1,0,0,0,0.2467695,"\int \frac{\log ^{-1+q}\left(c x^n\right) \left(a x^m+b \log ^q\left(c x^n\right)\right)^p}{x} \, dx","Int[(Log[c*x^n]^(-1 + q)*(a*x^m + b*Log[c*x^n]^q)^p)/x,x]","\int \frac{\log ^{-1+q}\left(c x^n\right) \left(a x^m+b \log ^q\left(c x^n\right)\right)^p}{x} \, dx","\frac{\left(a x^m+b \log ^q\left(c x^n\right)\right)^{p+1}}{b n (p+1) q}-\frac{a m \text{Int}\left(x^{m-1} \left(a x^m+b \log ^q\left(c x^n\right)\right)^p,x\right)}{b n q}",0,"(a*x^m + b*Log[c*x^n]^q)^(1 + p)/(b*n*(1 + p)*q) - (a*m*Defer[Int][x^(-1 + m)*(a*x^m + b*Log[c*x^n]^q)^p, x])/(b*n*q)","A",0,0,0,0,-1,"{}"
2,1,231,0,0.3483532,"\int \frac{\log ^{-1+q}\left(c x^n\right) \left(a x^m+b \log ^q\left(c x^n\right)\right)^3}{x} \, dx","Int[(Log[c*x^n]^(-1 + q)*(a*x^m + b*Log[c*x^n]^q)^3)/x,x]","-\frac{3 a^2 b 4^{-q} x^{2 m} \left(c x^n\right)^{-\frac{2 m}{n}} \log ^{2 q}\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-2 q} \text{Gamma}\left(2 q,-\frac{2 m \log \left(c x^n\right)}{n}\right)}{n}-\frac{a^3 3^{-q} x^{3 m} \left(c x^n\right)^{-\frac{3 m}{n}} \log ^q\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-q} \text{Gamma}\left(q,-\frac{3 m \log \left(c x^n\right)}{n}\right)}{n}-\frac{3 a b^2 x^m \left(c x^n\right)^{-\frac{m}{n}} \log ^{3 q}\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-3 q} \text{Gamma}\left(3 q,-\frac{m \log \left(c x^n\right)}{n}\right)}{n}+\frac{b^3 \log ^{4 q}\left(c x^n\right)}{4 n q}","-\frac{3 a^2 b 4^{-q} x^{2 m} \left(c x^n\right)^{-\frac{2 m}{n}} \log ^{2 q}\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-2 q} \text{Gamma}\left(2 q,-\frac{2 m \log \left(c x^n\right)}{n}\right)}{n}-\frac{a^3 3^{-q} x^{3 m} \left(c x^n\right)^{-\frac{3 m}{n}} \log ^q\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-q} \text{Gamma}\left(q,-\frac{3 m \log \left(c x^n\right)}{n}\right)}{n}-\frac{3 a b^2 x^m \left(c x^n\right)^{-\frac{m}{n}} \log ^{3 q}\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-3 q} \text{Gamma}\left(3 q,-\frac{m \log \left(c x^n\right)}{n}\right)}{n}+\frac{b^3 \log ^{4 q}\left(c x^n\right)}{4 n q}",1,"(b^3*Log[c*x^n]^(4*q))/(4*n*q) - (3*a*b^2*x^m*Gamma[3*q, -((m*Log[c*x^n])/n)]*Log[c*x^n]^(3*q))/(n*(c*x^n)^(m/n)*(-((m*Log[c*x^n])/n))^(3*q)) - (3*a^2*b*x^(2*m)*Gamma[2*q, (-2*m*Log[c*x^n])/n]*Log[c*x^n]^(2*q))/(4^q*n*(c*x^n)^((2*m)/n)*(-((m*Log[c*x^n])/n))^(2*q)) - (a^3*x^(3*m)*Gamma[q, (-3*m*Log[c*x^n])/n]*Log[c*x^n]^q)/(3^q*n*(c*x^n)^((3*m)/n)*(-((m*Log[c*x^n])/n))^q)","A",10,5,32,0.1562,1,"{2539, 2310, 2181, 2302, 30}"
3,1,156,0,0.2736883,"\int \frac{\log ^{-1+q}\left(c x^n\right) \left(a x^m+b \log ^q\left(c x^n\right)\right)^2}{x} \, dx","Int[(Log[c*x^n]^(-1 + q)*(a*x^m + b*Log[c*x^n]^q)^2)/x,x]","-\frac{a^2 2^{-q} x^{2 m} \left(c x^n\right)^{-\frac{2 m}{n}} \log ^q\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-q} \text{Gamma}\left(q,-\frac{2 m \log \left(c x^n\right)}{n}\right)}{n}-\frac{2 a b x^m \left(c x^n\right)^{-\frac{m}{n}} \log ^{2 q}\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-2 q} \text{Gamma}\left(2 q,-\frac{m \log \left(c x^n\right)}{n}\right)}{n}+\frac{b^2 \log ^{3 q}\left(c x^n\right)}{3 n q}","-\frac{a^2 2^{-q} x^{2 m} \left(c x^n\right)^{-\frac{2 m}{n}} \log ^q\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-q} \text{Gamma}\left(q,-\frac{2 m \log \left(c x^n\right)}{n}\right)}{n}-\frac{2 a b x^m \left(c x^n\right)^{-\frac{m}{n}} \log ^{2 q}\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-2 q} \text{Gamma}\left(2 q,-\frac{m \log \left(c x^n\right)}{n}\right)}{n}+\frac{b^2 \log ^{3 q}\left(c x^n\right)}{3 n q}",1,"(b^2*Log[c*x^n]^(3*q))/(3*n*q) - (2*a*b*x^m*Gamma[2*q, -((m*Log[c*x^n])/n)]*Log[c*x^n]^(2*q))/(n*(c*x^n)^(m/n)*(-((m*Log[c*x^n])/n))^(2*q)) - (a^2*x^(2*m)*Gamma[q, (-2*m*Log[c*x^n])/n]*Log[c*x^n]^q)/(2^q*n*(c*x^n)^((2*m)/n)*(-((m*Log[c*x^n])/n))^q)","A",8,5,32,0.1562,1,"{2539, 2310, 2181, 2302, 30}"
4,1,81,0,0.1574631,"\int \frac{\log ^{-1+q}\left(c x^n\right) \left(a x^m+b \log ^q\left(c x^n\right)\right)}{x} \, dx","Int[(Log[c*x^n]^(-1 + q)*(a*x^m + b*Log[c*x^n]^q))/x,x]","\frac{b \log ^{2 q}\left(c x^n\right)}{2 n q}-\frac{a x^m \left(c x^n\right)^{-\frac{m}{n}} \log ^q\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-q} \text{Gamma}\left(q,-\frac{m \log \left(c x^n\right)}{n}\right)}{n}","\frac{b \log ^{2 q}\left(c x^n\right)}{2 n q}-\frac{a x^m \left(c x^n\right)^{-\frac{m}{n}} \log ^q\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-q} \text{Gamma}\left(q,-\frac{m \log \left(c x^n\right)}{n}\right)}{n}",1,"(b*Log[c*x^n]^(2*q))/(2*n*q) - (a*x^m*Gamma[q, -((m*Log[c*x^n])/n)]*Log[c*x^n]^q)/(n*(c*x^n)^(m/n)*(-((m*Log[c*x^n])/n))^q)","A",6,5,30,0.1667,1,"{2539, 2310, 2181, 2302, 30}"
5,1,15,0,0.0217537,"\int \frac{\log ^{-1+q}\left(c x^n\right)}{x} \, dx","Int[Log[c*x^n]^(-1 + q)/x,x]","\frac{\log ^q\left(c x^n\right)}{n q}","\frac{\log ^q\left(c x^n\right)}{n q}",1,"Log[c*x^n]^q/(n*q)","A",2,2,14,0.1429,1,"{2302, 30}"
6,0,0,0,0.2446734,"\int \frac{\log ^{-1+q}\left(c x^n\right)}{x \left(a x^m+b \log ^q\left(c x^n\right)\right)} \, dx","Int[Log[c*x^n]^(-1 + q)/(x*(a*x^m + b*Log[c*x^n]^q)),x]","\int \frac{\log ^{-1+q}\left(c x^n\right)}{x \left(a x^m+b \log ^q\left(c x^n\right)\right)} \, dx","\frac{\log \left(a x^m+b \log ^q\left(c x^n\right)\right)}{b n q}-\frac{a m \text{Int}\left(\frac{x^{m-1}}{a x^m+b \log ^q\left(c x^n\right)},x\right)}{b n q}",0,"Log[a*x^m + b*Log[c*x^n]^q]/(b*n*q) - (a*m*Defer[Int][x^(-1 + m)/(a*x^m + b*Log[c*x^n]^q), x])/(b*n*q)","A",0,0,0,0,-1,"{}"
7,0,0,0,0.2889233,"\int \frac{\log ^{-1+q}\left(c x^n\right)}{x \left(a x^m+b \log ^q\left(c x^n\right)\right)^2} \, dx","Int[Log[c*x^n]^(-1 + q)/(x*(a*x^m + b*Log[c*x^n]^q)^2),x]","\int \frac{\log ^{-1+q}\left(c x^n\right)}{x \left(a x^m+b \log ^q\left(c x^n\right)\right)^2} \, dx","-\frac{a m \text{Int}\left(\frac{x^{m-1}}{\left(a x^m+b \log ^q\left(c x^n\right)\right)^2},x\right)}{b n q}-\frac{1}{b n q \left(a x^m+b \log ^q\left(c x^n\right)\right)}",0,"-(1/(b*n*q*(a*x^m + b*Log[c*x^n]^q))) - (a*m*Defer[Int][x^(-1 + m)/(a*x^m + b*Log[c*x^n]^q)^2, x])/(b*n*q)","A",0,0,0,0,-1,"{}"
8,0,0,0,0.2451092,"\int \frac{\log ^{-1+q}\left(c x^n\right)}{x \left(a x^m+b \log ^q\left(c x^n\right)\right)^3} \, dx","Int[Log[c*x^n]^(-1 + q)/(x*(a*x^m + b*Log[c*x^n]^q)^3),x]","\int \frac{\log ^{-1+q}\left(c x^n\right)}{x \left(a x^m+b \log ^q\left(c x^n\right)\right)^3} \, dx","-\frac{a m \text{Int}\left(\frac{x^{m-1}}{\left(a x^m+b \log ^q\left(c x^n\right)\right)^3},x\right)}{b n q}-\frac{1}{2 b n q \left(a x^m+b \log ^q\left(c x^n\right)\right)^2}",0,"-1/(2*b*n*q*(a*x^m + b*Log[c*x^n]^q)^2) - (a*m*Defer[Int][x^(-1 + m)/(a*x^m + b*Log[c*x^n]^q)^3, x])/(b*n*q)","A",0,0,0,0,-1,"{}"
9,1,272,0,0.3050713,"\int \frac{\log \left(c x^n\right) \left(a x^m+b \log ^2\left(c x^n\right)\right)^3}{x} \, dx","Int[(Log[c*x^n]*(a*x^m + b*Log[c*x^n]^2)^3)/x,x]","\frac{9 a^2 b n^2 x^{2 m} \log \left(c x^n\right)}{4 m^3}-\frac{9 a^2 b n x^{2 m} \log ^2\left(c x^n\right)}{4 m^2}+\frac{3 a^2 b x^{2 m} \log ^3\left(c x^n\right)}{2 m}-\frac{9 a^2 b n^3 x^{2 m}}{8 m^4}+\frac{a^3 x^{3 m} \log \left(c x^n\right)}{3 m}-\frac{a^3 n x^{3 m}}{9 m^2}+\frac{60 a b^2 n^2 x^m \log ^3\left(c x^n\right)}{m^3}-\frac{180 a b^2 n^3 x^m \log ^2\left(c x^n\right)}{m^4}+\frac{360 a b^2 n^4 x^m \log \left(c x^n\right)}{m^5}-\frac{15 a b^2 n x^m \log ^4\left(c x^n\right)}{m^2}+\frac{3 a b^2 x^m \log ^5\left(c x^n\right)}{m}-\frac{360 a b^2 n^5 x^m}{m^6}+\frac{b^3 \log ^8\left(c x^n\right)}{8 n}","\frac{9 a^2 b n^2 x^{2 m} \log \left(c x^n\right)}{4 m^3}-\frac{9 a^2 b n x^{2 m} \log ^2\left(c x^n\right)}{4 m^2}+\frac{3 a^2 b x^{2 m} \log ^3\left(c x^n\right)}{2 m}-\frac{9 a^2 b n^3 x^{2 m}}{8 m^4}+\frac{a^3 x^{3 m} \log \left(c x^n\right)}{3 m}-\frac{a^3 n x^{3 m}}{9 m^2}+\frac{60 a b^2 n^2 x^m \log ^3\left(c x^n\right)}{m^3}-\frac{180 a b^2 n^3 x^m \log ^2\left(c x^n\right)}{m^4}+\frac{360 a b^2 n^4 x^m \log \left(c x^n\right)}{m^5}-\frac{15 a b^2 n x^m \log ^4\left(c x^n\right)}{m^2}+\frac{3 a b^2 x^m \log ^5\left(c x^n\right)}{m}-\frac{360 a b^2 n^5 x^m}{m^6}+\frac{b^3 \log ^8\left(c x^n\right)}{8 n}",1,"(-360*a*b^2*n^5*x^m)/m^6 - (9*a^2*b*n^3*x^(2*m))/(8*m^4) - (a^3*n*x^(3*m))/(9*m^2) + (360*a*b^2*n^4*x^m*Log[c*x^n])/m^5 + (9*a^2*b*n^2*x^(2*m)*Log[c*x^n])/(4*m^3) + (a^3*x^(3*m)*Log[c*x^n])/(3*m) - (180*a*b^2*n^3*x^m*Log[c*x^n]^2)/m^4 - (9*a^2*b*n*x^(2*m)*Log[c*x^n]^2)/(4*m^2) + (60*a*b^2*n^2*x^m*Log[c*x^n]^3)/m^3 + (3*a^2*b*x^(2*m)*Log[c*x^n]^3)/(2*m) - (15*a*b^2*n*x^m*Log[c*x^n]^4)/m^2 + (3*a*b^2*x^m*Log[c*x^n]^5)/m + (b^3*Log[c*x^n]^8)/(8*n)","A",13,5,28,0.1786,1,"{2539, 2304, 2305, 2302, 30}"
10,1,125,0,0.1658949,"\int \frac{\log \left(c x^n\right) \left(a x^m+b \log ^2\left(c x^n\right)\right)^2}{x} \, dx","Int[(Log[c*x^n]*(a*x^m + b*Log[c*x^n]^2)^2)/x,x]","\frac{a^2 x^{2 m} \log \left(c x^n\right)}{2 m}-\frac{a^2 n x^{2 m}}{4 m^2}+\frac{12 a b n^2 x^m \log \left(c x^n\right)}{m^3}-\frac{6 a b n x^m \log ^2\left(c x^n\right)}{m^2}+\frac{2 a b x^m \log ^3\left(c x^n\right)}{m}-\frac{12 a b n^3 x^m}{m^4}+\frac{b^2 \log ^6\left(c x^n\right)}{6 n}","\frac{a^2 x^{2 m} \log \left(c x^n\right)}{2 m}-\frac{a^2 n x^{2 m}}{4 m^2}+\frac{12 a b n^2 x^m \log \left(c x^n\right)}{m^3}-\frac{6 a b n x^m \log ^2\left(c x^n\right)}{m^2}+\frac{2 a b x^m \log ^3\left(c x^n\right)}{m}-\frac{12 a b n^3 x^m}{m^4}+\frac{b^2 \log ^6\left(c x^n\right)}{6 n}",1,"(-12*a*b*n^3*x^m)/m^4 - (a^2*n*x^(2*m))/(4*m^2) + (12*a*b*n^2*x^m*Log[c*x^n])/m^3 + (a^2*x^(2*m)*Log[c*x^n])/(2*m) - (6*a*b*n*x^m*Log[c*x^n]^2)/m^2 + (2*a*b*x^m*Log[c*x^n]^3)/m + (b^2*Log[c*x^n]^6)/(6*n)","A",8,5,28,0.1786,1,"{2539, 2304, 2305, 2302, 30}"
11,1,41,0,0.0771009,"\int \frac{\log \left(c x^n\right) \left(a x^m+b \log ^2\left(c x^n\right)\right)}{x} \, dx","Int[(Log[c*x^n]*(a*x^m + b*Log[c*x^n]^2))/x,x]","\frac{a x^m \log \left(c x^n\right)}{m}-\frac{a n x^m}{m^2}+\frac{b \log ^4\left(c x^n\right)}{4 n}","\frac{a x^m \log \left(c x^n\right)}{m}-\frac{a n x^m}{m^2}+\frac{b \log ^4\left(c x^n\right)}{4 n}",1,"-((a*n*x^m)/m^2) + (a*x^m*Log[c*x^n])/m + (b*Log[c*x^n]^4)/(4*n)","A",5,4,26,0.1538,1,"{2539, 2304, 2302, 30}"
12,1,15,0,0.0074127,"\int \frac{\log \left(c x^n\right)}{x} \, dx","Int[Log[c*x^n]/x,x]","\frac{\log ^2\left(c x^n\right)}{2 n}","\frac{\log ^2\left(c x^n\right)}{2 n}",1,"Log[c*x^n]^2/(2*n)","A",1,1,10,0.1000,1,"{2301}"
13,0,0,0,0.1917578,"\int \frac{\log \left(c x^n\right)}{x \left(a x^m+b \log ^2\left(c x^n\right)\right)} \, dx","Int[Log[c*x^n]/(x*(a*x^m + b*Log[c*x^n]^2)),x]","\int \frac{\log \left(c x^n\right)}{x \left(a x^m+b \log ^2\left(c x^n\right)\right)} \, dx","\frac{\log \left(a x^m+b \log ^2\left(c x^n\right)\right)}{2 b n}-\frac{a m \text{Int}\left(\frac{x^{m-1}}{a x^m+b \log ^2\left(c x^n\right)},x\right)}{2 b n}",0,"Log[a*x^m + b*Log[c*x^n]^2]/(2*b*n) - (a*m*Defer[Int][x^(-1 + m)/(a*x^m + b*Log[c*x^n]^2), x])/(2*b*n)","A",0,0,0,0,-1,"{}"
14,0,0,0,0.1964316,"\int \frac{\log \left(c x^n\right)}{x \left(a x^m+b \log ^2\left(c x^n\right)\right)^2} \, dx","Int[Log[c*x^n]/(x*(a*x^m + b*Log[c*x^n]^2)^2),x]","\int \frac{\log \left(c x^n\right)}{x \left(a x^m+b \log ^2\left(c x^n\right)\right)^2} \, dx","-\frac{a m \text{Int}\left(\frac{x^{m-1}}{\left(a x^m+b \log ^2\left(c x^n\right)\right)^2},x\right)}{2 b n}-\frac{1}{2 b n \left(a x^m+b \log ^2\left(c x^n\right)\right)}",0,"-1/(2*b*n*(a*x^m + b*Log[c*x^n]^2)) - (a*m*Defer[Int][x^(-1 + m)/(a*x^m + b*Log[c*x^n]^2)^2, x])/(2*b*n)","A",0,0,0,0,-1,"{}"
15,0,0,0,0.1774907,"\int \frac{\log \left(c x^n\right)}{x \left(a x^m+b \log ^2\left(c x^n\right)\right)^3} \, dx","Int[Log[c*x^n]/(x*(a*x^m + b*Log[c*x^n]^2)^3),x]","\int \frac{\log \left(c x^n\right)}{x \left(a x^m+b \log ^2\left(c x^n\right)\right)^3} \, dx","-\frac{a m \text{Int}\left(\frac{x^{m-1}}{\left(a x^m+b \log ^2\left(c x^n\right)\right)^3},x\right)}{2 b n}-\frac{1}{4 b n \left(a x^m+b \log ^2\left(c x^n\right)\right)^2}",0,"-1/(4*b*n*(a*x^m + b*Log[c*x^n]^2)^2) - (a*m*Defer[Int][x^(-1 + m)/(a*x^m + b*Log[c*x^n]^2)^3, x])/(2*b*n)","A",0,0,0,0,-1,"{}"
16,1,26,0,0.171346,"\int \frac{\left(a m x^m+b n q \log ^{-1+q}\left(c x^n\right)\right) \left(a x^m+b \log ^q\left(c x^n\right)\right)^p}{x} \, dx","Int[((a*m*x^m + b*n*q*Log[c*x^n]^(-1 + q))*(a*x^m + b*Log[c*x^n]^q)^p)/x,x]","\frac{\left(a x^m+b \log ^q\left(c x^n\right)\right)^{p+1}}{p+1}","\frac{\left(a x^m+b \log ^q\left(c x^n\right)\right)^{p+1}}{p+1}",1,"(a*x^m + b*Log[c*x^n]^q)^(1 + p)/(1 + p)","A",1,1,43,0.02326,1,"{2544}"
17,1,22,0,0.1727194,"\int \frac{\left(a m x^m+b n q \log ^{-1+q}\left(c x^n\right)\right) \left(a x^m+b \log ^q\left(c x^n\right)\right)^2}{x} \, dx","Int[((a*m*x^m + b*n*q*Log[c*x^n]^(-1 + q))*(a*x^m + b*Log[c*x^n]^q)^2)/x,x]","\frac{1}{3} \left(a x^m+b \log ^q\left(c x^n\right)\right)^3","\frac{1}{3} \left(a x^m+b \log ^q\left(c x^n\right)\right)^3",1,"(a*x^m + b*Log[c*x^n]^q)^3/3","A",1,1,43,0.02326,1,"{2544}"
18,1,22,0,0.1091308,"\int \frac{\left(a m x^m+b n q \log ^{-1+q}\left(c x^n\right)\right) \left(a x^m+b \log ^q\left(c x^n\right)\right)}{x} \, dx","Int[((a*m*x^m + b*n*q*Log[c*x^n]^(-1 + q))*(a*x^m + b*Log[c*x^n]^q))/x,x]","\frac{1}{2} \left(a x^m+b \log ^q\left(c x^n\right)\right)^2","\frac{1}{2} \left(a x^m+b \log ^q\left(c x^n\right)\right)^2",1,"(a*x^m + b*Log[c*x^n]^q)^2/2","A",1,1,41,0.02439,1,"{2544}"
19,1,16,0,0.034799,"\int \frac{a m x^m+b n q \log ^{-1+q}\left(c x^n\right)}{x} \, dx","Int[(a*m*x^m + b*n*q*Log[c*x^n]^(-1 + q))/x,x]","a x^m+b \log ^q\left(c x^n\right)","a x^m+b \log ^q\left(c x^n\right)",1,"a*x^m + b*Log[c*x^n]^q","A",4,3,25,0.1200,1,"{14, 2302, 30}"
20,1,17,0,0.1853798,"\int \frac{a m x^m+b n q \log ^{-1+q}\left(c x^n\right)}{x \left(a x^m+b \log ^q\left(c x^n\right)\right)} \, dx","Int[(a*m*x^m + b*n*q*Log[c*x^n]^(-1 + q))/(x*(a*x^m + b*Log[c*x^n]^q)),x]","\log \left(a x^m+b \log ^q\left(c x^n\right)\right)","\log \left(a x^m+b \log ^q\left(c x^n\right)\right)",1,"Log[a*x^m + b*Log[c*x^n]^q]","A",1,1,43,0.02326,1,"{2541}"
21,1,20,0,0.1819821,"\int \frac{a m x^m+b n q \log ^{-1+q}\left(c x^n\right)}{x \left(a x^m+b \log ^q\left(c x^n\right)\right)^2} \, dx","Int[(a*m*x^m + b*n*q*Log[c*x^n]^(-1 + q))/(x*(a*x^m + b*Log[c*x^n]^q)^2),x]","-\frac{1}{a x^m+b \log ^q\left(c x^n\right)}","-\frac{1}{a x^m+b \log ^q\left(c x^n\right)}",1,"-(a*x^m + b*Log[c*x^n]^q)^(-1)","A",1,1,43,0.02326,1,"{2544}"
22,1,22,0,0.1800282,"\int \frac{a m x^m+b n q \log ^{-1+q}\left(c x^n\right)}{x \left(a x^m+b \log ^q\left(c x^n\right)\right)^3} \, dx","Int[(a*m*x^m + b*n*q*Log[c*x^n]^(-1 + q))/(x*(a*x^m + b*Log[c*x^n]^q)^3),x]","-\frac{1}{2 \left(a x^m+b \log ^q\left(c x^n\right)\right)^2}","-\frac{1}{2 \left(a x^m+b \log ^q\left(c x^n\right)\right)^2}",1,"-1/(2*(a*x^m + b*Log[c*x^n]^q)^2)","A",1,1,43,0.02326,1,"{2544}"
23,1,20,0,0.1517531,"\int \left(\frac{a}{x^2}+\frac{2 b n \log \left(c x^n\right)}{x^3}\right) \left(a x^2+b x \log ^2\left(c x^n\right)\right)^2 \, dx","Int[(a/x^2 + (2*b*n*Log[c*x^n])/x^3)*(a*x^2 + b*x*Log[c*x^n]^2)^2,x]","\frac{1}{3} \left(a x+b \log ^2\left(c x^n\right)\right)^3","\frac{1}{3} \left(a x+b \log ^2\left(c x^n\right)\right)^3",1,"(a*x + b*Log[c*x^n]^2)^3/3","A",3,2,39,0.05128,1,"{2561, 2544}"
24,1,20,0,0.0929345,"\int \left(\frac{a}{x}+\frac{2 b n \log \left(c x^n\right)}{x^2}\right) \left(a x^2+b x \log ^2\left(c x^n\right)\right) \, dx","Int[(a/x + (2*b*n*Log[c*x^n])/x^2)*(a*x^2 + b*x*Log[c*x^n]^2),x]","\frac{1}{2} \left(a x+b \log ^2\left(c x^n\right)\right)^2","\frac{1}{2} \left(a x+b \log ^2\left(c x^n\right)\right)^2",1,"(a*x + b*Log[c*x^n]^2)^2/2","A",3,2,37,0.05405,1,"{2561, 2544}"
25,1,14,0,0.0092727,"\int \left(a+\frac{2 b n \log \left(c x^n\right)}{x}\right) \, dx","Int[a + (2*b*n*Log[c*x^n])/x,x]","a x+b \log ^2\left(c x^n\right)","a x+b \log ^2\left(c x^n\right)",1,"a*x + b*Log[c*x^n]^2","A",2,1,15,0.06667,1,"{2301}"
26,1,15,0,0.0820021,"\int \frac{a x+2 b n \log \left(c x^n\right)}{a x^2+b x \log ^2\left(c x^n\right)} \, dx","Int[(a*x + 2*b*n*Log[c*x^n])/(a*x^2 + b*x*Log[c*x^n]^2),x]","\log \left(a x+b \log ^2\left(c x^n\right)\right)","\log \left(a x+b \log ^2\left(c x^n\right)\right)",1,"Log[a*x + b*Log[c*x^n]^2]","A",2,2,34,0.05882,1,"{2561, 2541}"
27,1,18,0,0.1331332,"\int \frac{a x^2+2 b n x \log \left(c x^n\right)}{\left(a x^2+b x \log ^2\left(c x^n\right)\right)^2} \, dx","Int[(a*x^2 + 2*b*n*x*Log[c*x^n])/(a*x^2 + b*x*Log[c*x^n]^2)^2,x]","-\frac{1}{a x+b \log ^2\left(c x^n\right)}","-\frac{1}{a x+b \log ^2\left(c x^n\right)}",1,"-(a*x + b*Log[c*x^n]^2)^(-1)","A",3,2,37,0.05405,1,"{2561, 2544}"
28,1,20,0,0.1599824,"\int \frac{a x^3+2 b n x^2 \log \left(c x^n\right)}{\left(a x^2+b x \log ^2\left(c x^n\right)\right)^3} \, dx","Int[(a*x^3 + 2*b*n*x^2*Log[c*x^n])/(a*x^2 + b*x*Log[c*x^n]^2)^3,x]","-\frac{1}{2 \left(a x+b \log ^2\left(c x^n\right)\right)^2}","-\frac{1}{2 \left(a x+b \log ^2\left(c x^n\right)\right)^2}",1,"-1/(2*(a*x + b*Log[c*x^n]^2)^2)","A",3,2,39,0.05128,1,"{2561, 2544}"
29,1,19,0,0.3208463,"\int \frac{a (-1+m) x^{-1+m}+b n q \log ^{-1+q}\left(c x^n\right)}{a x^m+b x \log ^q\left(c x^n\right)} \, dx","Int[(a*(-1 + m)*x^(-1 + m) + b*n*q*Log[c*x^n]^(-1 + q))/(a*x^m + b*x*Log[c*x^n]^q),x]","\log \left(a x^{m-1}+b \log ^q\left(c x^n\right)\right)","\log \left(a x^{m-1}+b \log ^q\left(c x^n\right)\right)",1,"Log[a*x^(-1 + m) + b*Log[c*x^n]^q]","A",2,2,45,0.04444,1,"{2561, 2541}"
30,0,0,0,0.2306623,"\int \frac{\left(d x^m+e \log ^{-1+q}\left(c x^n\right)\right) \left(a x^m+b \log ^q\left(c x^n\right)\right)^p}{x} \, dx","Int[((d*x^m + e*Log[c*x^n]^(-1 + q))*(a*x^m + b*Log[c*x^n]^q)^p)/x,x]","\int \frac{\left(d x^m+e \log ^{-1+q}\left(c x^n\right)\right) \left(a x^m+b \log ^q\left(c x^n\right)\right)^p}{x} \, dx","\left(d-\frac{a e m}{b n q}\right) \text{Int}\left(x^{m-1} \left(a x^m+b \log ^q\left(c x^n\right)\right)^p,x\right)+\frac{e \left(a x^m+b \log ^q\left(c x^n\right)\right)^{p+1}}{b n (p+1) q}",0,"(e*(a*x^m + b*Log[c*x^n]^q)^(1 + p))/(b*n*(1 + p)*q) + (d - (a*e*m)/(b*n*q))*Defer[Int][x^(-1 + m)*(a*x^m + b*Log[c*x^n]^q)^p, x]","A",0,0,0,0,-1,"{}"
31,1,331,0,0.5037417,"\int \frac{\left(d x^m+e \log ^{-1+q}\left(c x^n\right)\right) \left(a x^m+b \log ^q\left(c x^n\right)\right)^3}{x} \, dx","Int[((d*x^m + e*Log[c*x^n]^(-1 + q))*(a*x^m + b*Log[c*x^n]^q)^3)/x,x]","-\frac{a^2 3^{-q} x^{3 m} \left(c x^n\right)^{-\frac{3 m}{n}} \log ^q\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-q} (a e m-b d n q) \text{Gamma}\left(q+1,-\frac{3 m \log \left(c x^n\right)}{n}\right)}{m n q}-\frac{b^2 x^m \left(c x^n\right)^{-\frac{m}{n}} \log ^{3 q}\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-3 q} (a e m-b d n q) \text{Gamma}\left(3 q+1,-\frac{m \log \left(c x^n\right)}{n}\right)}{m n q}-\frac{3 a b 2^{-2 q-1} x^{2 m} \left(c x^n\right)^{-\frac{2 m}{n}} \log ^{2 q}\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-2 q} (a e m-b d n q) \text{Gamma}\left(2 q+1,-\frac{2 m \log \left(c x^n\right)}{n}\right)}{m n q}-\frac{a^3 x^{4 m} (a e m-b d n q)}{4 b m n q}+\frac{e \left(a x^m+b \log ^q\left(c x^n\right)\right)^4}{4 b n q}","-\frac{a^2 3^{-q} x^{3 m} \left(c x^n\right)^{-\frac{3 m}{n}} \log ^q\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-q} (a e m-b d n q) \text{Gamma}\left(q+1,-\frac{3 m \log \left(c x^n\right)}{n}\right)}{m n q}-\frac{b^2 x^m \left(c x^n\right)^{-\frac{m}{n}} \log ^{3 q}\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-3 q} (a e m-b d n q) \text{Gamma}\left(3 q+1,-\frac{m \log \left(c x^n\right)}{n}\right)}{m n q}-\frac{3 a b 2^{-2 q-1} x^{2 m} \left(c x^n\right)^{-\frac{2 m}{n}} \log ^{2 q}\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-2 q} (a e m-b d n q) \text{Gamma}\left(2 q+1,-\frac{2 m \log \left(c x^n\right)}{n}\right)}{m n q}-\frac{a^3 x^{4 m} (a e m-b d n q)}{4 b m n q}+\frac{e \left(a x^m+b \log ^q\left(c x^n\right)\right)^4}{4 b n q}",1,"-(a^3*(a*e*m - b*d*n*q)*x^(4*m))/(4*b*m*n*q) - (b^2*(a*e*m - b*d*n*q)*x^m*Gamma[1 + 3*q, -((m*Log[c*x^n])/n)]*Log[c*x^n]^(3*q))/(m*n*q*(c*x^n)^(m/n)*(-((m*Log[c*x^n])/n))^(3*q)) - (3*2^(-1 - 2*q)*a*b*(a*e*m - b*d*n*q)*x^(2*m)*Gamma[1 + 2*q, (-2*m*Log[c*x^n])/n]*Log[c*x^n]^(2*q))/(m*n*q*(c*x^n)^((2*m)/n)*(-((m*Log[c*x^n])/n))^(2*q)) - (a^2*(a*e*m - b*d*n*q)*x^(3*m)*Gamma[1 + q, (-3*m*Log[c*x^n])/n]*Log[c*x^n]^q)/(3^q*m*n*q*(c*x^n)^((3*m)/n)*(-((m*Log[c*x^n])/n))^q) + (e*(a*x^m + b*Log[c*x^n]^q)^4)/(4*b*n*q)","A",9,4,40,0.1000,1,"{2545, 6742, 2310, 2181}"
32,1,235,0,0.395189,"\int \frac{\left(d x^m+e \log ^{-1+q}\left(c x^n\right)\right) \left(a x^m+b \log ^q\left(c x^n\right)\right)^2}{x} \, dx","Int[((d*x^m + e*Log[c*x^n]^(-1 + q))*(a*x^m + b*Log[c*x^n]^q)^2)/x,x]","-\frac{b x^m \left(c x^n\right)^{-\frac{m}{n}} \log ^{2 q}\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-2 q} (a e m-b d n q) \text{Gamma}\left(2 q+1,-\frac{m \log \left(c x^n\right)}{n}\right)}{m n q}-\frac{a 2^{-q} x^{2 m} \left(c x^n\right)^{-\frac{2 m}{n}} \log ^q\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-q} (a e m-b d n q) \text{Gamma}\left(q+1,-\frac{2 m \log \left(c x^n\right)}{n}\right)}{m n q}-\frac{a^2 x^{3 m} (a e m-b d n q)}{3 b m n q}+\frac{e \left(a x^m+b \log ^q\left(c x^n\right)\right)^3}{3 b n q}","-\frac{b x^m \left(c x^n\right)^{-\frac{m}{n}} \log ^{2 q}\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-2 q} (a e m-b d n q) \text{Gamma}\left(2 q+1,-\frac{m \log \left(c x^n\right)}{n}\right)}{m n q}-\frac{a 2^{-q} x^{2 m} \left(c x^n\right)^{-\frac{2 m}{n}} \log ^q\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-q} (a e m-b d n q) \text{Gamma}\left(q+1,-\frac{2 m \log \left(c x^n\right)}{n}\right)}{m n q}-\frac{a^2 x^{3 m} (a e m-b d n q)}{3 b m n q}+\frac{e \left(a x^m+b \log ^q\left(c x^n\right)\right)^3}{3 b n q}",1,"-(a^2*(a*e*m - b*d*n*q)*x^(3*m))/(3*b*m*n*q) - (b*(a*e*m - b*d*n*q)*x^m*Gamma[1 + 2*q, -((m*Log[c*x^n])/n)]*Log[c*x^n]^(2*q))/(m*n*q*(c*x^n)^(m/n)*(-((m*Log[c*x^n])/n))^(2*q)) - (a*(a*e*m - b*d*n*q)*x^(2*m)*Gamma[1 + q, (-2*m*Log[c*x^n])/n]*Log[c*x^n]^q)/(2^q*m*n*q*(c*x^n)^((2*m)/n)*(-((m*Log[c*x^n])/n))^q) + (e*(a*x^m + b*Log[c*x^n]^q)^3)/(3*b*n*q)","A",7,4,40,0.1000,1,"{2545, 6742, 2310, 2181}"
33,1,139,0,0.1709082,"\int \frac{\left(d x^m+e \log ^{-1+q}\left(c x^n\right)\right) \left(a x^m+b \log ^q\left(c x^n\right)\right)}{x} \, dx","Int[((d*x^m + e*Log[c*x^n]^(-1 + q))*(a*x^m + b*Log[c*x^n]^q))/x,x]","x^m \left(c x^n\right)^{-\frac{m}{n}} \log ^q\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-q} \left(\frac{b d}{m}-\frac{a e}{n q}\right) \text{Gamma}\left(q+1,-\frac{m \log \left(c x^n\right)}{n}\right)+\frac{e \left(a x^m+b \log ^q\left(c x^n\right)\right)^2}{2 b n q}-\frac{a x^{2 m} (a e m-b d n q)}{2 b m n q}","x^m \left(c x^n\right)^{-\frac{m}{n}} \log ^q\left(c x^n\right) \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-q} \left(\frac{b d}{m}-\frac{a e}{n q}\right) \text{Gamma}\left(q+1,-\frac{m \log \left(c x^n\right)}{n}\right)+\frac{e \left(a x^m+b \log ^q\left(c x^n\right)\right)^2}{2 b n q}-\frac{a x^{2 m} (a e m-b d n q)}{2 b m n q}",1,"-(a*(a*e*m - b*d*n*q)*x^(2*m))/(2*b*m*n*q) + (((b*d)/m - (a*e)/(n*q))*x^m*Gamma[1 + q, -((m*Log[c*x^n])/n)]*Log[c*x^n]^q)/((c*x^n)^(m/n)*(-((m*Log[c*x^n])/n))^q) + (e*(a*x^m + b*Log[c*x^n]^q)^2)/(2*b*n*q)","A",5,4,38,0.1053,1,"{2545, 14, 2310, 2181}"
34,1,25,0,0.0338121,"\int \frac{d x^m+e \log ^{-1+q}\left(c x^n\right)}{x} \, dx","Int[(d*x^m + e*Log[c*x^n]^(-1 + q))/x,x]","\frac{e \log ^q\left(c x^n\right)}{n q}+\frac{d x^m}{m}","\frac{e \log ^q\left(c x^n\right)}{n q}+\frac{d x^m}{m}",1,"(d*x^m)/m + (e*Log[c*x^n]^q)/(n*q)","A",4,3,22,0.1364,1,"{14, 2302, 30}"
35,0,0,0,0.2674189,"\int \frac{d x^m+e \log ^{-1+q}\left(c x^n\right)}{x \left(a x^m+b \log ^q\left(c x^n\right)\right)} \, dx","Int[(d*x^m + e*Log[c*x^n]^(-1 + q))/(x*(a*x^m + b*Log[c*x^n]^q)),x]","\int \frac{d x^m+e \log ^{-1+q}\left(c x^n\right)}{x \left(a x^m+b \log ^q\left(c x^n\right)\right)} \, dx","\left(d-\frac{a e m}{b n q}\right) \text{Int}\left(\frac{x^{m-1}}{a x^m+b \log ^q\left(c x^n\right)},x\right)+\frac{e \log \left(a x^m+b \log ^q\left(c x^n\right)\right)}{b n q}",0,"(e*Log[a*x^m + b*Log[c*x^n]^q])/(b*n*q) + (d - (a*e*m)/(b*n*q))*Defer[Int][x^(-1 + m)/(a*x^m + b*Log[c*x^n]^q), x]","A",0,0,0,0,-1,"{}"
36,0,0,0,0.282174,"\int \frac{d x^m+e \log ^{-1+q}\left(c x^n\right)}{x \left(a x^m+b \log ^q\left(c x^n\right)\right)^2} \, dx","Int[(d*x^m + e*Log[c*x^n]^(-1 + q))/(x*(a*x^m + b*Log[c*x^n]^q)^2),x]","\int \frac{d x^m+e \log ^{-1+q}\left(c x^n\right)}{x \left(a x^m+b \log ^q\left(c x^n\right)\right)^2} \, dx","\left(d-\frac{a e m}{b n q}\right) \text{Int}\left(\frac{x^{m-1}}{\left(a x^m+b \log ^q\left(c x^n\right)\right)^2},x\right)-\frac{e}{b n q \left(a x^m+b \log ^q\left(c x^n\right)\right)}",0,"-(e/(b*n*q*(a*x^m + b*Log[c*x^n]^q))) + (d - (a*e*m)/(b*n*q))*Defer[Int][x^(-1 + m)/(a*x^m + b*Log[c*x^n]^q)^2, x]","A",0,0,0,0,-1,"{}"
37,0,0,0,0.2492274,"\int \frac{d x^m+e \log ^{-1+q}\left(c x^n\right)}{x \left(a x^m+b \log ^q\left(c x^n\right)\right)^3} \, dx","Int[(d*x^m + e*Log[c*x^n]^(-1 + q))/(x*(a*x^m + b*Log[c*x^n]^q)^3),x]","\int \frac{d x^m+e \log ^{-1+q}\left(c x^n\right)}{x \left(a x^m+b \log ^q\left(c x^n\right)\right)^3} \, dx","\left(d-\frac{a e m}{b n q}\right) \text{Int}\left(\frac{x^{m-1}}{\left(a x^m+b \log ^q\left(c x^n\right)\right)^3},x\right)-\frac{e}{2 b n q \left(a x^m+b \log ^q\left(c x^n\right)\right)^2}",0,"-e/(2*b*n*q*(a*x^m + b*Log[c*x^n]^q)^2) + (d - (a*e*m)/(b*n*q))*Defer[Int][x^(-1 + m)/(a*x^m + b*Log[c*x^n]^q)^3, x]","A",0,0,0,0,-1,"{}"
38,1,26,0,0.2452212,"\int \frac{a d n x^m-a d m x^m \log \left(c x^n\right)-b d n (-1+q) \log ^q\left(c x^n\right)}{x \left(a x^m+b \log ^q\left(c x^n\right)\right)^2} \, dx","Int[(a*d*n*x^m - a*d*m*x^m*Log[c*x^n] - b*d*n*(-1 + q)*Log[c*x^n]^q)/(x*(a*x^m + b*Log[c*x^n]^q)^2),x]","\frac{d \log \left(c x^n\right)}{a x^m+b \log ^q\left(c x^n\right)}","\frac{d \log \left(c x^n\right)}{a x^m+b \log ^q\left(c x^n\right)}",1,"(d*Log[c*x^n])/(a*x^m + b*Log[c*x^n]^q)","A",1,1,60,0.01667,1,"{2546}"
39,0,0,0,0.1525686,"\int \frac{n q-\log \left(c x^n\right)}{\left(a x+b \log ^q\left(c x^n\right)\right)^2} \, dx","Int[(n*q - Log[c*x^n])/(a*x + b*Log[c*x^n]^q)^2,x]","\int \frac{n q-\log \left(c x^n\right)}{\left(a x+b \log ^q\left(c x^n\right)\right)^2} \, dx","\frac{\log \left(c x^n\right)}{a \left(a x+b \log ^q\left(c x^n\right)\right)}-\frac{n (1-q) \text{Int}\left(\frac{1}{x \left(a x+b \log ^q\left(c x^n\right)\right)},x\right)}{a}",0,"Log[c*x^n]/(a*(a*x + b*Log[c*x^n]^q)) - (n*(1 - q)*Defer[Int][1/(x*(a*x + b*Log[c*x^n]^q)), x])/a","A",0,0,0,0,-1,"{}"
