1,1,188,0,0.1431003,"\int (a g+b g x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Int[(a*g + b*g*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^4 (a+b x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 b}+\frac{B g^4 n x (b c-a d)^4}{5 d^4}-\frac{B g^4 n (a+b x)^2 (b c-a d)^3}{10 b d^3}+\frac{B g^4 n (a+b x)^3 (b c-a d)^2}{15 b d^2}-\frac{B g^4 n (b c-a d)^5 \log (c+d x)}{5 b d^5}-\frac{B g^4 n (a+b x)^4 (b c-a d)}{20 b d}","\frac{g^4 (a+b x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 b}+\frac{B g^4 n x (b c-a d)^4}{5 d^4}-\frac{B g^4 n (a+b x)^2 (b c-a d)^3}{10 b d^3}+\frac{B g^4 n (a+b x)^3 (b c-a d)^2}{15 b d^2}-\frac{B g^4 n (b c-a d)^5 \log (c+d x)}{5 b d^5}-\frac{B g^4 n (a+b x)^4 (b c-a d)}{20 b d}",1,"(B*(b*c - a*d)^4*g^4*n*x)/(5*d^4) - (B*(b*c - a*d)^3*g^4*n*(a + b*x)^2)/(10*b*d^3) + (B*(b*c - a*d)^2*g^4*n*(a + b*x)^3)/(15*b*d^2) - (B*(b*c - a*d)*g^4*n*(a + b*x)^4)/(20*b*d) + (g^4*(a + b*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(5*b) - (B*(b*c - a*d)^5*g^4*n*Log[c + d*x])/(5*b*d^5)","A",4,3,33,0.09091,1,"{2525, 12, 43}"
2,1,156,0,0.1058311,"\int (a g+b g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Int[(a*g + b*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^3 (a+b x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{4 b}-\frac{B g^3 n x (b c-a d)^3}{4 d^3}+\frac{B g^3 n (a+b x)^2 (b c-a d)^2}{8 b d^2}+\frac{B g^3 n (b c-a d)^4 \log (c+d x)}{4 b d^4}-\frac{B g^3 n (a+b x)^3 (b c-a d)}{12 b d}","\frac{g^3 (a+b x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{4 b}-\frac{B g^3 n x (b c-a d)^3}{4 d^3}+\frac{B g^3 n (a+b x)^2 (b c-a d)^2}{8 b d^2}+\frac{B g^3 n (b c-a d)^4 \log (c+d x)}{4 b d^4}-\frac{B g^3 n (a+b x)^3 (b c-a d)}{12 b d}",1,"-(B*(b*c - a*d)^3*g^3*n*x)/(4*d^3) + (B*(b*c - a*d)^2*g^3*n*(a + b*x)^2)/(8*b*d^2) - (B*(b*c - a*d)*g^3*n*(a + b*x)^3)/(12*b*d) + (g^3*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(4*b) + (B*(b*c - a*d)^4*g^3*n*Log[c + d*x])/(4*b*d^4)","A",4,3,33,0.09091,1,"{2525, 12, 43}"
3,1,124,0,0.089504,"\int (a g+b g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Int[(a*g + b*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^2 (a+b x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b}+\frac{B g^2 n x (b c-a d)^2}{3 d^2}-\frac{B g^2 n (b c-a d)^3 \log (c+d x)}{3 b d^3}-\frac{B g^2 n (a+b x)^2 (b c-a d)}{6 b d}","\frac{g^2 (a+b x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b}+\frac{B g^2 n x (b c-a d)^2}{3 d^2}-\frac{B g^2 n (b c-a d)^3 \log (c+d x)}{3 b d^3}-\frac{B g^2 n (a+b x)^2 (b c-a d)}{6 b d}",1,"(B*(b*c - a*d)^2*g^2*n*x)/(3*d^2) - (B*(b*c - a*d)*g^2*n*(a + b*x)^2)/(6*b*d) + (g^2*(a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*b) - (B*(b*c - a*d)^3*g^2*n*Log[c + d*x])/(3*b*d^3)","A",4,3,33,0.09091,1,"{2525, 12, 43}"
4,1,86,0,0.0614864,"\int (a g+b g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Int[(a*g + b*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 b}+\frac{B g n (b c-a d)^2 \log (c+d x)}{2 b d^2}-\frac{B g n x (b c-a d)}{2 d}","\frac{g (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 b}+\frac{B g n (b c-a d)^2 \log (c+d x)}{2 b d^2}-\frac{B g n x (b c-a d)}{2 d}",1,"-(B*(b*c - a*d)*g*n*x)/(2*d) + (g*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*b) + (B*(b*c - a*d)^2*g*n*Log[c + d*x])/(2*b*d^2)","A",4,3,31,0.09677,1,"{2525, 12, 43}"
5,1,126,0,0.2093361,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{a g+b g x} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(a*g + b*g*x),x]","\frac{B n \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g}+\frac{\log (a g+b g x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b g}+\frac{B n \log (a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{B n \log ^2(g (a+b x))}{2 b g}","\frac{B n \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{b g}-\frac{\log \left(-\frac{b c-a d}{d (a+b x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b g}",1,"-(B*n*Log[g*(a + b*x)]^2)/(2*b*g) + ((A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[a*g + b*g*x])/(b*g) + (B*n*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x])/(b*g) + (B*n*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g)","A",9,8,33,0.2424,1,"{2524, 2418, 2390, 12, 2301, 2394, 2393, 2391}"
6,1,108,0,0.0904321,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a g+b g x)^2} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(a*g + b*g*x)^2,x]","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{b g^2 (a+b x)}-\frac{B d n \log (a+b x)}{b g^2 (b c-a d)}+\frac{B d n \log (c+d x)}{b g^2 (b c-a d)}-\frac{B n}{b g^2 (a+b x)}","-\frac{(c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^2 (a+b x) (b c-a d)}-\frac{B n}{b g^2 (a+b x)}",1,"-((B*n)/(b*g^2*(a + b*x))) - (B*d*n*Log[a + b*x])/(b*(b*c - a*d)*g^2) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])/(b*g^2*(a + b*x)) + (B*d*n*Log[c + d*x])/(b*(b*c - a*d)*g^2)","A",4,3,33,0.09091,1,"{2525, 12, 44}"
7,1,151,0,0.1228868,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a g+b g x)^3} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(a*g + b*g*x)^3,x]","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{2 b g^3 (a+b x)^2}+\frac{B d^2 n \log (a+b x)}{2 b g^3 (b c-a d)^2}-\frac{B d^2 n \log (c+d x)}{2 b g^3 (b c-a d)^2}+\frac{B d n}{2 b g^3 (a+b x) (b c-a d)}-\frac{B n}{4 b g^3 (a+b x)^2}","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{2 b g^3 (a+b x)^2}+\frac{B d^2 n \log (a+b x)}{2 b g^3 (b c-a d)^2}-\frac{B d^2 n \log (c+d x)}{2 b g^3 (b c-a d)^2}+\frac{B d n}{2 b g^3 (a+b x) (b c-a d)}-\frac{B n}{4 b g^3 (a+b x)^2}",1,"-(B*n)/(4*b*g^3*(a + b*x)^2) + (B*d*n)/(2*b*(b*c - a*d)*g^3*(a + b*x)) + (B*d^2*n*Log[a + b*x])/(2*b*(b*c - a*d)^2*g^3) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])/(2*b*g^3*(a + b*x)^2) - (B*d^2*n*Log[c + d*x])/(2*b*(b*c - a*d)^2*g^3)","A",4,3,33,0.09091,1,"{2525, 12, 44}"
8,1,183,0,0.1519058,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a g+b g x)^4} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(a*g + b*g*x)^4,x]","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{3 b g^4 (a+b x)^3}-\frac{B d^2 n}{3 b g^4 (a+b x) (b c-a d)^2}-\frac{B d^3 n \log (a+b x)}{3 b g^4 (b c-a d)^3}+\frac{B d^3 n \log (c+d x)}{3 b g^4 (b c-a d)^3}+\frac{B d n}{6 b g^4 (a+b x)^2 (b c-a d)}-\frac{B n}{9 b g^4 (a+b x)^3}","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{3 b g^4 (a+b x)^3}-\frac{B d^2 n}{3 b g^4 (a+b x) (b c-a d)^2}-\frac{B d^3 n \log (a+b x)}{3 b g^4 (b c-a d)^3}+\frac{B d^3 n \log (c+d x)}{3 b g^4 (b c-a d)^3}+\frac{B d n}{6 b g^4 (a+b x)^2 (b c-a d)}-\frac{B n}{9 b g^4 (a+b x)^3}",1,"-(B*n)/(9*b*g^4*(a + b*x)^3) + (B*d*n)/(6*b*(b*c - a*d)*g^4*(a + b*x)^2) - (B*d^2*n)/(3*b*(b*c - a*d)^2*g^4*(a + b*x)) - (B*d^3*n*Log[a + b*x])/(3*b*(b*c - a*d)^3*g^4) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])/(3*b*g^4*(a + b*x)^3) + (B*d^3*n*Log[c + d*x])/(3*b*(b*c - a*d)^3*g^4)","A",4,3,33,0.09091,1,"{2525, 12, 44}"
9,1,215,0,0.1890607,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a g+b g x)^5} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(a*g + b*g*x)^5,x]","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{4 b g^5 (a+b x)^4}+\frac{B d^3 n}{4 b g^5 (a+b x) (b c-a d)^3}-\frac{B d^2 n}{8 b g^5 (a+b x)^2 (b c-a d)^2}+\frac{B d^4 n \log (a+b x)}{4 b g^5 (b c-a d)^4}-\frac{B d^4 n \log (c+d x)}{4 b g^5 (b c-a d)^4}+\frac{B d n}{12 b g^5 (a+b x)^3 (b c-a d)}-\frac{B n}{16 b g^5 (a+b x)^4}","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{4 b g^5 (a+b x)^4}+\frac{B d^3 n}{4 b g^5 (a+b x) (b c-a d)^3}-\frac{B d^2 n}{8 b g^5 (a+b x)^2 (b c-a d)^2}+\frac{B d^4 n \log (a+b x)}{4 b g^5 (b c-a d)^4}-\frac{B d^4 n \log (c+d x)}{4 b g^5 (b c-a d)^4}+\frac{B d n}{12 b g^5 (a+b x)^3 (b c-a d)}-\frac{B n}{16 b g^5 (a+b x)^4}",1,"-(B*n)/(16*b*g^5*(a + b*x)^4) + (B*d*n)/(12*b*(b*c - a*d)*g^5*(a + b*x)^3) - (B*d^2*n)/(8*b*(b*c - a*d)^2*g^5*(a + b*x)^2) + (B*d^3*n)/(4*b*(b*c - a*d)^3*g^5*(a + b*x)) + (B*d^4*n*Log[a + b*x])/(4*b*(b*c - a*d)^4*g^5) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])/(4*b*g^5*(a + b*x)^4) - (B*d^4*n*Log[c + d*x])/(4*b*(b*c - a*d)^4*g^5)","A",4,3,33,0.09091,1,"{2525, 12, 44}"
10,1,602,0,0.8706196,"\int (a g+b g x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Int[(a*g + b*g*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{2 B^2 g^4 n^2 (b c-a d)^5 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{5 b d^5}-\frac{2 B g^4 n (b c-a d)^5 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 b d^5}-\frac{B g^4 n (a+b x)^2 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 b d^3}+\frac{2 B g^4 n (a+b x)^3 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{15 b d^2}+\frac{2 A B g^4 n x (b c-a d)^4}{5 d^4}-\frac{B g^4 n (a+b x)^4 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{10 b d}+\frac{g^4 (a+b x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{5 b}+\frac{2 B^2 g^4 n (a+b x) (b c-a d)^4 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{5 b d^4}+\frac{13 B^2 g^4 n^2 x (b c-a d)^4}{30 d^4}-\frac{7 B^2 g^4 n^2 (a+b x)^2 (b c-a d)^3}{60 b d^3}+\frac{B^2 g^4 n^2 (a+b x)^3 (b c-a d)^2}{30 b d^2}-\frac{B^2 g^4 n^2 (b c-a d)^5 \log ^2(c+d x)}{5 b d^5}-\frac{5 B^2 g^4 n^2 (b c-a d)^5 \log (c+d x)}{6 b d^5}+\frac{2 B^2 g^4 n^2 (b c-a d)^5 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{5 b d^5}","\frac{2 B^2 g^4 n^2 (b c-a d)^5 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{5 b d^5}+\frac{B g^4 n (b c-a d)^5 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(12 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+12 A+25 B n\right)}{30 b d^5}+\frac{B g^4 n (a+b x) (b c-a d)^4 \left(12 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+12 A+13 B n\right)}{30 b d^4}-\frac{B g^4 n (a+b x)^2 (b c-a d)^3 \left(12 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+12 A+7 B n\right)}{60 b d^3}+\frac{B g^4 n (a+b x)^3 (b c-a d)^2 \left(4 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+4 A+B n\right)}{30 b d^2}-\frac{B g^4 n (a+b x)^4 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{10 b d}+\frac{g^4 (a+b x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{5 b}",1,"(2*A*B*(b*c - a*d)^4*g^4*n*x)/(5*d^4) + (13*B^2*(b*c - a*d)^4*g^4*n^2*x)/(30*d^4) - (7*B^2*(b*c - a*d)^3*g^4*n^2*(a + b*x)^2)/(60*b*d^3) + (B^2*(b*c - a*d)^2*g^4*n^2*(a + b*x)^3)/(30*b*d^2) + (2*B^2*(b*c - a*d)^4*g^4*n*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/(5*b*d^4) - (B*(b*c - a*d)^3*g^4*n*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(5*b*d^3) + (2*B*(b*c - a*d)^2*g^4*n*(a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(15*b*d^2) - (B*(b*c - a*d)*g^4*n*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(10*b*d) + (g^4*(a + b*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(5*b) - (5*B^2*(b*c - a*d)^5*g^4*n^2*Log[c + d*x])/(6*b*d^5) + (2*B^2*(b*c - a*d)^5*g^4*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(5*b*d^5) - (2*B*(b*c - a*d)^5*g^4*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(5*b*d^5) - (B^2*(b*c - a*d)^5*g^4*n^2*Log[c + d*x]^2)/(5*b*d^5) + (2*B^2*(b*c - a*d)^5*g^4*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(5*b*d^5)","A",27,13,35,0.3714,1,"{2525, 12, 2528, 2486, 31, 43, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
11,1,512,0,0.7069992,"\int (a g+b g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Int[(a*g + b*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","-\frac{B^2 g^3 n^2 (b c-a d)^4 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{2 b d^4}+\frac{B g^3 n (b c-a d)^4 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 b d^4}+\frac{B g^3 n (a+b x)^2 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{4 b d^2}-\frac{A B g^3 n x (b c-a d)^3}{2 d^3}-\frac{B g^3 n (a+b x)^3 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{6 b d}+\frac{g^3 (a+b x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{4 b}-\frac{B^2 g^3 n (a+b x) (b c-a d)^3 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{2 b d^3}-\frac{5 B^2 g^3 n^2 x (b c-a d)^3}{12 d^3}+\frac{B^2 g^3 n^2 (a+b x)^2 (b c-a d)^2}{12 b d^2}+\frac{B^2 g^3 n^2 (b c-a d)^4 \log ^2(c+d x)}{4 b d^4}+\frac{11 B^2 g^3 n^2 (b c-a d)^4 \log (c+d x)}{12 b d^4}-\frac{B^2 g^3 n^2 (b c-a d)^4 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{2 b d^4}","-\frac{B^2 g^3 n^2 (b c-a d)^4 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{2 b d^4}-\frac{B g^3 n (b c-a d)^4 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+6 A+11 B n\right)}{12 b d^4}-\frac{B g^3 n (a+b x) (b c-a d)^3 \left(6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+6 A+5 B n\right)}{12 b d^3}+\frac{B g^3 n (a+b x)^2 (b c-a d)^2 \left(3 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+3 A+B n\right)}{12 b d^2}-\frac{B g^3 n (a+b x)^3 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{6 b d}+\frac{g^3 (a+b x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{4 b}",1,"-(A*B*(b*c - a*d)^3*g^3*n*x)/(2*d^3) - (5*B^2*(b*c - a*d)^3*g^3*n^2*x)/(12*d^3) + (B^2*(b*c - a*d)^2*g^3*n^2*(a + b*x)^2)/(12*b*d^2) - (B^2*(b*c - a*d)^3*g^3*n*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/(2*b*d^3) + (B*(b*c - a*d)^2*g^3*n*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(4*b*d^2) - (B*(b*c - a*d)*g^3*n*(a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(6*b*d) + (g^3*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(4*b) + (11*B^2*(b*c - a*d)^4*g^3*n^2*Log[c + d*x])/(12*b*d^4) - (B^2*(b*c - a*d)^4*g^3*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(2*b*d^4) + (B*(b*c - a*d)^4*g^3*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(2*b*d^4) + (B^2*(b*c - a*d)^4*g^3*n^2*Log[c + d*x]^2)/(4*b*d^4) - (B^2*(b*c - a*d)^4*g^3*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*b*d^4)","A",23,13,35,0.3714,1,"{2525, 12, 2528, 2486, 31, 43, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
12,1,420,0,0.5828955,"\int (a g+b g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Int[(a*g + b*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{2 B^2 g^2 n^2 (b c-a d)^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 b d^3}-\frac{2 B g^2 n (b c-a d)^3 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b d^3}+\frac{2 A B g^2 n x (b c-a d)^2}{3 d^2}-\frac{B g^2 n (a+b x)^2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b d}+\frac{g^2 (a+b x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{3 b}+\frac{2 B^2 g^2 n (a+b x) (b c-a d)^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{3 b d^2}+\frac{B^2 g^2 n^2 x (b c-a d)^2}{3 d^2}-\frac{B^2 g^2 n^2 (b c-a d)^3 \log ^2(c+d x)}{3 b d^3}-\frac{B^2 g^2 n^2 (b c-a d)^3 \log (c+d x)}{b d^3}+\frac{2 B^2 g^2 n^2 (b c-a d)^3 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 b d^3}","\frac{2 B^2 g^2 n^2 (b c-a d)^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{3 b d^3}+\frac{B g^2 n (b c-a d)^3 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 A+3 B n\right)}{3 b d^3}+\frac{B g^2 n (a+b x) (b c-a d)^2 \left(2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 A+B n\right)}{3 b d^2}-\frac{B g^2 n (a+b x)^2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b d}+\frac{g^2 (a+b x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{3 b}",1,"(2*A*B*(b*c - a*d)^2*g^2*n*x)/(3*d^2) + (B^2*(b*c - a*d)^2*g^2*n^2*x)/(3*d^2) + (2*B^2*(b*c - a*d)^2*g^2*n*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/(3*b*d^2) - (B*(b*c - a*d)*g^2*n*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*b*d) + (g^2*(a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(3*b) - (B^2*(b*c - a*d)^3*g^2*n^2*Log[c + d*x])/(b*d^3) + (2*B^2*(b*c - a*d)^3*g^2*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*b*d^3) - (2*B*(b*c - a*d)^3*g^2*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(3*b*d^3) - (B^2*(b*c - a*d)^3*g^2*n^2*Log[c + d*x]^2)/(3*b*d^3) + (2*B^2*(b*c - a*d)^3*g^2*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*b*d^3)","A",19,13,35,0.3714,1,"{2525, 12, 2528, 2486, 31, 43, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
13,1,309,0,0.442832,"\int (a g+b g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Int[(a*g + b*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","-\frac{B^2 g n^2 (b c-a d)^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b d^2}+\frac{B g n (b c-a d)^2 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b d^2}+\frac{g (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 b}-\frac{A B g n x (b c-a d)}{d}+\frac{B^2 g n^2 (b c-a d)^2 \log ^2(c+d x)}{2 b d^2}+\frac{B^2 g n^2 (b c-a d)^2 \log (c+d x)}{b d^2}-\frac{B^2 g n^2 (b c-a d)^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b d^2}-\frac{B^2 g n (a+b x) (b c-a d) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b d}","-\frac{B^2 g n^2 (b c-a d)^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}-\frac{B g n (b c-a d)^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A+B n\right)}{b d^2}-\frac{B g n (a+b x) (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b d}+\frac{g (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 b}",1,"-((A*B*(b*c - a*d)*g*n*x)/d) - (B^2*(b*c - a*d)*g*n*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/(b*d) + (g*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(2*b) + (B^2*(b*c - a*d)^2*g*n^2*Log[c + d*x])/(b*d^2) - (B^2*(b*c - a*d)^2*g*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*d^2) + (B*(b*c - a*d)^2*g*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(b*d^2) + (B^2*(b*c - a*d)^2*g*n^2*Log[c + d*x]^2)/(2*b*d^2) - (B^2*(b*c - a*d)^2*g*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*d^2)","A",15,12,33,0.3636,1,"{2525, 12, 2528, 2486, 31, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
14,1,789,0,3.5728882,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{a g+b g x} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(a*g + b*g*x),x]","\frac{2 A B n \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g}-\frac{2 B^2 n \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+\log \left((a+b x)^n\right)+\log \left((c+d x)^{-n}\right)\right)}{b g}-\frac{2 B^2 n^2 \text{PolyLog}\left(3,-\frac{d (a+b x)}{b c-a d}\right)}{b g}-\frac{2 B^2 n^2 \text{PolyLog}\left(3,\frac{b (c+d x)}{b c-a d}\right)}{b g}+\frac{2 B^2 n \log \left((a+b x)^n\right) \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g}-\frac{2 B^2 n \log \left((c+d x)^{-n}\right) \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g}+\frac{\log (a g+b g x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{b g}+\frac{2 A B n \log (a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{A B n \log ^2(g (a+b x))}{b g}-\frac{B^2 n \log ^2(a g+b g x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b g}-\frac{2 B^2 n \log (a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+\log \left((a+b x)^n\right)+\log \left((c+d x)^{-n}\right)\right)}{b g}-\frac{B^2 n^2 \log (-c-d x) \log ^2(g (a+b x))}{b g}+\frac{B^2 n^2 \log ^2(g (a+b x)) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{B^2 n^2 \log ^2(a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{B^2 \log (g (a+b x)) \log ^2\left((c+d x)^{-n}\right)}{b g}+\frac{B^2 \log ^2\left((c+d x)^{-n}\right) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g}-\frac{B^2 \log (-c-d x) \log ^2\left((a+b x)^n\right)}{b g}+\frac{B^2 \log ^2\left((a+b x)^n\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}+\frac{2 B^2 n \log (-c-d x) \log (g (a+b x)) \log \left((a+b x)^n\right)}{b g}+\frac{B^2 n^2 \log ^3(g (a+b x))}{3 b g}","\frac{2 B n \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b g}+\frac{2 B^2 n^2 \text{PolyLog}\left(3,\frac{b (c+d x)}{d (a+b x)}\right)}{b g}-\frac{\log \left(1-\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{b g}",1,"-((A*B*n*Log[g*(a + b*x)]^2)/(b*g)) + (B^2*n^2*Log[g*(a + b*x)]^3)/(3*b*g) - (B^2*n^2*Log[g*(a + b*x)]^2*Log[-c - d*x])/(b*g) + (2*B^2*n*Log[g*(a + b*x)]*Log[(a + b*x)^n]*Log[-c - d*x])/(b*g) - (B^2*Log[(a + b*x)^n]^2*Log[-c - d*x])/(b*g) + (B^2*n^2*Log[g*(a + b*x)]^2*Log[(b*(c + d*x))/(b*c - a*d)])/(b*g) + (B^2*Log[(a + b*x)^n]^2*Log[(b*(c + d*x))/(b*c - a*d)])/(b*g) + (B^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[(c + d*x)^(-n)]^2)/(b*g) - (B^2*Log[g*(a + b*x)]*Log[(c + d*x)^(-n)]^2)/(b*g) + ((A + B*Log[e*((a + b*x)/(c + d*x))^n])^2*Log[a*g + b*g*x])/(b*g) + (2*A*B*n*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x])/(b*g) - (2*B^2*n*Log[(b*(c + d*x))/(b*c - a*d)]*(Log[(a + b*x)^n] - Log[e*((a + b*x)/(c + d*x))^n] + Log[(c + d*x)^(-n)])*Log[a*g + b*g*x])/(b*g) - (B^2*n*Log[e*((a + b*x)/(c + d*x))^n]*Log[a*g + b*g*x]^2)/(b*g) - (B^2*n^2*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x]^2)/(b*g) + (2*A*B*n*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g) + (2*B^2*n*Log[(a + b*x)^n]*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g) - (2*B^2*n*(Log[(a + b*x)^n] - Log[e*((a + b*x)/(c + d*x))^n] + Log[(c + d*x)^(-n)])*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g) - (2*B^2*n*Log[(c + d*x)^(-n)]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*g) - (2*B^2*n^2*PolyLog[3, -((d*(a + b*x))/(b*c - a*d))])/(b*g) - (2*B^2*n^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])/(b*g)","B",45,23,35,0.6571,1,"{2524, 2528, 2418, 2390, 2301, 2394, 2393, 2391, 6688, 12, 6742, 2500, 2440, 2434, 2433, 2375, 2317, 2374, 6589, 2499, 2302, 30, 2396}"
15,1,512,0,0.8404408,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{(a g+b g x)^2} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(a*g + b*g*x)^2,x]","-\frac{2 B^2 d n^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g^2 (b c-a d)}-\frac{2 B^2 d n^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g^2 (b c-a d)}-\frac{2 B d n \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b g^2 (b c-a d)}-\frac{2 B n \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b g^2 (a+b x)}+\frac{2 B d n \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b g^2 (b c-a d)}-\frac{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{b g^2 (a+b x)}+\frac{B^2 d n^2 \log ^2(a+b x)}{b g^2 (b c-a d)}+\frac{B^2 d n^2 \log ^2(c+d x)}{b g^2 (b c-a d)}-\frac{2 B^2 d n^2 \log (a+b x)}{b g^2 (b c-a d)}-\frac{2 B^2 d n^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g^2 (b c-a d)}+\frac{2 B^2 d n^2 \log (c+d x)}{b g^2 (b c-a d)}-\frac{2 B^2 d n^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g^2 (b c-a d)}-\frac{2 B^2 n^2}{b g^2 (a+b x)}","-\frac{2 B n (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^2 (a+b x) (b c-a d)}-\frac{(c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g^2 (a+b x) (b c-a d)}-\frac{2 B^2 n^2 (c+d x)}{g^2 (a+b x) (b c-a d)}",1,"(-2*B^2*n^2)/(b*g^2*(a + b*x)) - (2*B^2*d*n^2*Log[a + b*x])/(b*(b*c - a*d)*g^2) + (B^2*d*n^2*Log[a + b*x]^2)/(b*(b*c - a*d)*g^2) - (2*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(b*g^2*(a + b*x)) - (2*B*d*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(b*(b*c - a*d)*g^2) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(b*g^2*(a + b*x)) + (2*B^2*d*n^2*Log[c + d*x])/(b*(b*c - a*d)*g^2) - (2*B^2*d*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*(b*c - a*d)*g^2) + (2*B*d*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(b*(b*c - a*d)*g^2) + (B^2*d*n^2*Log[c + d*x]^2)/(b*(b*c - a*d)*g^2) - (2*B^2*d*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)*g^2) - (2*B^2*d*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*(b*c - a*d)*g^2) - (2*B^2*d*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)*g^2)","C",24,11,35,0.3143,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
16,1,626,0,0.9227851,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{(a g+b g x)^3} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(a*g + b*g*x)^3,x]","\frac{B^2 d^2 n^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}+\frac{B^2 d^2 n^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}+\frac{B d^2 n \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b g^3 (b c-a d)^2}-\frac{B d^2 n \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b g^3 (b c-a d)^2}+\frac{B d n \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b g^3 (a+b x) (b c-a d)}-\frac{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 b g^3 (a+b x)^2}-\frac{B n \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 b g^3 (a+b x)^2}-\frac{B^2 d^2 n^2 \log ^2(a+b x)}{2 b g^3 (b c-a d)^2}-\frac{B^2 d^2 n^2 \log ^2(c+d x)}{2 b g^3 (b c-a d)^2}+\frac{3 B^2 d^2 n^2 \log (a+b x)}{2 b g^3 (b c-a d)^2}-\frac{3 B^2 d^2 n^2 \log (c+d x)}{2 b g^3 (b c-a d)^2}+\frac{B^2 d^2 n^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}+\frac{B^2 d^2 n^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}+\frac{3 B^2 d n^2}{2 b g^3 (a+b x) (b c-a d)}-\frac{B^2 n^2}{4 b g^3 (a+b x)^2}","-\frac{b B n (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 g^3 (a+b x)^2 (b c-a d)^2}+\frac{2 B d n (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^3 (a+b x) (b c-a d)^2}-\frac{b (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 g^3 (a+b x)^2 (b c-a d)^2}+\frac{d (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g^3 (a+b x) (b c-a d)^2}-\frac{b B^2 n^2 (c+d x)^2}{4 g^3 (a+b x)^2 (b c-a d)^2}+\frac{2 B^2 d n^2 (c+d x)}{g^3 (a+b x) (b c-a d)^2}",1,"-(B^2*n^2)/(4*b*g^3*(a + b*x)^2) + (3*B^2*d*n^2)/(2*b*(b*c - a*d)*g^3*(a + b*x)) + (3*B^2*d^2*n^2*Log[a + b*x])/(2*b*(b*c - a*d)^2*g^3) - (B^2*d^2*n^2*Log[a + b*x]^2)/(2*b*(b*c - a*d)^2*g^3) - (B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*b*g^3*(a + b*x)^2) + (B*d*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(b*(b*c - a*d)*g^3*(a + b*x)) + (B*d^2*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(b*(b*c - a*d)^2*g^3) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(2*b*g^3*(a + b*x)^2) - (3*B^2*d^2*n^2*Log[c + d*x])/(2*b*(b*c - a*d)^2*g^3) + (B^2*d^2*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*(b*c - a*d)^2*g^3) - (B*d^2*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(b*(b*c - a*d)^2*g^3) - (B^2*d^2*n^2*Log[c + d*x]^2)/(2*b*(b*c - a*d)^2*g^3) + (B^2*d^2*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)^2*g^3) + (B^2*d^2*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*(b*c - a*d)^2*g^3) + (B^2*d^2*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)^2*g^3)","C",28,11,35,0.3143,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
17,1,736,0,1.0865568,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{(a g+b g x)^4} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(a*g + b*g*x)^4,x]","-\frac{2 B^2 d^3 n^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}-\frac{2 B^2 d^3 n^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}-\frac{2 B d^3 n \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b g^4 (b c-a d)^3}+\frac{2 B d^3 n \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b g^4 (b c-a d)^3}-\frac{2 B d^2 n \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b g^4 (a+b x) (b c-a d)^2}+\frac{B d n \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b g^4 (a+b x)^2 (b c-a d)}-\frac{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{3 b g^4 (a+b x)^3}-\frac{2 B n \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{9 b g^4 (a+b x)^3}-\frac{11 B^2 d^2 n^2}{9 b g^4 (a+b x) (b c-a d)^2}+\frac{B^2 d^3 n^2 \log ^2(a+b x)}{3 b g^4 (b c-a d)^3}+\frac{B^2 d^3 n^2 \log ^2(c+d x)}{3 b g^4 (b c-a d)^3}-\frac{11 B^2 d^3 n^2 \log (a+b x)}{9 b g^4 (b c-a d)^3}+\frac{11 B^2 d^3 n^2 \log (c+d x)}{9 b g^4 (b c-a d)^3}-\frac{2 B^2 d^3 n^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}-\frac{2 B^2 d^3 n^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}+\frac{5 B^2 d n^2}{18 b g^4 (a+b x)^2 (b c-a d)}-\frac{2 B^2 n^2}{27 b g^4 (a+b x)^3}","-\frac{b^2 (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{3 g^4 (a+b x)^3 (b c-a d)^3}-\frac{2 b^2 B n (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{9 g^4 (a+b x)^3 (b c-a d)^3}-\frac{d^2 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g^4 (a+b x) (b c-a d)^3}-\frac{2 B d^2 n (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^4 (a+b x) (b c-a d)^3}+\frac{b d (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g^4 (a+b x)^2 (b c-a d)^3}+\frac{b B d n (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^4 (a+b x)^2 (b c-a d)^3}-\frac{2 b^2 B^2 n^2 (c+d x)^3}{27 g^4 (a+b x)^3 (b c-a d)^3}-\frac{2 B^2 d^2 n^2 (c+d x)}{g^4 (a+b x) (b c-a d)^3}+\frac{b B^2 d n^2 (c+d x)^2}{2 g^4 (a+b x)^2 (b c-a d)^3}",1,"(-2*B^2*n^2)/(27*b*g^4*(a + b*x)^3) + (5*B^2*d*n^2)/(18*b*(b*c - a*d)*g^4*(a + b*x)^2) - (11*B^2*d^2*n^2)/(9*b*(b*c - a*d)^2*g^4*(a + b*x)) - (11*B^2*d^3*n^2*Log[a + b*x])/(9*b*(b*c - a*d)^3*g^4) + (B^2*d^3*n^2*Log[a + b*x]^2)/(3*b*(b*c - a*d)^3*g^4) - (2*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(9*b*g^4*(a + b*x)^3) + (B*d*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*b*(b*c - a*d)*g^4*(a + b*x)^2) - (2*B*d^2*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*b*(b*c - a*d)^2*g^4*(a + b*x)) - (2*B*d^3*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*b*(b*c - a*d)^3*g^4) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(3*b*g^4*(a + b*x)^3) + (11*B^2*d^3*n^2*Log[c + d*x])/(9*b*(b*c - a*d)^3*g^4) - (2*B^2*d^3*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*b*(b*c - a*d)^3*g^4) + (2*B*d^3*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(3*b*(b*c - a*d)^3*g^4) + (B^2*d^3*n^2*Log[c + d*x]^2)/(3*b*(b*c - a*d)^3*g^4) - (2*B^2*d^3*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3*b*(b*c - a*d)^3*g^4) - (2*B^2*d^3*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(3*b*(b*c - a*d)^3*g^4) - (2*B^2*d^3*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*b*(b*c - a*d)^3*g^4)","C",32,11,35,0.3143,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
18,1,826,0,1.3140498,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{(a g+b g x)^5} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(a*g + b*g*x)^5,x]","-\frac{B^2 n^2 \log ^2(a+b x) d^4}{4 b (b c-a d)^4 g^5}-\frac{B^2 n^2 \log ^2(c+d x) d^4}{4 b (b c-a d)^4 g^5}+\frac{25 B^2 n^2 \log (a+b x) d^4}{24 b (b c-a d)^4 g^5}+\frac{B n \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) d^4}{2 b (b c-a d)^4 g^5}-\frac{25 B^2 n^2 \log (c+d x) d^4}{24 b (b c-a d)^4 g^5}+\frac{B^2 n^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) d^4}{2 b (b c-a d)^4 g^5}-\frac{B n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \log (c+d x) d^4}{2 b (b c-a d)^4 g^5}+\frac{B^2 n^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) d^4}{2 b (b c-a d)^4 g^5}+\frac{B^2 n^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) d^4}{2 b (b c-a d)^4 g^5}+\frac{B^2 n^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) d^4}{2 b (b c-a d)^4 g^5}+\frac{B n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) d^3}{2 b (b c-a d)^3 g^5 (a+b x)}+\frac{25 B^2 n^2 d^3}{24 b (b c-a d)^3 g^5 (a+b x)}-\frac{B n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) d^2}{4 b (b c-a d)^2 g^5 (a+b x)^2}-\frac{13 B^2 n^2 d^2}{48 b (b c-a d)^2 g^5 (a+b x)^2}+\frac{B n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) d}{6 b (b c-a d) g^5 (a+b x)^3}+\frac{7 B^2 n^2 d}{72 b (b c-a d) g^5 (a+b x)^3}-\frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{4 b g^5 (a+b x)^4}-\frac{B n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{8 b g^5 (a+b x)^4}-\frac{B^2 n^2}{32 b g^5 (a+b x)^4}","-\frac{b^3 (c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{4 g^5 (a+b x)^4 (b c-a d)^4}-\frac{b^3 B n (c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{8 g^5 (a+b x)^4 (b c-a d)^4}+\frac{b^2 d (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g^5 (a+b x)^3 (b c-a d)^4}+\frac{2 b^2 B d n (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 g^5 (a+b x)^3 (b c-a d)^4}-\frac{3 b d^2 (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 g^5 (a+b x)^2 (b c-a d)^4}-\frac{3 b B d^2 n (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 g^5 (a+b x)^2 (b c-a d)^4}+\frac{d^3 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g^5 (a+b x) (b c-a d)^4}+\frac{2 B d^3 n (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^5 (a+b x) (b c-a d)^4}-\frac{b^3 B^2 n^2 (c+d x)^4}{32 g^5 (a+b x)^4 (b c-a d)^4}+\frac{2 b^2 B^2 d n^2 (c+d x)^3}{9 g^5 (a+b x)^3 (b c-a d)^4}-\frac{3 b B^2 d^2 n^2 (c+d x)^2}{4 g^5 (a+b x)^2 (b c-a d)^4}+\frac{2 B^2 d^3 n^2 (c+d x)}{g^5 (a+b x) (b c-a d)^4}",1,"-(B^2*n^2)/(32*b*g^5*(a + b*x)^4) + (7*B^2*d*n^2)/(72*b*(b*c - a*d)*g^5*(a + b*x)^3) - (13*B^2*d^2*n^2)/(48*b*(b*c - a*d)^2*g^5*(a + b*x)^2) + (25*B^2*d^3*n^2)/(24*b*(b*c - a*d)^3*g^5*(a + b*x)) + (25*B^2*d^4*n^2*Log[a + b*x])/(24*b*(b*c - a*d)^4*g^5) - (B^2*d^4*n^2*Log[a + b*x]^2)/(4*b*(b*c - a*d)^4*g^5) - (B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(8*b*g^5*(a + b*x)^4) + (B*d*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(6*b*(b*c - a*d)*g^5*(a + b*x)^3) - (B*d^2*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(4*b*(b*c - a*d)^2*g^5*(a + b*x)^2) + (B*d^3*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*b*(b*c - a*d)^3*g^5*(a + b*x)) + (B*d^4*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*b*(b*c - a*d)^4*g^5) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(4*b*g^5*(a + b*x)^4) - (25*B^2*d^4*n^2*Log[c + d*x])/(24*b*(b*c - a*d)^4*g^5) + (B^2*d^4*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(2*b*(b*c - a*d)^4*g^5) - (B*d^4*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(2*b*(b*c - a*d)^4*g^5) - (B^2*d^4*n^2*Log[c + d*x]^2)/(4*b*(b*c - a*d)^4*g^5) + (B^2*d^4*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(2*b*(b*c - a*d)^4*g^5) + (B^2*d^4*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(2*b*(b*c - a*d)^4*g^5) + (B^2*d^4*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*b*(b*c - a*d)^4*g^5)","C",36,11,35,0.3143,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
