(d (e+f x)^m\right)^n\right)\right)\right)\right)}{f}","-24 a b^3 m^3 n^3 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}-\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,"((e + f*x)*(a + b*Log[c*(d*(e + f*x)^m)^n])^4 - 4*b*m*n*((e + f*x)*(a + b*Log[c*(d*(e + f*x)^m)^n])^3 - 3*b*m*n*((e + f*x)*(a + b*Log[c*(d*(e + f*x)^m)^n])^2 - 2*b*m*n*(f*(a - b*m*n)*x + b*(e + f*x)*Log[c*(d*(e + f*x)^m)^n]))))/f","A",1
405,1,100,121,0.0138672,"\int \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^3 \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^m)^n])^3,x]","\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^3-3 b m n \left((e+f x) \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^2-2 b m n \left(f x (a-b m n)+b (e+f x) \log \left(c \left(d (e+f x)^m\right)^n\right)\right)\right)}{f}","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,"((e + f*x)*(a + b*Log[c*(d*(e + f*x)^m)^n])^3 - 3*b*m*n*((e + f*x)*(a + b*Log[c*(d*(e + f*x)^m)^n])^2 - 2*b*m*n*(f*(a - b*m*n)*x + b*(e + f*x)*Log[c*(d*(e + f*x)^m)^n])))/f","A",1
406,1,69,78,0.0101475,"\int \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^2 \, dx","Integrate[(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 b m n \left(a x+\frac{b (e+f x) \log \left(c \left(d (e+f x)^m\right)^n\right)}{f}-b m n x\right)","\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,"((e + f*x)*(a + b*Log[c*(d*(e + f*x)^m)^n])^2)/f - 2*b*m*n*(a*x - b*m*n*x + (b*(e + f*x)*Log[c*(d*(e + f*x)^m)^n])/f)","A",1
407,1,34,34,0.0072202,"\int \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right) \, dx","Integrate[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",1
408,1,83,83,0.1173245,"\int \frac{1}{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)} \, dx","Integrate[(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",1
409,1,163,123,0.1179123,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^2} \, dx","Integrate[(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}} \left(b m n 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) \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}\right)\right)}{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) 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)*(b*E^(a/(b*m*n))*m*n*(c*(d*(e + f*x)^m)^n)^(1/(m*n)) - ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^m)^n])/(b*m*n)]*(a + b*Log[c*(d*(e + f*x)^m)^n])))/(b^2*E^(a/(b*m*n))*f*m^2*n^2*(c*(d*(e + f*x)^m)^n)^(1/(m*n))*(a + b*Log[c*(d*(e + f*x)^m)^n])))","A",1
410,1,189,169,0.1910626,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^3} \, dx","Integrate[(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}} \left(b m n 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)+b m n\right)-\left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^2 \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}\right)\right)}{2 b^3 f m^3 n^3 \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,"-1/2*((e + f*x)*(-(ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^m)^n])/(b*m*n)]*(a + b*Log[c*(d*(e + f*x)^m)^n])^2) + b*E^(a/(b*m*n))*m*n*(c*(d*(e + f*x)^m)^n)^(1/(m*n))*(a + b*m*n + b*Log[c*(d*(e + f*x)^m)^n])))/(b^3*E^(a/(b*m*n))*f*m^3*n^3*(c*(d*(e + f*x)^m)^n)^(1/(m*n))*(a + b*Log[c*(d*(e + f*x)^m)^n])^2)","A",1
411,1,190,219,0.3289493,"\int \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{5/2} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^m)^n])^(5/2),x]","\frac{(e+f x) \left(8 \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{5/2}-5 b m n \left(3 \sqrt{\pi } b^{3/2} m^{3/2} n^{3/2} 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 \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)} \left(2 a+2 b \log \left(c \left(d (e+f x)^m\right)^n\right)-3 b m n\right)\right)\right)}{8 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,"((e + f*x)*(8*(a + b*Log[c*(d*(e + f*x)^m)^n])^(5/2) - 5*b*m*n*((3*b^(3/2)*m^(3/2)*n^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]]/(Sqrt[b]*Sqrt[m]*Sqrt[n])])/(E^(a/(b*m*n))*(c*(d*(e + f*x)^m)^n)^(1/(m*n))) + 2*Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]]*(2*a - 3*b*m*n + 2*b*Log[c*(d*(e + f*x)^m)^n]))))/(8*f)","A",1
412,1,160,176,0.0642921,"\int \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{3/2} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^m)^n])^(3/2),x]","\frac{(e+f x) \left(3 \sqrt{\pi } b^{3/2} m^{3/2} n^{3/2} 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 \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)} \left(2 a+2 b \log \left(c \left(d (e+f x)^m\right)^n\right)-3 b m n\right)\right)}{4 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,"((e + f*x)*((3*b^(3/2)*m^(3/2)*n^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]]/(Sqrt[b]*Sqrt[m]*Sqrt[n])])/(E^(a/(b*m*n))*(c*(d*(e + f*x)^m)^n)^(1/(m*n))) + 2*Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]]*(2*a - 3*b*m*n + 2*b*Log[c*(d*(e + f*x)^m)^n])))/(4*f)","A",1
413,1,134,139,0.0638591,"\int \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)} \, dx","Integrate[Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]],x]","\frac{(e+f x) \left(2 \sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}-\sqrt{\pi } \sqrt{b} \sqrt{m} \sqrt{n} 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)\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,"((e + f*x)*(-((Sqrt[b]*Sqrt[m]*Sqrt[n]*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]]/(Sqrt[b]*Sqrt[m]*Sqrt[n])])/(E^(a/(b*m*n))*(c*(d*(e + f*x)^m)^n)^(1/(m*n)))) + 2*Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]]))/(2*f)","A",1
414,1,104,104,0.0221659,"\int \frac{1}{\sqrt{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}} \, dx","Integrate[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",1
415,1,181,147,0.2298608,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{3/2}} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^m)^n])^(-3/2),x]","-\frac{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}} \left(e^{\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{\frac{1}{m n}}-\sqrt{-\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}} \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}\right)\right)}{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*(e + f*x)*(E^(a/(b*m*n))*(c*(d*(e + f*x)^m)^n)^(1/(m*n)) - Gamma[1/2, -((a + b*Log[c*(d*(e + f*x)^m)^n])/(b*m*n))]*Sqrt[-((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))*Sqrt[a + b*Log[c*(d*(e + f*x)^m)^n]])","A",1
416,1,211,194,0.3342394,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{5/2}} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^m)^n])^(-5/2),x]","-\frac{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}} \left(e^{\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{\frac{1}{m n}} \left(2 a+2 b \log \left(c \left(d (e+f x)^m\right)^n\right)+b m n\right)+2 b m n \left(-\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}\right)\right)}{3 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{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,"(-2*(e + f*x)*(2*b*m*n*Gamma[1/2, -((a + b*Log[c*(d*(e + f*x)^m)^n])/(b*m*n))]*(-((a + b*Log[c*(d*(e + f*x)^m)^n])/(b*m*n)))^(3/2) + E^(a/(b*m*n))*(c*(d*(e + f*x)^m)^n)^(1/(m*n))*(2*a + b*m*n + 2*b*Log[c*(d*(e + f*x)^m)^n])))/(3*b^2*E^(a/(b*m*n))*f*m^2*n^2*(c*(d*(e + f*x)^m)^n)^(1/(m*n))*(a + b*Log[c*(d*(e + f*x)^m)^n])^(3/2))","A",1
417,1,272,237,0.4514665,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^{7/2}} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^m)^n])^(-7/2),x]","-\frac{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}} \left(e^{\frac{a}{b m n}} \left(c \left(d (e+f x)^m\right)^n\right)^{\frac{1}{m n}} \left(4 a^2+2 b (4 a+b m n) \log \left(c \left(d (e+f x)^m\right)^n\right)+2 a b m n+4 b^2 \log ^2\left(c \left(d (e+f x)^m\right)^n\right)+3 b^2 m^2 n^2\right)-4 \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^2 \sqrt{-\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}} \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c \left(d (e+f x)^m\right)^n\right)}{b m n}\right)\right)}{15 b^3 f m^3 n^3 \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,"(-2*(e + f*x)*(-4*Gamma[1/2, -((a + b*Log[c*(d*(e + f*x)^m)^n])/(b*m*n))]*(a + b*Log[c*(d*(e + f*x)^m)^n])^2*Sqrt[-((a + b*Log[c*(d*(e + f*x)^m)^n])/(b*m*n))] + E^(a/(b*m*n))*(c*(d*(e + f*x)^m)^n)^(1/(m*n))*(4*a^2 + 2*a*b*m*n + 3*b^2*m^2*n^2 + 2*b*(4*a + b*m*n)*Log[c*(d*(e + f*x)^m)^n] + 4*b^2*Log[c*(d*(e + f*x)^m)^n]^2)))/(15*b^3*E^(a/(b*m*n))*f*m^3*n^3*(c*(d*(e + f*x)^m)^n)^(1/(m*n))*(a + b*Log[c*(d*(e + f*x)^m)^n])^(5/2))","A",1
418,1,131,131,0.1834428,"\int \left(a+b \log \left(c \left(d (e+f x)^m\right)^n\right)\right)^p \, dx","Integrate[(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} \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} \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",1
419,1,109,109,0.1209456,"\int \left(a+b \log \left(c \sqrt{d \sqrt{e+f x}}\right)\right)^p \, dx","Integrate[(a + b*Log[c*Sqrt[d*Sqrt[e + f*x]]])^p,x]","\frac{2^{-2 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} \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} \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)/(2^(2*p)*c^4*d^2*E^((4*a)/b)*f*(-((a + b*Log[c*Sqrt[d*Sqrt[e + f*x]]])/b))^p)","A",1
420,1,232,158,0.3095426,"\int (g+h x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \, dx","Integrate[(g + h*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\frac{f x \left(12 a f^3 \left(4 g^3+6 g^2 h x+4 g h^2 x^2+h^3 x^3\right)-b p q \left(-12 e^3 h^3+6 e^2 f h^2 (8 g+h x)-4 e f^2 h \left(18 g^2+6 g h x+h^2 x^2\right)+f^3 \left(48 g^3+36 g^2 h x+16 g h^2 x^2+3 h^3 x^3\right)\right)\right)+12 b f^3 \left(4 e g^3+f x \left(4 g^3+6 g^2 h x+4 g h^2 x^2+h^3 x^3\right)\right) \log \left(c \left(d (e+f x)^p\right)^q\right)-12 b e^2 h p q \left(e^2 h^2-4 e f g h+6 f^2 g^2\right) \log (e+f x)}{48 f^4}","\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 (f g-e h)^4 \log (e+f x)}{4 f^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 (g+h x)^3 (f g-e h)}{12 f h}-\frac{b p q (g+h x)^4}{16 h}",1,"(f*x*(12*a*f^3*(4*g^3 + 6*g^2*h*x + 4*g*h^2*x^2 + h^3*x^3) - b*p*q*(-12*e^3*h^3 + 6*e^2*f*h^2*(8*g + h*x) - 4*e*f^2*h*(18*g^2 + 6*g*h*x + h^2*x^2) + f^3*(48*g^3 + 36*g^2*h*x + 16*g*h^2*x^2 + 3*h^3*x^3))) - 12*b*e^2*h*(6*f^2*g^2 - 4*e*f*g*h + e^2*h^2)*p*q*Log[e + f*x] + 12*b*f^3*(4*e*g^3 + f*x*(4*g^3 + 6*g^2*h*x + 4*g*h^2*x^2 + h^3*x^3))*Log[c*(d*(e + f*x)^p)^q])/(48*f^4)","A",1
421,1,156,128,0.1931841,"\int (g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \, dx","Integrate[(g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\frac{f \left(x \left(6 a f^2 \left(3 g^2+3 g h x+h^2 x^2\right)-b p q \left(6 e^2 h^2-3 e f h (6 g+h x)+f^2 \left(18 g^2+9 g h x+2 h^2 x^2\right)\right)\right)+6 b f \left(3 e g^2+f x \left(3 g^2+3 g h x+h^2 x^2\right)\right) \log \left(c \left(d (e+f x)^p\right)^q\right)\right)+6 b e^2 h p q (e h-3 f g) \log (e+f x)}{18 f^3}","\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 (f g-e h)^3 \log (e+f x)}{3 f^3 h}-\frac{b p q x (f g-e h)^2}{3 f^2}-\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,"(6*b*e^2*h*(-3*f*g + e*h)*p*q*Log[e + f*x] + f*(x*(6*a*f^2*(3*g^2 + 3*g*h*x + h^2*x^2) - b*p*q*(6*e^2*h^2 - 3*e*f*h*(6*g + h*x) + f^2*(18*g^2 + 9*g*h*x + 2*h^2*x^2))) + 6*b*f*(3*e*g^2 + f*x*(3*g^2 + 3*g*h*x + h^2*x^2))*Log[c*(d*(e + f*x)^p)^q]))/(18*f^3)","A",1
422,1,113,98,0.0613366,"\int (g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \, dx","Integrate[(g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","a g x+\frac{1}{2} a h x^2+\frac{b g (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f}+\frac{1}{2} b h x^2 \log \left(c \left(d (e+f x)^p\right)^q\right)-\frac{b e^2 h p q \log (e+f x)}{2 f^2}+\frac{b e h p q x}{2 f}-b g p q x-\frac{1}{4} b h p q x^2","\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,"a*g*x - b*g*p*q*x + (b*e*h*p*q*x)/(2*f) + (a*h*x^2)/2 - (b*h*p*q*x^2)/4 - (b*e^2*h*p*q*Log[e + f*x])/(2*f^2) + (b*h*x^2*Log[c*(d*(e + f*x)^p)^q])/2 + (b*g*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/f","A",1
423,1,34,34,0.0091334,"\int \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \, dx","Integrate[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",1
424,1,67,68,0.0161313,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{g+h x} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x),x]","\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{Li}_2\left(\frac{h (e+f x)}{e h-f g}\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{Li}_2\left(-\frac{h (e+f x)}{f g-e h}\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",1
425,1,69,80,0.1026742,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x)^2} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x)^2,x]","\frac{-\frac{a}{g+h x}-\frac{b \log \left(c \left(d (e+f x)^p\right)^q\right)}{g+h x}+\frac{b f p q (\log (e+f x)-\log (g+h x))}{f g-e h}}{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,"(-(a/(g + h*x)) - (b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x) + (b*f*p*q*(Log[e + f*x] - Log[g + h*x]))/(f*g - e*h))/h","A",1
426,1,88,119,0.1637171,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x)^3} \, dx","Integrate[(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)-\frac{b f p q (g+h x) (f (g+h x) \log (e+f x)-e h-f (g+h x) \log (g+h x)+f g)}{(f g-e h)^2}}{2 h (g+h x)^2}","-\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,"-1/2*(a + b*Log[c*(d*(e + f*x)^p)^q] - (b*f*p*q*(g + h*x)*(f*g - e*h + f*(g + h*x)*Log[e + f*x] - f*(g + h*x)*Log[g + h*x]))/(f*g - e*h)^2)/(h*(g + h*x)^2)","A",1
427,1,115,149,0.201921,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x)^4} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x)^4,x]","\frac{-2 a-2 b \log \left(c \left(d (e+f x)^p\right)^q\right)+\frac{b f p q (g+h x) \left(2 f^2 (g+h x)^2 \log (e+f x)+(f g-e h) (-e h+3 f g+2 f h x)-2 f^2 (g+h x)^2 \log (g+h x)\right)}{(f g-e h)^3}}{6 h (g+h x)^3}","-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{3 h (g+h x)^3}+\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^2 p q}{3 h (g+h x) (f g-e h)^2}+\frac{b f p q}{6 h (g+h x)^2 (f g-e h)}",1,"(-2*a - 2*b*Log[c*(d*(e + f*x)^p)^q] + (b*f*p*q*(g + h*x)*((f*g - e*h)*(3*f*g - e*h + 2*f*h*x) + 2*f^2*(g + h*x)^2*Log[e + f*x] - 2*f^2*(g + h*x)^2*Log[g + h*x]))/(f*g - e*h)^3)/(6*h*(g + h*x)^3)","A",1
428,1,400,409,0.2888383,"\int (g+h x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \, dx","Integrate[(g + h*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q])^2,x]","\frac{64 b h^2 p q (f g-e h) \left(b f p q x \left(3 e^2+3 e f x+f^2 x^2\right)-3 (e+f x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)\right)+9 b h^3 p q \left(b f p q x \left(4 e^3+6 e^2 f x+4 e f^2 x^2+f^3 x^3\right)-4 (e+f x)^4 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)\right)+288 h^2 (e+f x)^3 (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2+432 h (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+288 (e+f x) (f g-e h)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2-576 b p q (f g-e h)^3 \left(f x (a-b p q)+b (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)\right)+216 b h p q (f g-e h)^2 \left(b f p q x (2 e+f x)-2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)\right)+72 h^3 (e+f x)^4 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{288 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{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^2 p^2 q^2 x (f g-e h)^3}{f^3}",1,"(288*(f*g - e*h)^3*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 + 432*h*(f*g - e*h)^2*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 + 288*h^2*(f*g - e*h)*(e + f*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 + 72*h^3*(e + f*x)^4*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 - 576*b*(f*g - e*h)^3*p*q*(f*(a - b*p*q)*x + b*(e + f*x)*Log[c*(d*(e + f*x)^p)^q]) + 216*b*h*(f*g - e*h)^2*p*q*(b*f*p*q*x*(2*e + f*x) - 2*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])) + 64*b*h^2*(f*g - e*h)*p*q*(b*f*p*q*x*(3*e^2 + 3*e*f*x + f^2*x^2) - 3*(e + f*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q])) + 9*b*h^3*p*q*(b*f*p*q*x*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3) - 4*(e + f*x)^4*(a + b*Log[c*(d*(e + f*x)^p)^q])))/(288*f^4)","A",1
429,1,277,323,0.2137946,"\int (g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \, dx","Integrate[(g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2,x]","\frac{4 b h^2 p q \left(b f p q x \left(3 e^2+3 e f x+f^2 x^2\right)-3 (e+f x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)\right)+54 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)^2+54 (e+f x) (f g-e h)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2-108 b p q (f g-e h)^2 \left(f x (a-b p q)+b (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)\right)+27 b h p q (f g-e h) \left(b f p q x (2 e+f x)-2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)\right)+18 h^2 (e+f x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{54 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{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^2 p^2 q^2 x (f g-e h)^2}{f^2}",1,"(54*(f*g - e*h)^2*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 + 54*h*(f*g - e*h)*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 + 18*h^2*(e + f*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 - 108*b*(f*g - e*h)^2*p*q*(f*(a - b*p*q)*x + b*(e + f*x)*Log[c*(d*(e + f*x)^p)^q]) + 27*b*h*(f*g - e*h)*p*q*(b*f*p*q*x*(2*e + f*x) - 2*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])) + 4*b*h^2*p*q*(b*f*p*q*x*(3*e^2 + 3*e*f*x + f^2*x^2) - 3*(e + f*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q])))/(54*f^3)","A",1
430,1,164,211,0.1122359,"\int (g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \, dx","Integrate[(g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2,x]","\frac{4 (e+f x) (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2-8 b p q (f g-e h) \left(f x (a-b p q)+b (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)\right)+2 h (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2+b h p q \left(b f p q x (2 e+f x)-2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)\right)}{4 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)^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,"(4*(f*g - e*h)*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 + 2*h*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 - 8*b*(f*g - e*h)*p*q*(f*(a - b*p*q)*x + b*(e + f*x)*Log[c*(d*(e + f*x)^p)^q]) + b*h*p*q*(b*f*p*q*x*(2*e + f*x) - 2*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])))/(4*f^2)","A",1
431,1,69,78,0.0176568,"\int \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \, dx","Integrate[(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 b p q \left(a x+\frac{b (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f}-b p q x\right)","\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,"((e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/f - 2*b*p*q*(a*x - b*p*q*x + (b*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/f)","A",1
432,1,324,123,0.2039294,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{g+h x} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/(g + h*x),x]","\frac{a^2 \log (g+h x)+2 b p q \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)+2 a b \log (g+h x) \log \left(c \left(d (e+f x)^p\right)^q\right)-2 a b p q \log (e+f x) \log (g+h x)+2 a b p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+b^2 \log (g+h x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right)-2 b^2 p q \log (e+f x) \log (g+h x) \log \left(c \left(d (e+f x)^p\right)^q\right)+2 b^2 p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) \log \left(c \left(d (e+f x)^p\right)^q\right)-2 b^2 p^2 q^2 \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right)+b^2 p^2 q^2 \log ^2(e+f x) \log (g+h x)-b^2 p^2 q^2 \log ^2(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)}{h}","\frac{2 b p q \text{Li}_2\left(-\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{\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^2 p^2 q^2 \text{Li}_3\left(-\frac{h (e+f x)}{f g-e h}\right)}{h}",1,"(a^2*Log[g + h*x] - 2*a*b*p*q*Log[e + f*x]*Log[g + h*x] + b^2*p^2*q^2*Log[e + f*x]^2*Log[g + h*x] + 2*a*b*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 2*b^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + b^2*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] + 2*a*b*p*q*Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] - b^2*p^2*q^2*Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 2*b^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*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)] - 2*b^2*p^2*q^2*PolyLog[3, (h*(e + f*x))/(-(f*g) + e*h)])/h","B",1
433,1,200,144,0.2328059,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(g+h x)^2} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/(g + h*x)^2,x]","\frac{-2 b f p q (g+h x) \log (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)+\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \left(a (f g-e h)+b (f g-e h) \log \left(c \left(d (e+f x)^p\right)^q\right)+2 b f p q (g+h x) \log \left(\frac{f (g+h x)}{f g-e h}\right)\right)+2 b^2 f p^2 q^2 (g+h x) \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)+b^2 f p^2 q^2 (g+h x) \log ^2(e+f x)}{h (g+h x) (e h-f g)}","-\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{Li}_2\left(-\frac{h (e+f x)}{f g-e h}\right)}{h (f g-e h)}",1,"(b^2*f*p^2*q^2*(g + h*x)*Log[e + f*x]^2 - 2*b*f*p*q*(g + h*x)*Log[e + f*x]*(a + b*Log[c*(d*(e + f*x)^p)^q]) + (a + b*Log[c*(d*(e + f*x)^p)^q])*(a*(f*g - e*h) + b*(f*g - e*h)*Log[c*(d*(e + f*x)^p)^q] + 2*b*f*p*q*(g + h*x)*Log[(f*(g + h*x))/(f*g - e*h)]) + 2*b^2*f*p^2*q^2*(g + h*x)*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)])/(h*(-(f*g) + e*h)*(g + h*x))","A",1
434,1,316,222,0.4694903,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{(g+h x)^3} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/(g + h*x)^3,x]","-\frac{\frac{2 b p q \left(h (e+f x) \log (e+f x) (e h-f (2 g+h x))+f (g+h x) \left(f (g+h x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+h (e+f x)\right)\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)}{(f g-e h)^2}+\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)^2+\frac{b^2 p^2 q^2 \left(2 f^2 (g+h x)^2 \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)-2 f^2 (g+h x)^2 \log \left(\frac{f (g+h x)}{f g-e h}\right)+h (e+f x) \log ^2(e+f x) (e h-f (2 g+h x))+2 f (g+h x) \log (e+f x) \left(f (g+h x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+h (e+f x)\right)\right)}{(f g-e h)^2}}{2 h (g+h x)^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 \text{Li}_2\left(-\frac{f g-e h}{h (e+f x)}\right)}{h (f g-e h)^2}+\frac{b^2 f^2 p^2 q^2 \log (g+h x)}{h (f g-e h)^2}",1,"-1/2*((a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2 + (2*b*p*q*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])*(h*(e + f*x)*(e*h - f*(2*g + h*x))*Log[e + f*x] + f*(g + h*x)*(h*(e + f*x) + f*(g + h*x)*Log[(f*(g + h*x))/(f*g - e*h)])))/(f*g - e*h)^2 + (b^2*p^2*q^2*(h*(e + f*x)*(e*h - f*(2*g + h*x))*Log[e + f*x]^2 - 2*f^2*(g + h*x)^2*Log[(f*(g + h*x))/(f*g - e*h)] + 2*f*(g + h*x)*Log[e + f*x]*(h*(e + f*x) + f*(g + h*x)*Log[(f*(g + h*x))/(f*g - e*h)]) + 2*f^2*(g + h*x)^2*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)]))/(f*g - e*h)^2)/(h*(g + h*x)^2)","A",1
