1,0,0,76,1.2643016,"\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","Integrate[(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,"Integrate[(Log[c*x^n]^(-1 + q)*(a*x^m + b*Log[c*x^n]^q)^p)/x, x]","A",-1
2,1,223,231,0.766512,"\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","Integrate[(Log[c*x^n]^(-1 + q)*(a*x^m + b*Log[c*x^n]^q)^3)/x,x]","\frac{\log ^q\left(c x^n\right) \left(-4 a^3 3^{-q} x^{3 m} \left(c x^n\right)^{-\frac{3 m}{n}} \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-q} \Gamma \left(q,-\frac{3 m \log \left(c x^n\right)}{n}\right)-3 a^2 b 4^{1-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)^{-2 q} \Gamma \left(2 q,-\frac{2 m \log \left(c x^n\right)}{n}\right)-12 a b^2 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)^{-3 q} \Gamma \left(3 q,-\frac{m \log \left(c x^n\right)}{n}\right)+\frac{b^3 \log ^{3 q}\left(c x^n\right)}{q}\right)}{4 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} \Gamma \left(q,-\frac{3 m \log \left(c x^n\right)}{n}\right)}{n}-\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} \Gamma \left(2 q,-\frac{2 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} \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,"(Log[c*x^n]^q*((b^3*Log[c*x^n]^(3*q))/q - (12*a*b^2*x^m*Gamma[3*q, -((m*Log[c*x^n])/n)]*Log[c*x^n]^(2*q))/((c*x^n)^(m/n)*(-((m*Log[c*x^n])/n))^(3*q)) - (3*4^(1 - q)*a^2*b*x^(2*m)*Gamma[2*q, (-2*m*Log[c*x^n])/n]*Log[c*x^n]^q)/((c*x^n)^((2*m)/n)*(-((m*Log[c*x^n])/n))^(2*q)) - (4*a^3*x^(3*m)*Gamma[q, (-3*m*Log[c*x^n])/n])/(3^q*(c*x^n)^((3*m)/n)*(-((m*Log[c*x^n])/n))^q)))/(4*n)","A",1
3,1,149,156,0.4414863,"\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","Integrate[(Log[c*x^n]^(-1 + q)*(a*x^m + b*Log[c*x^n]^q)^2)/x,x]","\frac{\log ^q\left(c x^n\right) \left(-3 a^2 2^{-q} x^{2 m} \left(c x^n\right)^{-\frac{2 m}{n}} \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-q} \Gamma \left(q,-\frac{2 m \log \left(c x^n\right)}{n}\right)-6 a b 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)^{-2 q} \Gamma \left(2 q,-\frac{m \log \left(c x^n\right)}{n}\right)+\frac{b^2 \log ^{2 q}\left(c x^n\right)}{q}\right)}{3 n}","-\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} \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} \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,"(Log[c*x^n]^q*((b^2*Log[c*x^n]^(2*q))/q - (6*a*b*x^m*Gamma[2*q, -((m*Log[c*x^n])/n)]*Log[c*x^n]^q)/((c*x^n)^(m/n)*(-((m*Log[c*x^n])/n))^(2*q)) - (3*a^2*x^(2*m)*Gamma[q, (-2*m*Log[c*x^n])/n])/(2^q*(c*x^n)^((2*m)/n)*(-((m*Log[c*x^n])/n))^q)))/(3*n)","A",1
4,1,77,81,0.1744095,"\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","Integrate[(Log[c*x^n]^(-1 + q)*(a*x^m + b*Log[c*x^n]^q))/x,x]","\frac{\log ^q\left(c x^n\right) \left(\frac{b \log ^q\left(c x^n\right)}{q}-2 a x^m \left(c x^n\right)^{-\frac{m}{n}} \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-q} \Gamma \left(q,-\frac{m \log \left(c x^n\right)}{n}\right)\right)}{2 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} \Gamma \left(q,-\frac{m \log \left(c x^n\right)}{n}\right)}{n}",1,"(Log[c*x^n]^q*((b*Log[c*x^n]^q)/q - (2*a*x^m*Gamma[q, -((m*Log[c*x^n])/n)])/((c*x^n)^(m/n)*(-((m*Log[c*x^n])/n))^q)))/(2*n)","A",1
5,1,15,15,0.002103,"\int \frac{\log ^{-1+q}\left(c x^n\right)}{x} \, dx","Integrate[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",1
6,0,0,68,0.1364087,"\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","Integrate[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,"Integrate[Log[c*x^n]^(-1 + q)/(x*(a*x^m + b*Log[c*x^n]^q)), x]","A",-1
7,0,0,70,0.7973668,"\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","Integrate[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,"Integrate[Log[c*x^n]^(-1 + q)/(x*(a*x^m + b*Log[c*x^n]^q)^2), x]","A",-1
8,0,0,72,1.6293434,"\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","Integrate[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,"Integrate[Log[c*x^n]^(-1 + q)/(x*(a*x^m + b*Log[c*x^n]^q)^3), x]","A",-1
9,1,230,272,0.2313562,"\int \frac{\log \left(c x^n\right) \left(a x^m+b \log ^2\left(c x^n\right)\right)^3}{x} \, dx","Integrate[(Log[c*x^n]*(a*x^m + b*Log[c*x^n]^2)^3)/x,x]","\frac{a x^m \log \left(c x^n\right) \left(4 a^2 m^4 x^{2 m}+27 a b m^2 n^2 x^m+4320 b^2 n^4\right)}{12 m^5}-\frac{a n x^m \left(8 a^2 m^4 x^{2 m}+81 a b m^2 n^2 x^m+25920 b^2 n^4\right)}{72 m^6}-\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{9 a b n x^m \log ^2\left(c x^n\right) \left(a m^2 x^m+80 b n^2\right)}{4 m^4}+\frac{3 a b x^m \log ^3\left(c x^n\right) \left(a m^2 x^m+40 b n^2\right)}{2 m^3}+\frac{b^3 \log ^8\left(c x^n\right)}{8 n}","\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{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{360 a b^2 n^4 x^m \log \left(c x^n\right)}{m^5}-\frac{180 a b^2 n^3 x^m \log ^2\left(c x^n\right)}{m^4}+\frac{60 a b^2 n^2 x^m \log ^3\left(c x^n\right)}{m^3}-\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,"-1/72*(a*n*x^m*(25920*b^2*n^4 + 81*a*b*m^2*n^2*x^m + 8*a^2*m^4*x^(2*m)))/m^6 + (a*x^m*(4320*b^2*n^4 + 27*a*b*m^2*n^2*x^m + 4*a^2*m^4*x^(2*m))*Log[c*x^n])/(12*m^5) - (9*a*b*n*x^m*(80*b*n^2 + a*m^2*x^m)*Log[c*x^n]^2)/(4*m^4) + (3*a*b*x^m*(40*b*n^2 + a*m^2*x^m)*Log[c*x^n]^3)/(2*m^3) - (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",1
10,1,115,125,0.1091335,"\int \frac{\log \left(c x^n\right) \left(a x^m+b \log ^2\left(c x^n\right)\right)^2}{x} \, dx","Integrate[(Log[c*x^n]*(a*x^m + b*Log[c*x^n]^2)^2)/x,x]","-\frac{6 a b n x^m \log ^2\left(c x^n\right)}{m^2}+\frac{a x^m \log \left(c x^n\right) \left(a m^2 x^m+24 b n^2\right)}{2 m^3}+\frac{2 a b x^m \log ^3\left(c x^n\right)}{m}-\frac{a n x^m \left(a m^2 x^m+48 b n^2\right)}{4 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,"-1/4*(a*n*x^m*(48*b*n^2 + a*m^2*x^m))/m^4 + (a*x^m*(24*b*n^2 + a*m^2*x^m)*Log[c*x^n])/(2*m^3) - (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",1
11,1,41,41,0.0355156,"\int \frac{\log \left(c x^n\right) \left(a x^m+b \log ^2\left(c x^n\right)\right)}{x} \, dx","Integrate[(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",1
12,1,15,15,0.0009842,"\int \frac{\log \left(c x^n\right)}{x} \, dx","Integrate[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
13,0,0,67,1.4629667,"\int \frac{\log \left(c x^n\right)}{x \left(a x^m+b \log ^2\left(c x^n\right)\right)} \, dx","Integrate[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,"Integrate[Log[c*x^n]/(x*(a*x^m + b*Log[c*x^n]^2)), x]","A",-1
14,0,0,68,1.6053439,"\int \frac{\log \left(c x^n\right)}{x \left(a x^m+b \log ^2\left(c x^n\right)\right)^2} \, dx","Integrate[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,"Integrate[Log[c*x^n]/(x*(a*x^m + b*Log[c*x^n]^2)^2), x]","A",-1
15,0,0,68,3.0146316,"\int \frac{\log \left(c x^n\right)}{x \left(a x^m+b \log ^2\left(c x^n\right)\right)^3} \, dx","Integrate[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,"Integrate[Log[c*x^n]/(x*(a*x^m + b*Log[c*x^n]^2)^3), x]","A",-1
16,1,26,26,0.0941978,"\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","Integrate[((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
17,1,22,22,0.0390779,"\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","Integrate[((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
18,1,22,22,0.0327801,"\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","Integrate[((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
19,1,16,16,0.0167442,"\int \frac{a m x^m+b n q \log ^{-1+q}\left(c x^n\right)}{x} \, dx","Integrate[(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",1
20,1,17,17,0.2377073,"\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","Integrate[(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
21,1,20,20,0.040373,"\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","Integrate[(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
22,1,22,22,0.0411275,"\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","Integrate[(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*1/(a*x^m + b*Log[c*x^n]^q)^2","A",1
23,1,20,20,0.0175676,"\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","Integrate[(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",1
24,1,38,20,0.0045651,"\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","Integrate[(a/x + (2*b*n*Log[c*x^n])/x^2)*(a*x^2 + b*x*Log[c*x^n]^2),x]","\frac{a^2 x^2}{2}+a b x \log ^2\left(c x^n\right)+\frac{1}{2} b^2 \log ^4\left(c x^n\right)","\frac{1}{2} \left(a x+b \log ^2\left(c x^n\right)\right)^2",1,"(a^2*x^2)/2 + a*b*x*Log[c*x^n]^2 + (b^2*Log[c*x^n]^4)/2","A",1
25,1,14,14,0.002082,"\int \left(a+\frac{2 b n \log \left(c x^n\right)}{x}\right) \, dx","Integrate[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",1
26,1,15,15,0.0982637,"\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","Integrate[(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",1
27,1,18,18,0.0141414,"\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","Integrate[(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",1
28,1,20,20,0.0148729,"\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","Integrate[(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*1/(a*x + b*Log[c*x^n]^2)^2","A",1
29,1,23,19,0.4751889,"\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","Integrate[(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+b x \log ^q\left(c x^n\right)\right)-\log (x)","\log \left(a x^{m-1}+b \log ^q\left(c x^n\right)\right)",1,"-Log[x] + Log[a*x^m + b*x*Log[c*x^n]^q]","A",1
30,0,0,81,1.8960032,"\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","Integrate[((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,"Integrate[((d*x^m + e*Log[c*x^n]^(-1 + q))*(a*x^m + b*Log[c*x^n]^q)^p)/x, x]","A",-1
31,1,445,331,1.6225682,"\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","Integrate[((d*x^m + e*Log[c*x^n]^(-1 + q))*(a*x^m + b*Log[c*x^n]^q)^3)/x,x]","\frac{3^{-q} 4^{-q-1} \left(c x^n\right)^{-\frac{3 m}{n}} \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-3 q} \left(\left(-\frac{m \log \left(c x^n\right)}{n}\right)^q \left(-4 a^2 b e m 3^{q+1} q x^{2 m} \left(c x^n\right)^{m/n} \log ^{2 q}\left(c x^n\right) \Gamma \left(2 q,-\frac{2 m \log \left(c x^n\right)}{n}\right)+4^q \left(-\frac{m \log \left(c x^n\right)}{n}\right)^q \left(3^q \left(c x^n\right)^{\frac{3 m}{n}} \left(-\frac{m \log \left(c x^n\right)}{n}\right)^q \left(a^3 d n q x^{4 m}+b^3 e m \log ^{4 q}\left(c x^n\right)\right)-4 a^3 e m q x^{3 m} \log ^q\left(c x^n\right) \Gamma \left(q,-\frac{3 m \log \left(c x^n\right)}{n}\right)+4 a^2 b d n q x^{3 m} \log ^q\left(c x^n\right) \Gamma \left(q+1,-\frac{3 m \log \left(c x^n\right)}{n}\right)\right)+2 a b^2 d n 3^{q+1} q x^{2 m} \left(c x^n\right)^{m/n} \log ^{2 q}\left(c x^n\right) \Gamma \left(2 q+1,-\frac{2 m \log \left(c x^n\right)}{n}\right)\right)+a b^2 e m \left(-12^{q+1}\right) q x^m \left(c x^n\right)^{\frac{2 m}{n}} \log ^{3 q}\left(c x^n\right) \Gamma \left(3 q,-\frac{m \log \left(c x^n\right)}{n}\right)+b^3 d n 3^q 4^{q+1} q x^m \left(c x^n\right)^{\frac{2 m}{n}} \log ^{3 q}\left(c x^n\right) \Gamma \left(3 q+1,-\frac{m \log \left(c x^n\right)}{n}\right)\right)}{m n q}","-\frac{a^3 x^{4 m} (a e m-b d n q)}{4 b m 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) \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) \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) \Gamma \left(2 q+1,-\frac{2 m \log \left(c x^n\right)}{n}\right)}{m n q}+\frac{e \left(a x^m+b \log ^q\left(c x^n\right)\right)^4}{4 b n q}",1,"(4^(-1 - q)*(-(12^(1 + q)*a*b^2*e*m*q*x^m*(c*x^n)^((2*m)/n)*Gamma[3*q, -((m*Log[c*x^n])/n)]*Log[c*x^n]^(3*q)) + 3^q*4^(1 + q)*b^3*d*n*q*x^m*(c*x^n)^((2*m)/n)*Gamma[1 + 3*q, -((m*Log[c*x^n])/n)]*Log[c*x^n]^(3*q) + (-((m*Log[c*x^n])/n))^q*(-4*3^(1 + q)*a^2*b*e*m*q*x^(2*m)*(c*x^n)^(m/n)*Gamma[2*q, (-2*m*Log[c*x^n])/n]*Log[c*x^n]^(2*q) + 2*3^(1 + q)*a*b^2*d*n*q*x^(2*m)*(c*x^n)^(m/n)*Gamma[1 + 2*q, (-2*m*Log[c*x^n])/n]*Log[c*x^n]^(2*q) + 4^q*(-((m*Log[c*x^n])/n))^q*(-4*a^3*e*m*q*x^(3*m)*Gamma[q, (-3*m*Log[c*x^n])/n]*Log[c*x^n]^q + 4*a^2*b*d*n*q*x^(3*m)*Gamma[1 + q, (-3*m*Log[c*x^n])/n]*Log[c*x^n]^q + 3^q*(c*x^n)^((3*m)/n)*(-((m*Log[c*x^n])/n))^q*(a^3*d*n*q*x^(4*m) + b^3*e*m*Log[c*x^n]^(4*q))))))/(3^q*m*n*q*(c*x^n)^((3*m)/n)*(-((m*Log[c*x^n])/n))^(3*q))","A",1
32,1,298,235,0.9502488,"\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","Integrate[((d*x^m + e*Log[c*x^n]^(-1 + q))*(a*x^m + b*Log[c*x^n]^q)^2)/x,x]","\frac{2^{-q} \left(c x^n\right)^{-\frac{2 m}{n}} \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-2 q} \left(\left(-\frac{m \log \left(c x^n\right)}{n}\right)^q \left(2^q \left(c x^n\right)^{\frac{2 m}{n}} \left(-\frac{m \log \left(c x^n\right)}{n}\right)^q \left(a^2 d n q x^{3 m}+b^2 e m \log ^{3 q}\left(c x^n\right)\right)-3 a^2 e m q x^{2 m} \log ^q\left(c x^n\right) \Gamma \left(q,-\frac{2 m \log \left(c x^n\right)}{n}\right)+3 a b d n q x^{2 m} \log ^q\left(c x^n\right) \Gamma \left(q+1,-\frac{2 m \log \left(c x^n\right)}{n}\right)\right)-3 a b e m 2^{q+1} q x^m \left(c x^n\right)^{m/n} \log ^{2 q}\left(c x^n\right) \Gamma \left(2 q,-\frac{m \log \left(c x^n\right)}{n}\right)+3 b^2 d n 2^q q x^m \left(c x^n\right)^{m/n} \log ^{2 q}\left(c x^n\right) \Gamma \left(2 q+1,-\frac{m \log \left(c x^n\right)}{n}\right)\right)}{3 m n q}","-\frac{a^2 x^{3 m} (a e m-b d n q)}{3 b 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) \Gamma \left(q+1,-\frac{2 m \log \left(c x^n\right)}{n}\right)}{m 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) \Gamma \left(2 q+1,-\frac{m \log \left(c x^n\right)}{n}\right)}{m n q}+\frac{e \left(a x^m+b \log ^q\left(c x^n\right)\right)^3}{3 b n q}",1,"(-3*2^(1 + q)*a*b*e*m*q*x^m*(c*x^n)^(m/n)*Gamma[2*q, -((m*Log[c*x^n])/n)]*Log[c*x^n]^(2*q) + 3*2^q*b^2*d*n*q*x^m*(c*x^n)^(m/n)*Gamma[1 + 2*q, -((m*Log[c*x^n])/n)]*Log[c*x^n]^(2*q) + (-((m*Log[c*x^n])/n))^q*(-3*a^2*e*m*q*x^(2*m)*Gamma[q, (-2*m*Log[c*x^n])/n]*Log[c*x^n]^q + 3*a*b*d*n*q*x^(2*m)*Gamma[1 + q, (-2*m*Log[c*x^n])/n]*Log[c*x^n]^q + 2^q*(c*x^n)^((2*m)/n)*(-((m*Log[c*x^n])/n))^q*(a^2*d*n*q*x^(3*m) + b^2*e*m*Log[c*x^n]^(3*q))))/(3*2^q*m*n*q*(c*x^n)^((2*m)/n)*(-((m*Log[c*x^n])/n))^(2*q))","A",1
33,1,157,139,0.4937519,"\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","Integrate[((d*x^m + e*Log[c*x^n]^(-1 + q))*(a*x^m + b*Log[c*x^n]^q))/x,x]","\frac{\left(c x^n\right)^{-\frac{m}{n}} \left(-\frac{m \log \left(c x^n\right)}{n}\right)^{-q} \left(\left(c x^n\right)^{m/n} \left(-\frac{m \log \left(c x^n\right)}{n}\right)^q \left(a d n q x^{2 m}+b e m \log ^{2 q}\left(c x^n\right)\right)-2 a e m q x^m \log ^q\left(c x^n\right) \Gamma \left(q,-\frac{m \log \left(c x^n\right)}{n}\right)+2 b d n q x^m \log ^q\left(c x^n\right) \Gamma \left(q+1,-\frac{m \log \left(c x^n\right)}{n}\right)\right)}{2 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) \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,"(-2*a*e*m*q*x^m*Gamma[q, -((m*Log[c*x^n])/n)]*Log[c*x^n]^q + 2*b*d*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*(a*d*n*q*x^(2*m) + b*e*m*Log[c*x^n]^(2*q)))/(2*m*n*q*(c*x^n)^(m/n)*(-((m*Log[c*x^n])/n))^q)","A",1
34,1,25,25,0.0260546,"\int \frac{d x^m+e \log ^{-1+q}\left(c x^n\right)}{x} \, dx","Integrate[(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",1
35,0,0,73,5.107529,"\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","Integrate[(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,"Integrate[(d*x^m + e*Log[c*x^n]^(-1 + q))/(x*(a*x^m + b*Log[c*x^n]^q)), x]","A",-1
36,0,0,75,7.528298,"\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","Integrate[(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,"Integrate[(d*x^m + e*Log[c*x^n]^(-1 + q))/(x*(a*x^m + b*Log[c*x^n]^q)^2), x]","A",-1
37,0,0,77,71.2221384,"\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","Integrate[(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,"Integrate[(d*x^m + e*Log[c*x^n]^(-1 + q))/(x*(a*x^m + b*Log[c*x^n]^q)^3), x]","A",-1
38,1,26,26,0.366855,"\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","Integrate[(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
39,0,0,61,80.0347122,"\int \frac{n q-\log \left(c x^n\right)}{\left(a x+b \log ^q\left(c x^n\right)\right)^2} \, dx","Integrate[(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,"Integrate[(n*q - Log[c*x^n])/(a*x + b*Log[c*x^n]^q)^2, x]","A",-1
40,1,625,49,0.4839365,"\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","Integrate[Log[(2*x*(d*Sqrt[-(e/d)] + e*x))/(d + e*x^2)]/(d + e*x^2),x]","\frac{2 \text{Li}_2\left(\frac{\sqrt{e} x+\sqrt{-d}}{\sqrt{-d}+\frac{\sqrt{e}}{\sqrt{-\frac{e}{d}}}}\right)+2 \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right)-2 \text{Li}_2\left(\frac{d-\sqrt{-d} \sqrt{e} x}{2 d}\right)+2 \text{Li}_2\left(\frac{d+\sqrt{-d} \sqrt{e} x}{2 d}\right)-2 \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right)-2 \text{Li}_2\left(\frac{\sqrt{-d} \sqrt{e}-e x}{\sqrt{-\frac{e}{d}} d+\sqrt{-d} \sqrt{e}}\right)+2 \log \left(\frac{2 x \left(d \sqrt{-\frac{e}{d}}+e x\right)}{d+e x^2}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)-2 \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(\frac{2 x \left(d \sqrt{-\frac{e}{d}}+e x\right)}{d+e x^2}\right)+\log ^2\left(\sqrt{-d}-\sqrt{e} x\right)-\log ^2\left(\sqrt{-d}+\sqrt{e} x\right)-2 \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)+2 \log \left(\frac{d-\sqrt{-d} \sqrt{e} x}{2 d}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)-2 \log \left(\frac{d \sqrt{-\frac{e}{d}}+e x}{d \sqrt{-\frac{e}{d}}+\sqrt{-d} \sqrt{e}}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)+2 \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right) \log \left(\sqrt{-d}+\sqrt{e} x\right)-2 \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(\frac{\sqrt{-d} \sqrt{e} x+d}{2 d}\right)+2 \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(\frac{d x \left(-\frac{e}{d}\right)^{3/2}+e}{\sqrt{-d} \sqrt{e} \sqrt{-\frac{e}{d}}+e}\right)}{4 \sqrt{-d} \sqrt{e}}","-\frac{\sqrt{-\frac{e}{d}} \text{Li}_2\left(1-\frac{2 x \left(\sqrt{-\frac{e}{d}} d+e x\right)}{e x^2+d}\right)}{2 e}",1,"(-2*Log[(Sqrt[e]*x)/Sqrt[-d]]*Log[Sqrt[-d] - Sqrt[e]*x] + Log[Sqrt[-d] - Sqrt[e]*x]^2 + 2*Log[(d*Sqrt[e]*x)/(-d)^(3/2)]*Log[Sqrt[-d] + Sqrt[e]*x] - Log[Sqrt[-d] + Sqrt[e]*x]^2 + 2*Log[Sqrt[-d] - Sqrt[e]*x]*Log[(d - Sqrt[-d]*Sqrt[e]*x)/(2*d)] - 2*Log[Sqrt[-d] + Sqrt[e]*x]*Log[(d + Sqrt[-d]*Sqrt[e]*x)/(2*d)] - 2*Log[Sqrt[-d] - Sqrt[e]*x]*Log[(d*Sqrt[-(e/d)] + e*x)/(Sqrt[-d]*Sqrt[e] + d*Sqrt[-(e/d)])] + 2*Log[Sqrt[-d] + Sqrt[e]*x]*Log[(e + d*(-(e/d))^(3/2)*x)/(e + Sqrt[-d]*Sqrt[e]*Sqrt[-(e/d)])] + 2*Log[Sqrt[-d] - Sqrt[e]*x]*Log[(2*x*(d*Sqrt[-(e/d)] + e*x))/(d + e*x^2)] - 2*Log[Sqrt[-d] + Sqrt[e]*x]*Log[(2*x*(d*Sqrt[-(e/d)] + e*x))/(d + e*x^2)] + 2*PolyLog[2, (Sqrt[-d] + Sqrt[e]*x)/(Sqrt[-d] + Sqrt[e]/Sqrt[-(e/d)])] + 2*PolyLog[2, 1 + (Sqrt[e]*x)/Sqrt[-d]] - 2*PolyLog[2, (d - Sqrt[-d]*Sqrt[e]*x)/(2*d)] + 2*PolyLog[2, (d + Sqrt[-d]*Sqrt[e]*x)/(2*d)] - 2*PolyLog[2, 1 + (d*Sqrt[e]*x)/(-d)^(3/2)] - 2*PolyLog[2, (Sqrt[-d]*Sqrt[e] - e*x)/(Sqrt[-d]*Sqrt[e] + d*Sqrt[-(e/d)])])/(4*Sqrt[-d]*Sqrt[e])","B",0