19,0,0,0,0.2328954,"\int \frac{(a g+b g x)^2}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Int[(a*g + b*g*x)^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\int \frac{(a g+b g x)^2}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","\text{Int}\left(\frac{(a g+b g x)^2}{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A},x\right)",0,"a^2*g^2*Defer[Int][(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-1), x] + 2*a*b*g^2*Defer[Int][x/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x] + b^2*g^2*Defer[Int][x^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x]","A",0,0,0,0,-1,"{}"
20,0,0,0,0.1147194,"\int \frac{a g+b g x}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Int[(a*g + b*g*x)/(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\int \frac{a g+b g x}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","\text{Int}\left(\frac{a g+b g x}{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A},x\right)",0,"a*g*Defer[Int][(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-1), x] + b*g*Defer[Int][x/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x]","A",0,0,0,0,-1,"{}"
21,0,0,0,0.081441,"\int \frac{1}{(a g+b g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","Int[1/((a*g + b*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])),x]","\int \frac{1}{(a g+b g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{(a g+b g x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)},x\right)",0,"Defer[Int][1/((a*g + b*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])), x]","A",0,0,0,0,-1,"{}"
22,0,0,0,0.0990798,"\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","Int[1/((a*g + b*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])),x]","\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","\frac{e^{\frac{A}{B n}} (c+d x) \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{\frac{1}{n}} \text{Ei}\left(-\frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{B n}\right)}{B g^2 n (a+b x) (b c-a d)}",1,"Defer[Int][1/((a*g + b*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])), x]","F",0,0,0,0,-1,"{}"
23,0,0,0,0.0821707,"\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","Int[1/((a*g + b*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])),x]","\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","\frac{b e^{\frac{2 A}{B n}} (c+d x)^2 \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{2/n} \text{Ei}\left(-\frac{2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{B n}\right)}{B g^3 n (a+b x)^2 (b c-a d)^2}-\frac{d e^{\frac{A}{B n}} (c+d x) \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{\frac{1}{n}} \text{Ei}\left(-\frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{B n}\right)}{B g^3 n (a+b x) (b c-a d)^2}",1,"Defer[Int][1/((a*g + b*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])), x]","F",0,0,0,0,-1,"{}"
24,0,0,0,0.2375313,"\int \frac{(a g+b g x)^2}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Int[(a*g + b*g*x)^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\int \frac{(a g+b g x)^2}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{(a g+b g x)^2}{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2},x\right)",0,"a^2*g^2*Defer[Int][(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-2), x] + 2*a*b*g^2*Defer[Int][x/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x] + b^2*g^2*Defer[Int][x^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x]","A",0,0,0,0,-1,"{}"
25,0,0,0,0.1256928,"\int \frac{a g+b g x}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Int[(a*g + b*g*x)/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\int \frac{a g+b g x}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{a g+b g x}{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2},x\right)",0,"a*g*Defer[Int][(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-2), x] + b*g*Defer[Int][x/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x]","A",0,0,0,0,-1,"{}"
26,0,0,0,0.0908582,"\int \frac{1}{(a g+b g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Int[1/((a*g + b*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2),x]","\int \frac{1}{(a g+b g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(a g+b g x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2},x\right)",0,"Defer[Int][1/((a*g + b*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2), x]","A",0,0,0,0,-1,"{}"
27,0,0,0,0.1045894,"\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Int[1/((a*g + b*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2),x]","\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","-\frac{e^{\frac{A}{B n}} (c+d x) \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{\frac{1}{n}} \text{Ei}\left(-\frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{B n}\right)}{B^2 g^2 n^2 (a+b x) (b c-a d)}-\frac{c+d x}{B g^2 n (a+b x) (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}",1,"Defer[Int][1/((a*g + b*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2), x]","F",0,0,0,0,-1,"{}"
28,0,0,0,0.0928482,"\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Int[1/((a*g + b*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2),x]","\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","-\frac{2 b e^{\frac{2 A}{B n}} (c+d x)^2 \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{2/n} \text{Ei}\left(-\frac{2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{B n}\right)}{B^2 g^3 n^2 (a+b x)^2 (b c-a d)^2}+\frac{d e^{\frac{A}{B n}} (c+d x) \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{\frac{1}{n}} \text{Ei}\left(-\frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{B n}\right)}{B^2 g^3 n^2 (a+b x) (b c-a d)^2}-\frac{b (c+d x)^2}{B g^3 n (a+b x)^2 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}+\frac{d (c+d x)}{B g^3 n (a+b x) (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}",1,"Defer[Int][1/((a*g + b*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2), x]","F",0,0,0,0,-1,"{}"
29,1,188,0,0.1278252,"\int (c g+d g x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Int[(c*g + d*g*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^4 (c+d x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 d}-\frac{B g^4 n x (b c-a d)^4}{5 b^4}-\frac{B g^4 n (c+d x)^2 (b c-a d)^3}{10 b^3 d}-\frac{B g^4 n (c+d x)^3 (b c-a d)^2}{15 b^2 d}-\frac{B g^4 n (b c-a d)^5 \log (a+b x)}{5 b^5 d}-\frac{B g^4 n (c+d x)^4 (b c-a d)}{20 b d}","\frac{g^4 (c+d x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 d}-\frac{B g^4 n x (b c-a d)^4}{5 b^4}-\frac{B g^4 n (c+d x)^2 (b c-a d)^3}{10 b^3 d}-\frac{B g^4 n (c+d x)^3 (b c-a d)^2}{15 b^2 d}-\frac{B g^4 n (b c-a d)^5 \log (a+b x)}{5 b^5 d}-\frac{B g^4 n (c+d x)^4 (b c-a d)}{20 b d}",1,"-(B*(b*c - a*d)^4*g^4*n*x)/(5*b^4) - (B*(b*c - a*d)^3*g^4*n*(c + d*x)^2)/(10*b^3*d) - (B*(b*c - a*d)^2*g^4*n*(c + d*x)^3)/(15*b^2*d) - (B*(b*c - a*d)*g^4*n*(c + d*x)^4)/(20*b*d) - (B*(b*c - a*d)^5*g^4*n*Log[a + b*x])/(5*b^5*d) + (g^4*(c + d*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(5*d)","A",4,3,33,0.09091,1,"{2525, 12, 43}"
30,1,156,0,0.1020996,"\int (c g+d g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Int[(c*g + d*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^3 (c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{4 d}-\frac{B g^3 n x (b c-a d)^3}{4 b^3}-\frac{B g^3 n (c+d x)^2 (b c-a d)^2}{8 b^2 d}-\frac{B g^3 n (b c-a d)^4 \log (a+b x)}{4 b^4 d}-\frac{B g^3 n (c+d x)^3 (b c-a d)}{12 b d}","\frac{g^3 (c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{4 d}-\frac{B g^3 n x (b c-a d)^3}{4 b^3}-\frac{B g^3 n (c+d x)^2 (b c-a d)^2}{8 b^2 d}-\frac{B g^3 n (b c-a d)^4 \log (a+b x)}{4 b^4 d}-\frac{B g^3 n (c+d x)^3 (b c-a d)}{12 b d}",1,"-(B*(b*c - a*d)^3*g^3*n*x)/(4*b^3) - (B*(b*c - a*d)^2*g^3*n*(c + d*x)^2)/(8*b^2*d) - (B*(b*c - a*d)*g^3*n*(c + d*x)^3)/(12*b*d) - (B*(b*c - a*d)^4*g^3*n*Log[a + b*x])/(4*b^4*d) + (g^3*(c + d*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(4*d)","A",4,3,33,0.09091,1,"{2525, 12, 43}"
31,1,124,0,0.0813244,"\int (c g+d g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Int[(c*g + d*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^2 (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 d}-\frac{B g^2 n x (b c-a d)^2}{3 b^2}-\frac{B g^2 n (b c-a d)^3 \log (a+b x)}{3 b^3 d}-\frac{B g^2 n (c+d x)^2 (b c-a d)}{6 b d}","\frac{g^2 (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 d}-\frac{B g^2 n x (b c-a d)^2}{3 b^2}-\frac{B g^2 n (b c-a d)^3 \log (a+b x)}{3 b^3 d}-\frac{B g^2 n (c+d x)^2 (b c-a d)}{6 b d}",1,"-(B*(b*c - a*d)^2*g^2*n*x)/(3*b^2) - (B*(b*c - a*d)*g^2*n*(c + d*x)^2)/(6*b*d) - (B*(b*c - a*d)^3*g^2*n*Log[a + b*x])/(3*b^3*d) + (g^2*(c + d*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*d)","A",4,3,33,0.09091,1,"{2525, 12, 43}"
32,1,86,0,0.0599644,"\int (c g+d g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Int[(c*g + d*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 d}-\frac{B g n (b c-a d)^2 \log (a+b x)}{2 b^2 d}-\frac{B g n x (b c-a d)}{2 b}","\frac{g (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 d}-\frac{B g n (b c-a d)^2 \log (a+b x)}{2 b^2 d}-\frac{B g n x (b c-a d)}{2 b}",1,"-(B*(b*c - a*d)*g*n*x)/(2*b) - (B*(b*c - a*d)^2*g*n*Log[a + b*x])/(2*b^2*d) + (g*(c + d*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*d)","A",4,3,31,0.09677,1,"{2525, 12, 43}"
33,1,128,0,0.2013795,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{c g+d g x} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(c*g + d*g*x),x]","-\frac{B n \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{d g}+\frac{\log (c g+d g x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{d g}-\frac{B n \log (c g+d g x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{d g}+\frac{B n \log ^2(g (c+d x))}{2 d g}","-\frac{B n \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{d g}-\frac{\log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{d g}",1,"(B*n*Log[g*(c + d*x)]^2)/(2*d*g) - (B*n*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c*g + d*g*x])/(d*g) + ((A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c*g + d*g*x])/(d*g) - (B*n*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(d*g)","A",9,8,33,0.2424,1,"{2524, 2418, 2394, 2393, 2391, 2390, 12, 2301}"
34,1,107,0,0.0873029,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(c g+d g x)^2} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(c*g + d*g*x)^2,x]","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{d g^2 (c+d x)}+\frac{b B n \log (a+b x)}{d g^2 (b c-a d)}-\frac{b B n \log (c+d x)}{d g^2 (b c-a d)}+\frac{B n}{d g^2 (c+d x)}","\frac{A (a+b x)}{g^2 (c+d x) (b c-a d)}+\frac{B (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{g^2 (c+d x) (b c-a d)}-\frac{B n (a+b x)}{g^2 (c+d x) (b c-a d)}",1,"(B*n)/(d*g^2*(c + d*x)) + (b*B*n*Log[a + b*x])/(d*(b*c - a*d)*g^2) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])/(d*g^2*(c + d*x)) - (b*B*n*Log[c + d*x])/(d*(b*c - a*d)*g^2)","A",4,3,33,0.09091,1,"{2525, 12, 44}"
35,1,151,0,0.1143009,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(c g+d g x)^3} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(c*g + d*g*x)^3,x]","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{2 d g^3 (c+d x)^2}+\frac{b^2 B n \log (a+b x)}{2 d g^3 (b c-a d)^2}-\frac{b^2 B n \log (c+d x)}{2 d g^3 (b c-a d)^2}+\frac{b B n}{2 d g^3 (c+d x) (b c-a d)}+\frac{B n}{4 d g^3 (c+d x)^2}","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{2 d g^3 (c+d x)^2}+\frac{b^2 B n \log (a+b x)}{2 d g^3 (b c-a d)^2}-\frac{b^2 B n \log (c+d x)}{2 d g^3 (b c-a d)^2}+\frac{b B n}{2 d g^3 (c+d x) (b c-a d)}+\frac{B n}{4 d g^3 (c+d x)^2}",1,"(B*n)/(4*d*g^3*(c + d*x)^2) + (b*B*n)/(2*d*(b*c - a*d)*g^3*(c + d*x)) + (b^2*B*n*Log[a + b*x])/(2*d*(b*c - a*d)^2*g^3) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])/(2*d*g^3*(c + d*x)^2) - (b^2*B*n*Log[c + d*x])/(2*d*(b*c - a*d)^2*g^3)","A",4,3,33,0.09091,1,"{2525, 12, 44}"
36,1,183,0,0.143203,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(c g+d g x)^4} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(c*g + d*g*x)^4,x]","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{3 d g^4 (c+d x)^3}+\frac{b^2 B n}{3 d g^4 (c+d x) (b c-a d)^2}+\frac{b^3 B n \log (a+b x)}{3 d g^4 (b c-a d)^3}-\frac{b^3 B n \log (c+d x)}{3 d g^4 (b c-a d)^3}+\frac{b B n}{6 d g^4 (c+d x)^2 (b c-a d)}+\frac{B n}{9 d g^4 (c+d x)^3}","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{3 d g^4 (c+d x)^3}+\frac{b^2 B n}{3 d g^4 (c+d x) (b c-a d)^2}+\frac{b^3 B n \log (a+b x)}{3 d g^4 (b c-a d)^3}-\frac{b^3 B n \log (c+d x)}{3 d g^4 (b c-a d)^3}+\frac{b B n}{6 d g^4 (c+d x)^2 (b c-a d)}+\frac{B n}{9 d g^4 (c+d x)^3}",1,"(B*n)/(9*d*g^4*(c + d*x)^3) + (b*B*n)/(6*d*(b*c - a*d)*g^4*(c + d*x)^2) + (b^2*B*n)/(3*d*(b*c - a*d)^2*g^4*(c + d*x)) + (b^3*B*n*Log[a + b*x])/(3*d*(b*c - a*d)^3*g^4) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])/(3*d*g^4*(c + d*x)^3) - (b^3*B*n*Log[c + d*x])/(3*d*(b*c - a*d)^3*g^4)","A",4,3,33,0.09091,1,"{2525, 12, 44}"
37,1,215,0,0.1756393,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(c g+d g x)^5} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(c*g + d*g*x)^5,x]","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{4 d g^5 (c+d x)^4}+\frac{b^3 B n}{4 d g^5 (c+d x) (b c-a d)^3}+\frac{b^2 B n}{8 d g^5 (c+d x)^2 (b c-a d)^2}+\frac{b^4 B n \log (a+b x)}{4 d g^5 (b c-a d)^4}-\frac{b^4 B n \log (c+d x)}{4 d g^5 (b c-a d)^4}+\frac{b B n}{12 d g^5 (c+d x)^3 (b c-a d)}+\frac{B n}{16 d g^5 (c+d x)^4}","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{4 d g^5 (c+d x)^4}+\frac{b^3 B n}{4 d g^5 (c+d x) (b c-a d)^3}+\frac{b^2 B n}{8 d g^5 (c+d x)^2 (b c-a d)^2}+\frac{b^4 B n \log (a+b x)}{4 d g^5 (b c-a d)^4}-\frac{b^4 B n \log (c+d x)}{4 d g^5 (b c-a d)^4}+\frac{b B n}{12 d g^5 (c+d x)^3 (b c-a d)}+\frac{B n}{16 d g^5 (c+d x)^4}",1,"(B*n)/(16*d*g^5*(c + d*x)^4) + (b*B*n)/(12*d*(b*c - a*d)*g^5*(c + d*x)^3) + (b^2*B*n)/(8*d*(b*c - a*d)^2*g^5*(c + d*x)^2) + (b^3*B*n)/(4*d*(b*c - a*d)^3*g^5*(c + d*x)) + (b^4*B*n*Log[a + b*x])/(4*d*(b*c - a*d)^4*g^5) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])/(4*d*g^5*(c + d*x)^4) - (b^4*B*n*Log[c + d*x])/(4*d*(b*c - a*d)^4*g^5)","A",4,3,33,0.09091,1,"{2525, 12, 44}"
38,1,634,0,0.8804683,"\int (c g+d g x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Int[(c*g + d*g*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","-\frac{2 B^2 g^4 n^2 (b c-a d)^5 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{5 b^5 d}-\frac{2 B g^4 n (b c-a d)^5 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 b^5 d}-\frac{B g^4 n (c+d x)^2 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 b^3 d}-\frac{2 B g^4 n (c+d x)^3 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{15 b^2 d}-\frac{2 A B g^4 n x (b c-a d)^4}{5 b^4}-\frac{B g^4 n (c+d x)^4 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{10 b d}+\frac{g^4 (c+d x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{5 d}-\frac{2 B^2 g^4 n (a+b x) (b c-a d)^4 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{5 b^5}+\frac{13 B^2 g^4 n^2 x (b c-a d)^4}{30 b^4}+\frac{7 B^2 g^4 n^2 (c+d x)^2 (b c-a d)^3}{60 b^3 d}+\frac{B^2 g^4 n^2 (c+d x)^3 (b c-a d)^2}{30 b^2 d}+\frac{B^2 g^4 n^2 (b c-a d)^5 \log ^2(a+b x)}{5 b^5 d}+\frac{13 B^2 g^4 n^2 (b c-a d)^5 \log (a+b x)}{30 b^5 d}+\frac{2 B^2 g^4 n^2 (b c-a d)^5 \log (c+d x)}{5 b^5 d}-\frac{2 B^2 g^4 n^2 (b c-a d)^5 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{5 b^5 d}","-\frac{2 B^2 g^4 n^2 (b c-a d)^5 \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right)}{5 b^5 d}+\frac{2 B g^4 n (b c-a d)^5 \log \left(1-\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 b^5 d}-\frac{2 B g^4 n (a+b x) (b c-a d)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 b^5}-\frac{B g^4 n (c+d x)^2 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 b^3 d}-\frac{2 B g^4 n (c+d x)^3 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{15 b^2 d}-\frac{B g^4 n (c+d x)^4 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{10 b d}+\frac{g^4 (c+d x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{5 d}+\frac{13 B^2 g^4 n^2 x (b c-a d)^4}{30 b^4}+\frac{7 B^2 g^4 n^2 (c+d x)^2 (b c-a d)^3}{60 b^3 d}+\frac{B^2 g^4 n^2 (c+d x)^3 (b c-a d)^2}{30 b^2 d}+\frac{13 B^2 g^4 n^2 (b c-a d)^5 \log \left(\frac{a+b x}{c+d x}\right)}{30 b^5 d}+\frac{5 B^2 g^4 n^2 (b c-a d)^5 \log (c+d x)}{6 b^5 d}",1,"(-2*A*B*(b*c - a*d)^4*g^4*n*x)/(5*b^4) + (13*B^2*(b*c - a*d)^4*g^4*n^2*x)/(30*b^4) + (7*B^2*(b*c - a*d)^3*g^4*n^2*(c + d*x)^2)/(60*b^3*d) + (B^2*(b*c - a*d)^2*g^4*n^2*(c + d*x)^3)/(30*b^2*d) + (13*B^2*(b*c - a*d)^5*g^4*n^2*Log[a + b*x])/(30*b^5*d) + (B^2*(b*c - a*d)^5*g^4*n^2*Log[a + b*x]^2)/(5*b^5*d) - (2*B^2*(b*c - a*d)^4*g^4*n*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/(5*b^5) - (B*(b*c - a*d)^3*g^4*n*(c + d*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(5*b^3*d) - (2*B*(b*c - a*d)^2*g^4*n*(c + d*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(15*b^2*d) - (B*(b*c - a*d)*g^4*n*(c + d*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(10*b*d) - (2*B*(b*c - a*d)^5*g^4*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(5*b^5*d) + (g^4*(c + d*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(5*d) + (2*B^2*(b*c - a*d)^5*g^4*n^2*Log[c + d*x])/(5*b^5*d) - (2*B^2*(b*c - a*d)^5*g^4*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(5*b^5*d) - (2*B^2*(b*c - a*d)^5*g^4*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(5*b^5*d)","A",27,13,35,0.3714,1,"{2525, 12, 2528, 2486, 31, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 43}"
39,1,544,0,0.6843564,"\int (c g+d g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Int[(c*g + d*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","-\frac{B^2 g^3 n^2 (b c-a d)^4 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{2 b^4 d}-\frac{B g^3 n (b c-a d)^4 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 b^4 d}-\frac{B g^3 n (c+d x)^2 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{4 b^2 d}-\frac{A B g^3 n x (b c-a d)^3}{2 b^3}-\frac{B g^3 n (c+d x)^3 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{6 b d}+\frac{g^3 (c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{4 d}-\frac{B^2 g^3 n (a+b x) (b c-a d)^3 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{2 b^4}+\frac{5 B^2 g^3 n^2 x (b c-a d)^3}{12 b^3}+\frac{B^2 g^3 n^2 (c+d x)^2 (b c-a d)^2}{12 b^2 d}+\frac{B^2 g^3 n^2 (b c-a d)^4 \log ^2(a+b x)}{4 b^4 d}+\frac{5 B^2 g^3 n^2 (b c-a d)^4 \log (a+b x)}{12 b^4 d}+\frac{B^2 g^3 n^2 (b c-a d)^4 \log (c+d x)}{2 b^4 d}-\frac{B^2 g^3 n^2 (b c-a d)^4 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{2 b^4 d}","-\frac{B^2 g^3 n^2 (b c-a d)^4 \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right)}{2 b^4 d}+\frac{B g^3 n (b c-a d)^4 \log \left(1-\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 b^4 d}-\frac{B g^3 n (a+b x) (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 b^4}-\frac{B g^3 n (c+d x)^2 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{4 b^2 d}-\frac{B g^3 n (c+d x)^3 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{6 b d}+\frac{g^3 (c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{4 d}+\frac{5 B^2 g^3 n^2 x (b c-a d)^3}{12 b^3}+\frac{B^2 g^3 n^2 (c+d x)^2 (b c-a d)^2}{12 b^2 d}+\frac{5 B^2 g^3 n^2 (b c-a d)^4 \log \left(\frac{a+b x}{c+d x}\right)}{12 b^4 d}+\frac{11 B^2 g^3 n^2 (b c-a d)^4 \log (c+d x)}{12 b^4 d}",1,"-(A*B*(b*c - a*d)^3*g^3*n*x)/(2*b^3) + (5*B^2*(b*c - a*d)^3*g^3*n^2*x)/(12*b^3) + (B^2*(b*c - a*d)^2*g^3*n^2*(c + d*x)^2)/(12*b^2*d) + (5*B^2*(b*c - a*d)^4*g^3*n^2*Log[a + b*x])/(12*b^4*d) + (B^2*(b*c - a*d)^4*g^3*n^2*Log[a + b*x]^2)/(4*b^4*d) - (B^2*(b*c - a*d)^3*g^3*n*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/(2*b^4) - (B*(b*c - a*d)^2*g^3*n*(c + d*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(4*b^2*d) - (B*(b*c - a*d)*g^3*n*(c + d*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(6*b*d) - (B*(b*c - a*d)^4*g^3*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*b^4*d) + (g^3*(c + d*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(4*d) + (B^2*(b*c - a*d)^4*g^3*n^2*Log[c + d*x])/(2*b^4*d) - (B^2*(b*c - a*d)^4*g^3*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(2*b^4*d) - (B^2*(b*c - a*d)^4*g^3*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(2*b^4*d)","A",23,13,35,0.3714,1,"{2525, 12, 2528, 2486, 31, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 43}"
40,1,454,0,0.5666234,"\int (c g+d g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Int[(c*g + d*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","-\frac{2 B^2 g^2 n^2 (b c-a d)^3 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{3 b^3 d}-\frac{2 B g^2 n (b c-a d)^3 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b^3 d}-\frac{2 A B g^2 n x (b c-a d)^2}{3 b^2}-\frac{B g^2 n (c+d x)^2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b d}+\frac{g^2 (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{3 d}-\frac{2 B^2 g^2 n (a+b x) (b c-a d)^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{3 b^3}+\frac{B^2 g^2 n^2 x (b c-a d)^2}{3 b^2}+\frac{B^2 g^2 n^2 (b c-a d)^3 \log ^2(a+b x)}{3 b^3 d}+\frac{B^2 g^2 n^2 (b c-a d)^3 \log (a+b x)}{3 b^3 d}+\frac{2 B^2 g^2 n^2 (b c-a d)^3 \log (c+d x)}{3 b^3 d}-\frac{2 B^2 g^2 n^2 (b c-a d)^3 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{3 b^3 d}","-\frac{2 B^2 g^2 n^2 (b c-a d)^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right)}{3 b^3 d}+\frac{2 B g^2 n (b c-a d)^3 \log \left(1-\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b^3 d}-\frac{2 B g^2 n (a+b x) (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b^3}-\frac{B g^2 n (c+d x)^2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b d}+\frac{g^2 (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{3 d}+\frac{B^2 g^2 n^2 x (b c-a d)^2}{3 b^2}+\frac{B^2 g^2 n^2 (b c-a d)^3 \log \left(\frac{a+b x}{c+d x}\right)}{3 b^3 d}+\frac{B^2 g^2 n^2 (b c-a d)^3 \log (c+d x)}{b^3 d}",1,"(-2*A*B*(b*c - a*d)^2*g^2*n*x)/(3*b^2) + (B^2*(b*c - a*d)^2*g^2*n^2*x)/(3*b^2) + (B^2*(b*c - a*d)^3*g^2*n^2*Log[a + b*x])/(3*b^3*d) + (B^2*(b*c - a*d)^3*g^2*n^2*Log[a + b*x]^2)/(3*b^3*d) - (2*B^2*(b*c - a*d)^2*g^2*n*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/(3*b^3) - (B*(b*c - a*d)*g^2*n*(c + d*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*b*d) - (2*B*(b*c - a*d)^3*g^2*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*b^3*d) + (g^2*(c + d*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(3*d) + (2*B^2*(b*c - a*d)^3*g^2*n^2*Log[c + d*x])/(3*b^3*d) - (2*B^2*(b*c - a*d)^3*g^2*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3*b^3*d) - (2*B^2*(b*c - a*d)^3*g^2*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(3*b^3*d)","A",19,13,35,0.3714,1,"{2525, 12, 2528, 2486, 31, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 43}"
41,1,307,0,0.4225984,"\int (c g+d g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Int[(c*g + d*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","-\frac{B^2 g n^2 (b c-a d)^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b^2 d}-\frac{B g n (b c-a d)^2 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b^2 d}+\frac{g (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 d}-\frac{A B g n x (b c-a d)}{b}-\frac{B^2 g n (a+b x) (b c-a d) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b^2}+\frac{B^2 g n^2 (b c-a d)^2 \log ^2(a+b x)}{2 b^2 d}+\frac{B^2 g n^2 (b c-a d)^2 \log (c+d x)}{b^2 d}-\frac{B^2 g n^2 (b c-a d)^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b^2 d}","-\frac{B^2 g n^2 (b c-a d)^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right)}{b^2 d}+\frac{B g n (b c-a d)^2 \log \left(1-\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b^2 d}-\frac{B g n (a+b x) (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b^2}+\frac{g (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 d}+\frac{B^2 g n^2 (b c-a d)^2 \log (c+d x)}{b^2 d}",1,"-((A*B*(b*c - a*d)*g*n*x)/b) + (B^2*(b*c - a*d)^2*g*n^2*Log[a + b*x]^2)/(2*b^2*d) - (B^2*(b*c - a*d)*g*n*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/b^2 - (B*(b*c - a*d)^2*g*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(b^2*d) + (g*(c + d*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(2*d) + (B^2*(b*c - a*d)^2*g*n^2*Log[c + d*x])/(b^2*d) - (B^2*(b*c - a*d)^2*g*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b^2*d) - (B^2*(b*c - a*d)^2*g*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b^2*d)","A",15,12,33,0.3636,1,"{2525, 12, 2528, 2486, 31, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
42,1,782,0,3.3023156,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{c g+d g x} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(c*g + d*g*x),x]","-\frac{2 A B n \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{d g}+\frac{2 B^2 n \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+\log \left((a+b x)^n\right)+\log \left((c+d x)^{-n}\right)\right)}{d g}-\frac{2 B^2 n^2 \text{PolyLog}\left(3,-\frac{d (a+b x)}{b c-a d}\right)}{d g}-\frac{2 B^2 n^2 \text{PolyLog}\left(3,\frac{b (c+d x)}{b c-a d}\right)}{d g}+\frac{2 B^2 n \log \left((a+b x)^n\right) \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{d g}-\frac{2 B^2 n \log \left((c+d x)^{-n}\right) \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{d g}+\frac{\log (c g+d g x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{d g}-\frac{2 A B n \log (c g+d g x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{d g}+\frac{B^2 n \log ^2(c g+d g x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{d g}+\frac{2 B^2 n \log (c g+d g x) \log \left(-\frac{d (a+b x)}{b c-a d}\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+\log \left((a+b x)^n\right)+\log \left((c+d x)^{-n}\right)\right)}{d g}-\frac{B^2 n^2 \log (a+b x) \log ^2(g (c+d x))}{d g}+\frac{B^2 n^2 \log ^2(g (c+d x)) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{d g}-\frac{B^2 n^2 \log ^2(c g+d g x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{d g}-\frac{B^2 \log ^2\left((a+b x)^n\right) \log (g (c+d x))}{d g}-\frac{B^2 \log (a+b x) \log ^2\left((c+d x)^{-n}\right)}{d g}+\frac{B^2 \log ^2\left((c+d x)^{-n}\right) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{d g}+\frac{B^2 \log ^2\left((a+b x)^n\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{d g}-\frac{2 B^2 n \log (a+b x) \log (g (c+d x)) \log \left((c+d x)^{-n}\right)}{d g}+\frac{A B n \log ^2(g (c+d x))}{d g}+\frac{B^2 n^2 \log ^3(g (c+d x))}{3 d g}","-\frac{2 B n \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{d g}+\frac{2 B^2 n^2 \text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right)}{d g}-\frac{\log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{d g}",1,"(B^2*Log[(a + b*x)^n]^2*Log[(b*(c + d*x))/(b*c - a*d)])/(d*g) - (B^2*Log[(a + b*x)^n]^2*Log[g*(c + d*x)])/(d*g) + (A*B*n*Log[g*(c + d*x)]^2)/(d*g) - (B^2*n^2*Log[a + b*x]*Log[g*(c + d*x)]^2)/(d*g) + (B^2*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[g*(c + d*x)]^2)/(d*g) + (B^2*n^2*Log[g*(c + d*x)]^3)/(3*d*g) - (2*B^2*n*Log[a + b*x]*Log[g*(c + d*x)]*Log[(c + d*x)^(-n)])/(d*g) - (B^2*Log[a + b*x]*Log[(c + d*x)^(-n)]^2)/(d*g) + (B^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[(c + d*x)^(-n)]^2)/(d*g) - (2*A*B*n*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c*g + d*g*x])/(d*g) + ((A + B*Log[e*((a + b*x)/(c + d*x))^n])^2*Log[c*g + d*g*x])/(d*g) + (2*B^2*n*Log[-((d*(a + b*x))/(b*c - a*d))]*(Log[(a + b*x)^n] - Log[e*((a + b*x)/(c + d*x))^n] + Log[(c + d*x)^(-n)])*Log[c*g + d*g*x])/(d*g) - (B^2*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c*g + d*g*x]^2)/(d*g) + (B^2*n*Log[e*((a + b*x)/(c + d*x))^n]*Log[c*g + d*g*x]^2)/(d*g) + (2*B^2*n*Log[(a + b*x)^n]*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(d*g) - (2*A*B*n*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(d*g) - (2*B^2*n*Log[(c + d*x)^(-n)]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(d*g) + (2*B^2*n*(Log[(a + b*x)^n] - Log[e*((a + b*x)/(c + d*x))^n] + Log[(c + d*x)^(-n)])*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(d*g) - (2*B^2*n^2*PolyLog[3, -((d*(a + b*x))/(b*c - a*d))])/(d*g) - (2*B^2*n^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])/(d*g)","B",45,23,35,0.6571,1,"{2524, 2528, 2418, 2390, 2301, 2394, 2393, 2391, 6688, 12, 6742, 2499, 2396, 2433, 2374, 6589, 2302, 30, 2500, 2375, 2317, 2440, 2434}"
43,1,514,0,0.7739674,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{(c g+d g x)^2} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(c*g + d*g*x)^2,x]","\frac{2 b B^2 n^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{d g^2 (b c-a d)}+\frac{2 b B^2 n^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{d g^2 (b c-a d)}+\frac{2 b B n \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{d g^2 (b c-a d)}+\frac{2 B n \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{d g^2 (c+d x)}-\frac{2 b B n \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{d g^2 (b c-a d)}-\frac{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{d g^2 (c+d x)}-\frac{b B^2 n^2 \log ^2(a+b x)}{d g^2 (b c-a d)}-\frac{b B^2 n^2 \log ^2(c+d x)}{d g^2 (b c-a d)}-\frac{2 b B^2 n^2 \log (a+b x)}{d g^2 (b c-a d)}+\frac{2 b B^2 n^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{d g^2 (b c-a d)}+\frac{2 b B^2 n^2 \log (c+d x)}{d g^2 (b c-a d)}+\frac{2 b B^2 n^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{d g^2 (b c-a d)}-\frac{2 B^2 n^2}{d g^2 (c+d x)}","\frac{(a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g^2 (c+d x) (b c-a d)}-\frac{2 A B n (a+b x)}{g^2 (c+d x) (b c-a d)}-\frac{2 B^2 n (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{g^2 (c+d x) (b c-a d)}+\frac{2 B^2 n^2 (a+b x)}{g^2 (c+d x) (b c-a d)}",1,"(-2*B^2*n^2)/(d*g^2*(c + d*x)) - (2*b*B^2*n^2*Log[a + b*x])/(d*(b*c - a*d)*g^2) - (b*B^2*n^2*Log[a + b*x]^2)/(d*(b*c - a*d)*g^2) + (2*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(d*g^2*(c + d*x)) + (2*b*B*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(d*(b*c - a*d)*g^2) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(d*g^2*(c + d*x)) + (2*b*B^2*n^2*Log[c + d*x])/(d*(b*c - a*d)*g^2) + (2*b*B^2*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(d*(b*c - a*d)*g^2) - (2*b*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(d*(b*c - a*d)*g^2) - (b*B^2*n^2*Log[c + d*x]^2)/(d*(b*c - a*d)*g^2) + (2*b*B^2*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(d*(b*c - a*d)*g^2) + (2*b*B^2*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(d*(b*c - a*d)*g^2) + (2*b*B^2*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(d*(b*c - a*d)*g^2)","C",24,11,35,0.3143,1,"{2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 44}"
44,1,626,0,0.9150453,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{(c g+d g x)^3} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(c*g + d*g*x)^3,x]","\frac{b^2 B^2 n^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{d g^3 (b c-a d)^2}+\frac{b^2 B^2 n^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{d g^3 (b c-a d)^2}+\frac{b^2 B n \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{d g^3 (b c-a d)^2}-\frac{b^2 B n \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{d g^3 (b c-a d)^2}+\frac{b B n \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{d g^3 (c+d x) (b c-a d)}-\frac{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 d g^3 (c+d x)^2}+\frac{B n \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 d g^3 (c+d x)^2}-\frac{b^2 B^2 n^2 \log ^2(a+b x)}{2 d g^3 (b c-a d)^2}-\frac{b^2 B^2 n^2 \log ^2(c+d x)}{2 d g^3 (b c-a d)^2}-\frac{3 b^2 B^2 n^2 \log (a+b x)}{2 d g^3 (b c-a d)^2}+\frac{3 b^2 B^2 n^2 \log (c+d x)}{2 d g^3 (b c-a d)^2}+\frac{b^2 B^2 n^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{d g^3 (b c-a d)^2}+\frac{b^2 B^2 n^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{d g^3 (b c-a d)^2}-\frac{3 b B^2 n^2}{2 d g^3 (c+d x) (b c-a d)}-\frac{B^2 n^2}{4 d g^3 (c+d x)^2}","\frac{B d n (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 g^3 (c+d x)^2 (b c-a d)^2}+\frac{b (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g^3 (c+d x) (b c-a d)^2}-\frac{d (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 g^3 (c+d x)^2 (b c-a d)^2}-\frac{2 A b B n (a+b x)}{g^3 (c+d x) (b c-a d)^2}-\frac{2 b B^2 n (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{g^3 (c+d x) (b c-a d)^2}+\frac{2 b B^2 n^2 (a+b x)}{g^3 (c+d x) (b c-a d)^2}-\frac{B^2 d n^2 (a+b x)^2}{4 g^3 (c+d x)^2 (b c-a d)^2}",1,"-(B^2*n^2)/(4*d*g^3*(c + d*x)^2) - (3*b*B^2*n^2)/(2*d*(b*c - a*d)*g^3*(c + d*x)) - (3*b^2*B^2*n^2*Log[a + b*x])/(2*d*(b*c - a*d)^2*g^3) - (b^2*B^2*n^2*Log[a + b*x]^2)/(2*d*(b*c - a*d)^2*g^3) + (B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*d*g^3*(c + d*x)^2) + (b*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(d*(b*c - a*d)*g^3*(c + d*x)) + (b^2*B*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(d*(b*c - a*d)^2*g^3) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(2*d*g^3*(c + d*x)^2) + (3*b^2*B^2*n^2*Log[c + d*x])/(2*d*(b*c - a*d)^2*g^3) + (b^2*B^2*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(d*(b*c - a*d)^2*g^3) - (b^2*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(d*(b*c - a*d)^2*g^3) - (b^2*B^2*n^2*Log[c + d*x]^2)/(2*d*(b*c - a*d)^2*g^3) + (b^2*B^2*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(d*(b*c - a*d)^2*g^3) + (b^2*B^2*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(d*(b*c - a*d)^2*g^3) + (b^2*B^2*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(d*(b*c - a*d)^2*g^3)","C",28,11,35,0.3143,1,"{2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 44}"