435,1,378,492,0.2934954,"\int (g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3 \, dx","Integrate[(g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^3,x]","\frac{-4 b h^2 p q \left(2 b p q \left(b f p q x \left(3 e^2+3 e f x+f^2 x^2\right)-3 (e+f x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)\right)+9 (e+f x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2\right)+108 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+108 (e+f x) (f g-e h)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3-324 b p q (f g-e h)^2 \left((e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2-2 b p q \left(f x (a-b p q)+b (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)\right)\right)-81 b h p q (f g-e h) \left(2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2+b p q \left(b f p q x (2 e+f x)-2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)\right)\right)+36 h^2 (e+f x)^3 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{108 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{2 b^3 h^2 p^3 q^3 (e+f x)^3}{27 f^3}-\frac{6 b^3 p^3 q^3 x (f g-e h)^2}{f^2}",1,"(108*(f*g - e*h)^2*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3 + 108*h*(f*g - e*h)*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^3 + 36*h^2*(e + f*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q])^3 - 324*b*(f*g - e*h)^2*p*q*((e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 - 2*b*p*q*(f*(a - b*p*q)*x + b*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])) - 81*b*h*(f*g - e*h)*p*q*(2*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 + b*p*q*(b*f*p*q*x*(2*e + f*x) - 2*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q]))) - 4*b*h^2*p*q*(9*(e + f*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 + 2*b*p*q*(b*f*p*q*x*(3*e^2 + 3*e*f*x + f^2*x^2) - 3*(e + f*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q]))))/(108*f^3)","A",1
436,1,231,306,0.132044,"\int (g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3 \, dx","Integrate[(g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3,x]","\frac{8 (e+f x) (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3-24 b p q (f g-e h) \left((e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2-2 b p q \left(f x (a-b p q)+b (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)\right)\right)+4 h (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3-3 b h p q \left(2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2+b p q \left(b f p q x (2 e+f x)-2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)\right)\right)}{8 f^2}","\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,"(8*(f*g - e*h)*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3 + 4*h*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^3 - 24*b*(f*g - e*h)*p*q*((e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 - 2*b*p*q*(f*(a - b*p*q)*x + b*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])) - 3*b*h*p*q*(2*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 + b*p*q*(b*f*p*q*x*(2*e + f*x) - 2*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q]))))/(8*f^2)","A",1
437,1,100,121,0.0259939,"\int \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3 \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^3,x]","\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3-3 b p q \left((e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2-2 b p q \left(f x (a-b p q)+b (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)\right)\right)}{f}","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,"((e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3 - 3*b*p*q*((e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 - 2*b*p*q*(f*(a - b*p*q)*x + b*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])))/f","A",1
438,1,646,177,0.2927516,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{g+h x} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^3/(g + h*x),x]","\frac{a^3 \log (g+h x)+3 a^2 b \log (g+h x) \log \left(c \left(d (e+f x)^p\right)^q\right)-3 a^2 b p q \log (e+f x) \log (g+h x)+3 a^2 b p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)-6 b^2 p^2 q^2 \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)+3 a b^2 \log (g+h x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right)-6 a b^2 p q \log (e+f x) \log (g+h x) \log \left(c \left(d (e+f x)^p\right)^q\right)+6 a b^2 p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) \log \left(c \left(d (e+f x)^p\right)^q\right)+3 a b^2 p^2 q^2 \log ^2(e+f x) \log (g+h x)-3 a b^2 p^2 q^2 \log ^2(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+3 b p q \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2+3 b^3 p^2 q^2 \log ^2(e+f x) \log (g+h x) \log \left(c \left(d (e+f x)^p\right)^q\right)-3 b^3 p^2 q^2 \log ^2(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) \log \left(c \left(d (e+f x)^p\right)^q\right)+b^3 \log (g+h x) \log ^3\left(c \left(d (e+f x)^p\right)^q\right)-3 b^3 p q \log (e+f x) \log (g+h x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right)+3 b^3 p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) \log ^2\left(c \left(d (e+f x)^p\right)^q\right)+6 b^3 p^3 q^3 \text{Li}_4\left(\frac{h (e+f x)}{e h-f g}\right)-b^3 p^3 q^3 \log ^3(e+f x) \log (g+h x)+b^3 p^3 q^3 \log ^3(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)}{h}","-\frac{6 b^2 p^2 q^2 \text{Li}_3\left(-\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{Li}_2\left(-\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{\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^3 p^3 q^3 \text{Li}_4\left(-\frac{h (e+f x)}{f g-e h}\right)}{h}",1,"(a^3*Log[g + h*x] - 3*a^2*b*p*q*Log[e + f*x]*Log[g + h*x] + 3*a*b^2*p^2*q^2*Log[e + f*x]^2*Log[g + h*x] - b^3*p^3*q^3*Log[e + f*x]^3*Log[g + h*x] + 3*a^2*b*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 6*a*b^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 3*b^3*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 3*a*b^2*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] - 3*b^3*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] + b^3*Log[c*(d*(e + f*x)^p)^q]^3*Log[g + h*x] + 3*a^2*b*p*q*Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] - 3*a*b^2*p^2*q^2*Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + b^3*p^3*q^3*Log[e + f*x]^3*Log[(f*(g + h*x))/(f*g - e*h)] + 6*a*b^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] - 3*b^3*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] + 3*b^3*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[(f*(g + h*x))/(f*g - e*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)] - 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)] + 6*b^3*p^3*q^3*PolyLog[4, (h*(e + f*x))/(-(f*g) + e*h)])/h","B",1
439,1,444,209,0.5450937,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{(g+h x)^2} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^3/(g + h*x)^2,x]","\frac{3 b^2 p^2 q^2 \left(\log (e+f x) \left(h (e+f x) \log (e+f x)-2 f (g+h x) \log \left(\frac{f (g+h x)}{f g-e h}\right)\right)-2 f (g+h x) \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)-3 b p q (f g-e h) \log (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)^2+3 b f p q (g+h x) \log (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)^2-3 b f p q (g+h x) \log (g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)^2-(f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)^3+b^3 p^3 q^3 \left(6 f (g+h x) \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right)-6 f (g+h x) \log (e+f x) \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)+\log ^2(e+f x) \left(h (e+f x) \log (e+f x)-3 f (g+h x) \log \left(\frac{f (g+h x)}{f g-e h}\right)\right)\right)}{h (g+h x) (f g-e h)}","-\frac{6 b^2 f p^2 q^2 \text{Li}_2\left(-\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{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^3 f p^3 q^3 \text{Li}_3\left(-\frac{h (e+f x)}{f g-e h}\right)}{h (f g-e h)}",1,"(-3*b*(f*g - e*h)*p*q*Log[e + f*x]*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2 + 3*b*f*p*q*(g + h*x)*Log[e + f*x]*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2 - (f*g - e*h)*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^3 - 3*b*f*p*q*(g + h*x)*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2*Log[g + h*x] + 3*b^2*p^2*q^2*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])*(Log[e + f*x]*(h*(e + f*x)*Log[e + f*x] - 2*f*(g + h*x)*Log[(f*(g + h*x))/(f*g - e*h)]) - 2*f*(g + h*x)*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)]) + b^3*p^3*q^3*(Log[e + f*x]^2*(h*(e + f*x)*Log[e + f*x] - 3*f*(g + h*x)*Log[(f*(g + h*x))/(f*g - e*h)]) - 6*f*(g + h*x)*Log[e + f*x]*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)] + 6*f*(g + h*x)*PolyLog[3, (h*(e + f*x))/(-(f*g) + e*h)]))/(h*(f*g - e*h)*(g + h*x))","B",1
440,1,660,376,0.9031041,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{(g+h x)^3} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^3/(g + h*x)^3,x]","-\frac{3 b^2 p^2 q^2 \left(2 f^2 (g+h x)^2 \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)-2 f^2 (g+h x)^2 \log \left(\frac{f (g+h x)}{f g-e h}\right)+h (e+f x) \log ^2(e+f x) (e h-f (2 g+h x))+2 f (g+h x) \log (e+f x) \left(f (g+h x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+h (e+f x)\right)\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)-3 b f^2 p q (g+h x)^2 \log (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)^2+3 b f^2 p q (g+h x)^2 \log (g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)^2-3 b f p q (g+h x) (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)^2+3 b p q (f g-e h)^2 \log (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)^2+(f g-e h)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)^3+b^3 p^3 q^3 \left(-6 f^2 (g+h x)^2 \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)-6 f^2 (g+h x)^2 \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right)-6 f^2 (g+h x)^2 \log (e+f x) \left(\log \left(\frac{f (g+h x)}{f g-e h}\right)-\text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)\right)+h (e+f x) \log ^3(e+f x) (e h-f (2 g+h x))+3 f (g+h x) \log ^2(e+f x) \left(f (g+h x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+h (e+f x)\right)\right)}{2 h (g+h x)^2 (f g-e h)^2}","\frac{3 b^2 f^2 p^2 q^2 \text{Li}_2\left(-\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^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}+\frac{3 b^3 f^2 p^3 q^3 \text{Li}_2\left(-\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{Li}_3\left(-\frac{f g-e h}{h (e+f x)}\right)}{h (f g-e h)^2}",1,"-1/2*(-3*b*f*(f*g - e*h)*p*q*(g + h*x)*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2 + 3*b*(f*g - e*h)^2*p*q*Log[e + f*x]*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2 - 3*b*f^2*p*q*(g + h*x)^2*Log[e + f*x]*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2 + (f*g - e*h)^2*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^3 + 3*b*f^2*p*q*(g + h*x)^2*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2*Log[g + h*x] + 3*b^2*p^2*q^2*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])*(h*(e + f*x)*(e*h - f*(2*g + h*x))*Log[e + f*x]^2 - 2*f^2*(g + h*x)^2*Log[(f*(g + h*x))/(f*g - e*h)] + 2*f*(g + h*x)*Log[e + f*x]*(h*(e + f*x) + f*(g + h*x)*Log[(f*(g + h*x))/(f*g - e*h)]) + 2*f^2*(g + h*x)^2*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)]) + b^3*p^3*q^3*(h*(e + f*x)*(e*h - f*(2*g + h*x))*Log[e + f*x]^3 + 3*f*(g + h*x)*Log[e + f*x]^2*(h*(e + f*x) + f*(g + h*x)*Log[(f*(g + h*x))/(f*g - e*h)]) - 6*f^2*(g + h*x)^2*Log[e + f*x]*(Log[(f*(g + h*x))/(f*g - e*h)] - PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)]) - 6*f^2*(g + h*x)^2*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)] - 6*f^2*(g + h*x)^2*PolyLog[3, (h*(e + f*x))/(-(f*g) + e*h)]))/(h*(f*g - e*h)^2*(g + h*x)^2)","A",1
441,1,132,160,0.0572256,"\int \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^4 \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^4,x]","\frac{(e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^4-4 b p q \left((e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3-3 b p q \left((e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2-2 b p q \left(f x (a-b p q)+b (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)\right)\right)\right)}{f}","-24 a b^3 p^3 q^3 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}-\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,"((e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^4 - 4*b*p*q*((e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3 - 3*b*p*q*((e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 - 2*b*p*q*(f*(a - b*p*q)*x + b*(e + f*x)*Log[c*(d*(e + f*x)^p)^q]))))/f","A",1
442,1,1095,231,0.4502542,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^4}{g+h x} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^4/(g + h*x),x]","\frac{\log (g+h x) a^4-4 b p q \log (e+f x) \log (g+h x) a^3+4 b \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a^3+4 b p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) a^3+6 b^2 p^2 q^2 \log ^2(e+f x) \log (g+h x) a^2+6 b^2 \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a^2-12 b^2 p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a^2-6 b^2 p^2 q^2 \log ^2(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) a^2+12 b^2 p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right) a^2-4 b^3 p^3 q^3 \log ^3(e+f x) \log (g+h x) a+4 b^3 \log ^3\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a-12 b^3 p q \log (e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a+12 b^3 p^2 q^2 \log ^2(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a+4 b^3 p^3 q^3 \log ^3(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) a+12 b^3 p q \log (e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right) a-12 b^3 p^2 q^2 \log ^2(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right) a+24 b^3 p^3 q^3 \text{Li}_4\left(\frac{h (e+f x)}{e h-f g}\right) a+b^4 p^4 q^4 \log ^4(e+f x) \log (g+h x)+b^4 \log ^4\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)-4 b^4 p q \log (e+f x) \log ^3\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)+6 b^4 p^2 q^2 \log ^2(e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)-4 b^4 p^3 q^3 \log ^3(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)-b^4 p^4 q^4 \log ^4(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+4 b^4 p q \log (e+f x) \log ^3\left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right)-6 b^4 p^2 q^2 \log ^2(e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right)+4 b^4 p^3 q^3 \log ^3(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right)+4 b p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3 \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)-12 b^2 p^2 q^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right)+24 b^4 p^3 q^3 \log \left(c \left(d (e+f x)^p\right)^q\right) \text{Li}_4\left(\frac{h (e+f x)}{e h-f g}\right)-24 b^4 p^4 q^4 \text{Li}_5\left(\frac{h (e+f x)}{e h-f g}\right)}{h}","\frac{24 b^3 p^3 q^3 \text{Li}_4\left(-\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{Li}_3\left(-\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{Li}_2\left(-\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{\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^4 p^4 q^4 \text{Li}_5\left(-\frac{h (e+f x)}{f g-e h}\right)}{h}",1,"(a^4*Log[g + h*x] - 4*a^3*b*p*q*Log[e + f*x]*Log[g + h*x] + 6*a^2*b^2*p^2*q^2*Log[e + f*x]^2*Log[g + h*x] - 4*a*b^3*p^3*q^3*Log[e + f*x]^3*Log[g + h*x] + b^4*p^4*q^4*Log[e + f*x]^4*Log[g + h*x] + 4*a^3*b*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 12*a^2*b^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 12*a*b^3*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 4*b^4*p^3*q^3*Log[e + f*x]^3*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 6*a^2*b^2*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] - 12*a*b^3*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] + 6*b^4*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] + 4*a*b^3*Log[c*(d*(e + f*x)^p)^q]^3*Log[g + h*x] - 4*b^4*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^3*Log[g + h*x] + b^4*Log[c*(d*(e + f*x)^p)^q]^4*Log[g + h*x] + 4*a^3*b*p*q*Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] - 6*a^2*b^2*p^2*q^2*Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 4*a*b^3*p^3*q^3*Log[e + f*x]^3*Log[(f*(g + h*x))/(f*g - e*h)] - b^4*p^4*q^4*Log[e + f*x]^4*Log[(f*(g + h*x))/(f*g - e*h)] + 12*a^2*b^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] - 12*a*b^3*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] + 4*b^4*p^3*q^3*Log[e + f*x]^3*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] + 12*a*b^3*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[(f*(g + h*x))/(f*g - e*h)] - 6*b^4*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 4*b^4*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^3*Log[(f*(g + h*x))/(f*g - e*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)] - 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)] + 24*a*b^3*p^3*q^3*PolyLog[4, (h*(e + f*x))/(-(f*g) + e*h)] + 24*b^4*p^3*q^3*Log[c*(d*(e + f*x)^p)^q]*PolyLog[4, (h*(e + f*x))/(-(f*g) + e*h)] - 24*b^4*p^4*q^4*PolyLog[5, (h*(e + f*x))/(-(f*g) + e*h)])/h","B",1
443,1,1301,274,0.5803525,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^4}{(g+h x)^2} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^4/(g + h*x)^2,x]","\frac{f g a^4-e h a^4-4 b f g p q \log (e+f x) a^3-4 b f h p q x \log (e+f x) a^3+4 b f g \log \left(c \left(d (e+f x)^p\right)^q\right) a^3-4 b e h \log \left(c \left(d (e+f x)^p\right)^q\right) a^3+4 b f g p q \log \left(\frac{f (g+h x)}{f g-e h}\right) a^3+4 b f h p q x \log \left(\frac{f (g+h x)}{f g-e h}\right) a^3+6 b^2 f g p^2 q^2 \log ^2(e+f x) a^2+6 b^2 f h p^2 q^2 x \log ^2(e+f x) a^2+6 b^2 f g \log ^2\left(c \left(d (e+f x)^p\right)^q\right) a^2-6 b^2 e h \log ^2\left(c \left(d (e+f x)^p\right)^q\right) a^2-12 b^2 f g p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) a^2-12 b^2 f h p q x \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) a^2+12 b^2 f g p q \log \left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right) a^2+12 b^2 f h p q x \log \left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right) a^2-4 b^3 f g p^3 q^3 \log ^3(e+f x) a-4 b^3 f h p^3 q^3 x \log ^3(e+f x) a+4 b^3 f g \log ^3\left(c \left(d (e+f x)^p\right)^q\right) a-4 b^3 e h \log ^3\left(c \left(d (e+f x)^p\right)^q\right) a-12 b^3 f g p q \log (e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right) a-12 b^3 f h p q x \log (e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right) a+12 b^3 f g p^2 q^2 \log ^2(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) a+12 b^3 f h p^2 q^2 x \log ^2(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) a+12 b^3 f g p q \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right) a+12 b^3 f h p q x \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right) a+b^4 f g p^4 q^4 \log ^4(e+f x)+b^4 f h p^4 q^4 x \log ^4(e+f x)+b^4 f g \log ^4\left(c \left(d (e+f x)^p\right)^q\right)-b^4 e h \log ^4\left(c \left(d (e+f x)^p\right)^q\right)-4 b^4 f g p q \log (e+f x) \log ^3\left(c \left(d (e+f x)^p\right)^q\right)-4 b^4 f h p q x \log (e+f x) \log ^3\left(c \left(d (e+f x)^p\right)^q\right)+6 b^4 f g p^2 q^2 \log ^2(e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right)+6 b^4 f h p^2 q^2 x \log ^2(e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right)-4 b^4 f g p^3 q^3 \log ^3(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)-4 b^4 f h p^3 q^3 x \log ^3(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)+4 b^4 f g p q \log ^3\left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right)+4 b^4 f h p q x \log ^3\left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right)+12 b^2 f p^2 q^2 (g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)-24 b^3 f p^3 q^3 (g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right)+24 b^4 f g p^4 q^4 \text{Li}_4\left(\frac{h (e+f x)}{e h-f g}\right)+24 b^4 f h p^4 q^4 x \text{Li}_4\left(\frac{h (e+f x)}{e h-f g}\right)}{h (e h-f g) (g+h x)}","\frac{24 b^3 f p^3 q^3 \text{Li}_3\left(-\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{Li}_2\left(-\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{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^4 f p^4 q^4 \text{Li}_4\left(-\frac{h (e+f x)}{f g-e h}\right)}{h (f g-e h)}",1,"(a^4*f*g - a^4*e*h - 4*a^3*b*f*g*p*q*Log[e + f*x] - 4*a^3*b*f*h*p*q*x*Log[e + f*x] + 6*a^2*b^2*f*g*p^2*q^2*Log[e + f*x]^2 + 6*a^2*b^2*f*h*p^2*q^2*x*Log[e + f*x]^2 - 4*a*b^3*f*g*p^3*q^3*Log[e + f*x]^3 - 4*a*b^3*f*h*p^3*q^3*x*Log[e + f*x]^3 + b^4*f*g*p^4*q^4*Log[e + f*x]^4 + b^4*f*h*p^4*q^4*x*Log[e + f*x]^4 + 4*a^3*b*f*g*Log[c*(d*(e + f*x)^p)^q] - 4*a^3*b*e*h*Log[c*(d*(e + f*x)^p)^q] - 12*a^2*b^2*f*g*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q] - 12*a^2*b^2*f*h*p*q*x*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q] + 12*a*b^3*f*g*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q] + 12*a*b^3*f*h*p^2*q^2*x*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q] - 4*b^4*f*g*p^3*q^3*Log[e + f*x]^3*Log[c*(d*(e + f*x)^p)^q] - 4*b^4*f*h*p^3*q^3*x*Log[e + f*x]^3*Log[c*(d*(e + f*x)^p)^q] + 6*a^2*b^2*f*g*Log[c*(d*(e + f*x)^p)^q]^2 - 6*a^2*b^2*e*h*Log[c*(d*(e + f*x)^p)^q]^2 - 12*a*b^3*f*g*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2 - 12*a*b^3*f*h*p*q*x*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2 + 6*b^4*f*g*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]^2 + 6*b^4*f*h*p^2*q^2*x*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]^2 + 4*a*b^3*f*g*Log[c*(d*(e + f*x)^p)^q]^3 - 4*a*b^3*e*h*Log[c*(d*(e + f*x)^p)^q]^3 - 4*b^4*f*g*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^3 - 4*b^4*f*h*p*q*x*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^3 + b^4*f*g*Log[c*(d*(e + f*x)^p)^q]^4 - b^4*e*h*Log[c*(d*(e + f*x)^p)^q]^4 + 4*a^3*b*f*g*p*q*Log[(f*(g + h*x))/(f*g - e*h)] + 4*a^3*b*f*h*p*q*x*Log[(f*(g + h*x))/(f*g - e*h)] + 12*a^2*b^2*f*g*p*q*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] + 12*a^2*b^2*f*h*p*q*x*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] + 12*a*b^3*f*g*p*q*Log[c*(d*(e + f*x)^p)^q]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 12*a*b^3*f*h*p*q*x*Log[c*(d*(e + f*x)^p)^q]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 4*b^4*f*g*p*q*Log[c*(d*(e + f*x)^p)^q]^3*Log[(f*(g + h*x))/(f*g - e*h)] + 4*b^4*f*h*p*q*x*Log[c*(d*(e + f*x)^p)^q]^3*Log[(f*(g + h*x))/(f*g - e*h)] + 12*b^2*f*p^2*q^2*(g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)] - 24*b^3*f*p^3*q^3*(g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[3, (h*(e + f*x))/(-(f*g) + e*h)] + 24*b^4*f*g*p^4*q^4*PolyLog[4, (h*(e + f*x))/(-(f*g) + e*h)] + 24*b^4*f*h*p^4*q^4*x*PolyLog[4, (h*(e + f*x))/(-(f*g) + e*h)])/(h*(-(f*g) + e*h)*(g + h*x))","B",1