41,1,642,50,0.3753503,"\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","Integrate[Log[(-2*x*(d*Sqrt[-(e/d)] - e*x))/(d + e*x^2)]/(d + e*x^2),x]","\frac{-2 \text{Li}_2\left(\frac{\sqrt{-\frac{e}{d}} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{e}+\sqrt{-d} \sqrt{-\frac{e}{d}}}\right)+2 \text{Li}_2\left(\frac{\sqrt{-\frac{e}{d}} \left(\sqrt{e} x+\sqrt{-d}\right)}{\sqrt{-d} \sqrt{-\frac{e}{d}}-\sqrt{e}}\right)+2 \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right)-2 \text{Li}_2\left(\frac{d-\sqrt{-d} \sqrt{e} x}{2 d}\right)+2 \text{Li}_2\left(\frac{d+\sqrt{-d} \sqrt{e} x}{2 d}\right)-2 \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right)+2 \log \left(\frac{2 e x \left(\frac{1}{\sqrt{-\frac{e}{d}}}+x\right)}{d+e x^2}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)-2 \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(\frac{2 e x \left(\frac{1}{\sqrt{-\frac{e}{d}}}+x\right)}{d+e x^2}\right)+\log ^2\left(\sqrt{-d}-\sqrt{e} x\right)-\log ^2\left(\sqrt{-d}+\sqrt{e} x\right)-2 \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)+2 \log \left(\frac{d-\sqrt{-d} \sqrt{e} x}{2 d}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)-2 \log \left(\frac{\sqrt{e} \left(x \sqrt{-\frac{e}{d}}+1\right)}{\sqrt{-d} \sqrt{-\frac{e}{d}}+\sqrt{e}}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)+2 \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right) \log \left(\sqrt{-d}+\sqrt{e} x\right)-2 \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(\frac{\sqrt{-d} \sqrt{e} x+d}{2 d}\right)+2 \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(\frac{\sqrt{e} \left(x \sqrt{-\frac{e}{d}}+1\right)}{\sqrt{e}-\sqrt{-d} \sqrt{-\frac{e}{d}}}\right)}{4 \sqrt{-d} \sqrt{e}}","\frac{\sqrt{-\frac{e}{d}} \text{Li}_2\left(\frac{2 x \left(d \sqrt{-\frac{e}{d}}-e x\right)}{e x^2+d}+1\right)}{2 e}",1,"(-2*Log[(Sqrt[e]*x)/Sqrt[-d]]*Log[Sqrt[-d] - Sqrt[e]*x] + Log[Sqrt[-d] - Sqrt[e]*x]^2 + 2*Log[(d*Sqrt[e]*x)/(-d)^(3/2)]*Log[Sqrt[-d] + Sqrt[e]*x] - Log[Sqrt[-d] + Sqrt[e]*x]^2 + 2*Log[Sqrt[-d] - Sqrt[e]*x]*Log[(d - Sqrt[-d]*Sqrt[e]*x)/(2*d)] - 2*Log[Sqrt[-d] + Sqrt[e]*x]*Log[(d + Sqrt[-d]*Sqrt[e]*x)/(2*d)] + 2*Log[Sqrt[-d] + Sqrt[e]*x]*Log[(Sqrt[e]*(1 + Sqrt[-(e/d)]*x))/(Sqrt[e] - Sqrt[-d]*Sqrt[-(e/d)])] - 2*Log[Sqrt[-d] - Sqrt[e]*x]*Log[(Sqrt[e]*(1 + Sqrt[-(e/d)]*x))/(Sqrt[e] + Sqrt[-d]*Sqrt[-(e/d)])] + 2*Log[Sqrt[-d] - Sqrt[e]*x]*Log[(2*e*x*(1/Sqrt[-(e/d)] + x))/(d + e*x^2)] - 2*Log[Sqrt[-d] + Sqrt[e]*x]*Log[(2*e*x*(1/Sqrt[-(e/d)] + x))/(d + e*x^2)] - 2*PolyLog[2, (Sqrt[-(e/d)]*(Sqrt[-d] - Sqrt[e]*x))/(Sqrt[e] + Sqrt[-d]*Sqrt[-(e/d)])] + 2*PolyLog[2, (Sqrt[-(e/d)]*(Sqrt[-d] + Sqrt[e]*x))/(-Sqrt[e] + Sqrt[-d]*Sqrt[-(e/d)])] + 2*PolyLog[2, 1 + (Sqrt[e]*x)/Sqrt[-d]] - 2*PolyLog[2, (d - Sqrt[-d]*Sqrt[e]*x)/(2*d)] + 2*PolyLog[2, (d + Sqrt[-d]*Sqrt[e]*x)/(2*d)] - 2*PolyLog[2, 1 + (d*Sqrt[e]*x)/(-d)^(3/2)])/(4*Sqrt[-d]*Sqrt[e])","B",1
42,1,320,53,0.2175864,"\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","Integrate[Log[(2*x*((d*Sqrt[e])/Sqrt[-d] + e*x))/(d + e*x^2)]/(d + e*x^2),x]","\frac{2 \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right)+2 \text{Li}_2\left(\frac{d+\sqrt{-d} \sqrt{e} x}{2 d}\right)-2 \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right)-2 \log \left(\frac{2 \left(e x^2-\sqrt{-d} \sqrt{e} x\right)}{d+e x^2}\right) \log \left(\sqrt{-d}+\sqrt{e} x\right)+2 \log \left(\sqrt{-d}-\sqrt{e} x\right) \log \left(\frac{2 \left(e x^2-\sqrt{-d} \sqrt{e} x\right)}{d+e x^2}\right)-\log ^2\left(\sqrt{-d}+\sqrt{e} x\right)+2 \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right) \log \left(\sqrt{-d}+\sqrt{e} x\right)-2 \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)+2 \log \left(\sqrt{-d}-\sqrt{e} x\right) \log \left(\frac{d-\sqrt{-d} \sqrt{e} x}{2 d}\right)}{4 \sqrt{-d} \sqrt{e}}","-\frac{\text{Li}_2\left(\frac{2 \sqrt{e} x \left(\sqrt{-d}-\sqrt{e} x\right)}{e x^2+d}+1\right)}{2 \sqrt{-d} \sqrt{e}}",1,"(-2*Log[(Sqrt[e]*x)/Sqrt[-d]]*Log[Sqrt[-d] - Sqrt[e]*x] + 2*Log[(d*Sqrt[e]*x)/(-d)^(3/2)]*Log[Sqrt[-d] + Sqrt[e]*x] - Log[Sqrt[-d] + Sqrt[e]*x]^2 + 2*Log[Sqrt[-d] - Sqrt[e]*x]*Log[(d - Sqrt[-d]*Sqrt[e]*x)/(2*d)] + 2*Log[Sqrt[-d] - Sqrt[e]*x]*Log[(2*(-(Sqrt[-d]*Sqrt[e]*x) + e*x^2))/(d + e*x^2)] - 2*Log[Sqrt[-d] + Sqrt[e]*x]*Log[(2*(-(Sqrt[-d]*Sqrt[e]*x) + e*x^2))/(d + e*x^2)] + 2*PolyLog[2, 1 + (Sqrt[e]*x)/Sqrt[-d]] + 2*PolyLog[2, (d + Sqrt[-d]*Sqrt[e]*x)/(2*d)] - 2*PolyLog[2, 1 + (d*Sqrt[e]*x)/(-d)^(3/2)])/(4*Sqrt[-d]*Sqrt[e])","B",1
43,1,316,52,0.1951272,"\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","Integrate[Log[(-2*x*((d*Sqrt[e])/Sqrt[-d] - e*x))/(d + e*x^2)]/(d + e*x^2),x]","\frac{2 \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right)-2 \text{Li}_2\left(\frac{d-\sqrt{-d} \sqrt{e} x}{2 d}\right)-2 \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right)+2 \log \left(\frac{2 \left(\sqrt{-d} \sqrt{e} x+e x^2\right)}{d+e x^2}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)-2 \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(\frac{2 \left(\sqrt{-d} \sqrt{e} x+e x^2\right)}{d+e x^2}\right)+\log ^2\left(\sqrt{-d}-\sqrt{e} x\right)-2 \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)+2 \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right) \log \left(\sqrt{-d}+\sqrt{e} x\right)-2 \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(\frac{\sqrt{-d} \sqrt{e} x+d}{2 d}\right)}{4 \sqrt{-d} \sqrt{e}}","\frac{\text{Li}_2\left(1-\frac{2 \sqrt{e} x \left(\sqrt{e} x+\sqrt{-d}\right)}{e x^2+d}\right)}{2 \sqrt{-d} \sqrt{e}}",1,"(-2*Log[(Sqrt[e]*x)/Sqrt[-d]]*Log[Sqrt[-d] - Sqrt[e]*x] + Log[Sqrt[-d] - Sqrt[e]*x]^2 + 2*Log[(d*Sqrt[e]*x)/(-d)^(3/2)]*Log[Sqrt[-d] + Sqrt[e]*x] - 2*Log[Sqrt[-d] + Sqrt[e]*x]*Log[(d + Sqrt[-d]*Sqrt[e]*x)/(2*d)] + 2*Log[Sqrt[-d] - Sqrt[e]*x]*Log[(2*(Sqrt[-d]*Sqrt[e]*x + e*x^2))/(d + e*x^2)] - 2*Log[Sqrt[-d] + Sqrt[e]*x]*Log[(2*(Sqrt[-d]*Sqrt[e]*x + e*x^2))/(d + e*x^2)] + 2*PolyLog[2, 1 + (Sqrt[e]*x)/Sqrt[-d]] - 2*PolyLog[2, (d - Sqrt[-d]*Sqrt[e]*x)/(2*d)] - 2*PolyLog[2, 1 + (d*Sqrt[e]*x)/(-d)^(3/2)])/(4*Sqrt[-d]*Sqrt[e])","B",1
44,1,641,49,0.3549037,"\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","Integrate[Log[(2*x*(Sqrt[d]*Sqrt[-e] + e*x))/(d + e*x^2)]/(d + e*x^2),x]","\frac{2 \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right)-2 \text{Li}_2\left(\frac{d-\sqrt{-d} \sqrt{e} x}{2 d}\right)+2 \text{Li}_2\left(\frac{d+\sqrt{-d} \sqrt{e} x}{2 d}\right)-2 \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right)-2 \text{Li}_2\left(\frac{\sqrt{-d} \sqrt{e}-e x}{\sqrt{d} \sqrt{-e}+\sqrt{-d} \sqrt{e}}\right)+2 \text{Li}_2\left(\frac{e x+\sqrt{-d} \sqrt{e}}{\sqrt{-d} \sqrt{e}-\sqrt{d} \sqrt{-e}}\right)+2 \log \left(\frac{2 x \left(\sqrt{d} \sqrt{-e}+e x\right)}{d+e x^2}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)-2 \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(\frac{2 x \left(\sqrt{d} \sqrt{-e}+e x\right)}{d+e x^2}\right)+\log ^2\left(\sqrt{-d}-\sqrt{e} x\right)-\log ^2\left(\sqrt{-d}+\sqrt{e} x\right)-2 \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)+2 \log \left(\frac{d-\sqrt{-d} \sqrt{e} x}{2 d}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)-2 \log \left(\frac{\sqrt{d} \sqrt{-e}+e x}{\sqrt{d} \sqrt{-e}+\sqrt{-d} \sqrt{e}}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)+2 \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right) \log \left(\sqrt{-d}+\sqrt{e} x\right)-2 \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(\frac{\sqrt{-d} \sqrt{e} x+d}{2 d}\right)+2 \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(\frac{\sqrt{d} \sqrt{-e}+e x}{\sqrt{d} \sqrt{-e}-\sqrt{-d} \sqrt{e}}\right)}{4 \sqrt{-d} \sqrt{e}}","\frac{\text{Li}_2\left(1-\frac{2 x \left(e x+\sqrt{d} \sqrt{-e}\right)}{e x^2+d}\right)}{2 \sqrt{d} \sqrt{-e}}",1,"(-2*Log[(Sqrt[e]*x)/Sqrt[-d]]*Log[Sqrt[-d] - Sqrt[e]*x] + Log[Sqrt[-d] - Sqrt[e]*x]^2 + 2*Log[(d*Sqrt[e]*x)/(-d)^(3/2)]*Log[Sqrt[-d] + Sqrt[e]*x] - Log[Sqrt[-d] + Sqrt[e]*x]^2 + 2*Log[Sqrt[-d] - Sqrt[e]*x]*Log[(d - Sqrt[-d]*Sqrt[e]*x)/(2*d)] - 2*Log[Sqrt[-d] + Sqrt[e]*x]*Log[(d + Sqrt[-d]*Sqrt[e]*x)/(2*d)] + 2*Log[Sqrt[-d] + Sqrt[e]*x]*Log[(Sqrt[d]*Sqrt[-e] + e*x)/(Sqrt[d]*Sqrt[-e] - Sqrt[-d]*Sqrt[e])] - 2*Log[Sqrt[-d] - Sqrt[e]*x]*Log[(Sqrt[d]*Sqrt[-e] + e*x)/(Sqrt[d]*Sqrt[-e] + Sqrt[-d]*Sqrt[e])] + 2*Log[Sqrt[-d] - Sqrt[e]*x]*Log[(2*x*(Sqrt[d]*Sqrt[-e] + e*x))/(d + e*x^2)] - 2*Log[Sqrt[-d] + Sqrt[e]*x]*Log[(2*x*(Sqrt[d]*Sqrt[-e] + e*x))/(d + e*x^2)] + 2*PolyLog[2, 1 + (Sqrt[e]*x)/Sqrt[-d]] - 2*PolyLog[2, (d - Sqrt[-d]*Sqrt[e]*x)/(2*d)] + 2*PolyLog[2, (d + Sqrt[-d]*Sqrt[e]*x)/(2*d)] - 2*PolyLog[2, 1 + (d*Sqrt[e]*x)/(-d)^(3/2)] - 2*PolyLog[2, (Sqrt[-d]*Sqrt[e] - e*x)/(Sqrt[d]*Sqrt[-e] + Sqrt[-d]*Sqrt[e])] + 2*PolyLog[2, (Sqrt[-d]*Sqrt[e] + e*x)/(-(Sqrt[d]*Sqrt[-e]) + Sqrt[-d]*Sqrt[e])])/(4*Sqrt[-d]*Sqrt[e])","B",1
45,1,645,50,0.2568044,"\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","Integrate[Log[(-2*x*(Sqrt[d]*Sqrt[-e] - e*x))/(d + e*x^2)]/(d + e*x^2),x]","\frac{2 \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right)-2 \text{Li}_2\left(\frac{d-\sqrt{-d} \sqrt{e} x}{2 d}\right)+2 \text{Li}_2\left(\frac{d+\sqrt{-d} \sqrt{e} x}{2 d}\right)-2 \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right)-2 \text{Li}_2\left(\frac{e x-\sqrt{-d} \sqrt{e}}{\sqrt{d} \sqrt{-e}-\sqrt{-d} \sqrt{e}}\right)+2 \text{Li}_2\left(\frac{e x+\sqrt{-d} \sqrt{e}}{\sqrt{d} \sqrt{-e}+\sqrt{-d} \sqrt{e}}\right)+2 \log \left(\frac{2 x \left(e x-\sqrt{d} \sqrt{-e}\right)}{d+e x^2}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)-2 \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(\frac{2 x \left(e x-\sqrt{d} \sqrt{-e}\right)}{d+e x^2}\right)+\log ^2\left(\sqrt{-d}-\sqrt{e} x\right)-\log ^2\left(\sqrt{-d}+\sqrt{e} x\right)-2 \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)+2 \log \left(\frac{d-\sqrt{-d} \sqrt{e} x}{2 d}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)-2 \log \left(\frac{\sqrt{d} \sqrt{-e}-e x}{\sqrt{d} \sqrt{-e}-\sqrt{-d} \sqrt{e}}\right) \log \left(\sqrt{-d}-\sqrt{e} x\right)+2 \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right) \log \left(\sqrt{-d}+\sqrt{e} x\right)-2 \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(\frac{\sqrt{-d} \sqrt{e} x+d}{2 d}\right)+2 \log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(\frac{\sqrt{d} \sqrt{-e}-e x}{\sqrt{d} \sqrt{-e}+\sqrt{-d} \sqrt{e}}\right)}{4 \sqrt{-d} \sqrt{e}}","-\frac{\text{Li}_2\left(\frac{2 x \left(\sqrt{d} \sqrt{-e}-e x\right)}{e x^2+d}+1\right)}{2 \sqrt{d} \sqrt{-e}}",1,"(-2*Log[(Sqrt[e]*x)/Sqrt[-d]]*Log[Sqrt[-d] - Sqrt[e]*x] + Log[Sqrt[-d] - Sqrt[e]*x]^2 + 2*Log[(d*Sqrt[e]*x)/(-d)^(3/2)]*Log[Sqrt[-d] + Sqrt[e]*x] - Log[Sqrt[-d] + Sqrt[e]*x]^2 + 2*Log[Sqrt[-d] - Sqrt[e]*x]*Log[(d - Sqrt[-d]*Sqrt[e]*x)/(2*d)] - 2*Log[Sqrt[-d] + Sqrt[e]*x]*Log[(d + Sqrt[-d]*Sqrt[e]*x)/(2*d)] - 2*Log[Sqrt[-d] - Sqrt[e]*x]*Log[(Sqrt[d]*Sqrt[-e] - e*x)/(Sqrt[d]*Sqrt[-e] - Sqrt[-d]*Sqrt[e])] + 2*Log[Sqrt[-d] + Sqrt[e]*x]*Log[(Sqrt[d]*Sqrt[-e] - e*x)/(Sqrt[d]*Sqrt[-e] + Sqrt[-d]*Sqrt[e])] + 2*Log[Sqrt[-d] - Sqrt[e]*x]*Log[(2*x*(-(Sqrt[d]*Sqrt[-e]) + e*x))/(d + e*x^2)] - 2*Log[Sqrt[-d] + Sqrt[e]*x]*Log[(2*x*(-(Sqrt[d]*Sqrt[-e]) + e*x))/(d + e*x^2)] + 2*PolyLog[2, 1 + (Sqrt[e]*x)/Sqrt[-d]] - 2*PolyLog[2, (d - Sqrt[-d]*Sqrt[e]*x)/(2*d)] + 2*PolyLog[2, (d + Sqrt[-d]*Sqrt[e]*x)/(2*d)] - 2*PolyLog[2, 1 + (d*Sqrt[e]*x)/(-d)^(3/2)] - 2*PolyLog[2, (-(Sqrt[-d]*Sqrt[e]) + e*x)/(Sqrt[d]*Sqrt[-e] - Sqrt[-d]*Sqrt[e])] + 2*PolyLog[2, (Sqrt[-d]*Sqrt[e] + e*x)/(Sqrt[d]*Sqrt[-e] + Sqrt[-d]*Sqrt[e])])/(4*Sqrt[-d]*Sqrt[e])","B",1
46,1,56,67,0.1372942,"\int (e x)^m \left(a+b \log \left(c \log ^p(d x)\right)\right) \, dx","Integrate[(e*x)^m*(a + b*Log[c*Log[d*x]^p]),x]","\frac{(d x)^{-m} (e x)^m \left(d x (d x)^m \left(a+b \log \left(c \log ^p(d x)\right)\right)-b p \text{Ei}((m+1) \log (d x))\right)}{d (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,"((e*x)^m*(-(b*p*ExpIntegralEi[(1 + m)*Log[d*x]]) + d*x*(d*x)^m*(a + b*Log[c*Log[d*x]^p])))/(d*(1 + m)*(d*x)^m)","A",1
47,1,59,79,0.168526,"\int (e x)^m \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)\right) \, dx","Integrate[(e*x)^m*(a + b*Log[c*Log[d*x^n]^p]),x]","\frac{x (e x)^m \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)-b p \left(d x^n\right)^{-\frac{m+1}{n}} \text{Ei}\left(\frac{(m+1) \log \left(d x^n\right)}{n}\right)\right)}{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,"(x*(e*x)^m*(a - (b*p*ExpIntegralEi[((1 + m)*Log[d*x^n])/n])/(d*x^n)^((1 + m)/n) + b*Log[c*Log[d*x^n]^p]))/(1 + m)","A",1
48,1,49,55,0.0624546,"\int x^2 \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)\right) \, dx","Integrate[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)-b p \left(d x^n\right)^{-3/n} \text{Ei}\left(\frac{3 \log \left(d x^n\right)}{n}\right)\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,"(x^3*(a - (b*p*ExpIntegralEi[(3*Log[d*x^n])/n])/(d*x^n)^(3/n) + b*Log[c*Log[d*x^n]^p]))/3","A",1
49,1,49,55,0.0589057,"\int x \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)\right) \, dx","Integrate[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)-b p \left(d x^n\right)^{-2/n} \text{Ei}\left(\frac{2 \log \left(d x^n\right)}{n}\right)\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,"(x^2*(a - (b*p*ExpIntegralEi[(2*Log[d*x^n])/n])/(d*x^n)^(2/n) + b*Log[c*Log[d*x^n]^p]))/2","A",1
50,1,43,45,0.0499048,"\int \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)\right) \, dx","Integrate[a + b*Log[c*Log[d*x^n]^p],x]","x \left(a+b \log \left(c \log ^p\left(d x^n\right)\right)-b p \left(d x^n\right)^{-1/n} \text{Ei}\left(\frac{\log \left(d x^n\right)}{n}\right)\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,"x*(a - (b*p*ExpIntegralEi[Log[d*x^n]/n])/(d*x^n)^n^(-1) + b*Log[c*Log[d*x^n]^p])","A",1
51,1,40,32,0.0122737,"\int \frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)}{x} \, dx","Integrate[(a + b*Log[c*Log[d*x^n]^p])/x,x]","a \log (x)+\frac{b \log \left(d x^n\right) \log \left(c \log ^p\left(d x^n\right)\right)}{n}-\frac{b p \log \left(d x^n\right)}{n}","\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,"a*Log[x] - (b*p*Log[d*x^n])/n + (b*Log[d*x^n]*Log[c*Log[d*x^n]^p])/n","A",1
52,1,45,48,0.0435293,"\int \frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)}{x^2} \, dx","Integrate[(a + b*Log[c*Log[d*x^n]^p])/x^2,x]","-\frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)-b p \left(d x^n\right)^{\frac{1}{n}} \text{Ei}\left(-\frac{\log \left(d x^n\right)}{n}\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,"-((a - b*p*(d*x^n)^n^(-1)*ExpIntegralEi[-(Log[d*x^n]/n)] + b*Log[c*Log[d*x^n]^p])/x)","A",1
53,1,49,55,0.0448448,"\int \frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)}{x^3} \, dx","Integrate[(a + b*Log[c*Log[d*x^n]^p])/x^3,x]","-\frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)-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{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,"-1/2*(a - b*p*(d*x^n)^(2/n)*ExpIntegralEi[(-2*Log[d*x^n])/n] + b*Log[c*Log[d*x^n]^p])/x^2","A",1
54,1,49,55,0.0467377,"\int \frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)}{x^4} \, dx","Integrate[(a + b*Log[c*Log[d*x^n]^p])/x^4,x]","-\frac{a+b \log \left(c \log ^p\left(d x^n\right)\right)-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{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,"-1/3*(a - b*p*(d*x^n)^(3/n)*ExpIntegralEi[(-3*Log[d*x^n])/n] + b*Log[c*Log[d*x^n]^p])/x^3","A",1
55,1,22,22,0.016031,"\int \log \left(c \log ^p(d x)\right) \, dx","Integrate[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",1
56,1,22,20,0.0068109,"\int \frac{\log \left(c \log ^p(d x)\right)}{x} \, dx","Integrate[Log[c*Log[d*x]^p]/x,x]","\log (d x) \log \left(c \log ^p(d x)\right)-p \log (d x)","\log (d x) \log \left(c \log ^p(d x)\right)-p \log (x)",1,"-(p*Log[d*x]) + Log[d*x]*Log[c*Log[d*x]^p]","A",1
57,1,39,40,0.0207993,"\int \log \left(c \log ^p\left(d x^n\right)\right) \, dx","Integrate[Log[c*Log[d*x^n]^p],x]","x \left(\log \left(c \log ^p\left(d x^n\right)\right)-p \left(d x^n\right)^{-1/n} \text{Ei}\left(\frac{\log \left(d x^n\right)}{n}\right)\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,"x*(-((p*ExpIntegralEi[Log[d*x^n]/n])/(d*x^n)^n^(-1)) + Log[c*Log[d*x^n]^p])","A",1
58,1,34,27,0.0104717,"\int \frac{\log \left(c \log ^p\left(d x^n\right)\right)}{x} \, dx","Integrate[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}-\frac{p \log \left(d x^n\right)}{n}","\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[d*x^n])/n) + (Log[d*x^n]*Log[c*Log[d*x^n]^p])/n","A",1
59,1,48,66,0.021499,"\int x^m \log \left(d \left(b x+c x^2\right)^n\right) \, dx","Integrate[x^m*Log[d*(b*x + c*x^2)^n],x]","\frac{x^{m+1} \left((m+1) \log \left(d (x (b+c x))^n\right)+n \, _2F_1\left(1,m+1;m+2;-\frac{c x}{b}\right)-2 n\right)}{(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,"(x^(1 + m)*(-2*n + n*Hypergeometric2F1[1, 1 + m, 2 + m, -((c*x)/b)] + (1 + m)*Log[d*(x*(b + c*x))^n]))/(1 + m)^2","A",1
60,1,85,99,0.0514359,"\int x^4 \log \left(d \left(b x+c x^2\right)^n\right) \, dx","Integrate[x^4*Log[d*(b*x + c*x^2)^n],x]","\frac{60 b^5 n \log (b+c x)+c n x \left(-60 b^4+30 b^3 c x-20 b^2 c^2 x^2+15 b c^3 x^3-24 c^4 x^4\right)+60 c^5 x^5 \log \left(d (x (b+c x))^n\right)}{300 c^5}","\frac{b^5 n \log (b+c x)}{5 c^5}-\frac{b^4 n x}{5 c^4}+\frac{b^3 n x^2}{10 c^3}-\frac{b^2 n x^3}{15 c^2}+\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,"(c*n*x*(-60*b^4 + 30*b^3*c*x - 20*b^2*c^2*x^2 + 15*b*c^3*x^3 - 24*c^4*x^4) + 60*b^5*n*Log[b + c*x] + 60*c^5*x^5*Log[d*(x*(b + c*x))^n])/(300*c^5)","A",1
61,1,74,85,0.037584,"\int x^3 \log \left(d \left(b x+c x^2\right)^n\right) \, dx","Integrate[x^3*Log[d*(b*x + c*x^2)^n],x]","\frac{-6 b^4 n \log (b+c x)+c n x \left(6 b^3-3 b^2 c x+2 b c^2 x^2-3 c^3 x^3\right)+6 c^4 x^4 \log \left(d (x (b+c x))^n\right)}{24 c^4}","-\frac{b^4 n \log (b+c x)}{4 c^4}+\frac{b^3 n x}{4 c^3}-\frac{b^2 n x^2}{8 c^2}+\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,"(c*n*x*(6*b^3 - 3*b^2*c*x + 2*b*c^2*x^2 - 3*c^3*x^3) - 6*b^4*n*Log[b + c*x] + 6*c^4*x^4*Log[d*(x*(b + c*x))^n])/(24*c^4)","A",1
62,1,63,71,0.0310024,"\int x^2 \log \left(d \left(b x+c x^2\right)^n\right) \, dx","Integrate[x^2*Log[d*(b*x + c*x^2)^n],x]","\frac{6 b^3 n \log (b+c x)+c n x \left(-6 b^2+3 b c x-4 c^2 x^2\right)+6 c^3 x^3 \log \left(d (x (b+c x))^n\right)}{18 c^3}","\frac{b^3 n \log (b+c x)}{3 c^3}-\frac{b^2 n x}{3 c^2}+\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,"(c*n*x*(-6*b^2 + 3*b*c*x - 4*c^2*x^2) + 6*b^3*n*Log[b + c*x] + 6*c^3*x^3*Log[d*(x*(b + c*x))^n])/(18*c^3)","A",1
63,1,49,57,0.0215433,"\int x \log \left(d \left(b x+c x^2\right)^n\right) \, dx","Integrate[x*Log[d*(b*x + c*x^2)^n],x]","\frac{1}{2} x^2 \log \left(d (x (b+c x))^n\right)-\frac{1}{2} n \left(\frac{b^2 \log (b+c x)}{c^2}-\frac{b x}{c}+x^2\right)","-\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,"-1/2*(n*(-((b*x)/c) + x^2 + (b^2*Log[b + c*x])/c^2)) + (x^2*Log[d*(x*(b + c*x))^n])/2","A",1
64,1,31,33,0.0078618,"\int \log \left(d \left(b x+c x^2\right)^n\right) \, dx","Integrate[Log[d*(b*x + c*x^2)^n],x]","x \log \left(d (x (b+c x))^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*(x*(b + c*x))^n]","A",1
65,1,50,53,0.0209598,"\int \frac{\log \left(d \left(b x+c x^2\right)^n\right)}{x} \, dx","Integrate[Log[d*(b*x + c*x^2)^n]/x,x]","\log (x) \log \left(d (x (b+c x))^n\right)-n \left(\text{Li}_2\left(-\frac{c x}{b}\right)+\log (x) \log \left(\frac{b+c x}{b}\right)+\frac{\log ^2(x)}{2}\right)","\log (x) \log \left(d \left(b x+c x^2\right)^n\right)-n \text{Li}_2\left(-\frac{c x}{b}\right)-n \log (x) \log \left(\frac{c x}{b}+1\right)-\frac{1}{2} n \log ^2(x)",1,"Log[x]*Log[d*(x*(b + c*x))^n] - n*(Log[x]^2/2 + Log[x]*Log[(b + c*x)/b] + PolyLog[2, -((c*x)/b)])","A",1
66,1,45,47,0.012318,"\int \frac{\log \left(d \left(b x+c x^2\right)^n\right)}{x^2} \, dx","Integrate[Log[d*(b*x + c*x^2)^n]/x^2,x]","-\frac{\log \left(d (x (b+c x))^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*(x*(b + c*x))^n]/x","A",1
67,1,65,72,0.0362039,"\int \frac{\log \left(d \left(b x+c x^2\right)^n\right)}{x^3} \, dx","Integrate[Log[d*(b*x + c*x^2)^n]/x^3,x]","\frac{1}{2} n \left(-\frac{c^2 \log (x)}{b^2}+\frac{c^2 \log (b+c x)}{b^2}-\frac{c}{b x}-\frac{1}{2 x^2}\right)-\frac{\log \left(d (x (b+c x))^n\right)}{2 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*(-1/2*1/x^2 - c/(b*x) - (c^2*Log[x])/b^2 + (c^2*Log[b + c*x])/b^2))/2 - Log[d*(x*(b + c*x))^n]/(2*x^2)","A",1
68,1,77,86,0.0362729,"\int \frac{\log \left(d \left(b x+c x^2\right)^n\right)}{x^4} \, dx","Integrate[Log[d*(b*x + c*x^2)^n]/x^4,x]","\frac{1}{3} n \left(\frac{c^3 \log (x)}{b^3}-\frac{c^3 \log (b+c x)}{b^3}+\frac{c^2}{b^2 x}-\frac{c}{2 b x^2}-\frac{1}{3 x^3}\right)-\frac{\log \left(d (x (b+c x))^n\right)}{3 x^3}","\frac{c^3 n \log (x)}{3 b^3}-\frac{c^3 n \log (b+c x)}{3 b^3}+\frac{c^2 n}{3 b^2 x}-\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*(-1/3*1/x^3 - c/(2*b*x^2) + c^2/(b^2*x) + (c^3*Log[x])/b^3 - (c^3*Log[b + c*x])/b^3))/3 - Log[d*(x*(b + c*x))^n]/(3*x^3)","A",1
69,1,87,100,0.0475461,"\int \frac{\log \left(d \left(b x+c x^2\right)^n\right)}{x^5} \, dx","Integrate[Log[d*(b*x + c*x^2)^n]/x^5,x]","-\frac{12 b^4 \log \left(d (x (b+c x))^n\right)+b n \left(3 b^3+4 b^2 c x-6 b c^2 x^2+12 c^3 x^3\right)-12 c^4 n x^4 \log (b+c x)+12 c^4 n x^4 \log (x)}{48 b^4 x^4}","-\frac{c^4 n \log (x)}{4 b^4}+\frac{c^4 n \log (b+c x)}{4 b^4}-\frac{c^3 n}{4 b^3 x}+\frac{c^2 n}{8 b^2 x^2}-\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,"-1/48*(b*n*(3*b^3 + 4*b^2*c*x - 6*b*c^2*x^2 + 12*c^3*x^3) + 12*c^4*n*x^4*Log[x] - 12*c^4*n*x^4*Log[b + c*x] + 12*b^4*Log[d*(x*(b + c*x))^n])/(b^4*x^4)","A",1