45,1,736,0,1.0980049,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{(c g+d g x)^4} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(c*g + d*g*x)^4,x]","\frac{2 b^3 B^2 n^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{3 d g^4 (b c-a d)^3}+\frac{2 b^3 B^2 n^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 d g^4 (b c-a d)^3}+\frac{2 b^3 B n \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 d g^4 (b c-a d)^3}-\frac{2 b^3 B n \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 d g^4 (b c-a d)^3}+\frac{2 b^2 B n \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 d g^4 (c+d x) (b c-a d)^2}+\frac{b B n \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 d g^4 (c+d x)^2 (b c-a d)}-\frac{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{3 d g^4 (c+d x)^3}+\frac{2 B n \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{9 d g^4 (c+d x)^3}-\frac{11 b^2 B^2 n^2}{9 d g^4 (c+d x) (b c-a d)^2}-\frac{b^3 B^2 n^2 \log ^2(a+b x)}{3 d g^4 (b c-a d)^3}-\frac{b^3 B^2 n^2 \log ^2(c+d x)}{3 d g^4 (b c-a d)^3}-\frac{11 b^3 B^2 n^2 \log (a+b x)}{9 d g^4 (b c-a d)^3}+\frac{11 b^3 B^2 n^2 \log (c+d x)}{9 d g^4 (b c-a d)^3}+\frac{2 b^3 B^2 n^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 d g^4 (b c-a d)^3}+\frac{2 b^3 B^2 n^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{3 d g^4 (b c-a d)^3}-\frac{5 b B^2 n^2}{18 d g^4 (c+d x)^2 (b c-a d)}-\frac{2 B^2 n^2}{27 d g^4 (c+d x)^3}","\frac{2 b^3 B n \log \left(\frac{a+b x}{c+d x}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 d g^4 (b c-a d)^3}-\frac{2 b^2 B n (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^4 (c+d x) (b c-a d)^3}-\frac{2 B d^2 n (a+b x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{9 g^4 (c+d x)^3 (b c-a d)^3}+\frac{b B d n (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^4 (c+d x)^2 (b c-a d)^3}-\frac{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{3 d g^4 (c+d x)^3}+\frac{2 b^2 B^2 n^2 (a+b x)}{g^4 (c+d x) (b c-a d)^3}-\frac{b^3 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)}{3 d g^4 (b c-a d)^3}+\frac{2 B^2 d^2 n^2 (a+b x)^3}{27 g^4 (c+d x)^3 (b c-a d)^3}-\frac{b B^2 d n^2 (a+b x)^2}{2 g^4 (c+d x)^2 (b c-a d)^3}",1,"(-2*B^2*n^2)/(27*d*g^4*(c + d*x)^3) - (5*b*B^2*n^2)/(18*d*(b*c - a*d)*g^4*(c + d*x)^2) - (11*b^2*B^2*n^2)/(9*d*(b*c - a*d)^2*g^4*(c + d*x)) - (11*b^3*B^2*n^2*Log[a + b*x])/(9*d*(b*c - a*d)^3*g^4) - (b^3*B^2*n^2*Log[a + b*x]^2)/(3*d*(b*c - a*d)^3*g^4) + (2*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(9*d*g^4*(c + d*x)^3) + (b*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*d*(b*c - a*d)*g^4*(c + d*x)^2) + (2*b^2*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*d*(b*c - a*d)^2*g^4*(c + d*x)) + (2*b^3*B*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*d*(b*c - a*d)^3*g^4) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(3*d*g^4*(c + d*x)^3) + (11*b^3*B^2*n^2*Log[c + d*x])/(9*d*(b*c - a*d)^3*g^4) + (2*b^3*B^2*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*d*(b*c - a*d)^3*g^4) - (2*b^3*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(3*d*(b*c - a*d)^3*g^4) - (b^3*B^2*n^2*Log[c + d*x]^2)/(3*d*(b*c - a*d)^3*g^4) + (2*b^3*B^2*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3*d*(b*c - a*d)^3*g^4) + (2*b^3*B^2*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(3*d*(b*c - a*d)^3*g^4) + (2*b^3*B^2*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*d*(b*c - a*d)^3*g^4)","C",32,11,35,0.3143,1,"{2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 44}"
46,1,826,0,1.2952832,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{(c g+d g x)^5} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(c*g + d*g*x)^5,x]","-\frac{B^2 n^2 \log ^2(a+b x) b^4}{4 d (b c-a d)^4 g^5}-\frac{B^2 n^2 \log ^2(c+d x) b^4}{4 d (b c-a d)^4 g^5}-\frac{25 B^2 n^2 \log (a+b x) b^4}{24 d (b c-a d)^4 g^5}+\frac{B n \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) b^4}{2 d (b c-a d)^4 g^5}+\frac{25 B^2 n^2 \log (c+d x) b^4}{24 d (b c-a d)^4 g^5}+\frac{B^2 n^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) b^4}{2 d (b c-a d)^4 g^5}-\frac{B n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \log (c+d x) b^4}{2 d (b c-a d)^4 g^5}+\frac{B^2 n^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) b^4}{2 d (b c-a d)^4 g^5}+\frac{B^2 n^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) b^4}{2 d (b c-a d)^4 g^5}+\frac{B^2 n^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) b^4}{2 d (b c-a d)^4 g^5}+\frac{B n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) b^3}{2 d (b c-a d)^3 g^5 (c+d x)}-\frac{25 B^2 n^2 b^3}{24 d (b c-a d)^3 g^5 (c+d x)}+\frac{B n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) b^2}{4 d (b c-a d)^2 g^5 (c+d x)^2}-\frac{13 B^2 n^2 b^2}{48 d (b c-a d)^2 g^5 (c+d x)^2}+\frac{B n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) b}{6 d (b c-a d) g^5 (c+d x)^3}-\frac{7 B^2 n^2 b}{72 d (b c-a d) g^5 (c+d x)^3}-\frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{4 d g^5 (c+d x)^4}+\frac{B n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{8 d g^5 (c+d x)^4}-\frac{B^2 n^2}{32 d g^5 (c+d x)^4}","\frac{b^4 B n \log \left(\frac{a+b x}{c+d x}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 d g^5 (b c-a d)^4}-\frac{2 b^3 B n (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^5 (c+d x) (b c-a d)^4}+\frac{3 b^2 B d n (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 g^5 (c+d x)^2 (b c-a d)^4}-\frac{2 b B d^2 n (a+b x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 g^5 (c+d x)^3 (b c-a d)^4}+\frac{B d^3 n (a+b x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{8 g^5 (c+d x)^4 (b c-a d)^4}-\frac{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{4 d g^5 (c+d x)^4}+\frac{2 b^3 B^2 n^2 (a+b x)}{g^5 (c+d x) (b c-a d)^4}-\frac{3 b^2 B^2 d n^2 (a+b x)^2}{4 g^5 (c+d x)^2 (b c-a d)^4}-\frac{b^4 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)}{4 d g^5 (b c-a d)^4}+\frac{2 b B^2 d^2 n^2 (a+b x)^3}{9 g^5 (c+d x)^3 (b c-a d)^4}-\frac{B^2 d^3 n^2 (a+b x)^4}{32 g^5 (c+d x)^4 (b c-a d)^4}",1,"-(B^2*n^2)/(32*d*g^5*(c + d*x)^4) - (7*b*B^2*n^2)/(72*d*(b*c - a*d)*g^5*(c + d*x)^3) - (13*b^2*B^2*n^2)/(48*d*(b*c - a*d)^2*g^5*(c + d*x)^2) - (25*b^3*B^2*n^2)/(24*d*(b*c - a*d)^3*g^5*(c + d*x)) - (25*b^4*B^2*n^2*Log[a + b*x])/(24*d*(b*c - a*d)^4*g^5) - (b^4*B^2*n^2*Log[a + b*x]^2)/(4*d*(b*c - a*d)^4*g^5) + (B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(8*d*g^5*(c + d*x)^4) + (b*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(6*d*(b*c - a*d)*g^5*(c + d*x)^3) + (b^2*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(4*d*(b*c - a*d)^2*g^5*(c + d*x)^2) + (b^3*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*d*(b*c - a*d)^3*g^5*(c + d*x)) + (b^4*B*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*d*(b*c - a*d)^4*g^5) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(4*d*g^5*(c + d*x)^4) + (25*b^4*B^2*n^2*Log[c + d*x])/(24*d*(b*c - a*d)^4*g^5) + (b^4*B^2*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(2*d*(b*c - a*d)^4*g^5) - (b^4*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(2*d*(b*c - a*d)^4*g^5) - (b^4*B^2*n^2*Log[c + d*x]^2)/(4*d*(b*c - a*d)^4*g^5) + (b^4*B^2*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(2*d*(b*c - a*d)^4*g^5) + (b^4*B^2*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(2*d*(b*c - a*d)^4*g^5) + (b^4*B^2*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*d*(b*c - a*d)^4*g^5)","C",36,11,35,0.3143,1,"{2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 44}"
47,0,0,0,0.2142939,"\int \frac{(c g+d g x)^2}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Int[(c*g + d*g*x)^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\int \frac{(c g+d g x)^2}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","\text{Int}\left(\frac{(c g+d g x)^2}{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A},x\right)",0,"c^2*g^2*Defer[Int][(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-1), x] + 2*c*d*g^2*Defer[Int][x/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x] + d^2*g^2*Defer[Int][x^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x]","A",0,0,0,0,-1,"{}"
48,0,0,0,0.114506,"\int \frac{c g+d g x}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Int[(c*g + d*g*x)/(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\int \frac{c g+d g x}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","\text{Int}\left(\frac{c g+d g x}{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A},x\right)",0,"c*g*Defer[Int][(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-1), x] + d*g*Defer[Int][x/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x]","A",0,0,0,0,-1,"{}"
49,0,0,0,0.0831093,"\int \frac{1}{(c g+d g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","Int[1/((c*g + d*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])),x]","\int \frac{1}{(c g+d g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{(c g+d g x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)},x\right)",0,"Defer[Int][1/((c*g + d*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])), x]","A",0,0,0,0,-1,"{}"
50,0,0,0,0.1002248,"\int \frac{1}{(c g+d g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","Int[1/((c*g + d*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])),x]","\int \frac{1}{(c g+d g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","\frac{(a+b x) e^{-\frac{A}{B n}} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-1/n} \text{Ei}\left(\frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{B n}\right)}{B g^2 n (c+d x) (b c-a d)}",1,"Defer[Int][1/((c*g + d*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])), x]","F",0,0,0,0,-1,"{}"
51,0,0,0,0.0828902,"\int \frac{1}{(c g+d g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","Int[1/((c*g + d*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])),x]","\int \frac{1}{(c g+d g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","\frac{b (a+b x) e^{-\frac{A}{B n}} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-1/n} \text{Ei}\left(\frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{B n}\right)}{B g^3 n (c+d x) (b c-a d)^2}-\frac{d (a+b x)^2 e^{-\frac{2 A}{B n}} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{B n}\right)}{B g^3 n (c+d x)^2 (b c-a d)^2}",1,"Defer[Int][1/((c*g + d*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])), x]","F",0,0,0,0,-1,"{}"
52,0,0,0,0.2328775,"\int \frac{(c g+d g x)^2}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Int[(c*g + d*g*x)^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\int \frac{(c g+d g x)^2}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{(c g+d g x)^2}{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2},x\right)",0,"c^2*g^2*Defer[Int][(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-2), x] + 2*c*d*g^2*Defer[Int][x/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x] + d^2*g^2*Defer[Int][x^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x]","A",0,0,0,0,-1,"{}"
53,0,0,0,0.1238482,"\int \frac{c g+d g x}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Int[(c*g + d*g*x)/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\int \frac{c g+d g x}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{c g+d g x}{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2},x\right)",0,"c*g*Defer[Int][(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-2), x] + d*g*Defer[Int][x/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x]","A",0,0,0,0,-1,"{}"
54,0,0,0,0.0903306,"\int \frac{1}{(c g+d g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Int[1/((c*g + d*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2),x]","\int \frac{1}{(c g+d g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(c g+d g x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2},x\right)",0,"Defer[Int][1/((c*g + d*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2), x]","A",0,0,0,0,-1,"{}"
55,0,0,0,0.1035818,"\int \frac{1}{(c g+d g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Int[1/((c*g + d*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2),x]","\int \frac{1}{(c g+d g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","\frac{(a+b x) e^{-\frac{A}{B n}} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-1/n} \text{Ei}\left(\frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{B n}\right)}{B^2 g^2 n^2 (c+d x) (b c-a d)}-\frac{a+b x}{B g^2 n (c+d x) (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}",1,"Defer[Int][1/((c*g + d*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2), x]","F",0,0,0,0,-1,"{}"
56,0,0,0,0.0943265,"\int \frac{1}{(c g+d g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Int[1/((c*g + d*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2),x]","\int \frac{1}{(c g+d g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","-\frac{2 d (a+b x)^2 e^{-\frac{2 A}{B n}} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{B n}\right)}{B^2 g^3 n^2 (c+d x)^2 (b c-a d)^2}+\frac{b (a+b x) e^{-\frac{A}{B n}} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-1/n} \text{Ei}\left(\frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{B n}\right)}{B^2 g^3 n^2 (c+d x) (b c-a d)^2}-\frac{a+b x}{B g^3 n (c+d x)^2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}",1,"Defer[Int][1/((c*g + d*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2), x]","F",0,0,0,0,-1,"{}"
57,1,348,0,0.6029329,"\int (f+g x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Int[(f + g*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","-\frac{B g^2 n x^2 (b c-a d) \left(a^2 d^2 g^2-a b d g (5 d f-c g)+b^2 \left(c^2 g^2-5 c d f g+10 d^2 f^2\right)\right)}{10 b^3 d^3}+\frac{B g n x \left(-10 a^2 b^2 d^4 f^2 g+5 a^3 b d^4 f g^2-a^4 d^4 g^3+10 a b^3 d^4 f^3+b^4 (-c) \left(5 c^2 d f g^2-c^3 g^3-10 c d^2 f^2 g+10 d^3 f^3\right)\right)}{5 b^4 d^4}+\frac{(f+g x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 g}-\frac{B g^3 n x^3 (b c-a d) (-a d g-b c g+5 b d f)}{15 b^2 d^2}-\frac{B n (b f-a g)^5 \log (a+b x)}{5 b^5 g}-\frac{B g^4 n x^4 (b c-a d)}{20 b d}+\frac{B n (d f-c g)^5 \log (c+d x)}{5 d^5 g}","-\frac{B g^2 n x^2 (b c-a d) \left(a^2 d^2 g^2-a b d g (5 d f-c g)+b^2 \left(c^2 g^2-5 c d f g+10 d^2 f^2\right)\right)}{10 b^3 d^3}+\frac{B g n x (b c-a d) \left(-a^2 b d^2 g^2 (5 d f-c g)+a^3 d^3 g^3+a b^2 d g \left(c^2 g^2-5 c d f g+10 d^2 f^2\right)+b^3 \left(-\left(5 c^2 d f g^2-c^3 g^3-10 c d^2 f^2 g+10 d^3 f^3\right)\right)\right)}{5 b^4 d^4}+\frac{(f+g x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 g}-\frac{B g^3 n x^3 (b c-a d) (-a d g-b c g+5 b d f)}{15 b^2 d^2}-\frac{B n (b f-a g)^5 \log (a+b x)}{5 b^5 g}-\frac{B g^4 n x^4 (b c-a d)}{20 b d}+\frac{B n (d f-c g)^5 \log (c+d x)}{5 d^5 g}",1,"(B*g*(10*a*b^3*d^4*f^3 - 10*a^2*b^2*d^4*f^2*g + 5*a^3*b*d^4*f*g^2 - a^4*d^4*g^3 - b^4*c*(10*d^3*f^3 - 10*c*d^2*f^2*g + 5*c^2*d*f*g^2 - c^3*g^3))*n*x)/(5*b^4*d^4) - (B*(b*c - a*d)*g^2*(a^2*d^2*g^2 - a*b*d*g*(5*d*f - c*g) + b^2*(10*d^2*f^2 - 5*c*d*f*g + c^2*g^2))*n*x^2)/(10*b^3*d^3) - (B*(b*c - a*d)*g^3*(5*b*d*f - b*c*g - a*d*g)*n*x^3)/(15*b^2*d^2) - (B*(b*c - a*d)*g^4*n*x^4)/(20*b*d) - (B*(b*f - a*g)^5*n*Log[a + b*x])/(5*b^5*g) + ((f + g*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(5*g) + (B*(d*f - c*g)^5*n*Log[c + d*x])/(5*d^5*g)","A",4,3,30,0.1000,1,"{2525, 12, 72}"
58,1,235,0,0.3594775,"\int (f+g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Int[(f + g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","-\frac{B g n x (b c-a d) \left(a^2 d^2 g^2-a b d g (4 d f-c g)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right)}{4 b^3 d^3}+\frac{(f+g x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{4 g}-\frac{B g^2 n x^2 (b c-a d) (-a d g-b c g+4 b d f)}{8 b^2 d^2}-\frac{B n (b f-a g)^4 \log (a+b x)}{4 b^4 g}-\frac{B g^3 n x^3 (b c-a d)}{12 b d}+\frac{B n (d f-c g)^4 \log (c+d x)}{4 d^4 g}","-\frac{B g n x (b c-a d) \left(a^2 d^2 g^2-a b d g (4 d f-c g)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right)}{4 b^3 d^3}+\frac{(f+g x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{4 g}-\frac{B g^2 n x^2 (b c-a d) (-a d g-b c g+4 b d f)}{8 b^2 d^2}-\frac{B n (b f-a g)^4 \log (a+b x)}{4 b^4 g}-\frac{B g^3 n x^3 (b c-a d)}{12 b d}+\frac{B n (d f-c g)^4 \log (c+d x)}{4 d^4 g}",1,"-(B*(b*c - a*d)*g*(a^2*d^2*g^2 - a*b*d*g*(4*d*f - c*g) + b^2*(6*d^2*f^2 - 4*c*d*f*g + c^2*g^2))*n*x)/(4*b^3*d^3) - (B*(b*c - a*d)*g^2*(4*b*d*f - b*c*g - a*d*g)*n*x^2)/(8*b^2*d^2) - (B*(b*c - a*d)*g^3*n*x^3)/(12*b*d) - (B*(b*f - a*g)^4*n*Log[a + b*x])/(4*b^4*g) + ((f + g*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(4*g) + (B*(d*f - c*g)^4*n*Log[c + d*x])/(4*d^4*g)","A",4,3,30,0.1000,1,"{2525, 12, 72}"
59,1,157,0,0.1804849,"\int (f+g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Int[(f + g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{(f+g x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 g}-\frac{B g n x (b c-a d) (-a d g-b c g+3 b d f)}{3 b^2 d^2}-\frac{B n (b f-a g)^3 \log (a+b x)}{3 b^3 g}-\frac{B g^2 n x^2 (b c-a d)}{6 b d}+\frac{B n (d f-c g)^3 \log (c+d x)}{3 d^3 g}","\frac{(f+g x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 g}-\frac{B g n x (b c-a d) (-a d g-b c g+3 b d f)}{3 b^2 d^2}-\frac{B n (b f-a g)^3 \log (a+b x)}{3 b^3 g}-\frac{B g^2 n x^2 (b c-a d)}{6 b d}+\frac{B n (d f-c g)^3 \log (c+d x)}{3 d^3 g}",1,"-(B*(b*c - a*d)*g*(3*b*d*f - b*c*g - a*d*g)*n*x)/(3*b^2*d^2) - (B*(b*c - a*d)*g^2*n*x^2)/(6*b*d) - (B*(b*f - a*g)^3*n*Log[a + b*x])/(3*b^3*g) + ((f + g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*g) + (B*(d*f - c*g)^3*n*Log[c + d*x])/(3*d^3*g)","A",4,3,30,0.1000,1,"{2525, 12, 72}"
60,1,115,0,0.1049791,"\int (f+g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Int[(f + g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{(f+g x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 g}-\frac{B n (b f-a g)^2 \log (a+b x)}{2 b^2 g}-\frac{B g n x (b c-a d)}{2 b d}+\frac{B n (d f-c g)^2 \log (c+d x)}{2 d^2 g}","\frac{(f+g x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 g}-\frac{B n (b f-a g)^2 \log (a+b x)}{2 b^2 g}-\frac{B g n x (b c-a d)}{2 b d}+\frac{B n (d f-c g)^2 \log (c+d x)}{2 d^2 g}",1,"-(B*(b*c - a*d)*g*n*x)/(2*b*d) - (B*(b*f - a*g)^2*n*Log[a + b*x])/(2*b^2*g) + ((f + g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*g) + (B*(d*f - c*g)^2*n*Log[c + d*x])/(2*d^2*g)","A",4,3,28,0.1071,1,"{2525, 12, 72}"
61,1,56,0,0.0327508,"\int \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Int[A + B*Log[e*((a + b*x)/(c + d*x))^n],x]","\frac{B (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b}-\frac{B n (b c-a d) \log (c+d x)}{b d}+A x","\frac{B (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b}-\frac{B n (b c-a d) \log (c+d x)}{b d}+A x",1,"A*x + (B*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/b - (B*(b*c - a*d)*n*Log[c + d*x])/(b*d)","A",3,2,22,0.09091,1,"{2486, 31}"
62,1,147,0,0.2256621,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f+g x} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x),x]","-\frac{B n \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{g}+\frac{B n \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{g}+\frac{\log (f+g x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g}-\frac{B n \log (f+g x) \log \left(-\frac{g (a+b x)}{b f-a g}\right)}{g}+\frac{B n \log (f+g x) \log \left(-\frac{g (c+d x)}{d f-c g}\right)}{g}","-\frac{B n \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{g}+\frac{B n \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{g}+\frac{\log (f+g x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g}-\frac{B n \log (f+g x) \log \left(-\frac{g (a+b x)}{b f-a g}\right)}{g}+\frac{B n \log (f+g x) \log \left(-\frac{g (c+d x)}{d f-c g}\right)}{g}",1,"-((B*n*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/g) + ((A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[f + g*x])/g + (B*n*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/g - (B*n*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/g + (B*n*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g","A",9,5,30,0.1667,1,"{2524, 2418, 2394, 2393, 2391}"
63,1,119,0,0.1247694,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(f+g x)^2} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x)^2,x]","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{g (f+g x)}+\frac{B n (b c-a d) \log (f+g x)}{(b f-a g) (d f-c g)}+\frac{b B n \log (a+b x)}{g (b f-a g)}-\frac{B d n \log (c+d x)}{g (d f-c g)}","\frac{(a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(f+g x) (b f-a g)}+\frac{B n (b c-a d) \log \left(\frac{f+g x}{c+d x}\right)}{(b f-a g) (d f-c g)}",1,"(b*B*n*Log[a + b*x])/(g*(b*f - a*g)) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])/(g*(f + g*x)) - (B*d*n*Log[c + d*x])/(g*(d*f - c*g)) + (B*(b*c - a*d)*n*Log[f + g*x])/((b*f - a*g)*(d*f - c*g))","A",4,3,30,0.1000,1,"{2525, 12, 72}"
64,1,190,0,0.2357994,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(f+g x)^3} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x)^3,x]","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{2 g (f+g x)^2}+\frac{b^2 B n \log (a+b x)}{2 g (b f-a g)^2}-\frac{B n (b c-a d)}{2 (f+g x) (b f-a g) (d f-c g)}+\frac{B n (b c-a d) \log (f+g x) (-a d g-b c g+2 b d f)}{2 (b f-a g)^2 (d f-c g)^2}-\frac{B d^2 n \log (c+d x)}{2 g (d f-c g)^2}","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{2 g (f+g x)^2}+\frac{b^2 B n \log (a+b x)}{2 g (b f-a g)^2}-\frac{B n (b c-a d)}{2 (f+g x) (b f-a g) (d f-c g)}+\frac{B n (b c-a d) \log (f+g x) (-a d g-b c g+2 b d f)}{2 (b f-a g)^2 (d f-c g)^2}-\frac{B d^2 n \log (c+d x)}{2 g (d f-c g)^2}",1,"-(B*(b*c - a*d)*n)/(2*(b*f - a*g)*(d*f - c*g)*(f + g*x)) + (b^2*B*n*Log[a + b*x])/(2*g*(b*f - a*g)^2) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])/(2*g*(f + g*x)^2) - (B*d^2*n*Log[c + d*x])/(2*g*(d*f - c*g)^2) + (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*n*Log[f + g*x])/(2*(b*f - a*g)^2*(d*f - c*g)^2)","A",4,3,30,0.1000,1,"{2525, 12, 72}"
65,1,283,0,0.4575075,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(f+g x)^4} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x)^4,x]","\frac{B n (b c-a d) \log (f+g x) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{3 (b f-a g)^3 (d f-c g)^3}-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{3 g (f+g x)^3}+\frac{b^3 B n \log (a+b x)}{3 g (b f-a g)^3}-\frac{B n (b c-a d) (-a d g-b c g+2 b d f)}{3 (f+g x) (b f-a g)^2 (d f-c g)^2}-\frac{B n (b c-a d)}{6 (f+g x)^2 (b f-a g) (d f-c g)}-\frac{B d^3 n \log (c+d x)}{3 g (d f-c g)^3}","\frac{B n (b c-a d) \log (f+g x) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{3 (b f-a g)^3 (d f-c g)^3}-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{3 g (f+g x)^3}+\frac{b^3 B n \log (a+b x)}{3 g (b f-a g)^3}-\frac{B n (b c-a d) (-a d g-b c g+2 b d f)}{3 (f+g x) (b f-a g)^2 (d f-c g)^2}-\frac{B n (b c-a d)}{6 (f+g x)^2 (b f-a g) (d f-c g)}-\frac{B d^3 n \log (c+d x)}{3 g (d f-c g)^3}",1,"-(B*(b*c - a*d)*n)/(6*(b*f - a*g)*(d*f - c*g)*(f + g*x)^2) - (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*n)/(3*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)) + (b^3*B*n*Log[a + b*x])/(3*g*(b*f - a*g)^3) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])/(3*g*(f + g*x)^3) - (B*d^3*n*Log[c + d*x])/(3*g*(d*f - c*g)^3) + (B*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*n*Log[f + g*x])/(3*(b*f - a*g)^3*(d*f - c*g)^3)","A",4,3,30,0.1000,1,"{2525, 12, 72}"
66,1,388,0,0.7131494,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(f+g x)^5} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x)^5,x]","-\frac{B n (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{4 (f+g x) (b f-a g)^3 (d f-c g)^3}-\frac{B n (b c-a d) \log (f+g x) (-a d g-b c g+2 b d f) \left(-a^2 d^2 g^2+2 a b d^2 f g+b^2 \left(-\left(c^2 g^2-2 c d f g+2 d^2 f^2\right)\right)\right)}{4 (b f-a g)^4 (d f-c g)^4}-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{4 g (f+g x)^4}+\frac{b^4 B n \log (a+b x)}{4 g (b f-a g)^4}-\frac{B n (b c-a d) (-a d g-b c g+2 b d f)}{8 (f+g x)^2 (b f-a g)^2 (d f-c g)^2}-\frac{B n (b c-a d)}{12 (f+g x)^3 (b f-a g) (d f-c g)}-\frac{B d^4 n \log (c+d x)}{4 g (d f-c g)^4}","-\frac{B n (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{4 (f+g x) (b f-a g)^3 (d f-c g)^3}-\frac{B n (b c-a d) \log (f+g x) (-a d g-b c g+2 b d f) \left(-a^2 d^2 g^2+2 a b d^2 f g+b^2 \left(-\left(c^2 g^2-2 c d f g+2 d^2 f^2\right)\right)\right)}{4 (b f-a g)^4 (d f-c g)^4}-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{4 g (f+g x)^4}+\frac{b^4 B n \log (a+b x)}{4 g (b f-a g)^4}-\frac{B n (b c-a d) (-a d g-b c g+2 b d f)}{8 (f+g x)^2 (b f-a g)^2 (d f-c g)^2}-\frac{B n (b c-a d)}{12 (f+g x)^3 (b f-a g) (d f-c g)}-\frac{B d^4 n \log (c+d x)}{4 g (d f-c g)^4}",1,"-(B*(b*c - a*d)*n)/(12*(b*f - a*g)*(d*f - c*g)*(f + g*x)^3) - (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*n)/(8*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)^2) - (B*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*n)/(4*(b*f - a*g)^3*(d*f - c*g)^3*(f + g*x)) + (b^4*B*n*Log[a + b*x])/(4*g*(b*f - a*g)^4) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])/(4*g*(f + g*x)^4) - (B*d^4*n*Log[c + d*x])/(4*g*(d*f - c*g)^4) - (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*n*Log[f + g*x])/(4*(b*f - a*g)^4*(d*f - c*g)^4)","A",4,3,30,0.1000,1,"{2525, 12, 72}"
67,1,1060,0,1.8353264,"\int (f+g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Int[(f + g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{B^2 n^2 \log ^2(a+b x) (b f-a g)^4}{4 b^4 g}-\frac{B n \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b f-a g)^4}{2 b^4 g}-\frac{B^2 n^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) (b f-a g)^4}{2 b^4 g}-\frac{B^2 n^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) (b f-a g)^4}{2 b^4 g}+\frac{B^2 (b c-a d)^2 g^3 n^2 x^2}{12 b^2 d^2}+\frac{(f+g x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{4 g}+\frac{B^2 (d f-c g)^4 n^2 \log ^2(c+d x)}{4 d^4 g}-\frac{B^2 (b c-a d)^2 (b c+a d) g^3 n^2 x}{6 b^3 d^3}+\frac{B^2 (b c-a d)^2 g^2 (4 b d f-b c g-a d g) n^2 x}{4 b^3 d^3}-\frac{A B (b c-a d) g \left(\left(6 d^2 f^2-4 c d g f+c^2 g^2\right) b^2-a d g (4 d f-c g) b+a^2 d^2 g^2\right) n x}{2 b^3 d^3}-\frac{a^3 B^2 (b c-a d) g^3 n^2 \log (a+b x)}{6 b^4 d}+\frac{a^2 B^2 (b c-a d) g^2 (4 b d f-b c g-a d g) n^2 \log (a+b x)}{4 b^4 d^2}-\frac{B^2 (b c-a d) g \left(\left(6 d^2 f^2-4 c d g f+c^2 g^2\right) b^2-a d g (4 d f-c g) b+a^2 d^2 g^2\right) n (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{2 b^4 d^3}-\frac{B (b c-a d) g^3 n x^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{6 b d}-\frac{B (b c-a d) g^2 (4 b d f-b c g-a d g) n x^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{4 b^2 d^2}+\frac{B^2 c^3 (b c-a d) g^3 n^2 \log (c+d x)}{6 b d^4}-\frac{B^2 c^2 (b c-a d) g^2 (4 b d f-b c g-a d g) n^2 \log (c+d x)}{4 b^2 d^4}+\frac{B^2 (b c-a d)^2 g \left(\left(6 d^2 f^2-4 c d g f+c^2 g^2\right) b^2-a d g (4 d f-c g) b+a^2 d^2 g^2\right) n^2 \log (c+d x)}{2 b^4 d^4}-\frac{B^2 (d f-c g)^4 n^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x)}{2 d^4 g}+\frac{B (d f-c g)^4 n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \log (c+d x)}{2 d^4 g}-\frac{B^2 (d f-c g)^4 n^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{2 d^4 g}","\frac{B^2 g^3 n^2 \log \left(\frac{a+b x}{c+d x}\right) (b c-a d)^4}{6 b^4 d^4}+\frac{B^2 g^3 n^2 \log (c+d x) (b c-a d)^4}{6 b^4 d^4}+\frac{B^2 g^3 n^2 x (b c-a d)^3}{6 b^3 d^3}+\frac{B^2 g^2 (4 b d f-3 b c g-a d g) n^2 \log \left(\frac{a+b x}{c+d x}\right) (b c-a d)^3}{4 b^4 d^4}+\frac{B^2 g^2 (4 b d f-3 b c g-a d g) n^2 \log (c+d x) (b c-a d)^3}{4 b^4 d^4}+\frac{B^2 g^3 n^2 (c+d x)^2 (b c-a d)^2}{12 b^2 d^4}+\frac{B^2 g^2 (4 b d f-3 b c g-a d g) n^2 x (b c-a d)^2}{4 b^3 d^3}+\frac{B^2 g \left(\left(6 d^2 f^2-8 c d g f+3 c^2 g^2\right) b^2-2 a d g (2 d f-c g) b+a^2 d^2 g^2\right) n^2 \log (c+d x) (b c-a d)^2}{2 b^4 d^4}-\frac{B g^3 n (c+d x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)}{6 b d^4}-\frac{B g^2 (4 b d f-3 b c g-a d g) n (c+d x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)}{4 b^2 d^4}-\frac{B g \left(\left(6 d^2 f^2-8 c d g f+3 c^2 g^2\right) b^2-2 a d g (2 d f-c g) b+a^2 d^2 g^2\right) n (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)}{2 b^4 d^3}-\frac{B (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \log \left(\frac{b c-a d}{b (c+d x)}\right) (b c-a d)}{2 b^4 d^4}-\frac{B^2 (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) n^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) (b c-a d)}{2 b^4 d^4}-\frac{(b f-a g)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{4 b^4 g}+\frac{(f+g x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{4 g}",1,"-(A*B*(b*c - a*d)*g*(a^2*d^2*g^2 - a*b*d*g*(4*d*f - c*g) + b^2*(6*d^2*f^2 - 4*c*d*f*g + c^2*g^2))*n*x)/(2*b^3*d^3) - (B^2*(b*c - a*d)^2*(b*c + a*d)*g^3*n^2*x)/(6*b^3*d^3) + (B^2*(b*c - a*d)^2*g^2*(4*b*d*f - b*c*g - a*d*g)*n^2*x)/(4*b^3*d^3) + (B^2*(b*c - a*d)^2*g^3*n^2*x^2)/(12*b^2*d^2) - (a^3*B^2*(b*c - a*d)*g^3*n^2*Log[a + b*x])/(6*b^4*d) + (a^2*B^2*(b*c - a*d)*g^2*(4*b*d*f - b*c*g - a*d*g)*n^2*Log[a + b*x])/(4*b^4*d^2) + (B^2*(b*f - a*g)^4*n^2*Log[a + b*x]^2)/(4*b^4*g) - (B^2*(b*c - a*d)*g*(a^2*d^2*g^2 - a*b*d*g*(4*d*f - c*g) + b^2*(6*d^2*f^2 - 4*c*d*f*g + c^2*g^2))*n*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/(2*b^4*d^3) - (B*(b*c - a*d)*g^2*(4*b*d*f - b*c*g - a*d*g)*n*x^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(4*b^2*d^2) - (B*(b*c - a*d)*g^3*n*x^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(6*b*d) - (B*(b*f - a*g)^4*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*b^4*g) + ((f + g*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(4*g) + (B^2*c^3*(b*c - a*d)*g^3*n^2*Log[c + d*x])/(6*b*d^4) - (B^2*c^2*(b*c - a*d)*g^2*(4*b*d*f - b*c*g - a*d*g)*n^2*Log[c + d*x])/(4*b^2*d^4) + (B^2*(b*c - a*d)^2*g*(a^2*d^2*g^2 - a*b*d*g*(4*d*f - c*g) + b^2*(6*d^2*f^2 - 4*c*d*f*g + c^2*g^2))*n^2*Log[c + d*x])/(2*b^4*d^4) - (B^2*(d*f - c*g)^4*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(2*d^4*g) + (B*(d*f - c*g)^4*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(2*d^4*g) + (B^2*(d*f - c*g)^4*n^2*Log[c + d*x]^2)/(4*d^4*g) - (B^2*(b*f - a*g)^4*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(2*b^4*g) - (B^2*(b*f - a*g)^4*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(2*b^4*g) - (B^2*(d*f - c*g)^4*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*d^4*g)","A",31,13,32,0.4062,1,"{2525, 12, 2528, 2486, 31, 72, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
68,1,699,0,1.1500427,"\int (f+g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Int[(f + g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","-\frac{2 B^2 n^2 (b f-a g)^3 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{3 b^3 g}-\frac{2 B^2 n^2 (d f-c g)^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 d^3 g}+\frac{a^2 B^2 g^2 n^2 (b c-a d) \log (a+b x)}{3 b^3 d}-\frac{2 A B g n x (b c-a d) (-a d g-b c g+3 b d f)}{3 b^2 d^2}-\frac{2 B n (b f-a g)^3 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b^3 g}+\frac{2 B n (d f-c g)^3 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 d^3 g}+\frac{(f+g x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{3 g}-\frac{B g^2 n x^2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b d}-\frac{2 B^2 g n (a+b x) (b c-a d) (-a d g-b c g+3 b d f) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{3 b^3 d^2}+\frac{2 B^2 g n^2 (b c-a d)^2 \log (c+d x) (-a d g-b c g+3 b d f)}{3 b^3 d^3}+\frac{B^2 g^2 n^2 x (b c-a d)^2}{3 b^2 d^2}-\frac{2 B^2 n^2 (b f-a g)^3 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{3 b^3 g}+\frac{B^2 n^2 (b f-a g)^3 \log ^2(a+b x)}{3 b^3 g}-\frac{B^2 c^2 g^2 n^2 (b c-a d) \log (c+d x)}{3 b d^3}-\frac{2 B^2 n^2 (d f-c g)^3 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 d^3 g}+\frac{B^2 n^2 (d f-c g)^3 \log ^2(c+d x)}{3 d^3 g}","\frac{2 B^2 n^2 (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{3 b^3 d^3}+\frac{2 B n (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b^3 d^3}-\frac{2 B g n (a+b x) (b c-a d) (-a d g-2 b c g+3 b d f) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b^3 d^2}-\frac{(b f-a g)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{3 b^3 g}-\frac{B g^2 n (c+d x)^2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b d^3}+\frac{(f+g x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{3 g}+\frac{2 B^2 g n^2 (b c-a d)^2 \log (c+d x) (-a d g-2 b c g+3 b d f)}{3 b^3 d^3}+\frac{B^2 g^2 n^2 x (b c-a d)^2}{3 b^2 d^2}+\frac{B^2 g^2 n^2 (b c-a d)^3 \log \left(\frac{a+b x}{c+d x}\right)}{3 b^3 d^3}+\frac{B^2 g^2 n^2 (b c-a d)^3 \log (c+d x)}{3 b^3 d^3}",1,"(-2*A*B*(b*c - a*d)*g*(3*b*d*f - b*c*g - a*d*g)*n*x)/(3*b^2*d^2) + (B^2*(b*c - a*d)^2*g^2*n^2*x)/(3*b^2*d^2) + (a^2*B^2*(b*c - a*d)*g^2*n^2*Log[a + b*x])/(3*b^3*d) + (B^2*(b*f - a*g)^3*n^2*Log[a + b*x]^2)/(3*b^3*g) - (2*B^2*(b*c - a*d)*g*(3*b*d*f - b*c*g - a*d*g)*n*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/(3*b^3*d^2) - (B*(b*c - a*d)*g^2*n*x^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*b*d) - (2*B*(b*f - a*g)^3*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*b^3*g) + ((f + g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(3*g) - (B^2*c^2*(b*c - a*d)*g^2*n^2*Log[c + d*x])/(3*b*d^3) + (2*B^2*(b*c - a*d)^2*g*(3*b*d*f - b*c*g - a*d*g)*n^2*Log[c + d*x])/(3*b^3*d^3) - (2*B^2*(d*f - c*g)^3*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*d^3*g) + (2*B*(d*f - c*g)^3*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(3*d^3*g) + (B^2*(d*f - c*g)^3*n^2*Log[c + d*x]^2)/(3*d^3*g) - (2*B^2*(b*f - a*g)^3*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3*b^3*g) - (2*B^2*(b*f - a*g)^3*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(3*b^3*g) - (2*B^2*(d*f - c*g)^3*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*d^3*g)","A",27,13,32,0.4062,1,"{2525, 12, 2528, 2486, 31, 72, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