40,1,49,0,0.099256,"\int \frac{\log \left(\frac{2 x \left(d \sqrt{-\frac{e}{d}}+e x\right)}{d+e x^2}\right)}{d+e x^2} \, dx","Int[Log[(2*x*(d*Sqrt[-(e/d)] + e*x))/(d + e*x^2)]/(d + e*x^2),x]","-\frac{\sqrt{-\frac{e}{d}} \text{PolyLog}\left(2,1-\frac{2 x \left(d \sqrt{-\frac{e}{d}}+e x\right)}{d+e x^2}\right)}{2 e}","-\frac{\sqrt{-\frac{e}{d}} \text{PolyLog}\left(2,1-\frac{2 x \left(d \sqrt{-\frac{e}{d}}+e x\right)}{d+e x^2}\right)}{2 e}",1,"-(Sqrt[-(e/d)]*PolyLog[2, 1 - (2*x*(d*Sqrt[-(e/d)] + e*x))/(d + e*x^2)])/(2*e)","A",1,1,39,0.02564,1,"{2447}"
41,1,50,0,0.0872988,"\int \frac{\log \left(-\frac{2 x \left(d \sqrt{-\frac{e}{d}}-e x\right)}{d+e x^2}\right)}{d+e x^2} \, dx","Int[Log[(-2*x*(d*Sqrt[-(e/d)] - e*x))/(d + e*x^2)]/(d + e*x^2),x]","\frac{\sqrt{-\frac{e}{d}} \text{PolyLog}\left(2,\frac{2 x \left(d \sqrt{-\frac{e}{d}}-e x\right)}{d+e x^2}+1\right)}{2 e}","\frac{\sqrt{-\frac{e}{d}} \text{PolyLog}\left(2,\frac{2 x \left(d \sqrt{-\frac{e}{d}}-e x\right)}{d+e x^2}+1\right)}{2 e}",1,"(Sqrt[-(e/d)]*PolyLog[2, 1 + (2*x*(d*Sqrt[-(e/d)] - e*x))/(d + e*x^2)])/(2*e)","A",1,1,40,0.02500,1,"{2447}"
42,1,53,0,0.0964644,"\int \frac{\log \left(\frac{2 x \left(\frac{d \sqrt{e}}{\sqrt{-d}}+e x\right)}{d+e x^2}\right)}{d+e x^2} \, dx","Int[Log[(2*x*((d*Sqrt[e])/Sqrt[-d] + e*x))/(d + e*x^2)]/(d + e*x^2),x]","-\frac{\text{PolyLog}\left(2,\frac{2 \sqrt{e} x \left(\sqrt{-d}-\sqrt{e} x\right)}{d+e x^2}+1\right)}{2 \sqrt{-d} \sqrt{e}}","-\frac{\text{PolyLog}\left(2,\frac{2 \sqrt{e} x \left(\sqrt{-d}-\sqrt{e} x\right)}{d+e x^2}+1\right)}{2 \sqrt{-d} \sqrt{e}}",1,"-PolyLog[2, 1 + (2*Sqrt[e]*x*(Sqrt[-d] - Sqrt[e]*x))/(d + e*x^2)]/(2*Sqrt[-d]*Sqrt[e])","A",1,1,41,0.02439,1,"{2447}"
43,1,52,0,0.0734183,"\int \frac{\log \left(-\frac{2 x \left(\frac{d \sqrt{e}}{\sqrt{-d}}-e x\right)}{d+e x^2}\right)}{d+e x^2} \, dx","Int[Log[(-2*x*((d*Sqrt[e])/Sqrt[-d] - e*x))/(d + e*x^2)]/(d + e*x^2),x]","\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{e} x \left(\sqrt{-d}+\sqrt{e} x\right)}{d+e x^2}\right)}{2 \sqrt{-d} \sqrt{e}}","\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{e} x \left(\sqrt{-d}+\sqrt{e} x\right)}{d+e x^2}\right)}{2 \sqrt{-d} \sqrt{e}}",1,"PolyLog[2, 1 - (2*Sqrt[e]*x*(Sqrt[-d] + Sqrt[e]*x))/(d + e*x^2)]/(2*Sqrt[-d]*Sqrt[e])","A",1,1,42,0.02381,1,"{2447}"
44,1,49,0,0.1021137,"\int \frac{\log \left(\frac{2 x \left(\sqrt{d} \sqrt{-e}+e x\right)}{d+e x^2}\right)}{d+e x^2} \, dx","Int[Log[(2*x*(Sqrt[d]*Sqrt[-e] + e*x))/(d + e*x^2)]/(d + e*x^2),x]","\frac{\text{PolyLog}\left(2,1-\frac{2 x \left(\sqrt{d} \sqrt{-e}+e x\right)}{d+e x^2}\right)}{2 \sqrt{d} \sqrt{-e}}","\frac{\text{PolyLog}\left(2,1-\frac{2 x \left(\sqrt{d} \sqrt{-e}+e x\right)}{d+e x^2}\right)}{2 \sqrt{d} \sqrt{-e}}",1,"PolyLog[2, 1 - (2*x*(Sqrt[d]*Sqrt[-e] + e*x))/(d + e*x^2)]/(2*Sqrt[d]*Sqrt[-e])","A",1,1,40,0.02500,1,"{2447}"
45,1,50,0,0.0783351,"\int \frac{\log \left(-\frac{2 x \left(\sqrt{d} \sqrt{-e}-e x\right)}{d+e x^2}\right)}{d+e x^2} \, dx","Int[Log[(-2*x*(Sqrt[d]*Sqrt[-e] - e*x))/(d + e*x^2)]/(d + e*x^2),x]","-\frac{\text{PolyLog}\left(2,\frac{2 x \left(\sqrt{d} \sqrt{-e}-e x\right)}{d+e x^2}+1\right)}{2 \sqrt{d} \sqrt{-e}}","-\frac{\text{PolyLog}\left(2,\frac{2 x \left(\sqrt{d} \sqrt{-e}-e x\right)}{d+e x^2}+1\right)}{2 \sqrt{d} \sqrt{-e}}",1,"-PolyLog[2, 1 + (2*x*(Sqrt[d]*Sqrt[-e] - e*x))/(d + e*x^2)]/(2*Sqrt[d]*Sqrt[-e])","A",1,1,41,0.02439,1,"{2447}"
46,1,67,0,0.0572072,"\int (e x)^m \left(a+b \log \left(c \log ^p(d x)\right)\right) \, dx","Int[(e*x)^m*(a + b*Log[c*Log[d*x]^p]),x]","\frac{(e x)^{m+1} \left(a+b \log \left(c \log ^p(d x)\right)\right)}{e (m+1)}-\frac{b p (d x)^{-m-1} (e x)^{m+1} \text{Ei}((m+1) \log (d x))}{e (m+1)}","\frac{(e x)^{m+1} \left(a+b \log \left(c \log ^p(d x)\right)\right)}{e (m+1)}-\frac{b p (d x)^{-m-1} (e x)^{m+1} \text{Ei}((m+1) \log (d x))}{e (m+1)}",1,"-((b*p*(d*x)^(-1 - m)*(e*x)^(1 + m)*ExpIntegralEi[(1 + m)*Log[d*x]])/(e*(1 + m))) + ((e*x)^(1 + m)*(a + b*Log[c*Log[d*x]^p]))/(e*(1 + m))","A",3,3,19,0.1579,1,"{2522, 2310, 2178}"
47,1,79,0,0.0608507,"\int (e x)^m \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)\right) \, dx","Int[(e*x)^m*(a + b*Log[c*Log[d*x^n]^p]),x]","\frac{(e x)^{m+1} \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)\right)}{e (m+1)}-\frac{b p (e x)^{m+1} \left(d x^n\right)^{-\frac{m+1}{n}} \text{Ei}\left(\frac{(m+1) \log \left(d x^n\right)}{n}\right)}{e (m+1)}","\frac{(e x)^{m+1} \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)\right)}{e (m+1)}-\frac{b p (e x)^{m+1} \left(d x^n\right)^{-\frac{m+1}{n}} \text{Ei}\left(\frac{(m+1) \log \left(d x^n\right)}{n}\right)}{e (m+1)}",1,"-((b*p*(e*x)^(1 + m)*ExpIntegralEi[((1 + m)*Log[d*x^n])/n])/(e*(1 + m)*(d*x^n)^((1 + m)/n))) + ((e*x)^(1 + m)*(a + b*Log[c*Log[d*x^n]^p]))/(e*(1 + m))","A",3,3,21,0.1429,1,"{2522, 2310, 2178}"
48,1,55,0,0.0487893,"\int x^2 \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)\right) \, dx","Int[x^2*(a + b*Log[c*Log[d*x^n]^p]),x]","\frac{1}{3} x^3 \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)\right)-\frac{1}{3} b p x^3 \left(d x^n\right)^{-3/n} \text{Ei}\left(\frac{3 \log \left(d x^n\right)}{n}\right)","\frac{1}{3} x^3 \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)\right)-\frac{1}{3} b p x^3 \left(d x^n\right)^{-3/n} \text{Ei}\left(\frac{3 \log \left(d x^n\right)}{n}\right)",1,"-(b*p*x^3*ExpIntegralEi[(3*Log[d*x^n])/n])/(3*(d*x^n)^(3/n)) + (x^3*(a + b*Log[c*Log[d*x^n]^p]))/3","A",3,3,19,0.1579,1,"{2522, 2310, 2178}"
49,1,55,0,0.0349517,"\int x \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)\right) \, dx","Int[x*(a + b*Log[c*Log[d*x^n]^p]),x]","\frac{1}{2} x^2 \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)\right)-\frac{1}{2} b p x^2 \left(d x^n\right)^{-2/n} \text{Ei}\left(\frac{2 \log \left(d x^n\right)}{n}\right)","\frac{1}{2} x^2 \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)\right)-\frac{1}{2} b p x^2 \left(d x^n\right)^{-2/n} \text{Ei}\left(\frac{2 \log \left(d x^n\right)}{n}\right)",1,"-(b*p*x^2*ExpIntegralEi[(2*Log[d*x^n])/n])/(2*(d*x^n)^(2/n)) + (x^2*(a + b*Log[c*Log[d*x^n]^p]))/2","A",3,3,17,0.1765,1,"{2522, 2310, 2178}"
50,1,45,0,0.0300297,"\int \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)\right) \, dx","Int[a + b*Log[c*Log[d*x^n]^p],x]","a x+b x \log \left(c \log ^p\left(d x^n\right)\right)-b p x \left(d x^n\right)^{-1/n} \text{Ei}\left(\frac{\log \left(d x^n\right)}{n}\right)","a x+b x \log \left(c \log ^p\left(d x^n\right)\right)-b p x \left(d x^n\right)^{-1/n} \text{Ei}\left(\frac{\log \left(d x^n\right)}{n}\right)",1,"a*x - (b*p*x*ExpIntegralEi[Log[d*x^n]/n])/(d*x^n)^n^(-1) + b*x*Log[c*Log[d*x^n]^p]","A",4,3,15,0.2000,1,"{2520, 2300, 2178}"
51,1,32,0,0.0171733,"\int \frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)}{x} \, dx","Int[(a + b*Log[c*Log[d*x^n]^p])/x,x]","\frac{\log \left(d x^n\right) \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)\right)}{n}-b p \log (x)","\frac{\log \left(d x^n\right) \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)\right)}{n}-b p \log (x)",1,"-(b*p*Log[x]) + (Log[d*x^n]*(a + b*Log[c*Log[d*x^n]^p]))/n","A",1,1,19,0.05263,1,"{2521}"
52,1,48,0,0.046958,"\int \frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)}{x^2} \, dx","Int[(a + b*Log[c*Log[d*x^n]^p])/x^2,x]","\frac{b p \left(d x^n\right)^{\frac{1}{n}} \text{Ei}\left(-\frac{\log \left(d x^n\right)}{n}\right)}{x}-\frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)}{x}","\frac{b p \left(d x^n\right)^{\frac{1}{n}} \text{Ei}\left(-\frac{\log \left(d x^n\right)}{n}\right)}{x}-\frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)}{x}",1,"(b*p*(d*x^n)^n^(-1)*ExpIntegralEi[-(Log[d*x^n]/n)])/x - (a + b*Log[c*Log[d*x^n]^p])/x","A",3,3,19,0.1579,1,"{2522, 2310, 2178}"
53,1,55,0,0.0462649,"\int \frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)}{x^3} \, dx","Int[(a + b*Log[c*Log[d*x^n]^p])/x^3,x]","\frac{b p \left(d x^n\right)^{2/n} \text{Ei}\left(-\frac{2 \log \left(d x^n\right)}{n}\right)}{2 x^2}-\frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)}{2 x^2}","\frac{b p \left(d x^n\right)^{2/n} \text{Ei}\left(-\frac{2 \log \left(d x^n\right)}{n}\right)}{2 x^2}-\frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)}{2 x^2}",1,"(b*p*(d*x^n)^(2/n)*ExpIntegralEi[(-2*Log[d*x^n])/n])/(2*x^2) - (a + b*Log[c*Log[d*x^n]^p])/(2*x^2)","A",3,3,19,0.1579,1,"{2522, 2310, 2178}"
54,1,55,0,0.0466476,"\int \frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)}{x^4} \, dx","Int[(a + b*Log[c*Log[d*x^n]^p])/x^4,x]","\frac{b p \left(d x^n\right)^{3/n} \text{Ei}\left(-\frac{3 \log \left(d x^n\right)}{n}\right)}{3 x^3}-\frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)}{3 x^3}","\frac{b p \left(d x^n\right)^{3/n} \text{Ei}\left(-\frac{3 \log \left(d x^n\right)}{n}\right)}{3 x^3}-\frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)}{3 x^3}",1,"(b*p*(d*x^n)^(3/n)*ExpIntegralEi[(-3*Log[d*x^n])/n])/(3*x^3) - (a + b*Log[c*Log[d*x^n]^p])/(3*x^3)","A",3,3,19,0.1579,1,"{2522, 2310, 2178}"
55,1,22,0,0.0067795,"\int \log \left(c \log ^p(d x)\right) \, dx","Int[Log[c*Log[d*x]^p],x]","x \log \left(c \log ^p(d x)\right)-\frac{p \text{li}(d x)}{d}","x \log \left(c \log ^p(d x)\right)-\frac{p \text{li}(d x)}{d}",1,"x*Log[c*Log[d*x]^p] - (p*LogIntegral[d*x])/d","A",2,2,9,0.2222,1,"{2520, 2298}"
56,1,20,0,0.0198224,"\int \frac{\log \left(c \log ^p(d x)\right)}{x} \, dx","Int[Log[c*Log[d*x]^p]/x,x]","\log (d x) \log \left(c \log ^p(d x)\right)-p \log (x)","\log (d x) \log \left(c \log ^p(d x)\right)-p \log (x)",1,"-(p*Log[x]) + Log[d*x]*Log[c*Log[d*x]^p]","A",1,1,13,0.07692,1,"{2521}"
57,1,40,0,0.0220154,"\int \log \left(c \log ^p\left(d x^n\right)\right) \, dx","Int[Log[c*Log[d*x^n]^p],x]","x \log \left(c \log ^p\left(d x^n\right)\right)-p x \left(d x^n\right)^{-1/n} \text{Ei}\left(\frac{\log \left(d x^n\right)}{n}\right)","x \log \left(c \log ^p\left(d x^n\right)\right)-p x \left(d x^n\right)^{-1/n} \text{Ei}\left(\frac{\log \left(d x^n\right)}{n}\right)",1,"-((p*x*ExpIntegralEi[Log[d*x^n]/n])/(d*x^n)^n^(-1)) + x*Log[c*Log[d*x^n]^p]","A",3,3,11,0.2727,1,"{2520, 2300, 2178}"
58,1,27,0,0.0211121,"\int \frac{\log \left(c \log ^p\left(d x^n\right)\right)}{x} \, dx","Int[Log[c*Log[d*x^n]^p]/x,x]","\frac{\log \left(d x^n\right) \log \left(c \log ^p\left(d x^n\right)\right)}{n}-p \log (x)","\frac{\log \left(d x^n\right) \log \left(c \log ^p\left(d x^n\right)\right)}{n}-p \log (x)",1,"-(p*Log[x]) + (Log[d*x^n]*Log[c*Log[d*x^n]^p])/n","A",1,1,15,0.06667,1,"{2521}"
59,1,66,0,0.059421,"\int x^m \log \left(d \left(b x+c x^2\right)^n\right) \, dx","Int[x^m*Log[d*(b*x + c*x^2)^n],x]","\frac{x^{m+1} \log \left(d \left(b x+c x^2\right)^n\right)}{m+1}+\frac{n x^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{c x}{b}\right)}{(m+1)^2}-\frac{2 n x^{m+1}}{(m+1)^2}","\frac{x^{m+1} \log \left(d \left(b x+c x^2\right)^n\right)}{m+1}+\frac{n x^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{c x}{b}\right)}{(m+1)^2}-\frac{2 n x^{m+1}}{(m+1)^2}",1,"(-2*n*x^(1 + m))/(1 + m)^2 + (n*x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((c*x)/b)])/(1 + m)^2 + (x^(1 + m)*Log[d*(b*x + c*x^2)^n])/(1 + m)","A",3,3,18,0.1667,1,"{2525, 80, 64}"
60,1,99,0,0.0731365,"\int x^4 \log \left(d \left(b x+c x^2\right)^n\right) \, dx","Int[x^4*Log[d*(b*x + c*x^2)^n],x]","\frac{b^3 n x^2}{10 c^3}-\frac{b^2 n x^3}{15 c^2}-\frac{b^4 n x}{5 c^4}+\frac{b^5 n \log (b+c x)}{5 c^5}+\frac{1}{5} x^5 \log \left(d \left(b x+c x^2\right)^n\right)+\frac{b n x^4}{20 c}-\frac{2 n x^5}{25}","\frac{b^3 n x^2}{10 c^3}-\frac{b^2 n x^3}{15 c^2}-\frac{b^4 n x}{5 c^4}+\frac{b^5 n \log (b+c x)}{5 c^5}+\frac{1}{5} x^5 \log \left(d \left(b x+c x^2\right)^n\right)+\frac{b n x^4}{20 c}-\frac{2 n x^5}{25}",1,"-(b^4*n*x)/(5*c^4) + (b^3*n*x^2)/(10*c^3) - (b^2*n*x^3)/(15*c^2) + (b*n*x^4)/(20*c) - (2*n*x^5)/25 + (b^5*n*Log[b + c*x])/(5*c^5) + (x^5*Log[d*(b*x + c*x^2)^n])/5","A",3,2,18,0.1111,1,"{2525, 77}"
61,1,85,0,0.0616151,"\int x^3 \log \left(d \left(b x+c x^2\right)^n\right) \, dx","Int[x^3*Log[d*(b*x + c*x^2)^n],x]","-\frac{b^2 n x^2}{8 c^2}+\frac{b^3 n x}{4 c^3}-\frac{b^4 n \log (b+c x)}{4 c^4}+\frac{1}{4} x^4 \log \left(d \left(b x+c x^2\right)^n\right)+\frac{b n x^3}{12 c}-\frac{n x^4}{8}","-\frac{b^2 n x^2}{8 c^2}+\frac{b^3 n x}{4 c^3}-\frac{b^4 n \log (b+c x)}{4 c^4}+\frac{1}{4} x^4 \log \left(d \left(b x+c x^2\right)^n\right)+\frac{b n x^3}{12 c}-\frac{n x^4}{8}",1,"(b^3*n*x)/(4*c^3) - (b^2*n*x^2)/(8*c^2) + (b*n*x^3)/(12*c) - (n*x^4)/8 - (b^4*n*Log[b + c*x])/(4*c^4) + (x^4*Log[d*(b*x + c*x^2)^n])/4","A",3,2,18,0.1111,1,"{2525, 77}"
62,1,71,0,0.0526,"\int x^2 \log \left(d \left(b x+c x^2\right)^n\right) \, dx","Int[x^2*Log[d*(b*x + c*x^2)^n],x]","-\frac{b^2 n x}{3 c^2}+\frac{b^3 n \log (b+c x)}{3 c^3}+\frac{1}{3} x^3 \log \left(d \left(b x+c x^2\right)^n\right)+\frac{b n x^2}{6 c}-\frac{2 n x^3}{9}","-\frac{b^2 n x}{3 c^2}+\frac{b^3 n \log (b+c x)}{3 c^3}+\frac{1}{3} x^3 \log \left(d \left(b x+c x^2\right)^n\right)+\frac{b n x^2}{6 c}-\frac{2 n x^3}{9}",1,"-(b^2*n*x)/(3*c^2) + (b*n*x^2)/(6*c) - (2*n*x^3)/9 + (b^3*n*Log[b + c*x])/(3*c^3) + (x^3*Log[d*(b*x + c*x^2)^n])/3","A",3,2,18,0.1111,1,"{2525, 77}"
63,1,57,0,0.040766,"\int x \log \left(d \left(b x+c x^2\right)^n\right) \, dx","Int[x*Log[d*(b*x + c*x^2)^n],x]","-\frac{b^2 n \log (b+c x)}{2 c^2}+\frac{1}{2} x^2 \log \left(d \left(b x+c x^2\right)^n\right)+\frac{b n x}{2 c}-\frac{n x^2}{2}","-\frac{b^2 n \log (b+c x)}{2 c^2}+\frac{1}{2} x^2 \log \left(d \left(b x+c x^2\right)^n\right)+\frac{b n x}{2 c}-\frac{n x^2}{2}",1,"(b*n*x)/(2*c) - (n*x^2)/2 - (b^2*n*Log[b + c*x])/(2*c^2) + (x^2*Log[d*(b*x + c*x^2)^n])/2","A",3,2,16,0.1250,1,"{2525, 77}"
64,1,33,0,0.0163603,"\int \log \left(d \left(b x+c x^2\right)^n\right) \, dx","Int[Log[d*(b*x + c*x^2)^n],x]","x \log \left(d \left(b x+c x^2\right)^n\right)+\frac{b n \log (b+c x)}{c}-2 n x","x \log \left(d \left(b x+c x^2\right)^n\right)+\frac{b n \log (b+c x)}{c}-2 n x",1,"-2*n*x + (b*n*Log[b + c*x])/c + x*Log[d*(b*x + c*x^2)^n]","A",3,2,14,0.1429,1,"{2523, 43}"
65,1,53,0,0.1257062,"\int \frac{\log \left(d \left(b x+c x^2\right)^n\right)}{x} \, dx","Int[Log[d*(b*x + c*x^2)^n]/x,x]","-n \text{PolyLog}\left(2,-\frac{c x}{b}\right)+\log (x) \log \left(d \left(b x+c x^2\right)^n\right)-n \log (x) \log \left(\frac{c x}{b}+1\right)-\frac{1}{2} n \log ^2(x)","-n \text{PolyLog}\left(2,-\frac{c x}{b}\right)+\log (x) \log \left(d \left(b x+c x^2\right)^n\right)-n \log (x) \log \left(\frac{c x}{b}+1\right)-\frac{1}{2} n \log ^2(x)",1,"-(n*Log[x]^2)/2 - n*Log[x]*Log[1 + (c*x)/b] + Log[x]*Log[d*(b*x + c*x^2)^n] - n*PolyLog[2, -((c*x)/b)]","A",7,6,18,0.3333,1,"{2524, 1593, 2357, 2301, 2317, 2391}"
66,1,47,0,0.0438773,"\int \frac{\log \left(d \left(b x+c x^2\right)^n\right)}{x^2} \, dx","Int[Log[d*(b*x + c*x^2)^n]/x^2,x]","-\frac{\log \left(d \left(b x+c x^2\right)^n\right)}{x}+\frac{c n \log (x)}{b}-\frac{c n \log (b+c x)}{b}-\frac{n}{x}","-\frac{\log \left(d \left(b x+c x^2\right)^n\right)}{x}+\frac{c n \log (x)}{b}-\frac{c n \log (b+c x)}{b}-\frac{n}{x}",1,"-(n/x) + (c*n*Log[x])/b - (c*n*Log[b + c*x])/b - Log[d*(b*x + c*x^2)^n]/x","A",3,2,18,0.1111,1,"{2525, 77}"
67,1,72,0,0.0497263,"\int \frac{\log \left(d \left(b x+c x^2\right)^n\right)}{x^3} \, dx","Int[Log[d*(b*x + c*x^2)^n]/x^3,x]","-\frac{c^2 n \log (x)}{2 b^2}+\frac{c^2 n \log (b+c x)}{2 b^2}-\frac{\log \left(d \left(b x+c x^2\right)^n\right)}{2 x^2}-\frac{c n}{2 b x}-\frac{n}{4 x^2}","-\frac{c^2 n \log (x)}{2 b^2}+\frac{c^2 n \log (b+c x)}{2 b^2}-\frac{\log \left(d \left(b x+c x^2\right)^n\right)}{2 x^2}-\frac{c n}{2 b x}-\frac{n}{4 x^2}",1,"-n/(4*x^2) - (c*n)/(2*b*x) - (c^2*n*Log[x])/(2*b^2) + (c^2*n*Log[b + c*x])/(2*b^2) - Log[d*(b*x + c*x^2)^n]/(2*x^2)","A",3,2,18,0.1111,1,"{2525, 77}"
68,1,86,0,0.0571364,"\int \frac{\log \left(d \left(b x+c x^2\right)^n\right)}{x^4} \, dx","Int[Log[d*(b*x + c*x^2)^n]/x^4,x]","\frac{c^2 n}{3 b^2 x}+\frac{c^3 n \log (x)}{3 b^3}-\frac{c^3 n \log (b+c x)}{3 b^3}-\frac{\log \left(d \left(b x+c x^2\right)^n\right)}{3 x^3}-\frac{c n}{6 b x^2}-\frac{n}{9 x^3}","\frac{c^2 n}{3 b^2 x}+\frac{c^3 n \log (x)}{3 b^3}-\frac{c^3 n \log (b+c x)}{3 b^3}-\frac{\log \left(d \left(b x+c x^2\right)^n\right)}{3 x^3}-\frac{c n}{6 b x^2}-\frac{n}{9 x^3}",1,"-n/(9*x^3) - (c*n)/(6*b*x^2) + (c^2*n)/(3*b^2*x) + (c^3*n*Log[x])/(3*b^3) - (c^3*n*Log[b + c*x])/(3*b^3) - Log[d*(b*x + c*x^2)^n]/(3*x^3)","A",3,2,18,0.1111,1,"{2525, 77}"
69,1,100,0,0.0632197,"\int \frac{\log \left(d \left(b x+c x^2\right)^n\right)}{x^5} \, dx","Int[Log[d*(b*x + c*x^2)^n]/x^5,x]","\frac{c^2 n}{8 b^2 x^2}-\frac{c^3 n}{4 b^3 x}-\frac{c^4 n \log (x)}{4 b^4}+\frac{c^4 n \log (b+c x)}{4 b^4}-\frac{\log \left(d \left(b x+c x^2\right)^n\right)}{4 x^4}-\frac{c n}{12 b x^3}-\frac{n}{16 x^4}","\frac{c^2 n}{8 b^2 x^2}-\frac{c^3 n}{4 b^3 x}-\frac{c^4 n \log (x)}{4 b^4}+\frac{c^4 n \log (b+c x)}{4 b^4}-\frac{\log \left(d \left(b x+c x^2\right)^n\right)}{4 x^4}-\frac{c n}{12 b x^3}-\frac{n}{16 x^4}",1,"-n/(16*x^4) - (c*n)/(12*b*x^3) + (c^2*n)/(8*b^2*x^2) - (c^3*n)/(4*b^3*x) - (c^4*n*Log[x])/(4*b^4) + (c^4*n*Log[b + c*x])/(4*b^4) - Log[d*(b*x + c*x^2)^n]/(4*x^4)","A",3,2,18,0.1111,1,"{2525, 77}"
70,1,157,0,0.2207723,"\int x^m \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Int[x^m*Log[d*(a + b*x + c*x^2)^n],x]","-\frac{2 c n x^{m+2} \, _2F_1\left(1,m+2;m+3;-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{(m+1) (m+2) \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 c n x^{m+2} \, _2F_1\left(1,m+2;m+3;-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{(m+1) (m+2) \left(\sqrt{b^2-4 a c}+b\right)}+\frac{x^{m+1} \log \left(d \left(a+b x+c x^2\right)^n\right)}{m+1}","-\frac{2 c n x^{m+2} \, _2F_1\left(1,m+2;m+3;-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{(m+1) (m+2) \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 c n x^{m+2} \, _2F_1\left(1,m+2;m+3;-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{(m+1) (m+2) \left(\sqrt{b^2-4 a c}+b\right)}+\frac{x^{m+1} \log \left(d \left(a+b x+c x^2\right)^n\right)}{m+1}",1,"(-2*c*n*x^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/((b - Sqrt[b^2 - 4*a*c])*(1 + m)*(2 + m)) - (2*c*n*x^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/((b + Sqrt[b^2 - 4*a*c])*(1 + m)*(2 + m)) + (x^(1 + m)*Log[d*(a + b*x + c*x^2)^n])/(1 + m)","A",5,3,19,0.1579,1,"{2525, 830, 64}"
71,1,207,0,0.2294865,"\int x^4 \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Int[x^4*Log[d*(a + b*x + c*x^2)^n],x]","\frac{b n \left(5 a^2 c^2-5 a b^2 c+b^4\right) \log \left(a+b x+c x^2\right)}{10 c^5}-\frac{n x \left(2 a^2 c^2-4 a b^2 c+b^4\right)}{5 c^4}+\frac{n \sqrt{b^2-4 a c} \left(a^2 c^2-3 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{5 c^5}-\frac{n x^3 \left(b^2-2 a c\right)}{15 c^2}+\frac{b n x^2 \left(b^2-3 a c\right)}{10 c^3}+\frac{1}{5} x^5 \log \left(d \left(a+b x+c x^2\right)^n\right)+\frac{b n x^4}{20 c}-\frac{2 n x^5}{25}","\frac{b n \left(5 a^2 c^2-5 a b^2 c+b^4\right) \log \left(a+b x+c x^2\right)}{10 c^5}-\frac{n x \left(2 a^2 c^2-4 a b^2 c+b^4\right)}{5 c^4}+\frac{n \sqrt{b^2-4 a c} \left(a^2 c^2-3 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{5 c^5}-\frac{n x^3 \left(b^2-2 a c\right)}{15 c^2}+\frac{b n x^2 \left(b^2-3 a c\right)}{10 c^3}+\frac{1}{5} x^5 \log \left(d \left(a+b x+c x^2\right)^n\right)+\frac{b n x^4}{20 c}-\frac{2 n x^5}{25}",1,"-((b^4 - 4*a*b^2*c + 2*a^2*c^2)*n*x)/(5*c^4) + (b*(b^2 - 3*a*c)*n*x^2)/(10*c^3) - ((b^2 - 2*a*c)*n*x^3)/(15*c^2) + (b*n*x^4)/(20*c) - (2*n*x^5)/25 + (Sqrt[b^2 - 4*a*c]*(b^4 - 3*a*b^2*c + a^2*c^2)*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(5*c^5) + (b*(b^4 - 5*a*b^2*c + 5*a^2*c^2)*n*Log[a + b*x + c*x^2])/(10*c^5) + (x^5*Log[d*(a + b*x + c*x^2)^n])/5","A",7,6,19,0.3158,1,"{2525, 800, 634, 618, 206, 628}"
72,1,167,0,0.1886719,"\int x^3 \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Int[x^3*Log[d*(a + b*x + c*x^2)^n],x]","-\frac{n \left(2 a^2 c^2-4 a b^2 c+b^4\right) \log \left(a+b x+c x^2\right)}{8 c^4}-\frac{n x^2 \left(b^2-2 a c\right)}{8 c^2}+\frac{b n x \left(b^2-3 a c\right)}{4 c^3}-\frac{b n \sqrt{b^2-4 a c} \left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{4 c^4}+\frac{1}{4} x^4 \log \left(d \left(a+b x+c x^2\right)^n\right)+\frac{b n x^3}{12 c}-\frac{n x^4}{8}","-\frac{n \left(2 a^2 c^2-4 a b^2 c+b^4\right) \log \left(a+b x+c x^2\right)}{8 c^4}-\frac{n x^2 \left(b^2-2 a c\right)}{8 c^2}+\frac{b n x \left(b^2-3 a c\right)}{4 c^3}-\frac{b n \sqrt{b^2-4 a c} \left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{4 c^4}+\frac{1}{4} x^4 \log \left(d \left(a+b x+c x^2\right)^n\right)+\frac{b n x^3}{12 c}-\frac{n x^4}{8}",1,"(b*(b^2 - 3*a*c)*n*x)/(4*c^3) - ((b^2 - 2*a*c)*n*x^2)/(8*c^2) + (b*n*x^3)/(12*c) - (n*x^4)/8 - (b*Sqrt[b^2 - 4*a*c]*(b^2 - 2*a*c)*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(4*c^4) - ((b^4 - 4*a*b^2*c + 2*a^2*c^2)*n*Log[a + b*x + c*x^2])/(8*c^4) + (x^4*Log[d*(a + b*x + c*x^2)^n])/4","A",7,6,19,0.3158,1,"{2525, 800, 634, 618, 206, 628}"
73,1,136,0,0.1490368,"\int x^2 \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Int[x^2*Log[d*(a + b*x + c*x^2)^n],x]","\frac{b n \left(b^2-3 a c\right) \log \left(a+b x+c x^2\right)}{6 c^3}-\frac{n x \left(b^2-2 a c\right)}{3 c^2}+\frac{n \sqrt{b^2-4 a c} \left(b^2-a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{3 c^3}+\frac{1}{3} x^3 \log \left(d \left(a+b x+c x^2\right)^n\right)+\frac{b n x^2}{6 c}-\frac{2 n x^3}{9}","\frac{b n \left(b^2-3 a c\right) \log \left(a+b x+c x^2\right)}{6 c^3}-\frac{n x \left(b^2-2 a c\right)}{3 c^2}+\frac{n \sqrt{b^2-4 a c} \left(b^2-a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{3 c^3}+\frac{1}{3} x^3 \log \left(d \left(a+b x+c x^2\right)^n\right)+\frac{b n x^2}{6 c}-\frac{2 n x^3}{9}",1,"-((b^2 - 2*a*c)*n*x)/(3*c^2) + (b*n*x^2)/(6*c) - (2*n*x^3)/9 + (Sqrt[b^2 - 4*a*c]*(b^2 - a*c)*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(3*c^3) + (b*(b^2 - 3*a*c)*n*Log[a + b*x + c*x^2])/(6*c^3) + (x^3*Log[d*(a + b*x + c*x^2)^n])/3","A",7,6,19,0.3158,1,"{2525, 800, 634, 618, 206, 628}"
74,1,109,0,0.1122371,"\int x \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Int[x*Log[d*(a + b*x + c*x^2)^n],x]","-\frac{n \left(b^2-2 a c\right) \log \left(a+b x+c x^2\right)}{4 c^2}-\frac{b n \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{2 c^2}+\frac{1}{2} x^2 \log \left(d \left(a+b x+c x^2\right)^n\right)+\frac{b n x}{2 c}-\frac{n x^2}{2}","-\frac{n \left(b^2-2 a c\right) \log \left(a+b x+c x^2\right)}{4 c^2}-\frac{b n \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{2 c^2}+\frac{1}{2} x^2 \log \left(d \left(a+b x+c x^2\right)^n\right)+\frac{b n x}{2 c}-\frac{n x^2}{2}",1,"(b*n*x)/(2*c) - (n*x^2)/2 - (b*Sqrt[b^2 - 4*a*c]*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(2*c^2) - ((b^2 - 2*a*c)*n*Log[a + b*x + c*x^2])/(4*c^2) + (x^2*Log[d*(a + b*x + c*x^2)^n])/2","A",7,6,17,0.3529,1,"{2525, 800, 634, 618, 206, 628}"
75,1,79,0,0.0607216,"\int \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Int[Log[d*(a + b*x + c*x^2)^n],x]","\frac{n \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c}+x \log \left(d \left(a+b x+c x^2\right)^n\right)+\frac{b n \log \left(a+b x+c x^2\right)}{2 c}-2 n x","\frac{n \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c}+x \log \left(d \left(a+b x+c x^2\right)^n\right)+\frac{b n \log \left(a+b x+c x^2\right)}{2 c}-2 n x",1,"-2*n*x + (Sqrt[b^2 - 4*a*c]*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/c + (b*n*Log[a + b*x + c*x^2])/(2*c) + x*Log[d*(a + b*x + c*x^2)^n]","A",6,6,15,0.4000,1,"{2523, 773, 634, 618, 206, 628}"
76,1,129,0,0.1759955,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{x} \, dx","Int[Log[d*(a + b*x + c*x^2)^n]/x,x]","-n \text{PolyLog}\left(2,-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)-n \text{PolyLog}\left(2,-\frac{2 c x}{\sqrt{b^2-4 a c}+b}\right)-n \log (x) \log \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)-n \log (x) \log \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)+\log (x) \log \left(d \left(a+b x+c x^2\right)^n\right)","-n \text{PolyLog}\left(2,-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)-n \text{PolyLog}\left(2,-\frac{2 c x}{\sqrt{b^2-4 a c}+b}\right)-n \log (x) \log \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)-n \log (x) \log \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)+\log (x) \log \left(d \left(a+b x+c x^2\right)^n\right)",1,"-(n*Log[x]*Log[1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c])]) - n*Log[x]*Log[1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c])] + Log[x]*Log[d*(a + b*x + c*x^2)^n] - n*PolyLog[2, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c])] - n*PolyLog[2, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])]","A",7,4,19,0.2105,1,"{2524, 2357, 2317, 2391}"
77,1,86,0,0.1132328,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{x^2} \, dx","Int[Log[d*(a + b*x + c*x^2)^n]/x^2,x]","\frac{n \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a}-\frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{x}-\frac{b n \log \left(a+b x+c x^2\right)}{2 a}+\frac{b n \log (x)}{a}","\frac{n \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a}-\frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{x}-\frac{b n \log \left(a+b x+c x^2\right)}{2 a}+\frac{b n \log (x)}{a}",1,"(Sqrt[b^2 - 4*a*c]*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/a + (b*n*Log[x])/a - (b*n*Log[a + b*x + c*x^2])/(2*a) - Log[d*(a + b*x + c*x^2)^n]/x","A",7,6,19,0.3158,1,"{2525, 800, 634, 618, 206, 628}"
78,1,121,0,0.1542165,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{x^3} \, dx","Int[Log[d*(a + b*x + c*x^2)^n]/x^3,x]","\frac{n \left(b^2-2 a c\right) \log \left(a+b x+c x^2\right)}{4 a^2}-\frac{n \log (x) \left(b^2-2 a c\right)}{2 a^2}-\frac{b n \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{2 a^2}-\frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{2 x^2}-\frac{b n}{2 a x}","\frac{n \left(b^2-2 a c\right) \log \left(a+b x+c x^2\right)}{4 a^2}-\frac{n \log (x) \left(b^2-2 a c\right)}{2 a^2}-\frac{b n \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{2 a^2}-\frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{2 x^2}-\frac{b n}{2 a x}",1,"-(b*n)/(2*a*x) - (b*Sqrt[b^2 - 4*a*c]*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(2*a^2) - ((b^2 - 2*a*c)*n*Log[x])/(2*a^2) + ((b^2 - 2*a*c)*n*Log[a + b*x + c*x^2])/(4*a^2) - Log[d*(a + b*x + c*x^2)^n]/(2*x^2)","A",7,6,19,0.3158,1,"{2525, 800, 634, 618, 206, 628}"