444,1,29,29,0.0100902,"\int \log \left(c \left(d (e+f x)^p\right)^q\right) \, dx","Integrate[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",1
445,1,252,279,0.8433606,"\int \frac{(g+h x)^2}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Integrate[(g + h*x)^2/(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\frac{(e+f x) e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \left(e^{\frac{2 a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{2}{p q}} \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)-h (e+f x) \left(-2 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{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b p q}\right)-h (e+f x) \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)\right)\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,"((e + f*x)*(E^((2*a)/(b*p*q))*(f*g - e*h)^2*(c*(d*(e + f*x)^p)^q)^(2/(p*q))*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)] - h*(e + f*x)*(-2*E^(a/(b*p*q))*(f*g - e*h)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*ExpIntegralEi[(2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)] - h*(e + f*x)*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",1
446,1,164,179,0.2709423,"\int \frac{g+h x}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Integrate[(g + h*x)/(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\frac{(e+f x) e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \left(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)+h (e+f x) \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)\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,"((e + f*x)*(E^(a/(b*p*q))*(f*g - e*h)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)] + h*(e + f*x)*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",1
447,1,83,83,0.0630326,"\int \frac{1}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Integrate[(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",1
448,0,0,31,0.2642429,"\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","Integrate[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,"Integrate[1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])), x]","A",-1
449,0,0,31,0.824872,"\int \frac{1}{(g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","Integrate[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,"Integrate[1/((g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])), x]","A",-1
450,1,1310,326,0.9848176,"\int \frac{(g+h x)^2}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","Integrate[(g + h*x)^2/(a + b*Log[c*(d*(e + f*x)^p)^q])^2,x]","\frac{e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \left(-4 a e e^{\frac{a}{b p q}} h^2 (e+f x)^2 \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) \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{1}{p q}}+4 a e^{\frac{a}{b p q}} f g h (e+f x)^2 \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) \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{1}{p q}}-4 b e e^{\frac{a}{b p q}} h^2 (e+f x)^2 \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) \log \left(c \left(d (e+f x)^p\right)^q\right) \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{1}{p q}}+4 b e^{\frac{a}{b p q}} f g h (e+f x)^2 \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) \log \left(c \left(d (e+f x)^p\right)^q\right) \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{1}{p q}}+a e^{\frac{2 a}{b p q}} f^2 g^2 (e+f x) \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right) \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{2}{p q}}+a e^2 e^{\frac{2 a}{b p q}} h^2 (e+f x) \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right) \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{2}{p q}}-2 a e e^{\frac{2 a}{b p q}} f g h (e+f x) \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right) \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{2}{p q}}+b e^{\frac{2 a}{b p q}} f^2 g^2 (e+f x) \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right) \log \left(c \left(d (e+f x)^p\right)^q\right) \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{2}{p q}}+b e^2 e^{\frac{2 a}{b p q}} h^2 (e+f x) \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right) \log \left(c \left(d (e+f x)^p\right)^q\right) \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{2}{p q}}-2 b e e^{\frac{2 a}{b p q}} f g h (e+f x) \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right) \log \left(c \left(d (e+f x)^p\right)^q\right) \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{2}{p q}}-b e^{\frac{3 a}{b p q}} f^3 h^2 p q x^3 \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{3}{p q}}-b e e^{\frac{3 a}{b p q}} f^2 h^2 p q x^2 \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{3}{p q}}-2 b e^{\frac{3 a}{b p q}} f^3 g h p q x^2 \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{3}{p q}}-b e e^{\frac{3 a}{b p q}} f^2 g^2 p q \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{3}{p q}}-b e^{\frac{3 a}{b p q}} f^3 g^2 p q x \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{3}{p q}}-2 b e e^{\frac{3 a}{b p q}} f^2 g h p q x \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{3}{p q}}+3 a h^2 (e+f x)^3 \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)+3 b h^2 (e+f x)^3 \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) \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{b^2 f^3 p^2 q^2 \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,"(-(b*e*E^((3*a)/(b*p*q))*f^2*g^2*p*q*(c*(d*(e + f*x)^p)^q)^(3/(p*q))) - b*E^((3*a)/(b*p*q))*f^3*g^2*p*q*x*(c*(d*(e + f*x)^p)^q)^(3/(p*q)) - 2*b*e*E^((3*a)/(b*p*q))*f^2*g*h*p*q*x*(c*(d*(e + f*x)^p)^q)^(3/(p*q)) - 2*b*E^((3*a)/(b*p*q))*f^3*g*h*p*q*x^2*(c*(d*(e + f*x)^p)^q)^(3/(p*q)) - b*e*E^((3*a)/(b*p*q))*f^2*h^2*p*q*x^2*(c*(d*(e + f*x)^p)^q)^(3/(p*q)) - b*E^((3*a)/(b*p*q))*f^3*h^2*p*q*x^3*(c*(d*(e + f*x)^p)^q)^(3/(p*q)) + a*E^((2*a)/(b*p*q))*f^2*g^2*(e + f*x)*(c*(d*(e + f*x)^p)^q)^(2/(p*q))*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)] - 2*a*e*E^((2*a)/(b*p*q))*f*g*h*(e + f*x)*(c*(d*(e + f*x)^p)^q)^(2/(p*q))*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)] + a*e^2*E^((2*a)/(b*p*q))*h^2*(e + f*x)*(c*(d*(e + f*x)^p)^q)^(2/(p*q))*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)] + 4*a*E^(a/(b*p*q))*f*g*h*(e + f*x)^2*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*ExpIntegralEi[(2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)] - 4*a*e*E^(a/(b*p*q))*h^2*(e + f*x)^2*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*ExpIntegralEi[(2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)] + 3*a*h^2*(e + f*x)^3*ExpIntegralEi[(3*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)] + b*E^((2*a)/(b*p*q))*f^2*g^2*(e + f*x)*(c*(d*(e + f*x)^p)^q)^(2/(p*q))*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)]*Log[c*(d*(e + f*x)^p)^q] - 2*b*e*E^((2*a)/(b*p*q))*f*g*h*(e + f*x)*(c*(d*(e + f*x)^p)^q)^(2/(p*q))*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)]*Log[c*(d*(e + f*x)^p)^q] + b*e^2*E^((2*a)/(b*p*q))*h^2*(e + f*x)*(c*(d*(e + f*x)^p)^q)^(2/(p*q))*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)]*Log[c*(d*(e + f*x)^p)^q] + 4*b*E^(a/(b*p*q))*f*g*h*(e + f*x)^2*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*ExpIntegralEi[(2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)]*Log[c*(d*(e + f*x)^p)^q] - 4*b*e*E^(a/(b*p*q))*h^2*(e + f*x)^2*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*ExpIntegralEi[(2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)]*Log[c*(d*(e + f*x)^p)^q] + 3*b*h^2*(e + f*x)^3*ExpIntegralEi[(3*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)]*Log[c*(d*(e + f*x)^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))*(a + b*Log[c*(d*(e + f*x)^p)^q]))","B",1
451,1,269,224,0.46233,"\int \frac{g+h x}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","Integrate[(g + h*x)/(a + b*Log[c*(d*(e + f*x)^p)^q])^2,x]","-\frac{(e+f x) e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \left(-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) \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)-2 h (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \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 p q (g+h x) e^{\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{2}{p q}}\right)}{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) 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,"-(((e + f*x)*(b*E^((2*a)/(b*p*q))*f*p*q*(c*(d*(e + f*x)^p)^q)^(2/(p*q))*(g + h*x) - E^(a/(b*p*q))*(f*g - e*h)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)]*(a + b*Log[c*(d*(e + f*x)^p)^q]) - 2*h*(e + f*x)*ExpIntegralEi[(2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)]*(a + b*Log[c*(d*(e + f*x)^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))*(a + b*Log[c*(d*(e + f*x)^p)^q])))","A",1
452,1,163,123,0.1205571,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","Integrate[(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}} \left(b p q 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) \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)\right)}{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) 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)*(b*E^(a/(b*p*q))*p*q*(c*(d*(e + f*x)^p)^q)^(1/(p*q)) - ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)]*(a + b*Log[c*(d*(e + f*x)^p)^q])))/(b^2*E^(a/(b*p*q))*f*p^2*q^2*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*(a + b*Log[c*(d*(e + f*x)^p)^q])))","A",1
453,0,0,31,1.3966697,"\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","Integrate[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,"Integrate[1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2), x]","A",-1
454,0,0,31,18.5993677,"\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","Integrate[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,"Integrate[1/((g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2), x]","A",-1
455,1,438,432,2.324765,"\int \frac{(g+h x)^2}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3} \, dx","Integrate[(g + h*x)^2/(a + b*Log[c*(d*(e + f*x)^p)^q])^3,x]","\frac{(e+f x) e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \left(-8 h (e+f x) e^{\frac{a}{b p q}} (e h-f g) \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)^2 \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)+e^{\frac{2 a}{b p q}} (f g-e h)^2 \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)^2 \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)+9 h^2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \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 p q (g+h x) e^{\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{3}{p q}} \left(a (2 e h+f g+3 f h x)+b (2 e h+f (g+3 h x)) \log \left(c \left(d (e+f x)^p\right)^q\right)+b f p q (g+h x)\right)\right)}{2 b^3 f^3 p^3 q^3 \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,"((e + f*x)*(E^((2*a)/(b*p*q))*(f*g - e*h)^2*(c*(d*(e + f*x)^p)^q)^(2/(p*q))*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)]*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 - 8*E^(a/(b*p*q))*h*(-(f*g) + e*h)*(e + f*x)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*ExpIntegralEi[(2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)]*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 + 9*h^2*(e + f*x)^2*ExpIntegralEi[(3*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)]*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 - b*E^((3*a)/(b*p*q))*f*p*q*(c*(d*(e + f*x)^p)^q)^(3/(p*q))*(g + h*x)*(b*f*p*q*(g + h*x) + a*(f*g + 2*e*h + 3*f*h*x) + b*(2*e*h + f*(g + 3*h*x))*Log[c*(d*(e + f*x)^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))*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)","A",1
456,1,322,322,0.8517934,"\int \frac{g+h x}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3} \, dx","Integrate[(g + h*x)/(a + b*Log[c*(d*(e + f*x)^p)^q])^3,x]","-\frac{(e+f x) e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \left(-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)^2 \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)-4 h (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \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 p q e^{\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{2}{p q}} \left(a (e h+f g+2 f h x)+b (e h+f (g+2 h x)) \log \left(c \left(d (e+f x)^p\right)^q\right)+b f p q (g+h x)\right)\right)}{2 b^3 f^2 p^3 q^3 \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,"-1/2*((e + f*x)*(-(E^(a/(b*p*q))*(f*g - e*h)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)]*(a + b*Log[c*(d*(e + f*x)^p)^q])^2) - 4*h*(e + f*x)*ExpIntegralEi[(2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)]*(a + b*Log[c*(d*(e + f*x)^p)^q])^2 + b*E^((2*a)/(b*p*q))*p*q*(c*(d*(e + f*x)^p)^q)^(2/(p*q))*(b*f*p*q*(g + h*x) + a*(f*g + e*h + 2*f*h*x) + b*(e*h + f*(g + 2*h*x))*Log[c*(d*(e + f*x)^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))*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)","A",1
457,1,189,169,0.3173532,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3} \, dx","Integrate[(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}} \left(b p q 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)+b p q\right)-\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \text{Ei}\left(\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)\right)}{2 b^3 f p^3 q^3 \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,"-1/2*((e + f*x)*(-(ExpIntegralEi[(a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)]*(a + b*Log[c*(d*(e + f*x)^p)^q])^2) + b*E^(a/(b*p*q))*p*q*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*(a + b*p*q + b*Log[c*(d*(e + f*x)^p)^q])))/(b^3*E^(a/(b*p*q))*f*p^3*q^3*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)","A",1
458,0,0,31,1.6441114,"\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3} \, dx","Integrate[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,"Integrate[1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3), x]","A",-1
459,0,0,31,39.7124398,"\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","Integrate[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,"Integrate[1/((g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^3), x]","A",-1
460,1,458,488,0.6907391,"\int (g+h x)^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Integrate[(g + h*x)^2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]","\frac{(e+f x) \left(9 \sqrt{2 \pi } \sqrt{b} h \sqrt{p} \sqrt{q} (e+f x) e^{-\frac{2 a}{b p q}} (e h-f g) \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)-18 \sqrt{\pi } \sqrt{b} \sqrt{p} \sqrt{q} 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 \sqrt{3 \pi } \sqrt{b} h^2 \sqrt{p} \sqrt{q} (e+f x)^2 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)+36 (f g-e h)^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}+36 h (e+f x) (f g-e h) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}+12 h^2 (e+f x)^2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}\right)}{36 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,"((e + f*x)*((-18*Sqrt[b]*(f*g - e*h)^2*Sqrt[p]*Sqrt[Pi]*Sqrt[q]*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(E^(a/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (9*Sqrt[b]*h*(-(f*g) + e*h)*Sqrt[p]*Sqrt[2*Pi]*Sqrt[q]*(e + f*x)*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(E^((2*a)/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) - (2*Sqrt[b]*h^2*Sqrt[p]*Sqrt[3*Pi]*Sqrt[q]*(e + f*x)^2*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(E^((3*a)/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(3/(p*q))) + 36*(f*g - e*h)^2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]] + 36*h*(f*g - e*h)*(e + f*x)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]] + 12*h^2*(e + f*x)^2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]))/(36*f^3)","A",1
461,1,298,311,0.3881858,"\int (g+h x) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Integrate[(g + h*x)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]","-\frac{(e+f x) e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \left(4 \sqrt{\pi } \sqrt{b} \sqrt{p} \sqrt{q} 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{2 \pi } \sqrt{b} h \sqrt{p} \sqrt{q} (e+f x) \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 e^{\frac{2 a}{b p q}} (-e h+2 f g+f h x) \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{2}{p q}} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}\right)}{8 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,"-1/8*((e + f*x)*(4*Sqrt[b]*E^(a/(b*p*q))*(f*g - e*h)*Sqrt[p]*Sqrt[Pi]*Sqrt[q]*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])] + Sqrt[b]*h*Sqrt[p]*Sqrt[2*Pi]*Sqrt[q]*(e + f*x)*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))*(c*(d*(e + f*x)^p)^q)^(2/(p*q))*(2*f*g - e*h + f*h*x)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]))/(E^((2*a)/(b*p*q))*f^2*(c*(d*(e + f*x)^p)^q)^(2/(p*q)))","A",1
462,1,134,139,0.0652164,"\int \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Integrate[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]","\frac{(e+f x) \left(2 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}-\sqrt{\pi } \sqrt{b} \sqrt{p} \sqrt{q} 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)\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,"((e + f*x)*(-((Sqrt[b]*Sqrt[p]*Sqrt[Pi]*Sqrt[q]*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(E^(a/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(1/(p*q)))) + 2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]))/(2*f)","A",1
463,0,0,33,1.2514142,"\int \frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{g+h x} \, dx","Integrate[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,"Integrate[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(g + h*x), x]","A",-1
464,0,0,33,0.3877764,"\int \frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{(g+h x)^2} \, dx","Integrate[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,"Integrate[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(g + h*x)^2, x]","A",-1
465,1,545,625,1.4126679,"\int (g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2} \, dx","Integrate[(g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2),x]","\frac{(e+f x) \left(108 b p q (f g-e h)^2 \left(\sqrt{\pi } \sqrt{b} \sqrt{p} \sqrt{q} 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 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}\right)+27 b h p q (e+f x) (f g-e h) \left(\sqrt{2 \pi } \sqrt{b} \sqrt{p} \sqrt{q} 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 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}\right)+4 b h^2 p q (e+f x)^2 \left(\sqrt{3 \pi } \sqrt{b} \sqrt{p} \sqrt{q} 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 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}\right)+144 (f g-e h)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}+144 h (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}+48 h^2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}\right)}{144 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,"((e + f*x)*(144*(f*g - e*h)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2) + 144*h*(f*g - e*h)*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2) + 48*h^2*(e + f*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2) + 4*b*h^2*p*q*(e + f*x)^2*((Sqrt[b]*Sqrt[p]*Sqrt[3*Pi]*Sqrt[q]*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(E^((3*a)/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(3/(p*q))) - 6*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]) + 27*b*h*(f*g - e*h)*p*q*(e + f*x)*((Sqrt[b]*Sqrt[p]*Sqrt[2*Pi]*Sqrt[q]*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(E^((2*a)/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) - 4*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]) + 108*b*(f*g - e*h)^2*p*q*((Sqrt[b]*Sqrt[p]*Sqrt[Pi]*Sqrt[q]*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(E^(a/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) - 2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])))/(144*f^3)","A",1
466,1,348,396,0.5712666,"\int (g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2} \, dx","Integrate[(g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2),x]","\frac{(e+f x) \left(24 b p q (f g-e h) \left(\sqrt{\pi } \sqrt{b} \sqrt{p} \sqrt{q} 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 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}\right)+3 b h p q (e+f x) \left(\sqrt{2 \pi } \sqrt{b} \sqrt{p} \sqrt{q} 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 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}\right)+32 (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}+16 h (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}\right)}{32 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,"((e + f*x)*(32*(f*g - e*h)*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2) + 16*h*(e + f*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2) + 3*b*h*p*q*(e + f*x)*((Sqrt[b]*Sqrt[p]*Sqrt[2*Pi]*Sqrt[q]*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(E^((2*a)/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) - 4*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]) + 24*b*(f*g - e*h)*p*q*((Sqrt[b]*Sqrt[p]*Sqrt[Pi]*Sqrt[q]*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(E^(a/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) - 2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])))/(32*f^2)","A",1
467,1,160,176,0.2126179,"\int \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2),x]","\frac{(e+f x) \left(3 \sqrt{\pi } b^{3/2} p^{3/2} q^{3/2} 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 \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \left(2 a+2 b \log \left(c \left(d (e+f x)^p\right)^q\right)-3 b p q\right)\right)}{4 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,"((e + f*x)*((3*b^(3/2)*p^(3/2)*Sqrt[Pi]*q^(3/2)*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])])/(E^(a/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + 2*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]*(2*a - 3*b*p*q + 2*b*Log[c*(d*(e + f*x)^p)^q])))/(4*f)","A",1
468,0,0,33,2.0018857,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}}{g+h x} \, dx","Integrate[(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,"Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2)/(g + h*x), x]","A",-1
469,0,0,33,2.2484876,"\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","Integrate[(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,"Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2)/(g + h*x)^2, x]","A",-1
470,1,315,355,0.3487245,"\int \frac{(g+h x)^2}{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","Integrate[(g + h*x)^2/Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]","\frac{\sqrt{\pi } (e+f x) e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \left(3 \sqrt{2} h (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{2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{b} \sqrt{p} \sqrt{q}}\right)+3 e^{\frac{2 a}{b p q}} (f g-e h)^2 \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{2}{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{3} h^2 (e+f x)^2 \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)\right)}{3 \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,"(Sqrt[Pi]*(e + f*x)*(3*E^((2*a)/(b*p*q))*(f*g - e*h)^2*(c*(d*(e + f*x)^p)^q)^(2/(p*q))*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])] + 3*Sqrt[2]*E^(a/(b*p*q))*h*(f*g - e*h)*(e + f*x)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])] + Sqrt[3]*h^2*(e + f*x)^2*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])]))/(3*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",1