69,1,481,0,0.8312659,"\int (f+g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Int[(f + g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","-\frac{B^2 n^2 (b f-a g)^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b^2 g}-\frac{B^2 n^2 (d f-c g)^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{d^2 g}-\frac{B n (b f-a g)^2 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b^2 g}+\frac{B n (d f-c g)^2 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{d^2 g}+\frac{(f+g x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 g}-\frac{A B g n x (b c-a d)}{b d}+\frac{B^2 g n^2 (b c-a d)^2 \log (c+d x)}{b^2 d^2}-\frac{B^2 g n (a+b x) (b c-a d) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b^2 d}-\frac{B^2 n^2 (b f-a g)^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b^2 g}+\frac{B^2 n^2 (b f-a g)^2 \log ^2(a+b x)}{2 b^2 g}-\frac{B^2 n^2 (d f-c g)^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{d^2 g}+\frac{B^2 n^2 (d f-c g)^2 \log ^2(c+d x)}{2 d^2 g}","\frac{B^2 n^2 (b c-a d) (-a d g-b c g+2 b d f) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b^2 d^2}+\frac{B n (b c-a d) (-a d g-b c g+2 b d f) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b^2 d^2}-\frac{(b f-a g)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 b^2 g}-\frac{B g n (a+b x) (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b^2 d}+\frac{(f+g x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 g}+\frac{B^2 g n^2 (b c-a d)^2 \log (c+d x)}{b^2 d^2}",1,"-((A*B*(b*c - a*d)*g*n*x)/(b*d)) + (B^2*(b*f - a*g)^2*n^2*Log[a + b*x]^2)/(2*b^2*g) - (B^2*(b*c - a*d)*g*n*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/(b^2*d) - (B*(b*f - a*g)^2*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(b^2*g) + ((f + g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(2*g) + (B^2*(b*c - a*d)^2*g*n^2*Log[c + d*x])/(b^2*d^2) - (B^2*(d*f - c*g)^2*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(d^2*g) + (B*(d*f - c*g)^2*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(d^2*g) + (B^2*(d*f - c*g)^2*n^2*Log[c + d*x]^2)/(2*d^2*g) - (B^2*(b*f - a*g)^2*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b^2*g) - (B^2*(b*f - a*g)^2*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b^2*g) - (B^2*(d*f - c*g)^2*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(d^2*g)","A",23,12,30,0.4000,1,"{2525, 12, 2528, 2486, 31, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
70,1,275,0,0.6173331,"\int \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{2 a B^2 n^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b}+\frac{2 B^2 c n^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{d}+\frac{2 a B n \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b}-\frac{2 B c n \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{d}+x \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2+\frac{2 B^2 c n^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{d}+\frac{2 a B^2 n^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b}-\frac{a B^2 n^2 \log ^2(a+b x)}{b}-\frac{B^2 c n^2 \log ^2(c+d x)}{d}","\frac{2 B^2 n^2 (b c-a d) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d}+\frac{2 B n (b c-a d) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b d}+\frac{(a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{b}",1,"-((a*B^2*n^2*Log[a + b*x]^2)/b) + (2*a*B*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/b + x*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (2*B^2*c*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/d - (2*B*c*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/d - (B^2*c*n^2*Log[c + d*x]^2)/d + (2*a*B^2*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/b + (2*a*B^2*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/b + (2*B^2*c*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/d","B",20,10,24,0.4167,1,"{2523, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
71,1,2233,0,5.1841126,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{f+g x} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(f + g*x),x]","\frac{n^2 \left(\log \left(\frac{b (c+d x)}{b c-a d}\right)+\log \left(\frac{b f-a g}{b (f+g x)}\right)-\log \left(\frac{(b f-a g) (c+d x)}{(b c-a d) (f+g x)}\right)\right) \log ^2\left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right) B^2}{g}-\frac{n^2 \left(\log \left(\frac{b (c+d x)}{b c-a d}\right)-\log \left(-\frac{g (c+d x)}{d f-c g}\right)\right) \left(\log (a+b x)+\log \left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right)\right)^2 B^2}{g}+\frac{n^2 \left(\log \left(-\frac{d (a+b x)}{b c-a d}\right)+\log \left(\frac{d f-c g}{d (f+g x)}\right)-\log \left(-\frac{(d f-c g) (a+b x)}{(b c-a d) (f+g x)}\right)\right) \log ^2\left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right) B^2}{g}-\frac{n^2 \left(\log \left(-\frac{d (a+b x)}{b c-a d}\right)-\log \left(-\frac{g (a+b x)}{b f-a g}\right)\right) \left(\log (c+d x)+\log \left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right)\right)^2 B^2}{g}-\frac{\log ^2\left((a+b x)^n\right) \log (f+g x) B^2}{g}-\frac{\log ^2\left((c+d x)^{-n}\right) \log (f+g x) B^2}{g}+\frac{2 n^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) \log (f+g x) B^2}{g}+\frac{2 n^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) \log (f+g x) B^2}{g}-\frac{2 n \left(n \log (a+b x)-\log \left((a+b x)^n\right)\right) \log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x) B^2}{g}+\frac{2 n \log \left(-\frac{g (a+b x)}{b f-a g}\right) \left(\log \left((a+b x)^n\right)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+\log \left((c+d x)^{-n}\right)\right) \log (f+g x) B^2}{g}-\frac{2 n \log \left(-\frac{g (c+d x)}{d f-c g}\right) \left(\log \left((a+b x)^n\right)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+\log \left((c+d x)^{-n}\right)\right) \log (f+g x) B^2}{g}-\frac{2 n \log \left(-\frac{g (a+b x)}{b f-a g}\right) \left(n \log (c+d x)+\log \left((c+d x)^{-n}\right)\right) \log (f+g x) B^2}{g}+\frac{\log ^2\left((a+b x)^n\right) \log \left(\frac{b (f+g x)}{b f-a g}\right) B^2}{g}+\frac{\log ^2\left((c+d x)^{-n}\right) \log \left(\frac{d (f+g x)}{d f-c g}\right) B^2}{g}+\frac{2 n^2 \left(\log (f+g x)-\log \left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right)\right) \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) B^2}{g}+\frac{2 n \log \left((a+b x)^n\right) \text{PolyLog}\left(2,-\frac{g (a+b x)}{b f-a g}\right) B^2}{g}+\frac{2 n^2 \left(\log (f+g x)-\log \left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right)\right) \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) B^2}{g}-\frac{2 n \log \left((c+d x)^{-n}\right) \text{PolyLog}\left(2,-\frac{g (c+d x)}{d f-c g}\right) B^2}{g}-\frac{2 n^2 \log \left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right) \text{PolyLog}\left(2,\frac{g (a+b x)}{b (f+g x)}\right) B^2}{g}+\frac{2 n^2 \log \left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right) \text{PolyLog}\left(2,-\frac{(d f-c g) (a+b x)}{(b c-a d) (f+g x)}\right) B^2}{g}-\frac{2 n^2 \log \left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right) \text{PolyLog}\left(2,\frac{g (c+d x)}{d (f+g x)}\right) B^2}{g}+\frac{2 n^2 \log \left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right) \text{PolyLog}\left(2,\frac{(b f-a g) (c+d x)}{(b c-a d) (f+g x)}\right) B^2}{g}+\frac{2 n \left(\log \left((a+b x)^n\right)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+\log \left((c+d x)^{-n}\right)\right) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right) B^2}{g}-\frac{2 n \left(n \log (c+d x)+\log \left((c+d x)^{-n}\right)\right) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right) B^2}{g}+\frac{2 n^2 \left(\log (c+d x)+\log \left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right)\right) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right) B^2}{g}-\frac{2 n \left(n \log (a+b x)-\log \left((a+b x)^n\right)\right) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right) B^2}{g}-\frac{2 n \left(\log \left((a+b x)^n\right)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+\log \left((c+d x)^{-n}\right)\right) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right) B^2}{g}+\frac{2 n^2 \left(\log (a+b x)+\log \left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right)\right) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right) B^2}{g}-\frac{2 n^2 \text{PolyLog}\left(3,-\frac{d (a+b x)}{b c-a d}\right) B^2}{g}-\frac{2 n^2 \text{PolyLog}\left(3,-\frac{g (a+b x)}{b f-a g}\right) B^2}{g}-\frac{2 n^2 \text{PolyLog}\left(3,\frac{b (c+d x)}{b c-a d}\right) B^2}{g}-\frac{2 n^2 \text{PolyLog}\left(3,-\frac{g (c+d x)}{d f-c g}\right) B^2}{g}-\frac{2 n^2 \text{PolyLog}\left(3,\frac{g (a+b x)}{b (f+g x)}\right) B^2}{g}+\frac{2 n^2 \text{PolyLog}\left(3,-\frac{(d f-c g) (a+b x)}{(b c-a d) (f+g x)}\right) B^2}{g}-\frac{2 n^2 \text{PolyLog}\left(3,\frac{g (c+d x)}{d (f+g x)}\right) B^2}{g}+\frac{2 n^2 \text{PolyLog}\left(3,\frac{(b f-a g) (c+d x)}{(b c-a d) (f+g x)}\right) B^2}{g}-\frac{2 n^2 \text{PolyLog}\left(3,\frac{b (f+g x)}{b f-a g}\right) B^2}{g}-\frac{2 n^2 \text{PolyLog}\left(3,\frac{d (f+g x)}{d f-c g}\right) B^2}{g}-\frac{2 A n \log \left(-\frac{g (a+b x)}{b f-a g}\right) \log (f+g x) B}{g}+\frac{2 A n \log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x) B}{g}-\frac{2 A n \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right) B}{g}+\frac{2 A n \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right) B}{g}+\frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \log (f+g x)}{g}","\frac{2 B n \text{PolyLog}\left(2,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g}-\frac{2 B n \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g}-\frac{2 B^2 n^2 \text{PolyLog}\left(3,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{g}+\frac{2 B^2 n^2 \text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right)}{g}+\frac{\log \left(1-\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g}-\frac{\log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g}",1,"(-2*A*B*n*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/g - (B^2*Log[(a + b*x)^n]^2*Log[f + g*x])/g + ((A + B*Log[e*((a + b*x)/(c + d*x))^n])^2*Log[f + g*x])/g + (2*B^2*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x]*Log[f + g*x])/g + (2*B^2*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)]*Log[f + g*x])/g + (2*A*B*n*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/g - (2*B^2*n*(n*Log[a + b*x] - Log[(a + b*x)^n])*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/g - (B^2*Log[(c + d*x)^(-n)]^2*Log[f + g*x])/g + (2*B^2*n*Log[-((g*(a + b*x))/(b*f - a*g))]*(Log[(a + b*x)^n] - Log[e*((a + b*x)/(c + d*x))^n] + Log[(c + d*x)^(-n)])*Log[f + g*x])/g - (2*B^2*n*Log[-((g*(c + d*x))/(d*f - c*g))]*(Log[(a + b*x)^n] - Log[e*((a + b*x)/(c + d*x))^n] + Log[(c + d*x)^(-n)])*Log[f + g*x])/g - (2*B^2*n*Log[-((g*(a + b*x))/(b*f - a*g))]*(n*Log[c + d*x] + Log[(c + d*x)^(-n)])*Log[f + g*x])/g + (B^2*Log[(a + b*x)^n]^2*Log[(b*(f + g*x))/(b*f - a*g)])/g + (B^2*Log[(c + d*x)^(-n)]^2*Log[(d*(f + g*x))/(d*f - c*g)])/g + (B^2*n^2*(Log[(b*(c + d*x))/(b*c - a*d)] + Log[(b*f - a*g)/(b*(f + g*x))] - Log[((b*f - a*g)*(c + d*x))/((b*c - a*d)*(f + g*x))])*Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))]^2)/g - (B^2*n^2*(Log[(b*(c + d*x))/(b*c - a*d)] - Log[-((g*(c + d*x))/(d*f - c*g))])*(Log[a + b*x] + Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))])^2)/g + (B^2*n^2*(Log[-((d*(a + b*x))/(b*c - a*d))] + Log[(d*f - c*g)/(d*(f + g*x))] - Log[-(((d*f - c*g)*(a + b*x))/((b*c - a*d)*(f + g*x)))])*Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))]^2)/g - (B^2*n^2*(Log[-((d*(a + b*x))/(b*c - a*d))] - Log[-((g*(a + b*x))/(b*f - a*g))])*(Log[c + d*x] + Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])^2)/g + (2*B^2*n^2*(Log[f + g*x] - Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))])*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/g + (2*B^2*n*Log[(a + b*x)^n]*PolyLog[2, -((g*(a + b*x))/(b*f - a*g))])/g + (2*B^2*n^2*(Log[f + g*x] - Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/g - (2*B^2*n*Log[(c + d*x)^(-n)]*PolyLog[2, -((g*(c + d*x))/(d*f - c*g))])/g - (2*B^2*n^2*Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))]*PolyLog[2, (g*(a + b*x))/(b*(f + g*x))])/g + (2*B^2*n^2*Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))]*PolyLog[2, -(((d*f - c*g)*(a + b*x))/((b*c - a*d)*(f + g*x)))])/g - (2*B^2*n^2*Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))]*PolyLog[2, (g*(c + d*x))/(d*(f + g*x))])/g + (2*B^2*n^2*Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))]*PolyLog[2, ((b*f - a*g)*(c + d*x))/((b*c - a*d)*(f + g*x))])/g - (2*A*B*n*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/g + (2*B^2*n*(Log[(a + b*x)^n] - Log[e*((a + b*x)/(c + d*x))^n] + Log[(c + d*x)^(-n)])*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/g - (2*B^2*n*(n*Log[c + d*x] + Log[(c + d*x)^(-n)])*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/g + (2*B^2*n^2*(Log[c + d*x] + Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/g + (2*A*B*n*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g - (2*B^2*n*(n*Log[a + b*x] - Log[(a + b*x)^n])*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g - (2*B^2*n*(Log[(a + b*x)^n] - Log[e*((a + b*x)/(c + d*x))^n] + Log[(c + d*x)^(-n)])*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g + (2*B^2*n^2*(Log[a + b*x] + Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))])*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g - (2*B^2*n^2*PolyLog[3, -((d*(a + b*x))/(b*c - a*d))])/g - (2*B^2*n^2*PolyLog[3, -((g*(a + b*x))/(b*f - a*g))])/g - (2*B^2*n^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])/g - (2*B^2*n^2*PolyLog[3, -((g*(c + d*x))/(d*f - c*g))])/g - (2*B^2*n^2*PolyLog[3, (g*(a + b*x))/(b*(f + g*x))])/g + (2*B^2*n^2*PolyLog[3, -(((d*f - c*g)*(a + b*x))/((b*c - a*d)*(f + g*x)))])/g - (2*B^2*n^2*PolyLog[3, (g*(c + d*x))/(d*(f + g*x))])/g + (2*B^2*n^2*PolyLog[3, ((b*f - a*g)*(c + d*x))/((b*c - a*d)*(f + g*x))])/g - (2*B^2*n^2*PolyLog[3, (b*(f + g*x))/(b*f - a*g)])/g - (2*B^2*n^2*PolyLog[3, (d*(f + g*x))/(d*f - c*g)])/g","B",43,21,32,0.6562,1,"{2524, 2528, 2418, 2390, 2301, 2394, 2393, 2391, 6688, 12, 6742, 2500, 2433, 2375, 2317, 2374, 6589, 2440, 2437, 2435, 2315}"
72,1,657,0,1.1337363,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{(f+g x)^2} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(f + g*x)^2,x]","\frac{2 b B^2 n^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{g (b f-a g)}+\frac{2 B^2 d n^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{g (d f-c g)}-\frac{2 B^2 n^2 (b c-a d) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{(b f-a g) (d f-c g)}+\frac{2 B^2 n^2 (b c-a d) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{(b f-a g) (d f-c g)}+\frac{2 b B n \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g (b f-a g)}-\frac{2 B d n \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g (d f-c g)}+\frac{2 B n (b c-a d) \log (f+g x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(b f-a g) (d f-c g)}-\frac{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g (f+g x)}+\frac{2 B^2 d n^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{g (d f-c g)}+\frac{2 b B^2 n^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{g (b f-a g)}-\frac{2 B^2 n^2 (b c-a d) \log (f+g x) \log \left(-\frac{g (a+b x)}{b f-a g}\right)}{(b f-a g) (d f-c g)}+\frac{2 B^2 n^2 (b c-a d) \log (f+g x) \log \left(-\frac{g (c+d x)}{d f-c g}\right)}{(b f-a g) (d f-c g)}-\frac{b B^2 n^2 \log ^2(a+b x)}{g (b f-a g)}-\frac{B^2 d n^2 \log ^2(c+d x)}{g (d f-c g)}","\frac{2 B^2 n^2 (b c-a d) \text{PolyLog}\left(2,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{(b f-a g) (d f-c g)}+\frac{2 B n (b c-a d) \log \left(1-\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(b f-a g) (d f-c g)}+\frac{(a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{(f+g x) (b f-a g)}",1,"-((b*B^2*n^2*Log[a + b*x]^2)/(g*(b*f - a*g))) + (2*b*B*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(g*(b*f - a*g)) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(g*(f + g*x)) + (2*B^2*d*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(g*(d*f - c*g)) - (2*B*d*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(g*(d*f - c*g)) - (B^2*d*n^2*Log[c + d*x]^2)/(g*(d*f - c*g)) + (2*b*B^2*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(g*(b*f - a*g)) - (2*B^2*(b*c - a*d)*n^2*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/((b*f - a*g)*(d*f - c*g)) + (2*B*(b*c - a*d)*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[f + g*x])/((b*f - a*g)*(d*f - c*g)) + (2*B^2*(b*c - a*d)*n^2*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/((b*f - a*g)*(d*f - c*g)) + (2*b*B^2*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(g*(b*f - a*g)) + (2*B^2*d*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(g*(d*f - c*g)) - (2*B^2*(b*c - a*d)*n^2*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/((b*f - a*g)*(d*f - c*g)) + (2*B^2*(b*c - a*d)*n^2*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/((b*f - a*g)*(d*f - c*g))","B",29,10,32,0.3125,1,"{2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
73,1,941,0,1.5610874,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{(f+g x)^3} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(f + g*x)^3,x]","-\frac{B^2 n^2 \log ^2(a+b x) b^2}{2 g (b f-a g)^2}+\frac{B n \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) b^2}{g (b f-a g)^2}+\frac{B^2 n^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) b^2}{g (b f-a g)^2}+\frac{B^2 n^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) b^2}{g (b f-a g)^2}+\frac{B^2 (b c-a d) n^2 \log (a+b x) b}{(b f-a g)^2 (d f-c g)}-\frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{2 g (f+g x)^2}-\frac{B^2 d^2 n^2 \log ^2(c+d x)}{2 g (d f-c g)^2}-\frac{B (b c-a d) n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{(b f-a g) (d f-c g) (f+g x)}-\frac{B^2 d (b c-a d) n^2 \log (c+d x)}{(b f-a g) (d f-c g)^2}+\frac{B^2 d^2 n^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x)}{g (d f-c g)^2}-\frac{B d^2 n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \log (c+d x)}{g (d f-c g)^2}+\frac{B^2 (b c-a d)^2 g n^2 \log (f+g x)}{(b f-a g)^2 (d f-c g)^2}-\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) n^2 \log \left(-\frac{g (a+b x)}{b f-a g}\right) \log (f+g x)}{(b f-a g)^2 (d f-c g)^2}+\frac{B (b c-a d) (2 b d f-b c g-a d g) n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \log (f+g x)}{(b f-a g)^2 (d f-c g)^2}+\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) n^2 \log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x)}{(b f-a g)^2 (d f-c g)^2}+\frac{B^2 d^2 n^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{g (d f-c g)^2}-\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) n^2 \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{(b f-a g)^2 (d f-c g)^2}+\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) n^2 \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{(b f-a g)^2 (d f-c g)^2}","\frac{B^2 n^2 (b c-a d) (-a d g-b c g+2 b d f) \text{PolyLog}\left(2,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{(b f-a g)^2 (d f-c g)^2}+\frac{b^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 g (b f-a g)^2}+\frac{B g n (a+b x) (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(f+g x) (b f-a g)^2 (d f-c g)}+\frac{B n (b c-a d) (-a d g-b c g+2 b d f) \log \left(1-\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(b f-a g)^2 (d f-c g)^2}-\frac{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 g (f+g x)^2}+\frac{B^2 g n^2 (b c-a d)^2 \log \left(\frac{f+g x}{c+d x}\right)}{(b f-a g)^2 (d f-c g)^2}",1,"(b*B^2*(b*c - a*d)*n^2*Log[a + b*x])/((b*f - a*g)^2*(d*f - c*g)) - (b^2*B^2*n^2*Log[a + b*x]^2)/(2*g*(b*f - a*g)^2) - (B*(b*c - a*d)*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/((b*f - a*g)*(d*f - c*g)*(f + g*x)) + (b^2*B*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(g*(b*f - a*g)^2) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(2*g*(f + g*x)^2) - (B^2*d*(b*c - a*d)*n^2*Log[c + d*x])/((b*f - a*g)*(d*f - c*g)^2) + (B^2*d^2*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(g*(d*f - c*g)^2) - (B*d^2*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(g*(d*f - c*g)^2) - (B^2*d^2*n^2*Log[c + d*x]^2)/(2*g*(d*f - c*g)^2) + (b^2*B^2*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(g*(b*f - a*g)^2) + (B^2*(b*c - a*d)^2*g*n^2*Log[f + g*x])/((b*f - a*g)^2*(d*f - c*g)^2) - (B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*n^2*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/((b*f - a*g)^2*(d*f - c*g)^2) + (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[f + g*x])/((b*f - a*g)^2*(d*f - c*g)^2) + (B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*n^2*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/((b*f - a*g)^2*(d*f - c*g)^2) + (b^2*B^2*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(g*(b*f - a*g)^2) + (B^2*d^2*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(g*(d*f - c*g)^2) - (B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*n^2*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/((b*f - a*g)^2*(d*f - c*g)^2) + (B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*n^2*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/((b*f - a*g)^2*(d*f - c*g)^2)","B",33,11,32,0.3438,1,"{2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 72}"
74,1,1427,0,2.5000958,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{(f+g x)^4} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(f + g*x)^4,x]","-\frac{B^2 n^2 \log ^2(a+b x) b^3}{3 g (b f-a g)^3}+\frac{2 B n \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) b^3}{3 g (b f-a g)^3}+\frac{2 B^2 n^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) b^3}{3 g (b f-a g)^3}+\frac{2 B^2 n^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) b^3}{3 g (b f-a g)^3}+\frac{B^2 (b c-a d) n^2 \log (a+b x) b^2}{3 (b f-a g)^3 (d f-c g)}+\frac{2 B^2 (b c-a d) (2 b d f-b c g-a d g) n^2 \log (a+b x) b}{3 (b f-a g)^3 (d f-c g)^2}-\frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{3 g (f+g x)^3}-\frac{B^2 d^3 n^2 \log ^2(c+d x)}{3 g (d f-c g)^3}-\frac{2 B (b c-a d) (2 b d f-b c g-a d g) n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{3 (b f-a g)^2 (d f-c g)^2 (f+g x)}-\frac{B (b c-a d) n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{3 (b f-a g) (d f-c g) (f+g x)^2}-\frac{2 B^2 d (b c-a d) (2 b d f-b c g-a d g) n^2 \log (c+d x)}{3 (b f-a g)^2 (d f-c g)^3}-\frac{B^2 d^2 (b c-a d) n^2 \log (c+d x)}{3 (b f-a g) (d f-c g)^3}+\frac{2 B^2 d^3 n^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x)}{3 g (d f-c g)^3}-\frac{2 B d^3 n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \log (c+d x)}{3 g (d f-c g)^3}+\frac{B^2 (b c-a d)^2 g (2 b d f-b c g-a d g) n^2 \log (f+g x)}{(b f-a g)^3 (d f-c g)^3}-\frac{2 B^2 (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) n^2 \log \left(-\frac{g (a+b x)}{b f-a g}\right) \log (f+g x)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{2 B (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \log (f+g x)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{2 B^2 (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) n^2 \log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{2 B^2 d^3 n^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 g (d f-c g)^3}-\frac{2 B^2 (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) n^2 \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{2 B^2 (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) n^2 \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{3 (b f-a g)^3 (d f-c g)^3}-\frac{B^2 (b c-a d)^2 g n^2}{3 (b f-a g)^2 (d f-c g)^2 (f+g x)}","\frac{2 B^2 n^2 (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right) \text{PolyLog}\left(2,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{2 B n (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right) \log \left(1-\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{b^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{3 g (b f-a g)^3}-\frac{B g^2 n (c+d x)^2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 (f+g x)^2 (b f-a g) (d f-c g)^3}-\frac{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{3 g (f+g x)^3}+\frac{2 B g n (a+b x) (b c-a d) (-2 a d g-b c g+3 b d f) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 (f+g x) (b f-a g)^3 (d f-c g)^2}+\frac{B^2 g^2 n^2 (c+d x) (b c-a d)^2}{3 (f+g x) (b f-a g)^2 (d f-c g)^3}+\frac{B^2 g^2 n^2 (b c-a d)^3 \log \left(\frac{a+b x}{c+d x}\right)}{3 (b f-a g)^3 (d f-c g)^3}-\frac{B^2 g^2 n^2 (b c-a d)^3 \log \left(\frac{f+g x}{c+d x}\right)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{2 B^2 g n^2 (b c-a d)^2 (-2 a d g-b c g+3 b d f) \log \left(\frac{f+g x}{c+d x}\right)}{3 (b f-a g)^3 (d f-c g)^3}",1,"-(B^2*(b*c - a*d)^2*g*n^2)/(3*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)) + (b^2*B^2*(b*c - a*d)*n^2*Log[a + b*x])/(3*(b*f - a*g)^3*(d*f - c*g)) + (2*b*B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*n^2*Log[a + b*x])/(3*(b*f - a*g)^3*(d*f - c*g)^2) - (b^3*B^2*n^2*Log[a + b*x]^2)/(3*g*(b*f - a*g)^3) - (B*(b*c - a*d)*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*(b*f - a*g)*(d*f - c*g)*(f + g*x)^2) - (2*B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)) + (2*b^3*B*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*g*(b*f - a*g)^3) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(3*g*(f + g*x)^3) - (B^2*d^2*(b*c - a*d)*n^2*Log[c + d*x])/(3*(b*f - a*g)*(d*f - c*g)^3) - (2*B^2*d*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*n^2*Log[c + d*x])/(3*(b*f - a*g)^2*(d*f - c*g)^3) + (2*B^2*d^3*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*g*(d*f - c*g)^3) - (2*B*d^3*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(3*g*(d*f - c*g)^3) - (B^2*d^3*n^2*Log[c + d*x]^2)/(3*g*(d*f - c*g)^3) + (2*b^3*B^2*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3*g*(b*f - a*g)^3) + (B^2*(b*c - a*d)^2*g*(2*b*d*f - b*c*g - a*d*g)*n^2*Log[f + g*x])/((b*f - a*g)^3*(d*f - c*g)^3) - (2*B^2*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*n^2*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/(3*(b*f - a*g)^3*(d*f - c*g)^3) + (2*B*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[f + g*x])/(3*(b*f - a*g)^3*(d*f - c*g)^3) + (2*B^2*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*n^2*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/(3*(b*f - a*g)^3*(d*f - c*g)^3) + (2*b^3*B^2*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(3*g*(b*f - a*g)^3) + (2*B^2*d^3*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*g*(d*f - c*g)^3) - (2*B^2*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*n^2*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/(3*(b*f - a*g)^3*(d*f - c*g)^3) + (2*B^2*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*n^2*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/(3*(b*f - a*g)^3*(d*f - c*g)^3)","A",37,11,32,0.3438,1,"{2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 72}"
75,1,1968,0,3.5454513,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{(f+g x)^5} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(f + g*x)^5,x]","-\frac{B^2 n^2 \log ^2(a+b x) b^4}{4 g (b f-a g)^4}+\frac{B n \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) b^4}{2 g (b f-a g)^4}+\frac{B^2 n^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) b^4}{2 g (b f-a g)^4}+\frac{B^2 n^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) b^4}{2 g (b f-a g)^4}+\frac{B^2 (b c-a d) n^2 \log (a+b x) b^3}{6 (b f-a g)^4 (d f-c g)}+\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) n^2 \log (a+b x) b^2}{4 (b f-a g)^4 (d f-c g)^2}+\frac{B^2 (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) n^2 \log (a+b x) b}{2 (b f-a g)^4 (d f-c g)^3}-\frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{4 g (f+g x)^4}-\frac{B^2 d^4 n^2 \log ^2(c+d x)}{4 g (d f-c g)^4}-\frac{B (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{2 (b f-a g)^3 (d f-c g)^3 (f+g x)}-\frac{B (b c-a d) (2 b d f-b c g-a d g) n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{4 (b f-a g)^2 (d f-c g)^2 (f+g x)^2}-\frac{B (b c-a d) n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{6 (b f-a g) (d f-c g) (f+g x)^3}-\frac{B^2 d^2 (b c-a d) (2 b d f-b c g-a d g) n^2 \log (c+d x)}{4 (b f-a g)^2 (d f-c g)^4}-\frac{B^2 d (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) n^2 \log (c+d x)}{2 (b f-a g)^3 (d f-c g)^4}-\frac{B^2 d^3 (b c-a d) n^2 \log (c+d x)}{6 (b f-a g) (d f-c g)^4}+\frac{B^2 d^4 n^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x)}{2 g (d f-c g)^4}-\frac{B d^4 n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \log (c+d x)}{2 g (d f-c g)^4}+\frac{B^2 (b c-a d)^2 g (2 b d f-b c g-a d g)^2 n^2 \log (f+g x)}{4 (b f-a g)^4 (d f-c g)^4}+\frac{2 B^2 (b c-a d)^2 g \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) n^2 \log (f+g x)}{3 (b f-a g)^4 (d f-c g)^4}+\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) n^2 \log \left(-\frac{g (a+b x)}{b f-a g}\right) \log (f+g x)}{2 (b f-a g)^4 (d f-c g)^4}-\frac{B (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \log (f+g x)}{2 (b f-a g)^4 (d f-c g)^4}-\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) n^2 \log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x)}{2 (b f-a g)^4 (d f-c g)^4}+\frac{B^2 d^4 n^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{2 g (d f-c g)^4}+\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) n^2 \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{2 (b f-a g)^4 (d f-c g)^4}-\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) n^2 \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{2 (b f-a g)^4 (d f-c g)^4}-\frac{5 B^2 (b c-a d)^2 g (2 b d f-b c g-a d g) n^2}{12 (b f-a g)^3 (d f-c g)^3 (f+g x)}-\frac{B^2 (b c-a d)^2 g n^2}{12 (b f-a g)^2 (d f-c g)^2 (f+g x)^2}","\frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 b^4}{4 g (b f-a g)^4}-\frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{4 g (f+g x)^4}+\frac{B (b c-a d) g \left(\left(6 d^2 f^2-4 c d g f+c^2 g^2\right) b^2-2 a d g (4 d f-c g) b+3 a^2 d^2 g^2\right) n (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{2 (b f-a g)^4 (d f-c g)^3 (f+g x)}-\frac{B (b c-a d) g^2 (4 b d f-b c g-3 a d g) n (c+d x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{4 (b f-a g)^2 (d f-c g)^4 (f+g x)^2}+\frac{B (b c-a d) g^3 n (c+d x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{6 (b f-a g) (d f-c g)^4 (f+g x)^3}+\frac{B^2 (b c-a d)^3 g^2 (4 b d f-b c g-3 a d g) n^2 \log \left(\frac{a+b x}{c+d x}\right)}{4 (b f-a g)^4 (d f-c g)^4}-\frac{B^2 (b c-a d)^4 g^3 n^2 \log \left(\frac{a+b x}{c+d x}\right)}{6 (b f-a g)^4 (d f-c g)^4}-\frac{B^2 (b c-a d)^3 g^2 (4 b d f-b c g-3 a d g) n^2 \log \left(\frac{f+g x}{c+d x}\right)}{4 (b f-a g)^4 (d f-c g)^4}+\frac{B^2 (b c-a d)^2 g \left(\left(6 d^2 f^2-4 c d g f+c^2 g^2\right) b^2-2 a d g (4 d f-c g) b+3 a^2 d^2 g^2\right) n^2 \log \left(\frac{f+g x}{c+d x}\right)}{2 (b f-a g)^4 (d f-c g)^4}+\frac{B^2 (b c-a d)^4 g^3 n^2 \log \left(\frac{f+g x}{c+d x}\right)}{6 (b f-a g)^4 (d f-c g)^4}-\frac{B (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \log \left(1-\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{2 (b f-a g)^4 (d f-c g)^4}-\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) n^2 \text{PolyLog}\left(2,\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{2 (b f-a g)^4 (d f-c g)^4}+\frac{B^2 (b c-a d)^2 g^2 (4 b d f-b c g-3 a d g) n^2 (c+d x)}{4 (b f-a g)^3 (d f-c g)^4 (f+g x)}-\frac{B^2 (b c-a d)^3 g^3 n^2 (c+d x)}{6 (b f-a g)^3 (d f-c g)^4 (f+g x)}-\frac{B^2 (b c-a d)^2 g^3 n^2 (c+d x)^2}{12 (b f-a g)^2 (d f-c g)^4 (f+g x)^2}",1,"-(B^2*(b*c - a*d)^2*g*n^2)/(12*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)^2) - (5*B^2*(b*c - a*d)^2*g*(2*b*d*f - b*c*g - a*d*g)*n^2)/(12*(b*f - a*g)^3*(d*f - c*g)^3*(f + g*x)) + (b^3*B^2*(b*c - a*d)*n^2*Log[a + b*x])/(6*(b*f - a*g)^4*(d*f - c*g)) + (b^2*B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*n^2*Log[a + b*x])/(4*(b*f - a*g)^4*(d*f - c*g)^2) + (b*B^2*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*n^2*Log[a + b*x])/(2*(b*f - a*g)^4*(d*f - c*g)^3) - (b^4*B^2*n^2*Log[a + b*x]^2)/(4*g*(b*f - a*g)^4) - (B*(b*c - a*d)*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(6*(b*f - a*g)*(d*f - c*g)*(f + g*x)^3) - (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(4*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)^2) - (B*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*(b*f - a*g)^3*(d*f - c*g)^3*(f + g*x)) + (b^4*B*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*g*(b*f - a*g)^4) - (A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(4*g*(f + g*x)^4) - (B^2*d^3*(b*c - a*d)*n^2*Log[c + d*x])/(6*(b*f - a*g)*(d*f - c*g)^4) - (B^2*d^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*n^2*Log[c + d*x])/(4*(b*f - a*g)^2*(d*f - c*g)^4) - (B^2*d*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*n^2*Log[c + d*x])/(2*(b*f - a*g)^3*(d*f - c*g)^4) + (B^2*d^4*n^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(2*g*(d*f - c*g)^4) - (B*d^4*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/(2*g*(d*f - c*g)^4) - (B^2*d^4*n^2*Log[c + d*x]^2)/(4*g*(d*f - c*g)^4) + (b^4*B^2*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(2*g*(b*f - a*g)^4) + (B^2*(b*c - a*d)^2*g*(2*b*d*f - b*c*g - a*d*g)^2*n^2*Log[f + g*x])/(4*(b*f - a*g)^4*(d*f - c*g)^4) + (2*B^2*(b*c - a*d)^2*g*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*n^2*Log[f + g*x])/(3*(b*f - a*g)^4*(d*f - c*g)^4) + (B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*n^2*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/(2*(b*f - a*g)^4*(d*f - c*g)^4) - (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[f + g*x])/(2*(b*f - a*g)^4*(d*f - c*g)^4) - (B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*n^2*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/(2*(b*f - a*g)^4*(d*f - c*g)^4) + (b^4*B^2*n^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(2*g*(b*f - a*g)^4) + (B^2*d^4*n^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*g*(d*f - c*g)^4) + (B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*n^2*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/(2*(b*f - a*g)^4*(d*f - c*g)^4) - (B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*n^2*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/(2*(b*f - a*g)^4*(d*f - c*g)^4)","A",41,11,32,0.3438,1,"{2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 72}"