70,1,137,157,0.1944359,"\int x^m \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Integrate[x^m*Log[d*(a + b*x + c*x^2)^n],x]","-\frac{x^{m+1} \left(n x \left(\sqrt{b^2-4 a c}+b\right) \, _2F_1\left(1,m+2;m+3;\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)+n x \left(b-\sqrt{b^2-4 a c}\right) \, _2F_1\left(1,m+2;m+3;-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)-2 a (m+2) \log \left(d (a+x (b+c x))^n\right)\right)}{2 a \left(m^2+3 m+2\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(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,"-1/2*(x^(1 + m)*((b + Sqrt[b^2 - 4*a*c])*n*x*Hypergeometric2F1[1, 2 + m, 3 + m, (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])] + (b - Sqrt[b^2 - 4*a*c])*n*x*Hypergeometric2F1[1, 2 + m, 3 + m, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])] - 2*a*(2 + m)*Log[d*(a + x*(b + c*x))^n]))/(a*(2 + 3*m + m^2))","A",1
71,1,190,207,0.2195225,"\int x^4 \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Integrate[x^4*Log[d*(a + b*x + c*x^2)^n],x]","\frac{30 b n \left(5 a^2 c^2-5 a b^2 c+b^4\right) \log (a+x (b+c x))+60 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)+c n x \left(-8 c^2 \left(15 a^2-5 a c x^2+3 c^2 x^4\right)-20 b^2 c \left(c x^2-12 a\right)+15 b c^2 x \left(c x^2-6 a\right)-60 b^4+30 b^3 c x\right)+60 c^5 x^5 \log \left(d (a+x (b+c x))^n\right)}{300 c^5}","\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 \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 \left(2 a^2 c^2-4 a b^2 c+b^4\right)}{5 c^4}+\frac{b n x^2 \left(b^2-3 a c\right)}{10 c^3}-\frac{n x^3 \left(b^2-2 a c\right)}{15 c^2}+\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,"(c*n*x*(-60*b^4 + 30*b^3*c*x - 20*b^2*c*(-12*a + c*x^2) + 15*b*c^2*x*(-6*a + c*x^2) - 8*c^2*(15*a^2 - 5*a*c*x^2 + 3*c^2*x^4)) + 60*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]] + 30*b*(b^4 - 5*a*b^2*c + 5*a^2*c^2)*n*Log[a + x*(b + c*x)] + 60*c^5*x^5*Log[d*(a + x*(b + c*x))^n])/(300*c^5)","A",1
72,1,151,167,0.1644564,"\int x^3 \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Integrate[x^3*Log[d*(a + b*x + c*x^2)^n],x]","\frac{-3 n \left(2 a^2 c^2-4 a b^2 c+b^4\right) \log (a+x (b+c x))-6 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)+c n x \left(2 b c \left(c x^2-9 a\right)-3 c^2 x \left(c x^2-2 a\right)+6 b^3-3 b^2 c x\right)+6 c^4 x^4 \log \left(d (a+x (b+c x))^n\right)}{24 c^4}","-\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{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{b n x \left(b^2-3 a c\right)}{4 c^3}-\frac{n x^2 \left(b^2-2 a c\right)}{8 c^2}+\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,"(c*n*x*(6*b^3 - 3*b^2*c*x + 2*b*c*(-9*a + c*x^2) - 3*c^2*x*(-2*a + c*x^2)) - 6*b*Sqrt[b^2 - 4*a*c]*(b^2 - 2*a*c)*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]] - 3*(b^4 - 4*a*b^2*c + 2*a^2*c^2)*n*Log[a + x*(b + c*x)] + 6*c^4*x^4*Log[d*(a + x*(b + c*x))^n])/(24*c^4)","A",1
73,1,122,136,0.1404883,"\int x^2 \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Integrate[x^2*Log[d*(a + b*x + c*x^2)^n],x]","\frac{c n x \left(-4 c \left(c x^2-3 a\right)-6 b^2+3 b c x\right)+3 b n \left(b^2-3 a c\right) \log (a+x (b+c x))+6 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)+6 c^3 x^3 \log \left(d (a+x (b+c x))^n\right)}{18 c^3}","\frac{b n \left(b^2-3 a c\right) \log \left(a+b x+c x^2\right)}{6 c^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 c^3}-\frac{n x \left(b^2-2 a c\right)}{3 c^2}+\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,"(c*n*x*(-6*b^2 + 3*b*c*x - 4*c*(-3*a + c*x^2)) + 6*Sqrt[b^2 - 4*a*c]*(b^2 - a*c)*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]] + 3*b*(b^2 - 3*a*c)*n*Log[a + x*(b + c*x)] + 6*c^3*x^3*Log[d*(a + x*(b + c*x))^n])/(18*c^3)","A",1
74,1,94,109,0.0964254,"\int x \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Integrate[x*Log[d*(a + b*x + c*x^2)^n],x]","-\frac{n \left(b^2-2 a c\right) \log (a+x (b+c x))+2 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 x \left(c x \log \left(d (a+x (b+c x))^n\right)+n (b-c x)\right)}{4 c^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,"-1/4*(2*b*Sqrt[b^2 - 4*a*c]*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]] + (b^2 - 2*a*c)*n*Log[a + x*(b + c*x)] - 2*c*x*(n*(b - c*x) + c*x*Log[d*(a + x*(b + c*x))^n]))/c^2","A",1
75,1,78,79,0.0627091,"\int \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Integrate[Log[d*(a + b*x + c*x^2)^n],x]","\frac{2 n \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)+2 c x \left(\log \left(d (a+x (b+c x))^n\right)-2 n\right)+b n \log (a+x (b+c x))}{2 c}","\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*Sqrt[b^2 - 4*a*c]*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]] + b*n*Log[a + x*(b + c*x)] + 2*c*x*(-2*n + Log[d*(a + x*(b + c*x))^n]))/(2*c)","A",1
76,1,156,129,0.2064828,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{x} \, dx","Integrate[Log[d*(a + b*x + c*x^2)^n]/x,x]","-n \text{Li}_2\left(-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)-n \text{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)-n \log (x) \log \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}\right)-n \log (x) \log \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}\right)+\log (x) \log \left(d (a+x (b+c x))^n\right)","-n \text{Li}_2\left(-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)-n \text{Li}_2\left(-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\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[(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c])]) - n*Log[x]*Log[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c])] + Log[x]*Log[d*(a + x*(b + c*x))^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",1
77,1,87,86,0.1176633,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{x^2} \, dx","Integrate[Log[d*(a + b*x + c*x^2)^n]/x^2,x]","\frac{2 n \sqrt{4 a c-b^2} \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)-\frac{2 a \log \left(d (a+x (b+c x))^n\right)}{x}-b n \log (a+x (b+c x))+2 b n \log (x)}{2 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,"(2*Sqrt[-b^2 + 4*a*c]*n*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]] + 2*b*n*Log[x] - b*n*Log[a + x*(b + c*x)] - (2*a*Log[d*(a + x*(b + c*x))^n])/x)/(2*a)","A",1
78,1,105,121,0.2446593,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{x^3} \, dx","Integrate[Log[d*(a + b*x + c*x^2)^n]/x^3,x]","-\frac{\frac{n x \left(2 x \log (x) \left(b^2-2 a c\right)-x \left(b^2-2 a c\right) \log (a+x (b+c x))+2 b x \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)+2 a b\right)}{a^2}+2 \log \left(d (a+x (b+c x))^n\right)}{4 x^2}","\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,"-1/4*((n*x*(2*a*b + 2*b*Sqrt[b^2 - 4*a*c]*x*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]] + 2*(b^2 - 2*a*c)*x*Log[x] - (b^2 - 2*a*c)*x*Log[a + x*(b + c*x)]))/a^2 + 2*Log[d*(a + x*(b + c*x))^n])/x^2","A",1
79,1,132,149,0.3708791,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{x^4} \, dx","Integrate[Log[d*(a + b*x + c*x^2)^n]/x^4,x]","-\frac{\frac{n x \left(a^2 b-2 b x^2 \log (x) \left(b^2-3 a c\right)+b x^2 \left(b^2-3 a c\right) \log (a+x (b+c x))-2 x^2 \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)-2 a x \left(b^2-2 a c\right)\right)}{a^3}+2 \log \left(d (a+x (b+c x))^n\right)}{6 x^3}","-\frac{b n \left(b^2-3 a c\right) \log \left(a+b x+c x^2\right)}{6 a^3}+\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{n \left(b^2-2 a c\right)}{3 a^2 x}-\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,"-1/6*((n*x*(a^2*b - 2*a*(b^2 - 2*a*c)*x - 2*Sqrt[b^2 - 4*a*c]*(b^2 - a*c)*x^2*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]] - 2*b*(b^2 - 3*a*c)*x^2*Log[x] + b*(b^2 - 3*a*c)*x^2*Log[a + x*(b + c*x)]))/a^3 + 2*Log[d*(a + x*(b + c*x))^n])/x^3","A",1
80,1,172,190,0.4627679,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{x^5} \, dx","Integrate[Log[d*(a + b*x + c*x^2)^n]/x^5,x]","-\frac{\frac{n x \left(2 a^3 b-3 a^2 x \left(b^2-2 a c\right)+6 x^3 \log (x) \left(2 a^2 c^2-4 a b^2 c+b^4\right)-3 x^3 \left(2 a^2 c^2-4 a b^2 c+b^4\right) \log (a+x (b+c x))+6 b x^3 \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)+6 a b x^2 \left(b^2-3 a c\right)\right)}{a^4}+6 \log \left(d (a+x (b+c x))^n\right)}{24 x^4}","-\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{b n \left(b^2-3 a c\right)}{4 a^3 x}+\frac{n \left(b^2-2 a c\right)}{8 a^2 x^2}+\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{\log \left(d \left(a+b x+c x^2\right)^n\right)}{4 x^4}-\frac{b n}{12 a x^3}",1,"-1/24*((n*x*(2*a^3*b - 3*a^2*(b^2 - 2*a*c)*x + 6*a*b*(b^2 - 3*a*c)*x^2 + 6*b*Sqrt[b^2 - 4*a*c]*(b^2 - 2*a*c)*x^3*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]] + 6*(b^4 - 4*a*b^2*c + 2*a^2*c^2)*x^3*Log[x] - 3*(b^4 - 4*a*b^2*c + 2*a^2*c^2)*x^3*Log[a + x*(b + c*x)]))/a^4 + 6*Log[d*(a + x*(b + c*x))^n])/x^4","A",1
81,1,35,42,0.0140638,"\int \log \left(1+x+x^2\right) \, dx","Integrate[Log[1 + x + x^2],x]","\left(x+\frac{1}{2}\right) \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]] + (1/2 + x)*Log[1 + x + x^2]","A",1
82,1,468,485,1.9659929,"\int (d+e x)^4 \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Integrate[(d + e*x)^4*Log[d*(a + b*x + c*x^2)^n],x]","\frac{(d+e x)^5 \log \left(d (a+x (b+c x))^n\right)-\frac{n \left(60 c e 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)+30 (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 (a+x (b+c x))-60 e \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)+30 c^2 e^2 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)+20 c^3 e^3 x^3 \left(-c e (2 a e+5 b d)+b^2 e^2+20 c^2 d^2\right)+15 c^4 e^4 x^4 (10 c d-b e)+24 c^5 e^5 x^5\right)}{60 c^5}}{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 (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 \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 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{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{(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,"(-1/60*(n*(60*c*e*(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))*x + 30*c^2*e^2*(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))*x^2 + 20*c^3*e^3*(20*c^2*d^2 + b^2*e^2 - c*e*(5*b*d + 2*a*e))*x^3 + 15*c^4*e^4*(10*c*d - b*e)*x^4 + 24*c^5*e^5*x^5 - 60*Sqrt[b^2 - 4*a*c]*e*(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))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]] + 30*(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))*Log[a + x*(b + c*x)]))/c^5 + (d + e*x)^5*Log[d*(a + x*(b + c*x))^n])/(5*e)","A",1
83,1,324,338,0.5336237,"\int (d+e x)^3 \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Integrate[(d + e*x)^3*Log[d*(a + b*x + c*x^2)^n],x]","\frac{(d+e x)^4 \log \left(d (a+x (b+c x))^n\right)-\frac{n \left(3 \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 (a+x (b+c x))+6 c e 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)+3 c^2 e^2 x^2 \left(-2 c e (a e+2 b d)+b^2 e^2+12 c^2 d^2\right)-6 e \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)+2 c^3 e^3 x^3 (8 c d-b e)+3 c^4 e^4 x^4\right)}{6 c^4}}{4 e}","-\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{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{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 \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,"(-1/6*(n*(6*c*e*(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))*x + 3*c^2*e^2*(12*c^2*d^2 + b^2*e^2 - 2*c*e*(2*b*d + a*e))*x^2 + 2*c^3*e^3*(8*c*d - b*e)*x^3 + 3*c^4*e^4*x^4 - 6*Sqrt[b^2 - 4*a*c]*e*(2*c*d - b*e)*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]] + 3*(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))*Log[a + x*(b + c*x)]))/c^4 + (d + e*x)^4*Log[d*(a + x*(b + c*x))^n])/(4*e)","A",1
84,1,204,226,0.4457104,"\int (d+e x)^2 \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Integrate[(d + e*x)^2*Log[d*(a + b*x + c*x^2)^n],x]","\frac{(d+e x)^3 \log \left(d (a+x (b+c x))^n\right)-\frac{n \left(c e x \left(-3 c e (4 a e+6 b d+b e x)+6 b^2 e^2+2 c^2 \left(18 d^2+9 d e x+2 e^2 x^2\right)\right)+3 (2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \log (a+x (b+c x))-6 e \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)\right)}{6 c^3}}{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 (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 \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,"(-1/6*(n*(c*e*x*(6*b^2*e^2 - 3*c*e*(6*b*d + 4*a*e + b*e*x) + 2*c^2*(18*d^2 + 9*d*e*x + 2*e^2*x^2)) - 6*Sqrt[b^2 - 4*a*c]*e*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]] + 3*(2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Log[a + x*(b + c*x)]))/c^3 + (d + e*x)^3*Log[d*(a + x*(b + c*x))^n])/(3*e)","A",1
85,1,123,154,0.2116171,"\int (d+e x) \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Integrate[(d + e*x)*Log[d*(a + b*x + c*x^2)^n],x]","\frac{n \left(2 a c e+b^2 (-e)+2 b c d\right) \log (a+x (b+c x))-2 n \sqrt{b^2-4 a c} (b e-2 c d) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)+2 c x \left(c (2 d+e x) \log \left(d (a+x (b+c x))^n\right)+b e n-c n (4 d+e x)\right)}{4 c^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,"(-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*b*c*d - b^2*e + 2*a*c*e)*n*Log[a + x*(b + c*x)] + 2*c*x*(b*e*n - c*n*(4*d + e*x) + c*(2*d + e*x)*Log[d*(a + x*(b + c*x))^n]))/(4*c^2)","A",1
86,1,78,79,0.0615107,"\int \log \left(d \left(a+b x+c x^2\right)^n\right) \, dx","Integrate[Log[d*(a + b*x + c*x^2)^n],x]","\frac{2 n \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)+2 c x \left(\log \left(d (a+x (b+c x))^n\right)-2 n\right)+b n \log (a+x (b+c x))}{2 c}","\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*Sqrt[b^2 - 4*a*c]*n*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]] + b*n*Log[a + x*(b + c*x)] + 2*c*x*(-2*n + Log[d*(a + x*(b + c*x))^n]))/(2*c)","A",1
87,1,226,228,0.2959877,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{d+e x} \, dx","Integrate[Log[d*(a + b*x + c*x^2)^n]/(d + e*x),x]","-\frac{n \text{Li}_2\left(\frac{2 c (d+e x)}{2 c d-b e+\sqrt{b^2-4 a c} e}\right)}{e}-\frac{n \text{Li}_2\left(\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\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 (a+x (b+c x))^n\right)}{e}","-\frac{n \text{Li}_2\left(\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{e}-\frac{n \text{Li}_2\left(\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\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 + x*(b + c*x))^n])/e - (n*PolyLog[2, (2*c*(d + e*x))/(2*c*d - b*e + 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",1
88,1,166,165,0.3156763,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{(d+e x)^2} \, dx","Integrate[Log[d*(a + b*x + c*x^2)^n]/(d + e*x)^2,x]","-\frac{n \sqrt{4 a c-b^2} \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{e (b d-a e)-c d^2}+\frac{n (b e-2 c d) \log (d+e x)}{e \left(e (a e-b d)+c d^2\right)}-\frac{n (b e-2 c d) \log (a+x (b+c x))}{2 e \left(e (a e-b d)+c d^2\right)}-\frac{\log \left(d (a+x (b+c x))^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*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-(c*d^2) + e*(b*d - a*e))) + ((-2*c*d + b*e)*n*Log[d + e*x])/(e*(c*d^2 + e*(-(b*d) + a*e))) - ((-2*c*d + b*e)*n*Log[a + x*(b + c*x)])/(2*e*(c*d^2 + e*(-(b*d) + a*e))) - Log[d*(a + x*(b + c*x))^n]/(e*(d + e*x))","A",1
89,1,215,259,0.556844,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{(d+e x)^3} \, dx","Integrate[Log[d*(a + b*x + c*x^2)^n]/(d + e*x)^3,x]","\frac{\frac{n (d+e x) \left(-2 (d+e x) \log (d+e x) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right)+(d+e x) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \log (a+x (b+c x))-2 e \sqrt{b^2-4 a c} (d+e x) (b e-2 c d) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)+2 (2 c d-b e) \left(e (a e-b d)+c d^2\right)\right)}{\left(e (a e-b d)+c d^2\right)^2}-2 \log \left(d (a+x (b+c x))^n\right)}{4 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,"((n*(d + e*x)*(2*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e)) - 2*Sqrt[b^2 - 4*a*c]*e*(-2*c*d + b*e)*(d + e*x)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]] - 2*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*(d + e*x)*Log[d + e*x] + (2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*(d + e*x)*Log[a + x*(b + c*x)]))/(c*d^2 + e*(-(b*d) + a*e))^2 - 2*Log[d*(a + x*(b + c*x))^n])/(4*e*(d + e*x)^2)","A",1
90,1,310,356,1.2079304,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{(d+e x)^4} \, dx","Integrate[Log[d*(a + b*x + c*x^2)^n]/(d + e*x)^4,x]","\frac{\frac{n (d+e x) \left(2 (d+e x) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \left(e (a e-b d)+c d^2\right)-2 (d+e x)^2 (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)+(d+e x)^2 (2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \log (a+x (b+c x))+2 e \sqrt{b^2-4 a c} (d+e x)^2 \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)+(2 c d-b e) \left(e (a e-b d)+c d^2\right)^2\right)}{\left(e (a e-b d)+c d^2\right)^3}-2 \log \left(d (a+x (b+c x))^n\right)}{6 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,"((n*(d + e*x)*((2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))^2 + 2*(c*d^2 + e*(-(b*d) + a*e))*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*(d + e*x) + 2*Sqrt[b^2 - 4*a*c]*e*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e))*(d + e*x)^2*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]] - 2*(2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*(d + e*x)^2*Log[d + e*x] + (2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*(d + e*x)^2*Log[a + x*(b + c*x)]))/(c*d^2 + e*(-(b*d) + a*e))^3 - 2*Log[d*(a + x*(b + c*x))^n])/(6*e*(d + e*x)^3)","A",1
91,1,469,519,2.0261375,"\int \frac{\log \left(d \left(a+b x+c x^2\right)^n\right)}{(d+e x)^5} \, dx","Integrate[Log[d*(a + b*x + c*x^2)^n]/(d + e*x)^5,x]","\frac{\frac{n (d+e x) \left(-6 (d+e x)^3 \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)+3 (d+e x)^3 \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 (a+x (b+c x))+3 (d+e x) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \left(e (a e-b d)+c d^2\right)^2+6 (d+e x)^2 (2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \left(e (a e-b d)+c d^2\right)+6 e \sqrt{b^2-4 a c} (d+e x)^3 (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)+2 (2 c d-b e) \left(e (a e-b d)+c d^2\right)^3\right)}{\left(e (a e-b d)+c d^2\right)^4}-6 \log \left(d (a+x (b+c x))^n\right)}{24 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,"((n*(d + e*x)*(2*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))^3 + 3*(c*d^2 + e*(-(b*d) + a*e))^2*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*(d + e*x) + 6*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*(d + e*x)^2 + 6*Sqrt[b^2 - 4*a*c]*e*(2*c*d - b*e)*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*(d + e*x)^3*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]] - 6*(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))*(d + e*x)^3*Log[d + e*x] + 3*(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))*(d + e*x)^3*Log[a + x*(b + c*x)]))/(c*d^2 + e*(-(b*d) + a*e))^4 - 6*Log[d*(a + x*(b + c*x))^n])/(24*e*(d + e*x)^4)","A",1
92,1,131,175,0.0506527,"\int \frac{\log \left(d \left(a+c x^2\right)^n\right)}{a e+c e x^2} \, dx","Integrate[Log[d*(a + c*x^2)^n]/(a*e + c*e*x^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(\log \left(d \left(a+c x^2\right)^n\right)+2 n \log \left(\frac{2 i}{-\frac{\sqrt{c} x}{\sqrt{a}}+i}\right)+i n \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)\right)+i n \text{Li}_2\left(\frac{\sqrt{c} x+i \sqrt{a}}{\sqrt{c} x-i \sqrt{a}}\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 \text{Li}_2\left(1-\frac{2 \sqrt{a}}{i \sqrt{c} x+\sqrt{a}}\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,"(ArcTan[(Sqrt[c]*x)/Sqrt[a]]*(I*n*ArcTan[(Sqrt[c]*x)/Sqrt[a]] + 2*n*Log[(2*I)/(I - (Sqrt[c]*x)/Sqrt[a])] + Log[d*(a + c*x^2)^n]) + I*n*PolyLog[2, (I*Sqrt[a] + Sqrt[c]*x)/((-I)*Sqrt[a] + Sqrt[c]*x)])/(Sqrt[a]*Sqrt[c]*e)","A",1