471,1,208,229,0.1856547,"\int \frac{g+h x}{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","Integrate[(g + h*x)/Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]","\frac{\sqrt{\pi } (e+f x) e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \left(2 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{2} h (e+f x) \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)\right)}{2 \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,"(Sqrt[Pi]*(e + f*x)*(2*E^(a/(b*p*q))*(f*g - e*h)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])] + Sqrt[2]*h*(e + f*x)*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])]))/(2*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",1
472,1,104,104,0.0220681,"\int \frac{1}{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","Integrate[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",1
473,0,0,33,0.1157567,"\int \frac{1}{(g+h x) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","Integrate[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,"Integrate[1/((g + h*x)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]), x]","A",-1
474,1,1040,404,2.5736785,"\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","Integrate[(g + h*x)^2/(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2),x]","\frac{2 \left(e^{-\frac{3 a}{b p q}} h^2 \sqrt{3 \pi } (e+f x)^3 \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{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}}-2 e e^{-\frac{2 a}{b p q}} h^2 \sqrt{2 \pi } (e+f x)^2 \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{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}}+2 e^{-\frac{2 a}{b p q}} f g h \sqrt{2 \pi } (e+f x)^2 \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{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}}+e^2 e^{-\frac{a}{b p q}} h^2 \sqrt{\pi } (e+f x) \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{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}}-4 e e^{-\frac{a}{b p q}} f g h \sqrt{\pi } (e+f x) \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{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}}+\sqrt{b} e^{-\frac{a}{b p q}} f^2 g^2 \sqrt{p} \sqrt{q} (e+f x) \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right) \sqrt{-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}}+2 \sqrt{b} e e^{-\frac{a}{b p q}} f g h \sqrt{p} \sqrt{q} (e+f x) \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right) \sqrt{-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{1}{p q}}-\sqrt{b} f^3 h^2 \sqrt{p} \sqrt{q} x^3-\sqrt{b} e f^2 h^2 \sqrt{p} \sqrt{q} x^2-2 \sqrt{b} f^3 g h \sqrt{p} \sqrt{q} x^2-\sqrt{b} f^3 g^2 \sqrt{p} \sqrt{q} x-2 \sqrt{b} e f^2 g h \sqrt{p} \sqrt{q} x-\sqrt{b} e f^2 g^2 \sqrt{p} \sqrt{q}\right)}{b^{3/2} f^3 p^{3/2} q^{3/2} \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*(-(Sqrt[b]*e*f^2*g^2*Sqrt[p]*Sqrt[q]) - Sqrt[b]*f^3*g^2*Sqrt[p]*Sqrt[q]*x - 2*Sqrt[b]*e*f^2*g*h*Sqrt[p]*Sqrt[q]*x - 2*Sqrt[b]*f^3*g*h*Sqrt[p]*Sqrt[q]*x^2 - Sqrt[b]*e*f^2*h^2*Sqrt[p]*Sqrt[q]*x^2 - Sqrt[b]*f^3*h^2*Sqrt[p]*Sqrt[q]*x^3 - (4*e*f*g*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[a + b*Log[c*(d*(e + f*x)^p)^q]])/(E^(a/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (e^2*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[a + b*Log[c*(d*(e + f*x)^p)^q]])/(E^(a/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (2*f*g*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[a + b*Log[c*(d*(e + f*x)^p)^q]])/(E^((2*a)/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) - (2*e*h^2*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[a + b*Log[c*(d*(e + f*x)^p)^q]])/(E^((2*a)/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(2/(p*q))) + (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])]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(E^((3*a)/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(3/(p*q))) + (Sqrt[b]*f^2*g^2*Sqrt[p]*Sqrt[q]*(e + f*x)*Gamma[1/2, -((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q))]*Sqrt[-((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q))])/(E^(a/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(1/(p*q))) + (2*Sqrt[b]*e*f*g*h*Sqrt[p]*Sqrt[q]*(e + f*x)*Gamma[1/2, -((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q))]*Sqrt[-((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q))])/(E^(a/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(1/(p*q)))))/(b^(3/2)*f^3*p^(3/2)*q^(3/2)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])","B",1
475,1,435,275,1.3396347,"\int \frac{g+h x}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}} \, dx","Integrate[(g + h*x)/(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2),x]","\frac{2 (e+f x) e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \left(-2 \sqrt{\pi } e h e^{\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{1}{p q}} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \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{2 \pi } h (e+f x) \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \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} \sqrt{p} \sqrt{q} e^{\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{1}{p q}} \left((e h+f g) \sqrt{-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}} \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)-f (g+h x) e^{\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{1}{p q}}\right)\right)}{b^{3/2} f^2 p^{3/2} q^{3/2} \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*(e + f*x)*(-2*e*E^(a/(b*p*q))*h*Sqrt[Pi]*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]] + h*Sqrt[2*Pi]*(e + f*x)*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]] + Sqrt[b]*E^(a/(b*p*q))*Sqrt[p]*Sqrt[q]*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*(-(E^(a/(b*p*q))*f*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*(g + h*x)) + (f*g + e*h)*Gamma[1/2, -((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q))]*Sqrt[-((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*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))*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])","A",1
476,1,181,147,0.1857179,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2}} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^(-3/2),x]","-\frac{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}} \left(e^{\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{1}{p q}}-\sqrt{-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}} \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)\right)}{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*(e + f*x)*(E^(a/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(1/(p*q)) - Gamma[1/2, -((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q))]*Sqrt[-((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))*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])","A",1
477,0,0,33,0.4761368,"\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","Integrate[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,"Integrate[1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2)), x]","A",-1
478,1,652,514,6.9279147,"\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","Integrate[(g + h*x)^2/(a + b*Log[c*(d*(e + f*x)^p)^q])^(5/2),x]","-\frac{2 (e+f x) e^{-\frac{3 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{3}{p q}} \left(\sqrt{b} \sqrt{p} \sqrt{q} e^{\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{2}{p q}} \left(2 b p q \left(2 e^2 h^2+6 e f g h+f^2 g^2\right) \left(-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)+f (g+h x) e^{\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{1}{p q}} \left(2 a (2 e h+f g+3 f h x)+2 b (2 e h+f (g+3 h x)) \log \left(c \left(d (e+f x)^p\right)^q\right)+b f p q (g+h x)\right)\right)+8 \sqrt{2 \pi } h (e+f x) e^{\frac{a}{b p q}} (e h-f g) \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)^{3/2} \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 \sqrt{\pi } e h e^{\frac{2 a}{b p q}} (e h+8 f g) \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)^{3/2} \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)-6 \sqrt{3 \pi } h^2 (e+f x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2} \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)\right)}{3 b^{5/2} f^3 p^{5/2} q^{5/2} \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,"(-2*(e + f*x)*(2*e*E^((2*a)/(b*p*q))*h*(8*f*g + e*h)*Sqrt[Pi]*(c*(d*(e + f*x)^p)^q)^(2/(p*q))*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])]*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2) + 8*E^(a/(b*p*q))*h*(-(f*g) + e*h)*Sqrt[2*Pi]*(e + f*x)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])]*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2) - 6*h^2*Sqrt[3*Pi]*(e + f*x)^2*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])]*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2) + Sqrt[b]*E^((2*a)/(b*p*q))*Sqrt[p]*Sqrt[q]*(c*(d*(e + f*x)^p)^q)^(2/(p*q))*(2*b*(f^2*g^2 + 6*e*f*g*h + 2*e^2*h^2)*p*q*Gamma[1/2, -((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q))]*(-((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)))^(3/2) + E^(a/(b*p*q))*f*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*(g + h*x)*(b*f*p*q*(g + h*x) + 2*a*(f*g + 2*e*h + 3*f*h*x) + 2*b*(2*e*h + f*(g + 3*h*x))*Log[c*(d*(e + f*x)^p)^q]))))/(3*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))*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2))","A",1
479,1,491,380,2.3148912,"\int \frac{g+h x}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{5/2}} \, dx","Integrate[(g + h*x)/(a + b*Log[c*(d*(e + f*x)^p)^q])^(5/2),x]","-\frac{2 (e+f x) e^{-\frac{2 a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{-\frac{2}{p q}} \left(8 \sqrt{\pi } e h 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)^{3/2} \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 \sqrt{2 \pi } h (e+f x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2} \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} \sqrt{p} \sqrt{q} e^{\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{1}{p q}} \left(e^{\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{1}{p q}} \left(2 a (e h+f g+2 f h x)+2 b (e h+f (g+2 h x)) \log \left(c \left(d (e+f x)^p\right)^q\right)+b f p q (g+h x)\right)+2 b p q (3 e h+f g) \left(-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)\right)\right)}{3 b^{5/2} f^2 p^{5/2} q^{5/2} \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,"(-2*(e + f*x)*(8*e*E^(a/(b*p*q))*h*Sqrt[Pi]*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*Erfi[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(Sqrt[b]*Sqrt[p]*Sqrt[q])]*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2) - 4*h*Sqrt[2*Pi]*(e + f*x)*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]])/(Sqrt[b]*Sqrt[p]*Sqrt[q])]*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2) + Sqrt[b]*E^(a/(b*p*q))*Sqrt[p]*Sqrt[q]*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*(2*b*(f*g + 3*e*h)*p*q*Gamma[1/2, -((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q))]*(-((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)))^(3/2) + E^(a/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*(b*f*p*q*(g + h*x) + 2*a*(f*g + e*h + 2*f*h*x) + 2*b*(e*h + f*(g + 2*h*x))*Log[c*(d*(e + f*x)^p)^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))*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2))","A",1
480,1,211,194,0.355695,"\int \frac{1}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{5/2}} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^(-5/2),x]","-\frac{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}} \left(e^{\frac{a}{b p q}} \left(c \left(d (e+f x)^p\right)^q\right)^{\frac{1}{p q}} \left(2 a+2 b \log \left(c \left(d (e+f x)^p\right)^q\right)+b p q\right)+2 b p q \left(-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)\right)}{3 b^2 f p^2 q^2 \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,"(-2*(e + f*x)*(2*b*p*q*Gamma[1/2, -((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q))]*(-((a + b*Log[c*(d*(e + f*x)^p)^q])/(b*p*q)))^(3/2) + E^(a/(b*p*q))*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*(2*a + b*p*q + 2*b*Log[c*(d*(e + f*x)^p)^q])))/(3*b^2*E^(a/(b*p*q))*f*p^2*q^2*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2))","A",1
481,0,0,33,0.8495812,"\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","Integrate[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,"Integrate[1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^(5/2)), x]","A",-1
482,1,153,171,0.3900015,"\int (g+h x)^{3/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \, dx","Integrate[(g + h*x)^(3/2)*(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\frac{2 \left(\frac{1}{5} a (g+h x)^{5/2}+\frac{1}{5} b (g+h x)^{5/2} \log \left(c \left(d (e+f x)^p\right)^q\right)-\frac{2}{75} b p q \left(\frac{5 (f g-e h) \left(\sqrt{f} \sqrt{g+h x} (-3 e h+4 f g+f h x)-3 (f g-e h)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)\right)}{f^{5/2}}+3 (g+h x)^{5/2}\right)\right)}{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 (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 \sqrt{g+h x} (f g-e h)^2}{5 f^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,"(2*((a*(g + h*x)^(5/2))/5 - (2*b*p*q*(3*(g + h*x)^(5/2) + (5*(f*g - e*h)*(Sqrt[f]*Sqrt[g + h*x]*(4*f*g - 3*e*h + f*h*x) - 3*(f*g - e*h)^(3/2)*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]))/f^(5/2)))/75 + (b*(g + h*x)^(5/2)*Log[c*(d*(e + f*x)^p)^q])/5))/h","A",1
483,1,124,139,0.1932673,"\int \sqrt{g+h x} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \, dx","Integrate[Sqrt[g + h*x]*(a + b*Log[c*(d*(e + f*x)^p)^q]),x]","\frac{2 \left(\sqrt{f} \sqrt{g+h x} \left(3 a f (g+h x)+3 b f (g+h x) \log \left(c \left(d (e+f x)^p\right)^q\right)-2 b p q (-3 e h+4 f g+f h x)\right)+6 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)\right)}{9 f^{3/2} 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,"(2*(6*b*(f*g - e*h)^(3/2)*p*q*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]] + Sqrt[f]*Sqrt[g + h*x]*(3*a*f*(g + h*x) - 2*b*p*q*(4*f*g - 3*e*h + f*h*x) + 3*b*f*(g + h*x)*Log[c*(d*(e + f*x)^p)^q])))/(9*f^(3/2)*h)","A",1
484,1,89,103,0.2978953,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{\sqrt{g+h x}} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/Sqrt[g + h*x],x]","\frac{2 \left(\sqrt{g+h x} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-2 b p q\right)+\frac{2 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}}\right)}{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,"(2*((2*b*Sqrt[f*g - e*h]*p*q*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]])/Sqrt[f] + Sqrt[g + h*x]*(a - 2*b*p*q + b*Log[c*(d*(e + f*x)^p)^q])))/h","A",1
485,1,84,86,0.1668423,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x)^{3/2}} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x)^(3/2),x]","\frac{-\frac{2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{\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)}{\sqrt{f g-e h}}}{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]])/Sqrt[f*g - e*h] - (2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/Sqrt[g + h*x])/h","A",1
486,1,91,120,0.0998648,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x)^{5/2}} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x)^(5/2),x]","\frac{2 (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)-4 b f p q (g+h x) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{f (g+h x)}{f g-e h}\right)}{3 h (g+h x)^{3/2} (e h-f g)}","-\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*(g + h*x)*Hypergeometric2F1[-1/2, 1, 1/2, (f*(g + h*x))/(f*g - e*h)] + 2*(f*g - e*h)*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(3*h*(-(f*g) + e*h)*(g + h*x)^(3/2))","C",1
487,1,91,152,0.0901497,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x)^{7/2}} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x)^(7/2),x]","\frac{6 (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)-4 b f p q (g+h x) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{f (g+h x)}{f g-e h}\right)}{15 h (g+h x)^{5/2} (e h-f g)}","-\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^{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^2 p q}{5 h \sqrt{g+h x} (f g-e h)^2}+\frac{4 b f p q}{15 h (g+h x)^{3/2} (f g-e h)}",1,"(-4*b*f*p*q*(g + h*x)*Hypergeometric2F1[-3/2, 1, -1/2, (f*(g + h*x))/(f*g - e*h)] + 6*(f*g - e*h)*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(15*h*(-(f*g) + e*h)*(g + h*x)^(5/2))","C",1
488,1,91,184,0.0996319,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x)^{9/2}} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x)^(9/2),x]","\frac{10 (f g-e h) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)-4 b f p q (g+h x) \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\frac{f (g+h x)}{f g-e h}\right)}{35 h (g+h x)^{7/2} (e h-f g)}","-\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^{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^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 p q}{35 h (g+h x)^{5/2} (f g-e h)}",1,"(-4*b*f*p*q*(g + h*x)*Hypergeometric2F1[-5/2, 1, -3/2, (f*(g + h*x))/(f*g - e*h)] + 10*(f*g - e*h)*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(35*h*(-(f*g) + e*h)*(g + h*x)^(7/2))","C",1
489,1,2450,635,8.9680072,"\int (g+h x)^{3/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \, dx","Integrate[(g + h*x)^(3/2)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2,x]","\text{Result too large to show}","\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 \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 (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{8 b^2 p^2 q^2 (f g-e h)^{5/2} \text{Li}_2\left(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^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{368 b^2 p^2 q^2 \sqrt{g+h x} (f g-e h)^2}{75 f^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,"(2*b^2*g*p^2*q^2*Sqrt[(f*g - e*h + h*(e + f*x))/f]*(3*h*(e + f*x)*HypergeometricPFQ[{-1/2, 1, 1, 1}, {2, 2, 2}, (h*(e + f*x))/(-(f*g) + e*h)] - 3*h*(e + f*x)*HypergeometricPFQ[{-1/2, 1, 1}, {2, 2}, (h*(e + f*x))/(-(f*g) + e*h)]*Log[e + f*x] - f*g*Log[e + f*x]^2 + e*h*Log[e + f*x]^2 + f*g*Sqrt[1 + (h*(e + f*x))/(f*g - e*h)]*Log[e + f*x]^2 - e*h*Sqrt[1 + (h*(e + f*x))/(f*g - e*h)]*Log[e + f*x]^2 + h*(e + f*x)*Sqrt[1 + (h*(e + f*x))/(f*g - e*h)]*Log[e + f*x]^2))/(3*f*h*Sqrt[1 + (h*(e + f*x))/(f*g - e*h)]) - (2*b^2*p^2*q^2*Sqrt[(f*g - e*h + h*(e + f*x))/f]*(10*f*g*h*(e + f*x)*HypergeometricPFQ[{-3/2, 1, 1, 1}, {2, 2, 2}, (h*(e + f*x))/(-(f*g) + e*h)] - 10*e*h^2*(e + f*x)*HypergeometricPFQ[{-3/2, 1, 1, 1}, {2, 2, 2}, (h*(e + f*x))/(-(f*g) + e*h)] + 15*e*h^2*(e + f*x)*HypergeometricPFQ[{-1/2, 1, 1, 1}, {2, 2, 2}, (h*(e + f*x))/(-(f*g) + e*h)] - 4*f^2*g^2*Log[e + f*x] + 8*e*f*g*h*Log[e + f*x] - 4*e^2*h^2*Log[e + f*x] + 4*f^2*g^2*Sqrt[(f*g - e*h + h*(e + f*x))/(f*g - e*h)]*Log[e + f*x] - 8*e*f*g*h*Sqrt[(f*g - e*h + h*(e + f*x))/(f*g - e*h)]*Log[e + f*x] + 4*e^2*h^2*Sqrt[(f*g - e*h + h*(e + f*x))/(f*g - e*h)]*Log[e + f*x] + 8*f*g*h*(e + f*x)*Sqrt[(f*g - e*h + h*(e + f*x))/(f*g - e*h)]*Log[e + f*x] - 8*e*h^2*(e + f*x)*Sqrt[(f*g - e*h + h*(e + f*x))/(f*g - e*h)]*Log[e + f*x] + 4*h^2*(e + f*x)^2*Sqrt[(f*g - e*h + h*(e + f*x))/(f*g - e*h)]*Log[e + f*x] - 15*e*h^2*(e + f*x)*HypergeometricPFQ[{-1/2, 1, 1}, {2, 2}, (h*(e + f*x))/(-(f*g) + e*h)]*Log[e + f*x] - 2*f^2*g^2*Log[e + f*x]^2 - e*f*g*h*Log[e + f*x]^2 + 3*e^2*h^2*Log[e + f*x]^2 + 2*f^2*g^2*Sqrt[(f*g - e*h + h*(e + f*x))/(f*g - e*h)]*Log[e + f*x]^2 + e*f*g*h*Sqrt[(f*g - e*h + h*(e + f*x))/(f*g - e*h)]*Log[e + f*x]^2 - 3*e^2*h^2*Sqrt[(f*g - e*h + h*(e + f*x))/(f*g - e*h)]*Log[e + f*x]^2 - f*g*h*(e + f*x)*Sqrt[(f*g - e*h + h*(e + f*x))/(f*g - e*h)]*Log[e + f*x]^2 + 6*e*h^2*(e + f*x)*Sqrt[(f*g - e*h + h*(e + f*x))/(f*g - e*h)]*Log[e + f*x]^2 - 3*h^2*(e + f*x)^2*Sqrt[(f*g - e*h + h*(e + f*x))/(f*g - e*h)]*Log[e + f*x]^2 + 10*h*(-(f*g) + e*h)*(e + f*x)*HypergeometricPFQ[{-3/2, 1, 1}, {2, 2}, (h*(e + f*x))/(-(f*g) + e*h)]*(1 + Log[e + f*x])))/(15*f^2*h*Sqrt[1 + (h*(e + f*x))/(f*g - e*h)]) + (4*b*g*p*q*((6*(f*g - e*h)^(3/2)*ArcTanh[(Sqrt[f]*Sqrt[(f*g - e*h + h*(e + f*x))/f])/Sqrt[f*g - e*h]])/Sqrt[f] - Sqrt[(f*g - e*h + h*(e + f*x))/f]*(h*(e + f*x)*(2 - 3*Log[e + f*x]) + (f*g - e*h)*(8 - 3*Log[e + f*x])))*(a + b*q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]) + b*(-(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p])) - Log[d*(e + f*x)^p]*(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p]) + Log[c*E^(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))*(d*(e + f*x)^p)^(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p])])))/(9*f*h) - (4*b*p*q*(30*(f*g - e*h)^(3/2)*(2*f*g + 3*e*h)*ArcTanh[(Sqrt[f]*Sqrt[(f*g - e*h + h*(e + f*x))/f])/Sqrt[f*g - e*h]] + Sqrt[f]*Sqrt[(f*g - e*h + h*(e + f*x))/f]*(9*h^2*(e + f*x)^2*(2 - 5*Log[e + f*x]) + (f*g - e*h)*(3*e*h*(-46 + 15*Log[e + f*x]) + 2*f*g*(-31 + 15*Log[e + f*x])) + h*(e + f*x)*(f*g*(16 - 15*Log[e + f*x]) + 6*e*h*(-11 + 15*Log[e + f*x]))))*(a + b*q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]) + b*(-(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p])) - Log[d*(e + f*x)^p]*(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p]) + Log[c*E^(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))*(d*(e + f*x)^p)^(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p])])))/(225*f^(5/2)*h) + Sqrt[g + h*x]*((2*g^2*(a + b*q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]) + b*(-(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p])) - Log[d*(e + f*x)^p]*(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p]) + Log[c*E^(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))*(d*(e + f*x)^p)^(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p])]))^2)/(5*h) + (4*g*x*(a + b*q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]) + b*(-(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p])) - Log[d*(e + f*x)^p]*(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p]) + Log[c*E^(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))*(d*(e + f*x)^p)^(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p])]))^2)/5 + (2*h*x^2*(a + b*q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]) + b*(-(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p])) - Log[d*(e + f*x)^p]*(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p]) + Log[c*E^(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))*(d*(e + f*x)^p)^(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p])]))^2)/5)","C",1