76,0,0,0,0.1885137,"\int \frac{(f+g x)^2}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Int[(f + g*x)^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\int \frac{(f+g x)^2}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","\text{Int}\left(\frac{(f+g x)^2}{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A},x\right)",0,"f^2*Defer[Int][(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-1), x] + 2*f*g*Defer[Int][x/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x] + g^2*Defer[Int][x^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x]","A",0,0,0,0,-1,"{}"
77,0,0,0,0.1017367,"\int \frac{f+g x}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Int[(f + g*x)/(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\int \frac{f+g x}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","\text{Int}\left(\frac{f+g x}{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A},x\right)",0,"f*Defer[Int][(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-1), x] + g*Defer[Int][x/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x]","A",0,0,0,0,-1,"{}"
78,0,0,0,0.0150083,"\int \frac{1}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-1),x]","\int \frac{1}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","\text{Int}\left(\frac{1}{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A},x\right)",0,"Defer[Int][(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-1), x]","A",0,0,0,0,-1,"{}"
79,0,0,0,0.0708478,"\int \frac{1}{(f+g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","Int[1/((f + g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])),x]","\int \frac{1}{(f+g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{(f+g x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)},x\right)",0,"Defer[Int][1/((f + g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])), x]","A",0,0,0,0,-1,"{}"
80,0,0,0,0.0748452,"\int \frac{1}{(f+g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","Int[1/((f + g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])),x]","\int \frac{1}{(f+g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{(f+g x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)},x\right)",0,"Defer[Int][1/((f + g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])), x]","A",0,0,0,0,-1,"{}"
81,0,0,0,0.0724352,"\int \frac{1}{(f+g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","Int[1/((f + g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])),x]","\int \frac{1}{(f+g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{(f+g x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)},x\right)",0,"Defer[Int][1/((f + g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])), x]","A",0,0,0,0,-1,"{}"
82,0,0,0,0.2070013,"\int \frac{(f+g x)^2}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Int[(f + g*x)^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\int \frac{(f+g x)^2}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{(f+g x)^2}{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2},x\right)",0,"f^2*Defer[Int][(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-2), x] + 2*f*g*Defer[Int][x/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x] + g^2*Defer[Int][x^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x]","A",0,0,0,0,-1,"{}"
83,0,0,0,0.1136453,"\int \frac{f+g x}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Int[(f + g*x)/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\int \frac{f+g x}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{f+g x}{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2},x\right)",0,"f*Defer[Int][(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-2), x] + g*Defer[Int][x/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x]","A",0,0,0,0,-1,"{}"
84,0,0,0,0.0147984,"\int \frac{1}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-2),x]","\int \frac{1}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2},x\right)",0,"Defer[Int][(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-2), x]","A",0,0,0,0,-1,"{}"
85,0,0,0,0.0782827,"\int \frac{1}{(f+g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Int[1/((f + g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2),x]","\int \frac{1}{(f+g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(f+g x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2},x\right)",0,"Defer[Int][1/((f + g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2), x]","A",0,0,0,0,-1,"{}"
86,0,0,0,0.0813881,"\int \frac{1}{(f+g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Int[1/((f + g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2),x]","\int \frac{1}{(f+g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(f+g x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2},x\right)",0,"Defer[Int][1/((f + g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2), x]","A",0,0,0,0,-1,"{}"
87,0,0,0,0.0798446,"\int \frac{1}{(f+g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Int[1/((f + g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2),x]","\int \frac{1}{(f+g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(f+g x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2},x\right)",0,"Defer[Int][1/((f + g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2), x]","A",0,0,0,0,-1,"{}"
88,1,180,0,0.1237449,"\int (a g+b g x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Int[(a*g + b*g*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g^4 (a+b x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{5 b}+\frac{B g^4 x (b c-a d)^4}{5 d^4}-\frac{B g^4 (a+b x)^2 (b c-a d)^3}{10 b d^3}+\frac{B g^4 (a+b x)^3 (b c-a d)^2}{15 b d^2}-\frac{B g^4 (b c-a d)^5 \log (c+d x)}{5 b d^5}-\frac{B g^4 (a+b x)^4 (b c-a d)}{20 b d}","\frac{g^4 (a+b x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{5 b}+\frac{B g^4 x (b c-a d)^4}{5 d^4}-\frac{B g^4 (a+b x)^2 (b c-a d)^3}{10 b d^3}+\frac{B g^4 (a+b x)^3 (b c-a d)^2}{15 b d^2}-\frac{B g^4 (b c-a d)^5 \log (c+d x)}{5 b d^5}-\frac{B g^4 (a+b x)^4 (b c-a d)}{20 b d}",1,"(B*(b*c - a*d)^4*g^4*x)/(5*d^4) - (B*(b*c - a*d)^3*g^4*(a + b*x)^2)/(10*b*d^3) + (B*(b*c - a*d)^2*g^4*(a + b*x)^3)/(15*b*d^2) - (B*(b*c - a*d)*g^4*(a + b*x)^4)/(20*b*d) + (g^4*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(5*b) - (B*(b*c - a*d)^5*g^4*Log[c + d*x])/(5*b*d^5)","A",4,3,30,0.1000,1,"{2525, 12, 43}"
89,1,149,0,0.0962254,"\int (a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Int[(a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g^3 (a+b x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 b}-\frac{B g^3 x (b c-a d)^3}{4 d^3}+\frac{B g^3 (a+b x)^2 (b c-a d)^2}{8 b d^2}+\frac{B g^3 (b c-a d)^4 \log (c+d x)}{4 b d^4}-\frac{B g^3 (a+b x)^3 (b c-a d)}{12 b d}","\frac{g^3 (a+b x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 b}-\frac{B g^3 x (b c-a d)^3}{4 d^3}+\frac{B g^3 (a+b x)^2 (b c-a d)^2}{8 b d^2}+\frac{B g^3 (b c-a d)^4 \log (c+d x)}{4 b d^4}-\frac{B g^3 (a+b x)^3 (b c-a d)}{12 b d}",1,"-(B*(b*c - a*d)^3*g^3*x)/(4*d^3) + (B*(b*c - a*d)^2*g^3*(a + b*x)^2)/(8*b*d^2) - (B*(b*c - a*d)*g^3*(a + b*x)^3)/(12*b*d) + (g^3*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(4*b) + (B*(b*c - a*d)^4*g^3*Log[c + d*x])/(4*b*d^4)","A",4,3,30,0.1000,1,"{2525, 12, 43}"
90,1,118,0,0.0792376,"\int (a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Int[(a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g^2 (a+b x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b}+\frac{B g^2 x (b c-a d)^2}{3 d^2}-\frac{B g^2 (b c-a d)^3 \log (c+d x)}{3 b d^3}-\frac{B g^2 (a+b x)^2 (b c-a d)}{6 b d}","\frac{g^2 (a+b x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b}+\frac{B g^2 x (b c-a d)^2}{3 d^2}-\frac{B g^2 (b c-a d)^3 \log (c+d x)}{3 b d^3}-\frac{B g^2 (a+b x)^2 (b c-a d)}{6 b d}",1,"(B*(b*c - a*d)^2*g^2*x)/(3*d^2) - (B*(b*c - a*d)*g^2*(a + b*x)^2)/(6*b*d) + (g^2*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(3*b) - (B*(b*c - a*d)^3*g^2*Log[c + d*x])/(3*b*d^3)","A",4,3,30,0.1000,1,"{2525, 12, 43}"
91,1,81,0,0.0528924,"\int (a g+b g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Int[(a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b}+\frac{B g (b c-a d)^2 \log (c+d x)}{2 b d^2}-\frac{B g x (b c-a d)}{2 d}","\frac{g (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b}+\frac{B g (b c-a d)^2 \log (c+d x)}{2 b d^2}-\frac{B g x (b c-a d)}{2 d}",1,"-(B*(b*c - a*d)*g*x)/(2*d) + (g*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(2*b) + (B*(b*c - a*d)^2*g*Log[c + d*x])/(2*b*d^2)","A",4,3,28,0.1071,1,"{2525, 12, 43}"
92,1,120,0,0.2174143,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{a g+b g x} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(a*g + b*g*x),x]","\frac{B \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g}+\frac{\log (a g+b g x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b g}+\frac{B \log (a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{B \log ^2(g (a+b x))}{2 b g}","\frac{B \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{b g}-\frac{\log \left(-\frac{b c-a d}{d (a+b x)}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b g}",1,"-(B*Log[g*(a + b*x)]^2)/(2*b*g) + ((A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[a*g + b*g*x])/(b*g) + (B*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x])/(b*g) + (B*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g)","A",10,8,30,0.2667,1,"{2524, 12, 2418, 2390, 2301, 2394, 2393, 2391}"
93,1,102,0,0.078977,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^2} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(a*g + b*g*x)^2,x]","-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{b g^2 (a+b x)}-\frac{B d \log (a+b x)}{b g^2 (b c-a d)}+\frac{B d \log (c+d x)}{b g^2 (b c-a d)}-\frac{B}{b g^2 (a+b x)}","-\frac{(c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^2 (a+b x) (b c-a d)}-\frac{B}{b g^2 (a+b x)}",1,"-(B/(b*g^2*(a + b*x))) - (B*d*Log[a + b*x])/(b*(b*c - a*d)*g^2) - (A + B*Log[(e*(a + b*x))/(c + d*x)])/(b*g^2*(a + b*x)) + (B*d*Log[c + d*x])/(b*(b*c - a*d)*g^2)","A",4,3,30,0.1000,1,"{2525, 12, 44}"
94,1,144,0,0.0999325,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^3} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(a*g + b*g*x)^3,x]","-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{2 b g^3 (a+b x)^2}+\frac{B d^2 \log (a+b x)}{2 b g^3 (b c-a d)^2}-\frac{B d^2 \log (c+d x)}{2 b g^3 (b c-a d)^2}+\frac{B d}{2 b g^3 (a+b x) (b c-a d)}-\frac{B}{4 b g^3 (a+b x)^2}","-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{2 b g^3 (a+b x)^2}+\frac{B d^2 \log (a+b x)}{2 b g^3 (b c-a d)^2}-\frac{B d^2 \log (c+d x)}{2 b g^3 (b c-a d)^2}+\frac{B d}{2 b g^3 (a+b x) (b c-a d)}-\frac{B}{4 b g^3 (a+b x)^2}",1,"-B/(4*b*g^3*(a + b*x)^2) + (B*d)/(2*b*(b*c - a*d)*g^3*(a + b*x)) + (B*d^2*Log[a + b*x])/(2*b*(b*c - a*d)^2*g^3) - (A + B*Log[(e*(a + b*x))/(c + d*x)])/(2*b*g^3*(a + b*x)^2) - (B*d^2*Log[c + d*x])/(2*b*(b*c - a*d)^2*g^3)","A",4,3,30,0.1000,1,"{2525, 12, 44}"
95,1,175,0,0.1295788,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^4} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(a*g + b*g*x)^4,x]","-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{3 b g^4 (a+b x)^3}-\frac{B d^2}{3 b g^4 (a+b x) (b c-a d)^2}-\frac{B d^3 \log (a+b x)}{3 b g^4 (b c-a d)^3}+\frac{B d^3 \log (c+d x)}{3 b g^4 (b c-a d)^3}+\frac{B d}{6 b g^4 (a+b x)^2 (b c-a d)}-\frac{B}{9 b g^4 (a+b x)^3}","-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{3 b g^4 (a+b x)^3}-\frac{B d^2}{3 b g^4 (a+b x) (b c-a d)^2}-\frac{B d^3 \log (a+b x)}{3 b g^4 (b c-a d)^3}+\frac{B d^3 \log (c+d x)}{3 b g^4 (b c-a d)^3}+\frac{B d}{6 b g^4 (a+b x)^2 (b c-a d)}-\frac{B}{9 b g^4 (a+b x)^3}",1,"-B/(9*b*g^4*(a + b*x)^3) + (B*d)/(6*b*(b*c - a*d)*g^4*(a + b*x)^2) - (B*d^2)/(3*b*(b*c - a*d)^2*g^4*(a + b*x)) - (B*d^3*Log[a + b*x])/(3*b*(b*c - a*d)^3*g^4) - (A + B*Log[(e*(a + b*x))/(c + d*x)])/(3*b*g^4*(a + b*x)^3) + (B*d^3*Log[c + d*x])/(3*b*(b*c - a*d)^3*g^4)","A",4,3,30,0.1000,1,"{2525, 12, 44}"
96,1,206,0,0.1565825,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^5} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(a*g + b*g*x)^5,x]","-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{4 b g^5 (a+b x)^4}+\frac{B d^3}{4 b g^5 (a+b x) (b c-a d)^3}-\frac{B d^2}{8 b g^5 (a+b x)^2 (b c-a d)^2}+\frac{B d^4 \log (a+b x)}{4 b g^5 (b c-a d)^4}-\frac{B d^4 \log (c+d x)}{4 b g^5 (b c-a d)^4}+\frac{B d}{12 b g^5 (a+b x)^3 (b c-a d)}-\frac{B}{16 b g^5 (a+b x)^4}","-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{4 b g^5 (a+b x)^4}+\frac{B d^3}{4 b g^5 (a+b x) (b c-a d)^3}-\frac{B d^2}{8 b g^5 (a+b x)^2 (b c-a d)^2}+\frac{B d^4 \log (a+b x)}{4 b g^5 (b c-a d)^4}-\frac{B d^4 \log (c+d x)}{4 b g^5 (b c-a d)^4}+\frac{B d}{12 b g^5 (a+b x)^3 (b c-a d)}-\frac{B}{16 b g^5 (a+b x)^4}",1,"-B/(16*b*g^5*(a + b*x)^4) + (B*d)/(12*b*(b*c - a*d)*g^5*(a + b*x)^3) - (B*d^2)/(8*b*(b*c - a*d)^2*g^5*(a + b*x)^2) + (B*d^3)/(4*b*(b*c - a*d)^3*g^5*(a + b*x)) + (B*d^4*Log[a + b*x])/(4*b*(b*c - a*d)^4*g^5) - (A + B*Log[(e*(a + b*x))/(c + d*x)])/(4*b*g^5*(a + b*x)^4) - (B*d^4*Log[c + d*x])/(4*b*(b*c - a*d)^4*g^5)","A",4,3,30,0.1000,1,"{2525, 12, 44}"
97,1,557,0,0.8545387,"\int (a g+b g x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Int[(a*g + b*g*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{2 B^2 g^4 (b c-a d)^5 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{5 b d^5}-\frac{2 B g^4 (b c-a d)^5 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{5 b d^5}-\frac{B g^4 (a+b x)^2 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{5 b d^3}+\frac{2 B g^4 (a+b x)^3 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{15 b d^2}+\frac{2 A B g^4 x (b c-a d)^4}{5 d^4}-\frac{B g^4 (a+b x)^4 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{10 b d}+\frac{g^4 (a+b x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{5 b}+\frac{2 B^2 g^4 (a+b x) (b c-a d)^4 \log \left(\frac{e (a+b x)}{c+d x}\right)}{5 b d^4}+\frac{13 B^2 g^4 x (b c-a d)^4}{30 d^4}-\frac{7 B^2 g^4 (a+b x)^2 (b c-a d)^3}{60 b d^3}+\frac{B^2 g^4 (a+b x)^3 (b c-a d)^2}{30 b d^2}-\frac{B^2 g^4 (b c-a d)^5 \log ^2(c+d x)}{5 b d^5}-\frac{5 B^2 g^4 (b c-a d)^5 \log (c+d x)}{6 b d^5}+\frac{2 B^2 g^4 (b c-a d)^5 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{5 b d^5}","\frac{2 B^2 g^4 (b c-a d)^5 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{5 b d^5}+\frac{B g^4 (b c-a d)^5 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(12 B \log \left(\frac{e (a+b x)}{c+d x}\right)+12 A+25 B\right)}{30 b d^5}+\frac{B g^4 (a+b x) (b c-a d)^4 \left(12 B \log \left(\frac{e (a+b x)}{c+d x}\right)+12 A+13 B\right)}{30 b d^4}-\frac{B g^4 (a+b x)^2 (b c-a d)^3 \left(12 B \log \left(\frac{e (a+b x)}{c+d x}\right)+12 A+7 B\right)}{60 b d^3}+\frac{B g^4 (a+b x)^3 (b c-a d)^2 \left(4 B \log \left(\frac{e (a+b x)}{c+d x}\right)+4 A+B\right)}{30 b d^2}-\frac{B g^4 (a+b x)^4 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{10 b d}+\frac{g^4 (a+b x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{5 b}",1,"(2*A*B*(b*c - a*d)^4*g^4*x)/(5*d^4) + (13*B^2*(b*c - a*d)^4*g^4*x)/(30*d^4) - (7*B^2*(b*c - a*d)^3*g^4*(a + b*x)^2)/(60*b*d^3) + (B^2*(b*c - a*d)^2*g^4*(a + b*x)^3)/(30*b*d^2) + (2*B^2*(b*c - a*d)^4*g^4*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)])/(5*b*d^4) - (B*(b*c - a*d)^3*g^4*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(5*b*d^3) + (2*B*(b*c - a*d)^2*g^4*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(15*b*d^2) - (B*(b*c - a*d)*g^4*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(10*b*d) + (g^4*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(5*b) - (5*B^2*(b*c - a*d)^5*g^4*Log[c + d*x])/(6*b*d^5) + (2*B^2*(b*c - a*d)^5*g^4*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(5*b*d^5) - (2*B*(b*c - a*d)^5*g^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/(5*b*d^5) - (B^2*(b*c - a*d)^5*g^4*Log[c + d*x]^2)/(5*b*d^5) + (2*B^2*(b*c - a*d)^5*g^4*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(5*b*d^5)","A",28,13,32,0.4062,1,"{2525, 12, 2528, 2486, 31, 43, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
98,1,474,0,0.6458302,"\int (a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Int[(a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","-\frac{B^2 g^3 (b c-a d)^4 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{2 b d^4}+\frac{B g^3 (b c-a d)^4 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b d^4}+\frac{B g^3 (a+b x)^2 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 b d^2}-\frac{A B g^3 x (b c-a d)^3}{2 d^3}-\frac{B g^3 (a+b x)^3 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{6 b d}+\frac{g^3 (a+b x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{4 b}-\frac{B^2 g^3 (a+b x) (b c-a d)^3 \log \left(\frac{e (a+b x)}{c+d x}\right)}{2 b d^3}-\frac{5 B^2 g^3 x (b c-a d)^3}{12 d^3}+\frac{B^2 g^3 (a+b x)^2 (b c-a d)^2}{12 b d^2}+\frac{B^2 g^3 (b c-a d)^4 \log ^2(c+d x)}{4 b d^4}+\frac{11 B^2 g^3 (b c-a d)^4 \log (c+d x)}{12 b d^4}-\frac{B^2 g^3 (b c-a d)^4 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{2 b d^4}","-\frac{B^2 g^3 (b c-a d)^4 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{2 b d^4}-\frac{B g^3 (b c-a d)^4 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(6 B \log \left(\frac{e (a+b x)}{c+d x}\right)+6 A+11 B\right)}{12 b d^4}-\frac{B g^3 (a+b x) (b c-a d)^3 \left(6 B \log \left(\frac{e (a+b x)}{c+d x}\right)+6 A+5 B\right)}{12 b d^3}+\frac{B g^3 (a+b x)^2 (b c-a d)^2 \left(3 B \log \left(\frac{e (a+b x)}{c+d x}\right)+3 A+B\right)}{12 b d^2}-\frac{B g^3 (a+b x)^3 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{6 b d}+\frac{g^3 (a+b x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{4 b}",1,"-(A*B*(b*c - a*d)^3*g^3*x)/(2*d^3) - (5*B^2*(b*c - a*d)^3*g^3*x)/(12*d^3) + (B^2*(b*c - a*d)^2*g^3*(a + b*x)^2)/(12*b*d^2) - (B^2*(b*c - a*d)^3*g^3*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)])/(2*b*d^3) + (B*(b*c - a*d)^2*g^3*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(4*b*d^2) - (B*(b*c - a*d)*g^3*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(6*b*d) + (g^3*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(4*b) + (11*B^2*(b*c - a*d)^4*g^3*Log[c + d*x])/(12*b*d^4) - (B^2*(b*c - a*d)^4*g^3*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(2*b*d^4) + (B*(b*c - a*d)^4*g^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/(2*b*d^4) + (B^2*(b*c - a*d)^4*g^3*Log[c + d*x]^2)/(4*b*d^4) - (B^2*(b*c - a*d)^4*g^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*b*d^4)","A",24,13,32,0.4062,1,"{2525, 12, 2528, 2486, 31, 43, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
99,1,389,0,0.5528175,"\int (a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Int[(a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{2 B^2 g^2 (b c-a d)^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 b d^3}-\frac{2 B g^2 (b c-a d)^3 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b d^3}+\frac{2 A B g^2 x (b c-a d)^2}{3 d^2}-\frac{B g^2 (a+b x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b d}+\frac{g^2 (a+b x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 b}+\frac{2 B^2 g^2 (a+b x) (b c-a d)^2 \log \left(\frac{e (a+b x)}{c+d x}\right)}{3 b d^2}+\frac{B^2 g^2 x (b c-a d)^2}{3 d^2}-\frac{B^2 g^2 (b c-a d)^3 \log ^2(c+d x)}{3 b d^3}-\frac{B^2 g^2 (b c-a d)^3 \log (c+d x)}{b d^3}+\frac{2 B^2 g^2 (b c-a d)^3 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 b d^3}","\frac{2 B^2 g^2 (b c-a d)^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{3 b d^3}+\frac{B g^2 (b c-a d)^3 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(2 B \log \left(\frac{e (a+b x)}{c+d x}\right)+2 A+3 B\right)}{3 b d^3}+\frac{B g^2 (a+b x) (b c-a d)^2 \left(2 B \log \left(\frac{e (a+b x)}{c+d x}\right)+2 A+B\right)}{3 b d^2}-\frac{B g^2 (a+b x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b d}+\frac{g^2 (a+b x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 b}",1,"(2*A*B*(b*c - a*d)^2*g^2*x)/(3*d^2) + (B^2*(b*c - a*d)^2*g^2*x)/(3*d^2) + (2*B^2*(b*c - a*d)^2*g^2*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)])/(3*b*d^2) - (B*(b*c - a*d)*g^2*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(3*b*d) + (g^2*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(3*b) - (B^2*(b*c - a*d)^3*g^2*Log[c + d*x])/(b*d^3) + (2*B^2*(b*c - a*d)^3*g^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*b*d^3) - (2*B*(b*c - a*d)^3*g^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/(3*b*d^3) - (B^2*(b*c - a*d)^3*g^2*Log[c + d*x]^2)/(3*b*d^3) + (2*B^2*(b*c - a*d)^3*g^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*b*d^3)","A",20,13,32,0.4062,1,"{2525, 12, 2528, 2486, 31, 43, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
100,1,285,0,0.4555562,"\int (a g+b g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Int[(a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","-\frac{B^2 g (b c-a d)^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b d^2}+\frac{B g (b c-a d)^2 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b d^2}+\frac{g (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 b}-\frac{A B g x (b c-a d)}{d}+\frac{B^2 g (b c-a d)^2 \log ^2(c+d x)}{2 b d^2}+\frac{B^2 g (b c-a d)^2 \log (c+d x)}{b d^2}-\frac{B^2 g (b c-a d)^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b d^2}-\frac{B^2 g (a+b x) (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)}{b d}","-\frac{B^2 g (b c-a d)^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}-\frac{B g (b c-a d)^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A+B\right)}{b d^2}-\frac{B g (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b d}+\frac{g (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 b}",1,"-((A*B*(b*c - a*d)*g*x)/d) - (B^2*(b*c - a*d)*g*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)])/(b*d) + (g*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(2*b) + (B^2*(b*c - a*d)^2*g*Log[c + d*x])/(b*d^2) - (B^2*(b*c - a*d)^2*g*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*d^2) + (B*(b*c - a*d)^2*g*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/(b*d^2) + (B^2*(b*c - a*d)^2*g*Log[c + d*x]^2)/(2*b*d^2) - (B^2*(b*c - a*d)^2*g*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*d^2)","A",16,12,30,0.4000,1,"{2525, 12, 2528, 2486, 31, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
101,1,728,0,3.4160285,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{a g+b g x} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(a*g + b*g*x),x]","\frac{2 A B \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g}-\frac{2 B^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) \left(-\log \left(\frac{e (a+b x)}{c+d x}\right)+\log (a+b x)+\log \left(\frac{1}{c+d x}\right)\right)}{b g}-\frac{2 B^2 \text{PolyLog}\left(3,-\frac{d (a+b x)}{b c-a d}\right)}{b g}-\frac{2 B^2 \text{PolyLog}\left(3,\frac{b (c+d x)}{b c-a d}\right)}{b g}+\frac{2 B^2 \log (a+b x) \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g}-\frac{2 B^2 \log \left(\frac{1}{c+d x}\right) \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g}+\frac{\log (a g+b g x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{b g}+\frac{2 A B \log (a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{A B \log ^2(g (a+b x))}{b g}-\frac{B^2 \log ^2(a g+b g x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{b g}-\frac{2 B^2 \log (a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right) \left(-\log \left(\frac{e (a+b x)}{c+d x}\right)+\log (a+b x)+\log \left(\frac{1}{c+d x}\right)\right)}{b g}-\frac{B^2 \log (-c-d x) \log ^2(g (a+b x))}{b g}+\frac{B^2 \log ^2(g (a+b x)) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{B^2 \log ^2\left(\frac{1}{c+d x}\right) \log (g (a+b x))}{b g}+\frac{B^2 \log ^2\left(\frac{1}{c+d x}\right) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g}-\frac{B^2 \log ^2(a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{B^2 \log ^2(a+b x) \log (-c-d x)}{b g}+\frac{B^2 \log ^2(a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}+\frac{2 B^2 \log (a+b x) \log (-c-d x) \log (g (a+b x))}{b g}+\frac{B^2 \log ^3(g (a+b x))}{3 b g}","\frac{2 B \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b g}+\frac{2 B^2 \text{PolyLog}\left(3,\frac{b (c+d x)}{d (a+b x)}\right)}{b g}-\frac{\log \left(1-\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{b g}",1,"-((A*B*Log[g*(a + b*x)]^2)/(b*g)) + (B^2*Log[g*(a + b*x)]^3)/(3*b*g) - (B^2*Log[a + b*x]^2*Log[-c - d*x])/(b*g) + (2*B^2*Log[a + b*x]*Log[g*(a + b*x)]*Log[-c - d*x])/(b*g) - (B^2*Log[g*(a + b*x)]^2*Log[-c - d*x])/(b*g) + (B^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[(c + d*x)^(-1)]^2)/(b*g) - (B^2*Log[g*(a + b*x)]*Log[(c + d*x)^(-1)]^2)/(b*g) + (B^2*Log[a + b*x]^2*Log[(b*(c + d*x))/(b*c - a*d)])/(b*g) + (B^2*Log[g*(a + b*x)]^2*Log[(b*(c + d*x))/(b*c - a*d)])/(b*g) + ((A + B*Log[(e*(a + b*x))/(c + d*x)])^2*Log[a*g + b*g*x])/(b*g) + (2*A*B*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x])/(b*g) - (2*B^2*(Log[a + b*x] + Log[(c + d*x)^(-1)] - Log[(e*(a + b*x))/(c + d*x)])*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x])/(b*g) - (B^2*Log[(e*(a + b*x))/(c + d*x)]*Log[a*g + b*g*x]^2)/(b*g) - (B^2*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x]^2)/(b*g) + (2*A*B*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g) + (2*B^2*Log[a + b*x]*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g) - (2*B^2*(Log[a + b*x] + Log[(c + d*x)^(-1)] - Log[(e*(a + b*x))/(c + d*x)])*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g) - (2*B^2*Log[(c + d*x)^(-1)]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*g) - (2*B^2*PolyLog[3, -((d*(a + b*x))/(b*c - a*d))])/(b*g) - (2*B^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])/(b*g)","B",46,23,32,0.7188,1,"{2524, 12, 2528, 2418, 2390, 2301, 2394, 2393, 2391, 6688, 6742, 2500, 2440, 2434, 2433, 2375, 2317, 2374, 6589, 2499, 2302, 30, 2396}"
102,1,470,0,0.7717874,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^2} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(a*g + b*g*x)^2,x]","-\frac{2 B^2 d \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g^2 (b c-a d)}-\frac{2 B^2 d \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g^2 (b c-a d)}-\frac{2 B d \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b g^2 (b c-a d)}-\frac{2 B \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b g^2 (a+b x)}+\frac{2 B d \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b g^2 (b c-a d)}-\frac{\left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{b g^2 (a+b x)}+\frac{B^2 d \log ^2(a+b x)}{b g^2 (b c-a d)}+\frac{B^2 d \log ^2(c+d x)}{b g^2 (b c-a d)}-\frac{2 B^2 d \log (a+b x)}{b g^2 (b c-a d)}-\frac{2 B^2 d \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g^2 (b c-a d)}+\frac{2 B^2 d \log (c+d x)}{b g^2 (b c-a d)}-\frac{2 B^2 d \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g^2 (b c-a d)}-\frac{2 B^2}{b g^2 (a+b x)}","-\frac{2 B (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^2 (a+b x) (b c-a d)}-\frac{(c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^2 (a+b x) (b c-a d)}-\frac{2 B^2 (c+d x)}{g^2 (a+b x) (b c-a d)}",1,"(-2*B^2)/(b*g^2*(a + b*x)) - (2*B^2*d*Log[a + b*x])/(b*(b*c - a*d)*g^2) + (B^2*d*Log[a + b*x]^2)/(b*(b*c - a*d)*g^2) - (2*B*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(b*g^2*(a + b*x)) - (2*B*d*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(b*(b*c - a*d)*g^2) - (A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(b*g^2*(a + b*x)) + (2*B^2*d*Log[c + d*x])/(b*(b*c - a*d)*g^2) - (2*B^2*d*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*(b*c - a*d)*g^2) + (2*B*d*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/(b*(b*c - a*d)*g^2) + (B^2*d*Log[c + d*x]^2)/(b*(b*c - a*d)*g^2) - (2*B^2*d*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)*g^2) - (2*B^2*d*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*(b*c - a*d)*g^2) - (2*B^2*d*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)*g^2)","C",26,11,32,0.3438,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
103,1,577,0,0.9095504,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^3} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(a*g + b*g*x)^3,x]","\frac{B^2 d^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}+\frac{B^2 d^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}+\frac{B d^2 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b g^3 (b c-a d)^2}-\frac{B d^2 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b g^3 (b c-a d)^2}+\frac{B d \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b g^3 (a+b x) (b c-a d)}-\frac{B \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b g^3 (a+b x)^2}-\frac{\left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 b g^3 (a+b x)^2}-\frac{B^2 d^2 \log ^2(a+b x)}{2 b g^3 (b c-a d)^2}-\frac{B^2 d^2 \log ^2(c+d x)}{2 b g^3 (b c-a d)^2}+\frac{3 B^2 d^2 \log (a+b x)}{2 b g^3 (b c-a d)^2}+\frac{B^2 d^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}-\frac{3 B^2 d^2 \log (c+d x)}{2 b g^3 (b c-a d)^2}+\frac{B^2 d^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}+\frac{3 B^2 d}{2 b g^3 (a+b x) (b c-a d)}-\frac{B^2}{4 b g^3 (a+b x)^2}","-\frac{b B (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^3 (a+b x)^2 (b c-a d)^2}+\frac{2 B d (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^3 (a+b x) (b c-a d)^2}-\frac{b (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 g^3 (a+b x)^2 (b c-a d)^2}+\frac{d (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^3 (a+b x) (b c-a d)^2}-\frac{b B^2 (c+d x)^2}{4 g^3 (a+b x)^2 (b c-a d)^2}+\frac{2 B^2 d (c+d x)}{g^3 (a+b x) (b c-a d)^2}",1,"-B^2/(4*b*g^3*(a + b*x)^2) + (3*B^2*d)/(2*b*(b*c - a*d)*g^3*(a + b*x)) + (3*B^2*d^2*Log[a + b*x])/(2*b*(b*c - a*d)^2*g^3) - (B^2*d^2*Log[a + b*x]^2)/(2*b*(b*c - a*d)^2*g^3) - (B*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(2*b*g^3*(a + b*x)^2) + (B*d*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(b*(b*c - a*d)*g^3*(a + b*x)) + (B*d^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(b*(b*c - a*d)^2*g^3) - (A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(2*b*g^3*(a + b*x)^2) - (3*B^2*d^2*Log[c + d*x])/(2*b*(b*c - a*d)^2*g^3) + (B^2*d^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*(b*c - a*d)^2*g^3) - (B*d^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/(b*(b*c - a*d)^2*g^3) - (B^2*d^2*Log[c + d*x]^2)/(2*b*(b*c - a*d)^2*g^3) + (B^2*d^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)^2*g^3) + (B^2*d^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*(b*c - a*d)^2*g^3) + (B^2*d^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)^2*g^3)","C",30,11,32,0.3438,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