93,1,339,258,0.1866285,"\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","Integrate[Log[d*(a + b*x + c*x^2)^n]/(a*e + b*e*x + c*e*x^2),x]","\frac{2 \log \left(-\sqrt{b^2-4 a c}+b+2 c x\right) \log \left(d (a+x (b+c x))^n\right)-2 \log \left(\sqrt{b^2-4 a c}+b+2 c x\right) \log \left(d (a+x (b+c x))^n\right)-2 n \text{Li}_2\left(\frac{-b-2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)+2 n \text{Li}_2\left(\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)-n \log ^2\left(-\sqrt{b^2-4 a c}+b+2 c x\right)+n \log ^2\left(\sqrt{b^2-4 a c}+b+2 c x\right)-2 n \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)+2 n \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)}{2 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 \text{Li}_2\left(-\frac{\frac{b}{\sqrt{b^2-4 a c}}+\frac{2 c x}{\sqrt{b^2-4 a c}}+1}{-\frac{b}{\sqrt{b^2-4 a c}}-\frac{2 c x}{\sqrt{b^2-4 a c}}+1}\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,"(-(n*Log[b - Sqrt[b^2 - 4*a*c] + 2*c*x]^2) + 2*n*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] + n*Log[b + Sqrt[b^2 - 4*a*c] + 2*c*x]^2 - 2*n*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])] + 2*Log[b - Sqrt[b^2 - 4*a*c] + 2*c*x]*Log[d*(a + x*(b + c*x))^n] - 2*Log[b + Sqrt[b^2 - 4*a*c] + 2*c*x]*Log[d*(a + x*(b + c*x))^n] - 2*n*PolyLog[2, (-b + Sqrt[b^2 - 4*a*c] - 2*c*x)/(2*Sqrt[b^2 - 4*a*c])] + 2*n*PolyLog[2, (b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/(2*Sqrt[b^2 - 4*a*c]*e)","A",1
94,1,626,762,1.0047459,"\int \frac{\log \left(g \left(a+b x+c x^2\right)^n\right)}{d+e x^2} \, dx","Integrate[Log[g*(a + b*x + c*x^2)^n]/(d + e*x^2),x]","\frac{-n \text{Li}_2\left(\frac{2 c \left(\sqrt{-d}-\sqrt{e} x\right)}{2 \sqrt{-d} c+\left(b-\sqrt{b^2-4 a c}\right) \sqrt{e}}\right)-n \text{Li}_2\left(\frac{2 c \left(\sqrt{-d}-\sqrt{e} x\right)}{2 \sqrt{-d} c+\left(b+\sqrt{b^2-4 a c}\right) \sqrt{e}}\right)+n \text{Li}_2\left(\frac{2 c \left(\sqrt{e} x+\sqrt{-d}\right)}{2 \sqrt{-d} c+\left(\sqrt{b^2-4 a c}-b\right) \sqrt{e}}\right)+n \text{Li}_2\left(\frac{2 c \left(\sqrt{e} x+\sqrt{-d}\right)}{2 c \sqrt{-d}-\left(b+\sqrt{b^2-4 a c}\right) \sqrt{e}}\right)-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)-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)+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)+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)+\log \left(\sqrt{-d}-\sqrt{e} x\right) \log \left(g (a+x (b+c x))^n\right)-\log \left(\sqrt{-d}+\sqrt{e} x\right) \log \left(g (a+x (b+c x))^n\right)}{2 \sqrt{-d} \sqrt{e}}","-\frac{n \text{Li}_2\left(\frac{2 c \left(\sqrt{-d}-\sqrt{e} x\right)}{2 \sqrt{-d} c+\left(b-\sqrt{b^2-4 a c}\right) \sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{n \text{Li}_2\left(\frac{2 c \left(\sqrt{-d}-\sqrt{e} x\right)}{2 \sqrt{-d} c+\left(b+\sqrt{b^2-4 a c}\right) \sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{n \text{Li}_2\left(\frac{2 c \left(\sqrt{e} x+\sqrt{-d}\right)}{2 c \sqrt{-d}-\left(b-\sqrt{b^2-4 a c}\right) \sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{n \text{Li}_2\left(\frac{2 c \left(\sqrt{e} x+\sqrt{-d}\right)}{2 c \sqrt{-d}-\left(b+\sqrt{b^2-4 a c}\right) \sqrt{e}}\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]) - 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] + 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] + 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] + Log[Sqrt[-d] - Sqrt[e]*x]*Log[g*(a + x*(b + c*x))^n] - Log[Sqrt[-d] + Sqrt[e]*x]*Log[g*(a + x*(b + c*x))^n] - n*PolyLog[2, (2*c*(Sqrt[-d] - Sqrt[e]*x))/(2*c*Sqrt[-d] + (b - Sqrt[b^2 - 4*a*c])*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])] + n*PolyLog[2, (2*c*(Sqrt[-d] + Sqrt[e]*x))/(2*c*Sqrt[-d] + (-b + Sqrt[b^2 - 4*a*c])*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",1
95,1,663,782,0.8508683,"\int \frac{\log \left(g \left(a+b x+c x^2\right)^n\right)}{d+e x+f x^2} \, dx","Integrate[Log[g*(a + b*x + c*x^2)^n]/(d + e*x + f*x^2),x]","\frac{-n \text{Li}_2\left(\frac{c \left(-e-2 f x+\sqrt{e^2-4 d f}\right)}{\left(b-\sqrt{b^2-4 a c}\right) f+c \left(\sqrt{e^2-4 d f}-e\right)}\right)-n \text{Li}_2\left(\frac{c \left(-e-2 f x+\sqrt{e^2-4 d f}\right)}{\left(b+\sqrt{b^2-4 a c}\right) f+c \left(\sqrt{e^2-4 d f}-e\right)}\right)+n \text{Li}_2\left(\frac{c \left(e+2 f x+\sqrt{e^2-4 d f}\right)}{\left(\sqrt{b^2-4 a c}-b\right) f+c \left(e+\sqrt{e^2-4 d f}\right)}\right)+n \text{Li}_2\left(\frac{c \left(e+2 f x+\sqrt{e^2-4 d f}\right)}{c \left(e+\sqrt{e^2-4 d f}\right)-\left(b+\sqrt{b^2-4 a c}\right) f}\right)-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)-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)+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)+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)+\log \left(-\sqrt{e^2-4 d f}+e+2 f x\right) \log \left(g (a+x (b+c x))^n\right)-\log \left(\sqrt{e^2-4 d f}+e+2 f x\right) \log \left(g (a+x (b+c x))^n\right)}{\sqrt{e^2-4 d f}}","-\frac{n \text{Li}_2\left(-\frac{c \left(e+2 f x-\sqrt{e^2-4 d f}\right)}{\left(b-\sqrt{b^2-4 a c}\right) f-c \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}-\frac{n \text{Li}_2\left(-\frac{c \left(e+2 f x-\sqrt{e^2-4 d f}\right)}{\left(b+\sqrt{b^2-4 a c}\right) f-c \left(e-\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{n \text{Li}_2\left(-\frac{c \left(e+2 f x+\sqrt{e^2-4 d f}\right)}{\left(b-\sqrt{b^2-4 a c}\right) f-c \left(e+\sqrt{e^2-4 d f}\right)}\right)}{\sqrt{e^2-4 d f}}+\frac{n \text{Li}_2\left(-\frac{c \left(e+2 f x+\sqrt{e^2-4 d f}\right)}{\left(b+\sqrt{b^2-4 a c}\right) f-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 \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]) - 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] + 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] + 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] + Log[e - Sqrt[e^2 - 4*d*f] + 2*f*x]*Log[g*(a + x*(b + c*x))^n] - Log[e + Sqrt[e^2 - 4*d*f] + 2*f*x]*Log[g*(a + x*(b + c*x))^n] - 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]))] - 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]))] + 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]))] + 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",1
96,1,111,144,0.0644519,"\int \log ^2\left(d \left(b x+c x^2\right)^n\right) \, dx","Integrate[Log[d*(b*x + c*x^2)^n]^2,x]","\frac{c x \left(\log ^2\left(d (x (b+c x))^n\right)-4 n \log \left(d (x (b+c x))^n\right)+8 n^2\right)-2 b n \log (b+c x) \left(-\log \left(d (x (b+c x))^n\right)+n \log \left(-\frac{c x}{b}\right)+2 n\right)-2 b n^2 \text{Li}_2\left(\frac{c x}{b}+1\right)-b n^2 \log ^2(b+c x)}{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{2 b n^2 \text{Li}_2\left(\frac{c x}{b}+1\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,"(-(b*n^2*Log[b + c*x]^2) - 2*b*n*Log[b + c*x]*(2*n + n*Log[-((c*x)/b)] - Log[d*(x*(b + c*x))^n]) + c*x*(8*n^2 - 4*n*Log[d*(x*(b + c*x))^n] + Log[d*(x*(b + c*x))^n]^2) - 2*b*n^2*PolyLog[2, 1 + (c*x)/b])/c","A",1
97,1,478,587,0.8495908,"\int \log ^2\left(d \left(a+b x+c x^2\right)^n\right) \, dx","Integrate[Log[d*(a + b*x + c*x^2)^n]^2,x]","\frac{n \left(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(d (a+x (b+c x))^n\right)+2 \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 (a+x (b+c x))^n\right)+n \left(\sqrt{b^2-4 a c}-b\right) \left(2 \text{Li}_2\left(\frac{-b-2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)+\log \left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(\log \left(-\sqrt{b^2-4 a c}+b+2 c x\right)+2 \log \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{2 \sqrt{b^2-4 a c}}\right)\right)\right)-n \left(\sqrt{b^2-4 a c}+b\right) \left(2 \text{Li}_2\left(\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)+\log \left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 \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)\right)\right)+4 n \left(-2 \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)-b \log (a+x (b+c x))+4 c x\right)-8 c x \log \left(d (a+x (b+c x))^n\right)\right)}{2 c}+x \log ^2\left(d (a+x (b+c x))^n\right)","\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) \text{Li}_2\left(-\frac{b+2 c x-\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c}-\frac{n^2 \left(\sqrt{b^2-4 a c}+b\right) \text{Li}_2\left(\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\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,"x*Log[d*(a + x*(b + c*x))^n]^2 + (n*(4*n*(4*c*x - 2*Sqrt[b^2 - 4*a*c]*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]] - b*Log[a + x*(b + c*x)]) - 8*c*x*Log[d*(a + x*(b + c*x))^n] + 2*(b - Sqrt[b^2 - 4*a*c])*Log[b - Sqrt[b^2 - 4*a*c] + 2*c*x]*Log[d*(a + x*(b + c*x))^n] + 2*(b + Sqrt[b^2 - 4*a*c])*Log[b + Sqrt[b^2 - 4*a*c] + 2*c*x]*Log[d*(a + x*(b + c*x))^n] + (-b + Sqrt[b^2 - 4*a*c])*n*(Log[b - Sqrt[b^2 - 4*a*c] + 2*c*x]*(Log[b - Sqrt[b^2 - 4*a*c] + 2*c*x] + 2*Log[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])]) + 2*PolyLog[2, (-b + Sqrt[b^2 - 4*a*c] - 2*c*x)/(2*Sqrt[b^2 - 4*a*c])]) - (b + Sqrt[b^2 - 4*a*c])*n*(Log[b + Sqrt[b^2 - 4*a*c] + 2*c*x]*(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]) + 2*PolyLog[2, (b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])))/(2*c)","A",1
98,1,290,311,0.2040596,"\int \frac{x^2 \log \left(1+x+x^2\right)}{2+3 x+x^2} \, dx","Integrate[(x^2*Log[1 + x + x^2])/(2 + 3*x + x^2),x]","-\text{Li}_2\left(\frac{2 (x+1)}{1+i \sqrt{3}}\right)-\text{Li}_2\left(\frac{2 i (x+1)}{i+\sqrt{3}}\right)+4 \left(\text{Li}_2\left(\frac{2 (x+2)}{3+i \sqrt{3}}\right)+\text{Li}_2\left(\frac{2 i (x+2)}{3 i+\sqrt{3}}\right)+\left(\log \left(\frac{-2 i x+\sqrt{3}-i}{\sqrt{3}+3 i}\right)+\log \left(\frac{2 i x+\sqrt{3}+i}{\sqrt{3}-3 i}\right)\right) \log (2 (x+2))\right)+x \log \left(x^2+x+1\right)+\log (2 (x+1)) \log \left(x^2+x+1\right)-4 \log (2 (x+2)) \log \left(x^2+x+1\right)+\frac{1}{2} \log \left(x^2+x+1\right)-2 x-\log \left(\frac{-2 i x+\sqrt{3}-i}{\sqrt{3}+i}\right) \log (2 (x+1))-\log \left(\frac{2 i x+\sqrt{3}+i}{\sqrt{3}-i}\right) \log (2 (x+1))+\sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)","-\text{Li}_2\left(\frac{2 (x+1)}{1-i \sqrt{3}}\right)-\text{Li}_2\left(\frac{2 (x+1)}{1+i \sqrt{3}}\right)+4 \text{Li}_2\left(\frac{2 (x+2)}{3-i \sqrt{3}}\right)+4 \text{Li}_2\left(\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[(-I + Sqrt[3] - (2*I)*x)/(I + Sqrt[3])]*Log[2*(1 + x)] - Log[(I + Sqrt[3] + (2*I)*x)/(-I + Sqrt[3])]*Log[2*(1 + x)] + Log[1 + x + x^2]/2 + x*Log[1 + x + x^2] + Log[2*(1 + x)]*Log[1 + x + x^2] - 4*Log[2*(2 + x)]*Log[1 + x + x^2] - PolyLog[2, (2*(1 + x))/(1 + I*Sqrt[3])] - PolyLog[2, ((2*I)*(1 + x))/(I + Sqrt[3])] + 4*((Log[(-I + Sqrt[3] - (2*I)*x)/(3*I + Sqrt[3])] + Log[(I + Sqrt[3] + (2*I)*x)/(-3*I + Sqrt[3])])*Log[2*(2 + x)] + PolyLog[2, (2*(2 + x))/(3 + I*Sqrt[3])] + PolyLog[2, ((2*I)*(2 + x))/(3*I + Sqrt[3])])","A",1
99,1,323,371,0.1584742,"\int \log ^2\left(1+x+x^2\right) \, dx","Integrate[Log[1 + x + x^2]^2,x]","-\frac{1}{2} i \left(\sqrt{3}-i\right) \left(2 \text{Li}_2\left(\frac{-2 i x+\sqrt{3}-i}{2 \sqrt{3}}\right)+\log \left(2 x+i \sqrt{3}+1\right) \left(2 \log \left(\frac{2 i x+\sqrt{3}+i}{2 \sqrt{3}}\right)+\log \left(2 x+i \sqrt{3}+1\right)\right)\right)+\frac{1}{2} i \left(\sqrt{3}+i\right) \left(2 \text{Li}_2\left(\frac{2 i x+\sqrt{3}+i}{2 \sqrt{3}}\right)+\log \left(2 x-i \sqrt{3}+1\right) \left(2 \log \left(\frac{-2 i x+\sqrt{3}-i}{2 \sqrt{3}}\right)+\log \left(2 x-i \sqrt{3}+1\right)\right)\right)+x \log ^2\left(x^2+x+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)+\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-4 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)","-\left(1+i \sqrt{3}\right) \text{Li}_2\left(-\frac{2 i x-\sqrt{3}+i}{2 \sqrt{3}}\right)-\left(1-i \sqrt{3}\right) \text{Li}_2\left(\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]] - 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 - (I/2)*(-I + Sqrt[3])*(Log[1 + I*Sqrt[3] + 2*x]*(2*Log[(I + Sqrt[3] + (2*I)*x)/(2*Sqrt[3])] + Log[1 + I*Sqrt[3] + 2*x]) + 2*PolyLog[2, (-I + Sqrt[3] - (2*I)*x)/(2*Sqrt[3])]) + (I/2)*(I + Sqrt[3])*(Log[1 - I*Sqrt[3] + 2*x]*(2*Log[(-I + Sqrt[3] - (2*I)*x)/(2*Sqrt[3])] + Log[1 - I*Sqrt[3] + 2*x]) + 2*PolyLog[2, (I + Sqrt[3] + (2*I)*x)/(2*Sqrt[3])])","A",1
100,1,826,443,0.816202,"\int \frac{\log ^2\left(-1+x+x^2\right)}{x^3} \, dx","Integrate[Log[-1 + x + x^2]^2/x^3,x]","\frac{x \left(\sqrt{5} x \log ^2\left(x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right)+3 x \log ^2\left(x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right)-2 \sqrt{5} x \log \left(-2 x+\sqrt{5}-1\right) \log \left(x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right)-6 x \log \left(-2 x+\sqrt{5}-1\right) \log \left(x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right)+12 x \log (x) \log \left(x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right)-12 x \log \left(\frac{2 x}{-1+\sqrt{5}}\right) \log \left(x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right)+2 \sqrt{5} x \log \left(2 x+\sqrt{5}+1\right) \log \left(x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right)-6 x \log \left(2 x+\sqrt{5}+1\right) \log \left(x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right)-2 \sqrt{5} x \log \left(\frac{2 x+\sqrt{5}+1}{2 \sqrt{5}}\right) \log \left(x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right)+6 x \log \left(\frac{2 x+\sqrt{5}+1}{2 \sqrt{5}}\right) \log \left(x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right)-\sqrt{5} x \log ^2\left(x+\frac{1}{2} \left(1+\sqrt{5}\right)\right)+3 x \log ^2\left(x+\frac{1}{2} \left(1+\sqrt{5}\right)\right)+4 x \log (x)-12 x \log \left(\frac{1}{2} \left(1+\sqrt{5}\right)\right) \log (x)-2 \sqrt{5} x \log \left(-2 x+\sqrt{5}-1\right) \log \left(x+\frac{1}{2} \left(1+\sqrt{5}\right)\right)-6 x \log \left(-2 x+\sqrt{5}-1\right) \log \left(x+\frac{1}{2} \left(1+\sqrt{5}\right)\right)+12 x \log (x) \log \left(x+\frac{1}{2} \left(1+\sqrt{5}\right)\right)-2 \sqrt{5} x \log \left(2 x-\sqrt{5}+1\right)-2 x \log \left(2 x-\sqrt{5}+1\right)+\sqrt{5} x \log (5) \log \left(2 x-\sqrt{5}+1\right)+3 x \log (5) \log \left(2 x-\sqrt{5}+1\right)+2 \sqrt{5} x \log \left(2 x+\sqrt{5}+1\right)-2 x \log \left(2 x+\sqrt{5}+1\right)+2 \sqrt{5} x \log \left(x+\frac{1}{2} \left(1+\sqrt{5}\right)\right) \log \left(2 x+\sqrt{5}+1\right)-6 x \log \left(x+\frac{1}{2} \left(1+\sqrt{5}\right)\right) \log \left(2 x+\sqrt{5}+1\right)+2 \sqrt{5} x \log \left(-2 x+\sqrt{5}-1\right) \log \left(x^2+x-1\right)+6 x \log \left(-2 x+\sqrt{5}-1\right) \log \left(x^2+x-1\right)-12 x \log (x) \log \left(x^2+x-1\right)-2 \sqrt{5} x \log \left(2 x+\sqrt{5}+1\right) \log \left(x^2+x-1\right)+6 x \log \left(2 x+\sqrt{5}+1\right) \log \left(x^2+x-1\right)+4 \log \left(x^2+x-1\right)-4 \sqrt{5} x \text{Li}_2\left(\frac{-2 x+\sqrt{5}-1}{2 \sqrt{5}}\right)-12 x \text{Li}_2\left(\frac{-2 x+\sqrt{5}-1}{-1+\sqrt{5}}\right)+12 x \text{Li}_2\left(-\frac{2 x}{1+\sqrt{5}}\right)\right)-2 \log ^2\left(x^2+x-1\right)}{4 x^2}","3 \text{Li}_2\left(-\frac{2 x}{1+\sqrt{5}}\right)-\frac{1}{2} \left(3+\sqrt{5}\right) \text{Li}_2\left(-\frac{2 x-\sqrt{5}+1}{2 \sqrt{5}}\right)-\frac{1}{2} \left(3-\sqrt{5}\right) \text{Li}_2\left(\frac{2 x+\sqrt{5}+1}{2 \sqrt{5}}\right)-3 \text{Li}_2\left(\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,"(-2*Log[-1 + x + x^2]^2 + x*(4*x*Log[x] - 12*x*Log[(1 + Sqrt[5])/2]*Log[x] - 6*x*Log[-1 + Sqrt[5] - 2*x]*Log[1/2 - Sqrt[5]/2 + x] - 2*Sqrt[5]*x*Log[-1 + Sqrt[5] - 2*x]*Log[1/2 - Sqrt[5]/2 + x] + 12*x*Log[x]*Log[1/2 - Sqrt[5]/2 + x] - 12*x*Log[(2*x)/(-1 + Sqrt[5])]*Log[1/2 - Sqrt[5]/2 + x] + 3*x*Log[1/2 - Sqrt[5]/2 + x]^2 + Sqrt[5]*x*Log[1/2 - Sqrt[5]/2 + x]^2 - 6*x*Log[-1 + Sqrt[5] - 2*x]*Log[(1 + Sqrt[5])/2 + x] - 2*Sqrt[5]*x*Log[-1 + Sqrt[5] - 2*x]*Log[(1 + Sqrt[5])/2 + x] + 12*x*Log[x]*Log[(1 + Sqrt[5])/2 + x] + 3*x*Log[(1 + Sqrt[5])/2 + x]^2 - Sqrt[5]*x*Log[(1 + Sqrt[5])/2 + x]^2 - 2*x*Log[1 - Sqrt[5] + 2*x] - 2*Sqrt[5]*x*Log[1 - Sqrt[5] + 2*x] + 3*x*Log[5]*Log[1 - Sqrt[5] + 2*x] + Sqrt[5]*x*Log[5]*Log[1 - Sqrt[5] + 2*x] - 2*x*Log[1 + Sqrt[5] + 2*x] + 2*Sqrt[5]*x*Log[1 + Sqrt[5] + 2*x] - 6*x*Log[1/2 - Sqrt[5]/2 + x]*Log[1 + Sqrt[5] + 2*x] + 2*Sqrt[5]*x*Log[1/2 - Sqrt[5]/2 + x]*Log[1 + Sqrt[5] + 2*x] - 6*x*Log[(1 + Sqrt[5])/2 + x]*Log[1 + Sqrt[5] + 2*x] + 2*Sqrt[5]*x*Log[(1 + Sqrt[5])/2 + x]*Log[1 + Sqrt[5] + 2*x] + 6*x*Log[1/2 - Sqrt[5]/2 + x]*Log[(1 + Sqrt[5] + 2*x)/(2*Sqrt[5])] - 2*Sqrt[5]*x*Log[1/2 - Sqrt[5]/2 + x]*Log[(1 + Sqrt[5] + 2*x)/(2*Sqrt[5])] + 4*Log[-1 + x + x^2] + 6*x*Log[-1 + Sqrt[5] - 2*x]*Log[-1 + x + x^2] + 2*Sqrt[5]*x*Log[-1 + Sqrt[5] - 2*x]*Log[-1 + x + x^2] - 12*x*Log[x]*Log[-1 + x + x^2] + 6*x*Log[1 + Sqrt[5] + 2*x]*Log[-1 + x + x^2] - 2*Sqrt[5]*x*Log[1 + Sqrt[5] + 2*x]*Log[-1 + x + x^2] - 4*Sqrt[5]*x*PolyLog[2, (-1 + Sqrt[5] - 2*x)/(2*Sqrt[5])] - 12*x*PolyLog[2, (-1 + Sqrt[5] - 2*x)/(-1 + Sqrt[5])] + 12*x*PolyLog[2, (-2*x)/(1 + Sqrt[5])]))/(4*x^2)","A",0
101,1,117,172,0.5142684,"\int x^3 \log \left(-1+4 x+4 \sqrt{(-1+x) x}\right) \, dx","Integrate[x^3*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]],x]","\frac{-3072 x^4+24576 x^4 \log \left(4 x+4 \sqrt{(x-1) x}-1\right)+512 x^3-96 x^2-8 \sqrt{(x-1) x} \left(384 x^3+640 x^2+764 x+1155\right)+24 x-6 \log (8 x+1)-4611 \log \left(-2 x-2 \sqrt{(x-1) x}+1\right)+3 \log \left(-10 x+6 \sqrt{(x-1) x}+1\right)}{98304}","-\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{\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{1}{4} x^4 \log \left(4 \sqrt{x^2-x}+4 x-1\right)+\frac{x}{4096}-\frac{\log (8 x+1)}{32768}",1,"(24*x - 96*x^2 + 512*x^3 - 3072*x^4 - 8*Sqrt[(-1 + x)*x]*(1155 + 764*x + 640*x^2 + 384*x^3) - 6*Log[1 + 8*x] - 4611*Log[1 - 2*x - 2*Sqrt[(-1 + x)*x]] + 24576*x^4*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]] + 3*Log[1 - 10*x + 6*Sqrt[(-1 + x)*x]])/98304","A",1
102,1,107,149,0.3479356,"\int x^2 \log \left(-1+4 x+4 \sqrt{(-1+x) x}\right) \, dx","Integrate[x^2*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]],x]","\frac{-512 x^3+3072 x^3 \log \left(4 x+4 \sqrt{(x-1) x}-1\right)+96 x^2-8 \sqrt{(x-1) x} \left(64 x^2+116 x+165\right)-24 x+6 \log (8 x+1)-669 \log \left(-2 x-2 \sqrt{(x-1) x}+1\right)-3 \log \left(-10 x+6 \sqrt{(x-1) x}+1\right)}{9216}","-\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{\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{1}{3} x^3 \log \left(4 \sqrt{x^2-x}+4 x-1\right)-\frac{x}{384}+\frac{\log (8 x+1)}{3072}",1,"(-24*x + 96*x^2 - 512*x^3 - 8*Sqrt[(-1 + x)*x]*(165 + 116*x + 64*x^2) + 6*Log[1 + 8*x] - 669*Log[1 - 2*x - 2*Sqrt[(-1 + x)*x]] + 3072*x^3*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]] - 3*Log[1 - 10*x + 6*Sqrt[(-1 + x)*x]])/9216","A",1
103,1,102,127,0.2906012,"\int x \log \left(-1+4 x+4 \sqrt{(-1+x) x}\right) \, dx","Integrate[x*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]],x]","\frac{1}{256} \left(-32 x^2+128 x^2 \log \left(4 x+4 \sqrt{(x-1) x}-1\right)-32 \sqrt{(x-1) x} x+8 x-72 \sqrt{(x-1) x}-2 \log (8 x+1)-33 \log \left(-2 x-2 \sqrt{(x-1) x}+1\right)+\log \left(-10 x+6 \sqrt{(x-1) x}+1\right)\right)","-\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,"(8*x - 32*x^2 - 72*Sqrt[(-1 + x)*x] - 32*x*Sqrt[(-1 + x)*x] - 2*Log[1 + 8*x] - 33*Log[1 - 2*x - 2*Sqrt[(-1 + x)*x]] + 128*x^2*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]] + Log[1 - 10*x + 6*Sqrt[(-1 + x)*x]])/256","A",1
104,1,85,95,0.03026,"\int \log \left(-1+4 x+4 \sqrt{(-1+x) x}\right) \, dx","Integrate[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]],x]","\frac{1}{16} \left(-8 x-8 \sqrt{(x-1) x}+16 x \log \left(4 x+4 \sqrt{(x-1) x}-1\right)+2 \log (8 x+1)-7 \log \left(-2 x-2 \sqrt{(x-1) x}+1\right)-\log \left(-10 x+6 \sqrt{(x-1) x}+1\right)\right)","-\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,"(-8*x - 8*Sqrt[(-1 + x)*x] + 2*Log[1 + 8*x] - 7*Log[1 - 2*x - 2*Sqrt[(-1 + x)*x]] + 16*x*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]] - Log[1 - 10*x + 6*Sqrt[(-1 + x)*x]])/16","A",1
105,0,0,26,0.4790032,"\int \frac{\log \left(-1+4 x+4 \sqrt{(-1+x) x}\right)}{x} \, dx","Integrate[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,"Integrate[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/x, x]","A",-1