79,1,149,0,0.1997323,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{x^4} \, dx","Int[Log[d*(a + b*x + c*x^2)^n]/x^4,x]","-\frac{b n \left(b^2-3 a c\right) \log \left(a+b x+c x^2\right)}{6 a^3}+\frac{n \left(b^2-2 a c\right)}{3 a^2 x}+\frac{b n \log (x) \left(b^2-3 a c\right)}{3 a^3}+\frac{n \sqrt{b^2-4 a c} \left(b^2-a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{3 a^3}-\frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{3 x^3}-\frac{b n}{6 a x^2}","-\frac{b n \left(b^2-3 a c\right) \log \left(a+b x+c x^2\right)}{6 a^3}+\frac{n \left(b^2-2 a c\right)}{3 a^2 x}+\frac{b n \log (x) \left(b^2-3 a c\right)}{3 a^3}+\frac{n \sqrt{b^2-4 a c} \left(b^2-a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{3 a^3}-\frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{3 x^3}-\frac{b n}{6 a x^2}",1,"-(b*n)/(6*a*x^2) + ((b^2 - 2*a*c)*n)/(3*a^2*x) + (Sqrt[b^2 - 4*a*c]*(b^2 - a*c)*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(3*a^3) + (b*(b^2 - 3*a*c)*n*Log[x])/(3*a^3) - (b*(b^2 - 3*a*c)*n*Log[a + b*x + c*x^2])/(6*a^3) - Log[d*(a + b*x + c*x^2)^n]/(3*x^3)","A",7,6,19,0.3158,1,"{2525, 800, 634, 618, 206, 628}"
80,1,190,0,0.222803,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{x^5} \, dx","Int[Log[d*(a + b*x + c*x^2)^n]/x^5,x]","\frac{n \left(2 a^2 c^2-4 a b^2 c+b^4\right) \log \left(a+b x+c x^2\right)}{8 a^4}-\frac{n \log (x) \left(2 a^2 c^2-4 a b^2 c+b^4\right)}{4 a^4}+\frac{n \left(b^2-2 a c\right)}{8 a^2 x^2}-\frac{b n \left(b^2-3 a c\right)}{4 a^3 x}-\frac{b n \sqrt{b^2-4 a c} \left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{4 a^4}-\frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{4 x^4}-\frac{b n}{12 a x^3}","\frac{n \left(2 a^2 c^2-4 a b^2 c+b^4\right) \log \left(a+b x+c x^2\right)}{8 a^4}-\frac{n \log (x) \left(2 a^2 c^2-4 a b^2 c+b^4\right)}{4 a^4}+\frac{n \left(b^2-2 a c\right)}{8 a^2 x^2}-\frac{b n \left(b^2-3 a c\right)}{4 a^3 x}-\frac{b n \sqrt{b^2-4 a c} \left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{4 a^4}-\frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{4 x^4}-\frac{b n}{12 a x^3}",1,"-(b*n)/(12*a*x^3) + ((b^2 - 2*a*c)*n)/(8*a^2*x^2) - (b*(b^2 - 3*a*c)*n)/(4*a^3*x) - (b*Sqrt[b^2 - 4*a*c]*(b^2 - 2*a*c)*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(4*a^4) - ((b^4 - 4*a*b^2*c + 2*a^2*c^2)*n*Log[x])/(4*a^4) + ((b^4 - 4*a*b^2*c + 2*a^2*c^2)*n*Log[a + b*x + c*x^2])/(8*a^4) - Log[d*(a + b*x + c*x^2)^n]/(4*x^4)","A",7,6,19,0.3158,1,"{2525, 800, 634, 618, 206, 628}"
81,1,42,0,0.0263058,"\int \log \left(1+x+x^2\right) \, dx","Int[Log[1 + x + x^2],x]","x \log \left(x^2+x+1\right)+\frac{1}{2} \log \left(x^2+x+1\right)-2 x+\sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)","x \log \left(x^2+x+1\right)+\frac{1}{2} \log \left(x^2+x+1\right)-2 x+\sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"-2*x + Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] + Log[1 + x + x^2]/2 + x*Log[1 + x + x^2]","A",6,6,7,0.8571,1,"{2523, 773, 634, 618, 204, 628}"
82,1,485,0,2.0576756,"\int (d+e x)^4 \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Int[(d + e*x)^4*Log[d*(a + b*x + c*x^2)^n],x]","-\frac{n (2 c d-b e) \left(c^2 e^2 \left(5 a^2 e^2+10 a b d e+4 b^2 d^2\right)-b^2 c e^3 (5 a e+3 b d)-2 c^3 d^2 e (5 a e+b d)+b^4 e^4+c^4 d^4\right) \log \left(a+b x+c x^2\right)}{10 c^5 e}-\frac{n x \left(c^2 e^2 \left(2 a^2 e^2+15 a b d e+10 b^2 d^2\right)-b^2 c e^3 (4 a e+5 b d)-10 c^3 d^2 e (2 a e+b d)+b^4 e^4+10 c^4 d^4\right)}{5 c^4}+\frac{n \sqrt{b^2-4 a c} \left(c^2 e^2 \left(a^2 e^2+10 a b d e+10 b^2 d^2\right)-b^2 c e^3 (3 a e+5 b d)-10 c^3 d^2 e (a e+b d)+b^4 e^4+5 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{5 c^5}-\frac{e^2 n x^3 \left(-c e (2 a e+5 b d)+b^2 e^2+20 c^2 d^2\right)}{15 c^2}-\frac{e n x^2 \left(-10 c^2 d e (a e+b d)+b c e^2 (3 a e+5 b d)-b^3 e^3+20 c^3 d^3\right)}{10 c^3}+\frac{(d+e x)^5 \log \left(d \left(a+b x+c x^2\right)^n\right)}{5 e}-\frac{e^3 n x^4 (10 c d-b e)}{20 c}-\frac{2}{25} e^4 n x^5","-\frac{n (2 c d-b e) \left(c^2 e^2 \left(5 a^2 e^2+10 a b d e+4 b^2 d^2\right)-b^2 c e^3 (5 a e+3 b d)-2 c^3 d^2 e (5 a e+b d)+b^4 e^4+c^4 d^4\right) \log \left(a+b x+c x^2\right)}{10 c^5 e}-\frac{n x \left(c^2 e^2 \left(2 a^2 e^2+15 a b d e+10 b^2 d^2\right)-b^2 c e^3 (4 a e+5 b d)-10 c^3 d^2 e (2 a e+b d)+b^4 e^4+10 c^4 d^4\right)}{5 c^4}+\frac{n \sqrt{b^2-4 a c} \left(c^2 e^2 \left(a^2 e^2+10 a b d e+10 b^2 d^2\right)-b^2 c e^3 (3 a e+5 b d)-10 c^3 d^2 e (a e+b d)+b^4 e^4+5 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{5 c^5}-\frac{e^2 n x^3 \left(-c e (2 a e+5 b d)+b^2 e^2+20 c^2 d^2\right)}{15 c^2}-\frac{e n x^2 \left(-10 c^2 d e (a e+b d)+b c e^2 (3 a e+5 b d)-b^3 e^3+20 c^3 d^3\right)}{10 c^3}+\frac{(d+e x)^5 \log \left(d \left(a+b x+c x^2\right)^n\right)}{5 e}-\frac{e^3 n x^4 (10 c d-b e)}{20 c}-\frac{2}{25} e^4 n x^5",1,"-((10*c^4*d^4 + b^4*e^4 - 10*c^3*d^2*e*(b*d + 2*a*e) - b^2*c*e^3*(5*b*d + 4*a*e) + c^2*e^2*(10*b^2*d^2 + 15*a*b*d*e + 2*a^2*e^2))*n*x)/(5*c^4) - (e*(20*c^3*d^3 - b^3*e^3 - 10*c^2*d*e*(b*d + a*e) + b*c*e^2*(5*b*d + 3*a*e))*n*x^2)/(10*c^3) - (e^2*(20*c^2*d^2 + b^2*e^2 - c*e*(5*b*d + 2*a*e))*n*x^3)/(15*c^2) - (e^3*(10*c*d - b*e)*n*x^4)/(20*c) - (2*e^4*n*x^5)/25 + (Sqrt[b^2 - 4*a*c]*(5*c^4*d^4 + b^4*e^4 - 10*c^3*d^2*e*(b*d + a*e) - b^2*c*e^3*(5*b*d + 3*a*e) + c^2*e^2*(10*b^2*d^2 + 10*a*b*d*e + a^2*e^2))*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(5*c^5) - ((2*c*d - b*e)*(c^4*d^4 + b^4*e^4 - 2*c^3*d^2*e*(b*d + 5*a*e) - b^2*c*e^3*(3*b*d + 5*a*e) + c^2*e^2*(4*b^2*d^2 + 10*a*b*d*e + 5*a^2*e^2))*n*Log[a + b*x + c*x^2])/(10*c^5*e) + ((d + e*x)^5*Log[d*(a + b*x + c*x^2)^n])/(5*e)","A",7,6,23,0.2609,1,"{2525, 800, 634, 618, 206, 628}"
83,1,338,0,0.5158172,"\int (d+e x)^3 \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Int[(d + e*x)^3*Log[d*(a + b*x + c*x^2)^n],x]","-\frac{n \left(2 c^2 e^2 \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)-4 b^2 c e^3 (a e+b d)-4 c^3 d^2 e (3 a e+b d)+b^4 e^4+2 c^4 d^4\right) \log \left(a+b x+c x^2\right)}{8 c^4 e}-\frac{e n x^2 \left(-2 c e (a e+2 b d)+b^2 e^2+12 c^2 d^2\right)}{8 c^2}-\frac{n x \left(-2 c^2 d e (4 a e+3 b d)+b c e^2 (3 a e+4 b d)-b^3 e^3+8 c^3 d^3\right)}{4 c^3}+\frac{n \sqrt{b^2-4 a c} (2 c d-b e) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{4 c^4}+\frac{(d+e x)^4 \log \left(d \left(a+b x+c x^2\right)^n\right)}{4 e}-\frac{e^2 n x^3 (8 c d-b e)}{12 c}-\frac{1}{8} e^3 n x^4","-\frac{n \left(2 c^2 e^2 \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)-4 b^2 c e^3 (a e+b d)-4 c^3 d^2 e (3 a e+b d)+b^4 e^4+2 c^4 d^4\right) \log \left(a+b x+c x^2\right)}{8 c^4 e}-\frac{e n x^2 \left(-2 c e (a e+2 b d)+b^2 e^2+12 c^2 d^2\right)}{8 c^2}-\frac{n x \left(-2 c^2 d e (4 a e+3 b d)+b c e^2 (3 a e+4 b d)-b^3 e^3+8 c^3 d^3\right)}{4 c^3}+\frac{n \sqrt{b^2-4 a c} (2 c d-b e) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{4 c^4}+\frac{(d+e x)^4 \log \left(d \left(a+b x+c x^2\right)^n\right)}{4 e}-\frac{e^2 n x^3 (8 c d-b e)}{12 c}-\frac{1}{8} e^3 n x^4",1,"-((8*c^3*d^3 - b^3*e^3 + b*c*e^2*(4*b*d + 3*a*e) - 2*c^2*d*e*(3*b*d + 4*a*e))*n*x)/(4*c^3) - (e*(12*c^2*d^2 + b^2*e^2 - 2*c*e*(2*b*d + a*e))*n*x^2)/(8*c^2) - (e^2*(8*c*d - b*e)*n*x^3)/(12*c) - (e^3*n*x^4)/8 + (Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(4*c^4) - ((2*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(b*d + a*e) - 4*c^3*d^2*e*(b*d + 3*a*e) + 2*c^2*e^2*(3*b^2*d^2 + 6*a*b*d*e + a^2*e^2))*n*Log[a + b*x + c*x^2])/(8*c^4*e) + ((d + e*x)^4*Log[d*(a + b*x + c*x^2)^n])/(4*e)","A",7,6,23,0.2609,1,"{2525, 800, 634, 618, 206, 628}"
84,1,226,0,0.3190688,"\int (d+e x)^2 \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Int[(d + e*x)^2*Log[d*(a + b*x + c*x^2)^n],x]","-\frac{n (2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \log \left(a+b x+c x^2\right)}{6 c^3 e}-\frac{n x \left(-c e (2 a e+3 b d)+b^2 e^2+6 c^2 d^2\right)}{3 c^2}+\frac{n \sqrt{b^2-4 a c} \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{3 c^3}+\frac{(d+e x)^3 \log \left(d \left(a+b x+c x^2\right)^n\right)}{3 e}-\frac{e n x^2 (6 c d-b e)}{6 c}-\frac{2}{9} e^2 n x^3","-\frac{n (2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \log \left(a+b x+c x^2\right)}{6 c^3 e}-\frac{n x \left(-c e (2 a e+3 b d)+b^2 e^2+6 c^2 d^2\right)}{3 c^2}+\frac{n \sqrt{b^2-4 a c} \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{3 c^3}+\frac{(d+e x)^3 \log \left(d \left(a+b x+c x^2\right)^n\right)}{3 e}-\frac{e n x^2 (6 c d-b e)}{6 c}-\frac{2}{9} e^2 n x^3",1,"-((6*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + 2*a*e))*n*x)/(3*c^2) - (e*(6*c*d - b*e)*n*x^2)/(6*c) - (2*e^2*n*x^3)/9 + (Sqrt[b^2 - 4*a*c]*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e))*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(3*c^3) - ((2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*n*Log[a + b*x + c*x^2])/(6*c^3*e) + ((d + e*x)^3*Log[d*(a + b*x + c*x^2)^n])/(3*e)","A",7,6,23,0.2609,1,"{2525, 800, 634, 618, 206, 628}"
85,1,154,0,0.186291,"\int (d+e x) \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Int[(d + e*x)*Log[d*(a + b*x + c*x^2)^n],x]","-\frac{n \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{4 c^2 e}+\frac{n \sqrt{b^2-4 a c} (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{2 c^2}+\frac{(d+e x)^2 \log \left(d \left(a+b x+c x^2\right)^n\right)}{2 e}-\frac{1}{2} n x \left(4 d-\frac{b e}{c}\right)-\frac{1}{2} e n x^2","-\frac{n \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{4 c^2 e}+\frac{n \sqrt{b^2-4 a c} (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{2 c^2}+\frac{(d+e x)^2 \log \left(d \left(a+b x+c x^2\right)^n\right)}{2 e}-\frac{1}{2} n x \left(4 d-\frac{b e}{c}\right)-\frac{1}{2} e n x^2",1,"-((4*d - (b*e)/c)*n*x)/2 - (e*n*x^2)/2 + (Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(2*c^2) - ((2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*n*Log[a + b*x + c*x^2])/(4*c^2*e) + ((d + e*x)^2*Log[d*(a + b*x + c*x^2)^n])/(2*e)","A",7,6,21,0.2857,1,"{2525, 800, 634, 618, 206, 628}"
86,1,79,0,0.0617153,"\int \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Int[Log[d*(a + b*x + c*x^2)^n],x]","\frac{n \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c}+x \log \left(d \left(a+b x+c x^2\right)^n\right)+\frac{b n \log \left(a+b x+c x^2\right)}{2 c}-2 n x","\frac{n \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c}+x \log \left(d \left(a+b x+c x^2\right)^n\right)+\frac{b n \log \left(a+b x+c x^2\right)}{2 c}-2 n x",1,"-2*n*x + (Sqrt[b^2 - 4*a*c]*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/c + (b*n*Log[a + b*x + c*x^2])/(2*c) + x*Log[d*(a + b*x + c*x^2)^n]","A",6,6,15,0.4000,1,"{2523, 773, 634, 618, 206, 628}"
87,1,228,0,0.4118192,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{d+e x} \, dx","Int[Log[d*(a + b*x + c*x^2)^n]/(d + e*x),x]","-\frac{n \text{PolyLog}\left(2,\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)}{e}-\frac{n \text{PolyLog}\left(2,\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)}{e}-\frac{n \log (d+e x) \log \left(-\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)}{e}-\frac{n \log (d+e x) \log \left(-\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)}{e}+\frac{\log (d+e x) \log \left(d \left(a+b x+c x^2\right)^n\right)}{e}","-\frac{n \text{PolyLog}\left(2,\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)}{e}-\frac{n \text{PolyLog}\left(2,\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)}{e}-\frac{n \log (d+e x) \log \left(-\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)}{e}-\frac{n \log (d+e x) \log \left(-\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)}{e}+\frac{\log (d+e x) \log \left(d \left(a+b x+c x^2\right)^n\right)}{e}",1,"-((n*Log[-((e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e))]*Log[d + e*x])/e) - (n*Log[-((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e))]*Log[d + e*x])/e + (Log[d + e*x]*Log[d*(a + b*x + c*x^2)^n])/e - (n*PolyLog[2, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)])/e - (n*PolyLog[2, (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/e","A",9,5,23,0.2174,1,"{2524, 2418, 2394, 2393, 2391}"
88,1,165,0,0.245178,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{(d+e x)^2} \, dx","Int[Log[d*(a + b*x + c*x^2)^n]/(d + e*x)^2,x]","\frac{n \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a e^2-b d e+c d^2}+\frac{n (2 c d-b e) \log \left(a+b x+c x^2\right)}{2 e \left(a e^2-b d e+c d^2\right)}-\frac{n (2 c d-b e) \log (d+e x)}{e \left(a e^2-b d e+c d^2\right)}-\frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{e (d+e x)}","\frac{n \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a e^2-b d e+c d^2}+\frac{n (2 c d-b e) \log \left(a+b x+c x^2\right)}{2 e \left(a e^2-b d e+c d^2\right)}-\frac{n (2 c d-b e) \log (d+e x)}{e \left(a e^2-b d e+c d^2\right)}-\frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{e (d+e x)}",1,"(Sqrt[b^2 - 4*a*c]*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c*d^2 - b*d*e + a*e^2) - ((2*c*d - b*e)*n*Log[d + e*x])/(e*(c*d^2 - b*d*e + a*e^2)) + ((2*c*d - b*e)*n*Log[a + b*x + c*x^2])/(2*e*(c*d^2 - b*d*e + a*e^2)) - Log[d*(a + b*x + c*x^2)^n]/(e*(d + e*x))","A",7,6,23,0.2609,1,"{2525, 800, 634, 618, 206, 628}"
89,1,259,0,0.405627,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{(d+e x)^3} \, dx","Int[Log[d*(a + b*x + c*x^2)^n]/(d + e*x)^3,x]","\frac{n \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{4 e \left(a e^2-b d e+c d^2\right)^2}-\frac{n \log (d+e x) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right)}{2 e \left(a e^2-b d e+c d^2\right)^2}+\frac{n \sqrt{b^2-4 a c} (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{2 \left(a e^2-b d e+c d^2\right)^2}+\frac{n (2 c d-b e)}{2 e (d+e x) \left(a e^2-b d e+c d^2\right)}-\frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{2 e (d+e x)^2}","\frac{n \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{4 e \left(a e^2-b d e+c d^2\right)^2}-\frac{n \log (d+e x) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right)}{2 e \left(a e^2-b d e+c d^2\right)^2}+\frac{n \sqrt{b^2-4 a c} (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{2 \left(a e^2-b d e+c d^2\right)^2}+\frac{n (2 c d-b e)}{2 e (d+e x) \left(a e^2-b d e+c d^2\right)}-\frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{2 e (d+e x)^2}",1,"((2*c*d - b*e)*n)/(2*e*(c*d^2 - b*d*e + a*e^2)*(d + e*x)) + (Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(2*(c*d^2 - b*d*e + a*e^2)^2) - ((2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*n*Log[d + e*x])/(2*e*(c*d^2 - b*d*e + a*e^2)^2) + ((2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*n*Log[a + b*x + c*x^2])/(4*e*(c*d^2 - b*d*e + a*e^2)^2) - Log[d*(a + b*x + c*x^2)^n]/(2*e*(d + e*x)^2)","A",7,6,23,0.2609,1,"{2525, 800, 634, 618, 206, 628}"
90,1,356,0,0.6207568,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{(d+e x)^4} \, dx","Int[Log[d*(a + b*x + c*x^2)^n]/(d + e*x)^4,x]","\frac{n (2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \log \left(a+b x+c x^2\right)}{6 e \left(a e^2-b d e+c d^2\right)^3}+\frac{n \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right)}{3 e (d+e x) \left(a e^2-b d e+c d^2\right)^2}-\frac{n (2 c d-b e) \log (d+e x) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{3 e \left(a e^2-b d e+c d^2\right)^3}+\frac{n \sqrt{b^2-4 a c} \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{3 \left(a e^2-b d e+c d^2\right)^3}+\frac{n (2 c d-b e)}{6 e (d+e x)^2 \left(a e^2-b d e+c d^2\right)}-\frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{3 e (d+e x)^3}","\frac{n (2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \log \left(a+b x+c x^2\right)}{6 e \left(a e^2-b d e+c d^2\right)^3}+\frac{n \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right)}{3 e (d+e x) \left(a e^2-b d e+c d^2\right)^2}-\frac{n (2 c d-b e) \log (d+e x) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{3 e \left(a e^2-b d e+c d^2\right)^3}+\frac{n \sqrt{b^2-4 a c} \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{3 \left(a e^2-b d e+c d^2\right)^3}+\frac{n (2 c d-b e)}{6 e (d+e x)^2 \left(a e^2-b d e+c d^2\right)}-\frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{3 e (d+e x)^3}",1,"((2*c*d - b*e)*n)/(6*e*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) + ((2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*n)/(3*e*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) + (Sqrt[b^2 - 4*a*c]*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e))*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(3*(c*d^2 - b*d*e + a*e^2)^3) - ((2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*n*Log[d + e*x])/(3*e*(c*d^2 - b*d*e + a*e^2)^3) + ((2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*n*Log[a + b*x + c*x^2])/(6*e*(c*d^2 - b*d*e + a*e^2)^3) - Log[d*(a + b*x + c*x^2)^n]/(3*e*(d + e*x)^3)","A",7,6,23,0.2609,1,"{2525, 800, 634, 618, 206, 628}"
91,1,519,0,1.0055681,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{(d+e x)^5} \, dx","Int[Log[d*(a + b*x + c*x^2)^n]/(d + e*x)^5,x]","\frac{n \left(2 c^2 e^2 \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)-4 b^2 c e^3 (a e+b d)-4 c^3 d^2 e (3 a e+b d)+b^4 e^4+2 c^4 d^4\right) \log \left(a+b x+c x^2\right)}{8 e \left(a e^2-b d e+c d^2\right)^4}-\frac{n \log (d+e x) \left(2 c^2 e^2 \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)-4 b^2 c e^3 (a e+b d)-4 c^3 d^2 e (3 a e+b d)+b^4 e^4+2 c^4 d^4\right)}{4 e \left(a e^2-b d e+c d^2\right)^4}+\frac{n (2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{4 e (d+e x) \left(a e^2-b d e+c d^2\right)^3}+\frac{n \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right)}{8 e (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}+\frac{n \sqrt{b^2-4 a c} (2 c d-b e) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{4 \left(a e^2-b d e+c d^2\right)^4}+\frac{n (2 c d-b e)}{12 e (d+e x)^3 \left(a e^2-b d e+c d^2\right)}-\frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{4 e (d+e x)^4}","\frac{n \left(2 c^2 e^2 \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)-4 b^2 c e^3 (a e+b d)-4 c^3 d^2 e (3 a e+b d)+b^4 e^4+2 c^4 d^4\right) \log \left(a+b x+c x^2\right)}{8 e \left(a e^2-b d e+c d^2\right)^4}-\frac{n \log (d+e x) \left(2 c^2 e^2 \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)-4 b^2 c e^3 (a e+b d)-4 c^3 d^2 e (3 a e+b d)+b^4 e^4+2 c^4 d^4\right)}{4 e \left(a e^2-b d e+c d^2\right)^4}+\frac{n (2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{4 e (d+e x) \left(a e^2-b d e+c d^2\right)^3}+\frac{n \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right)}{8 e (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}+\frac{n \sqrt{b^2-4 a c} (2 c d-b e) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{4 \left(a e^2-b d e+c d^2\right)^4}+\frac{n (2 c d-b e)}{12 e (d+e x)^3 \left(a e^2-b d e+c d^2\right)}-\frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{4 e (d+e x)^4}",1,"((2*c*d - b*e)*n)/(12*e*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^3) + ((2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*n)/(8*e*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2) + ((2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*n)/(4*e*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)) + (Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(4*(c*d^2 - b*d*e + a*e^2)^4) - ((2*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(b*d + a*e) - 4*c^3*d^2*e*(b*d + 3*a*e) + 2*c^2*e^2*(3*b^2*d^2 + 6*a*b*d*e + a^2*e^2))*n*Log[d + e*x])/(4*e*(c*d^2 - b*d*e + a*e^2)^4) + ((2*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(b*d + a*e) - 4*c^3*d^2*e*(b*d + 3*a*e) + 2*c^2*e^2*(3*b^2*d^2 + 6*a*b*d*e + a^2*e^2))*n*Log[a + b*x + c*x^2])/(8*e*(c*d^2 - b*d*e + a*e^2)^4) - Log[d*(a + b*x + c*x^2)^n]/(4*e*(d + e*x)^4)","A",7,6,23,0.2609,1,"{2525, 800, 634, 618, 206, 628}"
92,1,175,0,0.1579019,"\int \frac{\log \left(d \left(a+c x^2\right)^n\right)}{a e+c e x^2} \, dx","Int[Log[d*(a + c*x^2)^n]/(a*e + c*e*x^2),x]","\frac{i n \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{c} x}\right)}{\sqrt{a} \sqrt{c} e}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \log \left(d \left(a+c x^2\right)^n\right)}{\sqrt{a} \sqrt{c} e}+\frac{i n \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)^2}{\sqrt{a} \sqrt{c} e}+\frac{2 n \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{c} x}\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c} e}","\frac{i n \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{c} x}\right)}{\sqrt{a} \sqrt{c} e}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \log \left(d \left(a+c x^2\right)^n\right)}{\sqrt{a} \sqrt{c} e}+\frac{i n \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)^2}{\sqrt{a} \sqrt{c} e}+\frac{2 n \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{c} x}\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c} e}",1,"(I*n*ArcTan[(Sqrt[c]*x)/Sqrt[a]]^2)/(Sqrt[a]*Sqrt[c]*e) + (2*n*ArcTan[(Sqrt[c]*x)/Sqrt[a]]*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[c]*x)])/(Sqrt[a]*Sqrt[c]*e) + (ArcTan[(Sqrt[c]*x)/Sqrt[a]]*Log[d*(a + c*x^2)^n])/(Sqrt[a]*Sqrt[c]*e) + (I*n*PolyLog[2, 1 - (2*Sqrt[a])/(Sqrt[a] + I*Sqrt[c]*x)])/(Sqrt[a]*Sqrt[c]*e)","A",6,7,25,0.2800,1,"{205, 2470, 12, 4920, 4854, 2402, 2315}"
93,1,258,0,0.3458189,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{a e+b e x+c e x^2} \, dx","Int[Log[d*(a + b*x + c*x^2)^n]/(a*e + b*e*x + c*e*x^2),x]","-\frac{2 n \text{PolyLog}\left(2,-\frac{\frac{2 c x}{\sqrt{b^2-4 a c}}+\frac{b}{\sqrt{b^2-4 a c}}+1}{-\frac{2 c x}{\sqrt{b^2-4 a c}}-\frac{b}{\sqrt{b^2-4 a c}}+1}\right)}{e \sqrt{b^2-4 a c}}-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \log \left(d \left(a+b x+c x^2\right)^n\right)}{e \sqrt{b^2-4 a c}}+\frac{2 n \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)^2}{e \sqrt{b^2-4 a c}}-\frac{4 n \log \left(\frac{2}{-\frac{2 c x}{\sqrt{b^2-4 a c}}-\frac{b}{\sqrt{b^2-4 a c}}+1}\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{e \sqrt{b^2-4 a c}}","-\frac{2 n \text{PolyLog}\left(2,-\frac{\frac{2 c x}{\sqrt{b^2-4 a c}}+\frac{b}{\sqrt{b^2-4 a c}}+1}{-\frac{2 c x}{\sqrt{b^2-4 a c}}-\frac{b}{\sqrt{b^2-4 a c}}+1}\right)}{e \sqrt{b^2-4 a c}}-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \log \left(d \left(a+b x+c x^2\right)^n\right)}{e \sqrt{b^2-4 a c}}+\frac{2 n \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)^2}{e \sqrt{b^2-4 a c}}-\frac{4 n \log \left(\frac{2}{-\frac{2 c x}{\sqrt{b^2-4 a c}}-\frac{b}{\sqrt{b^2-4 a c}}+1}\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{e \sqrt{b^2-4 a c}}",1,"(2*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]]^2)/(Sqrt[b^2 - 4*a*c]*e) - (4*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]]*Log[2/(1 - b/Sqrt[b^2 - 4*a*c] - (2*c*x)/Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*e) - (2*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]]*Log[d*(a + b*x + c*x^2)^n])/(Sqrt[b^2 - 4*a*c]*e) - (2*n*PolyLog[2, -((1 + b/Sqrt[b^2 - 4*a*c] + (2*c*x)/Sqrt[b^2 - 4*a*c])/(1 - b/Sqrt[b^2 - 4*a*c] - (2*c*x)/Sqrt[b^2 - 4*a*c]))])/(Sqrt[b^2 - 4*a*c]*e)","A",8,9,32,0.2812,1,"{618, 206, 2527, 12, 6121, 5984, 5918, 2402, 2315}"
94,1,762,0,1.4520209,"\int \frac{\log \left(g \left(a+b x+c x^2\right)^n\right)}{d+e x^2} \, dx","Int[Log[g*(a + b*x + c*x^2)^n]/(d + e*x^2),x]","-\frac{n \text{PolyLog}\left(2,\frac{2 c \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{e} \left(b-\sqrt{b^2-4 a c}\right)+2 c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{n \text{PolyLog}\left(2,\frac{2 c \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{e} \left(\sqrt{b^2-4 a c}+b\right)+2 c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{n \text{PolyLog}\left(2,\frac{2 c \left(\sqrt{-d}+\sqrt{e} x\right)}{2 c \sqrt{-d}-\sqrt{e} \left(b-\sqrt{b^2-4 a c}\right)}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{n \text{PolyLog}\left(2,\frac{2 c \left(\sqrt{-d}+\sqrt{e} x\right)}{2 c \sqrt{-d}-\sqrt{e} \left(\sqrt{b^2-4 a c}+b\right)}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{n \log \left(\sqrt{-d}-\sqrt{e} x\right) \log \left(\frac{\sqrt{e} \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{\sqrt{e} \left(b-\sqrt{b^2-4 a c}\right)+2 c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{n \log \left(\sqrt{-d}-\sqrt{e} x\right) \log \left(\frac{\sqrt{e} \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{\sqrt{e} \left(\sqrt{b^2-4 a c}+b\right)+2 c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{n \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(-\frac{\sqrt{e} \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{2 c \sqrt{-d}-\sqrt{e} \left(b-\sqrt{b^2-4 a c}\right)}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{n \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(-\frac{\sqrt{e} \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{2 c \sqrt{-d}-\sqrt{e} \left(\sqrt{b^2-4 a c}+b\right)}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\log \left(\sqrt{-d}-\sqrt{e} x\right) \log \left(g \left(a+b x+c x^2\right)^n\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(g \left(a+b x+c x^2\right)^n\right)}{2 \sqrt{-d} \sqrt{e}}","-\frac{n \text{PolyLog}\left(2,\frac{2 c \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{e} \left(b-\sqrt{b^2-4 a c}\right)+2 c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{n \text{PolyLog}\left(2,\frac{2 c \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{e} \left(\sqrt{b^2-4 a c}+b\right)+2 c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{n \text{PolyLog}\left(2,\frac{2 c \left(\sqrt{-d}+\sqrt{e} x\right)}{2 c \sqrt{-d}-\sqrt{e} \left(b-\sqrt{b^2-4 a c}\right)}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{n \text{PolyLog}\left(2,\frac{2 c \left(\sqrt{-d}+\sqrt{e} x\right)}{2 c \sqrt{-d}-\sqrt{e} \left(\sqrt{b^2-4 a c}+b\right)}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{n \log \left(\sqrt{-d}-\sqrt{e} x\right) \log \left(\frac{\sqrt{e} \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{\sqrt{e} \left(b-\sqrt{b^2-4 a c}\right)+2 c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{n \log \left(\sqrt{-d}-\sqrt{e} x\right) \log \left(\frac{\sqrt{e} \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{\sqrt{e} \left(\sqrt{b^2-4 a c}+b\right)+2 c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{n \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(-\frac{\sqrt{e} \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{2 c \sqrt{-d}-\sqrt{e} \left(b-\sqrt{b^2-4 a c}\right)}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{n \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(-\frac{\sqrt{e} \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{2 c \sqrt{-d}-\sqrt{e} \left(\sqrt{b^2-4 a c}+b\right)}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\log \left(\sqrt{-d}-\sqrt{e} x\right) \log \left(g \left(a+b x+c x^2\right)^n\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(g \left(a+b x+c x^2\right)^n\right)}{2 \sqrt{-d} \sqrt{e}}",1,"-(n*Log[(Sqrt[e]*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*Sqrt[-d] + (b - Sqrt[b^2 - 4*a*c])*Sqrt[e])]*Log[Sqrt[-d] - Sqrt[e]*x])/(2*Sqrt[-d]*Sqrt[e]) - (n*Log[(Sqrt[e]*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*Sqrt[-d] + (b + Sqrt[b^2 - 4*a*c])*Sqrt[e])]*Log[Sqrt[-d] - Sqrt[e]*x])/(2*Sqrt[-d]*Sqrt[e]) + (n*Log[-((Sqrt[e]*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*Sqrt[-d] - (b - Sqrt[b^2 - 4*a*c])*Sqrt[e]))]*Log[Sqrt[-d] + Sqrt[e]*x])/(2*Sqrt[-d]*Sqrt[e]) + (n*Log[-((Sqrt[e]*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*Sqrt[-d] - (b + Sqrt[b^2 - 4*a*c])*Sqrt[e]))]*Log[Sqrt[-d] + Sqrt[e]*x])/(2*Sqrt[-d]*Sqrt[e]) + (Log[Sqrt[-d] - Sqrt[e]*x]*Log[g*(a + b*x + c*x^2)^n])/(2*Sqrt[-d]*Sqrt[e]) - (Log[Sqrt[-d] + Sqrt[e]*x]*Log[g*(a + b*x + c*x^2)^n])/(2*Sqrt[-d]*Sqrt[e]) - (n*PolyLog[2, (2*c*(Sqrt[-d] - Sqrt[e]*x))/(2*c*Sqrt[-d] + (b - Sqrt[b^2 - 4*a*c])*Sqrt[e])])/(2*Sqrt[-d]*Sqrt[e]) - (n*PolyLog[2, (2*c*(Sqrt[-d] - Sqrt[e]*x))/(2*c*Sqrt[-d] + (b + Sqrt[b^2 - 4*a*c])*Sqrt[e])])/(2*Sqrt[-d]*Sqrt[e]) + (n*PolyLog[2, (2*c*(Sqrt[-d] + Sqrt[e]*x))/(2*c*Sqrt[-d] - (b - Sqrt[b^2 - 4*a*c])*Sqrt[e])])/(2*Sqrt[-d]*Sqrt[e]) + (n*PolyLog[2, (2*c*(Sqrt[-d] + Sqrt[e]*x))/(2*c*Sqrt[-d] - (b + Sqrt[b^2 - 4*a*c])*Sqrt[e])])/(2*Sqrt[-d]*Sqrt[e])","A",20,6,25,0.2400,1,"{2528, 2524, 2418, 2394, 2393, 2391}"