104,1,680,0,1.0589911,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^4} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(a*g + b*g*x)^4,x]","-\frac{2 B^2 d^3 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}-\frac{2 B^2 d^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}-\frac{2 B d^3 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b g^4 (b c-a d)^3}+\frac{2 B d^3 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b g^4 (b c-a d)^3}-\frac{2 B d^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b g^4 (a+b x) (b c-a d)^2}+\frac{B d \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b g^4 (a+b x)^2 (b c-a d)}-\frac{\left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 b g^4 (a+b x)^3}-\frac{2 B \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{9 b g^4 (a+b x)^3}-\frac{11 B^2 d^2}{9 b g^4 (a+b x) (b c-a d)^2}+\frac{B^2 d^3 \log ^2(a+b x)}{3 b g^4 (b c-a d)^3}+\frac{B^2 d^3 \log ^2(c+d x)}{3 b g^4 (b c-a d)^3}-\frac{11 B^2 d^3 \log (a+b x)}{9 b g^4 (b c-a d)^3}-\frac{2 B^2 d^3 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}+\frac{11 B^2 d^3 \log (c+d x)}{9 b g^4 (b c-a d)^3}-\frac{2 B^2 d^3 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}+\frac{5 B^2 d}{18 b g^4 (a+b x)^2 (b c-a d)}-\frac{2 B^2}{27 b g^4 (a+b x)^3}","-\frac{b^2 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 g^4 (a+b x)^3 (b c-a d)^3}-\frac{2 b^2 B (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{9 g^4 (a+b x)^3 (b c-a d)^3}-\frac{d^2 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^4 (a+b x) (b c-a d)^3}-\frac{2 B d^2 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^4 (a+b x) (b c-a d)^3}+\frac{b d (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^4 (a+b x)^2 (b c-a d)^3}+\frac{b B d (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^4 (a+b x)^2 (b c-a d)^3}-\frac{2 b^2 B^2 (c+d x)^3}{27 g^4 (a+b x)^3 (b c-a d)^3}-\frac{2 B^2 d^2 (c+d x)}{g^4 (a+b x) (b c-a d)^3}+\frac{b B^2 d (c+d x)^2}{2 g^4 (a+b x)^2 (b c-a d)^3}",1,"(-2*B^2)/(27*b*g^4*(a + b*x)^3) + (5*B^2*d)/(18*b*(b*c - a*d)*g^4*(a + b*x)^2) - (11*B^2*d^2)/(9*b*(b*c - a*d)^2*g^4*(a + b*x)) - (11*B^2*d^3*Log[a + b*x])/(9*b*(b*c - a*d)^3*g^4) + (B^2*d^3*Log[a + b*x]^2)/(3*b*(b*c - a*d)^3*g^4) - (2*B*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(9*b*g^4*(a + b*x)^3) + (B*d*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(3*b*(b*c - a*d)*g^4*(a + b*x)^2) - (2*B*d^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(3*b*(b*c - a*d)^2*g^4*(a + b*x)) - (2*B*d^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(3*b*(b*c - a*d)^3*g^4) - (A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(3*b*g^4*(a + b*x)^3) + (11*B^2*d^3*Log[c + d*x])/(9*b*(b*c - a*d)^3*g^4) - (2*B^2*d^3*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*b*(b*c - a*d)^3*g^4) + (2*B*d^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/(3*b*(b*c - a*d)^3*g^4) + (B^2*d^3*Log[c + d*x]^2)/(3*b*(b*c - a*d)^3*g^4) - (2*B^2*d^3*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3*b*(b*c - a*d)^3*g^4) - (2*B^2*d^3*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(3*b*(b*c - a*d)^3*g^4) - (2*B^2*d^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*b*(b*c - a*d)^3*g^4)","C",34,11,32,0.3438,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
105,1,763,0,1.2272155,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^5} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(a*g + b*g*x)^5,x]","\frac{B^2 d^4 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{2 b g^5 (b c-a d)^4}+\frac{B^2 d^4 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{2 b g^5 (b c-a d)^4}+\frac{B d^4 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b g^5 (b c-a d)^4}-\frac{B d^4 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b g^5 (b c-a d)^4}+\frac{B d^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b g^5 (a+b x) (b c-a d)^3}-\frac{B d^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 b g^5 (a+b x)^2 (b c-a d)^2}+\frac{B d \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{6 b g^5 (a+b x)^3 (b c-a d)}-\frac{\left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{4 b g^5 (a+b x)^4}-\frac{B \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{8 b g^5 (a+b x)^4}+\frac{25 B^2 d^3}{24 b g^5 (a+b x) (b c-a d)^3}-\frac{13 B^2 d^2}{48 b g^5 (a+b x)^2 (b c-a d)^2}-\frac{B^2 d^4 \log ^2(a+b x)}{4 b g^5 (b c-a d)^4}-\frac{B^2 d^4 \log ^2(c+d x)}{4 b g^5 (b c-a d)^4}+\frac{25 B^2 d^4 \log (a+b x)}{24 b g^5 (b c-a d)^4}+\frac{B^2 d^4 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{2 b g^5 (b c-a d)^4}-\frac{25 B^2 d^4 \log (c+d x)}{24 b g^5 (b c-a d)^4}+\frac{B^2 d^4 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{2 b g^5 (b c-a d)^4}+\frac{7 B^2 d}{72 b g^5 (a+b x)^3 (b c-a d)}-\frac{B^2}{32 b g^5 (a+b x)^4}","-\frac{b^3 (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{4 g^5 (a+b x)^4 (b c-a d)^4}-\frac{b^3 B (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{8 g^5 (a+b x)^4 (b c-a d)^4}+\frac{b^2 d (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^5 (a+b x)^3 (b c-a d)^4}+\frac{2 b^2 B d (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 g^5 (a+b x)^3 (b c-a d)^4}-\frac{3 b d^2 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 g^5 (a+b x)^2 (b c-a d)^4}-\frac{3 b B d^2 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^5 (a+b x)^2 (b c-a d)^4}+\frac{d^3 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^5 (a+b x) (b c-a d)^4}+\frac{2 B d^3 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^5 (a+b x) (b c-a d)^4}-\frac{b^3 B^2 (c+d x)^4}{32 g^5 (a+b x)^4 (b c-a d)^4}+\frac{2 b^2 B^2 d (c+d x)^3}{9 g^5 (a+b x)^3 (b c-a d)^4}-\frac{3 b B^2 d^2 (c+d x)^2}{4 g^5 (a+b x)^2 (b c-a d)^4}+\frac{2 B^2 d^3 (c+d x)}{g^5 (a+b x) (b c-a d)^4}",1,"-B^2/(32*b*g^5*(a + b*x)^4) + (7*B^2*d)/(72*b*(b*c - a*d)*g^5*(a + b*x)^3) - (13*B^2*d^2)/(48*b*(b*c - a*d)^2*g^5*(a + b*x)^2) + (25*B^2*d^3)/(24*b*(b*c - a*d)^3*g^5*(a + b*x)) + (25*B^2*d^4*Log[a + b*x])/(24*b*(b*c - a*d)^4*g^5) - (B^2*d^4*Log[a + b*x]^2)/(4*b*(b*c - a*d)^4*g^5) - (B*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(8*b*g^5*(a + b*x)^4) + (B*d*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(6*b*(b*c - a*d)*g^5*(a + b*x)^3) - (B*d^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(4*b*(b*c - a*d)^2*g^5*(a + b*x)^2) + (B*d^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(2*b*(b*c - a*d)^3*g^5*(a + b*x)) + (B*d^4*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(2*b*(b*c - a*d)^4*g^5) - (A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(4*b*g^5*(a + b*x)^4) - (25*B^2*d^4*Log[c + d*x])/(24*b*(b*c - a*d)^4*g^5) + (B^2*d^4*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(2*b*(b*c - a*d)^4*g^5) - (B*d^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/(2*b*(b*c - a*d)^4*g^5) - (B^2*d^4*Log[c + d*x]^2)/(4*b*(b*c - a*d)^4*g^5) + (B^2*d^4*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(2*b*(b*c - a*d)^4*g^5) + (B^2*d^4*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(2*b*(b*c - a*d)^4*g^5) + (B^2*d^4*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*b*(b*c - a*d)^4*g^5)","C",38,11,32,0.3438,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
106,1,29,0,0.0224578,"\int \frac{\log \left(\frac{d (a+b x)}{b (c+d x)}\right)}{c f+d f x} \, dx","Int[Log[(d*(a + b*x))/(b*(c + d*x))]/(c*f + d*f*x),x]","\frac{\text{PolyLog}\left(2,1-\frac{d (a+b x)}{b (c+d x)}\right)}{d f}","\frac{\text{PolyLog}\left(2,\frac{b c-a d}{b (c+d x)}\right)}{d f}",1,"PolyLog[2, 1 - (d*(a + b*x))/(b*(c + d*x))]/(d*f)","A",1,1,29,0.03448,1,"{2447}"
107,1,15,0,0.0140898,"\int \frac{\log \left(1+\frac{1}{a+b x}\right)}{a+b x} \, dx","Int[Log[1 + (a + b*x)^(-1)]/(a + b*x),x]","\frac{\text{PolyLog}\left(2,-\frac{1}{a+b x}\right)}{b}","\frac{\text{PolyLog}\left(2,-\frac{1}{a+b x}\right)}{b}",1,"PolyLog[2, -(a + b*x)^(-1)]/b","A",1,1,18,0.05556,1,"{2447}"
108,1,13,0,0.013087,"\int \frac{\log \left(1-\frac{1}{a+b x}\right)}{a+b x} \, dx","Int[Log[1 - (a + b*x)^(-1)]/(a + b*x),x]","\frac{\text{PolyLog}\left(2,\frac{1}{a+b x}\right)}{b}","\frac{\text{PolyLog}\left(2,\frac{1}{a+b x}\right)}{b}",1,"PolyLog[2, (a + b*x)^(-1)]/b","A",1,1,20,0.05000,1,"{2447}"
109,0,0,0,0.2002498,"\int \frac{(a g+b g x)^2}{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)} \, dx","Int[(a*g + b*g*x)^2/(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\int \frac{(a g+b g x)^2}{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)} \, dx","\text{Int}\left(\frac{(a g+b g x)^2}{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A},x\right)",0,"a^2*g^2*Defer[Int][(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-1), x] + 2*a*b*g^2*Defer[Int][x/(A + B*Log[(e*(a + b*x))/(c + d*x)]), x] + b^2*g^2*Defer[Int][x^2/(A + B*Log[(e*(a + b*x))/(c + d*x)]), x]","A",0,0,0,0,-1,"{}"
110,0,0,0,0.1006462,"\int \frac{a g+b g x}{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)} \, dx","Int[(a*g + b*g*x)/(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\int \frac{a g+b g x}{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)} \, dx","\text{Int}\left(\frac{a g+b g x}{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A},x\right)",0,"a*g*Defer[Int][(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-1), x] + b*g*Defer[Int][x/(A + B*Log[(e*(a + b*x))/(c + d*x)]), x]","A",0,0,0,0,-1,"{}"
111,0,0,0,0.0718844,"\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)} \, dx","Int[1/((a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])),x]","\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{(a g+b g x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)},x\right)",0,"Defer[Int][1/((a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])), x]","A",0,0,0,0,-1,"{}"
112,0,0,0,0.0900594,"\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)} \, dx","Int[1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])),x]","\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)} \, dx","\frac{e e^{A/B} \text{Ei}\left(-\frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{B}\right)}{B g^2 (b c-a d)}",1,"Defer[Int][1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])), x]","F",0,0,0,0,-1,"{}"
113,0,0,0,0.0729636,"\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)} \, dx","Int[1/((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])),x]","\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)} \, dx","\frac{b e^2 e^{\frac{2 A}{B}} \text{Ei}\left(-\frac{2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{B}\right)}{B g^3 (b c-a d)^2}-\frac{d e e^{A/B} \text{Ei}\left(-\frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{B}\right)}{B g^3 (b c-a d)^2}",1,"Defer[Int][1/((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])), x]","F",0,0,0,0,-1,"{}"
114,0,0,0,0.2061227,"\int \frac{(a g+b g x)^2}{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Int[(a*g + b*g*x)^2/(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\int \frac{(a g+b g x)^2}{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","\text{Int}\left(\frac{(a g+b g x)^2}{\left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2},x\right)",0,"a^2*g^2*Defer[Int][(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-2), x] + 2*a*b*g^2*Defer[Int][x/(A + B*Log[(e*(a + b*x))/(c + d*x)])^2, x] + b^2*g^2*Defer[Int][x^2/(A + B*Log[(e*(a + b*x))/(c + d*x)])^2, x]","A",0,0,0,0,-1,"{}"
115,0,0,0,0.1067846,"\int \frac{a g+b g x}{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Int[(a*g + b*g*x)/(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\int \frac{a g+b g x}{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","\text{Int}\left(\frac{a g+b g x}{\left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2},x\right)",0,"a*g*Defer[Int][(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-2), x] + b*g*Defer[Int][x/(A + B*Log[(e*(a + b*x))/(c + d*x)])^2, x]","A",0,0,0,0,-1,"{}"
116,0,0,0,0.0808696,"\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Int[1/((a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2),x]","\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(a g+b g x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2},x\right)",0,"Defer[Int][1/((a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2), x]","A",0,0,0,0,-1,"{}"
117,0,0,0,0.094921,"\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Int[1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2),x]","\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","-\frac{e e^{A/B} \text{Ei}\left(-\frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{B}\right)}{B^2 g^2 (b c-a d)}-\frac{c+d x}{B g^2 (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}",1,"Defer[Int][1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2), x]","F",0,0,0,0,-1,"{}"
118,0,0,0,0.0837941,"\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Int[1/((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2),x]","\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","-\frac{2 b e^2 e^{\frac{2 A}{B}} \text{Ei}\left(-\frac{2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{B}\right)}{B^2 g^3 (b c-a d)^2}+\frac{d e e^{A/B} \text{Ei}\left(-\frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{B}\right)}{B^2 g^3 (b c-a d)^2}-\frac{b (c+d x)^2}{B g^3 (a+b x)^2 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}+\frac{d (c+d x)}{B g^3 (a+b x) (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}",1,"Defer[Int][1/((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2), x]","F",0,0,0,0,-1,"{}"
119,1,182,0,0.1095193,"\int (a g+b g x)^4 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \, dx","Int[(a*g + b*g*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\frac{g^4 (a+b x)^5 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{5 b}+\frac{2 B g^4 x (b c-a d)^4}{5 d^4}-\frac{B g^4 (a+b x)^2 (b c-a d)^3}{5 b d^3}+\frac{2 B g^4 (a+b x)^3 (b c-a d)^2}{15 b d^2}-\frac{2 B g^4 (b c-a d)^5 \log (c+d x)}{5 b d^5}-\frac{B g^4 (a+b x)^4 (b c-a d)}{10 b d}","\frac{g^4 (a+b x)^5 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{5 b}+\frac{2 B g^4 x (b c-a d)^4}{5 d^4}-\frac{B g^4 (a+b x)^2 (b c-a d)^3}{5 b d^3}+\frac{2 B g^4 (a+b x)^3 (b c-a d)^2}{15 b d^2}-\frac{2 B g^4 (b c-a d)^5 \log (c+d x)}{5 b d^5}-\frac{B g^4 (a+b x)^4 (b c-a d)}{10 b d}",1,"(2*B*(b*c - a*d)^4*g^4*x)/(5*d^4) - (B*(b*c - a*d)^3*g^4*(a + b*x)^2)/(5*b*d^3) + (2*B*(b*c - a*d)^2*g^4*(a + b*x)^3)/(15*b*d^2) - (B*(b*c - a*d)*g^4*(a + b*x)^4)/(10*b*d) + (g^4*(a + b*x)^5*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(5*b) - (2*B*(b*c - a*d)^5*g^4*Log[c + d*x])/(5*b*d^5)","A",4,3,32,0.09375,1,"{2525, 12, 43}"
120,1,151,0,0.0970548,"\int (a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \, dx","Int[(a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\frac{g^3 (a+b x)^4 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{4 b}-\frac{B g^3 x (b c-a d)^3}{2 d^3}+\frac{B g^3 (a+b x)^2 (b c-a d)^2}{4 b d^2}+\frac{B g^3 (b c-a d)^4 \log (c+d x)}{2 b d^4}-\frac{B g^3 (a+b x)^3 (b c-a d)}{6 b d}","\frac{g^3 (a+b x)^4 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{4 b}-\frac{B g^3 x (b c-a d)^3}{2 d^3}+\frac{B g^3 (a+b x)^2 (b c-a d)^2}{4 b d^2}+\frac{B g^3 (b c-a d)^4 \log (c+d x)}{2 b d^4}-\frac{B g^3 (a+b x)^3 (b c-a d)}{6 b d}",1,"-(B*(b*c - a*d)^3*g^3*x)/(2*d^3) + (B*(b*c - a*d)^2*g^3*(a + b*x)^2)/(4*b*d^2) - (B*(b*c - a*d)*g^3*(a + b*x)^3)/(6*b*d) + (g^3*(a + b*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(4*b) + (B*(b*c - a*d)^4*g^3*Log[c + d*x])/(2*b*d^4)","A",4,3,32,0.09375,1,"{2525, 12, 43}"
121,1,120,0,0.0741202,"\int (a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \, dx","Int[(a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\frac{g^2 (a+b x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b}+\frac{2 B g^2 x (b c-a d)^2}{3 d^2}-\frac{2 B g^2 (b c-a d)^3 \log (c+d x)}{3 b d^3}-\frac{B g^2 (a+b x)^2 (b c-a d)}{3 b d}","\frac{g^2 (a+b x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b}+\frac{2 B g^2 x (b c-a d)^2}{3 d^2}-\frac{2 B g^2 (b c-a d)^3 \log (c+d x)}{3 b d^3}-\frac{B g^2 (a+b x)^2 (b c-a d)}{3 b d}",1,"(2*B*(b*c - a*d)^2*g^2*x)/(3*d^2) - (B*(b*c - a*d)*g^2*(a + b*x)^2)/(3*b*d) + (g^2*(a + b*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(3*b) - (2*B*(b*c - a*d)^3*g^2*Log[c + d*x])/(3*b*d^3)","A",4,3,32,0.09375,1,"{2525, 12, 43}"
122,1,78,0,0.0568225,"\int (a g+b g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \, dx","Int[(a*g + b*g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\frac{g (a+b x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{2 b}+\frac{B g (b c-a d)^2 \log (c+d x)}{b d^2}-\frac{B g x (b c-a d)}{d}","\frac{g (a+b x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{2 b}+\frac{B g (b c-a d)^2 \log (c+d x)}{b d^2}-\frac{B g x (b c-a d)}{d}",1,"-((B*(b*c - a*d)*g*x)/d) + (g*(a + b*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(2*b) + (B*(b*c - a*d)^2*g*Log[c + d*x])/(b*d^2)","A",4,3,30,0.1000,1,"{2525, 12, 43}"
123,1,122,0,0.2920009,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{a g+b g x} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(a*g + b*g*x),x]","\frac{2 B \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g}+\frac{\log (a g+b g x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b g}+\frac{2 B \log (a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{B \log ^2(g (a+b x))}{b g}","\frac{2 B \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{b g}-\frac{\log \left(-\frac{b c-a d}{d (a+b x)}\right) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b g}",1,"-((B*Log[g*(a + b*x)]^2)/(b*g)) + ((A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[a*g + b*g*x])/(b*g) + (2*B*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x])/(b*g) + (2*B*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g)","A",10,8,32,0.2500,1,"{2524, 12, 2418, 2390, 2301, 2394, 2393, 2391}"
124,1,105,0,0.0774241,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{(a g+b g x)^2} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(a*g + b*g*x)^2,x]","-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{b g^2 (a+b x)}-\frac{2 B d \log (a+b x)}{b g^2 (b c-a d)}+\frac{2 B d \log (c+d x)}{b g^2 (b c-a d)}-\frac{2 B}{b g^2 (a+b x)}","-\frac{(c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{g^2 (a+b x) (b c-a d)}-\frac{2 B}{b g^2 (a+b x)}",1,"(-2*B)/(b*g^2*(a + b*x)) - (2*B*d*Log[a + b*x])/(b*(b*c - a*d)*g^2) - (A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(b*g^2*(a + b*x)) + (2*B*d*Log[c + d*x])/(b*(b*c - a*d)*g^2)","A",4,3,32,0.09375,1,"{2525, 12, 44}"
125,1,138,0,0.0934478,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{(a g+b g x)^3} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(a*g + b*g*x)^3,x]","-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{2 b g^3 (a+b x)^2}+\frac{B d^2 \log (a+b x)}{b g^3 (b c-a d)^2}-\frac{B d^2 \log (c+d x)}{b g^3 (b c-a d)^2}+\frac{B d}{b g^3 (a+b x) (b c-a d)}-\frac{B}{2 b g^3 (a+b x)^2}","-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{2 b g^3 (a+b x)^2}+\frac{B d^2 \log (a+b x)}{b g^3 (b c-a d)^2}-\frac{B d^2 \log (c+d x)}{b g^3 (b c-a d)^2}+\frac{B d}{b g^3 (a+b x) (b c-a d)}-\frac{B}{2 b g^3 (a+b x)^2}",1,"-B/(2*b*g^3*(a + b*x)^2) + (B*d)/(b*(b*c - a*d)*g^3*(a + b*x)) + (B*d^2*Log[a + b*x])/(b*(b*c - a*d)^2*g^3) - (A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(2*b*g^3*(a + b*x)^2) - (B*d^2*Log[c + d*x])/(b*(b*c - a*d)^2*g^3)","A",4,3,32,0.09375,1,"{2525, 12, 44}"
126,1,177,0,0.1149847,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{(a g+b g x)^4} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(a*g + b*g*x)^4,x]","-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{3 b g^4 (a+b x)^3}-\frac{2 B d^2}{3 b g^4 (a+b x) (b c-a d)^2}-\frac{2 B d^3 \log (a+b x)}{3 b g^4 (b c-a d)^3}+\frac{2 B d^3 \log (c+d x)}{3 b g^4 (b c-a d)^3}+\frac{B d}{3 b g^4 (a+b x)^2 (b c-a d)}-\frac{2 B}{9 b g^4 (a+b x)^3}","-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{3 b g^4 (a+b x)^3}-\frac{2 B d^2}{3 b g^4 (a+b x) (b c-a d)^2}-\frac{2 B d^3 \log (a+b x)}{3 b g^4 (b c-a d)^3}+\frac{2 B d^3 \log (c+d x)}{3 b g^4 (b c-a d)^3}+\frac{B d}{3 b g^4 (a+b x)^2 (b c-a d)}-\frac{2 B}{9 b g^4 (a+b x)^3}",1,"(-2*B)/(9*b*g^4*(a + b*x)^3) + (B*d)/(3*b*(b*c - a*d)*g^4*(a + b*x)^2) - (2*B*d^2)/(3*b*(b*c - a*d)^2*g^4*(a + b*x)) - (2*B*d^3*Log[a + b*x])/(3*b*(b*c - a*d)^3*g^4) - (A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(3*b*g^4*(a + b*x)^3) + (2*B*d^3*Log[c + d*x])/(3*b*(b*c - a*d)^3*g^4)","A",4,3,32,0.09375,1,"{2525, 12, 44}"
127,1,208,0,0.1443972,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{(a g+b g x)^5} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(a*g + b*g*x)^5,x]","-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{4 b g^5 (a+b x)^4}+\frac{B d^3}{2 b g^5 (a+b x) (b c-a d)^3}-\frac{B d^2}{4 b g^5 (a+b x)^2 (b c-a d)^2}+\frac{B d^4 \log (a+b x)}{2 b g^5 (b c-a d)^4}-\frac{B d^4 \log (c+d x)}{2 b g^5 (b c-a d)^4}+\frac{B d}{6 b g^5 (a+b x)^3 (b c-a d)}-\frac{B}{8 b g^5 (a+b x)^4}","-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{4 b g^5 (a+b x)^4}+\frac{B d^3}{2 b g^5 (a+b x) (b c-a d)^3}-\frac{B d^2}{4 b g^5 (a+b x)^2 (b c-a d)^2}+\frac{B d^4 \log (a+b x)}{2 b g^5 (b c-a d)^4}-\frac{B d^4 \log (c+d x)}{2 b g^5 (b c-a d)^4}+\frac{B d}{6 b g^5 (a+b x)^3 (b c-a d)}-\frac{B}{8 b g^5 (a+b x)^4}",1,"-B/(8*b*g^5*(a + b*x)^4) + (B*d)/(6*b*(b*c - a*d)*g^5*(a + b*x)^3) - (B*d^2)/(4*b*(b*c - a*d)^2*g^5*(a + b*x)^2) + (B*d^3)/(2*b*(b*c - a*d)^3*g^5*(a + b*x)) + (B*d^4*Log[a + b*x])/(2*b*(b*c - a*d)^4*g^5) - (A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(4*b*g^5*(a + b*x)^4) - (B*d^4*Log[c + d*x])/(2*b*(b*c - a*d)^4*g^5)","A",4,3,32,0.09375,1,"{2525, 12, 44}"
128,1,569,0,0.8719668,"\int (a g+b g x)^4 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2 \, dx","Int[(a*g + b*g*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","\frac{8 B^2 g^4 (b c-a d)^5 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{5 b d^5}-\frac{4 B g^4 (b c-a d)^5 \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{5 b d^5}-\frac{2 B g^4 (a+b x)^2 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{5 b d^3}+\frac{4 B g^4 (a+b x)^3 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{15 b d^2}+\frac{4 A B g^4 x (b c-a d)^4}{5 d^4}-\frac{B g^4 (a+b x)^4 (b c-a d) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{5 b d}+\frac{g^4 (a+b x)^5 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{5 b}+\frac{4 B^2 g^4 (a+b x) (b c-a d)^4 \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{5 b d^4}+\frac{26 B^2 g^4 x (b c-a d)^4}{15 d^4}-\frac{7 B^2 g^4 (a+b x)^2 (b c-a d)^3}{15 b d^3}+\frac{2 B^2 g^4 (a+b x)^3 (b c-a d)^2}{15 b d^2}-\frac{4 B^2 g^4 (b c-a d)^5 \log ^2(c+d x)}{5 b d^5}-\frac{10 B^2 g^4 (b c-a d)^5 \log (c+d x)}{3 b d^5}+\frac{8 B^2 g^4 (b c-a d)^5 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{5 b d^5}","\frac{8 B^2 g^4 (b c-a d)^5 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{5 b d^5}+\frac{2 B g^4 (b c-a d)^5 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(6 B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+6 A+25 B\right)}{15 b d^5}+\frac{2 B g^4 (a+b x) (b c-a d)^4 \left(6 B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+6 A+13 B\right)}{15 b d^4}-\frac{B g^4 (a+b x)^2 (b c-a d)^3 \left(6 B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+6 A+7 B\right)}{15 b d^3}+\frac{2 B g^4 (a+b x)^3 (b c-a d)^2 \left(2 B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+2 A+B\right)}{15 b d^2}-\frac{B g^4 (a+b x)^4 (b c-a d) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{5 b d}+\frac{g^4 (a+b x)^5 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{5 b}",1,"(4*A*B*(b*c - a*d)^4*g^4*x)/(5*d^4) + (26*B^2*(b*c - a*d)^4*g^4*x)/(15*d^4) - (7*B^2*(b*c - a*d)^3*g^4*(a + b*x)^2)/(15*b*d^3) + (2*B^2*(b*c - a*d)^2*g^4*(a + b*x)^3)/(15*b*d^2) + (4*B^2*(b*c - a*d)^4*g^4*(a + b*x)*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(5*b*d^4) - (2*B*(b*c - a*d)^3*g^4*(a + b*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(5*b*d^3) + (4*B*(b*c - a*d)^2*g^4*(a + b*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(15*b*d^2) - (B*(b*c - a*d)*g^4*(a + b*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(5*b*d) + (g^4*(a + b*x)^5*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2)/(5*b) - (10*B^2*(b*c - a*d)^5*g^4*Log[c + d*x])/(3*b*d^5) + (8*B^2*(b*c - a*d)^5*g^4*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(5*b*d^5) - (4*B*(b*c - a*d)^5*g^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/(5*b*d^5) - (4*B^2*(b*c - a*d)^5*g^4*Log[c + d*x]^2)/(5*b*d^5) + (8*B^2*(b*c - a*d)^5*g^4*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(5*b*d^5)","A",28,13,34,0.3824,1,"{2525, 12, 2528, 2486, 31, 43, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
129,1,470,0,0.7598144,"\int (a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2 \, dx","Int[(a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","-\frac{2 B^2 g^3 (b c-a d)^4 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b d^4}+\frac{B g^3 (b c-a d)^4 \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b d^4}+\frac{B g^3 (a+b x)^2 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{2 b d^2}-\frac{A B g^3 x (b c-a d)^3}{d^3}-\frac{B g^3 (a+b x)^3 (b c-a d) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b d}+\frac{g^3 (a+b x)^4 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{4 b}-\frac{B^2 g^3 (a+b x) (b c-a d)^3 \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{b d^3}-\frac{5 B^2 g^3 x (b c-a d)^3}{3 d^3}+\frac{B^2 g^3 (a+b x)^2 (b c-a d)^2}{3 b d^2}+\frac{B^2 g^3 (b c-a d)^4 \log ^2(c+d x)}{b d^4}+\frac{11 B^2 g^3 (b c-a d)^4 \log (c+d x)}{3 b d^4}-\frac{2 B^2 g^3 (b c-a d)^4 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b d^4}","-\frac{2 B^2 g^3 (b c-a d)^4 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d^4}-\frac{B g^3 (b c-a d)^4 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(3 B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+3 A+11 B\right)}{3 b d^4}-\frac{B g^3 (a+b x) (b c-a d)^3 \left(3 B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+3 A+5 B\right)}{3 b d^3}+\frac{B g^3 (a+b x)^2 (b c-a d)^2 \left(3 B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+3 A+2 B\right)}{6 b d^2}-\frac{B g^3 (a+b x)^3 (b c-a d) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b d}+\frac{g^3 (a+b x)^4 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{4 b}",1,"-((A*B*(b*c - a*d)^3*g^3*x)/d^3) - (5*B^2*(b*c - a*d)^3*g^3*x)/(3*d^3) + (B^2*(b*c - a*d)^2*g^3*(a + b*x)^2)/(3*b*d^2) - (B^2*(b*c - a*d)^3*g^3*(a + b*x)*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(b*d^3) + (B*(b*c - a*d)^2*g^3*(a + b*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(2*b*d^2) - (B*(b*c - a*d)*g^3*(a + b*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(3*b*d) + (g^3*(a + b*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2)/(4*b) + (11*B^2*(b*c - a*d)^4*g^3*Log[c + d*x])/(3*b*d^4) - (2*B^2*(b*c - a*d)^4*g^3*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*d^4) + (B*(b*c - a*d)^4*g^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/(b*d^4) + (B^2*(b*c - a*d)^4*g^3*Log[c + d*x]^2)/(b*d^4) - (2*B^2*(b*c - a*d)^4*g^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*d^4)","A",24,13,34,0.3824,1,"{2525, 12, 2528, 2486, 31, 43, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
130,1,397,0,0.6214535,"\int (a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2 \, dx","Int[(a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","\frac{8 B^2 g^2 (b c-a d)^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 b d^3}-\frac{4 B g^2 (b c-a d)^3 \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b d^3}+\frac{4 A B g^2 x (b c-a d)^2}{3 d^2}-\frac{2 B g^2 (a+b x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b d}+\frac{g^2 (a+b x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{3 b}+\frac{4 B^2 g^2 (a+b x) (b c-a d)^2 \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{3 b d^2}+\frac{4 B^2 g^2 x (b c-a d)^2}{3 d^2}-\frac{4 B^2 g^2 (b c-a d)^3 \log ^2(c+d x)}{3 b d^3}-\frac{4 B^2 g^2 (b c-a d)^3 \log (c+d x)}{b d^3}+\frac{8 B^2 g^2 (b c-a d)^3 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 b d^3}","\frac{8 B^2 g^2 (b c-a d)^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{3 b d^3}+\frac{4 B g^2 (b c-a d)^3 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A+3 B\right)}{3 b d^3}+\frac{4 B g^2 (a+b x) (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A+B\right)}{3 b d^2}-\frac{2 B g^2 (a+b x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b d}+\frac{g^2 (a+b x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{3 b}",1,"(4*A*B*(b*c - a*d)^2*g^2*x)/(3*d^2) + (4*B^2*(b*c - a*d)^2*g^2*x)/(3*d^2) + (4*B^2*(b*c - a*d)^2*g^2*(a + b*x)*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(3*b*d^2) - (2*B*(b*c - a*d)*g^2*(a + b*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(3*b*d) + (g^2*(a + b*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2)/(3*b) - (4*B^2*(b*c - a*d)^3*g^2*Log[c + d*x])/(b*d^3) + (8*B^2*(b*c - a*d)^3*g^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*b*d^3) - (4*B*(b*c - a*d)^3*g^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/(3*b*d^3) - (4*B^2*(b*c - a*d)^3*g^2*Log[c + d*x]^2)/(3*b*d^3) + (8*B^2*(b*c - a*d)^3*g^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*b*d^3)","A",20,13,34,0.3824,1,"{2525, 12, 2528, 2486, 31, 43, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
131,1,291,0,0.4925356,"\int (a g+b g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2 \, dx","Int[(a*g + b*g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","-\frac{4 B^2 g (b c-a d)^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b d^2}+\frac{2 B g (b c-a d)^2 \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b d^2}+\frac{g (a+b x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{2 b}-\frac{2 A B g x (b c-a d)}{d}+\frac{2 B^2 g (b c-a d)^2 \log ^2(c+d x)}{b d^2}+\frac{4 B^2 g (b c-a d)^2 \log (c+d x)}{b d^2}-\frac{4 B^2 g (b c-a d)^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b d^2}-\frac{2 B^2 g (a+b x) (b c-a d) \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{b d}","-\frac{4 B^2 g (b c-a d)^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}-\frac{2 B g (b c-a d)^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A+2 B\right)}{b d^2}-\frac{2 B g (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b d}+\frac{g (a+b x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{2 b}",1,"(-2*A*B*(b*c - a*d)*g*x)/d - (2*B^2*(b*c - a*d)*g*(a + b*x)*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(b*d) + (g*(a + b*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2)/(2*b) + (4*B^2*(b*c - a*d)^2*g*Log[c + d*x])/(b*d^2) - (4*B^2*(b*c - a*d)^2*g*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*d^2) + (2*B*(b*c - a*d)^2*g*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/(b*d^2) + (2*B^2*(b*c - a*d)^2*g*Log[c + d*x]^2)/(b*d^2) - (4*B^2*(b*c - a*d)^2*g*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*d^2)","A",16,12,32,0.3750,1,"{2525, 12, 2528, 2486, 31, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
132,1,749,0,4.1410647,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{a g+b g x} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(a*g + b*g*x),x]","\frac{4 A B \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g}-\frac{4 B^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) \left(-\log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+\log \left((a+b x)^2\right)+\log \left(\frac{1}{(c+d x)^2}\right)\right)}{b g}-\frac{8 B^2 \text{PolyLog}\left(3,-\frac{d (a+b x)}{b c-a d}\right)}{b g}-\frac{8 B^2 \text{PolyLog}\left(3,\frac{b (c+d x)}{b c-a d}\right)}{b g}+\frac{4 B^2 \log \left((a+b x)^2\right) \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g}-\frac{4 B^2 \log \left(\frac{1}{(c+d x)^2}\right) \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g}+\frac{\log (a g+b g x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{b g}+\frac{4 A B \log (a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{2 A B \log ^2(g (a+b x))}{b g}-\frac{2 B^2 \log ^2(a g+b g x) \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{b g}-\frac{4 B^2 \log (a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right) \left(-\log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+\log \left((a+b x)^2\right)+\log \left(\frac{1}{(c+d x)^2}\right)\right)}{b g}-\frac{4 B^2 \log (-c-d x) \log ^2(g (a+b x))}{b g}+\frac{4 B^2 \log ^2(g (a+b x)) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{B^2 \log ^2\left(\frac{1}{(c+d x)^2}\right) \log (g (a+b x))}{b g}+\frac{B^2 \log ^2\left(\frac{1}{(c+d x)^2}\right) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g}-\frac{4 B^2 \log ^2(a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{B^2 \log ^2\left((a+b x)^2\right) \log (-c-d x)}{b g}+\frac{B^2 \log ^2\left((a+b x)^2\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}+\frac{4 B^2 \log \left((a+b x)^2\right) \log (-c-d x) \log (g (a+b x))}{b g}+\frac{4 B^2 \log ^3(g (a+b x))}{3 b g}","\frac{4 B \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b g}+\frac{8 B^2 \text{PolyLog}\left(3,\frac{b (c+d x)}{d (a+b x)}\right)}{b g}-\frac{\log \left(1-\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{b g}",1,"(-2*A*B*Log[g*(a + b*x)]^2)/(b*g) + (4*B^2*Log[g*(a + b*x)]^3)/(3*b*g) - (4*B^2*Log[g*(a + b*x)]^2*Log[-c - d*x])/(b*g) + (4*B^2*Log[g*(a + b*x)]*Log[(a + b*x)^2]*Log[-c - d*x])/(b*g) - (B^2*Log[(a + b*x)^2]^2*Log[-c - d*x])/(b*g) + (B^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[(c + d*x)^(-2)]^2)/(b*g) - (B^2*Log[g*(a + b*x)]*Log[(c + d*x)^(-2)]^2)/(b*g) + (4*B^2*Log[g*(a + b*x)]^2*Log[(b*(c + d*x))/(b*c - a*d)])/(b*g) + (B^2*Log[(a + b*x)^2]^2*Log[(b*(c + d*x))/(b*c - a*d)])/(b*g) + ((A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2*Log[a*g + b*g*x])/(b*g) + (4*A*B*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x])/(b*g) - (4*B^2*(Log[(a + b*x)^2] + Log[(c + d*x)^(-2)] - Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x])/(b*g) - (2*B^2*Log[(e*(a + b*x)^2)/(c + d*x)^2]*Log[a*g + b*g*x]^2)/(b*g) - (4*B^2*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x]^2)/(b*g) + (4*A*B*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g) + (4*B^2*Log[(a + b*x)^2]*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g) - (4*B^2*(Log[(a + b*x)^2] + Log[(c + d*x)^(-2)] - Log[(e*(a + b*x)^2)/(c + d*x)^2])*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g) - (4*B^2*Log[(c + d*x)^(-2)]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*g) - (8*B^2*PolyLog[3, -((d*(a + b*x))/(b*c - a*d))])/(b*g) - (8*B^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])/(b*g)","B",46,23,34,0.6765,1,"{2524, 12, 2528, 2418, 2390, 2301, 2394, 2393, 2391, 6688, 6742, 2500, 2440, 2434, 2433, 2375, 2317, 2374, 6589, 2499, 2302, 30, 2396}"