106,1,68,76,0.2517949,"\int \frac{\log \left(-1+4 x+4 \sqrt{(-1+x) x}\right)}{x^2} \, dx","Integrate[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/x^2,x]","\frac{4 \sqrt{(x-1) x}}{x}+4 \log (x)-8 \log (8 x+1)-\frac{\log \left(4 x+4 \sqrt{(x-1) x}-1\right)}{x}+4 \log \left(-10 x+6 \sqrt{(x-1) x}+1\right)","\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[(-1 + x)*x])/x + 4*Log[x] - 8*Log[1 + 8*x] - Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/x + 4*Log[1 - 10*x + 6*Sqrt[(-1 + x)*x]]","A",1
107,1,82,101,0.2977075,"\int \frac{\log \left(-1+4 x+4 \sqrt{(-1+x) x}\right)}{x^3} \, dx","Integrate[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/x^3,x]","-\frac{2 \sqrt{(x-1) x} (16 x-1)}{3 x^2}-\frac{\log \left(4 x+4 \sqrt{(x-1) x}-1\right)}{2 x^2}-\frac{2}{x}-16 \log (x)+32 \log (8 x+1)-16 \log \left(-10 x+6 \sqrt{(x-1) x}+1\right)","-\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 \left(x^2-x\right)^{3/2}}{3 x^3}-\frac{2}{x}-16 \log (x)+16 \log (8 x+1)",1,"-2/x - (2*Sqrt[(-1 + x)*x]*(-1 + 16*x))/(3*x^2) - 16*Log[x] + 32*Log[1 + 8*x] - Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/(2*x^2) - 16*Log[1 - 10*x + 6*Sqrt[(-1 + x)*x]]","A",1
108,1,232,187,0.8735943,"\int x^{3/2} \log \left(-1+4 x+4 \sqrt{(-1+x) x}\right) \, dx","Integrate[x^(3/2)*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]],x]","\frac{-3072 x^{5/2}-3072 \sqrt{(x-1) x} x^{3/2}+640 x^{3/2}+15360 x^{5/2} \log \left(4 x+4 \sqrt{(x-1) x}-1\right)-6016 \sqrt{(x-1) x} \sqrt{x}-240 \sqrt{x}-\frac{11312 \sqrt{(x-1) x}}{\sqrt{x}}-30 i \sqrt{2} \log \left(4 (8 x+1)^2\right)+15 i \sqrt{2} \log \left((8 x+1) \left(-10 x-6 \sqrt{(x-1) x}+1\right)\right)+15 i \sqrt{2} \log \left((8 x+1) \left(-10 x+6 \sqrt{(x-1) x}+1\right)\right)+60 \sqrt{2} \tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)-60 \sqrt{2} \tan ^{-1}\left(\frac{2 \sqrt{2} \sqrt{(x-1) x}}{3 \sqrt{x}}\right)}{38400}","-\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{\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{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}}{160}+\frac{\tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)}{320 \sqrt{2}}",1,"(-240*Sqrt[x] + 640*x^(3/2) - 3072*x^(5/2) - (11312*Sqrt[(-1 + x)*x])/Sqrt[x] - 6016*Sqrt[x]*Sqrt[(-1 + x)*x] - 3072*x^(3/2)*Sqrt[(-1 + x)*x] + 60*Sqrt[2]*ArcTan[2*Sqrt[2]*Sqrt[x]] - 60*Sqrt[2]*ArcTan[(2*Sqrt[2]*Sqrt[(-1 + x)*x])/(3*Sqrt[x])] - (30*I)*Sqrt[2]*Log[4*(1 + 8*x)^2] + (15*I)*Sqrt[2]*Log[(1 + 8*x)*(1 - 10*x - 6*Sqrt[(-1 + x)*x])] + 15360*x^(5/2)*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]] + (15*I)*Sqrt[2]*Log[(1 + 8*x)*(1 - 10*x + 6*Sqrt[(-1 + x)*x])])/38400","C",1
109,1,209,158,0.6494944,"\int \sqrt{x} \log \left(-1+4 x+4 \sqrt{(-1+x) x}\right) \, dx","Integrate[Sqrt[x]*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]],x]","\frac{1}{576} \left(-128 x^{3/2}+384 x^{3/2} \log \left(4 x+4 \sqrt{(x-1) x}-1\right)-128 \sqrt{(x-1) x} \sqrt{x}+48 \sqrt{x}-\frac{400 \sqrt{(x-1) x}}{\sqrt{x}}+6 i \sqrt{2} \log \left(4 (8 x+1)^2\right)-3 i \sqrt{2} \log \left((8 x+1) \left(-10 x-6 \sqrt{(x-1) x}+1\right)\right)-3 i \sqrt{2} \log \left((8 x+1) \left(-10 x+6 \sqrt{(x-1) x}+1\right)\right)-12 \sqrt{2} \tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)+12 \sqrt{2} \tan ^{-1}\left(\frac{2 \sqrt{2} \sqrt{(x-1) x}}{3 \sqrt{x}}\right)\right)","-\frac{2 x^{3/2}}{9}-\frac{11 \sqrt{x^2-x}}{12 \sqrt{x}}+\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{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}}{12}-\frac{\tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)}{24 \sqrt{2}}",1,"(48*Sqrt[x] - 128*x^(3/2) - (400*Sqrt[(-1 + x)*x])/Sqrt[x] - 128*Sqrt[x]*Sqrt[(-1 + x)*x] - 12*Sqrt[2]*ArcTan[2*Sqrt[2]*Sqrt[x]] + 12*Sqrt[2]*ArcTan[(2*Sqrt[2]*Sqrt[(-1 + x)*x])/(3*Sqrt[x])] + (6*I)*Sqrt[2]*Log[4*(1 + 8*x)^2] - (3*I)*Sqrt[2]*Log[(1 + 8*x)*(1 - 10*x - 6*Sqrt[(-1 + x)*x])] + 384*x^(3/2)*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]] - (3*I)*Sqrt[2]*Log[(1 + 8*x)*(1 - 10*x + 6*Sqrt[(-1 + x)*x])])/576","C",1
110,1,186,118,0.5737637,"\int \frac{\log \left(-1+4 x+4 \sqrt{(-1+x) x}\right)}{\sqrt{x}} \, dx","Integrate[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/Sqrt[x],x]","\frac{1}{8} \left(-16 \sqrt{x}-\frac{16 \sqrt{(x-1) x}}{\sqrt{x}}-2 i \sqrt{2} \log \left(4 (8 x+1)^2\right)+i \sqrt{2} \log \left((8 x+1) \left(-10 x-6 \sqrt{(x-1) x}+1\right)\right)+16 \sqrt{x} \log \left(4 x+4 \sqrt{(x-1) x}-1\right)+i \sqrt{2} \log \left((8 x+1) \left(-10 x+6 \sqrt{(x-1) x}+1\right)\right)+4 \sqrt{2} \tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)-4 \sqrt{2} \tan ^{-1}\left(\frac{2 \sqrt{2} \sqrt{(x-1) x}}{3 \sqrt{x}}\right)\right)","-\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,"(-16*Sqrt[x] - (16*Sqrt[(-1 + x)*x])/Sqrt[x] + 4*Sqrt[2]*ArcTan[2*Sqrt[2]*Sqrt[x]] - 4*Sqrt[2]*ArcTan[(2*Sqrt[2]*Sqrt[(-1 + x)*x])/(3*Sqrt[x])] - (2*I)*Sqrt[2]*Log[4*(1 + 8*x)^2] + I*Sqrt[2]*Log[(1 + 8*x)*(1 - 10*x - 6*Sqrt[(-1 + x)*x])] + 16*Sqrt[x]*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]] + I*Sqrt[2]*Log[(1 + 8*x)*(1 - 10*x + 6*Sqrt[(-1 + x)*x])])/8","C",1
111,1,177,114,0.455031,"\int \frac{\log \left(-1+4 x+4 \sqrt{(-1+x) x}\right)}{x^{3/2}} \, dx","Integrate[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/x^(3/2),x]","-2 i \sqrt{2} \log \left(4 (8 x+1)^2\right)+i \sqrt{2} \log \left((8 x+1) \left(-10 x-6 \sqrt{(x-1) x}+1\right)\right)-\frac{2 \log \left(4 x+4 \sqrt{(x-1) x}-1\right)}{\sqrt{x}}+i \sqrt{2} \log \left((8 x+1) \left(-10 x+6 \sqrt{(x-1) x}+1\right)\right)+4 \sqrt{2} \tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)+8 \tan ^{-1}\left(\frac{\sqrt{(x-1) x}}{\sqrt{x}}\right)-4 \sqrt{2} \tan ^{-1}\left(\frac{2 \sqrt{2} \sqrt{(x-1) x}}{3 \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]*ArcTan[2*Sqrt[2]*Sqrt[x]] + 8*ArcTan[Sqrt[(-1 + x)*x]/Sqrt[x]] - 4*Sqrt[2]*ArcTan[(2*Sqrt[2]*Sqrt[(-1 + x)*x])/(3*Sqrt[x])] - (2*I)*Sqrt[2]*Log[4*(1 + 8*x)^2] + I*Sqrt[2]*Log[(1 + 8*x)*(1 - 10*x - 6*Sqrt[(-1 + x)*x])] - (2*Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]])/Sqrt[x] + I*Sqrt[2]*Log[(1 + 8*x)*(1 - 10*x + 6*Sqrt[(-1 + x)*x])]","C",1
112,1,204,151,0.7303145,"\int \frac{\log \left(-1+4 x+4 \sqrt{(-1+x) x}\right)}{x^{5/2}} \, dx","Integrate[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/x^(5/2),x]","\frac{2}{3} \left(\frac{2 \sqrt{(x-1) x}}{x^{3/2}}-\frac{\log \left(4 x+4 \sqrt{(x-1) x}-1\right)}{x^{3/2}}-\frac{8}{\sqrt{x}}+8 i \sqrt{2} \log \left(4 (8 x+1)^2\right)-4 i \sqrt{2} \log \left((8 x+1) \left(-10 x-6 \sqrt{(x-1) x}+1\right)\right)-4 i \sqrt{2} \log \left((8 x+1) \left(-10 x+6 \sqrt{(x-1) x}+1\right)\right)-16 \sqrt{2} \tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)-22 \tan ^{-1}\left(\frac{\sqrt{(x-1) x}}{\sqrt{x}}\right)+16 \sqrt{2} \tan ^{-1}\left(\frac{2 \sqrt{2} \sqrt{(x-1) x}}{3 \sqrt{x}}\right)\right)","\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{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{16}{3 \sqrt{x}}-\frac{32}{3} \sqrt{2} \tan ^{-1}\left(2 \sqrt{2} \sqrt{x}\right)",1,"(2*(-8/Sqrt[x] + (2*Sqrt[(-1 + x)*x])/x^(3/2) - 16*Sqrt[2]*ArcTan[2*Sqrt[2]*Sqrt[x]] - 22*ArcTan[Sqrt[(-1 + x)*x]/Sqrt[x]] + 16*Sqrt[2]*ArcTan[(2*Sqrt[2]*Sqrt[(-1 + x)*x])/(3*Sqrt[x])] + (8*I)*Sqrt[2]*Log[4*(1 + 8*x)^2] - (4*I)*Sqrt[2]*Log[(1 + 8*x)*(1 - 10*x - 6*Sqrt[(-1 + x)*x])] - Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/x^(3/2) - (4*I)*Sqrt[2]*Log[(1 + 8*x)*(1 - 10*x + 6*Sqrt[(-1 + x)*x])]))/3","C",1
113,1,93,93,0.0079014,"\int x^3 \log \left(a+b e^x\right) \, dx","Integrate[x^3*Log[a + b*E^x],x]","-x^3 \text{Li}_2\left(-\frac{b e^x}{a}\right)+3 x^2 \text{Li}_3\left(-\frac{b e^x}{a}\right)-6 x \text{Li}_4\left(-\frac{b e^x}{a}\right)+6 \text{Li}_5\left(-\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{Li}_2\left(-\frac{b e^x}{a}\right)+3 x^2 \text{Li}_3\left(-\frac{b e^x}{a}\right)-6 x \text{Li}_4\left(-\frac{b e^x}{a}\right)+6 \text{Li}_5\left(-\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",1
114,1,77,77,0.0064442,"\int x^2 \log \left(a+b e^x\right) \, dx","Integrate[x^2*Log[a + b*E^x],x]","-x^2 \text{Li}_2\left(-\frac{b e^x}{a}\right)+2 x \text{Li}_3\left(-\frac{b e^x}{a}\right)-2 \text{Li}_4\left(-\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{Li}_2\left(-\frac{b e^x}{a}\right)+2 x \text{Li}_3\left(-\frac{b e^x}{a}\right)-2 \text{Li}_4\left(-\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",1
115,1,59,59,0.00472,"\int x \log \left(a+b e^x\right) \, dx","Integrate[x*Log[a + b*E^x],x]","-x \text{Li}_2\left(-\frac{b e^x}{a}\right)+\text{Li}_3\left(-\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{Li}_2\left(-\frac{b e^x}{a}\right)+\text{Li}_3\left(-\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",1
116,1,38,38,0.0023358,"\int \log \left(a+b e^x\right) \, dx","Integrate[Log[a + b*E^x],x]","-\text{Li}_2\left(-\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{Li}_2\left(-\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",1
117,0,0,15,0.0513975,"\int \frac{\log \left(a+b e^x\right)}{x} \, dx","Integrate[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,"Integrate[Log[a + b*E^x]/x, x]","A",-1
118,1,132,132,0.0135759,"\int x^3 \log \left(1+e \left(f^{c (a+b x)}\right)^n\right) \, dx","Integrate[x^3*Log[1 + e*(f^(c*(a + b*x)))^n],x]","\frac{6 \text{Li}_5\left(-e \left(f^{c (a+b x)}\right)^n\right)}{b^4 c^4 n^4 \log ^4(f)}-\frac{6 x \text{Li}_4\left(-e \left(f^{c (a+b x)}\right)^n\right)}{b^3 c^3 n^3 \log ^3(f)}+\frac{3 x^2 \text{Li}_3\left(-e \left(f^{c (a+b x)}\right)^n\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{x^3 \text{Li}_2\left(-e \left(f^{c (a+b x)}\right)^n\right)}{b c n \log (f)}","\frac{6 \text{Li}_5\left(-e \left(f^{c (a+b x)}\right)^n\right)}{b^4 c^4 n^4 \log ^4(f)}-\frac{6 x \text{Li}_4\left(-e \left(f^{c (a+b x)}\right)^n\right)}{b^3 c^3 n^3 \log ^3(f)}+\frac{3 x^2 \text{Li}_3\left(-e \left(f^{c (a+b x)}\right)^n\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{x^3 \text{Li}_2\left(-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",1
119,1,98,98,0.0058705,"\int x^2 \log \left(1+e \left(f^{c (a+b x)}\right)^n\right) \, dx","Integrate[x^2*Log[1 + e*(f^(c*(a + b*x)))^n],x]","-\frac{2 \text{Li}_4\left(-e \left(f^{c (a+b x)}\right)^n\right)}{b^3 c^3 n^3 \log ^3(f)}+\frac{2 x \text{Li}_3\left(-e \left(f^{c (a+b x)}\right)^n\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{x^2 \text{Li}_2\left(-e \left(f^{c (a+b x)}\right)^n\right)}{b c n \log (f)}","-\frac{2 \text{Li}_4\left(-e \left(f^{c (a+b x)}\right)^n\right)}{b^3 c^3 n^3 \log ^3(f)}+\frac{2 x \text{Li}_3\left(-e \left(f^{c (a+b x)}\right)^n\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{x^2 \text{Li}_2\left(-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",1
120,1,63,63,0.0049581,"\int x \log \left(1+e \left(f^{c (a+b x)}\right)^n\right) \, dx","Integrate[x*Log[1 + e*(f^(c*(a + b*x)))^n],x]","\frac{\text{Li}_3\left(-e \left(f^{c (a+b x)}\right)^n\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{x \text{Li}_2\left(-e \left(f^{c (a+b x)}\right)^n\right)}{b c n \log (f)}","\frac{\text{Li}_3\left(-e \left(f^{c (a+b x)}\right)^n\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{x \text{Li}_2\left(-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",1
121,1,31,31,0.0013601,"\int \log \left(1+e \left(f^{c (a+b x)}\right)^n\right) \, dx","Integrate[Log[1 + e*(f^(c*(a + b*x)))^n],x]","-\frac{\text{Li}_2\left(-e \left(f^{c (a+b x)}\right)^n\right)}{b c n \log (f)}","-\frac{\text{Li}_2\left(-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",1
122,0,0,23,0.3075476,"\int \frac{\log \left(1+e \left(f^{c (a+b x)}\right)^n\right)}{x} \, dx","Integrate[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,"Integrate[Log[1 + e*(f^(c*(a + b*x)))^n]/x, x]","A",-1
123,1,193,193,0.0089785,"\int x^3 \log \left(d+e \left(f^{c (a+b x)}\right)^n\right) \, dx","Integrate[x^3*Log[d + e*(f^(c*(a + b*x)))^n],x]","\frac{6 \text{Li}_5\left(-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^4 c^4 n^4 \log ^4(f)}-\frac{6 x \text{Li}_4\left(-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^3 c^3 n^3 \log ^3(f)}+\frac{3 x^2 \text{Li}_3\left(-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{x^3 \text{Li}_2\left(-\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{6 \text{Li}_5\left(-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^4 c^4 n^4 \log ^4(f)}-\frac{6 x \text{Li}_4\left(-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^3 c^3 n^3 \log ^3(f)}+\frac{3 x^2 \text{Li}_3\left(-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{x^3 \text{Li}_2\left(-\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",1
124,1,156,156,0.0071102,"\int x^2 \log \left(d+e \left(f^{c (a+b x)}\right)^n\right) \, dx","Integrate[x^2*Log[d + e*(f^(c*(a + b*x)))^n],x]","-\frac{2 \text{Li}_4\left(-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^3 c^3 n^3 \log ^3(f)}+\frac{2 x \text{Li}_3\left(-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{x^2 \text{Li}_2\left(-\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 \text{Li}_4\left(-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^3 c^3 n^3 \log ^3(f)}+\frac{2 x \text{Li}_3\left(-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{x^2 \text{Li}_2\left(-\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",1
125,1,118,118,0.005833,"\int x \log \left(d+e \left(f^{c (a+b x)}\right)^n\right) \, dx","Integrate[x*Log[d + e*(f^(c*(a + b*x)))^n],x]","\frac{\text{Li}_3\left(-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{x \text{Li}_2\left(-\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{Li}_3\left(-\frac{e \left(f^{c (a+b x)}\right)^n}{d}\right)}{b^2 c^2 n^2 \log ^2(f)}-\frac{x \text{Li}_2\left(-\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",1
126,1,75,75,0.0033493,"\int \log \left(d+e \left(f^{c (a+b x)}\right)^n\right) \, dx","Integrate[Log[d + e*(f^(c*(a + b*x)))^n],x]","-\frac{\text{Li}_2\left(-\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{Li}_2\left(-\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",1
127,0,0,23,0.2978539,"\int \frac{\log \left(d+e \left(f^{c (a+b x)}\right)^n\right)}{x} \, dx","Integrate[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,"Integrate[Log[d + e*(f^(c*(a + b*x)))^n]/x, x]","A",-1
128,1,39,39,0.0090509,"\int \log \left(b \left(F^{e (c+d x)}\right)^n+\pi \right) \, dx","Integrate[Log[b*(F^(e*(c + d*x)))^n + Pi],x]","x \log (\pi )-\frac{\text{Li}_2\left(-\frac{b \left(F^{e (c+d x)}\right)^n}{\pi }\right)}{d e n \log (F)}","x \log (\pi )-\frac{\text{Li}_2\left(-\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",1
129,1,5,5,0.0094352,"\int \frac{1}{x (3+\log (x))} \, dx","Integrate[1/(x*(3 + Log[x])),x]","\log (\log (x)+3)","\log (\log (x)+3)",1,"Log[3 + Log[x]]","A",1
130,1,12,12,0.003591,"\int \frac{\sqrt{1+\log (x)}}{x} \, dx","Integrate[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",1
131,1,10,10,0.0026647,"\int \frac{(1+\log (x))^5}{x} \, dx","Integrate[(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",1
132,1,8,8,0.001674,"\int \frac{1}{x \sqrt{\log (x)}} \, dx","Integrate[1/(x*Sqrt[Log[x]]),x]","2 \sqrt{\log (x)}","2 \sqrt{\log (x)}",1,"2*Sqrt[Log[x]]","A",1
133,1,3,3,0.0122919,"\int \frac{1}{x \left(1+\log ^2(x)\right)} \, dx","Integrate[1/(x*(1 + Log[x]^2)),x]","\tan ^{-1}(\log (x))","\tan ^{-1}(\log (x))",1,"ArcTan[Log[x]]","A",1
134,1,42,14,0.0161386,"\int \frac{1}{x \sqrt{-3+\log ^2(x)}} \, dx","Integrate[1/(x*Sqrt[-3 + Log[x]^2]),x]","\frac{1}{2} \log \left(\frac{\log (x)}{\sqrt{\log ^2(x)-3}}+1\right)-\frac{1}{2} \log \left(1-\frac{\log (x)}{\sqrt{\log ^2(x)-3}}\right)","\tanh ^{-1}\left(\frac{\log (x)}{\sqrt{\log ^2(x)-3}}\right)",1,"-1/2*Log[1 - Log[x]/Sqrt[-3 + Log[x]^2]] + Log[1 + Log[x]/Sqrt[-3 + Log[x]^2]]/2","B",1
135,1,11,11,0.0202555,"\int \frac{1}{x \sqrt{4-9 \log ^2(x)}} \, dx","Integrate[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",1
136,1,7,7,0.0165906,"\int \frac{1}{x \sqrt{4+\log ^2(x)}} \, dx","Integrate[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",1
137,1,106,111,0.0766383,"\int \frac{1}{x \left(2+3 \log ^3(6 x)\right)} \, dx","Integrate[1/(x*(2 + 3*Log[6*x]^3)),x]","\frac{\sqrt{3} \left(2 \log \left(2^{2/3} \sqrt[3]{3} \log (6 x)+2\right)-\log \left(\sqrt[3]{2} 3^{2/3} \log ^2(6 x)-2^{2/3} \sqrt[3]{3} \log (6 x)+2\right)\right)+6 \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{3} \log (6 x)-1}{\sqrt{3}}\right)}{6\ 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,"(6*ArcTan[(-1 + 2^(2/3)*3^(1/3)*Log[6*x])/Sqrt[3]] + Sqrt[3]*(2*Log[2 + 2^(2/3)*3^(1/3)*Log[6*x]] - Log[2 - 2^(2/3)*3^(1/3)*Log[6*x] + 2^(1/3)*3^(2/3)*Log[6*x]^2]))/(6*2^(2/3)*3^(5/6))","A",1
138,1,11,11,0.0042037,"\int \frac{\log (\log (6 x))}{x \log (6 x)} \, dx","Integrate[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",1
139,1,9,9,0.0071225,"\int \frac{2^{\log (x)}}{x} \, dx","Integrate[2^Log[x]/x,x]","\frac{2^{\log (x)}}{\log (2)}","\frac{2^{\log (x)}}{\log (2)}",1,"2^Log[x]/Log[2]","A",1
140,1,16,17,0.0148618,"\int \frac{\sin ^2(\log (x))}{x} \, dx","Integrate[Sin[Log[x]]^2/x,x]","\frac{\log (x)}{2}-\frac{1}{4} \sin (2 \log (x))","\frac{\log (x)}{2}-\frac{1}{2} \sin (\log (x)) \cos (\log (x))",1,"Log[x]/2 - Sin[2*Log[x]]/4","A",1
141,1,12,12,0.0280852,"\int \frac{7-\log (x)}{x (3+\log (x))} \, dx","Integrate[(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",1
142,1,29,21,0.0152566,"\int \frac{(2-\log (x)) (3+\log (x))^2}{x} \, dx","Integrate[((2 - Log[x])*(3 + Log[x])^2)/x,x]","-\frac{1}{4} \log ^4(x)-\frac{4 \log ^3(x)}{3}+\frac{3 \log ^2(x)}{2}+18 \log (x)","\frac{5}{3} (\log (x)+3)^3-\frac{1}{4} (\log (x)+3)^4",1,"18*Log[x] + (3*Log[x]^2)/2 - (4*Log[x]^3)/3 - Log[x]^4/4","A",1
143,1,31,42,0.0220434,"\int \frac{\log ^2(x) \sqrt{1+\log ^2(x)}}{x} \, dx","Integrate[(Log[x]^2*Sqrt[1 + Log[x]^2])/x,x]","\frac{1}{8} \left(\log (x) \sqrt{\log ^2(x)+1} \left(2 \log ^2(x)+1\right)-\sinh ^{-1}(\log (x))\right)","\frac{1}{8} \sqrt{\log ^2(x)+1} \log (x)+\frac{1}{4} \sqrt{\log ^2(x)+1} \log ^3(x)-\frac{1}{8} \sinh ^{-1}(\log (x))",1,"(-ArcSinh[Log[x]] + Log[x]*Sqrt[1 + Log[x]^2]*(1 + 2*Log[x]^2))/8","A",1
144,1,20,24,0.0409664,"\int \frac{1+\log (x)}{x (3+2 \log (x))^2} \, dx","Integrate[(1 + Log[x])/(x*(3 + 2*Log[x])^2),x]","\frac{1}{4} \left(\log (2 \log (x)+3)+\frac{1}{2 \log (x)+3}\right)","\frac{1}{4} \log (2 \log (x)+3)+\frac{1}{4 (2 \log (x)+3)}",1,"((3 + 2*Log[x])^(-1) + Log[3 + 2*Log[x]])/4","A",1
145,1,16,23,0.0179397,"\int \frac{\log (x)}{x \sqrt{1+\log (x)}} \, dx","Integrate[Log[x]/(x*Sqrt[1 + Log[x]]),x]","\frac{2}{3} (\log (x)-2) \sqrt{\log (x)+1}","\frac{2}{3} (\log (x)+1)^{3/2}-2 \sqrt{\log (x)+1}",1,"(2*(-2 + Log[x])*Sqrt[1 + Log[x]])/3","A",1
146,1,20,29,0.0219458,"\int \frac{\log (x)}{x \sqrt{-1+4 \log (x)}} \, dx","Integrate[Log[x]/(x*Sqrt[-1 + 4*Log[x]]),x]","\frac{1}{12} (2 \log (x)+1) \sqrt{4 \log (x)-1}","\frac{1}{24} (4 \log (x)-1)^{3/2}+\frac{1}{8} \sqrt{4 \log (x)-1}",1,"((1 + 2*Log[x])*Sqrt[-1 + 4*Log[x]])/12","A",1
147,1,22,22,0.0198921,"\int \frac{\sqrt{1+\log (x)}}{x \log (x)} \, dx","Integrate[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",1
148,1,22,27,0.0443834,"\int \frac{1-4 \log (x)+\log ^2(x)}{x (-1+\log (x))^4} \, dx","Integrate[(1 - 4*Log[x] + Log[x]^2)/(x*(-1 + Log[x])^4),x]","\frac{-3 \log ^2(x)+9 \log (x)-4}{3 (\log (x)-1)^3}","\frac{1}{(\log (x)-1)^2}+\frac{1}{1-\log (x)}-\frac{2}{3 (1-\log (x))^3}",1,"(-4 + 9*Log[x] - 3*Log[x]^2)/(3*(-1 + Log[x])^3)","A",1
149,1,27,27,0.011663,"\int \frac{\log ^2\left(a x^n\right)^p}{x} \, dx","Integrate[(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",1
150,1,27,27,0.0061581,"\int \frac{\log ^m\left(a x^n\right)^p}{x} \, dx","Integrate[(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",1
151,1,25,25,0.0081928,"\int \frac{\sqrt{\log ^2\left(a x^n\right)}}{x} \, dx","Integrate[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",1
152,1,29,29,0.0062191,"\int \frac{\left(b \log ^m\left(a x^n\right)\right)^p}{x} \, dx","Integrate[(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",1
153,1,21,31,0.0091499,"\int \frac{1}{x \log \left(e^x\right)} \, dx","Integrate[1/(x*Log[E^x]),x]","\frac{\log \left(\log \left(e^x\right)\right)-\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] + Log[Log[E^x]])/(x - Log[E^x])","A",1