490,1,365,547,2.1579155,"\int \sqrt{g+h x} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \, dx","Integrate[Sqrt[g + h*x]*(a + b*Log[c*(d*(e + f*x)^p)^q])^2,x]","\frac{2 \left(\frac{3 b^2 p^2 q^2 \sqrt{g+h x} \left(3 h (e+f x) \, _4F_3\left(-\frac{1}{2},1,1,1;2,2,2;\frac{h (e+f x)}{e h-f g}\right)+\log (e+f x) \left(\log (e+f x) \left(f h x \sqrt{\frac{f (g+h x)}{f g-e h}}+f g \left(\sqrt{\frac{f (g+h x)}{f g-e h}}-1\right)+e h\right)-3 h (e+f x) \, _3F_2\left(-\frac{1}{2},1,1;2,2;\frac{h (e+f x)}{e h-f g}\right)\right)\right)}{f \sqrt{\frac{f (g+h x)}{f g-e h}}}-\frac{2 b p q \left(\sqrt{f} \sqrt{g+h x} (3 f (g+h x) \log (e+f x)+6 e h-2 f (4 g+h x))+6 (f g-e h)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)\right) \left(-a-b \log \left(c \left(d (e+f x)^p\right)^q\right)+b p q \log (e+f x)\right)}{f^{3/2}}+3 (g+h x)^{3/2} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)^2\right)}{9 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} \text{Li}_2\left(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^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,"(2*((3*b^2*p^2*q^2*Sqrt[g + h*x]*(3*h*(e + f*x)*HypergeometricPFQ[{-1/2, 1, 1, 1}, {2, 2, 2}, (h*(e + f*x))/(-(f*g) + e*h)] + Log[e + f*x]*(-3*h*(e + f*x)*HypergeometricPFQ[{-1/2, 1, 1}, {2, 2}, (h*(e + f*x))/(-(f*g) + e*h)] + (e*h + f*h*x*Sqrt[(f*(g + h*x))/(f*g - e*h)] + f*g*(-1 + Sqrt[(f*(g + h*x))/(f*g - e*h)]))*Log[e + f*x])))/(f*Sqrt[(f*(g + h*x))/(f*g - e*h)]) - (2*b*p*q*(6*(f*g - e*h)^(3/2)*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]] + Sqrt[f]*Sqrt[g + h*x]*(6*e*h - 2*f*(4*g + h*x) + 3*f*(g + h*x)*Log[e + f*x]))*(-a + b*p*q*Log[e + f*x] - b*Log[c*(d*(e + f*x)^p)^q]))/f^(3/2) + 3*(g + h*x)^(3/2)*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2))/(9*h)","C",1
491,1,646,447,1.6833304,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{\sqrt{g+h x}} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/Sqrt[g + h*x],x]","\frac{2 \left(b^2 h p^2 q^2 (e+f x) \sqrt{\frac{f (g+h x)}{f g-e h}} \, _4F_3\left(\frac{1}{2},1,1,1;2,2,2;\frac{h (e+f x)}{e h-f g}\right)-b^2 h p^2 q^2 (e+f x) \log (e+f x) \sqrt{\frac{f (g+h x)}{f g-e h}} \, _3F_2\left(\frac{1}{2},1,1;2,2;\frac{h (e+f x)}{e h-f g}\right)+a^2 f g+a^2 f h x+2 a b f g \log \left(c \left(d (e+f x)^p\right)^q\right)+2 a b f h x \log \left(c \left(d (e+f x)^p\right)^q\right)+4 a b \sqrt{f} p q \sqrt{g+h x} \sqrt{f g-e h} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)-4 a b f g p q-4 a b f h p q x+4 b^2 \sqrt{f} p q \sqrt{g+h x} \sqrt{f g-e h} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right) \log \left(c \left(d (e+f x)^p\right)^q\right)+b^2 f g \log ^2\left(c \left(d (e+f x)^p\right)^q\right)-4 b^2 f g p q \log \left(c \left(d (e+f x)^p\right)^q\right)+b^2 f h x \log ^2\left(c \left(d (e+f x)^p\right)^q\right)-4 b^2 f h p q x \log \left(c \left(d (e+f x)^p\right)^q\right)-b^2 f g p^2 q^2 \log ^2(e+f x) \sqrt{\frac{f (g+h x)}{f g-e h}}+b^2 e h p^2 q^2 \log ^2(e+f x) \sqrt{\frac{f (g+h x)}{f g-e h}}-4 b^2 \sqrt{f} p^2 q^2 \sqrt{g+h x} \sqrt{f g-e h} \log (e+f x) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)+4 b^2 f g p^2 q^2 \log (e+f x)+4 b^2 f h p^2 q^2 x \log (e+f x)\right)}{f h \sqrt{g+h x}}","-\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} \text{Li}_2\left(1-\frac{2}{1-\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}}\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,"(2*(a^2*f*g - 4*a*b*f*g*p*q + a^2*f*h*x - 4*a*b*f*h*p*q*x + 4*a*b*Sqrt[f]*Sqrt[f*g - e*h]*p*q*Sqrt[g + h*x]*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]] + b^2*h*p^2*q^2*(e + f*x)*Sqrt[(f*(g + h*x))/(f*g - e*h)]*HypergeometricPFQ[{1/2, 1, 1, 1}, {2, 2, 2}, (h*(e + f*x))/(-(f*g) + e*h)] + 4*b^2*f*g*p^2*q^2*Log[e + f*x] + 4*b^2*f*h*p^2*q^2*x*Log[e + f*x] - 4*b^2*Sqrt[f]*Sqrt[f*g - e*h]*p^2*q^2*Sqrt[g + h*x]*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*Log[e + f*x] - b^2*h*p^2*q^2*(e + f*x)*Sqrt[(f*(g + h*x))/(f*g - e*h)]*HypergeometricPFQ[{1/2, 1, 1}, {2, 2}, (h*(e + f*x))/(-(f*g) + e*h)]*Log[e + f*x] - b^2*f*g*p^2*q^2*Sqrt[(f*(g + h*x))/(f*g - e*h)]*Log[e + f*x]^2 + b^2*e*h*p^2*q^2*Sqrt[(f*(g + h*x))/(f*g - e*h)]*Log[e + f*x]^2 + 2*a*b*f*g*Log[c*(d*(e + f*x)^p)^q] - 4*b^2*f*g*p*q*Log[c*(d*(e + f*x)^p)^q] + 2*a*b*f*h*x*Log[c*(d*(e + f*x)^p)^q] - 4*b^2*f*h*p*q*x*Log[c*(d*(e + f*x)^p)^q] + 4*b^2*Sqrt[f]*Sqrt[f*g - e*h]*p*q*Sqrt[g + h*x]*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*Log[c*(d*(e + f*x)^p)^q] + b^2*f*g*Log[c*(d*(e + f*x)^p)^q]^2 + b^2*f*h*x*Log[c*(d*(e + f*x)^p)^q]^2))/(f*h*Sqrt[g + h*x])","C",1
492,1,356,330,3.7700413,"\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","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/(g + h*x)^(3/2),x]","\frac{2 \left(\frac{b^2 p^2 q^2 \left(h (e+f x) \sqrt{\frac{f (g+h x)}{f g-e h}} \, _4F_3\left(1,1,1,\frac{3}{2};2,2,2;\frac{h (e+f x)}{e h-f g}\right)+(f g-e h) \log (e+f x) \left(\log (e+f x) \left(\sqrt{\frac{f (g+h x)}{f g-e h}}-1\right)-4 \sqrt{\frac{f (g+h x)}{f g-e h}} \log \left(\frac{1}{2} \left(\sqrt{\frac{f (g+h x)}{f g-e h}}+1\right)\right)\right)\right)}{\sqrt{g+h x} (f g-e h)}-\frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)^2}{\sqrt{g+h x}}+\frac{2 b p q \left(\sqrt{g+h x} \sqrt{f g-e h} \log (e+f x)+2 \sqrt{f} (g+h x) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)\right) \left(-a-b \log \left(c \left(d (e+f x)^p\right)^q\right)+b p q \log (e+f x)\right)}{(g+h x) \sqrt{f g-e h}}\right)}{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 \text{Li}_2\left(1-\frac{2}{1-\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 \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,"(2*((2*b*p*q*(2*Sqrt[f]*(g + h*x)*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]] + Sqrt[f*g - e*h]*Sqrt[g + h*x]*Log[e + f*x])*(-a + b*p*q*Log[e + f*x] - b*Log[c*(d*(e + f*x)^p)^q]))/(Sqrt[f*g - e*h]*(g + h*x)) - (a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2/Sqrt[g + h*x] + (b^2*p^2*q^2*(h*(e + f*x)*Sqrt[(f*(g + h*x))/(f*g - e*h)]*HypergeometricPFQ[{1, 1, 1, 3/2}, {2, 2, 2}, (h*(e + f*x))/(-(f*g) + e*h)] + (f*g - e*h)*Log[e + f*x]*((-1 + Sqrt[(f*(g + h*x))/(f*g - e*h)])*Log[e + f*x] - 4*Sqrt[(f*(g + h*x))/(f*g - e*h)]*Log[(1 + Sqrt[(f*(g + h*x))/(f*g - e*h)])/2])))/((f*g - e*h)*Sqrt[g + h*x])))/h","C",1
493,1,657,449,6.1988148,"\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","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/(g + h*x)^(5/2),x]","\frac{2 \left(3 b^2 f h p^2 q^2 (e+f x) (g+h x) \sqrt{\frac{f (g+h x)}{f g-e h}} \, _4F_3\left(1,1,1,\frac{5}{2};2,2,2;\frac{h (e+f x)}{e h-f g}\right)-(f g-e h)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)^2-4 a b f^{3/2} p q (g+h x)^{3/2} \sqrt{f g-e h} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)+2 a b p q (f g-e h) ((e h-f g) \log (e+f x)+2 f (g+h x))-4 b^2 f^{3/2} p q (g+h x)^{3/2} \sqrt{f g-e h} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right) \log \left(c \left(d (e+f x)^p\right)^q\right)+2 b^2 p q (f g-e h) ((e h-f g) \log (e+f x)+2 f (g+h x)) \log \left(c \left(d (e+f x)^p\right)^q\right)+4 b^2 f^{3/2} p^2 q^2 (g+h x)^{3/2} \sqrt{f g-e h} \log (e+f x) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{g+h x}}{\sqrt{f g-e h}}\right)-2 b^2 p^2 q^2 (f g-e h) \log (e+f x) ((e h-f g) \log (e+f x)+2 f (g+h x))+b^2 p^2 q^2 (f g-e h) \log (e+f x) \left(\log (e+f x) \left(f h x \sqrt{\frac{f (g+h x)}{f g-e h}}+f g \left(\sqrt{\frac{f (g+h x)}{f g-e h}}-1\right)+e h\right)-4 f (g+h x) \left(\sqrt{\frac{f (g+h x)}{f g-e h}}+\sqrt{\frac{f (g+h x)}{f g-e h}} \log \left(\frac{1}{2} \left(\sqrt{\frac{f (g+h x)}{f g-e h}}+1\right)\right)-1\right)\right)\right)}{3 h (g+h x)^{3/2} (f g-e h)^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 \text{Li}_2\left(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^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,"(2*(-4*a*b*f^(3/2)*Sqrt[f*g - e*h]*p*q*(g + h*x)^(3/2)*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]] + 3*b^2*f*h*p^2*q^2*(e + f*x)*(g + h*x)*Sqrt[(f*(g + h*x))/(f*g - e*h)]*HypergeometricPFQ[{1, 1, 1, 5/2}, {2, 2, 2}, (h*(e + f*x))/(-(f*g) + e*h)] + 4*b^2*f^(3/2)*Sqrt[f*g - e*h]*p^2*q^2*(g + h*x)^(3/2)*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*Log[e + f*x] + 2*a*b*(f*g - e*h)*p*q*(2*f*(g + h*x) + (-(f*g) + e*h)*Log[e + f*x]) - 2*b^2*(f*g - e*h)*p^2*q^2*Log[e + f*x]*(2*f*(g + h*x) + (-(f*g) + e*h)*Log[e + f*x]) - 4*b^2*f^(3/2)*Sqrt[f*g - e*h]*p*q*(g + h*x)^(3/2)*ArcTanh[(Sqrt[f]*Sqrt[g + h*x])/Sqrt[f*g - e*h]]*Log[c*(d*(e + f*x)^p)^q] + 2*b^2*(f*g - e*h)*p*q*(2*f*(g + h*x) + (-(f*g) + e*h)*Log[e + f*x])*Log[c*(d*(e + f*x)^p)^q] - (f*g - e*h)^2*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2 + b^2*(f*g - e*h)*p^2*q^2*Log[e + f*x]*((e*h + f*h*x*Sqrt[(f*(g + h*x))/(f*g - e*h)] + f*g*(-1 + Sqrt[(f*(g + h*x))/(f*g - e*h)]))*Log[e + f*x] - 4*f*(g + h*x)*(-1 + Sqrt[(f*(g + h*x))/(f*g - e*h)] + Sqrt[(f*(g + h*x))/(f*g - e*h)]*Log[(1 + Sqrt[(f*(g + h*x))/(f*g - e*h)])/2]))))/(3*h*(f*g - e*h)^2*(g + h*x)^(3/2))","C",1
494,1,1183,537,7.7464813,"\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","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/(g + h*x)^(7/2),x]","\frac{4 a b p q \left(\frac{\sqrt{f} \sqrt{\frac{f g-e h+h (e+f x)}{f}} \left(-3 \log (e+f x) (f g-e h)^2+2 (f g+f h x) (f g-e h)+6 (f g+f h x)^2\right)}{(f g-e h)^2 (f g+f h x)^3}-\frac{6 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{\frac{f g-e h+h (e+f x)}{f}}}{\sqrt{f g-e h}}\right)}{(f g-e h)^{5/2}}\right) f^{5/2}}{15 h}+\frac{4 b^2 p q^2 \left(\frac{\sqrt{f} \sqrt{\frac{f g-e h+h (e+f x)}{f}} \left(-3 \log (e+f x) (f g-e h)^2+2 (f g+f h x) (f g-e h)+6 (f g+f h x)^2\right)}{(f g-e h)^2 (f g+f h x)^3}-\frac{6 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{\frac{f g-e h+h (e+f x)}{f}}}{\sqrt{f g-e h}}\right)}{(f g-e h)^{5/2}}\right) \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right) f^{5/2}}{15 h}+\frac{4 b^2 p q \left(\frac{\sqrt{f} \sqrt{\frac{f g-e h+h (e+f x)}{f}} \left(-3 \log (e+f x) (f g-e h)^2+2 (f g+f h x) (f g-e h)+6 (f g+f h x)^2\right)}{(f g-e h)^2 (f g+f h x)^3}-\frac{6 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{\frac{f g-e h+h (e+f x)}{f}}}{\sqrt{f g-e h}}\right)}{(f g-e h)^{5/2}}\right) \left(-q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)-\log \left(d (e+f x)^p\right) \left(q-\frac{q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)}{\log \left(d (e+f x)^p\right)}\right)+\log \left(c e^{q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)} \left(d (e+f x)^p\right)^{q-\frac{q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)}{\log \left(d (e+f x)^p\right)}}\right)\right) f^{5/2}}{15 h}-\frac{2 \left(a+b q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)+b \left(-q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)-\log \left(d (e+f x)^p\right) \left(q-\frac{q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)}{\log \left(d (e+f x)^p\right)}\right)+\log \left(c e^{q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)} \left(d (e+f x)^p\right)^{q-\frac{q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)}{\log \left(d (e+f x)^p\right)}}\right)\right)\right)^2}{5 h (g+h x)^{5/2}}+\frac{2 b^2 p^2 q^2 \left(\frac{h (e+f x)}{f g-e h}+1\right) \left(f g \log ^2(e+f x) \left(\frac{f g-e h+h (e+f x)}{f g-e h}\right)^{5/2}-e h \log ^2(e+f x) \left(\frac{f g-e h+h (e+f x)}{f g-e h}\right)^{5/2}+5 h (e+f x) \, _4F_3\left(1,1,1,\frac{7}{2};2,2,2;\frac{h (e+f x)}{e h-f g}\right) \left(\frac{f g-e h+h (e+f x)}{f g-e h}\right)^{5/2}-5 h (e+f x) \, _3F_2\left(1,1,\frac{7}{2};2,2;\frac{h (e+f x)}{e h-f g}\right) \log (e+f x) \left(\frac{f g-e h+h (e+f x)}{f g-e h}\right)^{5/2}-f g \log ^2(e+f x)+e h \log ^2(e+f x)\right)}{5 h \left(\frac{f g-e h+h (e+f x)}{f}\right)^{7/2} f}","-\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^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 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{8 b^2 f^{5/2} p^2 q^2 \text{Li}_2\left(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^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{16 b^2 f^2 p^2 q^2}{15 h \sqrt{g+h x} (f g-e h)^2}",1,"(2*b^2*p^2*q^2*(1 + (h*(e + f*x))/(f*g - e*h))*(5*h*(e + f*x)*((f*g - e*h + h*(e + f*x))/(f*g - e*h))^(5/2)*HypergeometricPFQ[{1, 1, 1, 7/2}, {2, 2, 2}, (h*(e + f*x))/(-(f*g) + e*h)] - 5*h*(e + f*x)*((f*g - e*h + h*(e + f*x))/(f*g - e*h))^(5/2)*HypergeometricPFQ[{1, 1, 7/2}, {2, 2}, (h*(e + f*x))/(-(f*g) + e*h)]*Log[e + f*x] - f*g*Log[e + f*x]^2 + e*h*Log[e + f*x]^2 + f*g*((f*g - e*h + h*(e + f*x))/(f*g - e*h))^(5/2)*Log[e + f*x]^2 - e*h*((f*g - e*h + h*(e + f*x))/(f*g - e*h))^(5/2)*Log[e + f*x]^2))/(5*f*h*((f*g - e*h + h*(e + f*x))/f)^(7/2)) + (4*a*b*f^(5/2)*p*q*((-6*ArcTanh[(Sqrt[f]*Sqrt[(f*g - e*h + h*(e + f*x))/f])/Sqrt[f*g - e*h]])/(f*g - e*h)^(5/2) + (Sqrt[f]*Sqrt[(f*g - e*h + h*(e + f*x))/f]*(2*(f*g - e*h)*(f*g + f*h*x) + 6*(f*g + f*h*x)^2 - 3*(f*g - e*h)^2*Log[e + f*x]))/((f*g - e*h)^2*(f*g + f*h*x)^3)))/(15*h) + (4*b^2*f^(5/2)*p*q^2*((-6*ArcTanh[(Sqrt[f]*Sqrt[(f*g - e*h + h*(e + f*x))/f])/Sqrt[f*g - e*h]])/(f*g - e*h)^(5/2) + (Sqrt[f]*Sqrt[(f*g - e*h + h*(e + f*x))/f]*(2*(f*g - e*h)*(f*g + f*h*x) + 6*(f*g + f*h*x)^2 - 3*(f*g - e*h)^2*Log[e + f*x]))/((f*g - e*h)^2*(f*g + f*h*x)^3))*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/(15*h) + (4*b^2*f^(5/2)*p*q*((-6*ArcTanh[(Sqrt[f]*Sqrt[(f*g - e*h + h*(e + f*x))/f])/Sqrt[f*g - e*h]])/(f*g - e*h)^(5/2) + (Sqrt[f]*Sqrt[(f*g - e*h + h*(e + f*x))/f]*(2*(f*g - e*h)*(f*g + f*h*x) + 6*(f*g + f*h*x)^2 - 3*(f*g - e*h)^2*Log[e + f*x]))/((f*g - e*h)^2*(f*g + f*h*x)^3))*(-(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p])) - Log[d*(e + f*x)^p]*(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p]) + Log[c*E^(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))*(d*(e + f*x)^p)^(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p])]))/(15*h) - (2*(a + b*q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]) + b*(-(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p])) - Log[d*(e + f*x)^p]*(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p]) + Log[c*E^(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))*(d*(e + f*x)^p)^(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p])]))^2)/(5*h*(g + h*x)^(5/2))","C",1
495,1,1249,625,7.8286339,"\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","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/(g + h*x)^(9/2),x]","\frac{4 a b p q \left(\frac{\sqrt{f} \sqrt{\frac{f g-e h+h (e+f x)}{f}} \left(-15 \log (e+f x) (f g-e h)^3+6 (f g+f h x) (f g-e h)^2+10 (f g+f h x)^2 (f g-e h)+30 (f g+f h x)^3\right)}{(f g-e h)^3 (f g+f h x)^4}-\frac{30 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{\frac{f g-e h+h (e+f x)}{f}}}{\sqrt{f g-e h}}\right)}{(f g-e h)^{7/2}}\right) f^{7/2}}{105 h}+\frac{4 b^2 p q^2 \left(\frac{\sqrt{f} \sqrt{\frac{f g-e h+h (e+f x)}{f}} \left(-15 \log (e+f x) (f g-e h)^3+6 (f g+f h x) (f g-e h)^2+10 (f g+f h x)^2 (f g-e h)+30 (f g+f h x)^3\right)}{(f g-e h)^3 (f g+f h x)^4}-\frac{30 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{\frac{f g-e h+h (e+f x)}{f}}}{\sqrt{f g-e h}}\right)}{(f g-e h)^{7/2}}\right) \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right) f^{7/2}}{105 h}+\frac{4 b^2 p q \left(\frac{\sqrt{f} \sqrt{\frac{f g-e h+h (e+f x)}{f}} \left(-15 \log (e+f x) (f g-e h)^3+6 (f g+f h x) (f g-e h)^2+10 (f g+f h x)^2 (f g-e h)+30 (f g+f h x)^3\right)}{(f g-e h)^3 (f g+f h x)^4}-\frac{30 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{\frac{f g-e h+h (e+f x)}{f}}}{\sqrt{f g-e h}}\right)}{(f g-e h)^{7/2}}\right) \left(-q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)-\log \left(d (e+f x)^p\right) \left(q-\frac{q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)}{\log \left(d (e+f x)^p\right)}\right)+\log \left(c e^{q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)} \left(d (e+f x)^p\right)^{q-\frac{q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)}{\log \left(d (e+f x)^p\right)}}\right)\right) f^{7/2}}{105 h}-\frac{2 \left(a+b q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)+b \left(-q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)-\log \left(d (e+f x)^p\right) \left(q-\frac{q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)}{\log \left(d (e+f x)^p\right)}\right)+\log \left(c e^{q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)} \left(d (e+f x)^p\right)^{q-\frac{q \left(\log \left(d (e+f x)^p\right)-p \log (e+f x)\right)}{\log \left(d (e+f x)^p\right)}}\right)\right)\right)^2}{7 h (g+h x)^{7/2}}+\frac{2 b^2 p^2 q^2 \left(\frac{h (e+f x)}{f g-e h}+1\right) \left(f g \log ^2(e+f x) \left(\frac{f g-e h+h (e+f x)}{f g-e h}\right)^{7/2}-e h \log ^2(e+f x) \left(\frac{f g-e h+h (e+f x)}{f g-e h}\right)^{7/2}+7 h (e+f x) \, _4F_3\left(1,1,1,\frac{9}{2};2,2,2;\frac{h (e+f x)}{e h-f g}\right) \left(\frac{f g-e h+h (e+f x)}{f g-e h}\right)^{7/2}-7 h (e+f x) \, _3F_2\left(1,1,\frac{9}{2};2,2;\frac{h (e+f x)}{e h-f g}\right) \log (e+f x) \left(\frac{f g-e h+h (e+f x)}{f g-e h}\right)^{7/2}-f g \log ^2(e+f x)+e h \log ^2(e+f x)\right)}{7 h \left(\frac{f g-e h+h (e+f x)}{f}\right)^{9/2} f}","-\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^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 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{8 b^2 f^{7/2} p^2 q^2 \text{Li}_2\left(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^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{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}",1,"(2*b^2*p^2*q^2*(1 + (h*(e + f*x))/(f*g - e*h))*(7*h*(e + f*x)*((f*g - e*h + h*(e + f*x))/(f*g - e*h))^(7/2)*HypergeometricPFQ[{1, 1, 1, 9/2}, {2, 2, 2}, (h*(e + f*x))/(-(f*g) + e*h)] - 7*h*(e + f*x)*((f*g - e*h + h*(e + f*x))/(f*g - e*h))^(7/2)*HypergeometricPFQ[{1, 1, 9/2}, {2, 2}, (h*(e + f*x))/(-(f*g) + e*h)]*Log[e + f*x] - f*g*Log[e + f*x]^2 + e*h*Log[e + f*x]^2 + f*g*((f*g - e*h + h*(e + f*x))/(f*g - e*h))^(7/2)*Log[e + f*x]^2 - e*h*((f*g - e*h + h*(e + f*x))/(f*g - e*h))^(7/2)*Log[e + f*x]^2))/(7*f*h*((f*g - e*h + h*(e + f*x))/f)^(9/2)) + (4*a*b*f^(7/2)*p*q*((-30*ArcTanh[(Sqrt[f]*Sqrt[(f*g - e*h + h*(e + f*x))/f])/Sqrt[f*g - e*h]])/(f*g - e*h)^(7/2) + (Sqrt[f]*Sqrt[(f*g - e*h + h*(e + f*x))/f]*(6*(f*g - e*h)^2*(f*g + f*h*x) + 10*(f*g - e*h)*(f*g + f*h*x)^2 + 30*(f*g + f*h*x)^3 - 15*(f*g - e*h)^3*Log[e + f*x]))/((f*g - e*h)^3*(f*g + f*h*x)^4)))/(105*h) + (4*b^2*f^(7/2)*p*q^2*((-30*ArcTanh[(Sqrt[f]*Sqrt[(f*g - e*h + h*(e + f*x))/f])/Sqrt[f*g - e*h]])/(f*g - e*h)^(7/2) + (Sqrt[f]*Sqrt[(f*g - e*h + h*(e + f*x))/f]*(6*(f*g - e*h)^2*(f*g + f*h*x) + 10*(f*g - e*h)*(f*g + f*h*x)^2 + 30*(f*g + f*h*x)^3 - 15*(f*g - e*h)^3*Log[e + f*x]))/((f*g - e*h)^3*(f*g + f*h*x)^4))*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/(105*h) + (4*b^2*f^(7/2)*p*q*((-30*ArcTanh[(Sqrt[f]*Sqrt[(f*g - e*h + h*(e + f*x))/f])/Sqrt[f*g - e*h]])/(f*g - e*h)^(7/2) + (Sqrt[f]*Sqrt[(f*g - e*h + h*(e + f*x))/f]*(6*(f*g - e*h)^2*(f*g + f*h*x) + 10*(f*g - e*h)*(f*g + f*h*x)^2 + 30*(f*g + f*h*x)^3 - 15*(f*g - e*h)^3*Log[e + f*x]))/((f*g - e*h)^3*(f*g + f*h*x)^4))*(-(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p])) - Log[d*(e + f*x)^p]*(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p]) + Log[c*E^(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))*(d*(e + f*x)^p)^(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p])]))/(105*h) - (2*(a + b*q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]) + b*(-(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p])) - Log[d*(e + f*x)^p]*(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p]) + Log[c*E^(q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))*(d*(e + f*x)^p)^(q - (q*(-(p*Log[e + f*x]) + Log[d*(e + f*x)^p]))/Log[d*(e + f*x)^p])]))^2)/(7*h*(g + h*x)^(7/2))","C",1
496,0,0,33,1.294113,"\int \frac{(g+h x)^{3/2}}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Integrate[(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,"Integrate[(g + h*x)^(3/2)/(a + b*Log[c*(d*(e + f*x)^p)^q]), x]","A",-1
497,0,0,33,1.1137874,"\int \frac{\sqrt{g+h x}}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Integrate[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,"Integrate[Sqrt[g + h*x]/(a + b*Log[c*(d*(e + f*x)^p)^q]), x]","A",-1
498,0,0,33,1.5996895,"\int \frac{1}{\sqrt{g+h x} \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","Integrate[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,"Integrate[1/(Sqrt[g + h*x]*(a + b*Log[c*(d*(e + f*x)^p)^q])), x]","A",-1
499,0,0,33,1.9581278,"\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","Integrate[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,"Integrate[1/((g + h*x)^(3/2)*(a + b*Log[c*(d*(e + f*x)^p)^q])), x]","A",-1
500,0,0,35,1.8102731,"\int \sqrt{g+h x} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Integrate[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,"Integrate[Sqrt[g + h*x]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]], x]","A",-1
501,0,0,35,2.0670955,"\int \frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{\sqrt{g+h x}} \, dx","Integrate[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,"Integrate[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/Sqrt[g + h*x], x]","A",-1
502,0,0,35,1.8464291,"\int \frac{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}}{(g+h x)^{3/2}} \, dx","Integrate[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,"Integrate[Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]/(g + h*x)^(3/2), x]","A",-1
503,0,0,35,7.7781893,"\int \frac{\sqrt{g+h x}}{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","Integrate[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,"Integrate[Sqrt[g + h*x]/Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]], x]","A",-1
504,0,0,35,4.129146,"\int \frac{1}{\sqrt{g+h x} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","Integrate[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,"Integrate[1/(Sqrt[g + h*x]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]), x]","A",-1
505,0,0,35,1.0240416,"\int \frac{1}{(g+h x)^{3/2} \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","Integrate[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,"Integrate[1/((g + h*x)^(3/2)*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]]), x]","A",-1
506,1,86,99,0.1162097,"\int (g+h x)^m \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \, dx","Integrate[(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)+\frac{b f p q (g+h x) \, _2F_1\left(1,m+2;m+3;\frac{f (g+h x)}{f g-e h}\right)}{(m+2) (f g-e h)}\right)}{h (m+1)}","\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,"((g + h*x)^(1 + m)*(a + (b*f*p*q*(g + h*x)*Hypergeometric2F1[1, 2 + m, 3 + m, (f*(g + h*x))/(f*g - e*h)])/((f*g - e*h)*(2 + m)) + b*Log[c*(d*(e + f*x)^p)^q]))/(h*(1 + m))","A",1
507,0,0,31,0.423521,"\int \frac{(g+h x)^m}{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Integrate[(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,"Integrate[(g + h*x)^m/(a + b*Log[c*(d*(e + f*x)^p)^q]), x]","A",-1
508,0,0,31,2.7325108,"\int \frac{(g+h x)^m}{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","Integrate[(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,"Integrate[(g + h*x)^m/(a + b*Log[c*(d*(e + f*x)^p)^q])^2, x]","A",-1