133,1,480,0,0.8884831,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{(a g+b g x)^2} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(a*g + b*g*x)^2,x]","-\frac{8 B^2 d \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g^2 (b c-a d)}-\frac{8 B^2 d \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g^2 (b c-a d)}-\frac{4 B d \log (a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b g^2 (b c-a d)}-\frac{4 B \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b g^2 (a+b x)}+\frac{4 B d \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b g^2 (b c-a d)}-\frac{\left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{b g^2 (a+b x)}+\frac{4 B^2 d \log ^2(a+b x)}{b g^2 (b c-a d)}+\frac{4 B^2 d \log ^2(c+d x)}{b g^2 (b c-a d)}-\frac{8 B^2 d \log (a+b x)}{b g^2 (b c-a d)}-\frac{8 B^2 d \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g^2 (b c-a d)}+\frac{8 B^2 d \log (c+d x)}{b g^2 (b c-a d)}-\frac{8 B^2 d \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g^2 (b c-a d)}-\frac{8 B^2}{b g^2 (a+b x)}","-\frac{4 B (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{g^2 (a+b x) (b c-a d)}-\frac{(c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{g^2 (a+b x) (b c-a d)}-\frac{8 B^2 (c+d x)}{g^2 (a+b x) (b c-a d)}",1,"(-8*B^2)/(b*g^2*(a + b*x)) - (8*B^2*d*Log[a + b*x])/(b*(b*c - a*d)*g^2) + (4*B^2*d*Log[a + b*x]^2)/(b*(b*c - a*d)*g^2) - (4*B*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(b*g^2*(a + b*x)) - (4*B*d*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(b*(b*c - a*d)*g^2) - (A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(b*g^2*(a + b*x)) + (8*B^2*d*Log[c + d*x])/(b*(b*c - a*d)*g^2) - (8*B^2*d*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*(b*c - a*d)*g^2) + (4*B*d*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/(b*(b*c - a*d)*g^2) + (4*B^2*d*Log[c + d*x]^2)/(b*(b*c - a*d)*g^2) - (8*B^2*d*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)*g^2) - (8*B^2*d*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*(b*c - a*d)*g^2) - (8*B^2*d*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)*g^2)","C",26,11,34,0.3235,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
134,1,579,0,1.0462054,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{(a g+b g x)^3} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(a*g + b*g*x)^3,x]","\frac{4 B^2 d^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}+\frac{4 B^2 d^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}+\frac{2 B d^2 \log (a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b g^3 (b c-a d)^2}-\frac{2 B d^2 \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b g^3 (b c-a d)^2}+\frac{2 B d \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b g^3 (a+b x) (b c-a d)}-\frac{B \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b g^3 (a+b x)^2}-\frac{\left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{2 b g^3 (a+b x)^2}-\frac{2 B^2 d^2 \log ^2(a+b x)}{b g^3 (b c-a d)^2}-\frac{2 B^2 d^2 \log ^2(c+d x)}{b g^3 (b c-a d)^2}+\frac{6 B^2 d^2 \log (a+b x)}{b g^3 (b c-a d)^2}+\frac{4 B^2 d^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}-\frac{6 B^2 d^2 \log (c+d x)}{b g^3 (b c-a d)^2}+\frac{4 B^2 d^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}+\frac{6 B^2 d}{b g^3 (a+b x) (b c-a d)}-\frac{B^2}{b g^3 (a+b x)^2}","-\frac{b B (c+d x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{g^3 (a+b x)^2 (b c-a d)^2}+\frac{4 B d (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{g^3 (a+b x) (b c-a d)^2}-\frac{b (c+d x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{2 g^3 (a+b x)^2 (b c-a d)^2}+\frac{d (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{g^3 (a+b x) (b c-a d)^2}-\frac{b B^2 (c+d x)^2}{g^3 (a+b x)^2 (b c-a d)^2}+\frac{8 B^2 d (c+d x)}{g^3 (a+b x) (b c-a d)^2}",1,"-(B^2/(b*g^3*(a + b*x)^2)) + (6*B^2*d)/(b*(b*c - a*d)*g^3*(a + b*x)) + (6*B^2*d^2*Log[a + b*x])/(b*(b*c - a*d)^2*g^3) - (2*B^2*d^2*Log[a + b*x]^2)/(b*(b*c - a*d)^2*g^3) - (B*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(b*g^3*(a + b*x)^2) + (2*B*d*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(b*(b*c - a*d)*g^3*(a + b*x)) + (2*B*d^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(b*(b*c - a*d)^2*g^3) - (A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(2*b*g^3*(a + b*x)^2) - (6*B^2*d^2*Log[c + d*x])/(b*(b*c - a*d)^2*g^3) + (4*B^2*d^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*(b*c - a*d)^2*g^3) - (2*B*d^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/(b*(b*c - a*d)^2*g^3) - (2*B^2*d^2*Log[c + d*x]^2)/(b*(b*c - a*d)^2*g^3) + (4*B^2*d^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)^2*g^3) + (4*B^2*d^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*(b*c - a*d)^2*g^3) + (4*B^2*d^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)^2*g^3)","C",30,11,34,0.3235,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
135,1,692,0,1.2252303,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{(a g+b g x)^4} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(a*g + b*g*x)^4,x]","-\frac{8 B^2 d^3 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}-\frac{8 B^2 d^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}-\frac{4 B d^3 \log (a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b g^4 (b c-a d)^3}+\frac{4 B d^3 \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b g^4 (b c-a d)^3}-\frac{4 B d^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b g^4 (a+b x) (b c-a d)^2}+\frac{2 B d \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b g^4 (a+b x)^2 (b c-a d)}-\frac{\left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{3 b g^4 (a+b x)^3}-\frac{4 B \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{9 b g^4 (a+b x)^3}-\frac{44 B^2 d^2}{9 b g^4 (a+b x) (b c-a d)^2}+\frac{4 B^2 d^3 \log ^2(a+b x)}{3 b g^4 (b c-a d)^3}+\frac{4 B^2 d^3 \log ^2(c+d x)}{3 b g^4 (b c-a d)^3}-\frac{44 B^2 d^3 \log (a+b x)}{9 b g^4 (b c-a d)^3}-\frac{8 B^2 d^3 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}+\frac{44 B^2 d^3 \log (c+d x)}{9 b g^4 (b c-a d)^3}-\frac{8 B^2 d^3 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}+\frac{10 B^2 d}{9 b g^4 (a+b x)^2 (b c-a d)}-\frac{8 B^2}{27 b g^4 (a+b x)^3}","-\frac{b^2 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{3 g^4 (a+b x)^3 (b c-a d)^3}-\frac{4 b^2 B (c+d x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{9 g^4 (a+b x)^3 (b c-a d)^3}-\frac{d^2 (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{g^4 (a+b x) (b c-a d)^3}-\frac{4 B d^2 (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{g^4 (a+b x) (b c-a d)^3}+\frac{b d (c+d x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{g^4 (a+b x)^2 (b c-a d)^3}+\frac{2 b B d (c+d x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{g^4 (a+b x)^2 (b c-a d)^3}-\frac{8 b^2 B^2 (c+d x)^3}{27 g^4 (a+b x)^3 (b c-a d)^3}-\frac{8 B^2 d^2 (c+d x)}{g^4 (a+b x) (b c-a d)^3}+\frac{2 b B^2 d (c+d x)^2}{g^4 (a+b x)^2 (b c-a d)^3}",1,"(-8*B^2)/(27*b*g^4*(a + b*x)^3) + (10*B^2*d)/(9*b*(b*c - a*d)*g^4*(a + b*x)^2) - (44*B^2*d^2)/(9*b*(b*c - a*d)^2*g^4*(a + b*x)) - (44*B^2*d^3*Log[a + b*x])/(9*b*(b*c - a*d)^3*g^4) + (4*B^2*d^3*Log[a + b*x]^2)/(3*b*(b*c - a*d)^3*g^4) - (4*B*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(9*b*g^4*(a + b*x)^3) + (2*B*d*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(3*b*(b*c - a*d)*g^4*(a + b*x)^2) - (4*B*d^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(3*b*(b*c - a*d)^2*g^4*(a + b*x)) - (4*B*d^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(3*b*(b*c - a*d)^3*g^4) - (A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(3*b*g^4*(a + b*x)^3) + (44*B^2*d^3*Log[c + d*x])/(9*b*(b*c - a*d)^3*g^4) - (8*B^2*d^3*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*b*(b*c - a*d)^3*g^4) + (4*B*d^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/(3*b*(b*c - a*d)^3*g^4) + (4*B^2*d^3*Log[c + d*x]^2)/(3*b*(b*c - a*d)^3*g^4) - (8*B^2*d^3*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3*b*(b*c - a*d)^3*g^4) - (8*B^2*d^3*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(3*b*(b*c - a*d)^3*g^4) - (8*B^2*d^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*b*(b*c - a*d)^3*g^4)","C",34,11,34,0.3235,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
136,1,757,0,1.3938743,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{(a g+b g x)^5} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(a*g + b*g*x)^5,x]","\frac{2 B^2 d^4 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g^5 (b c-a d)^4}+\frac{2 B^2 d^4 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g^5 (b c-a d)^4}+\frac{B d^4 \log (a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b g^5 (b c-a d)^4}-\frac{B d^4 \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b g^5 (b c-a d)^4}+\frac{B d^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b g^5 (a+b x) (b c-a d)^3}-\frac{B d^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{2 b g^5 (a+b x)^2 (b c-a d)^2}+\frac{B d \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b g^5 (a+b x)^3 (b c-a d)}-\frac{\left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{4 b g^5 (a+b x)^4}-\frac{B \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{4 b g^5 (a+b x)^4}+\frac{25 B^2 d^3}{6 b g^5 (a+b x) (b c-a d)^3}-\frac{13 B^2 d^2}{12 b g^5 (a+b x)^2 (b c-a d)^2}-\frac{B^2 d^4 \log ^2(a+b x)}{b g^5 (b c-a d)^4}-\frac{B^2 d^4 \log ^2(c+d x)}{b g^5 (b c-a d)^4}+\frac{25 B^2 d^4 \log (a+b x)}{6 b g^5 (b c-a d)^4}+\frac{2 B^2 d^4 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g^5 (b c-a d)^4}-\frac{25 B^2 d^4 \log (c+d x)}{6 b g^5 (b c-a d)^4}+\frac{2 B^2 d^4 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g^5 (b c-a d)^4}+\frac{7 B^2 d}{18 b g^5 (a+b x)^3 (b c-a d)}-\frac{B^2}{8 b g^5 (a+b x)^4}","-\frac{b^3 (c+d x)^4 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{4 g^5 (a+b x)^4 (b c-a d)^4}-\frac{b^3 B (c+d x)^4 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{4 g^5 (a+b x)^4 (b c-a d)^4}+\frac{b^2 d (c+d x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{g^5 (a+b x)^3 (b c-a d)^4}+\frac{4 b^2 B d (c+d x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 g^5 (a+b x)^3 (b c-a d)^4}-\frac{3 b d^2 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{2 g^5 (a+b x)^2 (b c-a d)^4}-\frac{3 b B d^2 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{g^5 (a+b x)^2 (b c-a d)^4}+\frac{d^3 (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{g^5 (a+b x) (b c-a d)^4}+\frac{4 B d^3 (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{g^5 (a+b x) (b c-a d)^4}-\frac{b^3 B^2 (c+d x)^4}{8 g^5 (a+b x)^4 (b c-a d)^4}+\frac{8 b^2 B^2 d (c+d x)^3}{9 g^5 (a+b x)^3 (b c-a d)^4}-\frac{3 b B^2 d^2 (c+d x)^2}{g^5 (a+b x)^2 (b c-a d)^4}+\frac{8 B^2 d^3 (c+d x)}{g^5 (a+b x) (b c-a d)^4}",1,"-B^2/(8*b*g^5*(a + b*x)^4) + (7*B^2*d)/(18*b*(b*c - a*d)*g^5*(a + b*x)^3) - (13*B^2*d^2)/(12*b*(b*c - a*d)^2*g^5*(a + b*x)^2) + (25*B^2*d^3)/(6*b*(b*c - a*d)^3*g^5*(a + b*x)) + (25*B^2*d^4*Log[a + b*x])/(6*b*(b*c - a*d)^4*g^5) - (B^2*d^4*Log[a + b*x]^2)/(b*(b*c - a*d)^4*g^5) - (B*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(4*b*g^5*(a + b*x)^4) + (B*d*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(3*b*(b*c - a*d)*g^5*(a + b*x)^3) - (B*d^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(2*b*(b*c - a*d)^2*g^5*(a + b*x)^2) + (B*d^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(b*(b*c - a*d)^3*g^5*(a + b*x)) + (B*d^4*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(b*(b*c - a*d)^4*g^5) - (A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(4*b*g^5*(a + b*x)^4) - (25*B^2*d^4*Log[c + d*x])/(6*b*(b*c - a*d)^4*g^5) + (2*B^2*d^4*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*(b*c - a*d)^4*g^5) - (B*d^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/(b*(b*c - a*d)^4*g^5) - (B^2*d^4*Log[c + d*x]^2)/(b*(b*c - a*d)^4*g^5) + (2*B^2*d^4*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)^4*g^5) + (2*B^2*d^4*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*(b*c - a*d)^4*g^5) + (2*B^2*d^4*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)^4*g^5)","C",38,11,34,0.3235,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
137,0,0,0,0.1966138,"\int \frac{(a g+b g x)^2}{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)} \, dx","Int[(a*g + b*g*x)^2/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\int \frac{(a g+b g x)^2}{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)} \, dx","\text{Int}\left(\frac{(a g+b g x)^2}{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A},x\right)",0,"a^2*g^2*Defer[Int][(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^(-1), x] + 2*a*b*g^2*Defer[Int][x/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]), x] + b^2*g^2*Defer[Int][x^2/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]), x]","A",0,0,0,0,-1,"{}"
138,0,0,0,0.1014489,"\int \frac{a g+b g x}{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)} \, dx","Int[(a*g + b*g*x)/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\int \frac{a g+b g x}{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)} \, dx","\text{Int}\left(\frac{a g+b g x}{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A},x\right)",0,"a*g*Defer[Int][(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^(-1), x] + b*g*Defer[Int][x/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]), x]","A",0,0,0,0,-1,"{}"
139,0,0,0,0.0731074,"\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)} \, dx","Int[1/((a*g + b*g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])),x]","\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)} \, dx","\text{Int}\left(\frac{1}{(a g+b g x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)},x\right)",0,"Defer[Int][1/((a*g + b*g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])), x]","A",0,0,0,0,-1,"{}"
140,0,0,0,0.0867152,"\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)} \, dx","Int[1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])),x]","\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)} \, dx","\frac{e^{\frac{A}{2 B}} (c+d x) \sqrt{\frac{e (a+b x)^2}{(c+d x)^2}} \text{Ei}\left(-\frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{2 B}\right)}{2 B g^2 (a+b x) (b c-a d)}",1,"Defer[Int][1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])), x]","F",0,0,0,0,-1,"{}"
141,0,0,0,0.0738272,"\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)} \, dx","Int[1/((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])),x]","\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)} \, dx","\frac{b e e^{A/B} \text{Ei}\left(-\frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{B}\right)}{2 B g^3 (b c-a d)^2}-\frac{d e^{\frac{A}{2 B}} (c+d x) \sqrt{\frac{e (a+b x)^2}{(c+d x)^2}} \text{Ei}\left(-\frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{2 B}\right)}{2 B g^3 (a+b x) (b c-a d)^2}",1,"Defer[Int][1/((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])), x]","F",0,0,0,0,-1,"{}"
142,0,0,0,0.2151038,"\int \frac{(a g+b g x)^2}{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","Int[(a*g + b*g*x)^2/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","\int \frac{(a g+b g x)^2}{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","\text{Int}\left(\frac{(a g+b g x)^2}{\left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2},x\right)",0,"a^2*g^2*Defer[Int][(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^(-2), x] + 2*a*b*g^2*Defer[Int][x/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2, x] + b^2*g^2*Defer[Int][x^2/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2, x]","A",0,0,0,0,-1,"{}"
143,0,0,0,0.1142151,"\int \frac{a g+b g x}{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","Int[(a*g + b*g*x)/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","\int \frac{a g+b g x}{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","\text{Int}\left(\frac{a g+b g x}{\left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2},x\right)",0,"a*g*Defer[Int][(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^(-2), x] + b*g*Defer[Int][x/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2, x]","A",0,0,0,0,-1,"{}"
144,0,0,0,0.0814711,"\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","Int[1/((a*g + b*g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2),x]","\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(a g+b g x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2},x\right)",0,"Defer[Int][1/((a*g + b*g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2), x]","A",0,0,0,0,-1,"{}"
145,0,0,0,0.0935896,"\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","Int[1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2),x]","\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","-\frac{e^{\frac{A}{2 B}} (c+d x) \sqrt{\frac{e (a+b x)^2}{(c+d x)^2}} \text{Ei}\left(-\frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{2 B}\right)}{4 B^2 g^2 (a+b x) (b c-a d)}-\frac{c+d x}{2 B g^2 (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}",1,"Defer[Int][1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2), x]","F",0,0,0,0,-1,"{}"
146,0,0,0,0.0824103,"\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","Int[1/((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2),x]","\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","\frac{d e^{\frac{A}{2 B}} (c+d x) \sqrt{\frac{e (a+b x)^2}{(c+d x)^2}} \text{Ei}\left(-\frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{2 B}\right)}{4 B^2 g^3 (a+b x) (b c-a d)^2}-\frac{b e e^{A/B} \text{Ei}\left(-\frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{B}\right)}{2 B^2 g^3 (b c-a d)^2}-\frac{b (c+d x)^2}{2 B g^3 (a+b x)^2 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}+\frac{d (c+d x)}{2 B g^3 (a+b x) (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}",1,"Defer[Int][1/((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2), x]","F",0,0,0,0,-1,"{}"
147,1,183,0,0.183445,"\int (a+b x)^4 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Int[(a + b*x)^4*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]),x]","\frac{A (a+b x)^5}{5 b}+\frac{B n x (b c-a d)^4}{5 d^4}-\frac{B n (a+b x)^2 (b c-a d)^3}{10 b d^3}+\frac{B n (a+b x)^3 (b c-a d)^2}{15 b d^2}-\frac{B n (b c-a d)^5 \log (c+d x)}{5 b d^5}+\frac{B (a+b x)^5 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{5 b}-\frac{B n (a+b x)^4 (b c-a d)}{20 b d}","\frac{(a+b x)^5 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{5 b}+\frac{B n x (b c-a d)^4}{5 d^4}-\frac{B n (a+b x)^2 (b c-a d)^3}{10 b d^3}+\frac{B n (a+b x)^3 (b c-a d)^2}{15 b d^2}-\frac{B n (b c-a d)^5 \log (c+d x)}{5 b d^5}-\frac{B n (a+b x)^4 (b c-a d)}{20 b d}",1,"(B*(b*c - a*d)^4*n*x)/(5*d^4) - (B*(b*c - a*d)^3*n*(a + b*x)^2)/(10*b*d^3) + (B*(b*c - a*d)^2*n*(a + b*x)^3)/(15*b*d^2) - (B*(b*c - a*d)*n*(a + b*x)^4)/(20*b*d) + (A*(a + b*x)^5)/(5*b) - (B*(b*c - a*d)^5*n*Log[c + d*x])/(5*b*d^5) + (B*(a + b*x)^5*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(5*b)","A",5,3,31,0.09677,1,"{6742, 2492, 43}"
148,1,154,0,0.1353109,"\int (a+b x)^3 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Int[(a + b*x)^3*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]),x]","\frac{A (a+b x)^4}{4 b}-\frac{B n x (b c-a d)^3}{4 d^3}+\frac{B n (a+b x)^2 (b c-a d)^2}{8 b d^2}+\frac{B n (b c-a d)^4 \log (c+d x)}{4 b d^4}+\frac{B (a+b x)^4 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{4 b}-\frac{B n (a+b x)^3 (b c-a d)}{12 b d}","\frac{(a+b x)^4 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{4 b}-\frac{B n x (b c-a d)^3}{4 d^3}+\frac{B n (a+b x)^2 (b c-a d)^2}{8 b d^2}+\frac{B n (b c-a d)^4 \log (c+d x)}{4 b d^4}-\frac{B n (a+b x)^3 (b c-a d)}{12 b d}",1,"-(B*(b*c - a*d)^3*n*x)/(4*d^3) + (B*(b*c - a*d)^2*n*(a + b*x)^2)/(8*b*d^2) - (B*(b*c - a*d)*n*(a + b*x)^3)/(12*b*d) + (A*(a + b*x)^4)/(4*b) + (B*(b*c - a*d)^4*n*Log[c + d*x])/(4*b*d^4) + (B*(a + b*x)^4*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(4*b)","A",5,3,31,0.09677,1,"{6742, 2492, 43}"
149,1,125,0,0.1209992,"\int (a+b x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Int[(a + b*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]),x]","\frac{A (a+b x)^3}{3 b}+\frac{B n x (b c-a d)^2}{3 d^2}-\frac{B n (b c-a d)^3 \log (c+d x)}{3 b d^3}+\frac{B (a+b x)^3 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b}-\frac{B n (a+b x)^2 (b c-a d)}{6 b d}","\frac{(a+b x)^3 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{3 b}+\frac{B n x (b c-a d)^2}{3 d^2}-\frac{B n (b c-a d)^3 \log (c+d x)}{3 b d^3}-\frac{B n (a+b x)^2 (b c-a d)}{6 b d}",1,"(B*(b*c - a*d)^2*n*x)/(3*d^2) - (B*(b*c - a*d)*n*(a + b*x)^2)/(6*b*d) + (A*(a + b*x)^3)/(3*b) - (B*(b*c - a*d)^3*n*Log[c + d*x])/(3*b*d^3) + (B*(a + b*x)^3*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b)","A",5,3,31,0.09677,1,"{6742, 2492, 43}"
150,1,96,0,0.0908031,"\int (a+b x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Int[(a + b*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]),x]","\frac{A (a+b x)^2}{2 b}+\frac{B n (b c-a d)^2 \log (c+d x)}{2 b d^2}+\frac{B (a+b x)^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{2 b}-\frac{B n x (b c-a d)}{2 d}","\frac{(a+b x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{2 b}+\frac{B n (b c-a d)^2 \log (c+d x)}{2 b d^2}-\frac{B n x (b c-a d)}{2 d}",1,"-(B*(b*c - a*d)*n*x)/(2*d) + (A*(a + b*x)^2)/(2*b) + (B*(b*c - a*d)^2*n*Log[c + d*x])/(2*b*d^2) + (B*(a + b*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*b)","A",5,3,29,0.1034,1,"{6742, 2492, 43}"
151,1,87,0,0.2678201,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{a+b x} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(a + b*x),x]","\frac{B n \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{b}+\frac{A \log (a+b x)}{b}-\frac{B \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b}","\frac{B n \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{b}-\frac{\log \left(-\frac{b c-a d}{d (a+b x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b}",1,"(A*Log[a + b*x])/b - (B*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/b + (B*n*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/b","A",7,6,31,0.1935,1,"{6742, 2488, 2411, 2343, 2333, 2315}"
152,1,72,0,0.0835585,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x)^2} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(a + b*x)^2,x]","-\frac{A}{b (a+b x)}-\frac{B (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x) (b c-a d)}-\frac{B n}{b (a+b x)}","-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A}{b (a+b x)}-\frac{B d n \log (a+b x)}{b (b c-a d)}+\frac{B d n \log (c+d x)}{b (b c-a d)}-\frac{B n}{b (a+b x)}",1,"-(A/(b*(a + b*x))) - (B*n)/(b*(a + b*x)) - (B*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((b*c - a*d)*(a + b*x))","A",4,3,31,0.09677,1,"{6742, 2490, 32}"
153,1,149,0,0.1541408,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x)^3} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(a + b*x)^3,x]","-\frac{A}{2 b (a+b x)^2}+\frac{B d^2 n \log (a+b x)}{2 b (b c-a d)^2}-\frac{B d^2 n \log (c+d x)}{2 b (b c-a d)^2}-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{2 b (a+b x)^2}+\frac{B d n}{2 b (a+b x) (b c-a d)}-\frac{B n}{4 b (a+b x)^2}","-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A}{2 b (a+b x)^2}+\frac{B d^2 n \log (a+b x)}{2 b (b c-a d)^2}-\frac{B d^2 n \log (c+d x)}{2 b (b c-a d)^2}+\frac{B d n}{2 b (a+b x) (b c-a d)}-\frac{B n}{4 b (a+b x)^2}",1,"-A/(2*b*(a + b*x)^2) - (B*n)/(4*b*(a + b*x)^2) + (B*d*n)/(2*b*(b*c - a*d)*(a + b*x)) + (B*d^2*n*Log[a + b*x])/(2*b*(b*c - a*d)^2) - (B*d^2*n*Log[c + d*x])/(2*b*(b*c - a*d)^2) - (B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*b*(a + b*x)^2)","A",5,3,31,0.09677,1,"{6742, 2492, 44}"
154,1,178,0,0.169881,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x)^4} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(a + b*x)^4,x]","-\frac{A}{3 b (a+b x)^3}-\frac{B d^2 n}{3 b (a+b x) (b c-a d)^2}-\frac{B d^3 n \log (a+b x)}{3 b (b c-a d)^3}+\frac{B d^3 n \log (c+d x)}{3 b (b c-a d)^3}-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b (a+b x)^3}+\frac{B d n}{6 b (a+b x)^2 (b c-a d)}-\frac{B n}{9 b (a+b x)^3}","-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A}{3 b (a+b x)^3}-\frac{B d^2 n}{3 b (a+b x) (b c-a d)^2}-\frac{B d^3 n \log (a+b x)}{3 b (b c-a d)^3}+\frac{B d^3 n \log (c+d x)}{3 b (b c-a d)^3}+\frac{B d n}{6 b (a+b x)^2 (b c-a d)}-\frac{B n}{9 b (a+b x)^3}",1,"-A/(3*b*(a + b*x)^3) - (B*n)/(9*b*(a + b*x)^3) + (B*d*n)/(6*b*(b*c - a*d)*(a + b*x)^2) - (B*d^2*n)/(3*b*(b*c - a*d)^2*(a + b*x)) - (B*d^3*n*Log[a + b*x])/(3*b*(b*c - a*d)^3) + (B*d^3*n*Log[c + d*x])/(3*b*(b*c - a*d)^3) - (B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b*(a + b*x)^3)","A",5,3,31,0.09677,1,"{6742, 2492, 44}"
155,1,207,0,0.1925583,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x)^5} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(a + b*x)^5,x]","-\frac{A}{4 b (a+b x)^4}+\frac{B d^3 n}{4 b (a+b x) (b c-a d)^3}-\frac{B d^2 n}{8 b (a+b x)^2 (b c-a d)^2}+\frac{B d^4 n \log (a+b x)}{4 b (b c-a d)^4}-\frac{B d^4 n \log (c+d x)}{4 b (b c-a d)^4}-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{4 b (a+b x)^4}+\frac{B d n}{12 b (a+b x)^3 (b c-a d)}-\frac{B n}{16 b (a+b x)^4}","-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A}{4 b (a+b x)^4}+\frac{B d^3 n}{4 b (a+b x) (b c-a d)^3}-\frac{B d^2 n}{8 b (a+b x)^2 (b c-a d)^2}+\frac{B d^4 n \log (a+b x)}{4 b (b c-a d)^4}-\frac{B d^4 n \log (c+d x)}{4 b (b c-a d)^4}+\frac{B d n}{12 b (a+b x)^3 (b c-a d)}-\frac{B n}{16 b (a+b x)^4}",1,"-A/(4*b*(a + b*x)^4) - (B*n)/(16*b*(a + b*x)^4) + (B*d*n)/(12*b*(b*c - a*d)*(a + b*x)^3) - (B*d^2*n)/(8*b*(b*c - a*d)^2*(a + b*x)^2) + (B*d^3*n)/(4*b*(b*c - a*d)^3*(a + b*x)) + (B*d^4*n*Log[a + b*x])/(4*b*(b*c - a*d)^4) - (B*d^4*n*Log[c + d*x])/(4*b*(b*c - a*d)^4) - (B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(4*b*(a + b*x)^4)","A",5,3,31,0.09677,1,"{6742, 2492, 44}"
156,1,542,0,0.771862,"\int (a+b x)^3 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 \, dx","Int[(a + b*x)^3*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2,x]","-\frac{B^2 n^2 (b c-a d)^4 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{2 b d^4}+\frac{A^2 (a+b x)^4}{4 b}-\frac{A B n x (b c-a d)^3}{2 d^3}+\frac{A B n (a+b x)^2 (b c-a d)^2}{4 b d^2}+\frac{A B n (b c-a d)^4 \log (c+d x)}{2 b d^4}+\frac{A B (a+b x)^4 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{2 b}-\frac{A B n (a+b x)^3 (b c-a d)}{6 b d}-\frac{B^2 n (b c-a d)^4 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{2 b d^4}-\frac{B^2 n (a+b x) (b c-a d)^3 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{2 b d^3}+\frac{B^2 n (a+b x)^2 (b c-a d)^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{4 b d^2}-\frac{5 B^2 n^2 x (b c-a d)^3}{12 d^3}+\frac{B^2 n^2 (a+b x)^2 (b c-a d)^2}{12 b d^2}+\frac{11 B^2 n^2 (b c-a d)^4 \log (c+d x)}{12 b d^4}+\frac{B^2 (a+b x)^4 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{4 b}-\frac{B^2 n (a+b x)^3 (b c-a d) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{6 b d}","-\frac{B^2 n^2 (b c-a d)^4 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{2 b d^4}-\frac{B n (b c-a d)^4 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(6 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+6 A+11 B n\right)}{12 b d^4}-\frac{B n (a+b x) (b c-a d)^3 \left(6 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+6 A+5 B n\right)}{12 b d^3}+\frac{B n (a+b x)^2 (b c-a d)^2 \left(3 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+3 A+B n\right)}{12 b d^2}-\frac{B n (a+b x)^3 (b c-a d) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{6 b d}+\frac{(a+b x)^4 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{4 b}",1,"-(A*B*(b*c - a*d)^3*n*x)/(2*d^3) - (5*B^2*(b*c - a*d)^3*n^2*x)/(12*d^3) + (A*B*(b*c - a*d)^2*n*(a + b*x)^2)/(4*b*d^2) + (B^2*(b*c - a*d)^2*n^2*(a + b*x)^2)/(12*b*d^2) - (A*B*(b*c - a*d)*n*(a + b*x)^3)/(6*b*d) + (A^2*(a + b*x)^4)/(4*b) + (A*B*(b*c - a*d)^4*n*Log[c + d*x])/(2*b*d^4) + (11*B^2*(b*c - a*d)^4*n^2*Log[c + d*x])/(12*b*d^4) - (B^2*(b*c - a*d)^3*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*b*d^3) + (B^2*(b*c - a*d)^2*n*(a + b*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(4*b*d^2) - (B^2*(b*c - a*d)*n*(a + b*x)^3*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(6*b*d) + (A*B*(a + b*x)^4*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*b) - (B^2*(b*c - a*d)^4*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*b*d^4) + (B^2*(a + b*x)^4*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(4*b) - (B^2*(b*c - a*d)^4*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(2*b*d^4)","A",21,11,33,0.3333,1,"{6742, 2492, 43, 2514, 2486, 31, 2488, 2411, 2343, 2333, 2315}"
157,1,427,0,0.6256379,"\int (a+b x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 \, dx","Int[(a + b*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2,x]","\frac{2 B^2 n^2 (b c-a d)^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{3 b d^3}+\frac{A^2 (a+b x)^3}{3 b}+\frac{2 A B n x (b c-a d)^2}{3 d^2}-\frac{2 A B n (b c-a d)^3 \log (c+d x)}{3 b d^3}+\frac{2 A B (a+b x)^3 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b}-\frac{A B n (a+b x)^2 (b c-a d)}{3 b d}+\frac{2 B^2 n (b c-a d)^3 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b d^3}+\frac{2 B^2 n (a+b x) (b c-a d)^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b d^2}+\frac{B^2 n^2 x (b c-a d)^2}{3 d^2}-\frac{B^2 n^2 (b c-a d)^3 \log (c+d x)}{b d^3}+\frac{B^2 (a+b x)^3 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b}-\frac{B^2 n (a+b x)^2 (b c-a d) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b d}","\frac{2 B^2 n^2 (b c-a d)^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{3 b d^3}+\frac{B n (b c-a d)^3 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(2 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 A+3 B n\right)}{3 b d^3}+\frac{B n (a+b x) (b c-a d)^2 \left(2 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 A+B n\right)}{3 b d^2}-\frac{B n (a+b x)^2 (b c-a d) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{3 b d}+\frac{(a+b x)^3 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{3 b}",1,"(2*A*B*(b*c - a*d)^2*n*x)/(3*d^2) + (B^2*(b*c - a*d)^2*n^2*x)/(3*d^2) - (A*B*(b*c - a*d)*n*(a + b*x)^2)/(3*b*d) + (A^2*(a + b*x)^3)/(3*b) - (2*A*B*(b*c - a*d)^3*n*Log[c + d*x])/(3*b*d^3) - (B^2*(b*c - a*d)^3*n^2*Log[c + d*x])/(b*d^3) + (2*B^2*(b*c - a*d)^2*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b*d^2) - (B^2*(b*c - a*d)*n*(a + b*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b*d) + (2*A*B*(a + b*x)^3*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b) + (2*B^2*(b*c - a*d)^3*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b*d^3) + (B^2*(a + b*x)^3*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(3*b) + (2*B^2*(b*c - a*d)^3*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(3*b*d^3)","A",18,11,33,0.3333,1,"{6742, 2492, 43, 2514, 2486, 31, 2488, 2411, 2343, 2333, 2315}"
158,1,308,0,0.4859031,"\int (a+b x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 \, dx","Int[(a + b*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2,x]","-\frac{B^2 n^2 (b c-a d)^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}+\frac{A^2 (a+b x)^2}{2 b}+\frac{A B n (b c-a d)^2 \log (c+d x)}{b d^2}+\frac{A B (a+b x)^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b}-\frac{A B n x (b c-a d)}{d}-\frac{B^2 n (b c-a d)^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b d^2}+\frac{B^2 n^2 (b c-a d)^2 \log (c+d x)}{b d^2}+\frac{B^2 (a+b x)^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 b}-\frac{B^2 n (a+b x) (b c-a d) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b d}","-\frac{B^2 n^2 (b c-a d)^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}-\frac{B n (b c-a d)^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A+B n\right)}{b d^2}-\frac{B n (a+b x) (b c-a d) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b d}+\frac{(a+b x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 b}",1,"-((A*B*(b*c - a*d)*n*x)/d) + (A^2*(a + b*x)^2)/(2*b) + (A*B*(b*c - a*d)^2*n*Log[c + d*x])/(b*d^2) + (B^2*(b*c - a*d)^2*n^2*Log[c + d*x])/(b*d^2) - (B^2*(b*c - a*d)*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*d) + (A*B*(a + b*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/b - (B^2*(b*c - a*d)^2*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*d^2) + (B^2*(a + b*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*b) - (B^2*(b*c - a*d)^2*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(b*d^2)","A",15,11,31,0.3548,1,"{6742, 2492, 43, 2514, 2486, 31, 2488, 2411, 2343, 2333, 2315}"