154,1,30,35,0.0518811,"\int \log (x) \sin (a+b x) \, dx","Integrate[Log[x]*Sin[a + b*x],x]","\frac{\cos (a) \text{Ci}(b x)-\sin (a) \text{Si}(b x)-\log (x) \cos (a+b x)}{b}","\frac{\cos (a) \text{Ci}(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] - Cos[a + b*x]*Log[x] - Sin[a]*SinIntegral[b*x])/b","A",1
155,1,50,66,0.0862855,"\int \log (x) \sin ^2(a+b x) \, dx","Integrate[Log[x]*Sin[a + b*x]^2,x]","\frac{\sin (2 a) \text{Ci}(2 b x)+\cos (2 a) \text{Si}(2 b x)-\log (x) \sin (2 (a+b x))-2 b x+2 b x \log (x)}{4 b}","\frac{\sin (2 a) \text{Ci}(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,"(-2*b*x + 2*b*x*Log[x] + CosIntegral[2*b*x]*Sin[2*a] - Log[x]*Sin[2*(a + b*x)] + Cos[2*a]*SinIntegral[2*b*x])/(4*b)","A",1
156,1,66,89,0.1175944,"\int \log (x) \sin ^3(a+b x) \, dx","Integrate[Log[x]*Sin[a + b*x]^3,x]","\frac{9 \cos (a) \text{Ci}(b x)-\cos (3 a) \text{Ci}(3 b x)-9 \sin (a) \text{Si}(b x)+\sin (3 a) \text{Si}(3 b x)-9 \log (x) \cos (a+b x)+\log (x) \cos (3 (a+b x))}{12 b}","\frac{3 \cos (a) \text{Ci}(b x)}{4 b}-\frac{\cos (3 a) \text{Ci}(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,"(9*Cos[a]*CosIntegral[b*x] - Cos[3*a]*CosIntegral[3*b*x] - 9*Cos[a + b*x]*Log[x] + Cos[3*(a + b*x)]*Log[x] - 9*Sin[a]*SinIntegral[b*x] + Sin[3*a]*SinIntegral[3*b*x])/(12*b)","A",1
157,1,30,35,0.0485924,"\int \cos (a+b x) \log (x) \, dx","Integrate[Cos[a + b*x]*Log[x],x]","-\frac{\sin (a) \text{Ci}(b x)+\cos (a) \text{Si}(b x)-\log (x) \sin (a+b x)}{b}","-\frac{\sin (a) \text{Ci}(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] - Log[x]*Sin[a + b*x] + Cos[a]*SinIntegral[b*x])/b)","A",1
158,1,50,66,0.1137719,"\int \cos ^2(a+b x) \log (x) \, dx","Integrate[Cos[a + b*x]^2*Log[x],x]","-\frac{\sin (2 a) \text{Ci}(2 b x)+\cos (2 a) \text{Si}(2 b x)-\log (x) \sin (2 (a+b x))+2 b x-2 b x \log (x)}{4 b}","-\frac{\sin (2 a) \text{Ci}(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,"-1/4*(2*b*x - 2*b*x*Log[x] + CosIntegral[2*b*x]*Sin[2*a] - Log[x]*Sin[2*(a + b*x)] + Cos[2*a]*SinIntegral[2*b*x])/b","A",1
159,1,66,88,0.1599589,"\int \cos ^3(a+b x) \log (x) \, dx","Integrate[Cos[a + b*x]^3*Log[x],x]","-\frac{9 \sin (a) \text{Ci}(b x)+\sin (3 a) \text{Ci}(3 b x)+9 \cos (a) \text{Si}(b x)+\cos (3 a) \text{Si}(3 b x)-9 \log (x) \sin (a+b x)-\log (x) \sin (3 (a+b x))}{12 b}","-\frac{3 \sin (a) \text{Ci}(b x)}{4 b}-\frac{\sin (3 a) \text{Ci}(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,"-1/12*(9*CosIntegral[b*x]*Sin[a] + CosIntegral[3*b*x]*Sin[3*a] - 9*Log[x]*Sin[a + b*x] - Log[x]*Sin[3*(a + b*x)] + 9*Cos[a]*SinIntegral[b*x] + Cos[3*a]*SinIntegral[3*b*x])/b","A",1
160,1,5,5,0.02415,"\int \left(\cos (x) \log (x)+\frac{\sin (x)}{x}\right) \, dx","Integrate[Cos[x]*Log[x] + Sin[x]/x,x]","\log (x) \sin (x)","\log (x) \sin (x)",1,"Log[x]*Sin[x]","A",1
161,1,42,47,0.0175621,"\int \log (a \sin (x)) \, dx","Integrate[Log[a*Sin[x]],x]","x \log (a \sin (x))+\frac{1}{2} i \left(x^2+\text{Li}_2\left(e^{2 i x}\right)\right)-x \log \left(1-e^{2 i x}\right)","x \log (a \sin (x))+\frac{1}{2} i \text{Li}_2\left(e^{2 i x}\right)+\frac{i x^2}{2}-x \log \left(1-e^{2 i x}\right)",1,"-(x*Log[1 - E^((2*I)*x)]) + x*Log[a*Sin[x]] + (I/2)*(x^2 + PolyLog[2, E^((2*I)*x)])","A",1
162,1,43,45,0.0183006,"\int \log \left(a \sin ^2(x)\right) \, dx","Integrate[Log[a*Sin[x]^2],x]","x \left(\log \left(a \sin ^2(x)\right)+i x-2 \log \left(1-e^{2 i x}\right)\right)+i \text{Li}_2\left(e^{2 i x}\right)","x \log \left(a \sin ^2(x)\right)+i \text{Li}_2\left(e^{2 i x}\right)+i x^2-2 x \log \left(1-e^{2 i x}\right)",1,"x*(I*x - 2*Log[1 - E^((2*I)*x)] + Log[a*Sin[x]^2]) + I*PolyLog[2, E^((2*I)*x)]","A",1
163,1,52,52,0.0254585,"\int \log \left(a \sin ^n(x)\right) \, dx","Integrate[Log[a*Sin[x]^n],x]","x \log \left(a \sin ^n(x)\right)+\frac{1}{2} i n \text{Li}_2\left(e^{2 i x}\right)+\frac{1}{2} i n x^2-n x \log \left(1-e^{2 i x}\right)","x \log \left(a \sin ^n(x)\right)+\frac{1}{2} i n \text{Li}_2\left(e^{2 i 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",1
164,1,47,47,0.0081096,"\int \log (a \cos (x)) \, dx","Integrate[Log[a*Cos[x]],x]","x \log (a \cos (x))+\frac{1}{2} i \text{Li}_2\left(-e^{2 i x}\right)+\frac{i x^2}{2}-x \log \left(1+e^{2 i x}\right)","x \log (a \cos (x))+\frac{1}{2} i \text{Li}_2\left(-e^{2 i x}\right)+\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",1
165,1,43,45,0.0220257,"\int \log \left(a \cos ^2(x)\right) \, dx","Integrate[Log[a*Cos[x]^2],x]","x \left(\log \left(a \cos ^2(x)\right)+i x-2 \log \left(1+e^{2 i x}\right)\right)+i \text{Li}_2\left(-e^{2 i x}\right)","x \log \left(a \cos ^2(x)\right)+i \text{Li}_2\left(-e^{2 i x}\right)+i x^2-2 x \log \left(1+e^{2 i x}\right)",1,"x*(I*x - 2*Log[1 + E^((2*I)*x)] + Log[a*Cos[x]^2]) + I*PolyLog[2, -E^((2*I)*x)]","A",1
166,1,52,52,0.0244111,"\int \log \left(a \cos ^n(x)\right) \, dx","Integrate[Log[a*Cos[x]^n],x]","x \log \left(a \cos ^n(x)\right)+\frac{1}{2} i n \text{Li}_2\left(-e^{2 i x}\right)+\frac{1}{2} i n x^2-n x \log \left(1+e^{2 i x}\right)","x \log \left(a \cos ^n(x)\right)+\frac{1}{2} i n \text{Li}_2\left(-e^{2 i 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",1
167,1,75,51,0.0108298,"\int \log (a \tan (x)) \, dx","Integrate[Log[a*Tan[x]],x]","-\frac{1}{2} i \log (-i (-\tan (x)+i)) \log (a \tan (x))+\frac{1}{2} i \log (-i (\tan (x)+i)) \log (a \tan (x))-\frac{1}{2} i \text{Li}_2(-i \tan (x))+\frac{1}{2} i \text{Li}_2(i \tan (x))","x \log (a \tan (x))-\frac{1}{2} i \text{Li}_2\left(-e^{2 i x}\right)+\frac{1}{2} i \text{Li}_2\left(e^{2 i x}\right)+2 x \tanh ^{-1}\left(e^{2 i x}\right)",1,"(-1/2*I)*Log[(-I)*(I - Tan[x])]*Log[a*Tan[x]] + (I/2)*Log[a*Tan[x]]*Log[(-I)*(I + Tan[x])] - (I/2)*PolyLog[2, (-I)*Tan[x]] + (I/2)*PolyLog[2, I*Tan[x]]","A",1
168,1,75,49,0.0117977,"\int \log \left(a \tan ^2(x)\right) \, dx","Integrate[Log[a*Tan[x]^2],x]","-\frac{1}{2} i \log (-i (-\tan (x)+i)) \log \left(a \tan ^2(x)\right)+\frac{1}{2} i \log (-i (\tan (x)+i)) \log \left(a \tan ^2(x)\right)-i \text{Li}_2(-i \tan (x))+i \text{Li}_2(i \tan (x))","x \log \left(a \tan ^2(x)\right)-i \text{Li}_2\left(-e^{2 i x}\right)+i \text{Li}_2\left(e^{2 i x}\right)+4 x \tanh ^{-1}\left(e^{2 i x}\right)",1,"(-1/2*I)*Log[(-I)*(I - Tan[x])]*Log[a*Tan[x]^2] + (I/2)*Log[a*Tan[x]^2]*Log[(-I)*(I + Tan[x])] - I*PolyLog[2, (-I)*Tan[x]] + I*PolyLog[2, I*Tan[x]]","A",1
169,1,81,56,0.0123512,"\int \log \left(a \tan ^n(x)\right) \, dx","Integrate[Log[a*Tan[x]^n],x]","-\frac{1}{2} i \log (-i (-\tan (x)+i)) \log \left(a \tan ^n(x)\right)+\frac{1}{2} i \log (-i (\tan (x)+i)) \log \left(a \tan ^n(x)\right)-\frac{1}{2} i n \text{Li}_2(-i \tan (x))+\frac{1}{2} i n \text{Li}_2(i \tan (x))","x \log \left(a \tan ^n(x)\right)-\frac{1}{2} i n \text{Li}_2\left(-e^{2 i x}\right)+\frac{1}{2} i n \text{Li}_2\left(e^{2 i x}\right)+2 n x \tanh ^{-1}\left(e^{2 i x}\right)",1,"(-1/2*I)*Log[(-I)*(I - Tan[x])]*Log[a*Tan[x]^n] + (I/2)*Log[a*Tan[x]^n]*Log[(-I)*(I + Tan[x])] - (I/2)*n*PolyLog[2, (-I)*Tan[x]] + (I/2)*n*PolyLog[2, I*Tan[x]]","A",1
170,1,75,51,0.011153,"\int \log (a \cot (x)) \, dx","Integrate[Log[a*Cot[x]],x]","\frac{1}{2} i \log (-i (-\cot (x)+i)) \log (a \cot (x))-\frac{1}{2} i \log (-i (\cot (x)+i)) \log (a \cot (x))+\frac{1}{2} i \text{Li}_2(-i \cot (x))-\frac{1}{2} i \text{Li}_2(i \cot (x))","x \log (a \cot (x))+\frac{1}{2} i \text{Li}_2\left(-e^{2 i x}\right)-\frac{1}{2} i \text{Li}_2\left(e^{2 i x}\right)-2 x \tanh ^{-1}\left(e^{2 i x}\right)",1,"(I/2)*Log[(-I)*(I - Cot[x])]*Log[a*Cot[x]] - (I/2)*Log[a*Cot[x]]*Log[(-I)*(I + Cot[x])] + (I/2)*PolyLog[2, (-I)*Cot[x]] - (I/2)*PolyLog[2, I*Cot[x]]","A",1
171,1,75,49,0.012414,"\int \log \left(a \cot ^2(x)\right) \, dx","Integrate[Log[a*Cot[x]^2],x]","-\frac{1}{2} i \log (-i (-\tan (x)+i)) \log \left(a \cot ^2(x)\right)+\frac{1}{2} i \log (-i (\tan (x)+i)) \log \left(a \cot ^2(x)\right)+i \text{Li}_2(-i \tan (x))-i \text{Li}_2(i \tan (x))","x \log \left(a \cot ^2(x)\right)+i \text{Li}_2\left(-e^{2 i x}\right)-i \text{Li}_2\left(e^{2 i x}\right)-4 x \tanh ^{-1}\left(e^{2 i x}\right)",1,"(-1/2*I)*Log[a*Cot[x]^2]*Log[(-I)*(I - Tan[x])] + (I/2)*Log[a*Cot[x]^2]*Log[(-I)*(I + Tan[x])] + I*PolyLog[2, (-I)*Tan[x]] - I*PolyLog[2, I*Tan[x]]","A",1
172,1,81,56,0.0155733,"\int \log \left(a \cot ^n(x)\right) \, dx","Integrate[Log[a*Cot[x]^n],x]","-\frac{1}{2} i \log (-i (-\tan (x)+i)) \log \left(a \cot ^n(x)\right)+\frac{1}{2} i \log (-i (\tan (x)+i)) \log \left(a \cot ^n(x)\right)+\frac{1}{2} i n \text{Li}_2(-i \tan (x))-\frac{1}{2} i n \text{Li}_2(i \tan (x))","x \log \left(a \cot ^n(x)\right)+\frac{1}{2} i n \text{Li}_2\left(-e^{2 i x}\right)-\frac{1}{2} i n \text{Li}_2\left(e^{2 i x}\right)-2 n x \tanh ^{-1}\left(e^{2 i x}\right)",1,"(-1/2*I)*Log[a*Cot[x]^n]*Log[(-I)*(I - Tan[x])] + (I/2)*Log[a*Cot[x]^n]*Log[(-I)*(I + Tan[x])] + (I/2)*n*PolyLog[2, (-I)*Tan[x]] - (I/2)*n*PolyLog[2, I*Tan[x]]","A",1
173,1,46,46,0.0072109,"\int \log (a \sec (x)) \, dx","Integrate[Log[a*Sec[x]],x]","x \log (a \sec (x))-\frac{1}{2} i \text{Li}_2\left(-e^{2 i x}\right)-\frac{i x^2}{2}+x \log \left(1+e^{2 i x}\right)","x \log (a \sec (x))-\frac{1}{2} i \text{Li}_2\left(-e^{2 i x}\right)-\frac{i x^2}{2}+x \log \left(1+e^{2 i x}\right)",1,"(-1/2*I)*x^2 + x*Log[1 + E^((2*I)*x)] + x*Log[a*Sec[x]] - (I/2)*PolyLog[2, -E^((2*I)*x)]","A",1
174,1,43,45,0.0211619,"\int \log \left(a \sec ^2(x)\right) \, dx","Integrate[Log[a*Sec[x]^2],x]","x \left(\log \left(a \sec ^2(x)\right)-i x+2 \log \left(1+e^{2 i x}\right)\right)-i \text{Li}_2\left(-e^{2 i x}\right)","x \log \left(a \sec ^2(x)\right)-i \text{Li}_2\left(-e^{2 i x}\right)-i x^2+2 x \log \left(1+e^{2 i x}\right)",1,"x*((-I)*x + 2*Log[1 + E^((2*I)*x)] + Log[a*Sec[x]^2]) - I*PolyLog[2, -E^((2*I)*x)]","A",1
175,1,51,51,0.0245228,"\int \log \left(a \sec ^n(x)\right) \, dx","Integrate[Log[a*Sec[x]^n],x]","x \log \left(a \sec ^n(x)\right)-\frac{1}{2} i n \text{Li}_2\left(-e^{2 i x}\right)-\frac{1}{2} i n x^2+n x \log \left(1+e^{2 i x}\right)","x \log \left(a \sec ^n(x)\right)-\frac{1}{2} i n \text{Li}_2\left(-e^{2 i x}\right)-\frac{1}{2} i n x^2+n x \log \left(1+e^{2 i x}\right)",1,"(-1/2*I)*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",1
176,1,41,46,0.0125937,"\int \log (a \csc (x)) \, dx","Integrate[Log[a*Csc[x]],x]","x \log (a \csc (x))-\frac{1}{2} i \left(x^2+\text{Li}_2\left(e^{2 i x}\right)\right)+x \log \left(1-e^{2 i x}\right)","x \log (a \csc (x))-\frac{1}{2} i \text{Li}_2\left(e^{2 i x}\right)-\frac{i x^2}{2}+x \log \left(1-e^{2 i x}\right)",1,"x*Log[1 - E^((2*I)*x)] + x*Log[a*Csc[x]] - (I/2)*(x^2 + PolyLog[2, E^((2*I)*x)])","A",1
177,1,42,45,0.0189732,"\int \log \left(a \csc ^2(x)\right) \, dx","Integrate[Log[a*Csc[x]^2],x]","x \log \left(a \csc ^2(x)\right)-i \left(x^2+\text{Li}_2\left(e^{2 i x}\right)\right)+2 x \log \left(1-e^{2 i x}\right)","x \log \left(a \csc ^2(x)\right)-i \text{Li}_2\left(e^{2 i x}\right)-i x^2+2 x \log \left(1-e^{2 i x}\right)",1,"2*x*Log[1 - E^((2*I)*x)] + x*Log[a*Csc[x]^2] - I*(x^2 + PolyLog[2, E^((2*I)*x)])","A",1
178,1,51,51,0.0228972,"\int \log \left(a \csc ^n(x)\right) \, dx","Integrate[Log[a*Csc[x]^n],x]","x \log \left(a \csc ^n(x)\right)-\frac{1}{2} i n \text{Li}_2\left(e^{2 i x}\right)-\frac{1}{2} i n x^2+n x \log \left(1-e^{2 i x}\right)","x \log \left(a \csc ^n(x)\right)-\frac{1}{2} i n \text{Li}_2\left(e^{2 i x}\right)-\frac{1}{2} i n x^2+n x \log \left(1-e^{2 i x}\right)",1,"(-1/2*I)*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",1
179,1,13,21,0.0045889,"\int \cos (x) \log \left(\frac{1}{2} (1-\cos (2 x))\right) \, dx","Integrate[Cos[x]*Log[(1 - Cos[2*x])/2],x]","\sin (x) \log \left(\sin ^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[Sin[x]^2]*Sin[x]","A",1
180,1,6,6,0.0143656,"\int \frac{\cot (x)}{\log (e \sin (x))} \, dx","Integrate[Cot[x]/Log[E*Sin[x]],x]","\log (\log (\sin (x))+1)","\log (\log (e \sin (x)))",1,"Log[1 + Log[Sin[x]]]","A",1
181,1,25,37,0.0357997,"\int \frac{\cot (x)}{\log \left(e^{\sin (x)}\right)} \, dx","Integrate[Cot[x]/Log[E^Sin[x]],x]","\frac{\log \left(\log \left(e^{\sin (x)}\right)\right)-\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[Sin[x]])/(-Log[E^Sin[x]] + Sin[x])","A",1
182,1,12,12,0.0174358,"\int \log (\cos (x)) \sec ^2(x) \, dx","Integrate[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",1
183,1,9,9,0.0041354,"\int \cot (x) \log (\sin (x)) \, dx","Integrate[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",1
184,1,15,20,0.0152658,"\int \cos (x) \log (\sin (x)) \sin ^2(x) \, dx","Integrate[Cos[x]*Log[Sin[x]]*Sin[x]^2,x]","\frac{1}{9} \sin ^3(x) (3 \log (\sin (x))-1)","\frac{1}{3} \sin ^3(x) \log (\sin (x))-\frac{\sin ^3(x)}{9}",1,"((-1 + 3*Log[Sin[x]])*Sin[x]^3)/9","A",1
185,1,33,50,0.0111787,"\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","Integrate[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(\frac{1}{2} \sin (a+b x)\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[Sin[a + b*x]/2]*Sin[a + b*x])/b","A",1
186,1,6,6,0.0085568,"\int \frac{\tan (x)}{\log (\cos (x))} \, dx","Integrate[Tan[x]/Log[Cos[x]],x]","-\log (\log (\cos (x)))","-\log (\log (\cos (x)))",1,"-Log[Log[Cos[x]]]","A",1
187,1,9,9,0.0033785,"\int \log (\cos (x)) \tan (x) \, dx","Integrate[Log[Cos[x]]*Tan[x],x]","-\frac{1}{2} \log ^2(\cos (x))","-\frac{1}{2} \log ^2(\cos (x))",1,"-1/2*Log[Cos[x]]^2","A",1
188,1,10,10,0.0078672,"\int \log (\cos (x)) \sin (x) \, dx","Integrate[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",1
189,1,43,14,0.0160371,"\int \cos (x) \log (\cos (x)) \, dx","Integrate[Cos[x]*Log[Cos[x]],x]","-\sin (x)-\log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)+\log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)+\sin (x) \log (\cos (x))","-\sin (x)+\tanh ^{-1}(\sin (x))+\sin (x) \log (\cos (x))",1,"-Log[Cos[x/2] - Sin[x/2]] + Log[Cos[x/2] + Sin[x/2]] - Sin[x] + Log[Cos[x]]*Sin[x]","B",1
190,1,11,11,0.0028837,"\int \cos (x) \log (\sin (x)) \, dx","Integrate[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",1
191,1,59,74,0.0583482,"\int \log (\sin (x)) \sin ^2(x) \, dx","Integrate[Log[Sin[x]]*Sin[x]^2,x]","\frac{1}{8} \left(2 i \text{Li}_2\left(e^{2 i x}\right)+2 x \left(i x-2 \log \left(1-e^{2 i x}\right)+2 \log (\sin (x))+1\right)+\sin (2 x) (1-2 \log (\sin (x)))\right)","\frac{1}{4} i \text{Li}_2\left(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,"(2*x*(1 + I*x - 2*Log[1 - E^((2*I)*x)] + 2*Log[Sin[x]]) + (2*I)*PolyLog[2, E^((2*I)*x)] + (1 - 2*Log[Sin[x]])*Sin[2*x])/8","A",1
192,1,47,40,0.0428447,"\int \log (\sin (x)) \sin ^3(x) \, dx","Integrate[Log[Sin[x]]*Sin[x]^3,x]","\frac{1}{36} \left(24 \left(\log \left(\sin \left(\frac{x}{2}\right)\right)-\log \left(\cos \left(\frac{x}{2}\right)\right)\right)+\cos (3 x) (3 \log (\sin (x))-1)-3 \cos (x) (9 \log (\sin (x))-7)\right)","-\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,"(24*(-Log[Cos[x/2]] + Log[Sin[x/2]]) + Cos[3*x]*(-1 + 3*Log[Sin[x]]) - 3*Cos[x]*(-7 + 9*Log[Sin[x]]))/36","A",1
193,1,88,79,0.0325701,"\int \log \left(\sin \left(\sqrt{x}\right)\right) \, dx","Integrate[Log[Sin[Sqrt[x]]],x]","-i \sqrt{x} \text{Li}_2\left(e^{-2 i \sqrt{x}}\right)-\frac{1}{2} \text{Li}_3\left(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)+\frac{i \pi ^3}{24}","i \sqrt{x} \text{Li}_2\left(e^{2 i \sqrt{x}}\right)-\frac{1}{2} \text{Li}_3\left(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/24)*Pi^3 - (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",1
194,1,15,15,0.0152042,"\int \csc ^2(x) \log (\sin (x)) \, dx","Integrate[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",1
195,1,30,35,0.0539035,"\int \log (x) \sinh (a+b x) \, dx","Integrate[Log[x]*Sinh[a + b*x],x]","-\frac{\cosh (a) \text{Chi}(b x)+\sinh (a) \text{Shi}(b x)-\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] - Cosh[a + b*x]*Log[x] + Sinh[a]*SinhIntegral[b*x])/b)","A",1
196,1,50,66,0.1196256,"\int \log (x) \sinh ^2(a+b x) \, dx","Integrate[Log[x]*Sinh[a + b*x]^2,x]","-\frac{\sinh (2 a) \text{Chi}(2 b x)+\cosh (2 a) \text{Shi}(2 b x)-\log (x) \sinh (2 (a+b x))-2 b x+2 b x \log (x)}{4 b}","-\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,"-1/4*(-2*b*x + 2*b*x*Log[x] + CoshIntegral[2*b*x]*Sinh[2*a] - Log[x]*Sinh[2*(a + b*x)] + Cosh[2*a]*SinhIntegral[2*b*x])/b","A",1
197,1,67,89,0.1145021,"\int \log (x) \sinh ^3(a+b x) \, dx","Integrate[Log[x]*Sinh[a + b*x]^3,x]","\frac{9 \cosh (a) \text{Chi}(b x)-\cosh (3 a) \text{Chi}(3 b x)+9 \sinh (a) \text{Shi}(b x)-\sinh (3 a) \text{Shi}(3 b x)-9 \log (x) \cosh (a+b x)+\log (x) \cosh (3 (a+b x))}{12 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,"(9*Cosh[a]*CoshIntegral[b*x] - Cosh[3*a]*CoshIntegral[3*b*x] - 9*Cosh[a + b*x]*Log[x] + Cosh[3*(a + b*x)]*Log[x] + 9*Sinh[a]*SinhIntegral[b*x] - Sinh[3*a]*SinhIntegral[3*b*x])/(12*b)","A",1
198,1,30,35,0.0404991,"\int \cosh (a+b x) \log (x) \, dx","Integrate[Cosh[a + b*x]*Log[x],x]","-\frac{\sinh (a) \text{Chi}(b x)+\cosh (a) \text{Shi}(b x)-\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] - Log[x]*Sinh[a + b*x] + Cosh[a]*SinhIntegral[b*x])/b)","A",1
199,1,50,66,0.0735743,"\int \cosh ^2(a+b x) \log (x) \, dx","Integrate[Cosh[a + b*x]^2*Log[x],x]","-\frac{\sinh (2 a) \text{Chi}(2 b x)+\cosh (2 a) \text{Shi}(2 b x)-\log (x) \sinh (2 (a+b x))+2 b x-2 b x \log (x)}{4 b}","-\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,"-1/4*(2*b*x - 2*b*x*Log[x] + CoshIntegral[2*b*x]*Sinh[2*a] - Log[x]*Sinh[2*(a + b*x)] + Cosh[2*a]*SinhIntegral[2*b*x])/b","A",1
200,1,66,88,0.1436374,"\int \cosh ^3(a+b x) \log (x) \, dx","Integrate[Cosh[a + b*x]^3*Log[x],x]","-\frac{9 \sinh (a) \text{Chi}(b x)+\sinh (3 a) \text{Chi}(3 b x)+9 \cosh (a) \text{Shi}(b x)+\cosh (3 a) \text{Shi}(3 b x)-9 \log (x) \sinh (a+b x)-\log (x) \sinh (3 (a+b x))}{12 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,"-1/12*(9*CoshIntegral[b*x]*Sinh[a] + CoshIntegral[3*b*x]*Sinh[3*a] - 9*Log[x]*Sinh[a + b*x] - Log[x]*Sinh[3*(a + b*x)] + 9*Cosh[a]*SinhIntegral[b*x] + Cosh[3*a]*SinhIntegral[3*b*x])/b","A",1
201,1,36,39,0.0218061,"\int \log (a \sinh (x)) \, dx","Integrate[Log[a*Sinh[x]],x]","\frac{1}{2} \left(\text{Li}_2\left(e^{-2 x}\right)-x \left(-2 \log (a \sinh (x))+x+2 \log \left(1-e^{-2 x}\right)\right)\right)","x \log (a \sinh (x))-\frac{\text{Li}_2\left(e^{2 x}\right)}{2}+\frac{x^2}{2}-x \log \left(1-e^{2 x}\right)",1,"(-(x*(x + 2*Log[1 - E^(-2*x)] - 2*Log[a*Sinh[x]])) + PolyLog[2, E^(-2*x)])/2","A",1
202,1,33,35,0.0183928,"\int \log \left(a \sinh ^2(x)\right) \, dx","Integrate[Log[a*Sinh[x]^2],x]","x \left(\log \left(a \sinh ^2(x)\right)-x-2 \log \left(1-e^{-2 x}\right)\right)+\text{Li}_2\left(e^{-2 x}\right)","x \log \left(a \sinh ^2(x)\right)-\text{Li}_2\left(e^{2 x}\right)+x^2-2 x \log \left(1-e^{2 x}\right)",1,"x*(-x - 2*Log[1 - E^(-2*x)] + Log[a*Sinh[x]^2]) + PolyLog[2, E^(-2*x)]","A",1
203,1,43,44,0.0286982,"\int \log \left(a \sinh ^n(x)\right) \, dx","Integrate[Log[a*Sinh[x]^n],x]","\frac{1}{2} \left(n \text{Li}_2\left(e^{-2 x}\right)-x \left(-2 \log \left(a \sinh ^n(x)\right)+n x+2 n \log \left(1-e^{-2 x}\right)\right)\right)","x \log \left(a \sinh ^n(x)\right)-\frac{1}{2} n \text{Li}_2\left(e^{2 x}\right)+\frac{n x^2}{2}-n x \log \left(1-e^{2 x}\right)",1,"(-(x*(n*x + 2*n*Log[1 - E^(-2*x)] - 2*Log[a*Sinh[x]^n])) + n*PolyLog[2, E^(-2*x)])/2","A",1
204,1,36,39,0.0207506,"\int \log (a \cosh (x)) \, dx","Integrate[Log[a*Cosh[x]],x]","\frac{1}{2} \left(\text{Li}_2\left(-e^{-2 x}\right)-x \left(-2 \log (a \cosh (x))+x+2 \log \left(e^{-2 x}+1\right)\right)\right)","x \log (a \cosh (x))-\frac{1}{2} \text{Li}_2\left(-e^{2 x}\right)+\frac{x^2}{2}-x \log \left(e^{2 x}+1\right)",1,"(-(x*(x + 2*Log[1 + E^(-2*x)] - 2*Log[a*Cosh[x]])) + PolyLog[2, -E^(-2*x)])/2","A",1
205,1,33,35,0.0178032,"\int \log \left(a \cosh ^2(x)\right) \, dx","Integrate[Log[a*Cosh[x]^2],x]","x \left(\log \left(a \cosh ^2(x)\right)-x-2 \log \left(e^{-2 x}+1\right)\right)+\text{Li}_2\left(-e^{-2 x}\right)","x \log \left(a \cosh ^2(x)\right)-\text{Li}_2\left(-e^{2 x}\right)+x^2-2 x \log \left(e^{2 x}+1\right)",1,"x*(-x - 2*Log[1 + E^(-2*x)] + Log[a*Cosh[x]^2]) + PolyLog[2, -E^(-2*x)]","A",1
206,1,43,44,0.0279836,"\int \log \left(a \cosh ^n(x)\right) \, dx","Integrate[Log[a*Cosh[x]^n],x]","\frac{1}{2} \left(n \text{Li}_2\left(-e^{-2 x}\right)-x \left(-2 \log \left(a \cosh ^n(x)\right)+n x+2 n \log \left(e^{-2 x}+1\right)\right)\right)","x \log \left(a \cosh ^n(x)\right)-\frac{1}{2} n \text{Li}_2\left(-e^{2 x}\right)+\frac{n x^2}{2}-n x \log \left(e^{2 x}+1\right)",1,"(-(x*(n*x + 2*n*Log[1 + E^(-2*x)] - 2*Log[a*Cosh[x]^n])) + n*PolyLog[2, -E^(-2*x)])/2","A",1