95,1,782,0,1.5144286,"\int \frac{\log \left(g \left(a+b x+c x^2\right)^n\right)}{d+e x+f x^2} \, dx","Int[Log[g*(a + b*x + c*x^2)^n]/(d + e*x + f*x^2),x]","-\frac{n \text{PolyLog}\left(2,-\frac{c \left(-\sqrt{e^2-4 d f}+e+2 f x\right)}{f \left(b-\sqrt{b^2-4 a c}\right)-c \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{n \text{PolyLog}\left(2,-\frac{c \left(-\sqrt{e^2-4 d f}+e+2 f x\right)}{f \left(\sqrt{b^2-4 a c}+b\right)-c \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{n \text{PolyLog}\left(2,-\frac{c \left(\sqrt{e^2-4 d f}+e+2 f x\right)}{f \left(b-\sqrt{b^2-4 a c}\right)-c \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{n \text{PolyLog}\left(2,-\frac{c \left(\sqrt{e^2-4 d f}+e+2 f x\right)}{f \left(\sqrt{b^2-4 a c}+b\right)-c \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{n \log \left(-\sqrt{e^2-4 d f}+e+2 f x\right) \log \left(-\frac{f \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{f \sqrt{b^2-4 a c}-b f-c \sqrt{e^2-4 d f}+c e}\right)}{\sqrt{e^2-4 d f}}-\frac{n \log \left(-\sqrt{e^2-4 d f}+e+2 f x\right) \log \left(\frac{f \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{f \left(\sqrt{b^2-4 a c}+b\right)-c \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{n \log \left(\sqrt{e^2-4 d f}+e+2 f x\right) \log \left(\frac{f \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{f \left(b-\sqrt{b^2-4 a c}\right)-c \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{n \log \left(\sqrt{e^2-4 d f}+e+2 f x\right) \log \left(\frac{f \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{f \left(\sqrt{b^2-4 a c}+b\right)-c \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{\log \left(-\sqrt{e^2-4 d f}+e+2 f x\right) \log \left(g \left(a+b x+c x^2\right)^n\right)}{\sqrt{e^2-4 d f}}-\frac{\log \left(\sqrt{e^2-4 d f}+e+2 f x\right) \log \left(g \left(a+b x+c x^2\right)^n\right)}{\sqrt{e^2-4 d f}}","-\frac{n \text{PolyLog}\left(2,-\frac{c \left(-\sqrt{e^2-4 d f}+e+2 f x\right)}{f \left(b-\sqrt{b^2-4 a c}\right)-c \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{n \text{PolyLog}\left(2,-\frac{c \left(-\sqrt{e^2-4 d f}+e+2 f x\right)}{f \left(\sqrt{b^2-4 a c}+b\right)-c \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{n \text{PolyLog}\left(2,-\frac{c \left(\sqrt{e^2-4 d f}+e+2 f x\right)}{f \left(b-\sqrt{b^2-4 a c}\right)-c \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{n \text{PolyLog}\left(2,-\frac{c \left(\sqrt{e^2-4 d f}+e+2 f x\right)}{f \left(\sqrt{b^2-4 a c}+b\right)-c \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{n \log \left(-\sqrt{e^2-4 d f}+e+2 f x\right) \log \left(-\frac{f \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{f \sqrt{b^2-4 a c}-b f-c \sqrt{e^2-4 d f}+c e}\right)}{\sqrt{e^2-4 d f}}-\frac{n \log \left(-\sqrt{e^2-4 d f}+e+2 f x\right) \log \left(\frac{f \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{f \left(\sqrt{b^2-4 a c}+b\right)-c \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{n \log \left(\sqrt{e^2-4 d f}+e+2 f x\right) \log \left(\frac{f \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{f \left(b-\sqrt{b^2-4 a c}\right)-c \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{n \log \left(\sqrt{e^2-4 d f}+e+2 f x\right) \log \left(\frac{f \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{f \left(\sqrt{b^2-4 a c}+b\right)-c \left(\sqrt{e^2-4 d f}+e\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{\log \left(-\sqrt{e^2-4 d f}+e+2 f x\right) \log \left(g \left(a+b x+c x^2\right)^n\right)}{\sqrt{e^2-4 d f}}-\frac{\log \left(\sqrt{e^2-4 d f}+e+2 f x\right) \log \left(g \left(a+b x+c x^2\right)^n\right)}{\sqrt{e^2-4 d f}}",1,"-((n*Log[-((f*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*e - b*f + Sqrt[b^2 - 4*a*c]*f - c*Sqrt[e^2 - 4*d*f]))]*Log[e - Sqrt[e^2 - 4*d*f] + 2*f*x])/Sqrt[e^2 - 4*d*f]) - (n*Log[(f*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((b + Sqrt[b^2 - 4*a*c])*f - c*(e - Sqrt[e^2 - 4*d*f]))]*Log[e - Sqrt[e^2 - 4*d*f] + 2*f*x])/Sqrt[e^2 - 4*d*f] + (n*Log[(f*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/((b - Sqrt[b^2 - 4*a*c])*f - c*(e + Sqrt[e^2 - 4*d*f]))]*Log[e + Sqrt[e^2 - 4*d*f] + 2*f*x])/Sqrt[e^2 - 4*d*f] + (n*Log[(f*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((b + Sqrt[b^2 - 4*a*c])*f - c*(e + Sqrt[e^2 - 4*d*f]))]*Log[e + Sqrt[e^2 - 4*d*f] + 2*f*x])/Sqrt[e^2 - 4*d*f] + (Log[e - Sqrt[e^2 - 4*d*f] + 2*f*x]*Log[g*(a + b*x + c*x^2)^n])/Sqrt[e^2 - 4*d*f] - (Log[e + Sqrt[e^2 - 4*d*f] + 2*f*x]*Log[g*(a + b*x + c*x^2)^n])/Sqrt[e^2 - 4*d*f] - (n*PolyLog[2, -((c*(e - Sqrt[e^2 - 4*d*f] + 2*f*x))/((b - Sqrt[b^2 - 4*a*c])*f - c*(e - Sqrt[e^2 - 4*d*f])))])/Sqrt[e^2 - 4*d*f] - (n*PolyLog[2, -((c*(e - Sqrt[e^2 - 4*d*f] + 2*f*x))/((b + Sqrt[b^2 - 4*a*c])*f - c*(e - Sqrt[e^2 - 4*d*f])))])/Sqrt[e^2 - 4*d*f] + (n*PolyLog[2, -((c*(e + Sqrt[e^2 - 4*d*f] + 2*f*x))/((b - Sqrt[b^2 - 4*a*c])*f - c*(e + Sqrt[e^2 - 4*d*f])))])/Sqrt[e^2 - 4*d*f] + (n*PolyLog[2, -((c*(e + Sqrt[e^2 - 4*d*f] + 2*f*x))/((b + Sqrt[b^2 - 4*a*c])*f - c*(e + Sqrt[e^2 - 4*d*f])))])/Sqrt[e^2 - 4*d*f]","A",20,6,28,0.2143,1,"{2528, 2524, 2418, 2394, 2393, 2391}"
96,1,144,0,0.2840027,"\int \log ^2\left(d \left(b x+c x^2\right)^n\right) \, dx","Int[Log[d*(b*x + c*x^2)^n]^2,x]","-\frac{2 b n^2 \text{PolyLog}\left(2,\frac{c x}{b}+1\right)}{c}+x \log ^2\left(d \left(b x+c x^2\right)^n\right)-4 n x \log \left(d \left(b x+c x^2\right)^n\right)+\frac{2 b n \log (b+c x) \log \left(d \left(b x+c x^2\right)^n\right)}{c}-\frac{b n^2 \log ^2(b+c x)}{c}-\frac{2 b n^2 \log \left(-\frac{c x}{b}\right) \log (b+c x)}{c}-\frac{4 b n^2 \log (b+c x)}{c}+8 n^2 x","-\frac{2 b n^2 \text{PolyLog}\left(2,\frac{c x}{b}+1\right)}{c}+x \log ^2\left(d \left(b x+c x^2\right)^n\right)-4 n x \log \left(d \left(b x+c x^2\right)^n\right)+\frac{2 b n \log (b+c x) \log \left(d \left(b x+c x^2\right)^n\right)}{c}-\frac{b n^2 \log ^2(b+c x)}{c}-\frac{2 b n^2 \log \left(-\frac{c x}{b}\right) \log (b+c x)}{c}-\frac{4 b n^2 \log (b+c x)}{c}+8 n^2 x",1,"8*n^2*x - (4*b*n^2*Log[b + c*x])/c - (2*b*n^2*Log[-((c*x)/b)]*Log[b + c*x])/c - (b*n^2*Log[b + c*x]^2)/c - 4*n*x*Log[d*(b*x + c*x^2)^n] + (2*b*n*Log[b + c*x]*Log[d*(b*x + c*x^2)^n])/c + x*Log[d*(b*x + c*x^2)^n]^2 - (2*b*n^2*PolyLog[2, 1 + (c*x)/b])/c","A",14,10,16,0.6250,1,"{2523, 2528, 43, 2524, 1593, 2418, 2394, 2315, 2390, 2301}"
97,1,587,0,0.9491041,"\int \log ^2\left(d \left(a+b x+c x^2\right)^n\right) \, dx","Int[Log[d*(a + b*x + c*x^2)^n]^2,x]","-\frac{n^2 \left(b-\sqrt{b^2-4 a c}\right) \text{PolyLog}\left(2,-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{2 \sqrt{b^2-4 a c}}\right)}{c}-\frac{n^2 \left(\sqrt{b^2-4 a c}+b\right) \text{PolyLog}\left(2,\frac{\sqrt{b^2-4 a c}+b+2 c x}{2 \sqrt{b^2-4 a c}}\right)}{c}+\frac{n \left(b-\sqrt{b^2-4 a c}\right) \log \left(-\sqrt{b^2-4 a c}+b+2 c x\right) \log \left(d \left(a+b x+c x^2\right)^n\right)}{c}+\frac{n \left(\sqrt{b^2-4 a c}+b\right) \log \left(\sqrt{b^2-4 a c}+b+2 c x\right) \log \left(d \left(a+b x+c x^2\right)^n\right)}{c}-\frac{n^2 \left(b-\sqrt{b^2-4 a c}\right) \log ^2\left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{2 c}-\frac{n^2 \left(\sqrt{b^2-4 a c}+b\right) \log ^2\left(\sqrt{b^2-4 a c}+b+2 c x\right)}{2 c}-\frac{n^2 \left(\sqrt{b^2-4 a c}+b\right) \log \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{2 \sqrt{b^2-4 a c}}\right) \log \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c}-\frac{n^2 \left(b-\sqrt{b^2-4 a c}\right) \log \left(-\sqrt{b^2-4 a c}+b+2 c x\right) \log \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{2 \sqrt{b^2-4 a c}}\right)}{c}-\frac{4 n^2 \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c}+x \log ^2\left(d \left(a+b x+c x^2\right)^n\right)-4 n x \log \left(d \left(a+b x+c x^2\right)^n\right)-\frac{2 b n^2 \log \left(a+b x+c x^2\right)}{c}+8 n^2 x","-\frac{n^2 \left(b-\sqrt{b^2-4 a c}\right) \text{PolyLog}\left(2,-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{2 \sqrt{b^2-4 a c}}\right)}{c}-\frac{n^2 \left(\sqrt{b^2-4 a c}+b\right) \text{PolyLog}\left(2,\frac{\sqrt{b^2-4 a c}+b+2 c x}{2 \sqrt{b^2-4 a c}}\right)}{c}+\frac{n \left(b-\sqrt{b^2-4 a c}\right) \log \left(-\sqrt{b^2-4 a c}+b+2 c x\right) \log \left(d \left(a+b x+c x^2\right)^n\right)}{c}+\frac{n \left(\sqrt{b^2-4 a c}+b\right) \log \left(\sqrt{b^2-4 a c}+b+2 c x\right) \log \left(d \left(a+b x+c x^2\right)^n\right)}{c}-\frac{n^2 \left(b-\sqrt{b^2-4 a c}\right) \log ^2\left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{2 c}-\frac{n^2 \left(\sqrt{b^2-4 a c}+b\right) \log ^2\left(\sqrt{b^2-4 a c}+b+2 c x\right)}{2 c}-\frac{n^2 \left(\sqrt{b^2-4 a c}+b\right) \log \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{2 \sqrt{b^2-4 a c}}\right) \log \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c}-\frac{n^2 \left(b-\sqrt{b^2-4 a c}\right) \log \left(-\sqrt{b^2-4 a c}+b+2 c x\right) \log \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{2 \sqrt{b^2-4 a c}}\right)}{c}-\frac{4 n^2 \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c}+x \log ^2\left(d \left(a+b x+c x^2\right)^n\right)-4 n x \log \left(d \left(a+b x+c x^2\right)^n\right)-\frac{2 b n^2 \log \left(a+b x+c x^2\right)}{c}+8 n^2 x",1,"8*n^2*x - (4*Sqrt[b^2 - 4*a*c]*n^2*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/c - ((b - Sqrt[b^2 - 4*a*c])*n^2*Log[b - Sqrt[b^2 - 4*a*c] + 2*c*x]^2)/(2*c) - ((b + Sqrt[b^2 - 4*a*c])*n^2*Log[-(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])]*Log[b + Sqrt[b^2 - 4*a*c] + 2*c*x])/c - ((b + Sqrt[b^2 - 4*a*c])*n^2*Log[b + Sqrt[b^2 - 4*a*c] + 2*c*x]^2)/(2*c) - ((b - Sqrt[b^2 - 4*a*c])*n^2*Log[b - Sqrt[b^2 - 4*a*c] + 2*c*x]*Log[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/c - (2*b*n^2*Log[a + b*x + c*x^2])/c - 4*n*x*Log[d*(a + b*x + c*x^2)^n] + ((b - Sqrt[b^2 - 4*a*c])*n*Log[b - Sqrt[b^2 - 4*a*c] + 2*c*x]*Log[d*(a + b*x + c*x^2)^n])/c + ((b + Sqrt[b^2 - 4*a*c])*n*Log[b + Sqrt[b^2 - 4*a*c] + 2*c*x]*Log[d*(a + b*x + c*x^2)^n])/c + x*Log[d*(a + b*x + c*x^2)^n]^2 - ((b - Sqrt[b^2 - 4*a*c])*n^2*PolyLog[2, -(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/c - ((b + Sqrt[b^2 - 4*a*c])*n^2*PolyLog[2, (b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/c","A",27,14,17,0.8235,1,"{2523, 2528, 773, 634, 618, 206, 628, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
98,1,311,0,0.4777894,"\int \frac{x^2 \log \left(1+x+x^2\right)}{2+3 x+x^2} \, dx","Int[(x^2*Log[1 + x + x^2])/(2 + 3*x + x^2),x]","-\text{PolyLog}\left(2,\frac{2 (x+1)}{1-i \sqrt{3}}\right)-\text{PolyLog}\left(2,\frac{2 (x+1)}{1+i \sqrt{3}}\right)+4 \text{PolyLog}\left(2,\frac{2 (x+2)}{3-i \sqrt{3}}\right)+4 \text{PolyLog}\left(2,\frac{2 (x+2)}{3+i \sqrt{3}}\right)+x \log \left(x^2+x+1\right)+\log (2 x+2) \log \left(x^2+x+1\right)-4 \log (2 x+4) \log \left(x^2+x+1\right)+\frac{1}{2} \log \left(x^2+x+1\right)-2 x-\log (2 x+2) \log \left(-\frac{2 x-i \sqrt{3}+1}{1+i \sqrt{3}}\right)+4 \log (2 x+4) \log \left(-\frac{2 x-i \sqrt{3}+1}{3+i \sqrt{3}}\right)-\log (2 x+2) \log \left(-\frac{2 x+i \sqrt{3}+1}{1-i \sqrt{3}}\right)+4 \log (2 x+4) \log \left(-\frac{2 x+i \sqrt{3}+1}{3-i \sqrt{3}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)","-\text{PolyLog}\left(2,\frac{2 (x+1)}{1-i \sqrt{3}}\right)-\text{PolyLog}\left(2,\frac{2 (x+1)}{1+i \sqrt{3}}\right)+4 \text{PolyLog}\left(2,\frac{2 (x+2)}{3-i \sqrt{3}}\right)+4 \text{PolyLog}\left(2,\frac{2 (x+2)}{3+i \sqrt{3}}\right)+x \log \left(x^2+x+1\right)+\log (2 x+2) \log \left(x^2+x+1\right)-4 \log (2 x+4) \log \left(x^2+x+1\right)+\frac{1}{2} \log \left(x^2+x+1\right)-2 x-\log (2 x+2) \log \left(-\frac{2 x-i \sqrt{3}+1}{1+i \sqrt{3}}\right)+4 \log (2 x+4) \log \left(-\frac{2 x-i \sqrt{3}+1}{3+i \sqrt{3}}\right)-\log (2 x+2) \log \left(-\frac{2 x+i \sqrt{3}+1}{1-i \sqrt{3}}\right)+4 \log (2 x+4) \log \left(-\frac{2 x+i \sqrt{3}+1}{3-i \sqrt{3}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"-2*x + Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - Log[2 + 2*x]*Log[-((1 - I*Sqrt[3] + 2*x)/(1 + I*Sqrt[3]))] + 4*Log[4 + 2*x]*Log[-((1 - I*Sqrt[3] + 2*x)/(3 + I*Sqrt[3]))] - Log[2 + 2*x]*Log[-((1 + I*Sqrt[3] + 2*x)/(1 - I*Sqrt[3]))] + 4*Log[4 + 2*x]*Log[-((1 + I*Sqrt[3] + 2*x)/(3 - I*Sqrt[3]))] + Log[1 + x + x^2]/2 + x*Log[1 + x + x^2] + Log[2 + 2*x]*Log[1 + x + x^2] - 4*Log[4 + 2*x]*Log[1 + x + x^2] - PolyLog[2, (2*(1 + x))/(1 - I*Sqrt[3])] - PolyLog[2, (2*(1 + x))/(1 + I*Sqrt[3])] + 4*PolyLog[2, (2*(2 + x))/(3 - I*Sqrt[3])] + 4*PolyLog[2, (2*(2 + x))/(3 + I*Sqrt[3])]","A",28,12,21,0.5714,1,"{2528, 2523, 773, 634, 618, 204, 628, 2524, 2418, 2394, 2393, 2391}"
99,1,371,0,0.5411757,"\int \log ^2\left(1+x+x^2\right) \, dx","Int[Log[1 + x + x^2]^2,x]","-\left(1+i \sqrt{3}\right) \text{PolyLog}\left(2,-\frac{2 i x-\sqrt{3}+i}{2 \sqrt{3}}\right)-\left(1-i \sqrt{3}\right) \text{PolyLog}\left(2,\frac{2 i x+\sqrt{3}+i}{2 \sqrt{3}}\right)+x \log ^2\left(x^2+x+1\right)+\left(1-i \sqrt{3}\right) \log \left(x^2+x+1\right) \log \left(2 x-i \sqrt{3}+1\right)-4 x \log \left(x^2+x+1\right)+\left(1+i \sqrt{3}\right) \log \left(2 x+i \sqrt{3}+1\right) \log \left(x^2+x+1\right)-2 \log \left(x^2+x+1\right)+8 x-\frac{1}{2} \left(1-i \sqrt{3}\right) \log ^2\left(2 x-i \sqrt{3}+1\right)-\frac{1}{2} \left(1+i \sqrt{3}\right) \log ^2\left(2 x+i \sqrt{3}+1\right)-\left(1-i \sqrt{3}\right) \log \left(-\frac{i \left(2 x+i \sqrt{3}+1\right)}{2 \sqrt{3}}\right) \log \left(2 x-i \sqrt{3}+1\right)-\left(1+i \sqrt{3}\right) \log \left(\frac{i \left(2 x-i \sqrt{3}+1\right)}{2 \sqrt{3}}\right) \log \left(2 x+i \sqrt{3}+1\right)-4 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)","-\left(1+i \sqrt{3}\right) \text{PolyLog}\left(2,-\frac{2 i x-\sqrt{3}+i}{2 \sqrt{3}}\right)-\left(1-i \sqrt{3}\right) \text{PolyLog}\left(2,\frac{2 i x+\sqrt{3}+i}{2 \sqrt{3}}\right)+x \log ^2\left(x^2+x+1\right)+\left(1-i \sqrt{3}\right) \log \left(x^2+x+1\right) \log \left(2 x-i \sqrt{3}+1\right)-4 x \log \left(x^2+x+1\right)+\left(1+i \sqrt{3}\right) \log \left(2 x+i \sqrt{3}+1\right) \log \left(x^2+x+1\right)-2 \log \left(x^2+x+1\right)+8 x-\frac{1}{2} \left(1-i \sqrt{3}\right) \log ^2\left(2 x-i \sqrt{3}+1\right)-\frac{1}{2} \left(1+i \sqrt{3}\right) \log ^2\left(2 x+i \sqrt{3}+1\right)-\left(1-i \sqrt{3}\right) \log \left(-\frac{i \left(2 x+i \sqrt{3}+1\right)}{2 \sqrt{3}}\right) \log \left(2 x-i \sqrt{3}+1\right)-\left(1+i \sqrt{3}\right) \log \left(\frac{i \left(2 x-i \sqrt{3}+1\right)}{2 \sqrt{3}}\right) \log \left(2 x+i \sqrt{3}+1\right)-4 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"8*x - 4*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - ((1 - I*Sqrt[3])*Log[1 - I*Sqrt[3] + 2*x]^2)/2 - (1 + I*Sqrt[3])*Log[((I/2)*(1 - I*Sqrt[3] + 2*x))/Sqrt[3]]*Log[1 + I*Sqrt[3] + 2*x] - ((1 + I*Sqrt[3])*Log[1 + I*Sqrt[3] + 2*x]^2)/2 - (1 - I*Sqrt[3])*Log[1 - I*Sqrt[3] + 2*x]*Log[((-I/2)*(1 + I*Sqrt[3] + 2*x))/Sqrt[3]] - 2*Log[1 + x + x^2] - 4*x*Log[1 + x + x^2] + (1 - I*Sqrt[3])*Log[1 - I*Sqrt[3] + 2*x]*Log[1 + x + x^2] + (1 + I*Sqrt[3])*Log[1 + I*Sqrt[3] + 2*x]*Log[1 + x + x^2] + x*Log[1 + x + x^2]^2 - (1 + I*Sqrt[3])*PolyLog[2, -(I - Sqrt[3] + (2*I)*x)/(2*Sqrt[3])] - (1 - I*Sqrt[3])*PolyLog[2, (I + Sqrt[3] + (2*I)*x)/(2*Sqrt[3])]","A",27,14,9,1.556,1,"{2523, 2528, 773, 634, 618, 204, 628, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
100,1,443,0,0.6838291,"\int \frac{\log ^2\left(-1+x+x^2\right)}{x^3} \, dx","Int[Log[-1 + x + x^2]^2/x^3,x]","3 \text{PolyLog}\left(2,-\frac{2 x}{1+\sqrt{5}}\right)-\frac{1}{2} \left(3+\sqrt{5}\right) \text{PolyLog}\left(2,-\frac{2 x-\sqrt{5}+1}{2 \sqrt{5}}\right)-\frac{1}{2} \left(3-\sqrt{5}\right) \text{PolyLog}\left(2,\frac{2 x+\sqrt{5}+1}{2 \sqrt{5}}\right)-3 \text{PolyLog}\left(2,\frac{2 x}{1-\sqrt{5}}+1\right)-\frac{\log ^2\left(x^2+x-1\right)}{2 x^2}+\frac{1}{2} \left(3+\sqrt{5}\right) \log \left(x^2+x-1\right) \log \left(2 x-\sqrt{5}+1\right)-3 \log (x) \log \left(x^2+x-1\right)+\frac{1}{2} \left(3-\sqrt{5}\right) \log \left(2 x+\sqrt{5}+1\right) \log \left(x^2+x-1\right)+\frac{\log \left(x^2+x-1\right)}{x}-\frac{1}{4} \left(3+\sqrt{5}\right) \log ^2\left(2 x-\sqrt{5}+1\right)-\frac{1}{4} \left(3-\sqrt{5}\right) \log ^2\left(2 x+\sqrt{5}+1\right)-\frac{1}{2} \left(3+\sqrt{5}\right) \log \left(\frac{2 x+\sqrt{5}+1}{2 \sqrt{5}}\right) \log \left(2 x-\sqrt{5}+1\right)+3 \log \left(\frac{1}{2} \left(\sqrt{5}-1\right)\right) \log \left(2 x-\sqrt{5}+1\right)-\frac{1}{2} \left(1+\sqrt{5}\right) \log \left(2 x-\sqrt{5}+1\right)+\log (x)-\frac{1}{2} \left(3-\sqrt{5}\right) \log \left(-\frac{2 x-\sqrt{5}+1}{2 \sqrt{5}}\right) \log \left(2 x+\sqrt{5}+1\right)-\frac{1}{2} \left(1-\sqrt{5}\right) \log \left(2 x+\sqrt{5}+1\right)+3 \log (x) \log \left(\frac{2 x}{1+\sqrt{5}}+1\right)","3 \text{PolyLog}\left(2,-\frac{2 x}{1+\sqrt{5}}\right)-\frac{1}{2} \left(3+\sqrt{5}\right) \text{PolyLog}\left(2,-\frac{2 x-\sqrt{5}+1}{2 \sqrt{5}}\right)-\frac{1}{2} \left(3-\sqrt{5}\right) \text{PolyLog}\left(2,\frac{2 x+\sqrt{5}+1}{2 \sqrt{5}}\right)-3 \text{PolyLog}\left(2,\frac{2 x}{1-\sqrt{5}}+1\right)-\frac{\log ^2\left(x^2+x-1\right)}{2 x^2}+\frac{1}{2} \left(3+\sqrt{5}\right) \log \left(x^2+x-1\right) \log \left(2 x-\sqrt{5}+1\right)-3 \log (x) \log \left(x^2+x-1\right)+\frac{1}{2} \left(3-\sqrt{5}\right) \log \left(2 x+\sqrt{5}+1\right) \log \left(x^2+x-1\right)+\frac{\log \left(x^2+x-1\right)}{x}-\frac{1}{4} \left(3+\sqrt{5}\right) \log ^2\left(2 x-\sqrt{5}+1\right)-\frac{1}{4} \left(3-\sqrt{5}\right) \log ^2\left(2 x+\sqrt{5}+1\right)-\frac{1}{2} \left(3+\sqrt{5}\right) \log \left(\frac{2 x+\sqrt{5}+1}{2 \sqrt{5}}\right) \log \left(2 x-\sqrt{5}+1\right)+3 \log \left(\frac{1}{2} \left(\sqrt{5}-1\right)\right) \log \left(2 x-\sqrt{5}+1\right)-\frac{1}{2} \left(1+\sqrt{5}\right) \log \left(2 x-\sqrt{5}+1\right)+\log (x)-\frac{1}{2} \left(3-\sqrt{5}\right) \log \left(-\frac{2 x-\sqrt{5}+1}{2 \sqrt{5}}\right) \log \left(2 x+\sqrt{5}+1\right)-\frac{1}{2} \left(1-\sqrt{5}\right) \log \left(2 x+\sqrt{5}+1\right)+3 \log (x) \log \left(\frac{2 x}{1+\sqrt{5}}+1\right)",1,"Log[x] - ((1 + Sqrt[5])*Log[1 - Sqrt[5] + 2*x])/2 + 3*Log[(-1 + Sqrt[5])/2]*Log[1 - Sqrt[5] + 2*x] - ((3 + Sqrt[5])*Log[1 - Sqrt[5] + 2*x]^2)/4 - ((1 - Sqrt[5])*Log[1 + Sqrt[5] + 2*x])/2 - ((3 - Sqrt[5])*Log[-(1 - Sqrt[5] + 2*x)/(2*Sqrt[5])]*Log[1 + Sqrt[5] + 2*x])/2 - ((3 - Sqrt[5])*Log[1 + Sqrt[5] + 2*x]^2)/4 - ((3 + Sqrt[5])*Log[1 - Sqrt[5] + 2*x]*Log[(1 + Sqrt[5] + 2*x)/(2*Sqrt[5])])/2 + 3*Log[x]*Log[1 + (2*x)/(1 + Sqrt[5])] + Log[-1 + x + x^2]/x - 3*Log[x]*Log[-1 + x + x^2] + ((3 + Sqrt[5])*Log[1 - Sqrt[5] + 2*x]*Log[-1 + x + x^2])/2 + ((3 - Sqrt[5])*Log[1 + Sqrt[5] + 2*x]*Log[-1 + x + x^2])/2 - Log[-1 + x + x^2]^2/(2*x^2) + 3*PolyLog[2, (-2*x)/(1 + Sqrt[5])] - ((3 + Sqrt[5])*PolyLog[2, -(1 - Sqrt[5] + 2*x)/(2*Sqrt[5])])/2 - ((3 - Sqrt[5])*PolyLog[2, (1 + Sqrt[5] + 2*x)/(2*Sqrt[5])])/2 - 3*PolyLog[2, 1 + (2*x)/(1 - Sqrt[5])]","A",34,16,13,1.231,1,"{2525, 2528, 800, 632, 31, 2524, 2357, 2316, 2315, 2317, 2391, 2418, 2390, 2301, 2394, 2393}"
101,1,172,0,0.3806693,"\int x^3 \log \left(-1+4 x+4 \sqrt{(-1+x) x}\right) \, dx","Int[x^3*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]],x]","-\frac{x^4}{32}+\frac{x^3}{192}-\frac{x^2}{1024}-\frac{1}{32} \left(x^2-x\right)^{3/2} x-\frac{1}{12} \left(x^2-x\right)^{3/2}+\frac{149 (1-2 x) \sqrt{x^2-x}}{2048}-\frac{683 \sqrt{x^2-x}}{4096}+\frac{1}{4} x^4 \log \left(4 \sqrt{x^2-x}+4 x-1\right)+\frac{\tanh ^{-1}\left(\frac{1-10 x}{6 \sqrt{x^2-x}}\right)}{32768}-\frac{1537 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-x}}\right)}{16384}+\frac{x}{4096}-\frac{\log (8 x+1)}{32768}","-\frac{x^4}{32}+\frac{x^3}{192}-\frac{x^2}{1024}-\frac{1}{32} \left(x^2-x\right)^{3/2} x-\frac{1}{12} \left(x^2-x\right)^{3/2}+\frac{149 (1-2 x) \sqrt{x^2-x}}{2048}-\frac{683 \sqrt{x^2-x}}{4096}+\frac{1}{4} x^4 \log \left(4 \sqrt{x^2-x}+4 x-1\right)+\frac{\tanh ^{-1}\left(\frac{1-10 x}{6 \sqrt{x^2-x}}\right)}{32768}-\frac{1537 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-x}}\right)}{16384}+\frac{x}{4096}-\frac{\log (8 x+1)}{32768}",1,"x/4096 - x^2/1024 + x^3/192 - x^4/32 - (683*Sqrt[-x + x^2])/4096 + (149*(1 - 2*x)*Sqrt[-x + x^2])/2048 - (-x + x^2)^(3/2)/12 - (x*(-x + x^2)^(3/2))/32 + ArcTanh[(1 - 10*x)/(6*Sqrt[-x + x^2])]/32768 - (1537*ArcTanh[x/Sqrt[-x + x^2]])/16384 - Log[1 + 8*x]/32768 + (x^4*Log[-1 + 4*x + 4*Sqrt[-x + x^2]])/4","A",25,11,21,0.5238,1,"{2537, 2535, 6742, 640, 620, 206, 612, 734, 843, 724, 670}"
102,1,149,0,0.2915568,"\int x^2 \log \left(-1+4 x+4 \sqrt{(-1+x) x}\right) \, dx","Int[x^2*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]],x]","-\frac{x^3}{18}+\frac{x^2}{96}-\frac{1}{18} \left(x^2-x\right)^{3/2}+\frac{5}{64} (1-2 x) \sqrt{x^2-x}-\frac{85 \sqrt{x^2-x}}{384}+\frac{1}{3} x^3 \log \left(4 \sqrt{x^2-x}+4 x-1\right)-\frac{\tanh ^{-1}\left(\frac{1-10 x}{6 \sqrt{x^2-x}}\right)}{3072}-\frac{223 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-x}}\right)}{1536}-\frac{x}{384}+\frac{\log (8 x+1)}{3072}","-\frac{x^3}{18}+\frac{x^2}{96}-\frac{1}{18} \left(x^2-x\right)^{3/2}+\frac{5}{64} (1-2 x) \sqrt{x^2-x}-\frac{85 \sqrt{x^2-x}}{384}+\frac{1}{3} x^3 \log \left(4 \sqrt{x^2-x}+4 x-1\right)-\frac{\tanh ^{-1}\left(\frac{1-10 x}{6 \sqrt{x^2-x}}\right)}{3072}-\frac{223 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-x}}\right)}{1536}-\frac{x}{384}+\frac{\log (8 x+1)}{3072}",1,"-x/384 + x^2/96 - x^3/18 - (85*Sqrt[-x + x^2])/384 + (5*(1 - 2*x)*Sqrt[-x + x^2])/64 - (-x + x^2)^(3/2)/18 - ArcTanh[(1 - 10*x)/(6*Sqrt[-x + x^2])]/3072 - (223*ArcTanh[x/Sqrt[-x + x^2]])/1536 + Log[1 + 8*x]/3072 + (x^3*Log[-1 + 4*x + 4*Sqrt[-x + x^2]])/3","A",20,10,21,0.4762,1,"{2537, 2535, 6742, 640, 620, 206, 612, 734, 843, 724}"
103,1,127,0,0.245347,"\int x \log \left(-1+4 x+4 \sqrt{(-1+x) x}\right) \, dx","Int[x*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]],x]","-\frac{x^2}{8}+\frac{1}{16} (1-2 x) \sqrt{x^2-x}-\frac{11 \sqrt{x^2-x}}{32}+\frac{1}{2} x^2 \log \left(4 \sqrt{x^2-x}+4 x-1\right)+\frac{1}{256} \tanh ^{-1}\left(\frac{1-10 x}{6 \sqrt{x^2-x}}\right)-\frac{33}{128} \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-x}}\right)+\frac{x}{32}-\frac{1}{256} \log (8 x+1)","-\frac{x^2}{8}+\frac{1}{16} (1-2 x) \sqrt{x^2-x}-\frac{11 \sqrt{x^2-x}}{32}+\frac{1}{2} x^2 \log \left(4 \sqrt{x^2-x}+4 x-1\right)+\frac{1}{256} \tanh ^{-1}\left(\frac{1-10 x}{6 \sqrt{x^2-x}}\right)-\frac{33}{128} \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-x}}\right)+\frac{x}{32}-\frac{1}{256} \log (8 x+1)",1,"x/32 - x^2/8 - (11*Sqrt[-x + x^2])/32 + ((1 - 2*x)*Sqrt[-x + x^2])/16 + ArcTanh[(1 - 10*x)/(6*Sqrt[-x + x^2])]/256 - (33*ArcTanh[x/Sqrt[-x + x^2]])/128 - Log[1 + 8*x]/256 + (x^2*Log[-1 + 4*x + 4*Sqrt[-x + x^2]])/2","A",16,10,19,0.5263,1,"{2537, 2535, 6742, 640, 620, 206, 612, 734, 843, 724}"
104,1,95,0,0.1623032,"\int \log \left(-1+4 x+4 \sqrt{(-1+x) x}\right) \, dx","Int[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]],x]","-\frac{\sqrt{x^2-x}}{2}+x \log \left(4 \sqrt{x^2-x}+4 x-1\right)-\frac{1}{16} \tanh ^{-1}\left(\frac{1-10 x}{6 \sqrt{x^2-x}}\right)-\frac{7}{8} \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-x}}\right)-\frac{x}{2}+\frac{1}{16} \log (8 x+1)","-\frac{\sqrt{x^2-x}}{2}+x \log \left(4 \sqrt{x^2-x}+4 x-1\right)-\frac{1}{16} \tanh ^{-1}\left(\frac{1-10 x}{6 \sqrt{x^2-x}}\right)-\frac{7}{8} \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-x}}\right)-\frac{x}{2}+\frac{1}{16} \log (8 x+1)",1,"-x/2 - Sqrt[-x + x^2]/2 - ArcTanh[(1 - 10*x)/(6*Sqrt[-x + x^2])]/16 - (7*ArcTanh[x/Sqrt[-x + x^2]])/8 + Log[1 + 8*x]/16 + x*Log[-1 + 4*x + 4*Sqrt[-x + x^2]]","A",13,9,17,0.5294,1,"{2537, 2533, 6742, 640, 620, 206, 734, 843, 724}"
105,0,0,0,0.0763766,"\int \frac{\log \left(-1+4 x+4 \sqrt{(-1+x) x}\right)}{x} \, dx","Int[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/x,x]","\int \frac{\log \left(-1+4 x+4 \sqrt{(-1+x) x}\right)}{x} \, dx","\text{Int}\left(\frac{\log \left(4 \sqrt{x^2-x}+4 x-1\right)}{x},x\right)",0,"Defer[Int][Log[-1 + 4*x + 4*Sqrt[-x + x^2]]/x, x]","A",0,0,0,0,-1,"{}"
106,1,76,0,0.262083,"\int \frac{\log \left(-1+4 x+4 \sqrt{(-1+x) x}\right)}{x^2} \, dx","Int[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/x^2,x]","\frac{4 \sqrt{x^2-x}}{x}-\frac{\log \left(4 \sqrt{x^2-x}+4 x-1\right)}{x}+4 \tanh ^{-1}\left(\frac{1-10 x}{6 \sqrt{x^2-x}}\right)+4 \log (x)-4 \log (8 x+1)","\frac{4 \sqrt{x^2-x}}{x}-\frac{\log \left(4 \sqrt{x^2-x}+4 x-1\right)}{x}+4 \tanh ^{-1}\left(\frac{1-10 x}{6 \sqrt{x^2-x}}\right)+4 \log (x)-4 \log (8 x+1)",1,"(4*Sqrt[-x + x^2])/x + 4*ArcTanh[(1 - 10*x)/(6*Sqrt[-x + x^2])] + 4*Log[x] - 4*Log[1 + 8*x] - Log[-1 + 4*x + 4*Sqrt[-x + x^2]]/x","A",19,11,21,0.5238,1,"{2537, 2535, 6742, 640, 620, 206, 662, 664, 734, 843, 724}"