509,0,0,33,9.7188546,"\int (g+h x)^m \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^{3/2} \, dx","Integrate[(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,"Integrate[(g + h*x)^m*(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2), x]","A",-1
510,0,0,33,0.0826989,"\int (g+h x)^m \sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)} \, dx","Integrate[(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,"Integrate[(g + h*x)^m*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]], x]","A",-1
511,0,0,33,4.1532536,"\int \frac{(g+h x)^m}{\sqrt{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}} \, dx","Integrate[(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,"Integrate[(g + h*x)^m/Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]], x]","A",-1
512,0,0,33,3.9773797,"\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","Integrate[(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,"Integrate[(g + h*x)^m/(a + b*Log[c*(d*(e + f*x)^p)^q])^(3/2), x]","A",-1
513,0,0,31,0.6533229,"\int (g+h x)^m \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \, dx","Integrate[(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,"Integrate[(g + h*x)^m*(a + b*Log[c*(d*(e + f*x)^p)^q])^n, x]","A",-1
514,1,326,432,1.0750296,"\int (g+h x)^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \, dx","Integrate[(g + h*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^n,x]","\frac{2^{-n} 3^{-n-1} (e+f x) 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} \left(3^{n+1} 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(2^n 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}} \Gamma \left(n+1,-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)+h (e+f x) \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)\right)+h^2 2^n (e+f x)^2 \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)\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} \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} \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} \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)*(e + f*x)*(2^n*h^2*(e + f*x)^2*Gamma[1 + n, (-3*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)] + 3^(1 + n)*E^(a/(b*p*q))*(f*g - e*h)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*(h*(e + f*x)*Gamma[1 + n, (-2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)] + 2^n*E^(a/(b*p*q))*(f*g - e*h)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*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)/(2^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)","A",1
515,1,227,281,0.3613201,"\int (g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \, dx","Integrate[(g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^n,x]","\frac{2^{-n-1} (e+f x) 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} \left(2^{n+1} 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}} \Gamma \left(n+1,-\frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{b p q}\right)+h (e+f x) \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)\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} \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} \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)*(e + f*x)*(h*(e + f*x)*Gamma[1 + n, (-2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(b*p*q)] + 2^(1 + n)*E^(a/(b*p*q))*(f*g - e*h)*(c*(d*(e + f*x)^p)^q)^(1/(p*q))*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^((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)","A",1
516,1,131,131,0.1333917,"\int \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n \, dx","Integrate[(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} \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} \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",1
517,0,0,31,0.3581689,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^n}{g+h x} \, dx","Integrate[(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,"Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^n/(g + h*x), x]","A",-1
518,1,190,249,0.1485627,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{g+h x^2} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x^2),x]","\frac{\left(\log \left(\frac{f \left(\sqrt{-g}-\sqrt{h} x\right)}{e \sqrt{h}+f \sqrt{-g}}\right)-\log \left(\frac{f \left(\sqrt{-g}+\sqrt{h} x\right)}{f \sqrt{-g}-e \sqrt{h}}\right)\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)-b p q \text{Li}_2\left(-\frac{\sqrt{h} (e+f x)}{f \sqrt{-g}-e \sqrt{h}}\right)+b p q \text{Li}_2\left(\frac{\sqrt{h} (e+f x)}{\sqrt{h} e+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{Li}_2\left(-\frac{\sqrt{h} (e+f x)}{f \sqrt{-g}-e \sqrt{h}}\right)}{2 \sqrt{-g} \sqrt{h}}+\frac{b p q \text{Li}_2\left(\frac{\sqrt{h} (e+f x)}{\sqrt{h} e+f \sqrt{-g}}\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])] - Log[(f*(Sqrt[-g] + Sqrt[h]*x))/(f*Sqrt[-g] - e*Sqrt[h])]) - b*p*q*PolyLog[2, -((Sqrt[h]*(e + f*x))/(f*Sqrt[-g] - e*Sqrt[h]))] + b*p*q*PolyLog[2, (Sqrt[h]*(e + f*x))/(f*Sqrt[-g] + e*Sqrt[h])])/(2*Sqrt[-g]*Sqrt[h])","A",1
519,1,284,335,0.2338141,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{\sqrt{2+h x^2}} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/Sqrt[2 + h*x^2],x]","\frac{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right) \left(2 a+2 b \log \left(c \left(d (e+f x)^p\right)^q\right)-2 b p q \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)-2 b p q \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)+b p q \sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right)\right)-2 b p q \text{Li}_2\left(\frac{\sqrt{2} e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right)} f}{\sqrt{h e^2+2 f^2}-e \sqrt{h}}\right)-2 b p q \text{Li}_2\left(-\frac{\sqrt{2} e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right)} f}{\sqrt{h} e+\sqrt{h e^2+2 f^2}}\right)}{2 \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 \text{Li}_2\left(-\frac{\sqrt{2} e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right)} f}{e \sqrt{h}-\sqrt{h e^2+2 f^2}}\right)}{\sqrt{h}}-\frac{b p q \text{Li}_2\left(-\frac{\sqrt{2} e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{2}}\right)} f}{\sqrt{h} e+\sqrt{h e^2+2 f^2}}\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,"(ArcSinh[(Sqrt[h]*x)/Sqrt[2]]*(2*a + b*p*q*ArcSinh[(Sqrt[h]*x)/Sqrt[2]] - 2*b*p*q*Log[1 + (Sqrt[2]*E^ArcSinh[(Sqrt[h]*x)/Sqrt[2]]*f)/(e*Sqrt[h] - Sqrt[2*f^2 + e^2*h])] - 2*b*p*q*Log[1 + (Sqrt[2]*E^ArcSinh[(Sqrt[h]*x)/Sqrt[2]]*f)/(e*Sqrt[h] + Sqrt[2*f^2 + e^2*h])] + 2*b*Log[c*(d*(e + f*x)^p)^q]) - 2*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])] - 2*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]))])/(2*Sqrt[h])","A",1
520,0,0,515,3.7933833,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{\sqrt{g+h x^2}} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/Sqrt[g + h*x^2],x]","\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{\sqrt{g+h x^2}} \, dx","\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} \text{Li}_2\left(-\frac{e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right)} f \sqrt{g}}{e \sqrt{h}-\sqrt{h e^2+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{Li}_2\left(-\frac{e^{\sinh ^{-1}\left(\frac{\sqrt{h} x}{\sqrt{g}}\right)} f \sqrt{g}}{\sqrt{h} e+\sqrt{h e^2+f^2 g}}\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,"Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/Sqrt[g + h*x^2], x]","F",-1
521,1,316,287,0.0305431,"\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","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/(Sqrt[2 - h*x]*Sqrt[2 + h*x]),x]","\frac{a \sin ^{-1}\left(\frac{h x}{2}\right)}{h}+\frac{b \sin ^{-1}\left(\frac{h x}{2}\right) \log \left(c \left(d (e+f x)^p\right)^q\right)}{h}+\frac{i b p q \text{Li}_2\left(\frac{2 i e^{i \sin ^{-1}\left(\frac{h x}{2}\right)} f}{e h-i \sqrt{4 f^2-e^2 h^2}}\right)}{h}+\frac{i b p q \text{Li}_2\left(\frac{2 i e^{i \sin ^{-1}\left(\frac{h x}{2}\right)} f}{e h+i \sqrt{4 f^2-e^2 h^2}}\right)}{h}-\frac{b p q \sin ^{-1}\left(\frac{h x}{2}\right) \log \left(1+\frac{f h e^{i \sin ^{-1}\left(\frac{h x}{2}\right)}}{-\frac{1}{2} h \sqrt{4 f^2-e^2 h^2}+\frac{1}{2} i e h^2}\right)}{h}-\frac{b p q \sin ^{-1}\left(\frac{h x}{2}\right) \log \left(1+\frac{f h e^{i \sin ^{-1}\left(\frac{h x}{2}\right)}}{\frac{1}{2} h \sqrt{4 f^2-e^2 h^2}+\frac{1}{2} i e h^2}\right)}{h}+\frac{i b p q \sin ^{-1}\left(\frac{h x}{2}\right)^2}{2 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{i b p q \text{Li}_2\left(-\frac{2 e^{i \sin ^{-1}\left(\frac{h x}{2}\right)} f}{i e h-\sqrt{4 f^2-e^2 h^2}}\right)}{h}+\frac{i b p q \text{Li}_2\left(-\frac{2 e^{i \sin ^{-1}\left(\frac{h x}{2}\right)} f}{i e h+\sqrt{4 f^2-e^2 h^2}}\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,"(a*ArcSin[(h*x)/2])/h + ((I/2)*b*p*q*ArcSin[(h*x)/2]^2)/h - (b*p*q*ArcSin[(h*x)/2]*Log[1 + (E^(I*ArcSin[(h*x)/2])*f*h)/((I/2)*e*h^2 - (h*Sqrt[4*f^2 - e^2*h^2])/2)])/h - (b*p*q*ArcSin[(h*x)/2]*Log[1 + (E^(I*ArcSin[(h*x)/2])*f*h)/((I/2)*e*h^2 + (h*Sqrt[4*f^2 - e^2*h^2])/2)])/h + (b*ArcSin[(h*x)/2]*Log[c*(d*(e + f*x)^p)^q])/h + (I*b*p*q*PolyLog[2, ((2*I)*E^(I*ArcSin[(h*x)/2])*f)/(e*h - I*Sqrt[4*f^2 - e^2*h^2])])/h + (I*b*p*q*PolyLog[2, ((2*I)*E^(I*ArcSin[(h*x)/2])*f)/(e*h + I*Sqrt[4*f^2 - e^2*h^2])])/h","A",1
522,1,1083,519,4.6345889,"\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","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/(Sqrt[g - h*x]*Sqrt[g + h*x]),x]","\frac{\tan ^{-1}\left(\frac{h x}{\sqrt{g-h x} \sqrt{g+h x}}\right) \left(a-b p q \log (e+f x)+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)}{h}-\frac{i b p q \sqrt{g-h x} \sqrt{\frac{g+h x}{g-h x}} \left(\log ^2\left(i-\sqrt{\frac{g+h x}{g-h x}}\right)+2 \log (e+f x) \log \left(i-\sqrt{\frac{g+h x}{g-h x}}\right)+2 \log \left(\frac{1}{2} \left(1-i \sqrt{\frac{g+h x}{g-h x}}\right)\right) \log \left(i-\sqrt{\frac{g+h x}{g-h x}}\right)-2 \log \left(\frac{\sqrt{f g-e h}-\sqrt{f g+e h} \sqrt{\frac{g+h x}{g-h x}}}{\sqrt{f g-e h}-i \sqrt{f g+e h}}\right) \log \left(i-\sqrt{\frac{g+h x}{g-h x}}\right)-2 \log \left(\frac{\sqrt{f g-e h}+\sqrt{f g+e h} \sqrt{\frac{g+h x}{g-h x}}}{\sqrt{f g-e h}+i \sqrt{f g+e h}}\right) \log \left(i-\sqrt{\frac{g+h x}{g-h x}}\right)-\log ^2\left(\sqrt{\frac{g+h x}{g-h x}}+i\right)-2 \log (e+f x) \log \left(\sqrt{\frac{g+h x}{g-h x}}+i\right)-2 \log \left(\frac{1}{2} \left(i \sqrt{\frac{g+h x}{g-h x}}+1\right)\right) \log \left(\sqrt{\frac{g+h x}{g-h x}}+i\right)+2 \log \left(\sqrt{\frac{g+h x}{g-h x}}+i\right) \log \left(\frac{\sqrt{f g-e h}-\sqrt{f g+e h} \sqrt{\frac{g+h x}{g-h x}}}{\sqrt{f g-e h}+i \sqrt{f g+e h}}\right)+2 \log \left(\sqrt{\frac{g+h x}{g-h x}}+i\right) \log \left(\frac{\sqrt{f g-e h}+\sqrt{f g+e h} \sqrt{\frac{g+h x}{g-h x}}}{\sqrt{f g-e h}-i \sqrt{f g+e h}}\right)-2 \text{Li}_2\left(\frac{1}{2}-\frac{1}{2} i \sqrt{\frac{g+h x}{g-h x}}\right)+2 \text{Li}_2\left(\frac{1}{2} i \sqrt{\frac{g+h x}{g-h x}}+\frac{1}{2}\right)+2 \text{Li}_2\left(\frac{\sqrt{f g+e h} \left(1-i \sqrt{\frac{g+h x}{g-h x}}\right)}{i \sqrt{f g-e h}+\sqrt{f g+e h}}\right)-2 \text{Li}_2\left(\frac{\sqrt{f g+e h} \left(i \sqrt{\frac{g+h x}{g-h x}}+1\right)}{\sqrt{f g+e h}-i \sqrt{f g-e h}}\right)-2 \text{Li}_2\left(\frac{\sqrt{f g+e h} \left(i \sqrt{\frac{g+h x}{g-h x}}+1\right)}{i \sqrt{f g-e h}+\sqrt{f g+e h}}\right)+2 \text{Li}_2\left(\frac{\sqrt{f g+e h} \left(\sqrt{\frac{g+h x}{g-h x}}+i\right)}{\sqrt{f g-e h}+i \sqrt{f g+e h}}\right)\right)}{2 h \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{i b g p q \sqrt{1-\frac{h^2 x^2}{g^2}} \text{Li}_2\left(-\frac{e^{i \sin ^{-1}\left(\frac{h x}{g}\right)} f g}{i e h-\sqrt{f^2 g^2-e^2 h^2}}\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{Li}_2\left(-\frac{e^{i \sin ^{-1}\left(\frac{h x}{g}\right)} f g}{i e h+\sqrt{f^2 g^2-e^2 h^2}}\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,"(ArcTan[(h*x)/(Sqrt[g - h*x]*Sqrt[g + h*x])]*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q]))/h - ((I/2)*b*p*q*Sqrt[g - h*x]*Sqrt[(g + h*x)/(g - h*x)]*(2*Log[e + f*x]*Log[I - Sqrt[(g + h*x)/(g - h*x)]] + Log[I - Sqrt[(g + h*x)/(g - h*x)]]^2 + 2*Log[I - Sqrt[(g + h*x)/(g - h*x)]]*Log[(1 - I*Sqrt[(g + h*x)/(g - h*x)])/2] - 2*Log[e + f*x]*Log[I + Sqrt[(g + h*x)/(g - h*x)]] - 2*Log[(1 + I*Sqrt[(g + h*x)/(g - h*x)])/2]*Log[I + Sqrt[(g + h*x)/(g - h*x)]] - Log[I + Sqrt[(g + h*x)/(g - h*x)]]^2 - 2*Log[I - Sqrt[(g + h*x)/(g - h*x)]]*Log[(Sqrt[f*g - e*h] - Sqrt[f*g + e*h]*Sqrt[(g + h*x)/(g - h*x)])/(Sqrt[f*g - e*h] - I*Sqrt[f*g + e*h])] + 2*Log[I + Sqrt[(g + h*x)/(g - h*x)]]*Log[(Sqrt[f*g - e*h] - Sqrt[f*g + e*h]*Sqrt[(g + h*x)/(g - h*x)])/(Sqrt[f*g - e*h] + I*Sqrt[f*g + e*h])] + 2*Log[I + Sqrt[(g + h*x)/(g - h*x)]]*Log[(Sqrt[f*g - e*h] + Sqrt[f*g + e*h]*Sqrt[(g + h*x)/(g - h*x)])/(Sqrt[f*g - e*h] - I*Sqrt[f*g + e*h])] - 2*Log[I - Sqrt[(g + h*x)/(g - h*x)]]*Log[(Sqrt[f*g - e*h] + Sqrt[f*g + e*h]*Sqrt[(g + h*x)/(g - h*x)])/(Sqrt[f*g - e*h] + I*Sqrt[f*g + e*h])] - 2*PolyLog[2, 1/2 - (I/2)*Sqrt[(g + h*x)/(g - h*x)]] + 2*PolyLog[2, 1/2 + (I/2)*Sqrt[(g + h*x)/(g - h*x)]] + 2*PolyLog[2, (Sqrt[f*g + e*h]*(1 - I*Sqrt[(g + h*x)/(g - h*x)]))/(I*Sqrt[f*g - e*h] + Sqrt[f*g + e*h])] - 2*PolyLog[2, (Sqrt[f*g + e*h]*(1 + I*Sqrt[(g + h*x)/(g - h*x)]))/((-I)*Sqrt[f*g - e*h] + Sqrt[f*g + e*h])] - 2*PolyLog[2, (Sqrt[f*g + e*h]*(1 + I*Sqrt[(g + h*x)/(g - h*x)]))/(I*Sqrt[f*g - e*h] + Sqrt[f*g + e*h])] + 2*PolyLog[2, (Sqrt[f*g + e*h]*(I + Sqrt[(g + h*x)/(g - h*x)]))/(Sqrt[f*g - e*h] + I*Sqrt[f*g + e*h])]))/(h*Sqrt[g + h*x])","B",1
523,1,386,427,0.7134835,"\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","Integrate[((i + j*x)^3*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(g + h*x),x]","\frac{f \left(h j x \left(6 a f^2 \left(6 g^2 j^2-3 g h j (6 i+j x)+h^2 \left(18 i^2+9 i j x+2 j^2 x^2\right)\right)-b p q \left(12 e^2 h^2 j^2-6 e f h j (-3 g j+9 h i+h j x)+f^2 \left(36 g^2 j^2-9 g h j (12 i+j x)+h^2 \left(108 i^2+27 i j x+4 j^2 x^2\right)\right)\right)\right)+36 a f^2 (h i-g j)^3 \log \left(\frac{f (g+h x)}{f g-e h}\right)+6 b f \log \left(c \left(d (e+f x)^p\right)^q\right) \left(h j \left(6 e \left(g^2 j^2-3 g h i j+3 h^2 i^2\right)+f x \left(6 g^2 j^2-3 g h j (6 i+j x)+h^2 \left(18 i^2+9 i j x+2 j^2 x^2\right)\right)\right)+6 f (h i-g j)^3 \log \left(\frac{f (g+h x)}{f g-e h}\right)\right)\right)+6 b e^2 h^2 j^2 p q \log (e+f x) (2 e h j+3 f g j-9 f h i)+36 b f^3 p q (h i-g j)^3 \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)}{36 f^3 h^4}","\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)^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{(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)^3 \log (e+f x)}{3 f^3 h}-\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 (h i-g j)^3 \text{Li}_2\left(-\frac{h (e+f x)}{f g-e h}\right)}{h^4}-\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 j p q x (h i-g j)^2}{h^3}-\frac{b p q (i+j x)^2 (h i-g j)}{4 h^2}-\frac{b p q (i+j x)^3}{9 h}",1,"(6*b*e^2*h^2*j^2*(-9*f*h*i + 3*f*g*j + 2*e*h*j)*p*q*Log[e + f*x] + f*(h*j*x*(6*a*f^2*(6*g^2*j^2 - 3*g*h*j*(6*i + j*x) + h^2*(18*i^2 + 9*i*j*x + 2*j^2*x^2)) - b*p*q*(12*e^2*h^2*j^2 - 6*e*f*h*j*(9*h*i - 3*g*j + h*j*x) + f^2*(36*g^2*j^2 - 9*g*h*j*(12*i + j*x) + h^2*(108*i^2 + 27*i*j*x + 4*j^2*x^2)))) + 36*a*f^2*(h*i - g*j)^3*Log[(f*(g + h*x))/(f*g - e*h)] + 6*b*f*Log[c*(d*(e + f*x)^p)^q]*(h*j*(6*e*(3*h^2*i^2 - 3*g*h*i*j + g^2*j^2) + f*x*(6*g^2*j^2 - 3*g*h*j*(6*i + j*x) + h^2*(18*i^2 + 9*i*j*x + 2*j^2*x^2))) + 6*f*(h*i - g*j)^3*Log[(f*(g + h*x))/(f*g - e*h)])) + 36*b*f^3*(h*i - g*j)^3*p*q*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)])/(36*f^3*h^4)","A",1
524,1,231,258,0.310643,"\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","Integrate[((i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(g + h*x),x]","\frac{f \left(h j x (2 a f (-2 g j+4 h i+h j x)+b p q (2 e h j-f (-4 g j+8 h i+h j x)))+4 a f (h i-g j)^2 \log \left(\frac{f (g+h x)}{f g-e h}\right)+2 b \log \left(c \left(d (e+f x)^p\right)^q\right) \left(h j (e (4 h i-2 g j)+f x (-2 g j+4 h i+h j x))+2 f (h i-g j)^2 \log \left(\frac{f (g+h x)}{f g-e h}\right)\right)\right)-2 b e^2 h^2 j^2 p q \log (e+f x)+4 b f^2 p q (h i-g j)^2 \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)}{4 f^2 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 p q (h i-g j)^2 \text{Li}_2\left(-\frac{h (e+f x)}{f g-e h}\right)}{h^3}-\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,"(-2*b*e^2*h^2*j^2*p*q*Log[e + f*x] + f*(h*j*x*(2*a*f*(4*h*i - 2*g*j + h*j*x) + b*p*q*(2*e*h*j - f*(8*h*i - 4*g*j + h*j*x))) + 4*a*f*(h*i - g*j)^2*Log[(f*(g + h*x))/(f*g - e*h)] + 2*b*Log[c*(d*(e + f*x)^p)^q]*(h*j*(e*(4*h*i - 2*g*j) + f*x*(4*h*i - 2*g*j + h*j*x)) + 2*f*(h*i - g*j)^2*Log[(f*(g + h*x))/(f*g - e*h)])) + 4*b*f^2*(h*i - g*j)^2*p*q*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)])/(4*f^2*h^3)","A",1
525,1,120,129,0.1239981,"\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","Integrate[((i + j*x)*(a + b*Log[c*(d*(e + f*x)^p)^q]))/(g + h*x),x]","\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)+a h j x+\frac{b h j (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)}{f}+b p q (h i-g j) \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)-b h j p q x}{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 p q (h i-g j) \text{Li}_2\left(-\frac{h (e+f x)}{f g-e h}\right)}{h^2}-\frac{b j p q x}{h}",1,"(a*h*j*x - b*h*j*p*q*x + (b*h*j*(e + f*x)*Log[c*(d*(e + f*x)^p)^q])/f + (h*i - g*j)*(a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(g + h*x))/(f*g - e*h)] + b*(h*i - g*j)*p*q*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)])/h^2","A",1
526,1,67,68,0.0073573,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{g+h x} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/(g + h*x),x]","\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{Li}_2\left(\frac{h (e+f x)}{e h-f g}\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{Li}_2\left(-\frac{h (e+f x)}{f g-e h}\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",1
527,1,117,165,0.0734013,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x) (i+j x)} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/((g + h*x)*(i + j*x)),x]","\frac{\left(\log \left(\frac{f (g+h x)}{f g-e h}\right)-\log \left(\frac{f (i+j x)}{f i-e j}\right)\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)+b p q \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)-b p q \text{Li}_2\left(\frac{j (e+f x)}{e j-f i}\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{Li}_2\left(-\frac{h (e+f x)}{f g-e h}\right)}{h i-g j}-\frac{b p q \text{Li}_2\left(-\frac{j (e+f x)}{f i-e j}\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)] - Log[(f*(i + j*x))/(f*i - e*j)]) + b*p*q*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)] - b*p*q*PolyLog[2, (j*(e + f*x))/(-(f*i) + e*j)])/(h*i - g*j)","A",1
528,1,225,268,0.2521359,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x) (i+j x)^2} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/((g + h*x)*(i + j*x)^2),x]","\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 \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)+\frac{a (h i-g j)}{i+j x}+\frac{b (h i-g j) \log \left(c \left(d (e+f x)^p\right)^q\right)}{i+j x}-\frac{b f p q (h i-g j) (\log (e+f x)-\log (i+j x))}{f i-e j}+b h p q \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)-b h p q \text{Li}_2\left(\frac{j (e+f x)}{e j-f i}\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 h p q \text{Li}_2\left(-\frac{h (e+f x)}{f g-e h}\right)}{(h i-g j)^2}-\frac{b h p q \text{Li}_2\left(-\frac{j (e+f x)}{f i-e j}\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,"((a*(h*i - g*j))/(i + j*x) + (b*(h*i - g*j)*Log[c*(d*(e + f*x)^p)^q])/(i + j*x) + h*(a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(g + h*x))/(f*g - e*h)] - (b*f*(h*i - g*j)*p*q*(Log[e + f*x] - Log[i + j*x]))/(f*i - e*j) - h*(a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(i + j*x))/(f*i - e*j)] + b*h*p*q*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)] - b*h*p*q*PolyLog[2, (j*(e + f*x))/(-(f*i) + e*j)])/(h*i - g*j)^2","A",1
529,1,363,425,0.4816227,"\int \frac{a+b \log \left(c \left(d (e+f x)^p\right)^q\right)}{(g+h x) (i+j x)^3} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])/((g + h*x)*(i + j*x)^3),x]","\frac{2 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)-2 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)+\frac{2 a h (h i-g j)}{i+j x}+\frac{a (h i-g j)^2}{(i+j x)^2}+\frac{2 b h (h i-g j) \log \left(c \left(d (e+f x)^p\right)^q\right)}{i+j x}+\frac{b (h i-g j)^2 \log \left(c \left(d (e+f x)^p\right)^q\right)}{(i+j x)^2}+2 b h^2 p q \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)-\frac{2 b f h p q (h i-g j) (\log (e+f x)-\log (i+j x))}{f i-e j}-\frac{b f p q (h i-g j)^2 (f (i+j x) \log (e+f x)-e j-f (i+j x) \log (i+j x)+f i)}{(i+j x) (f i-e j)^2}-2 b h^2 p q \text{Li}_2\left(\frac{j (e+f x)}{e j-f i}\right)}{2 (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 h^2 p q \text{Li}_2\left(-\frac{h (e+f x)}{f g-e h}\right)}{(h i-g j)^3}-\frac{b h^2 p q \text{Li}_2\left(-\frac{j (e+f x)}{f i-e j}\right)}{(h i-g j)^3}-\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,"((a*(h*i - g*j)^2)/(i + j*x)^2 + (2*a*h*(h*i - g*j))/(i + j*x) + (b*(h*i - g*j)^2*Log[c*(d*(e + f*x)^p)^q])/(i + j*x)^2 + (2*b*h*(h*i - g*j)*Log[c*(d*(e + f*x)^p)^q])/(i + j*x) + 2*h^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(g + h*x))/(f*g - e*h)] - (2*b*f*h*(h*i - g*j)*p*q*(Log[e + f*x] - Log[i + j*x]))/(f*i - e*j) - (b*f*(h*i - g*j)^2*p*q*(f*i - e*j + f*(i + j*x)*Log[e + f*x] - f*(i + j*x)*Log[i + j*x]))/((f*i - e*j)^2*(i + j*x)) - 2*h^2*(a + b*Log[c*(d*(e + f*x)^p)^q])*Log[(f*(i + j*x))/(f*i - e*j)] + 2*b*h^2*p*q*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)] - 2*b*h^2*p*q*PolyLog[2, (j*(e + f*x))/(-(f*i) + e*j)])/(2*(h*i - g*j)^3)","A",1