207,1,35,39,0.0074666,"\int \log (\tanh (x)) \, dx","Integrate[Log[Tanh[x]],x]","\frac{1}{2} \text{Li}_2(1-\tanh (x))+\frac{1}{2} \text{Li}_2(-\tanh (x))+\frac{1}{2} \log (\tanh (x)) \log (\tanh (x)+1)","\frac{1}{2} \text{Li}_2\left(-e^{2 x}\right)-\frac{\text{Li}_2\left(e^{2 x}\right)}{2}+2 x \tanh ^{-1}\left(e^{2 x}\right)+x \log (\tanh (x))",1,"(Log[Tanh[x]]*Log[1 + Tanh[x]])/2 + PolyLog[2, 1 - Tanh[x]]/2 + PolyLog[2, -Tanh[x]]/2","A",1
208,1,49,41,0.008426,"\int \log (a \tanh (x)) \, dx","Integrate[Log[a*Tanh[x]],x]","-\frac{1}{2} \log (1-\tanh (x)) \log (a \tanh (x))+\frac{1}{2} \log (\tanh (x)+1) \log (a \tanh (x))+\frac{1}{2} \text{Li}_2(-\tanh (x))-\frac{\text{Li}_2(\tanh (x))}{2}","x \log (a \tanh (x))+\frac{1}{2} \text{Li}_2\left(-e^{2 x}\right)-\frac{\text{Li}_2\left(e^{2 x}\right)}{2}+2 x \tanh ^{-1}\left(e^{2 x}\right)",1,"-1/2*(Log[1 - Tanh[x]]*Log[a*Tanh[x]]) + (Log[a*Tanh[x]]*Log[1 + Tanh[x]])/2 + PolyLog[2, -Tanh[x]]/2 - PolyLog[2, Tanh[x]]/2","A",1
209,1,47,37,0.0105213,"\int \log \left(a \tanh ^2(x)\right) \, dx","Integrate[Log[a*Tanh[x]^2],x]","-\frac{1}{2} \log (1-\tanh (x)) \log \left(a \tanh ^2(x)\right)+\frac{1}{2} \log (\tanh (x)+1) \log \left(a \tanh ^2(x)\right)+\text{Li}_2(-\tanh (x))-\text{Li}_2(\tanh (x))","x \log \left(a \tanh ^2(x)\right)+\text{Li}_2\left(-e^{2 x}\right)-\text{Li}_2\left(e^{2 x}\right)+4 x \tanh ^{-1}\left(e^{2 x}\right)",1,"-1/2*(Log[1 - Tanh[x]]*Log[a*Tanh[x]^2]) + (Log[a*Tanh[x]^2]*Log[1 + Tanh[x]])/2 + PolyLog[2, -Tanh[x]] - PolyLog[2, Tanh[x]]","A",1
210,1,55,46,0.0111858,"\int \log \left(a \tanh ^n(x)\right) \, dx","Integrate[Log[a*Tanh[x]^n],x]","-\frac{1}{2} \log (1-\tanh (x)) \log \left(a \tanh ^n(x)\right)+\frac{1}{2} \log (\tanh (x)+1) \log \left(a \tanh ^n(x)\right)+\frac{1}{2} n \text{Li}_2(-\tanh (x))-\frac{1}{2} n \text{Li}_2(\tanh (x))","x \log \left(a \tanh ^n(x)\right)+\frac{1}{2} n \text{Li}_2\left(-e^{2 x}\right)-\frac{1}{2} n \text{Li}_2\left(e^{2 x}\right)+2 n x \tanh ^{-1}\left(e^{2 x}\right)",1,"-1/2*(Log[1 - Tanh[x]]*Log[a*Tanh[x]^n]) + (Log[a*Tanh[x]^n]*Log[1 + Tanh[x]])/2 + (n*PolyLog[2, -Tanh[x]])/2 - (n*PolyLog[2, Tanh[x]])/2","A",1
211,1,35,39,0.0069942,"\int \log (\coth (x)) \, dx","Integrate[Log[Coth[x]],x]","\frac{1}{2} \text{Li}_2(1-\coth (x))+\frac{1}{2} \text{Li}_2(-\coth (x))+\frac{1}{2} \log (\coth (x)) \log (\coth (x)+1)","-\frac{1}{2} \text{Li}_2\left(-e^{2 x}\right)+\frac{\text{Li}_2\left(e^{2 x}\right)}{2}-2 x \tanh ^{-1}\left(e^{2 x}\right)+x \log (\coth (x))",1,"(Log[Coth[x]]*Log[1 + Coth[x]])/2 + PolyLog[2, 1 - Coth[x]]/2 + PolyLog[2, -Coth[x]]/2","A",1
212,1,49,41,0.0081311,"\int \log (a \coth (x)) \, dx","Integrate[Log[a*Coth[x]],x]","-\frac{1}{2} \log (1-\coth (x)) \log (a \coth (x))+\frac{1}{2} \log (\coth (x)+1) \log (a \coth (x))+\frac{1}{2} \text{Li}_2(-\coth (x))-\frac{\text{Li}_2(\coth (x))}{2}","x \log (a \coth (x))-\frac{1}{2} \text{Li}_2\left(-e^{2 x}\right)+\frac{\text{Li}_2\left(e^{2 x}\right)}{2}-2 x \tanh ^{-1}\left(e^{2 x}\right)",1,"-1/2*(Log[1 - Coth[x]]*Log[a*Coth[x]]) + (Log[a*Coth[x]]*Log[1 + Coth[x]])/2 + PolyLog[2, -Coth[x]]/2 - PolyLog[2, Coth[x]]/2","A",1
213,1,47,37,0.0104559,"\int \log \left(a \coth ^2(x)\right) \, dx","Integrate[Log[a*Coth[x]^2],x]","-\frac{1}{2} \log (1-\tanh (x)) \log \left(a \coth ^2(x)\right)+\frac{1}{2} \log (\tanh (x)+1) \log \left(a \coth ^2(x)\right)-\text{Li}_2(-\tanh (x))+\text{Li}_2(\tanh (x))","x \log \left(a \coth ^2(x)\right)-\text{Li}_2\left(-e^{2 x}\right)+\text{Li}_2\left(e^{2 x}\right)-4 x \tanh ^{-1}\left(e^{2 x}\right)",1,"-1/2*(Log[a*Coth[x]^2]*Log[1 - Tanh[x]]) + (Log[a*Coth[x]^2]*Log[1 + Tanh[x]])/2 - PolyLog[2, -Tanh[x]] + PolyLog[2, Tanh[x]]","A",1
214,1,55,46,0.0119535,"\int \log \left(a \coth ^n(x)\right) \, dx","Integrate[Log[a*Coth[x]^n],x]","-\frac{1}{2} \log (1-\tanh (x)) \log \left(a \coth ^n(x)\right)+\frac{1}{2} \log (\tanh (x)+1) \log \left(a \coth ^n(x)\right)-\frac{1}{2} n \text{Li}_2(-\tanh (x))+\frac{1}{2} n \text{Li}_2(\tanh (x))","x \log \left(a \coth ^n(x)\right)-\frac{1}{2} n \text{Li}_2\left(-e^{2 x}\right)+\frac{1}{2} n \text{Li}_2\left(e^{2 x}\right)-2 n x \tanh ^{-1}\left(e^{2 x}\right)",1,"-1/2*(Log[a*Coth[x]^n]*Log[1 - Tanh[x]]) + (Log[a*Coth[x]^n]*Log[1 + Tanh[x]])/2 - (n*PolyLog[2, -Tanh[x]])/2 + (n*PolyLog[2, Tanh[x]])/2","A",1
215,1,37,38,0.0157892,"\int \log (a \text{sech}(x)) \, dx","Integrate[Log[a*Sech[x]],x]","\frac{1}{2} \left(x \left(2 \log (a \text{sech}(x))+x+2 \log \left(e^{-2 x}+1\right)\right)-\text{Li}_2\left(-e^{-2 x}\right)\right)","x \log (a \text{sech}(x))+\frac{1}{2} \text{Li}_2\left(-e^{2 x}\right)-\frac{x^2}{2}+x \log \left(e^{2 x}+1\right)",1,"(x*(x + 2*Log[1 + E^(-2*x)] + 2*Log[a*Sech[x]]) - PolyLog[2, -E^(-2*x)])/2","A",1
216,1,33,35,0.0180817,"\int \log \left(a \text{sech}^2(x)\right) \, dx","Integrate[Log[a*Sech[x]^2],x]","x \left(\log \left(a \text{sech}^2(x)\right)+x+2 \log \left(e^{-2 x}+1\right)\right)-\text{Li}_2\left(-e^{-2 x}\right)","x \log \left(a \text{sech}^2(x)\right)+\text{Li}_2\left(-e^{2 x}\right)-x^2+2 x \log \left(e^{2 x}+1\right)",1,"x*(x + 2*Log[1 + E^(-2*x)] + Log[a*Sech[x]^2]) - PolyLog[2, -E^(-2*x)]","A",1
217,1,43,43,0.022605,"\int \log \left(a \text{sech}^n(x)\right) \, dx","Integrate[Log[a*Sech[x]^n],x]","x \log \left(a \text{sech}^n(x)\right)-\frac{1}{2} n \text{Li}_2\left(-e^{-2 x}\right)+\frac{n x^2}{2}+n x \log \left(e^{-2 x}+1\right)","x \log \left(a \text{sech}^n(x)\right)+\frac{1}{2} n \text{Li}_2\left(-e^{2 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",1
218,1,37,38,0.0164869,"\int \log (a \text{csch}(x)) \, dx","Integrate[Log[a*Csch[x]],x]","\frac{1}{2} \left(x \left(2 \log (a \text{csch}(x))+x+2 \log \left(1-e^{-2 x}\right)\right)-\text{Li}_2\left(e^{-2 x}\right)\right)","x \log (a \text{csch}(x))+\frac{\text{Li}_2\left(e^{2 x}\right)}{2}-\frac{x^2}{2}+x \log \left(1-e^{2 x}\right)",1,"(x*(x + 2*Log[1 - E^(-2*x)] + 2*Log[a*Csch[x]]) - PolyLog[2, E^(-2*x)])/2","A",1
219,1,33,35,0.017985,"\int \log \left(a \text{csch}^2(x)\right) \, dx","Integrate[Log[a*Csch[x]^2],x]","x \left(\log \left(a \text{csch}^2(x)\right)+x+2 \log \left(1-e^{-2 x}\right)\right)-\text{Li}_2\left(e^{-2 x}\right)","x \log \left(a \text{csch}^2(x)\right)+\text{Li}_2\left(e^{2 x}\right)-x^2+2 x \log \left(1-e^{2 x}\right)",1,"x*(x + 2*Log[1 - E^(-2*x)] + Log[a*Csch[x]^2]) - PolyLog[2, E^(-2*x)]","A",1
220,1,43,43,0.0232354,"\int \log \left(a \text{csch}^n(x)\right) \, dx","Integrate[Log[a*Csch[x]^n],x]","x \log \left(a \text{csch}^n(x)\right)-\frac{1}{2} n \text{Li}_2\left(e^{-2 x}\right)+\frac{n x^2}{2}+n x \log \left(1-e^{-2 x}\right)","x \log \left(a \text{csch}^n(x)\right)+\frac{1}{2} n \text{Li}_2\left(e^{2 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",1
221,1,33,50,0.0108949,"\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","Integrate[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(\frac{1}{2} \sinh (a+b x)\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[Sinh[a + b*x]/2]*Sinh[a + b*x])/b","A",1
222,1,13,13,0.0086279,"\int \log \left(\cosh ^2(x)\right) \sinh (x) \, dx","Integrate[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",1
223,1,11,17,0.001932,"\int \frac{\log (x)}{\sqrt{x}} \, dx","Integrate[Log[x]/Sqrt[x],x]","2 \sqrt{x} (\log (x)-2)","2 \sqrt{x} \log (x)-4 \sqrt{x}",1,"2*Sqrt[x]*(-2 + Log[x])","A",1
224,1,26,27,0.0041018,"\int x \log \left(2-3 x^2\right) \, dx","Integrate[x*Log[2 - 3*x^2],x]","\frac{1}{6} \left(\left(3 x^2-2\right) \log \left(2-3 x^2\right)-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,"(-3*x^2 + (-2 + 3*x^2)*Log[2 - 3*x^2])/6","A",1
225,1,3,3,0.0186434,"\int \frac{1}{x \sqrt{1-\log ^2(x)}} \, dx","Integrate[1/(x*Sqrt[1 - Log[x]^2]),x]","\sin ^{-1}(\log (x))","\sin ^{-1}(\log (x))",1,"ArcSin[Log[x]]","A",1
226,1,30,24,0.0014241,"\int 16 x^3 \log ^2(x) \, dx","Integrate[16*x^3*Log[x]^2,x]","16 \left(\frac{x^4}{32}+\frac{1}{4} x^4 \log ^2(x)-\frac{1}{8} x^4 \log (x)\right)","\frac{x^4}{2}+4 x^4 \log ^2(x)-2 x^4 \log (x)",1,"16*(x^4/32 - (x^4*Log[x])/8 + (x^4*Log[x]^2)/4)","A",1
227,1,23,25,0.0049328,"\int \log \left(\sqrt{a+b x}\right) \, dx","Integrate[Log[Sqrt[a + b*x]],x]","\frac{1}{2} \left(\frac{(a+b x) \log (a+b x)}{b}-x\right)","\frac{(a+b x) \log \left(\sqrt{a+b x}\right)}{b}-\frac{x}{2}",1,"(-x + ((a + b*x)*Log[a + b*x])/b)/2","A",1
228,1,30,34,0.0065429,"\int x \log \left(\sqrt{2+x}\right) \, dx","Integrate[x*Log[Sqrt[2 + x]],x]","\frac{1}{2} \left(-\frac{x^2}{4}+\frac{1}{2} x^2 \log (x+2)+x-2 \log (x+2)\right)","-\frac{x^2}{8}+\frac{1}{2} x^2 \log \left(\sqrt{x+2}\right)+\frac{x}{2}-\log (x+2)",1,"(x - x^2/4 - 2*Log[2 + x] + (x^2*Log[2 + x])/2)/2","A",1
229,1,40,40,0.0085632,"\int x \log \left(\sqrt[3]{1+3 x}\right) \, dx","Integrate[x*Log[(1 + 3*x)^(1/3)],x]","\frac{1}{3} \left(-\frac{x^2}{4}+\frac{1}{2} x^2 \log (3 x+1)+\frac{x}{6}-\frac{1}{18} \log (3 x+1)\right)","-\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/6 - x^2/4 - Log[1 + 3*x]/18 + (x^2*Log[1 + 3*x])/2)/3","A",1
230,1,31,31,0.0080528,"\int x \log \left(x+x^3\right) \, dx","Integrate[x*Log[x + x^3],x]","-\frac{3 x^2}{4}+\frac{1}{2} \log \left(x^2+1\right)+\frac{1}{2} x^2 \log \left(x^3+x\right)","-\frac{3 x^2}{4}+\frac{1}{2} \log \left(x^2+1\right)+\frac{1}{2} x^2 \log \left(x^3+x\right)",1,"(-3*x^2)/4 + Log[1 + x^2]/2 + (x^2*Log[x + x^3])/2","A",1
231,1,26,26,0.0167082,"\int \log \left(x+\sqrt{1+x^2}\right) \, dx","Integrate[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",1
232,1,26,26,0.0166288,"\int \log \left(x+\sqrt{-1+x^2}\right) \, dx","Integrate[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",1
233,1,26,26,0.0179209,"\int \log \left(x-\sqrt{-1+x^2}\right) \, dx","Integrate[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",1
234,1,43,43,0.0241412,"\int \log \left(\sqrt{x}+\sqrt{1+x}\right) \, dx","Integrate[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,"-1/2*(Sqrt[x]*Sqrt[1 + x]) + ArcSinh[Sqrt[x]]/2 + x*Log[Sqrt[x] + Sqrt[1 + x]]","A",1
235,1,15,21,0.0025687,"\int \sqrt[3]{x} \log (x) \, dx","Integrate[x^(1/3)*Log[x],x]","\frac{3}{16} x^{4/3} (4 \log (x)-3)","\frac{3}{4} x^{4/3} \log (x)-\frac{9 x^{4/3}}{16}",1,"(3*x^(4/3)*(-3 + 4*Log[x]))/16","A",1
236,1,12,13,0.0028276,"\int 2^{\log (x)} \, dx","Integrate[2^Log[x],x]","\frac{x 2^{\log (x)}}{1+\log (2)}","\frac{x^{1+\log (2)}}{1+\log (2)}",1,"(2^Log[x]*x)/(1 + Log[2])","A",1
237,1,6,6,0.0013763,"\int \frac{1-\log (x)}{x^2} \, dx","Integrate[(1 - Log[x])/x^2,x]","\frac{\log (x)}{x}","\frac{\log (x)}{x}",1,"Log[x]/x","A",1
238,1,38,32,0.0152158,"\int \log \left(1+x+\sqrt{1+x}\right) \, dx","Integrate[Log[1 + x + Sqrt[1 + x]],x]","-x+\sqrt{x+1}-\log \left(\sqrt{x+1}+1\right)+(x+1) \log \left(x+\sqrt{x+1}+1\right)","-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 + Sqrt[1 + x]] + (1 + x)*Log[1 + x + Sqrt[1 + x]]","A",1
239,1,16,16,0.0026011,"\int \log \left(x+x^3\right) \, dx","Integrate[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",1
240,1,20,20,0.0070672,"\int 2^{\log (-8+7 x)} \, dx","Integrate[2^Log[-8 + 7*x],x]","\frac{(7 x-8) 2^{\log (7 x-8)}}{7+\log (128)}","\frac{(7 x-8)^{1+\log (2)}}{7 (1+\log (2))}",1,"(2^Log[-8 + 7*x]*(-8 + 7*x))/(7 + Log[128])","A",1
241,1,31,35,0.00532,"\int \log \left(\frac{-11+5 x}{5+76 x}\right) \, dx","Integrate[Log[(-11 + 5*x)/(5 + 76*x)],x]","\left(x-\frac{11}{5}\right) \log \left(\frac{5 x-11}{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)] - (861*Log[5 + 76*x])/380","A",1
242,1,12,12,0.002278,"\int \log \left(\frac{1}{13+x}\right) \, dx","Integrate[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",1
243,1,27,36,0.0096596,"\int x \log \left(\frac{1+x}{x^2}\right) \, dx","Integrate[x*Log[(1 + x)/x^2],x]","\frac{1}{4} \left(x \left(2 x \log \left(\frac{x+1}{x^2}\right)+x+2\right)-2 \log (x+1)\right)","\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,"(-2*Log[1 + x] + x*(2 + x + 2*x*Log[(1 + x)/x^2]))/4","A",1
244,1,54,54,0.0147158,"\int x^3 \log \left(\frac{7+5 x}{x^2}\right) \, dx","Integrate[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",1
245,1,33,35,0.0211828,"\int (a+b x) \log (a+b x) \, dx","Integrate[(a + b*x)*Log[a + b*x],x]","\frac{(a+b x)^2 \log (a+b x)}{2 b}-\frac{1}{4} x (2 a+b x)","\frac{(a+b x)^2 \log (a+b x)}{2 b}-\frac{(a+b x)^2}{4 b}",1,"-1/4*(x*(2*a + b*x)) + ((a + b*x)^2*Log[a + b*x])/(2*b)","A",1
246,1,44,35,0.017153,"\int (a+b x)^2 \log (a+b x) \, dx","Integrate[(a + b*x)^2*Log[a + b*x],x]","\frac{(a+b x)^3 \log (a+b x)}{3 b}-\frac{1}{9} x \left(3 a^2+3 a b x+b^2 x^2\right)","\frac{(a+b x)^3 \log (a+b x)}{3 b}-\frac{(a+b x)^3}{9 b}",1,"-1/9*(x*(3*a^2 + 3*a*b*x + b^2*x^2)) + ((a + b*x)^3*Log[a + b*x])/(3*b)","A",1
247,1,15,15,0.0015171,"\int \frac{\log (a+b x)}{a+b x} \, dx","Integrate[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",1
248,1,21,31,0.0064822,"\int \frac{\log (a+b x)}{(a+b x)^2} \, dx","Integrate[Log[a + b*x]/(a + b*x)^2,x]","-\frac{\log (a+b x)+1}{a b+b^2 x}","-\frac{1}{b (a+b x)}-\frac{\log (a+b x)}{b (a+b x)}",1,"-((1 + Log[a + b*x])/(a*b + b^2*x))","A",1
249,1,30,44,0.0143199,"\int (a+b x)^n \log (a+b x) \, dx","Integrate[(a + b*x)^n*Log[a + b*x],x]","\frac{(a+b x)^{n+1} ((n+1) \log (a+b x)-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)*(-1 + (1 + n)*Log[a + b*x]))/(b*(1 + n)^2)","A",1
250,1,18,18,0.0181216,"\int \frac{1}{a x+b x \log \left(c x^n\right)} \, dx","Integrate[(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",1
251,1,32,32,0.0250509,"\int \frac{1}{a x+b x \log ^2\left(c x^n\right)} \, dx","Integrate[(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",1
252,1,112,144,0.0513463,"\int \frac{1}{a x+b x \log ^3\left(c x^n\right)} \, dx","Integrate[(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)-2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \log \left(c x^n\right)\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} \log \left(c x^n\right)}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{6 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,"-1/6*(2*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*Log[c*x^n])/a^(1/3))/Sqrt[3]] - 2*Log[a^(1/3) + b^(1/3)*Log[c*x^n]] + Log[a^(2/3) - a^(1/3)*b^(1/3)*Log[c*x^n] + b^(2/3)*Log[c*x^n]^2])/(a^(2/3)*b^(1/3)*n)","A",1
253,1,167,227,0.0651501,"\int \frac{1}{a x+b x \log ^4\left(c x^n\right)} \, dx","Integrate[(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)+\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)-2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \log \left(c x^n\right)}{\sqrt[4]{a}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \log \left(c x^n\right)}{\sqrt[4]{a}}+1\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{\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,"(-2*ArcTan[1 - (Sqrt[2]*b^(1/4)*Log[c*x^n])/a^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*b^(1/4)*Log[c*x^n])/a^(1/4)] - Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Log[c*x^n] + Sqrt[b]*Log[c*x^n]^2] + 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",1
254,1,34,27,0.0161629,"\int \frac{1}{a x+\frac{b x}{\log \left(c x^n\right)}} \, dx","Integrate[(a*x + (b*x)/Log[c*x^n])^(-1),x]","\frac{\log \left(c x^n\right)}{a n}-\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[c*x^n]/(a*n) - (b*Log[b + a*Log[c*x^n]])/(a^2*n)","A",1
255,1,47,40,0.0256774,"\int \frac{1}{a x+\frac{b x}{\log ^2\left(c x^n\right)}} \, dx","Integrate[(a*x + (b*x)/Log[c*x^n]^2)^(-1),x]","\frac{\log \left(c x^n\right)}{a n}-\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[c*x^n]/(a*n)","A",1
256,1,132,149,0.0526879,"\int \frac{1}{a x+\frac{b x}{\log ^3\left(c x^n\right)}} \, dx","Integrate[(a*x + (b*x)/Log[c*x^n]^3)^(-1),x]","\frac{\sqrt[3]{b} \left(\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)-2 \log \left(\sqrt[3]{a} \log \left(c x^n\right)+\sqrt[3]{b}\right)\right)+2 \sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} \log \left(c x^n\right)}{\sqrt[3]{b}}}{\sqrt{3}}\right)+6 \sqrt[3]{a} \log \left(c x^n\right)}{6 a^{4/3} n}","\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,"(2*Sqrt[3]*b^(1/3)*ArcTan[(1 - (2*a^(1/3)*Log[c*x^n])/b^(1/3))/Sqrt[3]] + 6*a^(1/3)*Log[c*x^n] + b^(1/3)*(-2*Log[b^(1/3) + a^(1/3)*Log[c*x^n]] + 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",1
257,1,211,233,0.0674508,"\int \frac{1}{a x+\frac{b x}{\log ^4\left(c x^n\right)}} \, dx","Integrate[(a*x + (b*x)/Log[c*x^n]^4)^(-1),x]","\frac{\sqrt{2} \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)-\sqrt{2} \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)+2 \sqrt{2} \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} \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \log \left(c x^n\right)}{\sqrt[4]{b}}+1\right)+8 \sqrt[4]{a} \log \left(c x^n\right)}{8 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} \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,"(2*Sqrt[2]*b^(1/4)*ArcTan[1 - (Sqrt[2]*a^(1/4)*Log[c*x^n])/b^(1/4)] - 2*Sqrt[2]*b^(1/4)*ArcTan[1 + (Sqrt[2]*a^(1/4)*Log[c*x^n])/b^(1/4)] + 8*a^(1/4)*Log[c*x^n] + Sqrt[2]*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] - Sqrt[2]*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])/(8*a^(5/4)*n)","A",1
258,1,22,22,0.030021,"\int \frac{1}{x+x \log (7 x)+x \log ^2(7 x)} \, dx","Integrate[(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",1
259,1,42,41,0.0919763,"\int \frac{-1+\log (3 x)}{x \left(1-\log (3 x)+\log ^2(3 x)\right)} \, dx","Integrate[(-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{2 \log (3 x)-1}{\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",1
260,1,42,41,0.0762365,"\int \frac{-1+\log ^2(3 x)}{x+x \log ^3(3 x)} \, dx","Integrate[(-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{2 \log (3 x)-1}{\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",1
261,1,44,42,0.0935333,"\int \frac{-1+\log ^2(3 x)}{x+x \log (3 x)+x \log ^2(3 x)} \, dx","Integrate[(-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 (3 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[3*x] - Log[1 + Log[3*x] + Log[3*x]^2]/2","A",1
262,1,32,32,0.0018647,"\int \frac{\log ^2\left(\frac{1}{x}\right)}{x^5} \, dx","Integrate[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*1/x^4 + Log[x^(-1)]/(8*x^4) - Log[x^(-1)]^2/(4*x^4)","A",1
263,1,59,40,0.0107597,"\int \frac{1}{\sqrt{-\log \left(a x^2\right)}} \, dx","Integrate[1/Sqrt[-Log[a*x^2]],x]","\frac{\sqrt{\frac{\pi }{2}} x \sqrt{\log \left(a x^2\right)} \text{erfi}\left(\frac{\sqrt{\log \left(a x^2\right)}}{\sqrt{2}}\right)}{\sqrt{a x^2} \sqrt{-\log \left(a x^2\right)}}","-\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*Erfi[Sqrt[Log[a*x^2]]/Sqrt[2]]*Sqrt[Log[a*x^2]])/(Sqrt[a*x^2]*Sqrt[-Log[a*x^2]])","A",1
264,1,60,39,0.013283,"\int \frac{1}{\sqrt{-\log \left(\frac{a}{x^2}\right)}} \, dx","Integrate[1/Sqrt[-Log[a/x^2]],x]","-\frac{\sqrt{\frac{\pi }{2}} x \sqrt{\frac{a}{x^2}} \sqrt{\log \left(\frac{a}{x^2}\right)} \text{erf}\left(\frac{\sqrt{\log \left(\frac{a}{x^2}\right)}}{\sqrt{2}}\right)}{\sqrt{-\log \left(\frac{a}{x^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*Erf[Sqrt[Log[a/x^2]]/Sqrt[2]]*Sqrt[Log[a/x^2]])/Sqrt[-Log[a/x^2]])","A",1
265,1,62,43,0.0100772,"\int \frac{1}{\sqrt{-\log \left(a x^n\right)}} \, dx","Integrate[1/Sqrt[-Log[a*x^n]],x]","\frac{\sqrt{\pi } x \left(a x^n\right)^{-1/n} \sqrt{\log \left(a x^n\right)} \text{erfi}\left(\frac{\sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{\sqrt{n} \sqrt{-\log \left(a x^n\right)}}","-\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*Erfi[Sqrt[Log[a*x^n]]/Sqrt[n]]*Sqrt[Log[a*x^n]])/(Sqrt[n]*(a*x^n)^n^(-1)*Sqrt[-Log[a*x^n]])","A",1
266,1,121,122,0.0775962,"\int \frac{\log \left(1+\sqrt{x}-x\right)}{x} \, dx","Integrate[Log[1 + Sqrt[x] - x]/x,x]","2 \text{Li}_2\left(\frac{-2 \sqrt{x}+\sqrt{5}+1}{1+\sqrt{5}}\right)-2 \text{Li}_2\left(-\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)+\left(\log \left(\sqrt{5}-1\right)-\log \left(2 \sqrt{x}+\sqrt{5}-1\right)\right) \log (x)+\log \left(-x+\sqrt{x}+1\right) \log (x)","2 \text{Li}_2\left(1-\frac{2 \sqrt{x}}{1+\sqrt{5}}\right)-2 \text{Li}_2\left(\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]] + (Log[-1 + Sqrt[5]] - Log[-1 + Sqrt[5] + 2*Sqrt[x]])*Log[x] + Log[1 + Sqrt[x] - x]*Log[x] + 2*PolyLog[2, (1 + Sqrt[5] - 2*Sqrt[x])/(1 + Sqrt[5])] - 2*PolyLog[2, (-2*Sqrt[x])/(-1 + Sqrt[5])]","A",1