107,1,101,0,0.2905846,"\int \frac{\log \left(-1+4 x+4 \sqrt{(-1+x) x}\right)}{x^3} \, dx","Int[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/x^3,x]","-\frac{2 \left(x^2-x\right)^{3/2}}{3 x^3}-\frac{10 \sqrt{x^2-x}}{x}-\frac{\log \left(4 \sqrt{x^2-x}+4 x-1\right)}{2 x^2}-16 \tanh ^{-1}\left(\frac{1-10 x}{6 \sqrt{x^2-x}}\right)-\frac{2}{x}-16 \log (x)+16 \log (8 x+1)","-\frac{2 \left(x^2-x\right)^{3/2}}{3 x^3}-\frac{10 \sqrt{x^2-x}}{x}-\frac{\log \left(4 \sqrt{x^2-x}+4 x-1\right)}{2 x^2}-16 \tanh ^{-1}\left(\frac{1-10 x}{6 \sqrt{x^2-x}}\right)-\frac{2}{x}-16 \log (x)+16 \log (8 x+1)",1,"-2/x - (10*Sqrt[-x + x^2])/x - (2*(-x + x^2)^(3/2))/(3*x^3) - 16*ArcTanh[(1 - 10*x)/(6*Sqrt[-x + x^2])] - 16*Log[x] + 16*Log[1 + 8*x] - Log[-1 + 4*x + 4*Sqrt[-x + x^2]]/(2*x^2)","A",20,12,21,0.5714,1,"{2537, 2535, 6742, 640, 620, 206, 734, 843, 724, 650, 662, 664}"
108,1,187,0,0.541197,"\int x^{3/2} \log \left(-1+4 x+4 \sqrt{(-1+x) x}\right) \, dx","Int[x^(3/2)*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]],x]","-\frac{2 x^{5/2}}{25}+\frac{x^{3/2}}{60}-\frac{2 \left(x^2-x\right)^{3/2}}{25 \sqrt{x}}-\frac{17 \sqrt{x^2-x}}{32 \sqrt{x}}-\frac{71 \left(x^2-x\right)^{3/2}}{300 x^{3/2}}+\frac{2}{5} x^{5/2} \log \left(4 \sqrt{x^2-x}+4 x-1\right)-\frac{\sqrt{x^2-x} \tan ^{-1}\left(\frac{2}{3} \sqrt{2} \sqrt{x-1}\right)}{320 \sqrt{2} \sqrt{x-1} \sqrt{x}}-\frac{\sqrt{x}}{160}+\frac{\tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)}{320 \sqrt{2}}","-\frac{2 x^{5/2}}{25}+\frac{x^{3/2}}{60}-\frac{2 \left(x^2-x\right)^{3/2}}{25 \sqrt{x}}-\frac{17 \sqrt{x^2-x}}{32 \sqrt{x}}-\frac{71 \left(x^2-x\right)^{3/2}}{300 x^{3/2}}+\frac{2}{5} x^{5/2} \log \left(4 \sqrt{x^2-x}+4 x-1\right)-\frac{\sqrt{x^2-x} \tan ^{-1}\left(\frac{2}{3} \sqrt{2} \sqrt{x-1}\right)}{320 \sqrt{2} \sqrt{x-1} \sqrt{x}}-\frac{\sqrt{x}}{160}+\frac{\tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)}{320 \sqrt{2}}",1,"-Sqrt[x]/160 + x^(3/2)/60 - (2*x^(5/2))/25 - (17*Sqrt[-x + x^2])/(32*Sqrt[x]) - (71*(-x + x^2)^(3/2))/(300*x^(3/2)) - (2*(-x + x^2)^(3/2))/(25*Sqrt[x]) - (Sqrt[-x + x^2]*ArcTan[(2*Sqrt[2]*Sqrt[-1 + x])/3])/(320*Sqrt[2]*Sqrt[-1 + x]*Sqrt[x]) + ArcTan[2*Sqrt[2]*Sqrt[x]]/(320*Sqrt[2]) + (2*x^(5/2)*Log[-1 + 4*x + 4*Sqrt[-x + x^2]])/5","A",15,12,23,0.5217,1,"{2537, 2535, 6733, 6742, 203, 1588, 2000, 2016, 1146, 444, 50, 63}"
109,1,158,0,0.4311561,"\int \sqrt{x} \log \left(-1+4 x+4 \sqrt{(-1+x) x}\right) \, dx","Int[Sqrt[x]*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]],x]","-\frac{2 x^{3/2}}{9}-\frac{11 \sqrt{x^2-x}}{12 \sqrt{x}}-\frac{2 \left(x^2-x\right)^{3/2}}{9 x^{3/2}}+\frac{2}{3} x^{3/2} \log \left(4 \sqrt{x^2-x}+4 x-1\right)+\frac{\sqrt{x^2-x} \tan ^{-1}\left(\frac{2}{3} \sqrt{2} \sqrt{x-1}\right)}{24 \sqrt{2} \sqrt{x-1} \sqrt{x}}+\frac{\sqrt{x}}{12}-\frac{\tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)}{24 \sqrt{2}}","-\frac{2 x^{3/2}}{9}-\frac{11 \sqrt{x^2-x}}{12 \sqrt{x}}-\frac{2 \left(x^2-x\right)^{3/2}}{9 x^{3/2}}+\frac{2}{3} x^{3/2} \log \left(4 \sqrt{x^2-x}+4 x-1\right)+\frac{\sqrt{x^2-x} \tan ^{-1}\left(\frac{2}{3} \sqrt{2} \sqrt{x-1}\right)}{24 \sqrt{2} \sqrt{x-1} \sqrt{x}}+\frac{\sqrt{x}}{12}-\frac{\tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)}{24 \sqrt{2}}",1,"Sqrt[x]/12 - (2*x^(3/2))/9 - (11*Sqrt[-x + x^2])/(12*Sqrt[x]) - (2*(-x + x^2)^(3/2))/(9*x^(3/2)) + (Sqrt[-x + x^2]*ArcTan[(2*Sqrt[2]*Sqrt[-1 + x])/3])/(24*Sqrt[2]*Sqrt[-1 + x]*Sqrt[x]) - ArcTan[2*Sqrt[2]*Sqrt[x]]/(24*Sqrt[2]) + (2*x^(3/2)*Log[-1 + 4*x + 4*Sqrt[-x + x^2]])/3","A",13,12,23,0.5217,1,"{2537, 2535, 6733, 6742, 203, 1588, 2000, 1146, 444, 50, 63, 204}"
110,1,118,0,0.3851409,"\int \frac{\log \left(-1+4 x+4 \sqrt{(-1+x) x}\right)}{\sqrt{x}} \, dx","Int[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/Sqrt[x],x]","-\frac{2 \sqrt{x^2-x}}{\sqrt{x}}+2 \sqrt{x} \log \left(4 \sqrt{x^2-x}+4 x-1\right)-\frac{\sqrt{x^2-x} \tan ^{-1}\left(\frac{2}{3} \sqrt{2} \sqrt{x-1}\right)}{\sqrt{2} \sqrt{x-1} \sqrt{x}}-2 \sqrt{x}+\frac{\tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)}{\sqrt{2}}","-\frac{2 \sqrt{x^2-x}}{\sqrt{x}}+2 \sqrt{x} \log \left(4 \sqrt{x^2-x}+4 x-1\right)-\frac{\sqrt{x^2-x} \tan ^{-1}\left(\frac{2}{3} \sqrt{2} \sqrt{x-1}\right)}{\sqrt{2} \sqrt{x-1} \sqrt{x}}-2 \sqrt{x}+\frac{\tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)}{\sqrt{2}}",1,"-2*Sqrt[x] - (2*Sqrt[-x + x^2])/Sqrt[x] - (Sqrt[-x + x^2]*ArcTan[(2*Sqrt[2]*Sqrt[-1 + x])/3])/(Sqrt[2]*Sqrt[-1 + x]*Sqrt[x]) + ArcTan[2*Sqrt[2]*Sqrt[x]]/Sqrt[2] + 2*Sqrt[x]*Log[-1 + 4*x + 4*Sqrt[-x + x^2]]","A",12,10,23,0.4348,1,"{2537, 2535, 6733, 6742, 203, 1588, 1146, 444, 50, 63}"
111,1,114,0,0.308602,"\int \frac{\log \left(-1+4 x+4 \sqrt{(-1+x) x}\right)}{x^{3/2}} \, dx","Int[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/x^(3/2),x]","-\frac{2 \log \left(4 \sqrt{x^2-x}+4 x-1\right)}{\sqrt{x}}-\frac{4 \sqrt{2} \sqrt{x^2-x} \tan ^{-1}\left(\frac{2}{3} \sqrt{2} \sqrt{x-1}\right)}{\sqrt{x-1} \sqrt{x}}-8 \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x^2-x}}\right)+4 \sqrt{2} \tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)","-\frac{2 \log \left(4 \sqrt{x^2-x}+4 x-1\right)}{\sqrt{x}}-\frac{4 \sqrt{2} \sqrt{x^2-x} \tan ^{-1}\left(\frac{2}{3} \sqrt{2} \sqrt{x-1}\right)}{\sqrt{x-1} \sqrt{x}}-8 \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x^2-x}}\right)+4 \sqrt{2} \tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)",1,"(-4*Sqrt[2]*Sqrt[-x + x^2]*ArcTan[(2*Sqrt[2]*Sqrt[-1 + x])/3])/(Sqrt[-1 + x]*Sqrt[x]) + 4*Sqrt[2]*ArcTan[2*Sqrt[2]*Sqrt[x]] - 8*ArcTan[Sqrt[x]/Sqrt[-x + x^2]] - (2*Log[-1 + 4*x + 4*Sqrt[-x + x^2]])/Sqrt[x]","A",15,13,23,0.5652,1,"{2537, 2535, 6733, 6742, 203, 1588, 2021, 2008, 1146, 444, 50, 63, 204}"
112,1,151,0,0.4783606,"\int \frac{\log \left(-1+4 x+4 \sqrt{(-1+x) x}\right)}{x^{5/2}} \, dx","Int[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/x^(5/2),x]","\frac{4 \sqrt{x^2-x}}{3 x^{3/2}}-\frac{2 \log \left(4 \sqrt{x^2-x}+4 x-1\right)}{3 x^{3/2}}+\frac{32 \sqrt{2} \sqrt{x^2-x} \tan ^{-1}\left(\frac{2}{3} \sqrt{2} \sqrt{x-1}\right)}{3 \sqrt{x-1} \sqrt{x}}+\frac{44}{3} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x^2-x}}\right)-\frac{16}{3 \sqrt{x}}-\frac{32}{3} \sqrt{2} \tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)","\frac{4 \sqrt{x^2-x}}{3 x^{3/2}}-\frac{2 \log \left(4 \sqrt{x^2-x}+4 x-1\right)}{3 x^{3/2}}+\frac{32 \sqrt{2} \sqrt{x^2-x} \tan ^{-1}\left(\frac{2}{3} \sqrt{2} \sqrt{x-1}\right)}{3 \sqrt{x-1} \sqrt{x}}+\frac{44}{3} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x^2-x}}\right)-\frac{16}{3 \sqrt{x}}-\frac{32}{3} \sqrt{2} \tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)",1,"-16/(3*Sqrt[x]) + (4*Sqrt[-x + x^2])/(3*x^(3/2)) + (32*Sqrt[2]*Sqrt[-x + x^2]*ArcTan[(2*Sqrt[2]*Sqrt[-1 + x])/3])/(3*Sqrt[-1 + x]*Sqrt[x]) - (32*Sqrt[2]*ArcTan[2*Sqrt[2]*Sqrt[x]])/3 + (44*ArcTan[Sqrt[x]/Sqrt[-x + x^2]])/3 - (2*Log[-1 + 4*x + 4*Sqrt[-x + x^2]])/(3*x^(3/2))","A",18,13,23,0.5652,1,"{2537, 2535, 6733, 6742, 203, 1588, 2020, 2008, 2021, 1146, 444, 50, 63}"
113,1,93,0,0.0730538,"\int x^3 \log \left(a+b e^x\right) \, dx","Int[x^3*Log[a + b*E^x],x]","-x^3 \text{PolyLog}\left(2,-\frac{b e^x}{a}\right)+3 x^2 \text{PolyLog}\left(3,-\frac{b e^x}{a}\right)-6 x \text{PolyLog}\left(4,-\frac{b e^x}{a}\right)+6 \text{PolyLog}\left(5,-\frac{b e^x}{a}\right)+\frac{1}{4} x^4 \log \left(a+b e^x\right)-\frac{1}{4} x^4 \log \left(\frac{b e^x}{a}+1\right)","-x^3 \text{PolyLog}\left(2,-\frac{b e^x}{a}\right)+3 x^2 \text{PolyLog}\left(3,-\frac{b e^x}{a}\right)-6 x \text{PolyLog}\left(4,-\frac{b e^x}{a}\right)+6 \text{PolyLog}\left(5,-\frac{b e^x}{a}\right)+\frac{1}{4} x^4 \log \left(a+b e^x\right)-\frac{1}{4} x^4 \log \left(\frac{b e^x}{a}+1\right)",1,"(x^4*Log[a + b*E^x])/4 - (x^4*Log[1 + (b*E^x)/a])/4 - x^3*PolyLog[2, -((b*E^x)/a)] + 3*x^2*PolyLog[3, -((b*E^x)/a)] - 6*x*PolyLog[4, -((b*E^x)/a)] + 6*PolyLog[5, -((b*E^x)/a)]","A",6,5,12,0.4167,1,"{2532, 2531, 6609, 2282, 6589}"
114,1,77,0,0.0584256,"\int x^2 \log \left(a+b e^x\right) \, dx","Int[x^2*Log[a + b*E^x],x]","-x^2 \text{PolyLog}\left(2,-\frac{b e^x}{a}\right)+2 x \text{PolyLog}\left(3,-\frac{b e^x}{a}\right)-2 \text{PolyLog}\left(4,-\frac{b e^x}{a}\right)+\frac{1}{3} x^3 \log \left(a+b e^x\right)-\frac{1}{3} x^3 \log \left(\frac{b e^x}{a}+1\right)","-x^2 \text{PolyLog}\left(2,-\frac{b e^x}{a}\right)+2 x \text{PolyLog}\left(3,-\frac{b e^x}{a}\right)-2 \text{PolyLog}\left(4,-\frac{b e^x}{a}\right)+\frac{1}{3} x^3 \log \left(a+b e^x\right)-\frac{1}{3} x^3 \log \left(\frac{b e^x}{a}+1\right)",1,"(x^3*Log[a + b*E^x])/3 - (x^3*Log[1 + (b*E^x)/a])/3 - x^2*PolyLog[2, -((b*E^x)/a)] + 2*x*PolyLog[3, -((b*E^x)/a)] - 2*PolyLog[4, -((b*E^x)/a)]","A",5,5,12,0.4167,1,"{2532, 2531, 6609, 2282, 6589}"
115,1,59,0,0.036611,"\int x \log \left(a+b e^x\right) \, dx","Int[x*Log[a + b*E^x],x]","-x \text{PolyLog}\left(2,-\frac{b e^x}{a}\right)+\text{PolyLog}\left(3,-\frac{b e^x}{a}\right)+\frac{1}{2} x^2 \log \left(a+b e^x\right)-\frac{1}{2} x^2 \log \left(\frac{b e^x}{a}+1\right)","-x \text{PolyLog}\left(2,-\frac{b e^x}{a}\right)+\text{PolyLog}\left(3,-\frac{b e^x}{a}\right)+\frac{1}{2} x^2 \log \left(a+b e^x\right)-\frac{1}{2} x^2 \log \left(\frac{b e^x}{a}+1\right)",1,"(x^2*Log[a + b*E^x])/2 - (x^2*Log[1 + (b*E^x)/a])/2 - x*PolyLog[2, -((b*E^x)/a)] + PolyLog[3, -((b*E^x)/a)]","A",4,4,10,0.4000,1,"{2532, 2531, 2282, 6589}"
116,1,38,0,0.0482474,"\int \log \left(a+b e^x\right) \, dx","Int[Log[a + b*E^x],x]","-\text{PolyLog}\left(2,-\frac{b e^x}{a}\right)+x \log \left(a+b e^x\right)-x \log \left(\frac{b e^x}{a}+1\right)","-\text{PolyLog}\left(2,-\frac{b e^x}{a}\right)+x \log \left(a+b e^x\right)-x \log \left(\frac{b e^x}{a}+1\right)",1,"x*Log[a + b*E^x] - x*Log[1 + (b*E^x)/a] - PolyLog[2, -((b*E^x)/a)]","A",4,4,8,0.5000,1,"{2280, 2190, 2279, 2391}"
117,0,0,0,0.0320759,"\int \frac{\log \left(a+b e^x\right)}{x} \, dx","Int[Log[a + b*E^x]/x,x]","\int \frac{\log \left(a+b e^x\right)}{x} \, dx","\text{Int}\left(\frac{\log \left(a+b e^x\right)}{x},x\right)",0,"Defer[Int][Log[a + b*E^x]/x, x]","A",0,0,0,0,-1,"{}"
118,1,132,0,0.0969669,"\int x^3 \log \left(1+e \left(f^{c (a+b x)}\right)^n\right) \, dx","Int[x^3*Log[1 + e*(f^(c*(a + b*x)))^n],x]","\frac{3 x^2 \text{PolyLog}\left(3,-e \left(f^{c (a+b x)}\right)^n\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{6 x \text{PolyLog}\left(4,-e \left(f^{c (a+b x)}\right)^n\right)}{b^3 c^3 n^3 \log ^3(f)}+\frac{6 \text{PolyLog}\left(5,-e \left(f^{c (a+b x)}\right)^n\right)}{b^4 c^4 n^4 \log ^4(f)}-\frac{x^3 \text{PolyLog}\left(2,-e \left(f^{c (a+b x)}\right)^n\right)}{b c n \log (f)}","\frac{3 x^2 \text{PolyLog}\left(3,-e \left(f^{c (a+b x)}\right)^n\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{6 x \text{PolyLog}\left(4,-e \left(f^{c (a+b x)}\right)^n\right)}{b^3 c^3 n^3 \log ^3(f)}+\frac{6 \text{PolyLog}\left(5,-e \left(f^{c (a+b x)}\right)^n\right)}{b^4 c^4 n^4 \log ^4(f)}-\frac{x^3 \text{PolyLog}\left(2,-e \left(f^{c (a+b x)}\right)^n\right)}{b c n \log (f)}",1,"-((x^3*PolyLog[2, -(e*(f^(c*(a + b*x)))^n)])/(b*c*n*Log[f])) + (3*x^2*PolyLog[3, -(e*(f^(c*(a + b*x)))^n)])/(b^2*c^2*n^2*Log[f]^2) - (6*x*PolyLog[4, -(e*(f^(c*(a + b*x)))^n)])/(b^3*c^3*n^3*Log[f]^3) + (6*PolyLog[5, -(e*(f^(c*(a + b*x)))^n)])/(b^4*c^4*n^4*Log[f]^4)","A",5,4,20,0.2000,1,"{2531, 6609, 2282, 6589}"
119,1,98,0,0.0615725,"\int x^2 \log \left(1+e \left(f^{c (a+b x)}\right)^n\right) \, dx","Int[x^2*Log[1 + e*(f^(c*(a + b*x)))^n],x]","\frac{2 x \text{PolyLog}\left(3,-e \left(f^{c (a+b x)}\right)^n\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{2 \text{PolyLog}\left(4,-e \left(f^{c (a+b x)}\right)^n\right)}{b^3 c^3 n^3 \log ^3(f)}-\frac{x^2 \text{PolyLog}\left(2,-e \left(f^{c (a+b x)}\right)^n\right)}{b c n \log (f)}","\frac{2 x \text{PolyLog}\left(3,-e \left(f^{c (a+b x)}\right)^n\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{2 \text{PolyLog}\left(4,-e \left(f^{c (a+b x)}\right)^n\right)}{b^3 c^3 n^3 \log ^3(f)}-\frac{x^2 \text{PolyLog}\left(2,-e \left(f^{c (a+b x)}\right)^n\right)}{b c n \log (f)}",1,"-((x^2*PolyLog[2, -(e*(f^(c*(a + b*x)))^n)])/(b*c*n*Log[f])) + (2*x*PolyLog[3, -(e*(f^(c*(a + b*x)))^n)])/(b^2*c^2*n^2*Log[f]^2) - (2*PolyLog[4, -(e*(f^(c*(a + b*x)))^n)])/(b^3*c^3*n^3*Log[f]^3)","A",4,4,20,0.2000,1,"{2531, 6609, 2282, 6589}"
120,1,63,0,0.0382002,"\int x \log \left(1+e \left(f^{c (a+b x)}\right)^n\right) \, dx","Int[x*Log[1 + e*(f^(c*(a + b*x)))^n],x]","\frac{\text{PolyLog}\left(3,-e \left(f^{c (a+b x)}\right)^n\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{x \text{PolyLog}\left(2,-e \left(f^{c (a+b x)}\right)^n\right)}{b c n \log (f)}","\frac{\text{PolyLog}\left(3,-e \left(f^{c (a+b x)}\right)^n\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{x \text{PolyLog}\left(2,-e \left(f^{c (a+b x)}\right)^n\right)}{b c n \log (f)}",1,"-((x*PolyLog[2, -(e*(f^(c*(a + b*x)))^n)])/(b*c*n*Log[f])) + PolyLog[3, -(e*(f^(c*(a + b*x)))^n)]/(b^2*c^2*n^2*Log[f]^2)","A",3,3,18,0.1667,1,"{2531, 2282, 6589}"
121,1,31,0,0.0145746,"\int \log \left(1+e \left(f^{c (a+b x)}\right)^n\right) \, dx","Int[Log[1 + e*(f^(c*(a + b*x)))^n],x]","-\frac{\text{PolyLog}\left(2,-e \left(f^{c (a+b x)}\right)^n\right)}{b c n \log (f)}","-\frac{\text{PolyLog}\left(2,-e \left(f^{c (a+b x)}\right)^n\right)}{b c n \log (f)}",1,"-(PolyLog[2, -(e*(f^(c*(a + b*x)))^n)]/(b*c*n*Log[f]))","A",2,2,16,0.1250,1,"{2279, 2391}"
122,0,0,0,0.0641357,"\int \frac{\log \left(1+e \left(f^{c (a+b x)}\right)^n\right)}{x} \, dx","Int[Log[1 + e*(f^(c*(a + b*x)))^n]/x,x]","\int \frac{\log \left(1+e \left(f^{c (a+b x)}\right)^n\right)}{x} \, dx","\text{Int}\left(\frac{\log \left(e \left(f^{c (a+b x)}\right)^n+1\right)}{x},x\right)",0,"Defer[Int][Log[1 + e*(f^(c*(a + b*x)))^n]/x, x]","A",0,0,0,0,-1,"{}"
123,1,193,0,0.1294645,"\int x^3 \log \left(d+e \left(f^{c (a+b x)}\right)^n\right) \, dx","Int[x^3*Log[d + e*(f^(c*(a + b*x)))^n],x]","\frac{3 x^2 \text{PolyLog}\left(3,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{6 x \text{PolyLog}\left(4,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^3 c^3 n^3 \log ^3(f)}+\frac{6 \text{PolyLog}\left(5,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^4 c^4 n^4 \log ^4(f)}-\frac{x^3 \text{PolyLog}\left(2,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b c n \log (f)}+\frac{1}{4} x^4 \log \left(e \left(f^{c (a+b x)}\right)^n+d\right)-\frac{1}{4} x^4 \log \left(\frac{e \left(f^{c (a+b x)}\right)^n}{d}+1\right)","\frac{3 x^2 \text{PolyLog}\left(3,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{6 x \text{PolyLog}\left(4,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^3 c^3 n^3 \log ^3(f)}+\frac{6 \text{PolyLog}\left(5,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^4 c^4 n^4 \log ^4(f)}-\frac{x^3 \text{PolyLog}\left(2,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b c n \log (f)}+\frac{1}{4} x^4 \log \left(e \left(f^{c (a+b x)}\right)^n+d\right)-\frac{1}{4} x^4 \log \left(\frac{e \left(f^{c (a+b x)}\right)^n}{d}+1\right)",1,"(x^4*Log[d + e*(f^(c*(a + b*x)))^n])/4 - (x^4*Log[1 + (e*(f^(c*(a + b*x)))^n)/d])/4 - (x^3*PolyLog[2, -((e*(f^(c*(a + b*x)))^n)/d)])/(b*c*n*Log[f]) + (3*x^2*PolyLog[3, -((e*(f^(c*(a + b*x)))^n)/d)])/(b^2*c^2*n^2*Log[f]^2) - (6*x*PolyLog[4, -((e*(f^(c*(a + b*x)))^n)/d)])/(b^3*c^3*n^3*Log[f]^3) + (6*PolyLog[5, -((e*(f^(c*(a + b*x)))^n)/d)])/(b^4*c^4*n^4*Log[f]^4)","A",6,5,20,0.2500,1,"{2532, 2531, 6609, 2282, 6589}"
124,1,156,0,0.0930105,"\int x^2 \log \left(d+e \left(f^{c (a+b x)}\right)^n\right) \, dx","Int[x^2*Log[d + e*(f^(c*(a + b*x)))^n],x]","\frac{2 x \text{PolyLog}\left(3,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{2 \text{PolyLog}\left(4,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^3 c^3 n^3 \log ^3(f)}-\frac{x^2 \text{PolyLog}\left(2,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b c n \log (f)}+\frac{1}{3} x^3 \log \left(e \left(f^{c (a+b x)}\right)^n+d\right)-\frac{1}{3} x^3 \log \left(\frac{e \left(f^{c (a+b x)}\right)^n}{d}+1\right)","\frac{2 x \text{PolyLog}\left(3,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{2 \text{PolyLog}\left(4,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^3 c^3 n^3 \log ^3(f)}-\frac{x^2 \text{PolyLog}\left(2,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b c n \log (f)}+\frac{1}{3} x^3 \log \left(e \left(f^{c (a+b x)}\right)^n+d\right)-\frac{1}{3} x^3 \log \left(\frac{e \left(f^{c (a+b x)}\right)^n}{d}+1\right)",1,"(x^3*Log[d + e*(f^(c*(a + b*x)))^n])/3 - (x^3*Log[1 + (e*(f^(c*(a + b*x)))^n)/d])/3 - (x^2*PolyLog[2, -((e*(f^(c*(a + b*x)))^n)/d)])/(b*c*n*Log[f]) + (2*x*PolyLog[3, -((e*(f^(c*(a + b*x)))^n)/d)])/(b^2*c^2*n^2*Log[f]^2) - (2*PolyLog[4, -((e*(f^(c*(a + b*x)))^n)/d)])/(b^3*c^3*n^3*Log[f]^3)","A",5,5,20,0.2500,1,"{2532, 2531, 6609, 2282, 6589}"
125,1,118,0,0.0650263,"\int x \log \left(d+e \left(f^{c (a+b x)}\right)^n\right) \, dx","Int[x*Log[d + e*(f^(c*(a + b*x)))^n],x]","\frac{\text{PolyLog}\left(3,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{x \text{PolyLog}\left(2,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b c n \log (f)}+\frac{1}{2} x^2 \log \left(e \left(f^{c (a+b x)}\right)^n+d\right)-\frac{1}{2} x^2 \log \left(\frac{e \left(f^{c (a+b x)}\right)^n}{d}+1\right)","\frac{\text{PolyLog}\left(3,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{x \text{PolyLog}\left(2,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b c n \log (f)}+\frac{1}{2} x^2 \log \left(e \left(f^{c (a+b x)}\right)^n+d\right)-\frac{1}{2} x^2 \log \left(\frac{e \left(f^{c (a+b x)}\right)^n}{d}+1\right)",1,"(x^2*Log[d + e*(f^(c*(a + b*x)))^n])/2 - (x^2*Log[1 + (e*(f^(c*(a + b*x)))^n)/d])/2 - (x*PolyLog[2, -((e*(f^(c*(a + b*x)))^n)/d)])/(b*c*n*Log[f]) + PolyLog[3, -((e*(f^(c*(a + b*x)))^n)/d)]/(b^2*c^2*n^2*Log[f]^2)","A",4,4,18,0.2222,1,"{2532, 2531, 2282, 6589}"
126,1,75,0,0.1273987,"\int \log \left(d+e \left(f^{c (a+b x)}\right)^n\right) \, dx","Int[Log[d + e*(f^(c*(a + b*x)))^n],x]","-\frac{\text{PolyLog}\left(2,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b c n \log (f)}+x \log \left(e \left(f^{c (a+b x)}\right)^n+d\right)-x \log \left(\frac{e \left(f^{c (a+b x)}\right)^n}{d}+1\right)","-\frac{\text{PolyLog}\left(2,-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b c n \log (f)}+x \log \left(e \left(f^{c (a+b x)}\right)^n+d\right)-x \log \left(\frac{e \left(f^{c (a+b x)}\right)^n}{d}+1\right)",1,"x*Log[d + e*(f^(c*(a + b*x)))^n] - x*Log[1 + (e*(f^(c*(a + b*x)))^n)/d] - PolyLog[2, -((e*(f^(c*(a + b*x)))^n)/d)]/(b*c*n*Log[f])","A",4,4,16,0.2500,1,"{2280, 2190, 2279, 2391}"
127,0,0,0,0.0624786,"\int \frac{\log \left(d+e \left(f^{c (a+b x)}\right)^n\right)}{x} \, dx","Int[Log[d + e*(f^(c*(a + b*x)))^n]/x,x]","\int \frac{\log \left(d+e \left(f^{c (a+b x)}\right)^n\right)}{x} \, dx","\text{Int}\left(\frac{\log \left(e \left(f^{c (a+b x)}\right)^n+d\right)}{x},x\right)",0,"Defer[Int][Log[d + e*(f^(c*(a + b*x)))^n]/x, x]","A",0,0,0,0,-1,"{}"
128,1,39,0,0.0259307,"\int \log \left(b \left(F^{e (c+d x)}\right)^n+\pi \right) \, dx","Int[Log[b*(F^(e*(c + d*x)))^n + Pi],x]","x \log (\pi )-\frac{\text{PolyLog}\left(2,-\frac{b \left(F^{e (c+d x)}\right)^n}{\pi }\right)}{d e n \log (F)}","x \log (\pi )-\frac{\text{PolyLog}\left(2,-\frac{b \left(F^{e (c+d x)}\right)^n}{\pi }\right)}{d e n \log (F)}",1,"x*Log[Pi] - PolyLog[2, -((b*(F^(e*(c + d*x)))^n)/Pi)]/(d*e*n*Log[F])","A",3,3,16,0.1875,1,"{2279, 2392, 2391}"
129,1,5,0,0.0178284,"\int \frac{1}{x (3+\log (x))} \, dx","Int[1/(x*(3 + Log[x])),x]","\log (\log (x)+3)","\log (\log (x)+3)",1,"Log[3 + Log[x]]","A",2,2,10,0.2000,1,"{2302, 29}"
130,1,12,0,0.0256897,"\int \frac{\sqrt{1+\log (x)}}{x} \, dx","Int[Sqrt[1 + Log[x]]/x,x]","\frac{2}{3} (\log (x)+1)^{3/2}","\frac{2}{3} (\log (x)+1)^{3/2}",1,"(2*(1 + Log[x])^(3/2))/3","A",2,2,12,0.1667,1,"{2302, 30}"
131,1,10,0,0.0165482,"\int \frac{(1+\log (x))^5}{x} \, dx","Int[(1 + Log[x])^5/x,x]","\frac{1}{6} (\log (x)+1)^6","\frac{1}{6} (\log (x)+1)^6",1,"(1 + Log[x])^6/6","A",2,2,10,0.2000,1,"{2302, 30}"
132,1,8,0,0.0139242,"\int \frac{1}{x \sqrt{\log (x)}} \, dx","Int[1/(x*Sqrt[Log[x]]),x]","2 \sqrt{\log (x)}","2 \sqrt{\log (x)}",1,"2*Sqrt[Log[x]]","A",2,2,10,0.2000,1,"{2302, 30}"
133,1,3,0,0.0200639,"\int \frac{1}{x \left(1+\log ^2(x)\right)} \, dx","Int[1/(x*(1 + Log[x]^2)),x]","\tan ^{-1}(\log (x))","\tan ^{-1}(\log (x))",1,"ArcTan[Log[x]]","A",2,1,12,0.08333,1,"{203}"
134,1,14,0,0.0323525,"\int \frac{1}{x \sqrt{-3+\log ^2(x)}} \, dx","Int[1/(x*Sqrt[-3 + Log[x]^2]),x]","\tanh ^{-1}\left(\frac{\log (x)}{\sqrt{\log ^2(x)-3}}\right)","\tanh ^{-1}\left(\frac{\log (x)}{\sqrt{\log ^2(x)-3}}\right)",1,"ArcTanh[Log[x]/Sqrt[-3 + Log[x]^2]]","A",3,2,14,0.1429,1,"{217, 206}"
135,1,11,0,0.0350316,"\int \frac{1}{x \sqrt{4-9 \log ^2(x)}} \, dx","Int[1/(x*Sqrt[4 - 9*Log[x]^2]),x]","\frac{1}{3} \sin ^{-1}\left(\frac{3 \log (x)}{2}\right)","\frac{1}{3} \sin ^{-1}\left(\frac{3 \log (x)}{2}\right)",1,"ArcSin[(3*Log[x])/2]/3","A",2,1,16,0.06250,1,"{216}"
136,1,7,0,0.0291678,"\int \frac{1}{x \sqrt{4+\log ^2(x)}} \, dx","Int[1/(x*Sqrt[4 + Log[x]^2]),x]","\sinh ^{-1}\left(\frac{\log (x)}{2}\right)","\sinh ^{-1}\left(\frac{\log (x)}{2}\right)",1,"ArcSinh[Log[x]/2]","A",2,1,14,0.07143,1,"{215}"
137,1,111,0,0.0998283,"\int \frac{1}{x \left(2+3 \log ^3(6 x)\right)} \, dx","Int[1/(x*(2 + 3*Log[6*x]^3)),x]","-\frac{\log \left(3^{2/3} \log ^2(6 x)-\sqrt[3]{6} \log (6 x)+2^{2/3}\right)}{6\ 2^{2/3} \sqrt[3]{3}}+\frac{\log \left(\sqrt[3]{3} \log (6 x)+\sqrt[3]{2}\right)}{3\ 2^{2/3} \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2^{2/3} \log (6 x)}{\sqrt[6]{3}}\right)}{2^{2/3} 3^{5/6}}","-\frac{\log \left(3^{2/3} \log ^2(6 x)-\sqrt[3]{6} \log (6 x)+2^{2/3}\right)}{6\ 2^{2/3} \sqrt[3]{3}}+\frac{\log \left(\sqrt[3]{3} \log (6 x)+\sqrt[3]{2}\right)}{3\ 2^{2/3} \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2^{2/3} \log (6 x)}{\sqrt[6]{3}}\right)}{2^{2/3} 3^{5/6}}",1,"-(ArcTan[1/Sqrt[3] - (2^(2/3)*Log[6*x])/3^(1/6)]/(2^(2/3)*3^(5/6))) + Log[2^(1/3) + 3^(1/3)*Log[6*x]]/(3*2^(2/3)*3^(1/3)) - Log[2^(2/3) - 6^(1/3)*Log[6*x] + 3^(2/3)*Log[6*x]^2]/(6*2^(2/3)*3^(1/3))","A",7,6,16,0.3750,1,"{200, 31, 634, 617, 204, 628}"
138,1,11,0,0.0283252,"\int \frac{\log (\log (6 x))}{x \log (6 x)} \, dx","Int[Log[Log[6*x]]/(x*Log[6*x]),x]","\frac{1}{2} \log ^2(\log (6 x))","\frac{1}{2} \log ^2(\log (6 x))",1,"Log[Log[6*x]]^2/2","A",2,1,15,0.06667,1,"{2301}"
139,1,9,0,0.0154783,"\int \frac{2^{\log (x)}}{x} \, dx","Int[2^Log[x]/x,x]","\frac{x^{\log (2)}}{\log (2)}","\frac{2^{\log (x)}}{\log (2)}",1,"x^Log[2]/Log[2]","A",2,2,8,0.2500,1,"{2274, 30}"
140,1,17,0,0.0199459,"\int \frac{\sin ^2(\log (x))}{x} \, dx","Int[Sin[Log[x]]^2/x,x]","\frac{\log (x)}{2}-\frac{1}{2} \sin (\log (x)) \cos (\log (x))","\frac{\log (x)}{2}-\frac{1}{2} \sin (\log (x)) \cos (\log (x))",1,"Log[x]/2 - (Cos[Log[x]]*Sin[Log[x]])/2","A",3,2,9,0.2222,1,"{2635, 8}"
141,1,12,0,0.0362636,"\int \frac{7-\log (x)}{x (3+\log (x))} \, dx","Int[(7 - Log[x])/(x*(3 + Log[x])),x]","10 \log (\log (x)+3)-\log (x)","10 \log (\log (x)+3)-\log (x)",1,"-Log[x] + 10*Log[3 + Log[x]]","A",3,2,16,0.1250,1,"{2365, 43}"
142,1,21,0,0.0359142,"\int \frac{(2-\log (x)) (3+\log (x))^2}{x} \, dx","Int[((2 - Log[x])*(3 + Log[x])^2)/x,x]","\frac{5}{3} (\log (x)+3)^3-\frac{1}{4} (\log (x)+3)^4","\frac{5}{3} (\log (x)+3)^3-\frac{1}{4} (\log (x)+3)^4",1,"(5*(3 + Log[x])^3)/3 - (3 + Log[x])^4/4","A",3,2,16,0.1250,1,"{2365, 43}"
143,1,42,0,0.0673748,"\int \frac{\log ^2(x) \sqrt{1+\log ^2(x)}}{x} \, dx","Int[(Log[x]^2*Sqrt[1 + Log[x]^2])/x,x]","\frac{1}{4} \sqrt{\log ^2(x)+1} \log ^3(x)+\frac{1}{8} \sqrt{\log ^2(x)+1} \log (x)-\frac{1}{8} \sinh ^{-1}(\log (x))","\frac{1}{4} \sqrt{\log ^2(x)+1} \log ^3(x)+\frac{1}{8} \sqrt{\log ^2(x)+1} \log (x)-\frac{1}{8} \sinh ^{-1}(\log (x))",1,"-ArcSinh[Log[x]]/8 + (Log[x]*Sqrt[1 + Log[x]^2])/8 + (Log[x]^3*Sqrt[1 + Log[x]^2])/4","A",4,3,18,0.1667,1,"{279, 321, 215}"
144,1,24,0,0.0405776,"\int \frac{1+\log (x)}{x (3+2 \log (x))^2} \, dx","Int[(1 + Log[x])/(x*(3 + 2*Log[x])^2),x]","\frac{1}{4} \log (2 \log (x)+3)+\frac{1}{4 (2 \log (x)+3)}","\frac{1}{4} \log (2 \log (x)+3)+\frac{1}{4 (2 \log (x)+3)}",1,"1/(4*(3 + 2*Log[x])) + Log[3 + 2*Log[x]]/4","A",3,2,16,0.1250,1,"{2365, 43}"
145,1,23,0,0.043482,"\int \frac{\log (x)}{x \sqrt{1+\log (x)}} \, dx","Int[Log[x]/(x*Sqrt[1 + Log[x]]),x]","\frac{2}{3} (\log (x)+1)^{3/2}-2 \sqrt{\log (x)+1}","\frac{2}{3} (\log (x)+1)^{3/2}-2 \sqrt{\log (x)+1}",1,"-2*Sqrt[1 + Log[x]] + (2*(1 + Log[x])^(3/2))/3","A",3,2,14,0.1429,1,"{2365, 43}"
146,1,29,0,0.0505343,"\int \frac{\log (x)}{x \sqrt{-1+4 \log (x)}} \, dx","Int[Log[x]/(x*Sqrt[-1 + 4*Log[x]]),x]","\frac{1}{24} (4 \log (x)-1)^{3/2}+\frac{1}{8} \sqrt{4 \log (x)-1}","\frac{1}{24} (4 \log (x)-1)^{3/2}+\frac{1}{8} \sqrt{4 \log (x)-1}",1,"Sqrt[-1 + 4*Log[x]]/8 + (-1 + 4*Log[x])^(3/2)/24","A",3,2,16,0.1250,1,"{2365, 43}"
147,1,22,0,0.0601711,"\int \frac{\sqrt{1+\log (x)}}{x \log (x)} \, dx","Int[Sqrt[1 + Log[x]]/(x*Log[x]),x]","2 \sqrt{\log (x)+1}-2 \tanh ^{-1}\left(\sqrt{\log (x)+1}\right)","2 \sqrt{\log (x)+1}-2 \tanh ^{-1}\left(\sqrt{\log (x)+1}\right)",1,"-2*ArcTanh[Sqrt[1 + Log[x]]] + 2*Sqrt[1 + Log[x]]","A",4,4,16,0.2500,1,"{2365, 50, 63, 207}"
148,1,27,0,0.0494096,"\int \frac{1-4 \log (x)+\log ^2(x)}{x (-1+\log (x))^4} \, dx","Int[(1 - 4*Log[x] + Log[x]^2)/(x*(-1 + Log[x])^4),x]","\frac{1}{(\log (x)-1)^2}+\frac{1}{1-\log (x)}-\frac{2}{3 (1-\log (x))^3}","\frac{1}{(\log (x)-1)^2}+\frac{1}{1-\log (x)}-\frac{2}{3 (1-\log (x))^3}",1,"-2/(3*(1 - Log[x])^3) + (1 - Log[x])^(-1) + (-1 + Log[x])^(-2)","A",3,1,20,0.05000,1,"{698}"
149,1,27,0,0.026034,"\int \frac{\log ^2\left(a x^n\right)^p}{x} \, dx","Int[(Log[a*x^n]^2)^p/x,x]","\frac{\log \left(a x^n\right) \log ^2\left(a x^n\right)^p}{n (2 p+1)}","\frac{\log \left(a x^n\right) \log ^2\left(a x^n\right)^p}{n (2 p+1)}",1,"(Log[a*x^n]*(Log[a*x^n]^2)^p)/(n*(1 + 2*p))","A",3,2,14,0.1429,1,"{15, 30}"
150,1,27,0,0.0347011,"\int \frac{\log ^m\left(a x^n\right)^p}{x} \, dx","Int[(Log[a*x^n]^m)^p/x,x]","\frac{\log \left(a x^n\right) \log ^m\left(a x^n\right)^p}{n (m p+1)}","\frac{\log \left(a x^n\right) \log ^m\left(a x^n\right)^p}{n (m p+1)}",1,"(Log[a*x^n]*(Log[a*x^n]^m)^p)/(n*(1 + m*p))","A",3,2,14,0.1429,1,"{15, 30}"
151,1,25,0,0.0200935,"\int \frac{\sqrt{\log ^2\left(a x^n\right)}}{x} \, dx","Int[Sqrt[Log[a*x^n]^2]/x,x]","\frac{\log \left(a x^n\right) \sqrt{\log ^2\left(a x^n\right)}}{2 n}","\frac{\log \left(a x^n\right) \sqrt{\log ^2\left(a x^n\right)}}{2 n}",1,"(Log[a*x^n]*Sqrt[Log[a*x^n]^2])/(2*n)","A",3,2,16,0.1250,1,"{15, 30}"