530,1,927,519,0.7461789,"\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","Integrate[((i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(g + h*x),x]","\frac{-8 b f^2 h^2 p q \left(-a+b p q \log (e+f x)-b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \left(\log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+\text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)\right) i^2+4 b^2 f^2 h^2 p^2 q^2 \left(\log \left(\frac{f (g+h x)}{f g-e h}\right) \log ^2(e+f x)+2 \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right) \log (e+f x)-2 \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right)\right) i^2-16 b f h j p q \left(-a+b p q \log (e+f x)-b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \left(-h (e+f x)+\log (e+f x) \left(e h+f x h-f g \log \left(\frac{f (g+h x)}{f g-e h}\right)\right)-f g \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)\right) i+8 b^2 f h j p^2 q^2 \left(h \left((e+f x) \log ^2(e+f x)-2 (e+f x) \log (e+f x)+2 f x\right)-f g \left(\log \left(\frac{f (g+h x)}{f g-e h}\right) \log ^2(e+f x)+2 \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right) \log (e+f x)-2 \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right)\right)\right) i+2 f^2 h^2 j^2 x^2 \left(a-b p q \log (e+f x)+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2+4 f^2 h j (2 h i-g j) x \left(a-b p q \log (e+f x)+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2+4 f^2 (h i-g j)^2 \left(a-b p q \log (e+f x)+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \log (g+h x)+2 b j^2 p q \left(-a+b p q \log (e+f x)-b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \left(-4 f^2 \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right) g^2+f h (f x (h x-4 g)-2 e (2 g+h x))+2 \log (e+f x) \left(h (e+f x) (2 f g+e h-f h x)-2 f^2 g^2 \log \left(\frac{f (g+h x)}{f g-e h}\right)\right)\right)-b^2 j^2 p^2 q^2 \left(-4 f^2 \left(\log \left(\frac{f (g+h x)}{f g-e h}\right) \log ^2(e+f x)+2 \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right) \log (e+f x)-2 \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right)\right) g^2+4 f h \left((e+f x) \log ^2(e+f x)-2 (e+f x) \log (e+f x)+2 f x\right) g+h^2 \left(2 \left(e^2-f^2 x^2\right) \log ^2(e+f x)+\left(-6 e^2-4 f x e+2 f^2 x^2\right) \log (e+f x)+f x (6 e-f x)\right)\right)}{4 f^2 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{2 b p q (h i-g j)^2 \text{Li}_2\left(-\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{(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{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{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 p^2 q^2 (h i-g j)^2 \text{Li}_3\left(-\frac{h (e+f x)}{f g-e h}\right)}{h^3}+\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,"(4*f^2*h*j*(2*h*i - g*j)*x*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2 + 2*f^2*h^2*j^2*x^2*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2 + 4*f^2*(h*i - g*j)^2*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2*Log[g + h*x] - 8*b*f^2*h^2*i^2*p*q*(-a + b*p*q*Log[e + f*x] - b*Log[c*(d*(e + f*x)^p)^q])*(Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] + PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)]) - 16*b*f*h*i*j*p*q*(-a + b*p*q*Log[e + f*x] - b*Log[c*(d*(e + f*x)^p)^q])*(-(h*(e + f*x)) + Log[e + f*x]*(e*h + f*h*x - f*g*Log[(f*(g + h*x))/(f*g - e*h)]) - f*g*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)]) + 2*b*j^2*p*q*(-a + b*p*q*Log[e + f*x] - b*Log[c*(d*(e + f*x)^p)^q])*(f*h*(f*x*(-4*g + h*x) - 2*e*(2*g + h*x)) + 2*Log[e + f*x]*(h*(e + f*x)*(2*f*g + e*h - f*h*x) - 2*f^2*g^2*Log[(f*(g + h*x))/(f*g - e*h)]) - 4*f^2*g^2*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)]) + 8*b^2*f*h*i*j*p^2*q^2*(h*(2*f*x - 2*(e + f*x)*Log[e + f*x] + (e + f*x)*Log[e + f*x]^2) - f*g*(Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 2*Log[e + f*x]*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)] - 2*PolyLog[3, (h*(e + f*x))/(-(f*g) + e*h)])) - b^2*j^2*p^2*q^2*(4*f*g*h*(2*f*x - 2*(e + f*x)*Log[e + f*x] + (e + f*x)*Log[e + f*x]^2) + h^2*(f*x*(6*e - f*x) + (-6*e^2 - 4*e*f*x + 2*f^2*x^2)*Log[e + f*x] + 2*(e^2 - f^2*x^2)*Log[e + f*x]^2) - 4*f^2*g^2*(Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 2*Log[e + f*x]*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)] - 2*PolyLog[3, (h*(e + f*x))/(-(f*g) + e*h)])) + 4*b^2*f^2*h^2*i^2*p^2*q^2*(Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 2*Log[e + f*x]*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)] - 2*PolyLog[3, (h*(e + f*x))/(-(f*g) + e*h)]))/(4*f^2*h^3)","A",1
531,1,852,240,0.3902638,"\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","Integrate[((i + j*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2)/(g + h*x),x]","\frac{f h j x a^2+f h i \log (g+h x) a^2-f g j \log (g+h x) a^2-2 b e h j p q a-2 b f h j p q x a+2 b e h j p q \log (e+f x) a+2 b f h j x \log \left(c \left(d (e+f x)^p\right)^q\right) a-2 b f h i p q \log (e+f x) \log (g+h x) a+2 b f g j p q \log (e+f x) \log (g+h x) a+2 b f h i \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a-2 b f g j \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a+2 b f h i p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) a-2 b f g j p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) a-b^2 e h j p^2 q^2 \log ^2(e+f x)+b^2 f h j x \log ^2\left(c \left(d (e+f x)^p\right)^q\right)+2 b^2 f h j p^2 q^2 x-2 b^2 e h j p q \log \left(c \left(d (e+f x)^p\right)^q\right)-2 b^2 f h j p q x \log \left(c \left(d (e+f x)^p\right)^q\right)+2 b^2 e h j p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)+b^2 f h i p^2 q^2 \log ^2(e+f x) \log (g+h x)-b^2 f g j p^2 q^2 \log ^2(e+f x) \log (g+h x)+b^2 f h i \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)-b^2 f g j \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)-2 b^2 f h i p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)+2 b^2 f g j p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)-b^2 f h i p^2 q^2 \log ^2(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+b^2 f g j p^2 q^2 \log ^2(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+2 b^2 f h i p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right)-2 b^2 f g j p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right)+2 b f (h i-g j) p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)+2 b^2 f (g j-h i) p^2 q^2 \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right)}{f h^2}","\frac{2 b p q (h i-g j) \text{Li}_2\left(-\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{(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 p^2 q^2 (h i-g j) \text{Li}_3\left(-\frac{h (e+f x)}{f g-e h}\right)}{h^2}+\frac{2 b^2 j p^2 q^2 x}{h}",1,"(-2*a*b*e*h*j*p*q + a^2*f*h*j*x - 2*a*b*f*h*j*p*q*x + 2*b^2*f*h*j*p^2*q^2*x + 2*a*b*e*h*j*p*q*Log[e + f*x] - b^2*e*h*j*p^2*q^2*Log[e + f*x]^2 - 2*b^2*e*h*j*p*q*Log[c*(d*(e + f*x)^p)^q] + 2*a*b*f*h*j*x*Log[c*(d*(e + f*x)^p)^q] - 2*b^2*f*h*j*p*q*x*Log[c*(d*(e + f*x)^p)^q] + 2*b^2*e*h*j*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q] + b^2*f*h*j*x*Log[c*(d*(e + f*x)^p)^q]^2 + a^2*f*h*i*Log[g + h*x] - a^2*f*g*j*Log[g + h*x] - 2*a*b*f*h*i*p*q*Log[e + f*x]*Log[g + h*x] + 2*a*b*f*g*j*p*q*Log[e + f*x]*Log[g + h*x] + b^2*f*h*i*p^2*q^2*Log[e + f*x]^2*Log[g + h*x] - b^2*f*g*j*p^2*q^2*Log[e + f*x]^2*Log[g + h*x] + 2*a*b*f*h*i*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 2*a*b*f*g*j*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 2*b^2*f*h*i*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 2*b^2*f*g*j*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + b^2*f*h*i*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] - b^2*f*g*j*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] + 2*a*b*f*h*i*p*q*Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] - 2*a*b*f*g*j*p*q*Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] - b^2*f*h*i*p^2*q^2*Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + b^2*f*g*j*p^2*q^2*Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 2*b^2*f*h*i*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] - 2*b^2*f*g*j*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] + 2*b*f*(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)] + 2*b^2*f*(-(h*i) + g*j)*p^2*q^2*PolyLog[3, (h*(e + f*x))/(-(f*g) + e*h)])/(f*h^2)","B",1
532,1,313,123,0.3036308,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2}{g+h x} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/(g + h*x),x]","\frac{a^2 \log (g+h x)}{h}+\frac{b \left(2 p q \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)+2 a \log (g+h x) \log \left(c \left(d (e+f x)^p\right)^q\right)-2 a p q \log (e+f x) \log (g+h x)+2 a p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+b \log (g+h x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right)-2 b p q \log (e+f x) \log (g+h x) \log \left(c \left(d (e+f x)^p\right)^q\right)+2 b p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) \log \left(c \left(d (e+f x)^p\right)^q\right)-2 b p^2 q^2 \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right)+b p^2 q^2 \log ^2(e+f x) \log (g+h x)-b p^2 q^2 \log ^2(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)\right)}{h}","\frac{2 b p q \text{Li}_2\left(-\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{\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^2 p^2 q^2 \text{Li}_3\left(-\frac{h (e+f x)}{f g-e h}\right)}{h}",1,"(a^2*Log[g + h*x])/h + (b*(-2*a*p*q*Log[e + f*x]*Log[g + h*x] + b*p^2*q^2*Log[e + f*x]^2*Log[g + h*x] + 2*a*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 2*b*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + b*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] + 2*a*p*q*Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] - b*p^2*q^2*Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 2*b*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] + 2*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)] - 2*b*p^2*q^2*PolyLog[3, (h*(e + f*x))/(-(f*g) + e*h)]))/h","B",1
533,1,652,288,0.3953261,"\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","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/((g + h*x)*(i + j*x)),x]","\frac{a^2 \log (g+h x)-a^2 \log (i+j x)+2 b p q \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)+2 a b \log (g+h x) \log \left(c \left(d (e+f x)^p\right)^q\right)-2 b p q \text{Li}_2\left(\frac{j (e+f x)}{e j-f i}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)-2 a b \log (i+j x) \log \left(c \left(d (e+f x)^p\right)^q\right)-2 a b p q \log (e+f x) \log (g+h x)+2 a b p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+2 a b p q \log (e+f x) \log (i+j x)-2 a b p q \log (e+f x) \log \left(\frac{f (i+j x)}{f i-e j}\right)+b^2 \log (g+h x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right)-2 b^2 p q \log (e+f x) \log (g+h x) \log \left(c \left(d (e+f x)^p\right)^q\right)+2 b^2 p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) \log \left(c \left(d (e+f x)^p\right)^q\right)-b^2 \log (i+j x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right)+2 b^2 p q \log (e+f x) \log (i+j x) \log \left(c \left(d (e+f x)^p\right)^q\right)-2 b^2 p q \log (e+f x) \log \left(\frac{f (i+j x)}{f i-e j}\right) \log \left(c \left(d (e+f x)^p\right)^q\right)-2 b^2 p^2 q^2 \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right)+b^2 p^2 q^2 \log ^2(e+f x) \log (g+h x)-b^2 p^2 q^2 \log ^2(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+2 b^2 p^2 q^2 \text{Li}_3\left(\frac{j (e+f x)}{e j-f i}\right)-b^2 p^2 q^2 \log ^2(e+f x) \log (i+j x)+b^2 p^2 q^2 \log ^2(e+f x) \log \left(\frac{f (i+j x)}{f i-e j}\right)}{h i-g j}","\frac{2 b p q \text{Li}_2\left(-\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{Li}_2\left(-\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{\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^2 p^2 q^2 \text{Li}_3\left(-\frac{h (e+f x)}{f g-e h}\right)}{h i-g j}+\frac{2 b^2 p^2 q^2 \text{Li}_3\left(-\frac{j (e+f x)}{f i-e j}\right)}{h i-g j}",1,"(a^2*Log[g + h*x] - 2*a*b*p*q*Log[e + f*x]*Log[g + h*x] + b^2*p^2*q^2*Log[e + f*x]^2*Log[g + h*x] + 2*a*b*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 2*b^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + b^2*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] + 2*a*b*p*q*Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] - b^2*p^2*q^2*Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 2*b^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] - a^2*Log[i + j*x] + 2*a*b*p*q*Log[e + f*x]*Log[i + j*x] - b^2*p^2*q^2*Log[e + f*x]^2*Log[i + j*x] - 2*a*b*Log[c*(d*(e + f*x)^p)^q]*Log[i + j*x] + 2*b^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[i + j*x] - b^2*Log[c*(d*(e + f*x)^p)^q]^2*Log[i + j*x] - 2*a*b*p*q*Log[e + f*x]*Log[(f*(i + j*x))/(f*i - e*j)] + b^2*p^2*q^2*Log[e + f*x]^2*Log[(f*(i + j*x))/(f*i - e*j)] - 2*b^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(i + j*x))/(f*i - e*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)] - 2*b*p*q*(a + b*Log[c*(d*(e + f*x)^p)^q])*PolyLog[2, (j*(e + f*x))/(-(f*i) + e*j)] - 2*b^2*p^2*q^2*PolyLog[3, (h*(e + f*x))/(-(f*g) + e*h)] + 2*b^2*p^2*q^2*PolyLog[3, (j*(e + f*x))/(-(f*i) + e*j)])/(h*i - g*j)","B",1
534,1,654,463,0.9578511,"\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","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^2/((g + h*x)*(i + j*x)^2),x]","\frac{-2 b p q \left(-h (i+j x) (f i-e j) \left(\text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)+\log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)\right)+(h i-g j) (j (e+f x) \log (e+f x)-f (i+j x) \log (i+j x))+h (i+j x) (f i-e j) \left(\text{Li}_2\left(\frac{j (e+f x)}{e j-f i}\right)+\log (e+f x) \log \left(\frac{f (i+j x)}{f i-e j}\right)\right)\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)+(f i-e j) (h i-g j) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)^2+h (i+j x) (f i-e j) \log (g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)^2-h (i+j x) (f i-e j) \log (i+j x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)-b p q \log (e+f x)\right)^2-b^2 p^2 q^2 \left(-h (i+j x) (f i-e j) \left(-2 \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right)+2 \log (e+f x) \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)+\log ^2(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)\right)+(h i-g j) \left(\log (e+f x) \left(j (e+f x) \log (e+f x)-2 f (i+j x) \log \left(\frac{f (i+j x)}{f i-e j}\right)\right)-2 f (i+j x) \text{Li}_2\left(\frac{j (e+f x)}{e j-f i}\right)\right)+h (i+j x) (f i-e j) \left(-2 \text{Li}_3\left(\frac{j (e+f x)}{e j-f i}\right)+2 \log (e+f x) \text{Li}_2\left(\frac{j (e+f x)}{e j-f i}\right)+\log ^2(e+f x) \log \left(\frac{f (i+j x)}{f i-e j}\right)\right)\right)}{(i+j x) (f i-e j) (h i-g j)^2}","\frac{2 b h p q \text{Li}_2\left(-\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{Li}_2\left(-\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 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^2 f p^2 q^2 \text{Li}_2\left(-\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{Li}_3\left(-\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{Li}_3\left(-\frac{j (e+f x)}{f i-e j}\right)}{(h i-g j)^2}",1,"((f*i - e*j)*(h*i - g*j)*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2 + h*(f*i - e*j)*(i + j*x)*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2*Log[g + h*x] - h*(f*i - e*j)*(i + j*x)*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2*Log[i + j*x] - 2*b*p*q*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])*((h*i - g*j)*(j*(e + f*x)*Log[e + f*x] - f*(i + j*x)*Log[i + j*x]) - h*(f*i - e*j)*(i + j*x)*(Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] + PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)]) + h*(f*i - e*j)*(i + j*x)*(Log[e + f*x]*Log[(f*(i + j*x))/(f*i - e*j)] + PolyLog[2, (j*(e + f*x))/(-(f*i) + e*j)])) - b^2*p^2*q^2*((h*i - g*j)*(Log[e + f*x]*(j*(e + f*x)*Log[e + f*x] - 2*f*(i + j*x)*Log[(f*(i + j*x))/(f*i - e*j)]) - 2*f*(i + j*x)*PolyLog[2, (j*(e + f*x))/(-(f*i) + e*j)]) - h*(f*i - e*j)*(i + j*x)*(Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 2*Log[e + f*x]*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)] - 2*PolyLog[3, (h*(e + f*x))/(-(f*g) + e*h)]) + h*(f*i - e*j)*(i + j*x)*(Log[e + f*x]^2*Log[(f*(i + j*x))/(f*i - e*j)] + 2*Log[e + f*x]*PolyLog[2, (j*(e + f*x))/(-(f*i) + e*j)] - 2*PolyLog[3, (j*(e + f*x))/(-(f*i) + e*j)])))/((f*i - e*j)*(h*i - g*j)^2*(i + j*x))","A",1
535,1,4056,742,1.6069972,"\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","Integrate[((i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/(g + h*x),x]","\text{Result too large to show}","\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 b^2 p^2 q^2 (h i-g j)^2 \text{Li}_3\left(-\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{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 p q (h i-g j)^2 \text{Li}_2\left(-\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{(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{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{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 p^3 q^3 (h i-g j)^2 \text{Li}_4\left(-\frac{h (e+f x)}{f g-e h}\right)}{h^3}-\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,"(-48*a^2*b*e*f*h^2*i*j*p*q + 24*a^2*b*e*f*g*h*j^2*p*q + 16*a^3*f^2*h^2*i*j*x - 8*a^3*f^2*g*h*j^2*x - 48*a^2*b*f^2*h^2*i*j*p*q*x + 24*a^2*b*f^2*g*h*j^2*p*q*x + 12*a^2*b*e*f*h^2*j^2*p*q*x + 96*a*b^2*f^2*h^2*i*j*p^2*q^2*x - 48*a*b^2*f^2*g*h*j^2*p^2*q^2*x - 36*a*b^2*e*f*h^2*j^2*p^2*q^2*x - 96*b^3*f^2*h^2*i*j*p^3*q^3*x + 48*b^3*f^2*g*h*j^2*p^3*q^3*x + 42*b^3*e*f*h^2*j^2*p^3*q^3*x + 4*a^3*f^2*h^2*j^2*x^2 - 6*a^2*b*f^2*h^2*j^2*p*q*x^2 + 6*a*b^2*f^2*h^2*j^2*p^2*q^2*x^2 - 3*b^3*f^2*h^2*j^2*p^3*q^3*x^2 + 48*a^2*b*e*f*h^2*i*j*p*q*Log[e + f*x] - 24*a^2*b*e*f*g*h*j^2*p*q*Log[e + f*x] - 12*a^2*b*e^2*h^2*j^2*p*q*Log[e + f*x] + 36*a*b^2*e^2*h^2*j^2*p^2*q^2*Log[e + f*x] + 96*b^3*e*f*h^2*i*j*p^3*q^3*Log[e + f*x] - 48*b^3*e*f*g*h*j^2*p^3*q^3*Log[e + f*x] - 42*b^3*e^2*h^2*j^2*p^3*q^3*Log[e + f*x] - 48*a*b^2*e*f*h^2*i*j*p^2*q^2*Log[e + f*x]^2 + 24*a*b^2*e*f*g*h*j^2*p^2*q^2*Log[e + f*x]^2 + 12*a*b^2*e^2*h^2*j^2*p^2*q^2*Log[e + f*x]^2 - 18*b^3*e^2*h^2*j^2*p^3*q^3*Log[e + f*x]^2 + 16*b^3*e*f*h^2*i*j*p^3*q^3*Log[e + f*x]^3 - 8*b^3*e*f*g*h*j^2*p^3*q^3*Log[e + f*x]^3 - 4*b^3*e^2*h^2*j^2*p^3*q^3*Log[e + f*x]^3 - 96*a*b^2*e*f*h^2*i*j*p*q*Log[c*(d*(e + f*x)^p)^q] + 48*a*b^2*e*f*g*h*j^2*p*q*Log[c*(d*(e + f*x)^p)^q] + 48*a^2*b*f^2*h^2*i*j*x*Log[c*(d*(e + f*x)^p)^q] - 24*a^2*b*f^2*g*h*j^2*x*Log[c*(d*(e + f*x)^p)^q] - 96*a*b^2*f^2*h^2*i*j*p*q*x*Log[c*(d*(e + f*x)^p)^q] + 48*a*b^2*f^2*g*h*j^2*p*q*x*Log[c*(d*(e + f*x)^p)^q] + 24*a*b^2*e*f*h^2*j^2*p*q*x*Log[c*(d*(e + f*x)^p)^q] + 96*b^3*f^2*h^2*i*j*p^2*q^2*x*Log[c*(d*(e + f*x)^p)^q] - 48*b^3*f^2*g*h*j^2*p^2*q^2*x*Log[c*(d*(e + f*x)^p)^q] - 36*b^3*e*f*h^2*j^2*p^2*q^2*x*Log[c*(d*(e + f*x)^p)^q] + 12*a^2*b*f^2*h^2*j^2*x^2*Log[c*(d*(e + f*x)^p)^q] - 12*a*b^2*f^2*h^2*j^2*p*q*x^2*Log[c*(d*(e + f*x)^p)^q] + 6*b^3*f^2*h^2*j^2*p^2*q^2*x^2*Log[c*(d*(e + f*x)^p)^q] + 96*a*b^2*e*f*h^2*i*j*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q] - 48*a*b^2*e*f*g*h*j^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q] - 24*a*b^2*e^2*h^2*j^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q] + 36*b^3*e^2*h^2*j^2*p^2*q^2*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q] - 48*b^3*e*f*h^2*i*j*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q] + 24*b^3*e*f*g*h*j^2*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q] + 12*b^3*e^2*h^2*j^2*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q] - 48*b^3*e*f*h^2*i*j*p*q*Log[c*(d*(e + f*x)^p)^q]^2 + 24*b^3*e*f*g*h*j^2*p*q*Log[c*(d*(e + f*x)^p)^q]^2 + 48*a*b^2*f^2*h^2*i*j*x*Log[c*(d*(e + f*x)^p)^q]^2 - 24*a*b^2*f^2*g*h*j^2*x*Log[c*(d*(e + f*x)^p)^q]^2 - 48*b^3*f^2*h^2*i*j*p*q*x*Log[c*(d*(e + f*x)^p)^q]^2 + 24*b^3*f^2*g*h*j^2*p*q*x*Log[c*(d*(e + f*x)^p)^q]^2 + 12*b^3*e*f*h^2*j^2*p*q*x*Log[c*(d*(e + f*x)^p)^q]^2 + 12*a*b^2*f^2*h^2*j^2*x^2*Log[c*(d*(e + f*x)^p)^q]^2 - 6*b^3*f^2*h^2*j^2*p*q*x^2*Log[c*(d*(e + f*x)^p)^q]^2 + 48*b^3*e*f*h^2*i*j*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2 - 24*b^3*e*f*g*h*j^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2 - 12*b^3*e^2*h^2*j^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2 + 16*b^3*f^2*h^2*i*j*x*Log[c*(d*(e + f*x)^p)^q]^3 - 8*b^3*f^2*g*h*j^2*x*Log[c*(d*(e + f*x)^p)^q]^3 + 4*b^3*f^2*h^2*j^2*x^2*Log[c*(d*(e + f*x)^p)^q]^3 + 8*a^3*f^2*h^2*i^2*Log[g + h*x] - 16*a^3*f^2*g*h*i*j*Log[g + h*x] + 8*a^3*f^2*g^2*j^2*Log[g + h*x] - 24*a^2*b*f^2*h^2*i^2*p*q*Log[e + f*x]*Log[g + h*x] + 48*a^2*b*f^2*g*h*i*j*p*q*Log[e + f*x]*Log[g + h*x] - 24*a^2*b*f^2*g^2*j^2*p*q*Log[e + f*x]*Log[g + h*x] + 24*a*b^2*f^2*h^2*i^2*p^2*q^2*Log[e + f*x]^2*Log[g + h*x] - 48*a*b^2*f^2*g*h*i*j*p^2*q^2*Log[e + f*x]^2*Log[g + h*x] + 24*a*b^2*f^2*g^2*j^2*p^2*q^2*Log[e + f*x]^2*Log[g + h*x] - 8*b^3*f^2*h^2*i^2*p^3*q^3*Log[e + f*x]^3*Log[g + h*x] + 16*b^3*f^2*g*h*i*j*p^3*q^3*Log[e + f*x]^3*Log[g + h*x] - 8*b^3*f^2*g^2*j^2*p^3*q^3*Log[e + f*x]^3*Log[g + h*x] + 24*a^2*b*f^2*h^2*i^2*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 48*a^2*b*f^2*g*h*i*j*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 24*a^2*b*f^2*g^2*j^2*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 48*a*b^2*f^2*h^2*i^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 96*a*b^2*f^2*g*h*i*j*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 48*a*b^2*f^2*g^2*j^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 24*b^3*f^2*h^2*i^2*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 48*b^3*f^2*g*h*i*j*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 24*b^3*f^2*g^2*j^2*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 24*a*b^2*f^2*h^2*i^2*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] - 48*a*b^2*f^2*g*h*i*j*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] + 24*a*b^2*f^2*g^2*j^2*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] - 24*b^3*f^2*h^2*i^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] + 48*b^3*f^2*g*h*i*j*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] - 24*b^3*f^2*g^2*j^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] + 8*b^3*f^2*h^2*i^2*Log[c*(d*(e + f*x)^p)^q]^3*Log[g + h*x] - 16*b^3*f^2*g*h*i*j*Log[c*(d*(e + f*x)^p)^q]^3*Log[g + h*x] + 8*b^3*f^2*g^2*j^2*Log[c*(d*(e + f*x)^p)^q]^3*Log[g + h*x] + 24*a^2*b*f^2*h^2*i^2*p*q*Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] - 48*a^2*b*f^2*g*h*i*j*p*q*Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] + 24*a^2*b*f^2*g^2*j^2*p*q*Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] - 24*a*b^2*f^2*h^2*i^2*p^2*q^2*Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 48*a*b^2*f^2*g*h*i*j*p^2*q^2*Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] - 24*a*b^2*f^2*g^2*j^2*p^2*q^2*Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 8*b^3*f^2*h^2*i^2*p^3*q^3*Log[e + f*x]^3*Log[(f*(g + h*x))/(f*g - e*h)] - 16*b^3*f^2*g*h*i*j*p^3*q^3*Log[e + f*x]^3*Log[(f*(g + h*x))/(f*g - e*h)] + 8*b^3*f^2*g^2*j^2*p^3*q^3*Log[e + f*x]^3*Log[(f*(g + h*x))/(f*g - e*h)] + 48*a*b^2*f^2*h^2*i^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] - 96*a*b^2*f^2*g*h*i*j*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] + 48*a*b^2*f^2*g^2*j^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] - 24*b^3*f^2*h^2*i^2*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] + 48*b^3*f^2*g*h*i*j*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] - 24*b^3*f^2*g^2*j^2*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] + 24*b^3*f^2*h^2*i^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[(f*(g + h*x))/(f*g - e*h)] - 48*b^3*f^2*g*h*i*j*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 24*b^3*f^2*g^2*j^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 24*b*f^2*(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)] - 48*b^2*f^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)] + 48*b^3*f^2*h^2*i^2*p^3*q^3*PolyLog[4, (h*(e + f*x))/(-(f*g) + e*h)] - 96*b^3*f^2*g*h*i*j*p^3*q^3*PolyLog[4, (h*(e + f*x))/(-(f*g) + e*h)] + 48*b^3*f^2*g^2*j^2*p^3*q^3*PolyLog[4, (h*(e + f*x))/(-(f*g) + e*h)])/(8*f^2*h^3)","B",1