267,1,73,81,0.032126,"\int \frac{x \log (c+d x)}{a+b x} \, dx","Integrate[(x*Log[c + d*x])/(a + b*x),x]","\frac{-a d \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(-a d \log \left(\frac{d (a+b x)}{a d-b c}\right)+b c+b d x\right)-b d x}{b^2 d}","-\frac{a \text{Li}_2\left(\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,"(-(b*d*x) + (b*c + b*d*x - a*d*Log[(d*(a + b*x))/(-(b*c) + a*d)])*Log[c + d*x] - a*d*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b^2*d)","A",1
268,1,9,9,0.0015805,"\int \frac{\log (x)}{-1+x} \, dx","Integrate[Log[x]/(-1 + x),x]","-\text{Li}_2(1-x)","-\text{Li}_2(1-x)",1,"-PolyLog[2, 1 - x]","A",1
269,1,35,43,0.0185166,"\int \frac{x \log (1-a-b x)}{a+b x} \, dx","Integrate[(x*Log[1 - a - b*x])/(a + b*x),x]","\frac{a \text{Li}_2(a+b x)+(a+b x-1) \log (-a-b x+1)-b x}{b^2}","\frac{a \text{Li}_2(a+b x)}{b^2}-\frac{(-a-b x+1) \log (-a-b x+1)}{b^2}-\frac{x}{b}",1,"(-(b*x) + (-1 + a + b*x)*Log[1 - a - b*x] + a*PolyLog[2, a + b*x])/b^2","A",1
270,1,31,30,0.0107806,"\int \frac{(b+2 c x) \log (x)}{x (b+c x)} \, dx","Integrate[((b + 2*c*x)*Log[x])/(x*(b + c*x)),x]","\text{Li}_2\left(-\frac{c x}{b}\right)+\log (x) \log \left(\frac{b+c x}{b}\right)+\frac{\log ^2(x)}{2}","\text{Li}_2\left(-\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[(b + c*x)/b] + PolyLog[2, -((c*x)/b)]","A",1
271,1,7,7,0.1122374,"\int (\sin (x \log (x))+\log (x) \sin (x \log (x))) \, dx","Integrate[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",1
272,1,63,68,0.0318985,"\int \frac{\log \left(\frac{1-(-1+x)^2}{1+(-1+x)^2}\right)}{x^2} \, dx","Integrate[Log[(1 - (-1 + x)^2)/(1 + (-1 + x)^2)]/x^2,x]","-\frac{\log \left(-\frac{(x-2) x}{x^2-2 x+2}\right)}{x}-\frac{1}{2} \log \left(x^2-2 x+2\right)-\frac{1}{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[2 - x]/2 + Log[x]/2 - Log[-(((-2 + x)*x)/(2 - 2*x + x^2))]/x - Log[2 - 2*x + x^2]/2","A",1
273,1,29,29,0.0121045,"\int \log \left(\sqrt{x}+x\right) \, dx","Integrate[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",1
274,1,18,18,0.0016374,"\int \log \left(-\frac{x}{1+x}\right) \, dx","Integrate[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",1
275,1,21,27,0.0034621,"\int \log \left(\frac{-1+x}{1+x}\right) \, dx","Integrate[Log[(-1 + x)/(1 + x)],x]","(x-1) \log \left(\frac{x-1}{x+1}\right)-2 \log (x+1)","-\left((1-x) \log \left(-\frac{1-x}{x+1}\right)\right)-2 \log (x+1)",1,"(-1 + x)*Log[(-1 + x)/(1 + x)] - 2*Log[1 + x]","A",1
276,1,60,57,0.0502293,"\int \frac{\log \left(\frac{1-x^2}{1+x^2}\right)}{(1+x)^2} \, dx","Integrate[Log[(1 - x^2)/(1 + x^2)]/(1 + x)^2,x]","\frac{1}{2} \left(\log \left(1-x^2\right)-\frac{2 \left(\log \left(\frac{1-x^2}{x^2+1}\right)+1\right)}{x+1}+(-1+i) \log (-x+i)-(1+i) \log (x+i)\right)","\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 + I)*Log[I - x] - (1 + I)*Log[I + x] + Log[1 - x^2] - (2*(1 + Log[(1 - x^2)/(1 + x^2)]))/(1 + x))/2","C",1
277,1,62,60,0.006762,"\int \frac{\log \left(c \left(1+x^2\right)^n\right)}{1+x^2} \, dx","Integrate[Log[c*(1 + x^2)^n]/(1 + x^2),x]","\tan ^{-1}(x) \log \left(c \left(x^2+1\right)^n\right)+i n \text{Li}_2\left(\frac{x+i}{x-i}\right)+i n \tan ^{-1}(x)^2+2 n \log \left(\frac{2 i}{-x+i}\right) \tan ^{-1}(x)","\tan ^{-1}(x) \log \left(c \left(x^2+1\right)^n\right)+i n \text{Li}_2\left(1-\frac{2}{i x+1}\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*I)/(I - x)] + ArcTan[x]*Log[c*(1 + x^2)^n] + I*n*PolyLog[2, (I + x)/(-I + x)]","A",1
278,1,239,61,0.0458209,"\int \frac{\log \left(\frac{x^2}{1+x^2}\right)}{1+x^2} \, dx","Integrate[Log[x^2/(1 + x^2)]/(1 + x^2),x]","-\frac{1}{2} i \text{Li}_2\left(-\frac{1}{2} i (i-x)\right)+i \text{Li}_2(-i (i-x))+\frac{1}{2} i \text{Li}_2\left(-\frac{1}{2} i (x+i)\right)-i \text{Li}_2(-i (x+i))-\frac{1}{2} i \log \left(\frac{x^2}{x^2+1}\right) \log (-x+i)+\frac{1}{2} i \log (x+i) \log \left(\frac{x^2}{x^2+1}\right)-\frac{1}{4} i \log ^2(-x+i)+\frac{1}{4} i \log ^2(x+i)+i \log (-i x) \log (-x+i)-\frac{1}{2} i \log \left(-\frac{1}{2} i (x+i)\right) \log (-x+i)+\frac{1}{2} i \log \left(-\frac{1}{2} i (-x+i)\right) \log (x+i)-i \log (i x) \log (x+i)","i \text{Li}_2\left(\frac{2}{1-i x}-1\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,"(-1/4*I)*Log[I - x]^2 + I*Log[I - x]*Log[(-I)*x] - (I/2)*Log[I - x]*Log[(-1/2*I)*(I + x)] + (I/2)*Log[(-1/2*I)*(I - x)]*Log[I + x] - I*Log[I*x]*Log[I + x] + (I/4)*Log[I + x]^2 - (I/2)*Log[I - x]*Log[x^2/(1 + x^2)] + (I/2)*Log[I + x]*Log[x^2/(1 + x^2)] - (I/2)*PolyLog[2, (-1/2*I)*(I - x)] + I*PolyLog[2, (-I)*(I - x)] + (I/2)*PolyLog[2, (-1/2*I)*(I + x)] - I*PolyLog[2, (-I)*(I + x)]","B",1
279,1,373,165,0.1957546,"\int \frac{\log \left(\frac{c x^2}{a+b x^2}\right)}{a+b x^2} \, dx","Integrate[Log[(c*x^2)/(a + b*x^2)]/(a + b*x^2),x]","\frac{2 \log \left(\sqrt{-a}-\sqrt{b} x\right) \log \left(\frac{c x^2}{a+b x^2}\right)-2 \log \left(\sqrt{-a}+\sqrt{b} x\right) \log \left(\frac{c x^2}{a+b x^2}\right)+4 \text{Li}_2\left(\frac{\sqrt{b} x}{\sqrt{-a}}+1\right)-2 \text{Li}_2\left(\frac{a-\sqrt{-a} \sqrt{b} x}{2 a}\right)+2 \text{Li}_2\left(\frac{a+\sqrt{-a} \sqrt{b} x}{2 a}\right)-4 \text{Li}_2\left(\frac{a \sqrt{b} x}{(-a)^{3/2}}+1\right)+\log ^2\left(\sqrt{-a}-\sqrt{b} x\right)-\log ^2\left(\sqrt{-a}+\sqrt{b} x\right)-4 \log \left(\frac{\sqrt{b} x}{\sqrt{-a}}\right) \log \left(\sqrt{-a}-\sqrt{b} x\right)+2 \log \left(\frac{a-\sqrt{-a} \sqrt{b} x}{2 a}\right) \log \left(\sqrt{-a}-\sqrt{b} x\right)+4 \log \left(\frac{a \sqrt{b} x}{(-a)^{3/2}}\right) \log \left(\sqrt{-a}+\sqrt{b} x\right)-2 \log \left(\sqrt{-a}+\sqrt{b} x\right) \log \left(\frac{\sqrt{-a} \sqrt{b} x+a}{2 a}\right)}{4 \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 \text{Li}_2\left(\frac{2 \sqrt{a}}{\sqrt{a}-i \sqrt{b} x}-1\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,"(-4*Log[(Sqrt[b]*x)/Sqrt[-a]]*Log[Sqrt[-a] - Sqrt[b]*x] + Log[Sqrt[-a] - Sqrt[b]*x]^2 + 4*Log[(a*Sqrt[b]*x)/(-a)^(3/2)]*Log[Sqrt[-a] + Sqrt[b]*x] - Log[Sqrt[-a] + Sqrt[b]*x]^2 + 2*Log[Sqrt[-a] - Sqrt[b]*x]*Log[(a - Sqrt[-a]*Sqrt[b]*x)/(2*a)] - 2*Log[Sqrt[-a] + Sqrt[b]*x]*Log[(a + Sqrt[-a]*Sqrt[b]*x)/(2*a)] + 2*Log[Sqrt[-a] - Sqrt[b]*x]*Log[(c*x^2)/(a + b*x^2)] - 2*Log[Sqrt[-a] + Sqrt[b]*x]*Log[(c*x^2)/(a + b*x^2)] + 4*PolyLog[2, 1 + (Sqrt[b]*x)/Sqrt[-a]] - 2*PolyLog[2, (a - Sqrt[-a]*Sqrt[b]*x)/(2*a)] + 2*PolyLog[2, (a + Sqrt[-a]*Sqrt[b]*x)/(2*a)] - 4*PolyLog[2, 1 + (a*Sqrt[b]*x)/(-a)^(3/2)])/(4*Sqrt[-a]*Sqrt[b])","B",1
280,1,134,29,0.6482279,"\int \frac{\log \left(1+\frac{i \sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Integrate[Log[1 + (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]]/(1 - a^2*x^2),x]","\frac{\text{Li}_2\left(-e^{-2 \tanh ^{-1}(a x)}\right)-2 \left(-\text{Li}_2\left(-i e^{-\tanh ^{-1}(a x)}\right)+\text{Li}_2\left(i e^{-\tanh ^{-1}(a x)}\right)+\tanh ^{-1}(a x) \left(\log \left(e^{-2 \tanh ^{-1}(a x)}+1\right)-\log \left(1-i e^{-\tanh ^{-1}(a x)}\right)+\log \left(1+i e^{-\tanh ^{-1}(a x)}\right)\right)\right)+4 \log \left(1+\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{4 a}","\frac{\text{Li}_2\left(-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}",1,"(4*ArcTanh[a*x]*Log[1 + (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]] + PolyLog[2, -E^(-2*ArcTanh[a*x])] - 2*(ArcTanh[a*x]*(Log[1 + E^(-2*ArcTanh[a*x])] - Log[1 - I/E^ArcTanh[a*x]] + Log[1 + I/E^ArcTanh[a*x]]) - PolyLog[2, (-I)/E^ArcTanh[a*x]] + PolyLog[2, I/E^ArcTanh[a*x]]))/(4*a)","B",0
281,1,134,29,0.5744886,"\int \frac{\log \left(1-\frac{i \sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Integrate[Log[1 - (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]]/(1 - a^2*x^2),x]","\frac{\text{Li}_2\left(-e^{-2 \tanh ^{-1}(a x)}\right)-2 \left(\text{Li}_2\left(-i e^{-\tanh ^{-1}(a x)}\right)-\text{Li}_2\left(i e^{-\tanh ^{-1}(a x)}\right)+\tanh ^{-1}(a x) \left(\log \left(e^{-2 \tanh ^{-1}(a x)}+1\right)+\log \left(1-i e^{-\tanh ^{-1}(a x)}\right)-\log \left(1+i e^{-\tanh ^{-1}(a x)}\right)\right)\right)+4 \log \left(1-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{4 a}","\frac{\text{Li}_2\left(\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}",1,"(4*ArcTanh[a*x]*Log[1 - (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]] + PolyLog[2, -E^(-2*ArcTanh[a*x])] - 2*(ArcTanh[a*x]*(Log[1 + E^(-2*ArcTanh[a*x])] + Log[1 - I/E^ArcTanh[a*x]] - Log[1 + I/E^ArcTanh[a*x]]) + PolyLog[2, (-I)/E^ArcTanh[a*x]] - PolyLog[2, I/E^ArcTanh[a*x]]))/(4*a)","B",0
282,1,17,17,0.0032379,"\int \log \left(e^{a+b x}\right) \, dx","Integrate[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",1
283,1,25,27,0.0264078,"\int \log \left(e^{a+b x^n}\right) \, dx","Integrate[Log[E^(a + b*x^n)],x]","x \left(\log \left(e^{a+b x^n}\right)-\frac{b n x^n}{n+1}\right)","x \log \left(e^{a+b x^n}\right)-\frac{b n x^{n+1}}{n+1}",1,"x*(-((b*n*x^n)/(1 + n)) + Log[E^(a + b*x^n)])","A",1
284,1,25,25,0.0239694,"\int e^x \log \left(a+b e^x\right) \, dx","Integrate[E^x*Log[a + b*E^x],x]","\frac{\left(a+b e^x\right) \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 + b*E^x)*Log[a + b*E^x])/b","A",1
285,1,22,26,0.0428485,"\int e^{a+b x} \log (x) \, dx","Integrate[E^(a + b*x)*Log[x],x]","\frac{e^a \left(e^{b x} \log (x)-\text{Ei}(b x)\right)}{b}","\frac{\log (x) e^{a+b x}}{b}-\frac{e^a \text{Ei}(b x)}{b}",1,"(E^a*(-ExpIntegralEi[b*x] + E^(b*x)*Log[x]))/b","A",1
286,0,0,13,7.0291424,"\int \frac{x^2}{x+\log (x)} \, dx","Integrate[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,"Integrate[x^2/(x + Log[x]), x]","A",-1
287,0,0,11,5.718705,"\int \frac{x}{x+\log (x)} \, dx","Integrate[x/(x + Log[x]),x]","\int \frac{x}{x+\log (x)} \, dx","\text{Int}\left(\frac{x}{x+\log (x)},x\right)",0,"Integrate[x/(x + Log[x]), x]","A",-1
288,0,0,9,0.0063054,"\int \frac{1}{x+\log (x)} \, dx","Integrate[(x + Log[x])^(-1),x]","\int \frac{1}{x+\log (x)} \, dx","\text{Int}\left(\frac{1}{x+\log (x)},x\right)",0,"Integrate[(x + Log[x])^(-1), x]","A",-1
289,0,0,13,0.0379411,"\int \frac{1}{x (x+\log (x))} \, dx","Integrate[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,"Integrate[1/(x*(x + Log[x])), x]","A",-1
290,0,0,13,6.6600441,"\int \frac{1}{x^2 (x+\log (x))} \, dx","Integrate[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,"Integrate[1/(x^2*(x + Log[x])), x]","A",-1
291,1,13,13,0.0088886,"\int \frac{\log (x)}{x+4 x \log ^2(x)} \, dx","Integrate[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",1
292,1,10,9,0.0510633,"\int \frac{1-\log (x)}{x (x+\log (x))} \, dx","Integrate[(1 - Log[x])/(x*(x + Log[x])),x]","\log (x+\log (x))-\log (x)","\log \left(\frac{\log (x)}{x}+1\right)",1,"-Log[x] + Log[x + Log[x]]","A",1
293,1,13,13,0.0411171,"\int \frac{1+x}{\log (x) (x+\log (x))} \, dx","Integrate[(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",1
294,1,53,67,0.0329116,"\int \log \left(2+\sqrt{\frac{1+x}{x}}\right) \, dx","Integrate[Log[2 + Sqrt[(1 + x)/x]],x]","x \log \left(\sqrt{\frac{1}{x}+1}+2\right)+\frac{1}{3} \tanh ^{-1}\left(\frac{1}{3} \left(2 \sqrt{\frac{1}{x}+1}+1\right)\right)-\tanh ^{-1}\left(2 \sqrt{\frac{1}{x}+1}+3\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,"ArcTanh[(1 + 2*Sqrt[1 + x^(-1)])/3]/3 - ArcTanh[3 + 2*Sqrt[1 + x^(-1)]] + x*Log[2 + Sqrt[1 + x^(-1)]]","A",1
295,1,53,50,0.0390776,"\int \log \left(1+\sqrt{\frac{1+x}{x}}\right) \, dx","Integrate[Log[1 + Sqrt[(1 + x)/x]],x]","\frac{1}{4} \left(-2 \sqrt{\frac{1}{x}+1} x+2 x+4 x \log \left(\sqrt{\frac{1}{x}+1}+1\right)+\log \left(\left(2 \sqrt{\frac{1}{x}+1}+2\right) x+1\right)\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,"(2*x - 2*Sqrt[1 + x^(-1)]*x + 4*x*Log[1 + Sqrt[1 + x^(-1)]] + Log[1 + (2 + 2*Sqrt[1 + x^(-1)])*x])/4","A",1
296,1,19,21,0.0035745,"\int \log \left(\sqrt{\frac{1+x}{x}}\right) \, dx","Integrate[Log[Sqrt[(1 + x)/x]],x]","\frac{1}{2} \left(\log (x)+(x+1) \log \left(\frac{x+1}{x}\right)\right)","x \log \left(\sqrt{\frac{1}{x}+1}\right)+\frac{1}{2} \log (x+1)",1,"(Log[x] + (1 + x)*Log[(1 + x)/x])/2","A",1
297,1,53,50,0.0395341,"\int \log \left(-1+\sqrt{\frac{1+x}{x}}\right) \, dx","Integrate[Log[-1 + Sqrt[(1 + x)/x]],x]","\frac{1}{2} \left(\sqrt{\frac{1}{x}+1}+1\right) x+x \log \left(\sqrt{\frac{1}{x}+1}-1\right)-\frac{1}{4} \log \left(\left(2 \sqrt{\frac{1}{x}+1}+2\right) 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 + Sqrt[1 + x^(-1)])*x)/2 + x*Log[-1 + Sqrt[1 + x^(-1)]] - Log[1 + (2 + 2*Sqrt[1 + x^(-1)])*x]/4","A",1
298,1,64,69,0.0290584,"\int \log \left(-2+\sqrt{\frac{1+x}{x}}\right) \, dx","Integrate[Log[-2 + Sqrt[(1 + x)/x]],x]","\frac{1}{6} \left(\log \left(2-\sqrt{\frac{1}{x}+1}\right)+6 x \log \left(\sqrt{\frac{1}{x}+1}-2\right)-\log \left(\sqrt{\frac{1}{x}+1}+1\right)-6 \tanh ^{-1}\left(3-2 \sqrt{\frac{1}{x}+1}\right)\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,"(-6*ArcTanh[3 - 2*Sqrt[1 + x^(-1)]] + Log[2 - Sqrt[1 + x^(-1)]] + 6*x*Log[-2 + Sqrt[1 + x^(-1)]] - Log[1 + Sqrt[1 + x^(-1)]])/6","A",1
299,1,9,9,0.0138514,"\int \left(x^{a x}+x^{a x} \log (x)\right) \, dx","Integrate[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",1
300,1,26,26,0.0138947,"\int \log ^m(x)^p \, dx","Integrate[(Log[x]^m)^p,x]","(-\log (x))^{-m p} \log ^m(x)^p \Gamma (m p+1,-\log (x))","(-\log (x))^{-m p} \log ^m(x)^p \Gamma (m p+1,-\log (x))",1,"(Gamma[1 + m*p, -Log[x]]*(Log[x]^m)^p)/(-Log[x])^(m*p)","A",1
301,1,72,60,0.1269588,"\int \frac{\log (x)}{\sqrt{a+b \log (x)}} \, dx","Integrate[Log[x]/Sqrt[a + b*Log[x]],x]","\frac{2 x (a+b \log (x))-(2 a+b) e^{-\frac{a}{b}} \sqrt{-\frac{a+b \log (x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \log (x)}{b}\right)}{2 b \sqrt{a+b \log (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}}",1,"(2*x*(a + b*Log[x]) - ((2*a + b)*Gamma[1/2, -((a + b*Log[x])/b)]*Sqrt[-((a + b*Log[x])/b)])/E^(a/b))/(2*b*Sqrt[a + b*Log[x]])","A",1
302,1,71,64,0.0969731,"\int \frac{\log (x)}{\sqrt{a-b \log (x)}} \, dx","Integrate[Log[x]/Sqrt[a - b*Log[x]],x]","\frac{-2 x (a-b \log (x))-\left((b-2 a) e^{a/b} \sqrt{\frac{a}{b}-\log (x)} \Gamma \left(\frac{1}{2},\frac{a}{b}-\log (x)\right)\right)}{2 b \sqrt{a-b \log (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}",1,"(-((-2*a + b)*E^(a/b)*Gamma[1/2, a/b - Log[x]]*Sqrt[a/b - Log[x]]) - 2*x*(a - b*Log[x]))/(2*b*Sqrt[a - b*Log[x]])","A",1
303,1,80,69,0.148459,"\int \frac{A+B \log (x)}{\sqrt{a+b \log (x)}} \, dx","Integrate[(A + B*Log[x])/Sqrt[a + b*Log[x]],x]","\frac{e^{-\frac{a}{b}} (2 A b-B (2 a+b)) \sqrt{-\frac{a+b \log (x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \log (x)}{b}\right)+2 B x (a+b \log (x))}{2 b \sqrt{a+b \log (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}",1,"(2*B*x*(a + b*Log[x]) + ((2*A*b - (2*a + b)*B)*Gamma[1/2, -((a + b*Log[x])/b)]*Sqrt[-((a + b*Log[x])/b)])/E^(a/b))/(2*b*Sqrt[a + b*Log[x]])","A",1
304,1,79,71,0.1301896,"\int \frac{A+B \log (x)}{\sqrt{a-b \log (x)}} \, dx","Integrate[(A + B*Log[x])/Sqrt[a - b*Log[x]],x]","\frac{e^{a/b} (2 a B+2 A b-b B) \sqrt{\frac{a}{b}-\log (x)} \Gamma \left(\frac{1}{2},\frac{a}{b}-\log (x)\right)-2 B x (a-b \log (x))}{2 b \sqrt{a-b \log (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}",1,"((2*A*b + 2*a*B - b*B)*E^(a/b)*Gamma[1/2, a/b - Log[x]]*Sqrt[a/b - Log[x]] - 2*B*x*(a - b*Log[x]))/(2*b*Sqrt[a - b*Log[x]])","A",1
305,1,95,98,0.061521,"\int x^2 \log (\log (x) \sin (x)) \, dx","Integrate[x^2*Log[Log[x]*Sin[x]],x]","\frac{1}{192} i \left(64 i \text{Ei}(3 \log (x))-96 x^2 \text{Li}_2\left(e^{-2 i x}\right)+96 i x \text{Li}_3\left(e^{-2 i x}\right)+48 \text{Li}_4\left(e^{-2 i x}\right)-16 x^4+64 i x^3 \log \left(1-e^{-2 i x}\right)-64 i x^3 \log (\log (x) \sin (x))+\pi ^4\right)","-\frac{1}{3} \text{Ei}(3 \log (x))+\frac{1}{2} i x^2 \text{Li}_2\left(e^{2 i x}\right)-\frac{1}{2} x \text{Li}_3\left(e^{2 i x}\right)-\frac{1}{4} i \text{Li}_4\left(e^{2 i x}\right)+\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/192)*(Pi^4 - 16*x^4 + (64*I)*ExpIntegralEi[3*Log[x]] + (64*I)*x^3*Log[1 - E^((-2*I)*x)] - (64*I)*x^3*Log[Log[x]*Sin[x]] - 96*x^2*PolyLog[2, E^((-2*I)*x)] + (96*I)*x*PolyLog[3, E^((-2*I)*x)] + 48*PolyLog[4, E^((-2*I)*x)])","A",1
306,1,79,80,0.0395695,"\int x \log (\log (x) \sin (x)) \, dx","Integrate[x*Log[Log[x]*Sin[x]],x]","\frac{1}{48} \left(-24 \text{Ei}(2 \log (x))-24 i x \text{Li}_2\left(e^{-2 i x}\right)-12 \text{Li}_3\left(e^{-2 i x}\right)-8 i x^3-24 x^2 \log \left(1-e^{-2 i x}\right)+24 x^2 \log (\log (x) \sin (x))+i \pi ^3\right)","-\frac{1}{2} \text{Ei}(2 \log (x))+\frac{1}{2} i x \text{Li}_2\left(e^{2 i x}\right)-\frac{1}{4} \text{Li}_3\left(e^{2 i x}\right)+\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*Pi^3 - (8*I)*x^3 - 24*ExpIntegralEi[2*Log[x]] - 24*x^2*Log[1 - E^((-2*I)*x)] + 24*x^2*Log[Log[x]*Sin[x]] - (24*I)*x*PolyLog[2, E^((-2*I)*x)] - 12*PolyLog[3, E^((-2*I)*x)])/48","A",1
307,1,47,52,0.031356,"\int \log (\log (x) \sin (x)) \, dx","Integrate[Log[Log[x]*Sin[x]],x]","-\text{li}(x)+\frac{1}{2} i \left(x^2+\text{Li}_2\left(e^{2 i x}\right)\right)-x \log \left(1-e^{2 i x}\right)+x \log (\log (x) \sin (x))","-\text{li}(x)+\frac{1}{2} i \text{Li}_2\left(e^{2 i x}\right)+\frac{i x^2}{2}-x \log \left(1-e^{2 i x}\right)+x \log (\log (x) \sin (x))",1,"-(x*Log[1 - E^((2*I)*x)]) + x*Log[Log[x]*Sin[x]] - LogIntegral[x] + (I/2)*(x^2 + PolyLog[2, E^((2*I)*x)])","A",1
308,0,0,13,2.3677105,"\int \frac{\log (\log (x) \sin (x))}{x} \, dx","Integrate[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,"Integrate[Log[Log[x]*Sin[x]]/x, x]","A",-1
309,0,0,26,2.0143975,"\int \frac{\log (\log (x) \sin (x))}{x^2} \, dx","Integrate[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,"Integrate[Log[Log[x]*Sin[x]]/x^2, x]","A",-1
310,1,100,103,0.0692386,"\int x^2 \log \left(e^x \log (x) \sin (x)\right) \, dx","Integrate[x^2*Log[E^x*Log[x]*Sin[x]],x]","\frac{1}{192} i \left(64 i \text{Ei}(3 \log (x))-96 x^2 \text{Li}_2\left(e^{-2 i x}\right)+96 i x \text{Li}_3\left(e^{-2 i x}\right)+48 \text{Li}_4\left(e^{-2 i x}\right)+(-16+16 i) x^4+64 i x^3 \log \left(1-e^{-2 i x}\right)-64 i x^3 \log \left(e^x \log (x) \sin (x)\right)+\pi ^4\right)","-\frac{1}{3} \text{Ei}(3 \log (x))+\frac{1}{2} i x^2 \text{Li}_2\left(e^{2 i x}\right)-\frac{1}{2} x \text{Li}_3\left(e^{2 i x}\right)-\frac{1}{4} i \text{Li}_4\left(e^{2 i x}\right)+\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,"(I/192)*(Pi^4 - (16 - 16*I)*x^4 + (64*I)*ExpIntegralEi[3*Log[x]] + (64*I)*x^3*Log[1 - E^((-2*I)*x)] - (64*I)*x^3*Log[E^x*Log[x]*Sin[x]] - 96*x^2*PolyLog[2, E^((-2*I)*x)] + (96*I)*x*PolyLog[3, E^((-2*I)*x)] + 48*PolyLog[4, E^((-2*I)*x)])","A",1
311,1,82,85,0.0670731,"\int x \log \left(e^x \log (x) \sin (x)\right) \, dx","Integrate[x*Log[E^x*Log[x]*Sin[x]],x]","\frac{1}{48} \left(-24 \text{Ei}(2 \log (x))-24 i x \text{Li}_2\left(e^{-2 i x}\right)-12 \text{Li}_3\left(e^{-2 i x}\right)+(-8-8 i) x^3-24 x^2 \log \left(1-e^{-2 i x}\right)+24 x^2 \log \left(e^x \log (x) \sin (x)\right)+i \pi ^3\right)","-\frac{1}{2} \text{Ei}(2 \log (x))+\frac{1}{2} i x \text{Li}_2\left(e^{2 i x}\right)-\frac{1}{4} \text{Li}_3\left(e^{2 i x}\right)+\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,"(I*Pi^3 - (8 + 8*I)*x^3 - 24*ExpIntegralEi[2*Log[x]] - 24*x^2*Log[1 - E^((-2*I)*x)] + 24*x^2*Log[E^x*Log[x]*Sin[x]] - (24*I)*x*PolyLog[2, E^((-2*I)*x)] - 12*PolyLog[3, E^((-2*I)*x)])/48","A",1
312,1,56,57,0.0299921,"\int \log \left(e^x \log (x) \sin (x)\right) \, dx","Integrate[Log[E^x*Log[x]*Sin[x]],x]","\frac{1}{2} \left(-2 \text{li}(x)+i \text{Li}_2\left(e^{2 i x}\right)+(-1+i) x^2-2 x \log \left(1-e^{2 i x}\right)+2 x \log \left(e^x \log (x) \sin (x)\right)\right)","-\text{li}(x)+\frac{1}{2} i \text{Li}_2\left(e^{2 i x}\right)+\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 + I)*x^2 - 2*x*Log[1 - E^((2*I)*x)] + 2*x*Log[E^x*Log[x]*Sin[x]] - 2*LogIntegral[x] + I*PolyLog[2, E^((2*I)*x)])/2","A",1
313,0,0,16,0.8764098,"\int \frac{\log \left(e^x \log (x) \sin (x)\right)}{x} \, dx","Integrate[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,"Integrate[Log[E^x*Log[x]*Sin[x]]/x, x]","A",-1
314,0,0,31,2.4648331,"\int \frac{\log \left(e^x \log (x) \sin (x)\right)}{x^2} \, dx","Integrate[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,"Integrate[Log[E^x*Log[x]*Sin[x]]/x^2, x]","A",-1