152,1,29,0,0.0376942,"\int \frac{\left(b \log ^m\left(a x^n\right)\right)^p}{x} \, dx","Int[(b*Log[a*x^n]^m)^p/x,x]","\frac{\log \left(a x^n\right) \left(b \log ^m\left(a x^n\right)\right)^p}{n (m p+1)}","\frac{\log \left(a x^n\right) \left(b \log ^m\left(a x^n\right)\right)^p}{n (m p+1)}",1,"(Log[a*x^n]*(b*Log[a*x^n]^m)^p)/(n*(1 + m*p))","A",3,2,16,0.1250,1,"{15, 30}"
153,1,31,0,0.0157068,"\int \frac{1}{x \log \left(e^x\right)} \, dx","Int[1/(x*Log[E^x]),x]","\frac{\log \left(\log \left(e^x\right)\right)}{x-\log \left(e^x\right)}-\frac{\log (x)}{x-\log \left(e^x\right)}","\frac{\log \left(\log \left(e^x\right)\right)}{x-\log \left(e^x\right)}-\frac{\log (x)}{x-\log \left(e^x\right)}",1,"-(Log[x]/(x - Log[E^x])) + Log[Log[E^x]]/(x - Log[E^x])","A",4,3,10,0.3000,1,"{2160, 2157, 29}"
154,1,35,0,0.0780172,"\int \log (x) \sin (a+b x) \, dx","Int[Log[x]*Sin[a + b*x],x]","\frac{\cos (a) \text{CosIntegral}(b x)}{b}-\frac{\sin (a) \text{Si}(b x)}{b}-\frac{\log (x) \cos (a+b x)}{b}","\frac{\cos (a) \text{CosIntegral}(b x)}{b}-\frac{\sin (a) \text{Si}(b x)}{b}-\frac{\log (x) \cos (a+b x)}{b}",1,"(Cos[a]*CosIntegral[b*x])/b - (Cos[a + b*x]*Log[x])/b - (Sin[a]*SinIntegral[b*x])/b","A",5,6,9,0.6667,1,"{2638, 2554, 12, 3303, 3299, 3302}"
155,1,66,0,0.1140008,"\int \log (x) \sin ^2(a+b x) \, dx","Int[Log[x]*Sin[a + b*x]^2,x]","\frac{\sin (2 a) \text{CosIntegral}(2 b x)}{4 b}+\frac{\cos (2 a) \text{Si}(2 b x)}{4 b}-\frac{\log (x) \sin (a+b x) \cos (a+b x)}{2 b}-\frac{x}{2}+\frac{1}{2} x \log (x)","\frac{\sin (2 a) \text{CosIntegral}(2 b x)}{4 b}+\frac{\cos (2 a) \text{Si}(2 b x)}{4 b}-\frac{\log (x) \sin (a+b x) \cos (a+b x)}{2 b}-\frac{x}{2}+\frac{1}{2} x \log (x)",1,"-x/2 + (x*Log[x])/2 + (CosIntegral[2*b*x]*Sin[2*a])/(4*b) - (Cos[a + b*x]*Log[x]*Sin[a + b*x])/(2*b) + (Cos[2*a]*SinIntegral[2*b*x])/(4*b)","A",5,6,11,0.5455,1,"{2635, 8, 2554, 3303, 3299, 3302}"
156,1,89,0,0.5177262,"\int \log (x) \sin ^3(a+b x) \, dx","Int[Log[x]*Sin[a + b*x]^3,x]","\frac{3 \cos (a) \text{CosIntegral}(b x)}{4 b}-\frac{\cos (3 a) \text{CosIntegral}(3 b x)}{12 b}-\frac{3 \sin (a) \text{Si}(b x)}{4 b}+\frac{\sin (3 a) \text{Si}(3 b x)}{12 b}+\frac{\log (x) \cos ^3(a+b x)}{3 b}-\frac{\log (x) \cos (a+b x)}{b}","\frac{3 \cos (a) \text{CosIntegral}(b x)}{4 b}-\frac{\cos (3 a) \text{CosIntegral}(3 b x)}{12 b}-\frac{3 \sin (a) \text{Si}(b x)}{4 b}+\frac{\sin (3 a) \text{Si}(3 b x)}{12 b}+\frac{\log (x) \cos ^3(a+b x)}{3 b}-\frac{\log (x) \cos (a+b x)}{b}",1,"(3*Cos[a]*CosIntegral[b*x])/(4*b) - (Cos[3*a]*CosIntegral[3*b*x])/(12*b) - (Cos[a + b*x]*Log[x])/b + (Cos[a + b*x]^3*Log[x])/(3*b) - (3*Sin[a]*SinIntegral[b*x])/(4*b) + (Sin[3*a]*SinIntegral[3*b*x])/(12*b)","A",15,8,11,0.7273,1,"{2633, 2554, 12, 6742, 3303, 3299, 3302, 3312}"
157,1,35,0,0.0611252,"\int \cos (a+b x) \log (x) \, dx","Int[Cos[a + b*x]*Log[x],x]","-\frac{\sin (a) \text{CosIntegral}(b x)}{b}-\frac{\cos (a) \text{Si}(b x)}{b}+\frac{\log (x) \sin (a+b x)}{b}","-\frac{\sin (a) \text{CosIntegral}(b x)}{b}-\frac{\cos (a) \text{Si}(b x)}{b}+\frac{\log (x) \sin (a+b x)}{b}",1,"-((CosIntegral[b*x]*Sin[a])/b) + (Log[x]*Sin[a + b*x])/b - (Cos[a]*SinIntegral[b*x])/b","A",5,6,9,0.6667,1,"{2637, 2554, 12, 3303, 3299, 3302}"
158,1,66,0,0.1214746,"\int \cos ^2(a+b x) \log (x) \, dx","Int[Cos[a + b*x]^2*Log[x],x]","-\frac{\sin (2 a) \text{CosIntegral}(2 b x)}{4 b}-\frac{\cos (2 a) \text{Si}(2 b x)}{4 b}+\frac{\log (x) \sin (a+b x) \cos (a+b x)}{2 b}-\frac{x}{2}+\frac{1}{2} x \log (x)","-\frac{\sin (2 a) \text{CosIntegral}(2 b x)}{4 b}-\frac{\cos (2 a) \text{Si}(2 b x)}{4 b}+\frac{\log (x) \sin (a+b x) \cos (a+b x)}{2 b}-\frac{x}{2}+\frac{1}{2} x \log (x)",1,"-x/2 + (x*Log[x])/2 - (CosIntegral[2*b*x]*Sin[2*a])/(4*b) + (Cos[a + b*x]*Log[x]*Sin[a + b*x])/(2*b) - (Cos[2*a]*SinIntegral[2*b*x])/(4*b)","A",7,8,11,0.7273,1,"{2635, 8, 2554, 12, 3327, 3303, 3299, 3302}"
159,1,88,0,0.468172,"\int \cos ^3(a+b x) \log (x) \, dx","Int[Cos[a + b*x]^3*Log[x],x]","-\frac{3 \sin (a) \text{CosIntegral}(b x)}{4 b}-\frac{\sin (3 a) \text{CosIntegral}(3 b x)}{12 b}-\frac{3 \cos (a) \text{Si}(b x)}{4 b}-\frac{\cos (3 a) \text{Si}(3 b x)}{12 b}-\frac{\log (x) \sin ^3(a+b x)}{3 b}+\frac{\log (x) \sin (a+b x)}{b}","-\frac{3 \sin (a) \text{CosIntegral}(b x)}{4 b}-\frac{\sin (3 a) \text{CosIntegral}(3 b x)}{12 b}-\frac{3 \cos (a) \text{Si}(b x)}{4 b}-\frac{\cos (3 a) \text{Si}(3 b x)}{12 b}-\frac{\log (x) \sin ^3(a+b x)}{3 b}+\frac{\log (x) \sin (a+b x)}{b}",1,"(-3*CosIntegral[b*x]*Sin[a])/(4*b) - (CosIntegral[3*b*x]*Sin[3*a])/(12*b) + (Log[x]*Sin[a + b*x])/b - (Log[x]*Sin[a + b*x]^3)/(3*b) - (3*Cos[a]*SinIntegral[b*x])/(4*b) - (Cos[3*a]*SinIntegral[3*b*x])/(12*b)","A",15,8,11,0.7273,1,"{2633, 2554, 12, 6742, 3303, 3299, 3302, 4430}"
160,1,5,0,0.0332612,"\int \left(\cos (x) \log (x)+\frac{\sin (x)}{x}\right) \, dx","Int[Cos[x]*Log[x] + Sin[x]/x,x]","\log (x) \sin (x)","\log (x) \sin (x)",1,"Log[x]*Sin[x]","A",4,3,12,0.2500,1,"{2637, 2554, 3299}"
161,1,47,0,0.0573425,"\int \log (a \sin (x)) \, dx","Int[Log[a*Sin[x]],x]","\frac{1}{2} i \text{PolyLog}\left(2,e^{2 i x}\right)+x \log (a \sin (x))+\frac{i x^2}{2}-x \log \left(1-e^{2 i x}\right)","\frac{1}{2} i \text{PolyLog}\left(2,e^{2 i x}\right)+x \log (a \sin (x))+\frac{i x^2}{2}-x \log \left(1-e^{2 i x}\right)",1,"(I/2)*x^2 - x*Log[1 - E^((2*I)*x)] + x*Log[a*Sin[x]] + (I/2)*PolyLog[2, E^((2*I)*x)]","A",5,5,5,1.000,1,"{2548, 3717, 2190, 2279, 2391}"
162,1,45,0,0.0590161,"\int \log \left(a \sin ^2(x)\right) \, dx","Int[Log[a*Sin[x]^2],x]","i \text{PolyLog}\left(2,e^{2 i x}\right)+x \log \left(a \sin ^2(x)\right)+i x^2-2 x \log \left(1-e^{2 i x}\right)","i \text{PolyLog}\left(2,e^{2 i x}\right)+x \log \left(a \sin ^2(x)\right)+i x^2-2 x \log \left(1-e^{2 i x}\right)",1,"I*x^2 - 2*x*Log[1 - E^((2*I)*x)] + x*Log[a*Sin[x]^2] + I*PolyLog[2, E^((2*I)*x)]","A",6,6,7,0.8571,1,"{2548, 12, 3717, 2190, 2279, 2391}"
163,1,52,0,0.0598711,"\int \log \left(a \sin ^n(x)\right) \, dx","Int[Log[a*Sin[x]^n],x]","\frac{1}{2} i n \text{PolyLog}\left(2,e^{2 i x}\right)+x \log \left(a \sin ^n(x)\right)+\frac{1}{2} i n x^2-n x \log \left(1-e^{2 i x}\right)","\frac{1}{2} i n \text{PolyLog}\left(2,e^{2 i x}\right)+x \log \left(a \sin ^n(x)\right)+\frac{1}{2} i n x^2-n x \log \left(1-e^{2 i x}\right)",1,"(I/2)*n*x^2 - n*x*Log[1 - E^((2*I)*x)] + x*Log[a*Sin[x]^n] + (I/2)*n*PolyLog[2, E^((2*I)*x)]","A",6,6,7,0.8571,1,"{2548, 12, 3717, 2190, 2279, 2391}"
164,1,47,0,0.0533219,"\int \log (a \cos (x)) \, dx","Int[Log[a*Cos[x]],x]","\frac{1}{2} i \text{PolyLog}\left(2,-e^{2 i x}\right)+x \log (a \cos (x))+\frac{i x^2}{2}-x \log \left(1+e^{2 i x}\right)","\frac{1}{2} i \text{PolyLog}\left(2,-e^{2 i x}\right)+x \log (a \cos (x))+\frac{i x^2}{2}-x \log \left(1+e^{2 i x}\right)",1,"(I/2)*x^2 - x*Log[1 + E^((2*I)*x)] + x*Log[a*Cos[x]] + (I/2)*PolyLog[2, -E^((2*I)*x)]","A",5,5,5,1.000,1,"{2548, 3719, 2190, 2279, 2391}"
165,1,45,0,0.0558014,"\int \log \left(a \cos ^2(x)\right) \, dx","Int[Log[a*Cos[x]^2],x]","i \text{PolyLog}\left(2,-e^{2 i x}\right)+x \log \left(a \cos ^2(x)\right)+i x^2-2 x \log \left(1+e^{2 i x}\right)","i \text{PolyLog}\left(2,-e^{2 i x}\right)+x \log \left(a \cos ^2(x)\right)+i x^2-2 x \log \left(1+e^{2 i x}\right)",1,"I*x^2 - 2*x*Log[1 + E^((2*I)*x)] + x*Log[a*Cos[x]^2] + I*PolyLog[2, -E^((2*I)*x)]","A",6,6,7,0.8571,1,"{2548, 12, 3719, 2190, 2279, 2391}"
166,1,52,0,0.0581344,"\int \log \left(a \cos ^n(x)\right) \, dx","Int[Log[a*Cos[x]^n],x]","\frac{1}{2} i n \text{PolyLog}\left(2,-e^{2 i x}\right)+x \log \left(a \cos ^n(x)\right)+\frac{1}{2} i n x^2-n x \log \left(1+e^{2 i x}\right)","\frac{1}{2} i n \text{PolyLog}\left(2,-e^{2 i x}\right)+x \log \left(a \cos ^n(x)\right)+\frac{1}{2} i n x^2-n x \log \left(1+e^{2 i x}\right)",1,"(I/2)*n*x^2 - n*x*Log[1 + E^((2*I)*x)] + x*Log[a*Cos[x]^n] + (I/2)*n*PolyLog[2, -E^((2*I)*x)]","A",6,6,7,0.8571,1,"{2548, 12, 3719, 2190, 2279, 2391}"
167,1,51,0,0.044377,"\int \log (a \tan (x)) \, dx","Int[Log[a*Tan[x]],x]","-\frac{1}{2} i \text{PolyLog}\left(2,-e^{2 i x}\right)+\frac{1}{2} i \text{PolyLog}\left(2,e^{2 i x}\right)+x \log (a \tan (x))+2 x \tanh ^{-1}\left(e^{2 i x}\right)","-\frac{1}{2} i \text{PolyLog}\left(2,-e^{2 i x}\right)+\frac{1}{2} i \text{PolyLog}\left(2,e^{2 i x}\right)+x \log (a \tan (x))+2 x \tanh ^{-1}\left(e^{2 i x}\right)",1,"2*x*ArcTanh[E^((2*I)*x)] + x*Log[a*Tan[x]] - (I/2)*PolyLog[2, -E^((2*I)*x)] + (I/2)*PolyLog[2, E^((2*I)*x)]","A",7,5,5,1.000,1,"{2548, 4419, 4183, 2279, 2391}"
168,1,49,0,0.0482655,"\int \log \left(a \tan ^2(x)\right) \, dx","Int[Log[a*Tan[x]^2],x]","-i \text{PolyLog}\left(2,-e^{2 i x}\right)+i \text{PolyLog}\left(2,e^{2 i x}\right)+x \log \left(a \tan ^2(x)\right)+4 x \tanh ^{-1}\left(e^{2 i x}\right)","-i \text{PolyLog}\left(2,-e^{2 i x}\right)+i \text{PolyLog}\left(2,e^{2 i x}\right)+x \log \left(a \tan ^2(x)\right)+4 x \tanh ^{-1}\left(e^{2 i x}\right)",1,"4*x*ArcTanh[E^((2*I)*x)] + x*Log[a*Tan[x]^2] - I*PolyLog[2, -E^((2*I)*x)] + I*PolyLog[2, E^((2*I)*x)]","A",8,6,7,0.8571,1,"{2548, 12, 4419, 4183, 2279, 2391}"
169,1,56,0,0.0482997,"\int \log \left(a \tan ^n(x)\right) \, dx","Int[Log[a*Tan[x]^n],x]","-\frac{1}{2} i n \text{PolyLog}\left(2,-e^{2 i x}\right)+\frac{1}{2} i n \text{PolyLog}\left(2,e^{2 i x}\right)+x \log \left(a \tan ^n(x)\right)+2 n x \tanh ^{-1}\left(e^{2 i x}\right)","-\frac{1}{2} i n \text{PolyLog}\left(2,-e^{2 i x}\right)+\frac{1}{2} i n \text{PolyLog}\left(2,e^{2 i x}\right)+x \log \left(a \tan ^n(x)\right)+2 n x \tanh ^{-1}\left(e^{2 i x}\right)",1,"2*n*x*ArcTanh[E^((2*I)*x)] + x*Log[a*Tan[x]^n] - (I/2)*n*PolyLog[2, -E^((2*I)*x)] + (I/2)*n*PolyLog[2, E^((2*I)*x)]","A",8,6,7,0.8571,1,"{2548, 12, 4419, 4183, 2279, 2391}"
170,1,51,0,0.046003,"\int \log (a \cot (x)) \, dx","Int[Log[a*Cot[x]],x]","\frac{1}{2} i \text{PolyLog}\left(2,-e^{2 i x}\right)-\frac{1}{2} i \text{PolyLog}\left(2,e^{2 i x}\right)+x \log (a \cot (x))-2 x \tanh ^{-1}\left(e^{2 i x}\right)","\frac{1}{2} i \text{PolyLog}\left(2,-e^{2 i x}\right)-\frac{1}{2} i \text{PolyLog}\left(2,e^{2 i x}\right)+x \log (a \cot (x))-2 x \tanh ^{-1}\left(e^{2 i x}\right)",1,"-2*x*ArcTanh[E^((2*I)*x)] + x*Log[a*Cot[x]] + (I/2)*PolyLog[2, -E^((2*I)*x)] - (I/2)*PolyLog[2, E^((2*I)*x)]","A",7,5,5,1.000,1,"{2548, 4419, 4183, 2279, 2391}"
171,1,49,0,0.0471132,"\int \log \left(a \cot ^2(x)\right) \, dx","Int[Log[a*Cot[x]^2],x]","i \text{PolyLog}\left(2,-e^{2 i x}\right)-i \text{PolyLog}\left(2,e^{2 i x}\right)+x \log \left(a \cot ^2(x)\right)-4 x \tanh ^{-1}\left(e^{2 i x}\right)","i \text{PolyLog}\left(2,-e^{2 i x}\right)-i \text{PolyLog}\left(2,e^{2 i x}\right)+x \log \left(a \cot ^2(x)\right)-4 x \tanh ^{-1}\left(e^{2 i x}\right)",1,"-4*x*ArcTanh[E^((2*I)*x)] + x*Log[a*Cot[x]^2] + I*PolyLog[2, -E^((2*I)*x)] - I*PolyLog[2, E^((2*I)*x)]","A",8,6,7,0.8571,1,"{2548, 12, 4419, 4183, 2279, 2391}"
172,1,56,0,0.0486499,"\int \log \left(a \cot ^n(x)\right) \, dx","Int[Log[a*Cot[x]^n],x]","\frac{1}{2} i n \text{PolyLog}\left(2,-e^{2 i x}\right)-\frac{1}{2} i n \text{PolyLog}\left(2,e^{2 i x}\right)+x \log \left(a \cot ^n(x)\right)-2 n x \tanh ^{-1}\left(e^{2 i x}\right)","\frac{1}{2} i n \text{PolyLog}\left(2,-e^{2 i x}\right)-\frac{1}{2} i n \text{PolyLog}\left(2,e^{2 i x}\right)+x \log \left(a \cot ^n(x)\right)-2 n x \tanh ^{-1}\left(e^{2 i x}\right)",1,"-2*n*x*ArcTanh[E^((2*I)*x)] + x*Log[a*Cot[x]^n] + (I/2)*n*PolyLog[2, -E^((2*I)*x)] - (I/2)*n*PolyLog[2, E^((2*I)*x)]","A",8,6,7,0.8571,1,"{2548, 12, 4419, 4183, 2279, 2391}"
173,1,46,0,0.0518107,"\int \log (a \sec (x)) \, dx","Int[Log[a*Sec[x]],x]","-\frac{1}{2} i \text{PolyLog}\left(2,-e^{2 i x}\right)+x \log (a \sec (x))-\frac{i x^2}{2}+x \log \left(1+e^{2 i x}\right)","-\frac{1}{2} i \text{PolyLog}\left(2,-e^{2 i x}\right)+x \log (a \sec (x))-\frac{i x^2}{2}+x \log \left(1+e^{2 i x}\right)",1,"(-I/2)*x^2 + x*Log[1 + E^((2*I)*x)] + x*Log[a*Sec[x]] - (I/2)*PolyLog[2, -E^((2*I)*x)]","A",5,5,5,1.000,1,"{2548, 3719, 2190, 2279, 2391}"
174,1,45,0,0.0543116,"\int \log \left(a \sec ^2(x)\right) \, dx","Int[Log[a*Sec[x]^2],x]","-i \text{PolyLog}\left(2,-e^{2 i x}\right)+x \log \left(a \sec ^2(x)\right)-i x^2+2 x \log \left(1+e^{2 i x}\right)","-i \text{PolyLog}\left(2,-e^{2 i x}\right)+x \log \left(a \sec ^2(x)\right)-i x^2+2 x \log \left(1+e^{2 i x}\right)",1,"(-I)*x^2 + 2*x*Log[1 + E^((2*I)*x)] + x*Log[a*Sec[x]^2] - I*PolyLog[2, -E^((2*I)*x)]","A",6,6,7,0.8571,1,"{2548, 12, 3719, 2190, 2279, 2391}"
175,1,51,0,0.0538001,"\int \log \left(a \sec ^n(x)\right) \, dx","Int[Log[a*Sec[x]^n],x]","-\frac{1}{2} i n \text{PolyLog}\left(2,-e^{2 i x}\right)+x \log \left(a \sec ^n(x)\right)-\frac{1}{2} i n x^2+n x \log \left(1+e^{2 i x}\right)","-\frac{1}{2} i n \text{PolyLog}\left(2,-e^{2 i x}\right)+x \log \left(a \sec ^n(x)\right)-\frac{1}{2} i n x^2+n x \log \left(1+e^{2 i x}\right)",1,"(-I/2)*n*x^2 + n*x*Log[1 + E^((2*I)*x)] + x*Log[a*Sec[x]^n] - (I/2)*n*PolyLog[2, -E^((2*I)*x)]","A",6,6,7,0.8571,1,"{2548, 12, 3719, 2190, 2279, 2391}"
176,1,46,0,0.0528519,"\int \log (a \csc (x)) \, dx","Int[Log[a*Csc[x]],x]","-\frac{1}{2} i \text{PolyLog}\left(2,e^{2 i x}\right)+x \log (a \csc (x))-\frac{i x^2}{2}+x \log \left(1-e^{2 i x}\right)","-\frac{1}{2} i \text{PolyLog}\left(2,e^{2 i x}\right)+x \log (a \csc (x))-\frac{i x^2}{2}+x \log \left(1-e^{2 i x}\right)",1,"(-I/2)*x^2 + x*Log[1 - E^((2*I)*x)] + x*Log[a*Csc[x]] - (I/2)*PolyLog[2, E^((2*I)*x)]","A",5,5,5,1.000,1,"{2548, 3717, 2190, 2279, 2391}"
177,1,45,0,0.057692,"\int \log \left(a \csc ^2(x)\right) \, dx","Int[Log[a*Csc[x]^2],x]","-i \text{PolyLog}\left(2,e^{2 i x}\right)+x \log \left(a \csc ^2(x)\right)-i x^2+2 x \log \left(1-e^{2 i x}\right)","-i \text{PolyLog}\left(2,e^{2 i x}\right)+x \log \left(a \csc ^2(x)\right)-i x^2+2 x \log \left(1-e^{2 i x}\right)",1,"(-I)*x^2 + 2*x*Log[1 - E^((2*I)*x)] + x*Log[a*Csc[x]^2] - I*PolyLog[2, E^((2*I)*x)]","A",6,6,7,0.8571,1,"{2548, 12, 3717, 2190, 2279, 2391}"
178,1,51,0,0.0601641,"\int \log \left(a \csc ^n(x)\right) \, dx","Int[Log[a*Csc[x]^n],x]","-\frac{1}{2} i n \text{PolyLog}\left(2,e^{2 i x}\right)+x \log \left(a \csc ^n(x)\right)-\frac{1}{2} i n x^2+n x \log \left(1-e^{2 i x}\right)","-\frac{1}{2} i n \text{PolyLog}\left(2,e^{2 i x}\right)+x \log \left(a \csc ^n(x)\right)-\frac{1}{2} i n x^2+n x \log \left(1-e^{2 i x}\right)",1,"(-I/2)*n*x^2 + n*x*Log[1 - E^((2*I)*x)] + x*Log[a*Csc[x]^n] - (I/2)*n*PolyLog[2, E^((2*I)*x)]","A",6,6,7,0.8571,1,"{2548, 12, 3717, 2190, 2279, 2391}"
179,1,21,0,0.021194,"\int \cos (x) \log \left(\frac{1}{2} (1-\cos (2 x))\right) \, dx","Int[Cos[x]*Log[(1 - Cos[2*x])/2],x]","\sin (x) \log \left(\frac{1}{2} (1-\cos (2 x))\right)-2 \sin (x)","\sin (x) \log \left(\frac{1}{2} (1-\cos (2 x))\right)-2 \sin (x)",1,"-2*Sin[x] + Log[(1 - Cos[2*x])/2]*Sin[x]","A",3,3,16,0.1875,1,"{2637, 2554, 12}"
180,1,6,0,0.0163892,"\int \frac{\cot (x)}{\log (e \sin (x))} \, dx","Int[Cot[x]/Log[E*Sin[x]],x]","\log (\log (\sin (x))+1)","\log (\log (e \sin (x)))",1,"Log[1 + Log[Sin[x]]]","A",3,2,10,0.2000,1,"{4338, 31}"
181,1,37,0,0.0281907,"\int \frac{\cot (x)}{\log \left(e^{\sin (x)}\right)} \, dx","Int[Cot[x]/Log[E^Sin[x]],x]","\frac{\log \left(\log \left(e^{\sin (x)}\right)\right)}{\sin (x)-\log \left(e^{\sin (x)}\right)}-\frac{\log (\sin (x))}{\sin (x)-\log \left(e^{\sin (x)}\right)}","\frac{\log \left(\log \left(e^{\sin (x)}\right)\right)}{\sin (x)-\log \left(e^{\sin (x)}\right)}-\frac{\log (\sin (x))}{\sin (x)-\log \left(e^{\sin (x)}\right)}",1,"Log[Log[E^Sin[x]]]/(-Log[E^Sin[x]] + Sin[x]) - Log[Sin[x]]/(-Log[E^Sin[x]] + Sin[x])","A",5,4,10,0.4000,1,"{4338, 2160, 2157, 29}"
182,1,12,0,0.023436,"\int \log (\cos (x)) \sec ^2(x) \, dx","Int[Log[Cos[x]]*Sec[x]^2,x]","-x+\tan (x)+\tan (x) \log (\cos (x))","-x+\tan (x)+\tan (x) \log (\cos (x))",1,"-x + Tan[x] + Log[Cos[x]]*Tan[x]","A",3,4,8,0.5000,1,"{3767, 8, 2554, 3473}"
183,1,9,0,0.0158706,"\int \cot (x) \log (\sin (x)) \, dx","Int[Cot[x]*Log[Sin[x]],x]","\frac{1}{2} \log ^2(\sin (x))","\frac{1}{2} \log ^2(\sin (x))",1,"Log[Sin[x]]^2/2","A",2,3,6,0.5000,1,"{3475, 4338, 2301}"
184,1,20,0,0.0388632,"\int \cos (x) \log (\sin (x)) \sin ^2(x) \, dx","Int[Cos[x]*Log[Sin[x]]*Sin[x]^2,x]","\frac{1}{3} \sin ^3(x) \log (\sin (x))-\frac{\sin ^3(x)}{9}","\frac{1}{3} \sin ^3(x) \log (\sin (x))-\frac{\sin ^3(x)}{9}",1,"-Sin[x]^3/9 + (Log[Sin[x]]*Sin[x]^3)/3","A",4,4,10,0.4000,1,"{2564, 30, 2554, 12}"
185,1,50,0,0.026015,"\int \cos (a+b x) \log \left(\cos \left(\frac{a}{2}+\frac{b x}{2}\right) \sin \left(\frac{a}{2}+\frac{b x}{2}\right)\right) \, dx","Int[Cos[a + b*x]*Log[Cos[a/2 + (b*x)/2]*Sin[a/2 + (b*x)/2]],x]","\frac{\sin (a+b x) \log \left(\sin \left(\frac{a}{2}+\frac{b x}{2}\right) \cos \left(\frac{a}{2}+\frac{b x}{2}\right)\right)}{b}-\frac{\sin (a+b x)}{b}","\frac{\sin (a+b x) \log \left(\sin \left(\frac{a}{2}+\frac{b x}{2}\right) \cos \left(\frac{a}{2}+\frac{b x}{2}\right)\right)}{b}-\frac{\sin (a+b x)}{b}",1,"-(Sin[a + b*x]/b) + (Log[Cos[a/2 + (b*x)/2]*Sin[a/2 + (b*x)/2]]*Sin[a + b*x])/b","A",2,2,35,0.05714,1,"{2637, 2554}"
186,1,6,0,0.0215558,"\int \frac{\tan (x)}{\log (\cos (x))} \, dx","Int[Tan[x]/Log[Cos[x]],x]","-\log (\log (\cos (x)))","-\log (\log (\cos (x)))",1,"-Log[Log[Cos[x]]]","A",3,3,8,0.3750,1,"{4339, 2302, 29}"
187,1,9,0,0.0148105,"\int \log (\cos (x)) \tan (x) \, dx","Int[Log[Cos[x]]*Tan[x],x]","-\frac{1}{2} \log ^2(\cos (x))","-\frac{1}{2} \log ^2(\cos (x))",1,"-Log[Cos[x]]^2/2","A",2,3,6,0.5000,1,"{3475, 4339, 2301}"
188,1,10,0,0.0078169,"\int \log (\cos (x)) \sin (x) \, dx","Int[Log[Cos[x]]*Sin[x],x]","\cos (x)-\cos (x) \log (\cos (x))","\cos (x)-\cos (x) \log (\cos (x))",1,"Cos[x] - Cos[x]*Log[Cos[x]]","A",2,2,6,0.3333,1,"{2638, 2554}"
189,1,14,0,0.0195638,"\int \cos (x) \log (\cos (x)) \, dx","Int[Cos[x]*Log[Cos[x]],x]","-\sin (x)+\tanh ^{-1}(\sin (x))+\sin (x) \log (\cos (x))","-\sin (x)+\tanh ^{-1}(\sin (x))+\sin (x) \log (\cos (x))",1,"ArcTanh[Sin[x]] - Sin[x] + Log[Cos[x]]*Sin[x]","A",4,5,6,0.8333,1,"{2637, 2554, 2592, 321, 206}"
190,1,11,0,0.0093442,"\int \cos (x) \log (\sin (x)) \, dx","Int[Cos[x]*Log[Sin[x]],x]","\sin (x) \log (\sin (x))-\sin (x)","\sin (x) \log (\sin (x))-\sin (x)",1,"-Sin[x] + Log[Sin[x]]*Sin[x]","A",2,2,6,0.3333,1,"{2637, 2554}"
191,1,74,0,0.1093894,"\int \log (\sin (x)) \sin ^2(x) \, dx","Int[Log[Sin[x]]*Sin[x]^2,x]","\frac{1}{4} i \text{PolyLog}\left(2,e^{2 i x}\right)+\frac{i x^2}{4}+\frac{x}{4}-\frac{1}{2} x \log \left(1-e^{2 i x}\right)+\frac{1}{2} x \log (\sin (x))+\frac{1}{4} \sin (x) \cos (x)-\frac{1}{2} \sin (x) \cos (x) \log (\sin (x))","\frac{1}{4} i \text{PolyLog}\left(2,e^{2 i x}\right)+\frac{i x^2}{4}+\frac{x}{4}-\frac{1}{2} x \log \left(1-e^{2 i x}\right)+\frac{1}{2} x \log (\sin (x))+\frac{1}{4} \sin (x) \cos (x)-\frac{1}{2} \sin (x) \cos (x) \log (\sin (x))",1,"x/4 + (I/4)*x^2 - (x*Log[1 - E^((2*I)*x)])/2 + (x*Log[Sin[x]])/2 + (I/4)*PolyLog[2, E^((2*I)*x)] + (Cos[x]*Sin[x])/4 - (Cos[x]*Log[Sin[x]]*Sin[x])/2","A",10,9,8,1.125,1,"{2635, 8, 2554, 12, 6742, 3717, 2190, 2279, 2391}"
192,1,40,0,0.0671791,"\int \log (\sin (x)) \sin ^3(x) \, dx","Int[Log[Sin[x]]*Sin[x]^3,x]","-\frac{\cos ^3(x)}{9}+\frac{2 \cos (x)}{3}-\frac{2}{3} \tanh ^{-1}(\cos (x))+\frac{1}{3} \cos ^3(x) \log (\sin (x))-\cos (x) \log (\sin (x))","-\frac{\cos ^3(x)}{9}+\frac{2 \cos (x)}{3}-\frac{2}{3} \tanh ^{-1}(\cos (x))+\frac{1}{3} \cos ^3(x) \log (\sin (x))-\cos (x) \log (\sin (x))",1,"(-2*ArcTanh[Cos[x]])/3 + (2*Cos[x])/3 - Cos[x]^3/9 - Cos[x]*Log[Sin[x]] + (Cos[x]^3*Log[Sin[x]])/3","A",7,7,8,0.8750,1,"{2633, 2554, 12, 4366, 459, 321, 206}"
193,1,79,0,0.1020982,"\int \log \left(\sin \left(\sqrt{x}\right)\right) \, dx","Int[Log[Sin[Sqrt[x]]],x]","i \sqrt{x} \text{PolyLog}\left(2,e^{2 i \sqrt{x}}\right)-\frac{1}{2} \text{PolyLog}\left(3,e^{2 i \sqrt{x}}\right)+\frac{1}{3} i x^{3/2}-x \log \left(1-e^{2 i \sqrt{x}}\right)+x \log \left(\sin \left(\sqrt{x}\right)\right)","i \sqrt{x} \text{PolyLog}\left(2,e^{2 i \sqrt{x}}\right)-\frac{1}{2} \text{PolyLog}\left(3,e^{2 i \sqrt{x}}\right)+\frac{1}{3} i x^{3/2}-x \log \left(1-e^{2 i \sqrt{x}}\right)+x \log \left(\sin \left(\sqrt{x}\right)\right)",1,"(I/3)*x^(3/2) - x*Log[1 - E^((2*I)*Sqrt[x])] + x*Log[Sin[Sqrt[x]]] + I*Sqrt[x]*PolyLog[2, E^((2*I)*Sqrt[x])] - PolyLog[3, E^((2*I)*Sqrt[x])]/2","A",8,8,7,1.143,1,"{2548, 12, 3748, 3717, 2190, 2531, 2282, 6589}"
194,1,15,0,0.0205751,"\int \csc ^2(x) \log (\sin (x)) \, dx","Int[Csc[x]^2*Log[Sin[x]],x]","-x-\cot (x)-\cot (x) \log (\sin (x))","-x-\cot (x)-\cot (x) \log (\sin (x))",1,"-x - Cot[x] - Cot[x]*Log[Sin[x]]","A",3,4,8,0.5000,1,"{3767, 8, 2554, 3473}"
195,1,35,0,0.07876,"\int \log (x) \sinh (a+b x) \, dx","Int[Log[x]*Sinh[a + b*x],x]","-\frac{\cosh (a) \text{Chi}(b x)}{b}-\frac{\sinh (a) \text{Shi}(b x)}{b}+\frac{\log (x) \cosh (a+b x)}{b}","-\frac{\cosh (a) \text{Chi}(b x)}{b}-\frac{\sinh (a) \text{Shi}(b x)}{b}+\frac{\log (x) \cosh (a+b x)}{b}",1,"-((Cosh[a]*CoshIntegral[b*x])/b) + (Cosh[a + b*x]*Log[x])/b - (Sinh[a]*SinhIntegral[b*x])/b","A",5,6,9,0.6667,1,"{2638, 2554, 12, 3303, 3298, 3301}"
196,1,66,0,0.1429007,"\int \log (x) \sinh ^2(a+b x) \, dx","Int[Log[x]*Sinh[a + b*x]^2,x]","-\frac{\sinh (2 a) \text{Chi}(2 b x)}{4 b}-\frac{\cosh (2 a) \text{Shi}(2 b x)}{4 b}+\frac{\log (x) \sinh (a+b x) \cosh (a+b x)}{2 b}+\frac{x}{2}-\frac{1}{2} x \log (x)","-\frac{\sinh (2 a) \text{Chi}(2 b x)}{4 b}-\frac{\cosh (2 a) \text{Shi}(2 b x)}{4 b}+\frac{\log (x) \sinh (a+b x) \cosh (a+b x)}{2 b}+\frac{x}{2}-\frac{1}{2} x \log (x)",1,"x/2 - (x*Log[x])/2 - (CoshIntegral[2*b*x]*Sinh[2*a])/(4*b) + (Cosh[a + b*x]*Log[x]*Sinh[a + b*x])/(2*b) - (Cosh[2*a]*SinhIntegral[2*b*x])/(4*b)","A",7,8,11,0.7273,1,"{2635, 8, 2554, 12, 5274, 3303, 3298, 3301}"
197,1,89,0,0.5170128,"\int \log (x) \sinh ^3(a+b x) \, dx","Int[Log[x]*Sinh[a + b*x]^3,x]","\frac{3 \cosh (a) \text{Chi}(b x)}{4 b}-\frac{\cosh (3 a) \text{Chi}(3 b x)}{12 b}+\frac{3 \sinh (a) \text{Shi}(b x)}{4 b}-\frac{\sinh (3 a) \text{Shi}(3 b x)}{12 b}+\frac{\log (x) \cosh ^3(a+b x)}{3 b}-\frac{\log (x) \cosh (a+b x)}{b}","\frac{3 \cosh (a) \text{Chi}(b x)}{4 b}-\frac{\cosh (3 a) \text{Chi}(3 b x)}{12 b}+\frac{3 \sinh (a) \text{Shi}(b x)}{4 b}-\frac{\sinh (3 a) \text{Shi}(3 b x)}{12 b}+\frac{\log (x) \cosh ^3(a+b x)}{3 b}-\frac{\log (x) \cosh (a+b x)}{b}",1,"(3*Cosh[a]*CoshIntegral[b*x])/(4*b) - (Cosh[3*a]*CoshIntegral[3*b*x])/(12*b) - (Cosh[a + b*x]*Log[x])/b + (Cosh[a + b*x]^3*Log[x])/(3*b) + (3*Sinh[a]*SinhIntegral[b*x])/(4*b) - (Sinh[3*a]*SinhIntegral[3*b*x])/(12*b)","A",15,8,11,0.7273,1,"{2633, 2554, 12, 6742, 3303, 3298, 3301, 3312}"
198,1,35,0,0.070019,"\int \cosh (a+b x) \log (x) \, dx","Int[Cosh[a + b*x]*Log[x],x]","-\frac{\sinh (a) \text{Chi}(b x)}{b}-\frac{\cosh (a) \text{Shi}(b x)}{b}+\frac{\log (x) \sinh (a+b x)}{b}","-\frac{\sinh (a) \text{Chi}(b x)}{b}-\frac{\cosh (a) \text{Shi}(b x)}{b}+\frac{\log (x) \sinh (a+b x)}{b}",1,"-((CoshIntegral[b*x]*Sinh[a])/b) + (Log[x]*Sinh[a + b*x])/b - (Cosh[a]*SinhIntegral[b*x])/b","A",5,6,9,0.6667,1,"{2637, 2554, 12, 3303, 3298, 3301}"
199,1,66,0,0.1317831,"\int \cosh ^2(a+b x) \log (x) \, dx","Int[Cosh[a + b*x]^2*Log[x],x]","-\frac{\sinh (2 a) \text{Chi}(2 b x)}{4 b}-\frac{\cosh (2 a) \text{Shi}(2 b x)}{4 b}+\frac{\log (x) \sinh (a+b x) \cosh (a+b x)}{2 b}-\frac{x}{2}+\frac{1}{2} x \log (x)","-\frac{\sinh (2 a) \text{Chi}(2 b x)}{4 b}-\frac{\cosh (2 a) \text{Shi}(2 b x)}{4 b}+\frac{\log (x) \sinh (a+b x) \cosh (a+b x)}{2 b}-\frac{x}{2}+\frac{1}{2} x \log (x)",1,"-x/2 + (x*Log[x])/2 - (CoshIntegral[2*b*x]*Sinh[2*a])/(4*b) + (Cosh[a + b*x]*Log[x]*Sinh[a + b*x])/(2*b) - (Cosh[2*a]*SinhIntegral[2*b*x])/(4*b)","A",7,8,11,0.7273,1,"{2635, 8, 2554, 12, 5274, 3303, 3298, 3301}"
200,1,88,0,0.4834115,"\int \cosh ^3(a+b x) \log (x) \, dx","Int[Cosh[a + b*x]^3*Log[x],x]","-\frac{3 \sinh (a) \text{Chi}(b x)}{4 b}-\frac{\sinh (3 a) \text{Chi}(3 b x)}{12 b}-\frac{3 \cosh (a) \text{Shi}(b x)}{4 b}-\frac{\cosh (3 a) \text{Shi}(3 b x)}{12 b}+\frac{\log (x) \sinh ^3(a+b x)}{3 b}+\frac{\log (x) \sinh (a+b x)}{b}","-\frac{3 \sinh (a) \text{Chi}(b x)}{4 b}-\frac{\sinh (3 a) \text{Chi}(3 b x)}{12 b}-\frac{3 \cosh (a) \text{Shi}(b x)}{4 b}-\frac{\cosh (3 a) \text{Shi}(3 b x)}{12 b}+\frac{\log (x) \sinh ^3(a+b x)}{3 b}+\frac{\log (x) \sinh (a+b x)}{b}",1,"(-3*CoshIntegral[b*x]*Sinh[a])/(4*b) - (CoshIntegral[3*b*x]*Sinh[3*a])/(12*b) + (Log[x]*Sinh[a + b*x])/b + (Log[x]*Sinh[a + b*x]^3)/(3*b) - (3*Cosh[a]*SinhIntegral[b*x])/(4*b) - (Cosh[3*a]*SinhIntegral[3*b*x])/(12*b)","A",15,8,11,0.7273,1,"{2633, 2554, 12, 6742, 3303, 3298, 3301, 3312}"
201,1,39,0,0.0594839,"\int \log (a \sinh (x)) \, dx","Int[Log[a*Sinh[x]],x]","-\frac{1}{2} \text{PolyLog}\left(2,e^{2 x}\right)+x \log (a \sinh (x))+\frac{x^2}{2}-x \log \left(1-e^{2 x}\right)","-\frac{1}{2} \text{PolyLog}\left(2,e^{2 x}\right)+x \log (a \sinh (x))+\frac{x^2}{2}-x \log \left(1-e^{2 x}\right)",1,"x^2/2 - x*Log[1 - E^(2*x)] + x*Log[a*Sinh[x]] - PolyLog[2, E^(2*x)]/2","A",5,5,5,1.000,1,"{2548, 3716, 2190, 2279, 2391}"
202,1,35,0,0.060352,"\int \log \left(a \sinh ^2(x)\right) \, dx","Int[Log[a*Sinh[x]^2],x]","-\text{PolyLog}\left(2,e^{2 x}\right)+x \log \left(a \sinh ^2(x)\right)+x^2-2 x \log \left(1-e^{2 x}\right)","-\text{PolyLog}\left(2,e^{2 x}\right)+x \log \left(a \sinh ^2(x)\right)+x^2-2 x \log \left(1-e^{2 x}\right)",1,"x^2 - 2*x*Log[1 - E^(2*x)] + x*Log[a*Sinh[x]^2] - PolyLog[2, E^(2*x)]","A",6,6,7,0.8571,1,"{2548, 12, 3716, 2190, 2279, 2391}"
203,1,44,0,0.0603837,"\int \log \left(a \sinh ^n(x)\right) \, dx","Int[Log[a*Sinh[x]^n],x]","-\frac{1}{2} n \text{PolyLog}\left(2,e^{2 x}\right)+x \log \left(a \sinh ^n(x)\right)+\frac{n x^2}{2}-n x \log \left(1-e^{2 x}\right)","-\frac{1}{2} n \text{PolyLog}\left(2,e^{2 x}\right)+x \log \left(a \sinh ^n(x)\right)+\frac{n x^2}{2}-n x \log \left(1-e^{2 x}\right)",1,"(n*x^2)/2 - n*x*Log[1 - E^(2*x)] + x*Log[a*Sinh[x]^n] - (n*PolyLog[2, E^(2*x)])/2","A",6,6,7,0.8571,1,"{2548, 12, 3716, 2190, 2279, 2391}"
204,1,39,0,0.0556963,"\int \log (a \cosh (x)) \, dx","Int[Log[a*Cosh[x]],x]","-\frac{1}{2} \text{PolyLog}\left(2,-e^{2 x}\right)+x \log (a \cosh (x))+\frac{x^2}{2}-x \log \left(e^{2 x}+1\right)","-\frac{1}{2} \text{PolyLog}\left(2,-e^{2 x}\right)+x \log (a \cosh (x))+\frac{x^2}{2}-x \log \left(e^{2 x}+1\right)",1,"x^2/2 - x*Log[1 + E^(2*x)] + x*Log[a*Cosh[x]] - PolyLog[2, -E^(2*x)]/2","A",5,5,5,1.000,1,"{2548, 3718, 2190, 2279, 2391}"
205,1,35,0,0.0562567,"\int \log \left(a \cosh ^2(x)\right) \, dx","Int[Log[a*Cosh[x]^2],x]","-\text{PolyLog}\left(2,-e^{2 x}\right)+x \log \left(a \cosh ^2(x)\right)+x^2-2 x \log \left(e^{2 x}+1\right)","-\text{PolyLog}\left(2,-e^{2 x}\right)+x \log \left(a \cosh ^2(x)\right)+x^2-2 x \log \left(e^{2 x}+1\right)",1,"x^2 - 2*x*Log[1 + E^(2*x)] + x*Log[a*Cosh[x]^2] - PolyLog[2, -E^(2*x)]","A",6,6,7,0.8571,1,"{2548, 12, 3718, 2190, 2279, 2391}"