536,1,1769,349,0.7861601,"\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","Integrate[((i + j*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/(g + h*x),x]","\frac{f h j x a^3+f h i \log (g+h x) a^3-f g j \log (g+h x) a^3-3 b e h j p q a^2-3 b f h j p q x a^2+3 b e h j p q \log (e+f x) a^2+3 b f h j x \log \left(c \left(d (e+f x)^p\right)^q\right) a^2-3 b f h i p q \log (e+f x) \log (g+h x) a^2+3 b f g j p q \log (e+f x) \log (g+h x) a^2+3 b f h i \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a^2-3 b f g j \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a^2+3 b f h i p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) a^2-3 b f g j p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) a^2-3 b^2 e h j p^2 q^2 \log ^2(e+f x) a+3 b^2 f h j x \log ^2\left(c \left(d (e+f x)^p\right)^q\right) a+6 b^2 f h j p^2 q^2 x a-6 b^2 e h j p q \log \left(c \left(d (e+f x)^p\right)^q\right) a-6 b^2 f h j p q x \log \left(c \left(d (e+f x)^p\right)^q\right) a+6 b^2 e h j p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) a+3 b^2 f h i p^2 q^2 \log ^2(e+f x) \log (g+h x) a-3 b^2 f g j p^2 q^2 \log ^2(e+f x) \log (g+h x) a+3 b^2 f h i \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a-3 b^2 f g j \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a-6 b^2 f h i p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a+6 b^2 f g j p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a-3 b^2 f h i p^2 q^2 \log ^2(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) a+3 b^2 f g j p^2 q^2 \log ^2(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) a+6 b^2 f h i p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right) a-6 b^2 f g j p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right) a+b^3 e h j p^3 q^3 \log ^3(e+f x)+b^3 f h j x \log ^3\left(c \left(d (e+f x)^p\right)^q\right)-3 b^3 e h j p q \log ^2\left(c \left(d (e+f x)^p\right)^q\right)-3 b^3 f h j p q x \log ^2\left(c \left(d (e+f x)^p\right)^q\right)+3 b^3 e h j p q \log (e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right)-6 b^3 f h j p^3 q^3 x+6 b^3 e h j p^3 q^3 \log (e+f x)-3 b^3 e h j p^2 q^2 \log ^2(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right)+6 b^3 f h j p^2 q^2 x \log \left(c \left(d (e+f x)^p\right)^q\right)-b^3 f h i p^3 q^3 \log ^3(e+f x) \log (g+h x)+b^3 f g j p^3 q^3 \log ^3(e+f x) \log (g+h x)+b^3 f h i \log ^3\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)-b^3 f g j \log ^3\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)-3 b^3 f h i p q \log (e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)+3 b^3 f g j p q \log (e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)+3 b^3 f h i p^2 q^2 \log ^2(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)-3 b^3 f g j p^2 q^2 \log ^2(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)+b^3 f h i p^3 q^3 \log ^3(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)-b^3 f g j p^3 q^3 \log ^3(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+3 b^3 f h i p q \log (e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right)-3 b^3 f g j p q \log (e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right)-3 b^3 f h i p^2 q^2 \log ^2(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right)+3 b^3 f g j p^2 q^2 \log ^2(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right)+3 b f (h i-g j) p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)-6 b^2 f (h i-g j) p^2 q^2 \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right)+6 b^3 f h i p^3 q^3 \text{Li}_4\left(\frac{h (e+f x)}{e h-f g}\right)-6 b^3 f g j p^3 q^3 \text{Li}_4\left(\frac{h (e+f x)}{e h-f g}\right)}{f h^2}","-\frac{6 b^2 p^2 q^2 (h i-g j) \text{Li}_3\left(-\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{6 a b^2 j p^2 q^2 x}{h}+\frac{3 b p q (h i-g j) \text{Li}_2\left(-\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{(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 p^3 q^3 (h i-g j) \text{Li}_4\left(-\frac{h (e+f x)}{f g-e h}\right)}{h^2}-\frac{6 b^3 j p^3 q^3 x}{h}",1,"(-3*a^2*b*e*h*j*p*q + a^3*f*h*j*x - 3*a^2*b*f*h*j*p*q*x + 6*a*b^2*f*h*j*p^2*q^2*x - 6*b^3*f*h*j*p^3*q^3*x + 3*a^2*b*e*h*j*p*q*Log[e + f*x] + 6*b^3*e*h*j*p^3*q^3*Log[e + f*x] - 3*a*b^2*e*h*j*p^2*q^2*Log[e + f*x]^2 + b^3*e*h*j*p^3*q^3*Log[e + f*x]^3 - 6*a*b^2*e*h*j*p*q*Log[c*(d*(e + f*x)^p)^q] + 3*a^2*b*f*h*j*x*Log[c*(d*(e + f*x)^p)^q] - 6*a*b^2*f*h*j*p*q*x*Log[c*(d*(e + f*x)^p)^q] + 6*b^3*f*h*j*p^2*q^2*x*Log[c*(d*(e + f*x)^p)^q] + 6*a*b^2*e*h*j*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q] - 3*b^3*e*h*j*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q] - 3*b^3*e*h*j*p*q*Log[c*(d*(e + f*x)^p)^q]^2 + 3*a*b^2*f*h*j*x*Log[c*(d*(e + f*x)^p)^q]^2 - 3*b^3*f*h*j*p*q*x*Log[c*(d*(e + f*x)^p)^q]^2 + 3*b^3*e*h*j*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2 + b^3*f*h*j*x*Log[c*(d*(e + f*x)^p)^q]^3 + a^3*f*h*i*Log[g + h*x] - a^3*f*g*j*Log[g + h*x] - 3*a^2*b*f*h*i*p*q*Log[e + f*x]*Log[g + h*x] + 3*a^2*b*f*g*j*p*q*Log[e + f*x]*Log[g + h*x] + 3*a*b^2*f*h*i*p^2*q^2*Log[e + f*x]^2*Log[g + h*x] - 3*a*b^2*f*g*j*p^2*q^2*Log[e + f*x]^2*Log[g + h*x] - b^3*f*h*i*p^3*q^3*Log[e + f*x]^3*Log[g + h*x] + b^3*f*g*j*p^3*q^3*Log[e + f*x]^3*Log[g + h*x] + 3*a^2*b*f*h*i*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 3*a^2*b*f*g*j*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 6*a*b^2*f*h*i*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 6*a*b^2*f*g*j*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 3*b^3*f*h*i*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 3*b^3*f*g*j*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 3*a*b^2*f*h*i*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] - 3*a*b^2*f*g*j*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] - 3*b^3*f*h*i*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] + 3*b^3*f*g*j*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] + b^3*f*h*i*Log[c*(d*(e + f*x)^p)^q]^3*Log[g + h*x] - b^3*f*g*j*Log[c*(d*(e + f*x)^p)^q]^3*Log[g + h*x] + 3*a^2*b*f*h*i*p*q*Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] - 3*a^2*b*f*g*j*p*q*Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] - 3*a*b^2*f*h*i*p^2*q^2*Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 3*a*b^2*f*g*j*p^2*q^2*Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + b^3*f*h*i*p^3*q^3*Log[e + f*x]^3*Log[(f*(g + h*x))/(f*g - e*h)] - b^3*f*g*j*p^3*q^3*Log[e + f*x]^3*Log[(f*(g + h*x))/(f*g - e*h)] + 6*a*b^2*f*h*i*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] - 6*a*b^2*f*g*j*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] - 3*b^3*f*h*i*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] + 3*b^3*f*g*j*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] + 3*b^3*f*h*i*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[(f*(g + h*x))/(f*g - e*h)] - 3*b^3*f*g*j*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 3*b*f*(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)] - 6*b^2*f*(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)] + 6*b^3*f*h*i*p^3*q^3*PolyLog[4, (h*(e + f*x))/(-(f*g) + e*h)] - 6*b^3*f*g*j*p^3*q^3*PolyLog[4, (h*(e + f*x))/(-(f*g) + e*h)])/(f*h^2)","B",1
537,1,646,177,0.2581557,"\int \frac{\left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3}{g+h x} \, dx","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^3/(g + h*x),x]","\frac{a^3 \log (g+h x)+3 a^2 b \log (g+h x) \log \left(c \left(d (e+f x)^p\right)^q\right)-3 a^2 b p q \log (e+f x) \log (g+h x)+3 a^2 b p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)-6 b^2 p^2 q^2 \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)+3 a b^2 \log (g+h x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right)-6 a b^2 p q \log (e+f x) \log (g+h x) \log \left(c \left(d (e+f x)^p\right)^q\right)+6 a b^2 p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) \log \left(c \left(d (e+f x)^p\right)^q\right)+3 a b^2 p^2 q^2 \log ^2(e+f x) \log (g+h x)-3 a b^2 p^2 q^2 \log ^2(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+3 b p q \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2+3 b^3 p^2 q^2 \log ^2(e+f x) \log (g+h x) \log \left(c \left(d (e+f x)^p\right)^q\right)-3 b^3 p^2 q^2 \log ^2(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) \log \left(c \left(d (e+f x)^p\right)^q\right)+b^3 \log (g+h x) \log ^3\left(c \left(d (e+f x)^p\right)^q\right)-3 b^3 p q \log (e+f x) \log (g+h x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right)+3 b^3 p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) \log ^2\left(c \left(d (e+f x)^p\right)^q\right)+6 b^3 p^3 q^3 \text{Li}_4\left(\frac{h (e+f x)}{e h-f g}\right)-b^3 p^3 q^3 \log ^3(e+f x) \log (g+h x)+b^3 p^3 q^3 \log ^3(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)}{h}","-\frac{6 b^2 p^2 q^2 \text{Li}_3\left(-\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{Li}_2\left(-\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{\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^3 p^3 q^3 \text{Li}_4\left(-\frac{h (e+f x)}{f g-e h}\right)}{h}",1,"(a^3*Log[g + h*x] - 3*a^2*b*p*q*Log[e + f*x]*Log[g + h*x] + 3*a*b^2*p^2*q^2*Log[e + f*x]^2*Log[g + h*x] - b^3*p^3*q^3*Log[e + f*x]^3*Log[g + h*x] + 3*a^2*b*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 6*a*b^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 3*b^3*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 3*a*b^2*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] - 3*b^3*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] + b^3*Log[c*(d*(e + f*x)^p)^q]^3*Log[g + h*x] + 3*a^2*b*p*q*Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] - 3*a*b^2*p^2*q^2*Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + b^3*p^3*q^3*Log[e + f*x]^3*Log[(f*(g + h*x))/(f*g - e*h)] + 6*a*b^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] - 3*b^3*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] + 3*b^3*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[(f*(g + h*x))/(f*g - e*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)] - 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)] + 6*b^3*p^3*q^3*PolyLog[4, (h*(e + f*x))/(-(f*g) + e*h)])/h","B",1
538,1,1350,410,0.5600734,"\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","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^3/((g + h*x)*(i + j*x)),x]","\frac{\log (g+h x) a^3-\log (i+j x) a^3-3 b p q \log (e+f x) \log (g+h x) a^2+3 b \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a^2+3 b p q \log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) a^2+3 b p q \log (e+f x) \log (i+j x) a^2-3 b \log \left(c \left(d (e+f x)^p\right)^q\right) \log (i+j x) a^2-3 b p q \log (e+f x) \log \left(\frac{f (i+j x)}{f i-e j}\right) a^2+3 b^2 p^2 q^2 \log ^2(e+f x) \log (g+h x) a+3 b^2 \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a-6 b^2 p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x) a-3 b^2 p^2 q^2 \log ^2(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right) a+6 b^2 p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right) a-3 b^2 p^2 q^2 \log ^2(e+f x) \log (i+j x) a-3 b^2 \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log (i+j x) a+6 b^2 p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log (i+j x) a+3 b^2 p^2 q^2 \log ^2(e+f x) \log \left(\frac{f (i+j x)}{f i-e j}\right) a-6 b^2 p q \log (e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (i+j x)}{f i-e j}\right) a-6 b^2 p^2 q^2 \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right) a+6 b^2 p^2 q^2 \text{Li}_3\left(\frac{j (e+f x)}{e j-f i}\right) a-b^3 p^3 q^3 \log ^3(e+f x) \log (g+h x)+b^3 \log ^3\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)-3 b^3 p q \log (e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)+3 b^3 p^2 q^2 \log ^2(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log (g+h x)+b^3 p^3 q^3 \log ^3(e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+3 b^3 p q \log (e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right)-3 b^3 p^2 q^2 \log ^2(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (g+h x)}{f g-e h}\right)+b^3 p^3 q^3 \log ^3(e+f x) \log (i+j x)-b^3 \log ^3\left(c \left(d (e+f x)^p\right)^q\right) \log (i+j x)+3 b^3 p q \log (e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log (i+j x)-3 b^3 p^2 q^2 \log ^2(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log (i+j x)-b^3 p^3 q^3 \log ^3(e+f x) \log \left(\frac{f (i+j x)}{f i-e j}\right)-3 b^3 p q \log (e+f x) \log ^2\left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (i+j x)}{f i-e j}\right)+3 b^3 p^2 q^2 \log ^2(e+f x) \log \left(c \left(d (e+f x)^p\right)^q\right) \log \left(\frac{f (i+j x)}{f i-e j}\right)+3 b p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)-3 b p q \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \text{Li}_2\left(\frac{j (e+f x)}{e j-f i}\right)-6 b^3 p^2 q^2 \log \left(c \left(d (e+f x)^p\right)^q\right) \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right)+6 b^3 p^2 q^2 \log \left(c \left(d (e+f x)^p\right)^q\right) \text{Li}_3\left(\frac{j (e+f x)}{e j-f i}\right)+6 b^3 p^3 q^3 \text{Li}_4\left(\frac{h (e+f x)}{e h-f g}\right)-6 b^3 p^3 q^3 \text{Li}_4\left(\frac{j (e+f x)}{e j-f i}\right)}{h i-g j}","-\frac{6 b^2 p^2 q^2 \text{Li}_3\left(-\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{Li}_3\left(-\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{Li}_2\left(-\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{Li}_2\left(-\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{\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^3 p^3 q^3 \text{Li}_4\left(-\frac{h (e+f x)}{f g-e h}\right)}{h i-g j}-\frac{6 b^3 p^3 q^3 \text{Li}_4\left(-\frac{j (e+f x)}{f i-e j}\right)}{h i-g j}",1,"(a^3*Log[g + h*x] - 3*a^2*b*p*q*Log[e + f*x]*Log[g + h*x] + 3*a*b^2*p^2*q^2*Log[e + f*x]^2*Log[g + h*x] - b^3*p^3*q^3*Log[e + f*x]^3*Log[g + h*x] + 3*a^2*b*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] - 6*a*b^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 3*b^3*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[g + h*x] + 3*a*b^2*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] - 3*b^3*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[g + h*x] + b^3*Log[c*(d*(e + f*x)^p)^q]^3*Log[g + h*x] + 3*a^2*b*p*q*Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] - 3*a*b^2*p^2*q^2*Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + b^3*p^3*q^3*Log[e + f*x]^3*Log[(f*(g + h*x))/(f*g - e*h)] + 6*a*b^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] - 3*b^3*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(g + h*x))/(f*g - e*h)] + 3*b^3*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[(f*(g + h*x))/(f*g - e*h)] - a^3*Log[i + j*x] + 3*a^2*b*p*q*Log[e + f*x]*Log[i + j*x] - 3*a*b^2*p^2*q^2*Log[e + f*x]^2*Log[i + j*x] + b^3*p^3*q^3*Log[e + f*x]^3*Log[i + j*x] - 3*a^2*b*Log[c*(d*(e + f*x)^p)^q]*Log[i + j*x] + 6*a*b^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[i + j*x] - 3*b^3*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[i + j*x] - 3*a*b^2*Log[c*(d*(e + f*x)^p)^q]^2*Log[i + j*x] + 3*b^3*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[i + j*x] - b^3*Log[c*(d*(e + f*x)^p)^q]^3*Log[i + j*x] - 3*a^2*b*p*q*Log[e + f*x]*Log[(f*(i + j*x))/(f*i - e*j)] + 3*a*b^2*p^2*q^2*Log[e + f*x]^2*Log[(f*(i + j*x))/(f*i - e*j)] - b^3*p^3*q^3*Log[e + f*x]^3*Log[(f*(i + j*x))/(f*i - e*j)] - 6*a*b^2*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(i + j*x))/(f*i - e*j)] + 3*b^3*p^2*q^2*Log[e + f*x]^2*Log[c*(d*(e + f*x)^p)^q]*Log[(f*(i + j*x))/(f*i - e*j)] - 3*b^3*p*q*Log[e + f*x]*Log[c*(d*(e + f*x)^p)^q]^2*Log[(f*(i + j*x))/(f*i - e*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)] - 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)] - 6*a*b^2*p^2*q^2*PolyLog[3, (h*(e + f*x))/(-(f*g) + e*h)] - 6*b^3*p^2*q^2*Log[c*(d*(e + f*x)^p)^q]*PolyLog[3, (h*(e + f*x))/(-(f*g) + e*h)] + 6*a*b^2*p^2*q^2*PolyLog[3, (j*(e + f*x))/(-(f*i) + e*j)] + 6*b^3*p^2*q^2*Log[c*(d*(e + f*x)^p)^q]*PolyLog[3, (j*(e + f*x))/(-(f*i) + e*j)] + 6*b^3*p^3*q^3*PolyLog[4, (h*(e + f*x))/(-(f*g) + e*h)] - 6*b^3*p^3*q^3*PolyLog[4, (j*(e + f*x))/(-(f*i) + e*j)])/(h*i - g*j)","B",1
539,1,1057,659,1.6870557,"\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","Integrate[(a + b*Log[c*(d*(e + f*x)^p)^q])^3/((g + h*x)*(i + j*x)^2),x]","\frac{-b^3 p^3 \left((h i-g j) \left(\left(j (e+f x) \log (e+f x)-3 f (i+j x) \log \left(\frac{f (i+j x)}{f i-e j}\right)\right) \log ^2(e+f x)-6 f (i+j x) \text{Li}_2\left(\frac{j (e+f x)}{e j-f i}\right) \log (e+f x)+6 f (i+j x) \text{Li}_3\left(\frac{j (e+f x)}{e j-f i}\right)\right)-h (f i-e j) (i+j x) \left(\log \left(\frac{f (g+h x)}{f g-e h}\right) \log ^3(e+f x)+3 \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right) \log ^2(e+f x)-6 \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right) \log (e+f x)+6 \text{Li}_4\left(\frac{h (e+f x)}{e h-f g}\right)\right)+h (f i-e j) (i+j x) \left(\log \left(\frac{f (i+j x)}{f i-e j}\right) \log ^3(e+f x)+3 \text{Li}_2\left(\frac{j (e+f x)}{e j-f i}\right) \log ^2(e+f x)-6 \text{Li}_3\left(\frac{j (e+f x)}{e j-f i}\right) \log (e+f x)+6 \text{Li}_4\left(\frac{j (e+f x)}{e j-f i}\right)\right)\right) q^3-3 b^2 p^2 \left(a-b p q \log (e+f x)+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right) \left((h i-g j) \left(\log (e+f x) \left(j (e+f x) \log (e+f x)-2 f (i+j x) \log \left(\frac{f (i+j x)}{f i-e j}\right)\right)-2 f (i+j x) \text{Li}_2\left(\frac{j (e+f x)}{e j-f i}\right)\right)-h (f i-e j) (i+j x) \left(\log \left(\frac{f (g+h x)}{f g-e h}\right) \log ^2(e+f x)+2 \text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right) \log (e+f x)-2 \text{Li}_3\left(\frac{h (e+f x)}{e h-f g}\right)\right)+h (f i-e j) (i+j x) \left(\log \left(\frac{f (i+j x)}{f i-e j}\right) \log ^2(e+f x)+2 \text{Li}_2\left(\frac{j (e+f x)}{e j-f i}\right) \log (e+f x)-2 \text{Li}_3\left(\frac{j (e+f x)}{e j-f i}\right)\right)\right) q^2-3 b p \left(a-b p q \log (e+f x)+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2 \left((h i-g j) (j (e+f x) \log (e+f x)-f (i+j x) \log (i+j x))-h (f i-e j) (i+j x) \left(\log (e+f x) \log \left(\frac{f (g+h x)}{f g-e h}\right)+\text{Li}_2\left(\frac{h (e+f x)}{e h-f g}\right)\right)+h (f i-e j) (i+j x) \left(\log (e+f x) \log \left(\frac{f (i+j x)}{f i-e j}\right)+\text{Li}_2\left(\frac{j (e+f x)}{e j-f i}\right)\right)\right) q+(f i-e j) (h i-g j) \left(a-b p q \log (e+f x)+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3+h (f i-e j) (i+j x) \left(a-b p q \log (e+f x)+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3 \log (g+h x)-h (f i-e j) (i+j x) \left(a-b p q \log (e+f x)+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^3 \log (i+j x)}{(f i-e j) (h i-g j)^2 (i+j x)}","\frac{6 b^2 f p^2 q^2 \text{Li}_2\left(-\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{Li}_3\left(-\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{Li}_3\left(-\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{Li}_2\left(-\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{Li}_2\left(-\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{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^3 f p^3 q^3 \text{Li}_3\left(-\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{Li}_4\left(-\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{Li}_4\left(-\frac{j (e+f x)}{f i-e j}\right)}{(h i-g j)^2}",1,"((f*i - e*j)*(h*i - g*j)*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^3 + h*(f*i - e*j)*(i + j*x)*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^3*Log[g + h*x] - h*(f*i - e*j)*(i + j*x)*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^3*Log[i + j*x] - 3*b*p*q*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])^2*((h*i - g*j)*(j*(e + f*x)*Log[e + f*x] - f*(i + j*x)*Log[i + j*x]) - h*(f*i - e*j)*(i + j*x)*(Log[e + f*x]*Log[(f*(g + h*x))/(f*g - e*h)] + PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)]) + h*(f*i - e*j)*(i + j*x)*(Log[e + f*x]*Log[(f*(i + j*x))/(f*i - e*j)] + PolyLog[2, (j*(e + f*x))/(-(f*i) + e*j)])) - 3*b^2*p^2*q^2*(a - b*p*q*Log[e + f*x] + b*Log[c*(d*(e + f*x)^p)^q])*((h*i - g*j)*(Log[e + f*x]*(j*(e + f*x)*Log[e + f*x] - 2*f*(i + j*x)*Log[(f*(i + j*x))/(f*i - e*j)]) - 2*f*(i + j*x)*PolyLog[2, (j*(e + f*x))/(-(f*i) + e*j)]) - h*(f*i - e*j)*(i + j*x)*(Log[e + f*x]^2*Log[(f*(g + h*x))/(f*g - e*h)] + 2*Log[e + f*x]*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)] - 2*PolyLog[3, (h*(e + f*x))/(-(f*g) + e*h)]) + h*(f*i - e*j)*(i + j*x)*(Log[e + f*x]^2*Log[(f*(i + j*x))/(f*i - e*j)] + 2*Log[e + f*x]*PolyLog[2, (j*(e + f*x))/(-(f*i) + e*j)] - 2*PolyLog[3, (j*(e + f*x))/(-(f*i) + e*j)])) - b^3*p^3*q^3*((h*i - g*j)*(Log[e + f*x]^2*(j*(e + f*x)*Log[e + f*x] - 3*f*(i + j*x)*Log[(f*(i + j*x))/(f*i - e*j)]) - 6*f*(i + j*x)*Log[e + f*x]*PolyLog[2, (j*(e + f*x))/(-(f*i) + e*j)] + 6*f*(i + j*x)*PolyLog[3, (j*(e + f*x))/(-(f*i) + e*j)]) - h*(f*i - e*j)*(i + j*x)*(Log[e + f*x]^3*Log[(f*(g + h*x))/(f*g - e*h)] + 3*Log[e + f*x]^2*PolyLog[2, (h*(e + f*x))/(-(f*g) + e*h)] - 6*Log[e + f*x]*PolyLog[3, (h*(e + f*x))/(-(f*g) + e*h)] + 6*PolyLog[4, (h*(e + f*x))/(-(f*g) + e*h)]) + h*(f*i - e*j)*(i + j*x)*(Log[e + f*x]^3*Log[(f*(i + j*x))/(f*i - e*j)] + 3*Log[e + f*x]^2*PolyLog[2, (j*(e + f*x))/(-(f*i) + e*j)] - 6*Log[e + f*x]*PolyLog[3, (j*(e + f*x))/(-(f*i) + e*j)] + 6*PolyLog[4, (j*(e + f*x))/(-(f*i) + e*j)])))/((f*i - e*j)*(h*i - g*j)^2*(i + j*x))","A",1
540,0,0,36,0.3405598,"\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","Integrate[(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,"Integrate[(i + j*x)/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])), x]","A",-1
541,0,0,31,0.0314828,"\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)} \, dx","Integrate[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,"Integrate[1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])), x]","A",-1
542,0,0,38,1.0664883,"\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","Integrate[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,"Integrate[1/((g + h*x)*(i + j*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])), x]","A",-1
543,0,0,38,4.268327,"\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","Integrate[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,"Integrate[1/((g + h*x)*(i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])), x]","A",-1
544,0,0,36,3.0736567,"\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","Integrate[(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,"Integrate[(i + j*x)/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2), x]","A",-1
545,0,0,31,0.183667,"\int \frac{1}{(g+h x) \left(a+b \log \left(c \left(d (e+f x)^p\right)^q\right)\right)^2} \, dx","Integrate[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,"Integrate[1/((g + h*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2), x]","A",-1
546,0,0,38,30.3988741,"\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","Integrate[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,"Integrate[1/((g + h*x)*(i + j*x)*(a + b*Log[c*(d*(e + f*x)^p)^q])^2), x]","A",-1
547,0,0,38,42.9625869,"\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","Integrate[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,"Integrate[1/((g + h*x)*(i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2), x]","A",-1