206,1,44,0,0.0566674,"\int \log \left(a \cosh ^n(x)\right) \, dx","Int[Log[a*Cosh[x]^n],x]","-\frac{1}{2} n \text{PolyLog}\left(2,-e^{2 x}\right)+x \log \left(a \cosh ^n(x)\right)+\frac{n x^2}{2}-n x \log \left(e^{2 x}+1\right)","-\frac{1}{2} n \text{PolyLog}\left(2,-e^{2 x}\right)+x \log \left(a \cosh ^n(x)\right)+\frac{n x^2}{2}-n x \log \left(e^{2 x}+1\right)",1,"(n*x^2)/2 - n*x*Log[1 + E^(2*x)] + x*Log[a*Cosh[x]^n] - (n*PolyLog[2, -E^(2*x)])/2","A",6,6,7,0.8571,1,"{2548, 12, 3718, 2190, 2279, 2391}"
207,1,39,0,0.0443632,"\int \log (\tanh (x)) \, dx","Int[Log[Tanh[x]],x]","\frac{1}{2} \text{PolyLog}\left(2,-e^{2 x}\right)-\frac{1}{2} \text{PolyLog}\left(2,e^{2 x}\right)+2 x \tanh ^{-1}\left(e^{2 x}\right)+x \log (\tanh (x))","\frac{1}{2} \text{PolyLog}\left(2,-e^{2 x}\right)-\frac{1}{2} \text{PolyLog}\left(2,e^{2 x}\right)+2 x \tanh ^{-1}\left(e^{2 x}\right)+x \log (\tanh (x))",1,"2*x*ArcTanh[E^(2*x)] + x*Log[Tanh[x]] + PolyLog[2, -E^(2*x)]/2 - PolyLog[2, E^(2*x)]/2","A",7,5,3,1.667,1,"{2548, 5461, 4182, 2279, 2391}"
208,1,41,0,0.0442116,"\int \log (a \tanh (x)) \, dx","Int[Log[a*Tanh[x]],x]","\frac{1}{2} \text{PolyLog}\left(2,-e^{2 x}\right)-\frac{1}{2} \text{PolyLog}\left(2,e^{2 x}\right)+x \log (a \tanh (x))+2 x \tanh ^{-1}\left(e^{2 x}\right)","\frac{1}{2} \text{PolyLog}\left(2,-e^{2 x}\right)-\frac{1}{2} \text{PolyLog}\left(2,e^{2 x}\right)+x \log (a \tanh (x))+2 x \tanh ^{-1}\left(e^{2 x}\right)",1,"2*x*ArcTanh[E^(2*x)] + x*Log[a*Tanh[x]] + PolyLog[2, -E^(2*x)]/2 - PolyLog[2, E^(2*x)]/2","A",7,5,5,1.000,1,"{2548, 5461, 4182, 2279, 2391}"
209,1,37,0,0.0470444,"\int \log \left(a \tanh ^2(x)\right) \, dx","Int[Log[a*Tanh[x]^2],x]","\text{PolyLog}\left(2,-e^{2 x}\right)-\text{PolyLog}\left(2,e^{2 x}\right)+x \log \left(a \tanh ^2(x)\right)+4 x \tanh ^{-1}\left(e^{2 x}\right)","\text{PolyLog}\left(2,-e^{2 x}\right)-\text{PolyLog}\left(2,e^{2 x}\right)+x \log \left(a \tanh ^2(x)\right)+4 x \tanh ^{-1}\left(e^{2 x}\right)",1,"4*x*ArcTanh[E^(2*x)] + x*Log[a*Tanh[x]^2] + PolyLog[2, -E^(2*x)] - PolyLog[2, E^(2*x)]","A",8,6,7,0.8571,1,"{2548, 12, 5461, 4182, 2279, 2391}"
210,1,46,0,0.0491043,"\int \log \left(a \tanh ^n(x)\right) \, dx","Int[Log[a*Tanh[x]^n],x]","\frac{1}{2} n \text{PolyLog}\left(2,-e^{2 x}\right)-\frac{1}{2} n \text{PolyLog}\left(2,e^{2 x}\right)+x \log \left(a \tanh ^n(x)\right)+2 n x \tanh ^{-1}\left(e^{2 x}\right)","\frac{1}{2} n \text{PolyLog}\left(2,-e^{2 x}\right)-\frac{1}{2} n \text{PolyLog}\left(2,e^{2 x}\right)+x \log \left(a \tanh ^n(x)\right)+2 n x \tanh ^{-1}\left(e^{2 x}\right)",1,"2*n*x*ArcTanh[E^(2*x)] + x*Log[a*Tanh[x]^n] + (n*PolyLog[2, -E^(2*x)])/2 - (n*PolyLog[2, E^(2*x)])/2","A",8,6,7,0.8571,1,"{2548, 12, 5461, 4182, 2279, 2391}"
211,1,39,0,0.0458674,"\int \log (\coth (x)) \, dx","Int[Log[Coth[x]],x]","-\frac{1}{2} \text{PolyLog}\left(2,-e^{2 x}\right)+\frac{1}{2} \text{PolyLog}\left(2,e^{2 x}\right)-2 x \tanh ^{-1}\left(e^{2 x}\right)+x \log (\coth (x))","-\frac{1}{2} \text{PolyLog}\left(2,-e^{2 x}\right)+\frac{1}{2} \text{PolyLog}\left(2,e^{2 x}\right)-2 x \tanh ^{-1}\left(e^{2 x}\right)+x \log (\coth (x))",1,"-2*x*ArcTanh[E^(2*x)] + x*Log[Coth[x]] - PolyLog[2, -E^(2*x)]/2 + PolyLog[2, E^(2*x)]/2","A",7,5,3,1.667,1,"{2548, 5461, 4182, 2279, 2391}"
212,1,41,0,0.0442162,"\int \log (a \coth (x)) \, dx","Int[Log[a*Coth[x]],x]","-\frac{1}{2} \text{PolyLog}\left(2,-e^{2 x}\right)+\frac{1}{2} \text{PolyLog}\left(2,e^{2 x}\right)+x \log (a \coth (x))-2 x \tanh ^{-1}\left(e^{2 x}\right)","-\frac{1}{2} \text{PolyLog}\left(2,-e^{2 x}\right)+\frac{1}{2} \text{PolyLog}\left(2,e^{2 x}\right)+x \log (a \coth (x))-2 x \tanh ^{-1}\left(e^{2 x}\right)",1,"-2*x*ArcTanh[E^(2*x)] + x*Log[a*Coth[x]] - PolyLog[2, -E^(2*x)]/2 + PolyLog[2, E^(2*x)]/2","A",7,5,5,1.000,1,"{2548, 5461, 4182, 2279, 2391}"
213,1,37,0,0.0484372,"\int \log \left(a \coth ^2(x)\right) \, dx","Int[Log[a*Coth[x]^2],x]","-\text{PolyLog}\left(2,-e^{2 x}\right)+\text{PolyLog}\left(2,e^{2 x}\right)+x \log \left(a \coth ^2(x)\right)-4 x \tanh ^{-1}\left(e^{2 x}\right)","-\text{PolyLog}\left(2,-e^{2 x}\right)+\text{PolyLog}\left(2,e^{2 x}\right)+x \log \left(a \coth ^2(x)\right)-4 x \tanh ^{-1}\left(e^{2 x}\right)",1,"-4*x*ArcTanh[E^(2*x)] + x*Log[a*Coth[x]^2] - PolyLog[2, -E^(2*x)] + PolyLog[2, E^(2*x)]","A",8,6,7,0.8571,1,"{2548, 12, 5461, 4182, 2279, 2391}"
214,1,46,0,0.0494245,"\int \log \left(a \coth ^n(x)\right) \, dx","Int[Log[a*Coth[x]^n],x]","-\frac{1}{2} n \text{PolyLog}\left(2,-e^{2 x}\right)+\frac{1}{2} n \text{PolyLog}\left(2,e^{2 x}\right)+x \log \left(a \coth ^n(x)\right)-2 n x \tanh ^{-1}\left(e^{2 x}\right)","-\frac{1}{2} n \text{PolyLog}\left(2,-e^{2 x}\right)+\frac{1}{2} n \text{PolyLog}\left(2,e^{2 x}\right)+x \log \left(a \coth ^n(x)\right)-2 n x \tanh ^{-1}\left(e^{2 x}\right)",1,"-2*n*x*ArcTanh[E^(2*x)] + x*Log[a*Coth[x]^n] - (n*PolyLog[2, -E^(2*x)])/2 + (n*PolyLog[2, E^(2*x)])/2","A",8,6,7,0.8571,1,"{2548, 12, 5461, 4182, 2279, 2391}"
215,1,38,0,0.0529435,"\int \log (a \text{sech}(x)) \, dx","Int[Log[a*Sech[x]],x]","\frac{1}{2} \text{PolyLog}\left(2,-e^{2 x}\right)+x \log (a \text{sech}(x))-\frac{x^2}{2}+x \log \left(e^{2 x}+1\right)","\frac{1}{2} \text{PolyLog}\left(2,-e^{2 x}\right)+x \log (a \text{sech}(x))-\frac{x^2}{2}+x \log \left(e^{2 x}+1\right)",1,"-x^2/2 + x*Log[1 + E^(2*x)] + x*Log[a*Sech[x]] + PolyLog[2, -E^(2*x)]/2","A",5,5,5,1.000,1,"{2548, 3718, 2190, 2279, 2391}"
216,1,35,0,0.0534823,"\int \log \left(a \text{sech}^2(x)\right) \, dx","Int[Log[a*Sech[x]^2],x]","\text{PolyLog}\left(2,-e^{2 x}\right)+x \log \left(a \text{sech}^2(x)\right)-x^2+2 x \log \left(e^{2 x}+1\right)","\text{PolyLog}\left(2,-e^{2 x}\right)+x \log \left(a \text{sech}^2(x)\right)-x^2+2 x \log \left(e^{2 x}+1\right)",1,"-x^2 + 2*x*Log[1 + E^(2*x)] + x*Log[a*Sech[x]^2] + PolyLog[2, -E^(2*x)]","A",6,6,7,0.8571,1,"{2548, 12, 3718, 2190, 2279, 2391}"
217,1,43,0,0.0553164,"\int \log \left(a \text{sech}^n(x)\right) \, dx","Int[Log[a*Sech[x]^n],x]","\frac{1}{2} n \text{PolyLog}\left(2,-e^{2 x}\right)+x \log \left(a \text{sech}^n(x)\right)-\frac{n x^2}{2}+n x \log \left(e^{2 x}+1\right)","\frac{1}{2} n \text{PolyLog}\left(2,-e^{2 x}\right)+x \log \left(a \text{sech}^n(x)\right)-\frac{n x^2}{2}+n x \log \left(e^{2 x}+1\right)",1,"-(n*x^2)/2 + n*x*Log[1 + E^(2*x)] + x*Log[a*Sech[x]^n] + (n*PolyLog[2, -E^(2*x)])/2","A",6,6,7,0.8571,1,"{2548, 12, 3718, 2190, 2279, 2391}"
218,1,38,0,0.0539876,"\int \log (a \text{csch}(x)) \, dx","Int[Log[a*Csch[x]],x]","\frac{1}{2} \text{PolyLog}\left(2,e^{2 x}\right)+x \log (a \text{csch}(x))-\frac{x^2}{2}+x \log \left(1-e^{2 x}\right)","\frac{1}{2} \text{PolyLog}\left(2,e^{2 x}\right)+x \log (a \text{csch}(x))-\frac{x^2}{2}+x \log \left(1-e^{2 x}\right)",1,"-x^2/2 + x*Log[1 - E^(2*x)] + x*Log[a*Csch[x]] + PolyLog[2, E^(2*x)]/2","A",5,5,5,1.000,1,"{2548, 3716, 2190, 2279, 2391}"
219,1,35,0,0.0584815,"\int \log \left(a \text{csch}^2(x)\right) \, dx","Int[Log[a*Csch[x]^2],x]","\text{PolyLog}\left(2,e^{2 x}\right)+x \log \left(a \text{csch}^2(x)\right)-x^2+2 x \log \left(1-e^{2 x}\right)","\text{PolyLog}\left(2,e^{2 x}\right)+x \log \left(a \text{csch}^2(x)\right)-x^2+2 x \log \left(1-e^{2 x}\right)",1,"-x^2 + 2*x*Log[1 - E^(2*x)] + x*Log[a*Csch[x]^2] + PolyLog[2, E^(2*x)]","A",6,6,7,0.8571,1,"{2548, 12, 3716, 2190, 2279, 2391}"
220,1,43,0,0.0641465,"\int \log \left(a \text{csch}^n(x)\right) \, dx","Int[Log[a*Csch[x]^n],x]","\frac{1}{2} n \text{PolyLog}\left(2,e^{2 x}\right)+x \log \left(a \text{csch}^n(x)\right)-\frac{n x^2}{2}+n x \log \left(1-e^{2 x}\right)","\frac{1}{2} n \text{PolyLog}\left(2,e^{2 x}\right)+x \log \left(a \text{csch}^n(x)\right)-\frac{n x^2}{2}+n x \log \left(1-e^{2 x}\right)",1,"-(n*x^2)/2 + n*x*Log[1 - E^(2*x)] + x*Log[a*Csch[x]^n] + (n*PolyLog[2, E^(2*x)])/2","A",6,6,7,0.8571,1,"{2548, 12, 3716, 2190, 2279, 2391}"
221,1,50,0,0.0286319,"\int \cosh (a+b x) \log \left(\cosh \left(\frac{a}{2}+\frac{b x}{2}\right) \sinh \left(\frac{a}{2}+\frac{b x}{2}\right)\right) \, dx","Int[Cosh[a + b*x]*Log[Cosh[a/2 + (b*x)/2]*Sinh[a/2 + (b*x)/2]],x]","\frac{\sinh (a+b x) \log \left(\sinh \left(\frac{a}{2}+\frac{b x}{2}\right) \cosh \left(\frac{a}{2}+\frac{b x}{2}\right)\right)}{b}-\frac{\sinh (a+b x)}{b}","\frac{\sinh (a+b x) \log \left(\sinh \left(\frac{a}{2}+\frac{b x}{2}\right) \cosh \left(\frac{a}{2}+\frac{b x}{2}\right)\right)}{b}-\frac{\sinh (a+b x)}{b}",1,"-(Sinh[a + b*x]/b) + (Log[Cosh[a/2 + (b*x)/2]*Sinh[a/2 + (b*x)/2]]*Sinh[a + b*x])/b","A",2,2,35,0.05714,1,"{2637, 2554}"
222,1,13,0,0.0191519,"\int \log \left(\cosh ^2(x)\right) \sinh (x) \, dx","Int[Log[Cosh[x]^2]*Sinh[x],x]","\cosh (x) \log \left(\cosh ^2(x)\right)-2 \cosh (x)","\cosh (x) \log \left(\cosh ^2(x)\right)-2 \cosh (x)",1,"-2*Cosh[x] + Cosh[x]*Log[Cosh[x]^2]","A",3,3,8,0.3750,1,"{2638, 2554, 12}"
223,1,17,0,0.0066523,"\int \frac{\log (x)}{\sqrt{x}} \, dx","Int[Log[x]/Sqrt[x],x]","2 \sqrt{x} \log (x)-4 \sqrt{x}","2 \sqrt{x} \log (x)-4 \sqrt{x}",1,"-4*Sqrt[x] + 2*Sqrt[x]*Log[x]","A",1,1,8,0.1250,1,"{2304}"
224,1,27,0,0.0212735,"\int x \log \left(2-3 x^2\right) \, dx","Int[x*Log[2 - 3*x^2],x]","-\frac{x^2}{2}-\frac{1}{6} \left(2-3 x^2\right) \log \left(2-3 x^2\right)","-\frac{x^2}{2}-\frac{1}{6} \left(2-3 x^2\right) \log \left(2-3 x^2\right)",1,"-x^2/2 - ((2 - 3*x^2)*Log[2 - 3*x^2])/6","A",3,3,10,0.3000,1,"{2454, 2389, 2295}"
225,1,3,0,0.0335502,"\int \frac{1}{x \sqrt{1-\log ^2(x)}} \, dx","Int[1/(x*Sqrt[1 - Log[x]^2]),x]","\sin ^{-1}(\log (x))","\sin ^{-1}(\log (x))",1,"ArcSin[Log[x]]","A",2,1,16,0.06250,1,"{216}"
226,1,24,0,0.0228337,"\int 16 x^3 \log ^2(x) \, dx","Int[16*x^3*Log[x]^2,x]","\frac{x^4}{2}+4 x^4 \log ^2(x)-2 x^4 \log (x)","\frac{x^4}{2}+4 x^4 \log ^2(x)-2 x^4 \log (x)",1,"x^4/2 - 2*x^4*Log[x] + 4*x^4*Log[x]^2","A",3,3,9,0.3333,1,"{12, 2305, 2304}"
227,1,25,0,0.009634,"\int \log \left(\sqrt{a+b x}\right) \, dx","Int[Log[Sqrt[a + b*x]],x]","\frac{(a+b x) \log \left(\sqrt{a+b x}\right)}{b}-\frac{x}{2}","\frac{(a+b x) \log \left(\sqrt{a+b x}\right)}{b}-\frac{x}{2}",1,"-x/2 + ((a + b*x)*Log[Sqrt[a + b*x]])/b","A",2,2,10,0.2000,1,"{2389, 2295}"
228,1,34,0,0.0135295,"\int x \log \left(\sqrt{2+x}\right) \, dx","Int[x*Log[Sqrt[2 + x]],x]","-\frac{x^2}{8}+\frac{1}{2} x^2 \log \left(\sqrt{x+2}\right)+\frac{x}{2}-\log (x+2)","-\frac{x^2}{8}+\frac{1}{2} x^2 \log \left(\sqrt{x+2}\right)+\frac{x}{2}-\log (x+2)",1,"x/2 - x^2/8 + (x^2*Log[Sqrt[2 + x]])/2 - Log[2 + x]","A",3,2,10,0.2000,1,"{2395, 43}"
229,1,40,0,0.0159573,"\int x \log \left(\sqrt[3]{1+3 x}\right) \, dx","Int[x*Log[(1 + 3*x)^(1/3)],x]","-\frac{x^2}{12}+\frac{1}{2} x^2 \log \left(\sqrt[3]{3 x+1}\right)+\frac{x}{18}-\frac{1}{54} \log (3 x+1)","-\frac{x^2}{12}+\frac{1}{2} x^2 \log \left(\sqrt[3]{3 x+1}\right)+\frac{x}{18}-\frac{1}{54} \log (3 x+1)",1,"x/18 - x^2/12 + (x^2*Log[(1 + 3*x)^(1/3)])/2 - Log[1 + 3*x]/54","A",3,2,12,0.1667,1,"{2395, 43}"
230,1,31,0,0.0293318,"\int x \log \left(x+x^3\right) \, dx","Int[x*Log[x + x^3],x]","-\frac{3 x^2}{4}+\frac{1}{2} x^2 \log \left(x^3+x\right)+\frac{1}{2} \log \left(x^2+1\right)","-\frac{3 x^2}{4}+\frac{1}{2} x^2 \log \left(x^3+x\right)+\frac{1}{2} \log \left(x^2+1\right)",1,"(-3*x^2)/4 + Log[1 + x^2]/2 + (x^2*Log[x + x^3])/2","A",4,3,8,0.3750,1,"{2525, 444, 43}"
231,1,26,0,0.0040469,"\int \log \left(x+\sqrt{1+x^2}\right) \, dx","Int[Log[x + Sqrt[1 + x^2]],x]","x \log \left(\sqrt{x^2+1}+x\right)-\sqrt{x^2+1}","x \log \left(\sqrt{x^2+1}+x\right)-\sqrt{x^2+1}",1,"-Sqrt[1 + x^2] + x*Log[x + Sqrt[1 + x^2]]","A",2,2,12,0.1667,1,"{2534, 261}"
232,1,26,0,0.0044315,"\int \log \left(x+\sqrt{-1+x^2}\right) \, dx","Int[Log[x + Sqrt[-1 + x^2]],x]","x \log \left(\sqrt{x^2-1}+x\right)-\sqrt{x^2-1}","x \log \left(\sqrt{x^2-1}+x\right)-\sqrt{x^2-1}",1,"-Sqrt[-1 + x^2] + x*Log[x + Sqrt[-1 + x^2]]","A",2,2,12,0.1667,1,"{2534, 261}"
233,1,26,0,0.0054906,"\int \log \left(x-\sqrt{-1+x^2}\right) \, dx","Int[Log[x - Sqrt[-1 + x^2]],x]","\sqrt{x^2-1}+x \log \left(x-\sqrt{x^2-1}\right)","\sqrt{x^2-1}+x \log \left(x-\sqrt{x^2-1}\right)",1,"Sqrt[-1 + x^2] + x*Log[x - Sqrt[-1 + x^2]]","A",2,2,14,0.1429,1,"{2534, 261}"
234,1,43,0,0.0123772,"\int \log \left(\sqrt{x}+\sqrt{1+x}\right) \, dx","Int[Log[Sqrt[x] + Sqrt[1 + x]],x]","-\frac{1}{2} \sqrt{x} \sqrt{x+1}+x \log \left(\sqrt{x}+\sqrt{x+1}\right)+\frac{1}{2} \sinh ^{-1}\left(\sqrt{x}\right)","-\frac{1}{2} \sqrt{x} \sqrt{x+1}+x \log \left(\sqrt{x}+\sqrt{x+1}\right)+\frac{1}{2} \sinh ^{-1}\left(\sqrt{x}\right)",1,"-(Sqrt[x]*Sqrt[1 + x])/2 + ArcSinh[Sqrt[x]]/2 + x*Log[Sqrt[x] + Sqrt[1 + x]]","A",6,6,14,0.4286,1,"{2548, 12, 1958, 50, 54, 215}"
235,1,21,0,0.0067835,"\int \sqrt[3]{x} \log (x) \, dx","Int[x^(1/3)*Log[x],x]","\frac{3}{4} x^{4/3} \log (x)-\frac{9 x^{4/3}}{16}","\frac{3}{4} x^{4/3} \log (x)-\frac{9 x^{4/3}}{16}",1,"(-9*x^(4/3))/16 + (3*x^(4/3)*Log[x])/4","A",1,1,8,0.1250,1,"{2304}"
236,1,13,0,0.0054808,"\int 2^{\log (x)} \, dx","Int[2^Log[x],x]","\frac{x^{1+\log (2)}}{1+\log (2)}","\frac{x^{1+\log (2)}}{1+\log (2)}",1,"x^(1 + Log[2])/(1 + Log[2])","A",2,2,4,0.5000,1,"{2274, 30}"
237,1,6,0,0.0104505,"\int \frac{1-\log (x)}{x^2} \, dx","Int[(1 - Log[x])/x^2,x]","\frac{\log (x)}{x}","\frac{\log (x)}{x}",1,"Log[x]/x","A",1,1,10,0.1000,1,"{2303}"
238,1,32,0,0.2052533,"\int \log \left(1+x+\sqrt{1+x}\right) \, dx","Int[Log[1 + x + Sqrt[1 + x]],x]","-x+\sqrt{x+1}+x \log \left(x+\sqrt{x+1}+1\right)+\frac{1}{2} \log (x+1)","-x+\sqrt{x+1}+x \log \left(x+\sqrt{x+1}+1\right)+\frac{1}{2} \log (x+1)",1,"-x + Sqrt[1 + x] + Log[1 + x]/2 + x*Log[1 + x + Sqrt[1 + x]]","A",3,1,11,0.09091,1,"{2548}"
239,1,16,0,0.0071385,"\int \log \left(x+x^3\right) \, dx","Int[Log[x + x^3],x]","x \log \left(x^3+x\right)-3 x+2 \tan ^{-1}(x)","x \log \left(x^3+x\right)-3 x+2 \tan ^{-1}(x)",1,"-3*x + 2*ArcTan[x] + x*Log[x + x^3]","A",3,3,6,0.5000,1,"{2523, 388, 203}"
240,1,20,0,0.004664,"\int 2^{\log (-8+7 x)} \, dx","Int[2^Log[-8 + 7*x],x]","\frac{(7 x-8)^{1+\log (2)}}{7 (1+\log (2))}","\frac{(7 x-8)^{1+\log (2)}}{7 (1+\log (2))}",1,"(-8 + 7*x)^(1 + Log[2])/(7*(1 + Log[2]))","A",2,2,8,0.2500,1,"{2274, 32}"
241,1,35,0,0.0058722,"\int \log \left(\frac{-11+5 x}{5+76 x}\right) \, dx","Int[Log[(-11 + 5*x)/(5 + 76*x)],x]","-\frac{1}{5} (11-5 x) \log \left(-\frac{11-5 x}{76 x+5}\right)-\frac{861}{380} \log (76 x+5)","-\frac{1}{5} (11-5 x) \log \left(-\frac{11-5 x}{76 x+5}\right)-\frac{861}{380} \log (76 x+5)",1,"-((11 - 5*x)*Log[-((11 - 5*x)/(5 + 76*x))])/5 - (861*Log[5 + 76*x])/380","A",2,2,14,0.1429,1,"{2486, 31}"
242,1,12,0,0.0026972,"\int \log \left(\frac{1}{13+x}\right) \, dx","Int[Log[(13 + x)^(-1)],x]","x+(x+13) \log \left(\frac{1}{x+13}\right)","x+(x+13) \log \left(\frac{1}{x+13}\right)",1,"x + (13 + x)*Log[(13 + x)^(-1)]","A",2,2,6,0.3333,1,"{2389, 2295}"
243,1,36,0,0.014721,"\int x \log \left(\frac{1+x}{x^2}\right) \, dx","Int[x*Log[(1 + x)/x^2],x]","\frac{x^2}{4}+\frac{1}{2} x^2 \log \left(\frac{x+1}{x^2}\right)+\frac{x}{2}-\frac{1}{2} \log (x+1)","\frac{x^2}{4}+\frac{1}{2} x^2 \log \left(\frac{x+1}{x^2}\right)+\frac{x}{2}-\frac{1}{2} \log (x+1)",1,"x/2 + x^2/4 - Log[1 + x]/2 + (x^2*Log[(1 + x)/x^2])/2","A",4,3,10,0.3000,1,"{2495, 30, 43}"
244,1,54,0,0.0392872,"\int x^3 \log \left(\frac{7+5 x}{x^2}\right) \, dx","Int[x^3*Log[(7 + 5*x)/x^2],x]","\frac{x^4}{16}+\frac{7 x^3}{60}-\frac{49 x^2}{200}+\frac{1}{4} x^4 \log \left(\frac{5 x+7}{x^2}\right)+\frac{343 x}{500}-\frac{2401 \log (5 x+7)}{2500}","\frac{x^4}{16}+\frac{7 x^3}{60}-\frac{49 x^2}{200}+\frac{1}{4} x^4 \log \left(\frac{5 x+7}{x^2}\right)+\frac{343 x}{500}-\frac{2401 \log (5 x+7)}{2500}",1,"(343*x)/500 - (49*x^2)/200 + (7*x^3)/60 + x^4/16 - (2401*Log[7 + 5*x])/2500 + (x^4*Log[(7 + 5*x)/x^2])/4","A",4,3,14,0.2143,1,"{2495, 30, 43}"
245,1,35,0,0.0146922,"\int (a+b x) \log (a+b x) \, dx","Int[(a + b*x)*Log[a + b*x],x]","\frac{(a+b x)^2 \log (a+b x)}{2 b}-\frac{(a+b x)^2}{4 b}","\frac{(a+b x)^2 \log (a+b x)}{2 b}-\frac{(a+b x)^2}{4 b}",1,"-(a + b*x)^2/(4*b) + ((a + b*x)^2*Log[a + b*x])/(2*b)","A",2,2,12,0.1667,1,"{2390, 2304}"
246,1,35,0,0.0246622,"\int (a+b x)^2 \log (a+b x) \, dx","Int[(a + b*x)^2*Log[a + b*x],x]","\frac{(a+b x)^3 \log (a+b x)}{3 b}-\frac{(a+b x)^3}{9 b}","\frac{(a+b x)^3 \log (a+b x)}{3 b}-\frac{(a+b x)^3}{9 b}",1,"-(a + b*x)^3/(9*b) + ((a + b*x)^3*Log[a + b*x])/(3*b)","A",2,2,14,0.1429,1,"{2390, 2304}"
247,1,15,0,0.0183944,"\int \frac{\log (a+b x)}{a+b x} \, dx","Int[Log[a + b*x]/(a + b*x),x]","\frac{\log ^2(a+b x)}{2 b}","\frac{\log ^2(a+b x)}{2 b}",1,"Log[a + b*x]^2/(2*b)","A",2,2,14,0.1429,1,"{2390, 2301}"
248,1,31,0,0.0218602,"\int \frac{\log (a+b x)}{(a+b x)^2} \, dx","Int[Log[a + b*x]/(a + b*x)^2,x]","-\frac{1}{b (a+b x)}-\frac{\log (a+b x)}{b (a+b x)}","-\frac{1}{b (a+b x)}-\frac{\log (a+b x)}{b (a+b x)}",1,"-(1/(b*(a + b*x))) - Log[a + b*x]/(b*(a + b*x))","A",2,2,14,0.1429,1,"{2390, 2304}"
249,1,44,0,0.0302658,"\int (a+b x)^n \log (a+b x) \, dx","Int[(a + b*x)^n*Log[a + b*x],x]","\frac{(a+b x)^{n+1} \log (a+b x)}{b (n+1)}-\frac{(a+b x)^{n+1}}{b (n+1)^2}","\frac{(a+b x)^{n+1} \log (a+b x)}{b (n+1)}-\frac{(a+b x)^{n+1}}{b (n+1)^2}",1,"-((a + b*x)^(1 + n)/(b*(1 + n)^2)) + ((a + b*x)^(1 + n)*Log[a + b*x])/(b*(1 + n))","A",2,2,14,0.1429,1,"{2390, 2304}"
250,1,18,0,0.0107713,"\int \frac{1}{a x+b x \log \left(c x^n\right)} \, dx","Int[(a*x + b*x*Log[c*x^n])^(-1),x]","\frac{\log \left(a+b \log \left(c x^n\right)\right)}{b n}","\frac{\log \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"Log[a + b*Log[c*x^n]]/(b*n)","A",2,1,15,0.06667,1,"{31}"
251,1,32,0,0.0182284,"\int \frac{1}{a x+b x \log ^2\left(c x^n\right)} \, dx","Int[(a*x + b*x*Log[c*x^n]^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \log \left(c x^n\right)}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} n}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \log \left(c x^n\right)}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} n}",1,"ArcTan[(Sqrt[b]*Log[c*x^n])/Sqrt[a]]/(Sqrt[a]*Sqrt[b]*n)","A",2,1,17,0.05882,1,"{205}"
252,1,144,0,0.0944799,"\int \frac{1}{a x+b x \log ^3\left(c x^n\right)} \, dx","Int[(a*x + b*x*Log[c*x^n]^3)^(-1),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \log \left(c x^n\right)+b^{2/3} \log ^2\left(c x^n\right)\right)}{6 a^{2/3} \sqrt[3]{b} n}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \log \left(c x^n\right)\right)}{3 a^{2/3} \sqrt[3]{b} n}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \log \left(c x^n\right)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b} n}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \log \left(c x^n\right)+b^{2/3} \log ^2\left(c x^n\right)\right)}{6 a^{2/3} \sqrt[3]{b} n}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} \log \left(c x^n\right)\right)}{3 a^{2/3} \sqrt[3]{b} n}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \log \left(c x^n\right)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b} n}",1,"-(ArcTan[(a^(1/3) - 2*b^(1/3)*Log[c*x^n])/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(2/3)*b^(1/3)*n)) + Log[a^(1/3) + b^(1/3)*Log[c*x^n]]/(3*a^(2/3)*b^(1/3)*n) - Log[a^(2/3) - a^(1/3)*b^(1/3)*Log[c*x^n] + b^(2/3)*Log[c*x^n]^2]/(6*a^(2/3)*b^(1/3)*n)","A",7,6,17,0.3529,1,"{200, 31, 634, 617, 204, 628}"
253,1,227,0,0.1624323,"\int \frac{1}{a x+b x \log ^4\left(c x^n\right)} \, dx","Int[(a*x + b*x*Log[c*x^n]^4)^(-1),x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \log \left(c x^n\right)+\sqrt{a}+\sqrt{b} \log ^2\left(c x^n\right)\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b} n}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \log \left(c x^n\right)+\sqrt{a}+\sqrt{b} \log ^2\left(c x^n\right)\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b} n}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \log \left(c x^n\right)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b} n}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \log \left(c x^n\right)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b} n}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \log \left(c x^n\right)+\sqrt{a}+\sqrt{b} \log ^2\left(c x^n\right)\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b} n}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \log \left(c x^n\right)+\sqrt{a}+\sqrt{b} \log ^2\left(c x^n\right)\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b} n}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \log \left(c x^n\right)}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b} n}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \log \left(c x^n\right)}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b} n}",1,"-ArcTan[1 - (Sqrt[2]*b^(1/4)*Log[c*x^n])/a^(1/4)]/(2*Sqrt[2]*a^(3/4)*b^(1/4)*n) + ArcTan[1 + (Sqrt[2]*b^(1/4)*Log[c*x^n])/a^(1/4)]/(2*Sqrt[2]*a^(3/4)*b^(1/4)*n) - Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Log[c*x^n] + Sqrt[b]*Log[c*x^n]^2]/(4*Sqrt[2]*a^(3/4)*b^(1/4)*n) + Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Log[c*x^n] + Sqrt[b]*Log[c*x^n]^2]/(4*Sqrt[2]*a^(3/4)*b^(1/4)*n)","A",10,6,17,0.3529,1,"{211, 1165, 628, 1162, 617, 204}"
254,1,27,0,0.023225,"\int \frac{1}{a x+\frac{b x}{\log \left(c x^n\right)}} \, dx","Int[(a*x + (b*x)/Log[c*x^n])^(-1),x]","\frac{\log (x)}{a}-\frac{b \log \left(a \log \left(c x^n\right)+b\right)}{a^2 n}","\frac{\log (x)}{a}-\frac{b \log \left(a \log \left(c x^n\right)+b\right)}{a^2 n}",1,"Log[x]/a - (b*Log[b + a*Log[c*x^n]])/(a^2*n)","A",3,1,17,0.05882,1,"{43}"
255,1,40,0,0.0271898,"\int \frac{1}{a x+\frac{b x}{\log ^2\left(c x^n\right)}} \, dx","Int[(a*x + (b*x)/Log[c*x^n]^2)^(-1),x]","\frac{\log (x)}{a}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \log \left(c x^n\right)}{\sqrt{b}}\right)}{a^{3/2} n}","\frac{\log (x)}{a}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \log \left(c x^n\right)}{\sqrt{b}}\right)}{a^{3/2} n}",1,"-((Sqrt[b]*ArcTan[(Sqrt[a]*Log[c*x^n])/Sqrt[b]])/(a^(3/2)*n)) + Log[x]/a","A",3,2,17,0.1176,1,"{321, 205}"
256,1,149,0,0.1094249,"\int \frac{1}{a x+\frac{b x}{\log ^3\left(c x^n\right)}} \, dx","Int[(a*x + (b*x)/Log[c*x^n]^3)^(-1),x]","\frac{\sqrt[3]{b} \log \left(a^{2/3} \log ^2\left(c x^n\right)-\sqrt[3]{a} \sqrt[3]{b} \log \left(c x^n\right)+b^{2/3}\right)}{6 a^{4/3} n}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a} \log \left(c x^n\right)+\sqrt[3]{b}\right)}{3 a^{4/3} n}+\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} \log \left(c x^n\right)}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} a^{4/3} n}+\frac{\log (x)}{a}","\frac{\sqrt[3]{b} \log \left(a^{2/3} \log ^2\left(c x^n\right)-\sqrt[3]{a} \sqrt[3]{b} \log \left(c x^n\right)+b^{2/3}\right)}{6 a^{4/3} n}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a} \log \left(c x^n\right)+\sqrt[3]{b}\right)}{3 a^{4/3} n}+\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} \log \left(c x^n\right)}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} a^{4/3} n}+\frac{\log (x)}{a}",1,"(b^(1/3)*ArcTan[(b^(1/3) - 2*a^(1/3)*Log[c*x^n])/(Sqrt[3]*b^(1/3))])/(Sqrt[3]*a^(4/3)*n) + Log[x]/a - (b^(1/3)*Log[b^(1/3) + a^(1/3)*Log[c*x^n]])/(3*a^(4/3)*n) + (b^(1/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*Log[c*x^n] + a^(2/3)*Log[c*x^n]^2])/(6*a^(4/3)*n)","A",8,7,17,0.4118,1,"{321, 200, 31, 634, 617, 204, 628}"
257,1,233,0,0.1828018,"\int \frac{1}{a x+\frac{b x}{\log ^4\left(c x^n\right)}} \, dx","Int[(a*x + (b*x)/Log[c*x^n]^4)^(-1),x]","\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \log \left(c x^n\right)+\sqrt{a} \log ^2\left(c x^n\right)+\sqrt{b}\right)}{4 \sqrt{2} a^{5/4} n}-\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \log \left(c x^n\right)+\sqrt{a} \log ^2\left(c x^n\right)+\sqrt{b}\right)}{4 \sqrt{2} a^{5/4} n}+\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} \log \left(c x^n\right)}{\sqrt[4]{b}}\right)}{2 \sqrt{2} a^{5/4} n}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \log \left(c x^n\right)}{\sqrt[4]{b}}+1\right)}{2 \sqrt{2} a^{5/4} n}+\frac{\log (x)}{a}","\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \log \left(c x^n\right)+\sqrt{a} \log ^2\left(c x^n\right)+\sqrt{b}\right)}{4 \sqrt{2} a^{5/4} n}-\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \log \left(c x^n\right)+\sqrt{a} \log ^2\left(c x^n\right)+\sqrt{b}\right)}{4 \sqrt{2} a^{5/4} n}+\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} \log \left(c x^n\right)}{\sqrt[4]{b}}\right)}{2 \sqrt{2} a^{5/4} n}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \log \left(c x^n\right)}{\sqrt[4]{b}}+1\right)}{2 \sqrt{2} a^{5/4} n}+\frac{\log (x)}{a}",1,"(b^(1/4)*ArcTan[1 - (Sqrt[2]*a^(1/4)*Log[c*x^n])/b^(1/4)])/(2*Sqrt[2]*a^(5/4)*n) - (b^(1/4)*ArcTan[1 + (Sqrt[2]*a^(1/4)*Log[c*x^n])/b^(1/4)])/(2*Sqrt[2]*a^(5/4)*n) + Log[x]/a + (b^(1/4)*Log[Sqrt[b] - Sqrt[2]*a^(1/4)*b^(1/4)*Log[c*x^n] + Sqrt[a]*Log[c*x^n]^2])/(4*Sqrt[2]*a^(5/4)*n) - (b^(1/4)*Log[Sqrt[b] + Sqrt[2]*a^(1/4)*b^(1/4)*Log[c*x^n] + Sqrt[a]*Log[c*x^n]^2])/(4*Sqrt[2]*a^(5/4)*n)","A",11,7,17,0.4118,1,"{321, 211, 1165, 628, 1162, 617, 204}"
258,1,22,0,0.0180555,"\int \frac{1}{x+x \log (7 x)+x \log ^2(7 x)} \, dx","Int[(x + x*Log[7*x] + x*Log[7*x]^2)^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{2 \log (7 x)+1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{2 \tan ^{-1}\left(\frac{2 \log (7 x)+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(2*ArcTan[(1 + 2*Log[7*x])/Sqrt[3]])/Sqrt[3]","A",3,2,18,0.1111,1,"{618, 204}"
259,1,41,0,0.0575292,"\int \frac{-1+\log (3 x)}{x \left(1-\log (3 x)+\log ^2(3 x)\right)} \, dx","Int[(-1 + Log[3*x])/(x*(1 - Log[3*x] + Log[3*x]^2)),x]","\frac{1}{2} \log \left(\log ^2(3 x)-\log (3 x)+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 \log (3 x)}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{2} \log \left(\log ^2(3 x)-\log (3 x)+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 \log (3 x)}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTan[(1 - 2*Log[3*x])/Sqrt[3]]/Sqrt[3] + Log[1 - Log[3*x] + Log[3*x]^2]/2","A",5,4,26,0.1538,1,"{634, 618, 204, 628}"
260,1,41,0,0.0332927,"\int \frac{-1+\log ^2(3 x)}{x+x \log ^3(3 x)} \, dx","Int[(-1 + Log[3*x]^2)/(x + x*Log[3*x]^3),x]","\frac{1}{2} \log \left(\log ^2(3 x)-\log (3 x)+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 \log (3 x)}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{2} \log \left(\log ^2(3 x)-\log (3 x)+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 \log (3 x)}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTan[(1 - 2*Log[3*x])/Sqrt[3]]/Sqrt[3] + Log[1 - Log[3*x] + Log[3*x]^2]/2","A",5,4,21,0.1905,1,"{634, 618, 204, 628}"
261,1,42,0,0.0460033,"\int \frac{-1+\log ^2(3 x)}{x+x \log (3 x)+x \log ^2(3 x)} \, dx","Int[(-1 + Log[3*x]^2)/(x + x*Log[3*x] + x*Log[3*x]^2),x]","-\frac{1}{2} \log \left(\log ^2(3 x)+\log (3 x)+1\right)+\log (x)-\sqrt{3} \tan ^{-1}\left(\frac{2 \log (3 x)+1}{\sqrt{3}}\right)","-\frac{1}{2} \log \left(\log ^2(3 x)+\log (3 x)+1\right)+\log (x)-\sqrt{3} \tan ^{-1}\left(\frac{2 \log (3 x)+1}{\sqrt{3}}\right)",1,"-(Sqrt[3]*ArcTan[(1 + 2*Log[3*x])/Sqrt[3]]) + Log[x] - Log[1 + Log[3*x] + Log[3*x]^2]/2","A",7,5,27,0.1852,1,"{1657, 634, 618, 204, 628}"
262,1,32,0,0.0211592,"\int \frac{\log ^2\left(\frac{1}{x}\right)}{x^5} \, dx","Int[Log[x^(-1)]^2/x^5,x]","-\frac{1}{32 x^4}-\frac{\log ^2\left(\frac{1}{x}\right)}{4 x^4}+\frac{\log \left(\frac{1}{x}\right)}{8 x^4}","-\frac{1}{32 x^4}-\frac{\log ^2\left(\frac{1}{x}\right)}{4 x^4}+\frac{\log \left(\frac{1}{x}\right)}{8 x^4}",1,"-1/(32*x^4) + Log[x^(-1)]/(8*x^4) - Log[x^(-1)]^2/(4*x^4)","A",2,2,10,0.2000,1,"{2305, 2304}"
263,1,40,0,0.0288386,"\int \frac{1}{\sqrt{-\log \left(a x^2\right)}} \, dx","Int[1/Sqrt[-Log[a*x^2]],x]","-\frac{\sqrt{\frac{\pi }{2}} x \text{Erf}\left(\frac{\sqrt{-\log \left(a x^2\right)}}{\sqrt{2}}\right)}{\sqrt{a x^2}}","-\frac{\sqrt{\frac{\pi }{2}} x \text{Erf}\left(\frac{\sqrt{-\log \left(a x^2\right)}}{\sqrt{2}}\right)}{\sqrt{a x^2}}",1,"-((Sqrt[Pi/2]*x*Erf[Sqrt[-Log[a*x^2]]/Sqrt[2]])/Sqrt[a*x^2])","A",3,3,12,0.2500,1,"{2300, 2180, 2205}"
264,1,39,0,0.0246292,"\int \frac{1}{\sqrt{-\log \left(\frac{a}{x^2}\right)}} \, dx","Int[1/Sqrt[-Log[a/x^2]],x]","\sqrt{\frac{\pi }{2}} x \sqrt{\frac{a}{x^2}} \text{Erfi}\left(\frac{\sqrt{-\log \left(\frac{a}{x^2}\right)}}{\sqrt{2}}\right)","\sqrt{\frac{\pi }{2}} x \sqrt{\frac{a}{x^2}} \text{Erfi}\left(\frac{\sqrt{-\log \left(\frac{a}{x^2}\right)}}{\sqrt{2}}\right)",1,"Sqrt[Pi/2]*Sqrt[a/x^2]*x*Erfi[Sqrt[-Log[a/x^2]]/Sqrt[2]]","A",3,3,12,0.2500,1,"{2300, 2180, 2204}"
265,1,43,0,0.0308945,"\int \frac{1}{\sqrt{-\log \left(a x^n\right)}} \, dx","Int[1/Sqrt[-Log[a*x^n]],x]","-\frac{\sqrt{\pi } x \left(a x^n\right)^{-1/n} \text{Erf}\left(\frac{\sqrt{-\log \left(a x^n\right)}}{\sqrt{n}}\right)}{\sqrt{n}}","-\frac{\sqrt{\pi } x \left(a x^n\right)^{-1/n} \text{Erf}\left(\frac{\sqrt{-\log \left(a x^n\right)}}{\sqrt{n}}\right)}{\sqrt{n}}",1,"-((Sqrt[Pi]*x*Erf[Sqrt[-Log[a*x^n]]/Sqrt[n]])/(Sqrt[n]*(a*x^n)^n^(-1)))","A",3,3,12,0.2500,1,"{2300, 2180, 2205}"
266,1,122,0,0.14536,"\int \frac{\log \left(1+\sqrt{x}-x\right)}{x} \, dx","Int[Log[1 + Sqrt[x] - x]/x,x]","2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{x}}{1+\sqrt{5}}\right)-2 \text{PolyLog}\left(2,\frac{2 \sqrt{x}}{1-\sqrt{5}}\right)-2 \log \left(\frac{1}{2} \left(1+\sqrt{5}\right)\right) \log \left(-2 \sqrt{x}+\sqrt{5}+1\right)-2 \log \left(1-\frac{2 \sqrt{x}}{1-\sqrt{5}}\right) \log \left(\sqrt{x}\right)+2 \log \left(-x+\sqrt{x}+1\right) \log \left(\sqrt{x}\right)","2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{x}}{1+\sqrt{5}}\right)-2 \text{PolyLog}\left(2,\frac{2 \sqrt{x}}{1-\sqrt{5}}\right)-2 \log \left(\frac{1}{2} \left(1+\sqrt{5}\right)\right) \log \left(-2 \sqrt{x}+\sqrt{5}+1\right)-2 \log \left(1-\frac{2 \sqrt{x}}{1-\sqrt{5}}\right) \log \left(\sqrt{x}\right)+2 \log \left(-x+\sqrt{x}+1\right) \log \left(\sqrt{x}\right)",1,"-2*Log[(1 + Sqrt[5])/2]*Log[1 + Sqrt[5] - 2*Sqrt[x]] - 2*Log[1 - (2*Sqrt[x])/(1 - Sqrt[5])]*Log[Sqrt[x]] + 2*Log[1 + Sqrt[x] - x]*Log[Sqrt[x]] + 2*PolyLog[2, 1 - (2*Sqrt[x])/(1 + Sqrt[5])] - 2*PolyLog[2, (2*Sqrt[x])/(1 - Sqrt[5])]","A",8,7,15,0.4667,1,"{2530, 2524, 2357, 2317, 2391, 2316, 2315}"
267,1,81,0,0.0994792,"\int \frac{x \log (c+d x)}{a+b x} \, dx","Int[(x*Log[c + d*x])/(a + b*x),x]","-\frac{a \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b^2}-\frac{a \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b^2}+\frac{(c+d x) \log (c+d x)}{b d}-\frac{x}{b}","-\frac{a \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b^2}-\frac{a \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b^2}+\frac{(c+d x) \log (c+d x)}{b d}-\frac{x}{b}",1,"-(x/b) + ((c + d*x)*Log[c + d*x])/(b*d) - (a*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/b^2 - (a*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/b^2","A",7,7,15,0.4667,1,"{43, 2416, 2389, 2295, 2394, 2393, 2391}"
268,1,9,0,0.0089794,"\int \frac{\log (x)}{-1+x} \, dx","Int[Log[x]/(-1 + x),x]","-\text{PolyLog}(2,1-x)","-\text{PolyLog}(2,1-x)",1,"-PolyLog[2, 1 - x]","A",1,1,8,0.1250,1,"{2315}"
269,1,43,0,0.0725418,"\int \frac{x \log (1-a-b x)}{a+b x} \, dx","Int[(x*Log[1 - a - b*x])/(a + b*x),x]","\frac{a \text{PolyLog}(2,a+b x)}{b^2}-\frac{(-a-b x+1) \log (-a-b x+1)}{b^2}-\frac{x}{b}","\frac{a \text{PolyLog}(2,a+b x)}{b^2}-\frac{(-a-b x+1) \log (-a-b x+1)}{b^2}-\frac{x}{b}",1,"-(x/b) - ((1 - a - b*x)*Log[1 - a - b*x])/b^2 + (a*PolyLog[2, a + b*x])/b^2","A",6,6,19,0.3158,1,"{43, 2416, 2389, 2295, 2393, 2391}"
270,1,30,0,0.0988166,"\int \frac{(b+2 c x) \log (x)}{x (b+c x)} \, dx","Int[((b + 2*c*x)*Log[x])/(x*(b + c*x)),x]","\text{PolyLog}\left(2,-\frac{c x}{b}\right)+\log (x) \log \left(\frac{c x}{b}+1\right)+\frac{\log ^2(x)}{2}","\text{PolyLog}\left(2,-\frac{c x}{b}\right)+\log (x) \log \left(\frac{c x}{b}+1\right)+\frac{\log ^2(x)}{2}",1,"Log[x]^2/2 + Log[x]*Log[1 + (c*x)/b] + PolyLog[2, -((c*x)/b)]","A",5,4,19,0.2105,1,"{2357, 2301, 2317, 2391}"
271,1,7,0,0.0269251,"\int (\sin (x \log (x))+\log (x) \sin (x \log (x))) \, dx","Int[Sin[x*Log[x]] + Log[x]*Sin[x*Log[x]],x]","-\cos (x \log (x))","-\cos (x \log (x))",1,"-Cos[x*Log[x]]","A",2,1,14,0.07143,1,"{4511}"
272,1,68,0,0.2508468,"\int \frac{\log \left(\frac{1-(-1+x)^2}{1+(-1+x)^2}\right)}{x^2} \, dx","Int[Log[(1 - (-1 + x)^2)/(1 + (-1 + x)^2)]/x^2,x]","-\frac{1}{2} \log \left(x^2-2 x+2\right)-\frac{1}{x}-\frac{\log \left(\frac{1-(1-x)^2}{(x-1)^2+1}\right)}{x}+\frac{1}{2} \log (2-x)+\frac{\log (x)}{2}+\tan ^{-1}(1-x)","-\frac{1}{2} \log \left(x^2-2 x+2\right)-\frac{1}{x}-\frac{\log \left(\frac{1-(1-x)^2}{(x-1)^2+1}\right)}{x}+\frac{1}{2} \log (2-x)+\frac{\log (x)}{2}+\tan ^{-1}(1-x)",1,"-x^(-1) + ArcTan[1 - x] - Log[(1 - (1 - x)^2)/(1 + (-1 + x)^2)]/x + Log[2 - x]/2 + Log[x]/2 - Log[2 - 2*x + x^2]/2","A",8,7,24,0.2917,1,"{2525, 12, 6728, 634, 617, 204, 628}"
273,1,29,0,0.0180576,"\int \log \left(\sqrt{x}+x\right) \, dx","Int[Log[Sqrt[x] + x],x]","-x+\sqrt{x}+x \log \left(x+\sqrt{x}\right)-\log \left(\sqrt{x}+1\right)","-x+\sqrt{x}+x \log \left(x+\sqrt{x}\right)-\log \left(\sqrt{x}+1\right)",1,"Sqrt[x] - x - Log[1 + Sqrt[x]] + x*Log[Sqrt[x] + x]","A",4,3,8,0.3750,1,"{2548, 376, 77}"
274,1,18,0,0.0035066,"\int \log \left(-\frac{x}{1+x}\right) \, dx","Int[Log[-(x/(1 + x))],x]","x \log \left(-\frac{x}{x+1}\right)-\log (x+1)","x \log \left(-\frac{x}{x+1}\right)-\log (x+1)",1,"x*Log[-(x/(1 + x))] - Log[1 + x]","A",2,2,9,0.2222,1,"{2486, 31}"
275,1,27,0,0.0049812,"\int \log \left(\frac{-1+x}{1+x}\right) \, dx","Int[Log[(-1 + x)/(1 + x)],x]","-(1-x) \log \left(-\frac{1-x}{x+1}\right)-2 \log (x+1)","-(1-x) \log \left(-\frac{1-x}{x+1}\right)-2 \log (x+1)",1,"-((1 - x)*Log[-((1 - x)/(1 + x))]) - 2*Log[1 + x]","A",2,2,10,0.2000,1,"{2486, 31}"
276,1,57,0,0.0569428,"\int \frac{\log \left(\frac{1-x^2}{1+x^2}\right)}{(1+x)^2} \, dx","Int[Log[(1 - x^2)/(1 + x^2)]/(1 + x)^2,x]","\frac{1}{2} \log \left(1-x^2\right)-\frac{\log \left(\frac{1-x^2}{x^2+1}\right)}{x+1}-\frac{1}{2} \log \left(x^2+1\right)-\frac{1}{x+1}-\tan ^{-1}(x)","\frac{1}{2} \log \left(1-x^2\right)-\frac{\log \left(\frac{1-x^2}{x^2+1}\right)}{x+1}-\frac{1}{2} \log \left(x^2+1\right)-\frac{1}{x+1}-\tan ^{-1}(x)",1,"-(1 + x)^(-1) - ArcTan[x] + Log[1 - x^2]/2 - Log[(1 - x^2)/(1 + x^2)]/(1 + x) - Log[1 + x^2]/2","A",8,6,22,0.2727,1,"{2525, 12, 2074, 260, 635, 203}"
277,1,60,0,0.0807481,"\int \frac{\log \left(c \left(1+x^2\right)^n\right)}{1+x^2} \, dx","Int[Log[c*(1 + x^2)^n]/(1 + x^2),x]","i n \text{PolyLog}\left(2,1-\frac{2}{1+i x}\right)+\tan ^{-1}(x) \log \left(c \left(x^2+1\right)^n\right)+i n \tan ^{-1}(x)^2+2 n \log \left(\frac{2}{1+i x}\right) \tan ^{-1}(x)","i n \text{PolyLog}\left(2,1-\frac{2}{1+i x}\right)+\tan ^{-1}(x) \log \left(c \left(x^2+1\right)^n\right)+i n \tan ^{-1}(x)^2+2 n \log \left(\frac{2}{1+i x}\right) \tan ^{-1}(x)",1,"I*n*ArcTan[x]^2 + 2*n*ArcTan[x]*Log[2/(1 + I*x)] + ArcTan[x]*Log[c*(1 + x^2)^n] + I*n*PolyLog[2, 1 - 2/(1 + I*x)]","A",5,6,18,0.3333,1,"{203, 2470, 4920, 4854, 2402, 2315}"
278,1,61,0,0.1054995,"\int \frac{\log \left(\frac{x^2}{1+x^2}\right)}{1+x^2} \, dx","Int[Log[x^2/(1 + x^2)]/(1 + x^2),x]","i \text{PolyLog}\left(2,-1+\frac{2}{1-i x}\right)+\log \left(\frac{x^2}{x^2+1}\right) \tan ^{-1}(x)+i \tan ^{-1}(x)^2-2 \log \left(2-\frac{2}{1-i x}\right) \tan ^{-1}(x)","i \text{PolyLog}\left(2,-1+\frac{2}{1-i x}\right)+\log \left(\frac{x^2}{x^2+1}\right) \tan ^{-1}(x)+i \tan ^{-1}(x)^2-2 \log \left(2-\frac{2}{1-i x}\right) \tan ^{-1}(x)",1,"I*ArcTan[x]^2 - 2*ArcTan[x]*Log[2 - 2/(1 - I*x)] + ArcTan[x]*Log[x^2/(1 + x^2)] + I*PolyLog[2, -1 + 2/(1 - I*x)]","A",5,6,20,0.3000,1,"{203, 2526, 12, 4924, 4868, 2447}"
279,1,165,0,0.1916759,"\int \frac{\log \left(\frac{c x^2}{a+b x^2}\right)}{a+b x^2} \, dx","Int[Log[(c*x^2)/(a + b*x^2)]/(a + b*x^2),x]","\frac{i \text{PolyLog}\left(2,-1+\frac{2 \sqrt{a}}{\sqrt{a}-i \sqrt{b} x}\right)}{\sqrt{a} \sqrt{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log \left(\frac{c x^2}{a+b x^2}\right)}{\sqrt{a} \sqrt{b}}+\frac{i \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2}{\sqrt{a} \sqrt{b}}-\frac{2 \log \left(2-\frac{2 \sqrt{a}}{\sqrt{a}-i \sqrt{b} x}\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}","\frac{i \text{PolyLog}\left(2,-1+\frac{2 \sqrt{a}}{\sqrt{a}-i \sqrt{b} x}\right)}{\sqrt{a} \sqrt{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log \left(\frac{c x^2}{a+b x^2}\right)}{\sqrt{a} \sqrt{b}}+\frac{i \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2}{\sqrt{a} \sqrt{b}}-\frac{2 \log \left(2-\frac{2 \sqrt{a}}{\sqrt{a}-i \sqrt{b} x}\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}",1,"(I*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2)/(Sqrt[a]*Sqrt[b]) + (ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[(c*x^2)/(a + b*x^2)])/(Sqrt[a]*Sqrt[b]) - (2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[2 - (2*Sqrt[a])/(Sqrt[a] - I*Sqrt[b]*x)])/(Sqrt[a]*Sqrt[b]) + (I*PolyLog[2, -1 + (2*Sqrt[a])/(Sqrt[a] - I*Sqrt[b]*x)])/(Sqrt[a]*Sqrt[b])","A",5,6,25,0.2400,1,"{205, 2526, 12, 4924, 4868, 2447}"
280,1,29,0,0.0335913,"\int \frac{\log \left(1+\frac{i \sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Int[Log[1 + (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]]/(1 - a^2*x^2),x]","\frac{\text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}","\frac{\text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}",1,"PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]]/a","A",1,1,39,0.02564,1,"{2518}"
281,1,29,0,0.034437,"\int \frac{\log \left(1-\frac{i \sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Int[Log[1 - (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]]/(1 - a^2*x^2),x]","\frac{\text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}","\frac{\text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}",1,"PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]]/a","A",1,1,39,0.02564,1,"{2518}"
282,1,17,0,0.003246,"\int \log \left(e^{a+b x}\right) \, dx","Int[Log[E^(a + b*x)],x]","\frac{\log ^2\left(e^{a+b x}\right)}{2 b}","\frac{\log ^2\left(e^{a+b x}\right)}{2 b}",1,"Log[E^(a + b*x)]^2/(2*b)","A",2,2,8,0.2500,1,"{2157, 30}"
283,1,27,0,0.0085458,"\int \log \left(e^{a+b x^n}\right) \, dx","Int[Log[E^(a + b*x^n)],x]","x \log \left(e^{a+b x^n}\right)-\frac{b n x^{n+1}}{n+1}","x \log \left(e^{a+b x^n}\right)-\frac{b n x^{n+1}}{n+1}",1,"-((b*n*x^(1 + n))/(1 + n)) + x*Log[E^(a + b*x^n)]","A",3,3,10,0.3000,1,"{2548, 12, 30}"
284,1,31,0,0.0525146,"\int e^x \log \left(a+b e^x\right) \, dx","Int[E^x*Log[a + b*E^x],x]","e^x \log \left(a+b e^x\right)+\frac{a \log \left(a+b e^x\right)}{b}-e^x","\frac{\left(a+b e^x\right) \log \left(a+b e^x\right)}{b}-e^x",1,"-E^x + (a*Log[a + b*E^x])/b + E^x*Log[a + b*E^x]","A",5,5,12,0.4167,1,"{2194, 2554, 12, 2248, 43}"
285,1,26,0,0.0354785,"\int e^{a+b x} \log (x) \, dx","Int[E^(a + b*x)*Log[x],x]","\frac{\log (x) e^{a+b x}}{b}-\frac{e^a \text{Ei}(b x)}{b}","\frac{\log (x) e^{a+b x}}{b}-\frac{e^a \text{Ei}(b x)}{b}",1,"-((E^a*ExpIntegralEi[b*x])/b) + (E^(a + b*x)*Log[x])/b","A",3,4,10,0.4000,1,"{2194, 2554, 12, 2178}"
286,0,0,0,0.0359061,"\int \frac{x^2}{x+\log (x)} \, dx","Int[x^2/(x + Log[x]),x]","\int \frac{x^2}{x+\log (x)} \, dx","\text{Int}\left(\frac{x^2}{x+\log (x)},x\right)",0,"Defer[Int][x^2/(x + Log[x]), x]","A",0,0,0,0,-1,"{}"
287,0,0,0,0.0220771,"\int \frac{x}{x+\log (x)} \, dx","Int[x/(x + Log[x]),x]","\int \frac{x}{x+\log (x)} \, dx","\text{Int}\left(\frac{x}{x+\log (x)},x\right)",0,"Defer[Int][x/(x + Log[x]), x]","A",0,0,0,0,-1,"{}"
288,0,0,0,0.0078645,"\int \frac{1}{x+\log (x)} \, dx","Int[(x + Log[x])^(-1),x]","\int \frac{1}{x+\log (x)} \, dx","\text{Int}\left(\frac{1}{x+\log (x)},x\right)",0,"Defer[Int][(x + Log[x])^(-1), x]","A",0,0,0,0,-1,"{}"
289,0,0,0,0.031951,"\int \frac{1}{x (x+\log (x))} \, dx","Int[1/(x*(x + Log[x])),x]","\int \frac{1}{x (x+\log (x))} \, dx","\text{Int}\left(\frac{1}{x (x+\log (x))},x\right)",0,"Defer[Int][1/(x*(x + Log[x])), x]","A",0,0,0,0,-1,"{}"
290,0,0,0,0.0341406,"\int \frac{1}{x^2 (x+\log (x))} \, dx","Int[1/(x^2*(x + Log[x])),x]","\int \frac{1}{x^2 (x+\log (x))} \, dx","\text{Int}\left(\frac{1}{x^2 (x+\log (x))},x\right)",0,"Defer[Int][1/(x^2*(x + Log[x])), x]","A",0,0,0,0,-1,"{}"
291,1,13,0,0.0243466,"\int \frac{\log (x)}{x+4 x \log ^2(x)} \, dx","Int[Log[x]/(x + 4*x*Log[x]^2),x]","\frac{1}{8} \log \left(4 \log ^2(x)+1\right)","\frac{1}{8} \log \left(4 \log ^2(x)+1\right)",1,"Log[1 + 4*Log[x]^2]/8","A",2,2,14,0.1429,1,"{203, 260}"
292,1,9,0,0.0718203,"\int \frac{1-\log (x)}{x (x+\log (x))} \, dx","Int[(1 - Log[x])/(x*(x + Log[x])),x]","\log \left(\frac{\log (x)}{x}+1\right)","\log \left(\frac{\log (x)}{x}+1\right)",1,"Log[1 + Log[x]/x]","A",2,2,16,0.1250,1,"{6712, 31}"
293,1,13,0,0.1424219,"\int \frac{1+x}{\log (x) (x+\log (x))} \, dx","Int[(1 + x)/(Log[x]*(x + Log[x])),x]","\text{li}(x)+\log (\log (x))-\log (x+\log (x))","\text{li}(x)+\log (\log (x))-\log (x+\log (x))",1,"Log[Log[x]] - Log[x + Log[x]] + LogIntegral[x]","A",8,6,14,0.4286,1,"{6742, 2353, 2298, 2302, 29, 6684}"
294,1,67,0,0.0742242,"\int \log \left(2+\sqrt{\frac{1+x}{x}}\right) \, dx","Int[Log[2 + Sqrt[(1 + x)/x]],x]","-\frac{1}{6} \log \left(1-\sqrt{\frac{1}{x}+1}\right)+\frac{1}{2} \log \left(\sqrt{\frac{1}{x}+1}+1\right)-\frac{1}{3} \log \left(\sqrt{\frac{1}{x}+1}+2\right)+x \log \left(\sqrt{\frac{x+1}{x}}+2\right)","-\frac{1}{6} \log \left(1-\sqrt{\frac{1}{x}+1}\right)+\frac{1}{2} \log \left(\sqrt{\frac{1}{x}+1}+1\right)-\frac{1}{3} \log \left(\sqrt{\frac{1}{x}+1}+2\right)+x \log \left(\sqrt{\frac{x+1}{x}}+2\right)",1,"-Log[1 - Sqrt[1 + x^(-1)]]/6 + Log[1 + Sqrt[1 + x^(-1)]]/2 - Log[2 + Sqrt[1 + x^(-1)]]/3 + x*Log[2 + Sqrt[(1 + x)/x]]","A",5,3,14,0.2143,1,"{2548, 12, 2058}"
295,1,50,0,0.056997,"\int \log \left(1+\sqrt{\frac{1+x}{x}}\right) \, dx","Int[Log[1 + Sqrt[(1 + x)/x]],x]","-\frac{1}{2 \left(\sqrt{\frac{1}{x}+1}+1\right)}+x \log \left(\sqrt{\frac{x+1}{x}}+1\right)+\frac{1}{2} \tanh ^{-1}\left(\sqrt{\frac{x+1}{x}}\right)","-\frac{1}{2 \left(\sqrt{\frac{1}{x}+1}+1\right)}+x \log \left(\sqrt{\frac{x+1}{x}}+1\right)+\frac{1}{2} \tanh ^{-1}\left(\sqrt{\frac{x+1}{x}}\right)",1,"-1/(2*(1 + Sqrt[1 + x^(-1)])) + ArcTanh[Sqrt[(1 + x)/x]]/2 + x*Log[1 + Sqrt[(1 + x)/x]]","A",6,4,14,0.2857,1,"{2548, 12, 44, 207}"
296,1,21,0,0.0078685,"\int \log \left(\sqrt{\frac{1+x}{x}}\right) \, dx","Int[Log[Sqrt[(1 + x)/x]],x]","x \log \left(\sqrt{\frac{1}{x}+1}\right)+\frac{1}{2} \log (x+1)","x \log \left(\sqrt{\frac{1}{x}+1}\right)+\frac{1}{2} \log (x+1)",1,"x*Log[Sqrt[1 + x^(-1)]] + Log[1 + x]/2","A",4,4,12,0.3333,1,"{2453, 2448, 263, 31}"
297,1,50,0,0.0487017,"\int \log \left(-1+\sqrt{\frac{1+x}{x}}\right) \, dx","Int[Log[-1 + Sqrt[(1 + x)/x]],x]","-\frac{1}{2 \left(1-\sqrt{\frac{1}{x}+1}\right)}+x \log \left(\sqrt{\frac{x+1}{x}}-1\right)-\frac{1}{2} \tanh ^{-1}\left(\sqrt{\frac{1}{x}+1}\right)","-\frac{1}{2 \left(1-\sqrt{\frac{1}{x}+1}\right)}+x \log \left(\sqrt{\frac{x+1}{x}}-1\right)-\frac{1}{2} \tanh ^{-1}\left(\sqrt{\frac{1}{x}+1}\right)",1,"-1/(2*(1 - Sqrt[1 + x^(-1)])) - ArcTanh[Sqrt[1 + x^(-1)]]/2 + x*Log[-1 + Sqrt[(1 + x)/x]]","A",5,3,14,0.2143,1,"{2548, 44, 207}"
298,1,69,0,0.0517545,"\int \log \left(-2+\sqrt{\frac{1+x}{x}}\right) \, dx","Int[Log[-2 + Sqrt[(1 + x)/x]],x]","\frac{1}{2} \log \left(1-\sqrt{\frac{1}{x}+1}\right)-\frac{1}{3} \log \left(2-\sqrt{\frac{1}{x}+1}\right)-\frac{1}{6} \log \left(\sqrt{\frac{1}{x}+1}+1\right)+x \log \left(\sqrt{\frac{x+1}{x}}-2\right)","\frac{1}{2} \log \left(1-\sqrt{\frac{1}{x}+1}\right)-\frac{1}{3} \log \left(2-\sqrt{\frac{1}{x}+1}\right)-\frac{1}{6} \log \left(\sqrt{\frac{1}{x}+1}+1\right)+x \log \left(\sqrt{\frac{x+1}{x}}-2\right)",1,"Log[1 - Sqrt[1 + x^(-1)]]/2 - Log[2 - Sqrt[1 + x^(-1)]]/3 - Log[1 + Sqrt[1 + x^(-1)]]/6 + x*Log[-2 + Sqrt[(1 + x)/x]]","A",7,4,14,0.2857,1,"{2548, 706, 31, 633}"
299,1,9,0,0.021677,"\int \left(x^{a x}+x^{a x} \log (x)\right) \, dx","Int[x^(a*x) + x^(a*x)*Log[x],x]","\frac{x^{a x}}{a}","\frac{x^{a x}}{a}",1,"x^(a*x)/a","A",2,1,14,0.07143,1,"{2553}"
300,1,26,0,0.0252434,"\int \log ^m(x)^p \, dx","Int[(Log[x]^m)^p,x]","(-\log (x))^{-m p} \log ^m(x)^p \text{Gamma}(m p+1,-\log (x))","(-\log (x))^{-m p} \log ^m(x)^p \text{Gamma}(m p+1,-\log (x))",1,"(Gamma[1 + m*p, -Log[x]]*(Log[x]^m)^p)/(-Log[x])^(m*p)","A",3,3,6,0.5000,1,"{6720, 2299, 2181}"
301,1,60,0,0.0692622,"\int \frac{\log (x)}{\sqrt{a+b \log (x)}} \, dx","Int[Log[x]/Sqrt[a + b*Log[x]],x]","\frac{x \sqrt{a+b \log (x)}}{b}-\frac{\sqrt{\pi } (2 a+b) e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \log (x)}}{\sqrt{b}}\right)}{2 b^{3/2}}","\frac{x \sqrt{a+b \log (x)}}{b}-\frac{\sqrt{\pi } (2 a+b) e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \log (x)}}{\sqrt{b}}\right)}{2 b^{3/2}}",1,"-((2*a + b)*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[x]]/Sqrt[b]])/(2*b^(3/2)*E^(a/b)) + (x*Sqrt[a + b*Log[x]])/b","A",4,4,13,0.3077,1,"{2294, 2299, 2180, 2204}"
302,1,64,0,0.0677266,"\int \frac{\log (x)}{\sqrt{a-b \log (x)}} \, dx","Int[Log[x]/Sqrt[a - b*Log[x]],x]","-\frac{\sqrt{\pi } (2 a-b) e^{a/b} \text{Erf}\left(\frac{\sqrt{a-b \log (x)}}{\sqrt{b}}\right)}{2 b^{3/2}}-\frac{x \sqrt{a-b \log (x)}}{b}","-\frac{\sqrt{\pi } (2 a-b) e^{a/b} \text{Erf}\left(\frac{\sqrt{a-b \log (x)}}{\sqrt{b}}\right)}{2 b^{3/2}}-\frac{x \sqrt{a-b \log (x)}}{b}",1,"-((2*a - b)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a - b*Log[x]]/Sqrt[b]])/(2*b^(3/2)) - (x*Sqrt[a - b*Log[x]])/b","A",4,4,14,0.2857,1,"{2294, 2299, 2180, 2205}"
303,1,69,0,0.0690086,"\int \frac{A+B \log (x)}{\sqrt{a+b \log (x)}} \, dx","Int[(A + B*Log[x])/Sqrt[a + b*Log[x]],x]","\frac{\sqrt{\pi } e^{-\frac{a}{b}} (2 A b-B (2 a+b)) \text{Erfi}\left(\frac{\sqrt{a+b \log (x)}}{\sqrt{b}}\right)}{2 b^{3/2}}+\frac{B x \sqrt{a+b \log (x)}}{b}","\frac{\sqrt{\pi } e^{-\frac{a}{b}} (2 A b-B (2 a+b)) \text{Erfi}\left(\frac{\sqrt{a+b \log (x)}}{\sqrt{b}}\right)}{2 b^{3/2}}+\frac{B x \sqrt{a+b \log (x)}}{b}",1,"((2*A*b - (2*a + b)*B)*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[x]]/Sqrt[b]])/(2*b^(3/2)*E^(a/b)) + (B*x*Sqrt[a + b*Log[x]])/b","A",4,4,17,0.2353,1,"{2294, 2299, 2180, 2204}"
304,1,71,0,0.0785237,"\int \frac{A+B \log (x)}{\sqrt{a-b \log (x)}} \, dx","Int[(A + B*Log[x])/Sqrt[a - b*Log[x]],x]","-\frac{\sqrt{\pi } e^{a/b} (2 a B+2 A b-b B) \text{Erf}\left(\frac{\sqrt{a-b \log (x)}}{\sqrt{b}}\right)}{2 b^{3/2}}-\frac{B x \sqrt{a-b \log (x)}}{b}","-\frac{\sqrt{\pi } e^{a/b} (2 a B+2 A b-b B) \text{Erf}\left(\frac{\sqrt{a-b \log (x)}}{\sqrt{b}}\right)}{2 b^{3/2}}-\frac{B x \sqrt{a-b \log (x)}}{b}",1,"-((2*A*b + 2*a*B - b*B)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a - b*Log[x]]/Sqrt[b]])/(2*b^(3/2)) - (B*x*Sqrt[a - b*Log[x]])/b","A",4,4,18,0.2222,1,"{2294, 2299, 2180, 2205}"
305,1,98,0,0.2901983,"\int x^2 \log (\log (x) \sin (x)) \, dx","Int[x^2*Log[Log[x]*Sin[x]],x]","\frac{1}{2} i x^2 \text{PolyLog}\left(2,e^{2 i x}\right)-\frac{1}{2} x \text{PolyLog}\left(3,e^{2 i x}\right)-\frac{1}{4} i \text{PolyLog}\left(4,e^{2 i x}\right)-\frac{1}{3} \text{Ei}(3 \log (x))+\frac{i x^4}{12}-\frac{1}{3} x^3 \log \left(1-e^{2 i x}\right)+\frac{1}{3} x^3 \log (\log (x) \sin (x))","\frac{1}{2} i x^2 \text{PolyLog}\left(2,e^{2 i x}\right)-\frac{1}{2} x \text{PolyLog}\left(3,e^{2 i x}\right)-\frac{1}{4} i \text{PolyLog}\left(4,e^{2 i x}\right)-\frac{1}{3} \text{Ei}(3 \log (x))+\frac{i x^4}{12}-\frac{1}{3} x^3 \log \left(1-e^{2 i x}\right)+\frac{1}{3} x^3 \log (\log (x) \sin (x))",1,"(I/12)*x^4 - ExpIntegralEi[3*Log[x]]/3 - (x^3*Log[1 - E^((2*I)*x)])/3 + (x^3*Log[Log[x]*Sin[x]])/3 + (I/2)*x^2*PolyLog[2, E^((2*I)*x)] - (x*PolyLog[3, E^((2*I)*x)])/2 - (I/4)*PolyLog[4, E^((2*I)*x)]","A",13,13,10,1.300,1,"{30, 2555, 12, 6688, 14, 3717, 2190, 2531, 6609, 2282, 6589, 2309, 2178}"
306,1,80,0,0.1815423,"\int x \log (\log (x) \sin (x)) \, dx","Int[x*Log[Log[x]*Sin[x]],x]","\frac{1}{2} i x \text{PolyLog}\left(2,e^{2 i x}\right)-\frac{1}{4} \text{PolyLog}\left(3,e^{2 i x}\right)-\frac{1}{2} \text{Ei}(2 \log (x))+\frac{i x^3}{6}-\frac{1}{2} x^2 \log \left(1-e^{2 i x}\right)+\frac{1}{2} x^2 \log (\log (x) \sin (x))","\frac{1}{2} i x \text{PolyLog}\left(2,e^{2 i x}\right)-\frac{1}{4} \text{PolyLog}\left(3,e^{2 i x}\right)-\frac{1}{2} \text{Ei}(2 \log (x))+\frac{i x^3}{6}-\frac{1}{2} x^2 \log \left(1-e^{2 i x}\right)+\frac{1}{2} x^2 \log (\log (x) \sin (x))",1,"(I/6)*x^3 - ExpIntegralEi[2*Log[x]]/2 - (x^2*Log[1 - E^((2*I)*x)])/2 + (x^2*Log[Log[x]*Sin[x]])/2 + (I/2)*x*PolyLog[2, E^((2*I)*x)] - PolyLog[3, E^((2*I)*x)]/4","A",12,12,8,1.500,1,"{30, 2555, 12, 6688, 14, 3717, 2190, 2531, 2282, 6589, 2309, 2178}"
307,1,52,0,0.0615273,"\int \log (\log (x) \sin (x)) \, dx","Int[Log[Log[x]*Sin[x]],x]","\frac{1}{2} i \text{PolyLog}\left(2,e^{2 i x}\right)-\text{li}(x)+\frac{i x^2}{2}-x \log \left(1-e^{2 i x}\right)+x \log (\log (x) \sin (x))","\frac{1}{2} i \text{PolyLog}\left(2,e^{2 i x}\right)-\text{li}(x)+\frac{i x^2}{2}-x \log \left(1-e^{2 i x}\right)+x \log (\log (x) \sin (x))",1,"(I/2)*x^2 - x*Log[1 - E^((2*I)*x)] + x*Log[Log[x]*Sin[x]] - LogIntegral[x] + (I/2)*PolyLog[2, E^((2*I)*x)]","A",7,6,6,1.000,1,"{2549, 3717, 2190, 2279, 2391, 2298}"
308,0,0,0,0.0187267,"\int \frac{\log (\log (x) \sin (x))}{x} \, dx","Int[Log[Log[x]*Sin[x]]/x,x]","\int \frac{\log (\log (x) \sin (x))}{x} \, dx","\text{Int}\left(\frac{\log (\log (x) \sin (x))}{x},x\right)",0,"Defer[Int][Log[Log[x]*Sin[x]]/x, x]","A",0,0,0,0,-1,"{}"
309,0,0,0,0.3445626,"\int \frac{\log (\log (x) \sin (x))}{x^2} \, dx","Int[Log[Log[x]*Sin[x]]/x^2,x]","\int \frac{\log (\log (x) \sin (x))}{x^2} \, dx","\text{Int}\left(\frac{\cot (x)}{x},x\right)+\text{Ei}(-\log (x))-\frac{\log (\log (x) \sin (x))}{x}",0,"ExpIntegralEi[-Log[x]] - Log[Log[x]*Sin[x]]/x + Defer[Int][Cot[x]/x, x]","A",0,0,0,0,-1,"{}"
310,1,103,0,0.2032962,"\int x^2 \log \left(e^x \log (x) \sin (x)\right) \, dx","Int[x^2*Log[E^x*Log[x]*Sin[x]],x]","\frac{1}{2} i x^2 \text{PolyLog}\left(2,e^{2 i x}\right)-\frac{1}{2} x \text{PolyLog}\left(3,e^{2 i x}\right)-\frac{1}{4} i \text{PolyLog}\left(4,e^{2 i x}\right)-\frac{1}{3} \text{Ei}(3 \log (x))+\left(-\frac{1}{12}+\frac{i}{12}\right) x^4-\frac{1}{3} x^3 \log \left(1-e^{2 i x}\right)+\frac{1}{3} x^3 \log \left(e^x \log (x) \sin (x)\right)","\frac{1}{2} i x^2 \text{PolyLog}\left(2,e^{2 i x}\right)-\frac{1}{2} x \text{PolyLog}\left(3,e^{2 i x}\right)-\frac{1}{4} i \text{PolyLog}\left(4,e^{2 i x}\right)-\frac{1}{3} \text{Ei}(3 \log (x))+\left(-\frac{1}{12}+\frac{i}{12}\right) x^4-\frac{1}{3} x^3 \log \left(1-e^{2 i x}\right)+\frac{1}{3} x^3 \log \left(e^x \log (x) \sin (x)\right)",1,"(-1/12 + I/12)*x^4 - ExpIntegralEi[3*Log[x]]/3 - (x^3*Log[1 - E^((2*I)*x)])/3 + (x^3*Log[E^x*Log[x]*Sin[x]])/3 + (I/2)*x^2*PolyLog[2, E^((2*I)*x)] - (x*PolyLog[3, E^((2*I)*x)])/2 - (I/4)*PolyLog[4, E^((2*I)*x)]","A",14,12,13,0.9231,1,"{30, 2555, 12, 14, 3717, 2190, 2531, 6609, 2282, 6589, 2309, 2178}"
311,1,85,0,0.138691,"\int x \log \left(e^x \log (x) \sin (x)\right) \, dx","Int[x*Log[E^x*Log[x]*Sin[x]],x]","\frac{1}{2} i x \text{PolyLog}\left(2,e^{2 i x}\right)-\frac{1}{4} \text{PolyLog}\left(3,e^{2 i x}\right)-\frac{1}{2} \text{Ei}(2 \log (x))+\left(-\frac{1}{6}+\frac{i}{6}\right) x^3-\frac{1}{2} x^2 \log \left(1-e^{2 i x}\right)+\frac{1}{2} x^2 \log \left(e^x \log (x) \sin (x)\right)","\frac{1}{2} i x \text{PolyLog}\left(2,e^{2 i x}\right)-\frac{1}{4} \text{PolyLog}\left(3,e^{2 i x}\right)-\frac{1}{2} \text{Ei}(2 \log (x))+\left(-\frac{1}{6}+\frac{i}{6}\right) x^3-\frac{1}{2} x^2 \log \left(1-e^{2 i x}\right)+\frac{1}{2} x^2 \log \left(e^x \log (x) \sin (x)\right)",1,"(-1/6 + I/6)*x^3 - ExpIntegralEi[2*Log[x]]/2 - (x^2*Log[1 - E^((2*I)*x)])/2 + (x^2*Log[E^x*Log[x]*Sin[x]])/2 + (I/2)*x*PolyLog[2, E^((2*I)*x)] - PolyLog[3, E^((2*I)*x)]/4","A",13,11,11,1.000,1,"{30, 2555, 12, 14, 3717, 2190, 2531, 2282, 6589, 2309, 2178}"
312,1,57,0,0.0642922,"\int \log \left(e^x \log (x) \sin (x)\right) \, dx","Int[Log[E^x*Log[x]*Sin[x]],x]","\frac{1}{2} i \text{PolyLog}\left(2,e^{2 i x}\right)-\text{li}(x)+\left(-\frac{1}{2}+\frac{i}{2}\right) x^2-x \log \left(1-e^{2 i x}\right)+x \log \left(e^x \log (x) \sin (x)\right)","\frac{1}{2} i \text{PolyLog}\left(2,e^{2 i x}\right)-\text{li}(x)+\left(-\frac{1}{2}+\frac{i}{2}\right) x^2-x \log \left(1-e^{2 i x}\right)+x \log \left(e^x \log (x) \sin (x)\right)",1,"(-1/2 + I/2)*x^2 - x*Log[1 - E^((2*I)*x)] + x*Log[E^x*Log[x]*Sin[x]] - LogIntegral[x] + (I/2)*PolyLog[2, E^((2*I)*x)]","A",7,6,9,0.6667,1,"{2549, 3717, 2190, 2279, 2391, 2298}"
313,0,0,0,0.0219818,"\int \frac{\log \left(e^x \log (x) \sin (x)\right)}{x} \, dx","Int[Log[E^x*Log[x]*Sin[x]]/x,x]","\int \frac{\log \left(e^x \log (x) \sin (x)\right)}{x} \, dx","\text{Int}\left(\frac{\log \left(e^x \log (x) \sin (x)\right)}{x},x\right)",0,"Defer[Int][Log[E^x*Log[x]*Sin[x]]/x, x]","A",0,0,0,0,-1,"{}"
314,0,0,0,0.0688721,"\int \frac{\log \left(e^x \log (x) \sin (x)\right)}{x^2} \, dx","Int[Log[E^x*Log[x]*Sin[x]]/x^2,x]","\int \frac{\log \left(e^x \log (x) \sin (x)\right)}{x^2} \, dx","\text{Int}\left(\frac{\cot (x)}{x},x\right)+\text{Ei}(-\log (x))+\log (x)-\frac{\log \left(e^x \log (x) \sin (x)\right)}{x}",0,"ExpIntegralEi[-Log[x]] + Log[x] - Log[E^x*Log[x]*Sin[x]]/x + Defer[Int][Cot[x]/x, x]","A",0,0,0,0,-1,"{}"