159,1,227,0,0.504468,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{a+b x} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(a + b*x),x]","\frac{2 A B n \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{b}+\frac{2 B^2 n \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b}+\frac{2 B^2 n^2 \text{PolyLog}\left(3,\frac{b c-a d}{d (a+b x)}+1\right)}{b}+\frac{A^2 \log (a+b x)}{b}-\frac{2 A B \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b}-\frac{B^2 \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{b}","\frac{2 B n \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b}+\frac{2 B^2 n^2 \text{PolyLog}\left(3,\frac{b (c+d x)}{d (a+b x)}\right)}{b}-\frac{\log \left(1-\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{b}",1,"(A^2*Log[a + b*x])/b - (2*A*B*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/b - (B^2*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/b + (2*A*B*n*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/b + (2*B^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/b + (2*B^2*n^2*PolyLog[3, 1 + (b*c - a*d)/(d*(a + b*x))])/b","A",10,8,33,0.2424,1,"{6742, 2488, 2411, 2343, 2333, 2315, 2506, 6610}"
160,1,189,0,0.182181,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{(a+b x)^2} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(a + b*x)^2,x]","-\frac{A^2}{b (a+b x)}-\frac{2 A B (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x) (b c-a d)}-\frac{2 A B n}{b (a+b x)}-\frac{B^2 (c+d x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x) (b c-a d)}-\frac{2 B^2 n (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x) (b c-a d)}-\frac{2 B^2 n^2}{b (a+b x)}","-\frac{2 B n (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{(a+b x) (b c-a d)}-\frac{(c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{(a+b x) (b c-a d)}-\frac{2 B^2 n^2 (c+d x)}{(a+b x) (b c-a d)}",1,"-(A^2/(b*(a + b*x))) - (2*A*B*n)/(b*(a + b*x)) - (2*B^2*n^2)/(b*(a + b*x)) - (2*A*B*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((b*c - a*d)*(a + b*x)) - (2*B^2*n*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((b*c - a*d)*(a + b*x)) - (B^2*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/((b*c - a*d)*(a + b*x))","A",7,3,33,0.09091,1,"{6742, 2490, 32}"
161,1,411,0,0.4232888,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{(a+b x)^3} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(a + b*x)^3,x]","-\frac{A^2}{2 b (a+b x)^2}+\frac{A B d^2 n \log (a+b x)}{b (b c-a d)^2}-\frac{A B d^2 n \log (c+d x)}{b (b c-a d)^2}-\frac{A B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b (a+b x)^2}+\frac{A B d n}{b (a+b x) (b c-a d)}-\frac{A B n}{2 b (a+b x)^2}-\frac{b B^2 (c+d x)^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 (a+b x)^2 (b c-a d)^2}+\frac{B^2 d (c+d x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x) (b c-a d)^2}-\frac{b B^2 n (c+d x)^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{2 (a+b x)^2 (b c-a d)^2}+\frac{2 B^2 d n (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x) (b c-a d)^2}-\frac{b B^2 n^2 (c+d x)^2}{4 (a+b x)^2 (b c-a d)^2}+\frac{2 B^2 d n^2}{b (a+b x) (b c-a d)}","-\frac{b B n (c+d x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{2 (a+b x)^2 (b c-a d)^2}+\frac{2 B d n (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{(a+b x) (b c-a d)^2}-\frac{b (c+d x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 (a+b x)^2 (b c-a d)^2}+\frac{d (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{(a+b x) (b c-a d)^2}-\frac{b B^2 n^2 (c+d x)^2}{4 (a+b x)^2 (b c-a d)^2}+\frac{2 B^2 d n^2 (c+d x)}{(a+b x) (b c-a d)^2}",1,"-A^2/(2*b*(a + b*x)^2) - (A*B*n)/(2*b*(a + b*x)^2) + (A*B*d*n)/(b*(b*c - a*d)*(a + b*x)) + (2*B^2*d*n^2)/(b*(b*c - a*d)*(a + b*x)) - (b*B^2*n^2*(c + d*x)^2)/(4*(b*c - a*d)^2*(a + b*x)^2) + (A*B*d^2*n*Log[a + b*x])/(b*(b*c - a*d)^2) - (A*B*d^2*n*Log[c + d*x])/(b*(b*c - a*d)^2) - (A*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*(a + b*x)^2) + (2*B^2*d*n*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((b*c - a*d)^2*(a + b*x)) - (b*B^2*n*(c + d*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*(b*c - a*d)^2*(a + b*x)^2) + (B^2*d*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/((b*c - a*d)^2*(a + b*x)) - (b*B^2*(c + d*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*(b*c - a*d)^2*(a + b*x)^2)","A",12,8,33,0.2424,1,"{6742, 2492, 44, 2491, 2490, 32, 2509, 37}"
162,1,730,0,1.2123526,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{(a+b x)^4} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(a + b*x)^4,x]","-\frac{2 B^2 d^3 n^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{3 b (b c-a d)^3}-\frac{2 B^2 d^3 n^2 \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{3 b (b c-a d)^3}-\frac{A^2}{3 b (a+b x)^3}-\frac{2 A B d^2 n}{3 b (a+b x) (b c-a d)^2}-\frac{2 A B d^3 n \log (a+b x)}{3 b (b c-a d)^3}+\frac{2 A B d^3 n \log (c+d x)}{3 b (b c-a d)^3}-\frac{2 A B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b (a+b x)^3}+\frac{A B d n}{3 b (a+b x)^2 (b c-a d)}-\frac{2 A B n}{9 b (a+b x)^3}+\frac{2 B^2 d^3 n \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b (b c-a d)^3}-\frac{2 B^2 d^3 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b (b c-a d)^3}-\frac{2 B^2 d^2 n (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 (a+b x) (b c-a d)^3}-\frac{11 B^2 d^2 n^2}{9 b (a+b x) (b c-a d)^2}-\frac{5 B^2 d^3 n^2 \log (a+b x)}{9 b (b c-a d)^3}+\frac{5 B^2 d^3 n^2 \log (c+d x)}{9 b (b c-a d)^3}-\frac{B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b (a+b x)^3}+\frac{B^2 d n \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b (a+b x)^2 (b c-a d)}-\frac{2 B^2 n \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{9 b (a+b x)^3}+\frac{5 B^2 d n^2}{18 b (a+b x)^2 (b c-a d)}-\frac{2 B^2 n^2}{27 b (a+b x)^3}","-\frac{b^2 (c+d x)^3 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{3 (a+b x)^3 (b c-a d)^3}-\frac{2 b^2 B n (c+d x)^3 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{9 (a+b x)^3 (b c-a d)^3}-\frac{d^2 (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{(a+b x) (b c-a d)^3}-\frac{2 B d^2 n (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{(a+b x) (b c-a d)^3}+\frac{b d (c+d x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{(a+b x)^2 (b c-a d)^3}+\frac{b B d n (c+d x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{(a+b x)^2 (b c-a d)^3}-\frac{2 b^2 B^2 n^2 (c+d x)^3}{27 (a+b x)^3 (b c-a d)^3}-\frac{2 B^2 d^2 n^2 (c+d x)}{(a+b x) (b c-a d)^3}+\frac{b B^2 d n^2 (c+d x)^2}{2 (a+b x)^2 (b c-a d)^3}",1,"-A^2/(3*b*(a + b*x)^3) - (2*A*B*n)/(9*b*(a + b*x)^3) - (2*B^2*n^2)/(27*b*(a + b*x)^3) + (A*B*d*n)/(3*b*(b*c - a*d)*(a + b*x)^2) + (5*B^2*d*n^2)/(18*b*(b*c - a*d)*(a + b*x)^2) - (2*A*B*d^2*n)/(3*b*(b*c - a*d)^2*(a + b*x)) - (11*B^2*d^2*n^2)/(9*b*(b*c - a*d)^2*(a + b*x)) - (2*A*B*d^3*n*Log[a + b*x])/(3*b*(b*c - a*d)^3) - (5*B^2*d^3*n^2*Log[a + b*x])/(9*b*(b*c - a*d)^3) + (2*A*B*d^3*n*Log[c + d*x])/(3*b*(b*c - a*d)^3) + (5*B^2*d^3*n^2*Log[c + d*x])/(9*b*(b*c - a*d)^3) - (2*A*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b*(a + b*x)^3) - (2*B^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(9*b*(a + b*x)^3) + (B^2*d*n*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b*(b*c - a*d)*(a + b*x)^2) - (2*B^2*d^2*n*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*(b*c - a*d)^3*(a + b*x)) + (2*B^2*d^3*n*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b*(b*c - a*d)^3) - (2*B^2*d^3*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b*(b*c - a*d)^3) - (B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(3*b*(a + b*x)^3) - (2*B^2*d^3*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(3*b*(b*c - a*d)^3) - (2*B^2*d^3*n^2*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(3*b*(b*c - a*d)^3)","C",26,11,33,0.3333,1,"{6742, 2492, 44, 2514, 2490, 32, 2488, 2411, 2343, 2333, 2315}"
163,1,843,0,1.4079737,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{(a+b x)^5} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(a + b*x)^5,x]","\frac{13 B^2 n^2 \log (a+b x) d^4}{24 b (b c-a d)^4}+\frac{A B n \log (a+b x) d^4}{2 b (b c-a d)^4}-\frac{13 B^2 n^2 \log (c+d x) d^4}{24 b (b c-a d)^4}-\frac{A B n \log (c+d x) d^4}{2 b (b c-a d)^4}-\frac{B^2 n \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) d^4}{2 b (b c-a d)^4}+\frac{B^2 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) d^4}{2 b (b c-a d)^4}+\frac{B^2 n^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) d^4}{2 b (b c-a d)^4}+\frac{B^2 n^2 \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right) d^4}{2 b (b c-a d)^4}+\frac{B^2 n (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) d^3}{2 (b c-a d)^4 (a+b x)}+\frac{25 B^2 n^2 d^3}{24 b (b c-a d)^3 (a+b x)}+\frac{A B n d^3}{2 b (b c-a d)^3 (a+b x)}-\frac{B^2 n \log \left(e (a+b x)^n (c+d x)^{-n}\right) d^2}{4 b (b c-a d)^2 (a+b x)^2}-\frac{13 B^2 n^2 d^2}{48 b (b c-a d)^2 (a+b x)^2}-\frac{A B n d^2}{4 b (b c-a d)^2 (a+b x)^2}+\frac{B^2 n \log \left(e (a+b x)^n (c+d x)^{-n}\right) d}{6 b (b c-a d) (a+b x)^3}+\frac{7 B^2 n^2 d}{72 b (b c-a d) (a+b x)^3}+\frac{A B n d}{6 b (b c-a d) (a+b x)^3}-\frac{B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{4 b (a+b x)^4}-\frac{A B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{2 b (a+b x)^4}-\frac{B^2 n \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{8 b (a+b x)^4}-\frac{B^2 n^2}{32 b (a+b x)^4}-\frac{A B n}{8 b (a+b x)^4}-\frac{A^2}{4 b (a+b x)^4}","-\frac{b^3 (c+d x)^4 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{4 (a+b x)^4 (b c-a d)^4}-\frac{b^3 B n (c+d x)^4 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{8 (a+b x)^4 (b c-a d)^4}+\frac{b^2 d (c+d x)^3 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{(a+b x)^3 (b c-a d)^4}+\frac{2 b^2 B d n (c+d x)^3 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{3 (a+b x)^3 (b c-a d)^4}-\frac{3 b d^2 (c+d x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 (a+b x)^2 (b c-a d)^4}-\frac{3 b B d^2 n (c+d x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{2 (a+b x)^2 (b c-a d)^4}+\frac{d^3 (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{(a+b x) (b c-a d)^4}+\frac{2 B d^3 n (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{(a+b x) (b c-a d)^4}-\frac{b^3 B^2 n^2 (c+d x)^4}{32 (a+b x)^4 (b c-a d)^4}+\frac{2 b^2 B^2 d n^2 (c+d x)^3}{9 (a+b x)^3 (b c-a d)^4}-\frac{3 b B^2 d^2 n^2 (c+d x)^2}{4 (a+b x)^2 (b c-a d)^4}+\frac{2 B^2 d^3 n^2 (c+d x)}{(a+b x) (b c-a d)^4}",1,"-A^2/(4*b*(a + b*x)^4) - (A*B*n)/(8*b*(a + b*x)^4) - (B^2*n^2)/(32*b*(a + b*x)^4) + (A*B*d*n)/(6*b*(b*c - a*d)*(a + b*x)^3) + (7*B^2*d*n^2)/(72*b*(b*c - a*d)*(a + b*x)^3) - (A*B*d^2*n)/(4*b*(b*c - a*d)^2*(a + b*x)^2) - (13*B^2*d^2*n^2)/(48*b*(b*c - a*d)^2*(a + b*x)^2) + (A*B*d^3*n)/(2*b*(b*c - a*d)^3*(a + b*x)) + (25*B^2*d^3*n^2)/(24*b*(b*c - a*d)^3*(a + b*x)) + (A*B*d^4*n*Log[a + b*x])/(2*b*(b*c - a*d)^4) + (13*B^2*d^4*n^2*Log[a + b*x])/(24*b*(b*c - a*d)^4) - (A*B*d^4*n*Log[c + d*x])/(2*b*(b*c - a*d)^4) - (13*B^2*d^4*n^2*Log[c + d*x])/(24*b*(b*c - a*d)^4) - (A*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*b*(a + b*x)^4) - (B^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(8*b*(a + b*x)^4) + (B^2*d*n*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(6*b*(b*c - a*d)*(a + b*x)^3) - (B^2*d^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(4*b*(b*c - a*d)^2*(a + b*x)^2) + (B^2*d^3*n*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*(b*c - a*d)^4*(a + b*x)) - (B^2*d^4*n*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*b*(b*c - a*d)^4) + (B^2*d^4*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*b*(b*c - a*d)^4) - (B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(4*b*(a + b*x)^4) + (B^2*d^4*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(2*b*(b*c - a*d)^4) + (B^2*d^4*n^2*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(2*b*(b*c - a*d)^4)","C",29,11,33,0.3333,1,"{6742, 2492, 44, 2514, 2490, 32, 2488, 2411, 2343, 2333, 2315}"
164,1,1203,0,2.403541,"\int (a+b x)^3 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 \, dx","Int[(a + b*x)^3*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3,x]","-\frac{3 B^3 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) (b c-a d)^4}{4 b d^4}+\frac{3 B^3 n^3 \log (c+d x) (b c-a d)^4}{2 b d^4}+\frac{11 A B^2 n^2 \log (c+d x) (b c-a d)^4}{4 b d^4}+\frac{3 A^2 B n \log (c+d x) (b c-a d)^4}{4 b d^4}-\frac{11 B^3 n^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) (b c-a d)^4}{4 b d^4}-\frac{3 A B^2 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) (b c-a d)^4}{2 b d^4}-\frac{11 B^3 n^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) (b c-a d)^4}{4 b d^4}-\frac{3 A B^2 n^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) (b c-a d)^4}{2 b d^4}-\frac{3 B^3 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) (b c-a d)^4}{2 b d^4}+\frac{3 B^3 n^3 \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right) (b c-a d)^4}{2 b d^4}-\frac{3 B^3 n (a+b x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) (b c-a d)^3}{4 b d^3}-\frac{B^3 n^3 x (b c-a d)^3}{4 d^3}-\frac{5 A B^2 n^2 x (b c-a d)^3}{4 d^3}-\frac{3 A^2 B n x (b c-a d)^3}{4 d^3}-\frac{5 B^3 n^2 (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) (b c-a d)^3}{4 b d^3}-\frac{3 A B^2 n (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) (b c-a d)^3}{2 b d^3}+\frac{A B^2 n^2 (a+b x)^2 (b c-a d)^2}{4 b d^2}+\frac{3 A^2 B n (a+b x)^2 (b c-a d)^2}{8 b d^2}+\frac{3 B^3 n (a+b x)^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) (b c-a d)^2}{8 b d^2}+\frac{B^3 n^2 (a+b x)^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) (b c-a d)^2}{4 b d^2}+\frac{3 A B^2 n (a+b x)^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) (b c-a d)^2}{4 b d^2}-\frac{A^2 B n (a+b x)^3 (b c-a d)}{4 b d}-\frac{B^3 n (a+b x)^3 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) (b c-a d)}{4 b d}-\frac{A B^2 n (a+b x)^3 \log \left(e (a+b x)^n (c+d x)^{-n}\right) (b c-a d)}{2 b d}+\frac{A^3 (a+b x)^4}{4 b}+\frac{B^3 (a+b x)^4 \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)}{4 b}+\frac{3 A B^2 (a+b x)^4 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{4 b}+\frac{3 A^2 B (a+b x)^4 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{4 b}","-\frac{3 B n \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 (b c-a d)^4}{4 b d^4}-\frac{B^3 n^3 \log \left(\frac{a+b x}{c+d x}\right) (b c-a d)^4}{4 b d^4}+\frac{3 B^3 n^3 \log (c+d x) (b c-a d)^4}{2 b d^4}-\frac{9 B^2 n^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) (b c-a d)^4}{2 b d^4}+\frac{7 B^2 n^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \log \left(1-\frac{b (c+d x)}{d (a+b x)}\right) (b c-a d)^4}{4 b d^4}-\frac{9 B^3 n^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) (b c-a d)^4}{2 b d^4}-\frac{3 B^2 n^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) (b c-a d)^4}{2 b d^4}-\frac{7 B^3 n^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right) (b c-a d)^4}{4 b d^4}+\frac{3 B^3 n^3 \text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right) (b c-a d)^4}{2 b d^4}-\frac{9 B n (a+b x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 (b c-a d)^3}{4 b d^3}-\frac{B^3 n^3 x (b c-a d)^3}{4 d^3}-\frac{7 B^2 n^2 (a+b x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) (b c-a d)^3}{4 b d^3}+\frac{9 b B n (c+d x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 (b c-a d)^2}{8 d^4}+\frac{b B^2 n^2 (c+d x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) (b c-a d)^2}{4 d^4}-\frac{b^2 B n (c+d x)^3 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 (b c-a d)}{4 d^4}+\frac{(a+b x)^4 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{4 b}",1,"(-3*A^2*B*(b*c - a*d)^3*n*x)/(4*d^3) - (5*A*B^2*(b*c - a*d)^3*n^2*x)/(4*d^3) - (B^3*(b*c - a*d)^3*n^3*x)/(4*d^3) + (3*A^2*B*(b*c - a*d)^2*n*(a + b*x)^2)/(8*b*d^2) + (A*B^2*(b*c - a*d)^2*n^2*(a + b*x)^2)/(4*b*d^2) - (A^2*B*(b*c - a*d)*n*(a + b*x)^3)/(4*b*d) + (A^3*(a + b*x)^4)/(4*b) + (3*A^2*B*(b*c - a*d)^4*n*Log[c + d*x])/(4*b*d^4) + (11*A*B^2*(b*c - a*d)^4*n^2*Log[c + d*x])/(4*b*d^4) + (3*B^3*(b*c - a*d)^4*n^3*Log[c + d*x])/(2*b*d^4) - (3*A*B^2*(b*c - a*d)^3*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*b*d^3) - (5*B^3*(b*c - a*d)^3*n^2*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(4*b*d^3) + (3*A*B^2*(b*c - a*d)^2*n*(a + b*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(4*b*d^2) + (B^3*(b*c - a*d)^2*n^2*(a + b*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(4*b*d^2) - (A*B^2*(b*c - a*d)*n*(a + b*x)^3*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*b*d) + (3*A^2*B*(a + b*x)^4*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(4*b) - (3*A*B^2*(b*c - a*d)^4*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*b*d^4) - (11*B^3*(b*c - a*d)^4*n^2*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(4*b*d^4) - (3*B^3*(b*c - a*d)^3*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(4*b*d^3) + (3*B^3*(b*c - a*d)^2*n*(a + b*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(8*b*d^2) - (B^3*(b*c - a*d)*n*(a + b*x)^3*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(4*b*d) + (3*A*B^2*(a + b*x)^4*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(4*b) - (3*B^3*(b*c - a*d)^4*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(4*b*d^4) + (B^3*(a + b*x)^4*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3)/(4*b) - (3*A*B^2*(b*c - a*d)^4*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(2*b*d^4) - (11*B^3*(b*c - a*d)^4*n^3*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(4*b*d^4) - (3*B^3*(b*c - a*d)^4*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/(2*b*d^4) + (3*B^3*(b*c - a*d)^4*n^3*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/(2*b*d^4)","A",56,13,33,0.3939,1,"{6742, 2492, 43, 2514, 2486, 31, 2488, 2411, 2343, 2333, 2315, 2506, 6610}"
165,1,915,0,1.736903,"\int (a+b x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 \, dx","Int[(a + b*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3,x]","\frac{(a+b x)^3 \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right) B^3}{3 b}-\frac{(b c-a d) n (a+b x)^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) B^3}{2 b d}+\frac{(b c-a d)^2 n (a+b x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) B^3}{b d^2}+\frac{(b c-a d)^3 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) B^3}{b d^3}-\frac{(b c-a d)^3 n^3 \log (c+d x) B^3}{b d^3}+\frac{(b c-a d)^2 n^2 (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) B^3}{b d^2}+\frac{3 (b c-a d)^3 n^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) B^3}{b d^3}+\frac{3 (b c-a d)^3 n^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) B^3}{b d^3}+\frac{2 (b c-a d)^3 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) B^3}{b d^3}-\frac{2 (b c-a d)^3 n^3 \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right) B^3}{b d^3}+\frac{A (a+b x)^3 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) B^2}{b}+\frac{A (b c-a d)^2 n^2 x B^2}{d^2}-\frac{3 A (b c-a d)^3 n^2 \log (c+d x) B^2}{b d^3}-\frac{A (b c-a d) n (a+b x)^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) B^2}{b d}+\frac{2 A (b c-a d)^2 n (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) B^2}{b d^2}+\frac{2 A (b c-a d)^3 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) B^2}{b d^3}+\frac{2 A (b c-a d)^3 n^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) B^2}{b d^3}-\frac{A^2 (b c-a d) n (a+b x)^2 B}{2 b d}+\frac{A^2 (b c-a d)^2 n x B}{d^2}-\frac{A^2 (b c-a d)^3 n \log (c+d x) B}{b d^3}+\frac{A^2 (a+b x)^3 \log \left(e (a+b x)^n (c+d x)^{-n}\right) B}{b}+\frac{A^3 (a+b x)^3}{3 b}","\frac{2 B^2 n^2 (b c-a d)^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b d^3}+\frac{4 B^3 n^3 (b c-a d)^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d^3}+\frac{B^3 n^3 (b c-a d)^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right)}{b d^3}-\frac{2 B^3 n^3 (b c-a d)^3 \text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right)}{b d^3}+\frac{4 B^2 n^2 (b c-a d)^3 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b d^3}-\frac{B^2 n^2 (b c-a d)^3 \log \left(1-\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b d^3}+\frac{B^2 n^2 (a+b x) (b c-a d)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b d^2}+\frac{B n (b c-a d)^3 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{b d^3}+\frac{2 B n (a+b x) (b c-a d)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{b d^2}-\frac{b B n (c+d x)^2 (b c-a d) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 d^3}+\frac{(a+b x)^3 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{3 b}-\frac{B^3 n^3 (b c-a d)^3 \log (c+d x)}{b d^3}",1,"(A^2*B*(b*c - a*d)^2*n*x)/d^2 + (A*B^2*(b*c - a*d)^2*n^2*x)/d^2 - (A^2*B*(b*c - a*d)*n*(a + b*x)^2)/(2*b*d) + (A^3*(a + b*x)^3)/(3*b) - (A^2*B*(b*c - a*d)^3*n*Log[c + d*x])/(b*d^3) - (3*A*B^2*(b*c - a*d)^3*n^2*Log[c + d*x])/(b*d^3) - (B^3*(b*c - a*d)^3*n^3*Log[c + d*x])/(b*d^3) + (2*A*B^2*(b*c - a*d)^2*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*d^2) + (B^3*(b*c - a*d)^2*n^2*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*d^2) - (A*B^2*(b*c - a*d)*n*(a + b*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*d) + (A^2*B*(a + b*x)^3*Log[(e*(a + b*x)^n)/(c + d*x)^n])/b + (2*A*B^2*(b*c - a*d)^3*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*d^3) + (3*B^3*(b*c - a*d)^3*n^2*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*d^3) + (B^3*(b*c - a*d)^2*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(b*d^2) - (B^3*(b*c - a*d)*n*(a + b*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*b*d) + (A*B^2*(a + b*x)^3*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/b + (B^3*(b*c - a*d)^3*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(b*d^3) + (B^3*(a + b*x)^3*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3)/(3*b) + (2*A*B^2*(b*c - a*d)^3*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(b*d^3) + (3*B^3*(b*c - a*d)^3*n^3*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(b*d^3) + (2*B^3*(b*c - a*d)^3*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*d^3) - (2*B^3*(b*c - a*d)^3*n^3*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*d^3)","A",40,13,33,0.3939,1,"{6742, 2492, 43, 2514, 2486, 31, 2488, 2411, 2343, 2333, 2315, 2506, 6610}"
166,1,700,0,1.1825014,"\int (a+b x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 \, dx","Int[(a + b*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3,x]","-\frac{3 A B^2 n^2 (b c-a d)^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}-\frac{3 B^3 n^2 (b c-a d)^2 \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b d^2}-\frac{3 B^3 n^3 (b c-a d)^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}+\frac{3 B^3 n^3 (b c-a d)^2 \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right)}{b d^2}+\frac{3 A^2 B n (b c-a d)^2 \log (c+d x)}{2 b d^2}+\frac{3 A^2 B (a+b x)^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{2 b}-\frac{3 A^2 B n x (b c-a d)}{2 d}+\frac{A^3 (a+b x)^2}{2 b}-\frac{3 A B^2 n (b c-a d)^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b d^2}+\frac{3 A B^2 n^2 (b c-a d)^2 \log (c+d x)}{b d^2}+\frac{3 A B^2 (a+b x)^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 b}-\frac{3 A B^2 n (a+b x) (b c-a d) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b d}-\frac{3 B^3 n^2 (b c-a d)^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b d^2}-\frac{3 B^3 n (b c-a d)^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 b d^2}+\frac{B^3 (a+b x)^2 \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 b}-\frac{3 B^3 n (a+b x) (b c-a d) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 b d}","-\frac{3 B^2 n^2 (b c-a d)^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b d^2}-\frac{3 B^3 n^3 (b c-a d)^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}+\frac{3 B^3 n^3 (b c-a d)^2 \text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}-\frac{3 B^2 n^2 (b c-a d)^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b d^2}-\frac{3 B n (b c-a d)^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 b d^2}-\frac{3 B n (a+b x) (b c-a d) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 b d}+\frac{(a+b x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{2 b}",1,"(-3*A^2*B*(b*c - a*d)*n*x)/(2*d) + (A^3*(a + b*x)^2)/(2*b) + (3*A^2*B*(b*c - a*d)^2*n*Log[c + d*x])/(2*b*d^2) + (3*A*B^2*(b*c - a*d)^2*n^2*Log[c + d*x])/(b*d^2) - (3*A*B^2*(b*c - a*d)*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*d) + (3*A^2*B*(a + b*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*b) - (3*A*B^2*(b*c - a*d)^2*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*d^2) - (3*B^3*(b*c - a*d)^2*n^2*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*d^2) - (3*B^3*(b*c - a*d)*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*b*d) + (3*A*B^2*(a + b*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*b) - (3*B^3*(b*c - a*d)^2*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*b*d^2) + (B^3*(a + b*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3)/(2*b) - (3*A*B^2*(b*c - a*d)^2*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(b*d^2) - (3*B^3*(b*c - a*d)^2*n^3*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(b*d^2) - (3*B^3*(b*c - a*d)^2*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*d^2) + (3*B^3*(b*c - a*d)^2*n^3*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*d^2)","A",27,13,31,0.4194,1,"{6742, 2492, 43, 2514, 2486, 31, 2488, 2411, 2343, 2333, 2315, 2506, 6610}"
167,1,424,0,0.8506577,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{a+b x} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(a + b*x),x]","\frac{3 A^2 B n \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{b}+\frac{6 A B^2 n \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b}+\frac{6 A B^2 n^2 \text{PolyLog}\left(3,\frac{b c-a d}{d (a+b x)}+1\right)}{b}+\frac{6 B^3 n^2 \text{PolyLog}\left(3,\frac{b c-a d}{d (a+b x)}+1\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b}+\frac{3 B^3 n \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{b}+\frac{6 B^3 n^3 \text{PolyLog}\left(4,\frac{b c-a d}{d (a+b x)}+1\right)}{b}-\frac{3 A^2 B \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b}+\frac{A^3 \log (a+b x)}{b}-\frac{3 A B^2 \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{b}-\frac{B^3 \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)}{b}","\frac{6 B^2 n^2 \text{PolyLog}\left(3,\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b}+\frac{3 B n \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{b}+\frac{6 B^3 n^3 \text{PolyLog}\left(4,\frac{b (c+d x)}{d (a+b x)}\right)}{b}-\frac{\log \left(1-\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{b}",1,"(A^3*Log[a + b*x])/b - (3*A^2*B*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/b - (3*A*B^2*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/b - (B^3*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3)/b + (3*A^2*B*n*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/b + (6*A*B^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/b + (3*B^3*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/b + (6*A*B^2*n^2*PolyLog[3, 1 + (b*c - a*d)/(d*(a + b*x))])/b + (6*B^3*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[3, 1 + (b*c - a*d)/(d*(a + b*x))])/b + (6*B^3*n^3*PolyLog[4, 1 + (b*c - a*d)/(d*(a + b*x))])/b","B",14,9,33,0.2727,1,"{6742, 2488, 2411, 2343, 2333, 2315, 2506, 6610, 2508}"
168,1,360,0,0.3146736,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(a+b x)^2} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(a + b*x)^2,x]","-\frac{3 A^2 B (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x) (b c-a d)}-\frac{3 A^2 B n}{b (a+b x)}-\frac{A^3}{b (a+b x)}-\frac{3 A B^2 (c+d x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x) (b c-a d)}-\frac{6 A B^2 n (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x) (b c-a d)}-\frac{6 A B^2 n^2}{b (a+b x)}-\frac{6 B^3 n^2 (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x) (b c-a d)}-\frac{B^3 (c+d x) \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x) (b c-a d)}-\frac{3 B^3 n (c+d x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x) (b c-a d)}-\frac{6 B^3 n^3}{b (a+b x)}","-\frac{6 B^2 n^2 (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{(a+b x) (b c-a d)}-\frac{3 B n (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{(a+b x) (b c-a d)}-\frac{(c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{(a+b x) (b c-a d)}-\frac{6 B^3 n^3 (c+d x)}{(a+b x) (b c-a d)}",1,"-(A^3/(b*(a + b*x))) - (3*A^2*B*n)/(b*(a + b*x)) - (6*A*B^2*n^2)/(b*(a + b*x)) - (6*B^3*n^3)/(b*(a + b*x)) - (3*A^2*B*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((b*c - a*d)*(a + b*x)) - (6*A*B^2*n*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((b*c - a*d)*(a + b*x)) - (6*B^3*n^2*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((b*c - a*d)*(a + b*x)) - (3*A*B^2*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/((b*c - a*d)*(a + b*x)) - (3*B^3*n*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/((b*c - a*d)*(a + b*x)) - (B^3*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3)/((b*c - a*d)*(a + b*x))","A",11,3,33,0.09091,1,"{6742, 2490, 32}"
169,1,811,0,0.8038928,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(a+b x)^3} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(a + b*x)^3,x]","-\frac{A^3}{2 b (a+b x)^2}+\frac{3 B d^2 n \log (a+b x) A^2}{2 b (b c-a d)^2}-\frac{3 B d^2 n \log (c+d x) A^2}{2 b (b c-a d)^2}-\frac{3 B \log \left(e (a+b x)^n (c+d x)^{-n}\right) A^2}{2 b (a+b x)^2}+\frac{3 B d n A^2}{2 b (b c-a d) (a+b x)}-\frac{3 B n A^2}{4 b (a+b x)^2}-\frac{3 b B^2 n^2 (c+d x)^2 A}{4 (b c-a d)^2 (a+b x)^2}-\frac{3 b B^2 (c+d x)^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) A}{2 (b c-a d)^2 (a+b x)^2}+\frac{3 B^2 d (c+d x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) A}{(b c-a d)^2 (a+b x)}-\frac{3 b B^2 n (c+d x)^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) A}{2 (b c-a d)^2 (a+b x)^2}+\frac{6 B^2 d n (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) A}{(b c-a d)^2 (a+b x)}+\frac{6 B^2 d n^2 A}{b (b c-a d) (a+b x)}-\frac{b B^3 (c+d x)^2 \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 (b c-a d)^2 (a+b x)^2}+\frac{B^3 d (c+d x) \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)}{(b c-a d)^2 (a+b x)}-\frac{3 b B^3 n^3 (c+d x)^2}{8 (b c-a d)^2 (a+b x)^2}-\frac{3 b B^3 n (c+d x)^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{4 (b c-a d)^2 (a+b x)^2}+\frac{3 B^3 d n (c+d x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{(b c-a d)^2 (a+b x)}-\frac{3 b B^3 n^2 (c+d x)^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{4 (b c-a d)^2 (a+b x)^2}+\frac{6 B^3 d n^2 (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(b c-a d)^2 (a+b x)}+\frac{6 B^3 d n^3}{b (b c-a d) (a+b x)}","-\frac{3 b B^2 n^2 (c+d x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{4 (a+b x)^2 (b c-a d)^2}+\frac{6 B^2 d n^2 (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{(a+b x) (b c-a d)^2}-\frac{3 b B n (c+d x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{4 (a+b x)^2 (b c-a d)^2}+\frac{3 B d n (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{(a+b x) (b c-a d)^2}-\frac{b (c+d x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{2 (a+b x)^2 (b c-a d)^2}+\frac{d (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{(a+b x) (b c-a d)^2}-\frac{3 b B^3 n^3 (c+d x)^2}{8 (a+b x)^2 (b c-a d)^2}+\frac{6 B^3 d n^3 (c+d x)}{(a+b x) (b c-a d)^2}",1,"-A^3/(2*b*(a + b*x)^2) - (3*A^2*B*n)/(4*b*(a + b*x)^2) + (3*A^2*B*d*n)/(2*b*(b*c - a*d)*(a + b*x)) + (6*A*B^2*d*n^2)/(b*(b*c - a*d)*(a + b*x)) + (6*B^3*d*n^3)/(b*(b*c - a*d)*(a + b*x)) - (3*A*b*B^2*n^2*(c + d*x)^2)/(4*(b*c - a*d)^2*(a + b*x)^2) - (3*b*B^3*n^3*(c + d*x)^2)/(8*(b*c - a*d)^2*(a + b*x)^2) + (3*A^2*B*d^2*n*Log[a + b*x])/(2*b*(b*c - a*d)^2) - (3*A^2*B*d^2*n*Log[c + d*x])/(2*b*(b*c - a*d)^2) - (3*A^2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*b*(a + b*x)^2) + (6*A*B^2*d*n*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((b*c - a*d)^2*(a + b*x)) + (6*B^3*d*n^2*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((b*c - a*d)^2*(a + b*x)) - (3*A*b*B^2*n*(c + d*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*(b*c - a*d)^2*(a + b*x)^2) - (3*b*B^3*n^2*(c + d*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(4*(b*c - a*d)^2*(a + b*x)^2) + (3*A*B^2*d*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/((b*c - a*d)^2*(a + b*x)) + (3*B^3*d*n*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/((b*c - a*d)^2*(a + b*x)) - (3*A*b*B^2*(c + d*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*(b*c - a*d)^2*(a + b*x)^2) - (3*b*B^3*n*(c + d*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(4*(b*c - a*d)^2*(a + b*x)^2) + (B^3*d*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3)/((b*c - a*d)^2*(a + b*x)) - (b*B^3*(c + d*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3)/(2*(b*c - a*d)^2*(a + b*x)^2)","B",21,8,33,0.2424,1,"{6742, 2492, 44, 2491, 2490, 32, 2509, 37}"
170,1,1876,0,3.4324187,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(a+b x)^4} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(a + b*x)^4,x]","-\frac{A^3}{3 b (a+b x)^3}-\frac{B d^3 n \log (a+b x) A^2}{b (b c-a d)^3}+\frac{B d^3 n \log (c+d x) A^2}{b (b c-a d)^3}-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right) A^2}{b (a+b x)^3}-\frac{B d^2 n A^2}{b (b c-a d)^2 (a+b x)}+\frac{B d n A^2}{2 b (b c-a d) (a+b x)^2}-\frac{B n A^2}{3 b (a+b x)^3}-\frac{B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) A}{b (a+b x)^3}-\frac{5 B^2 d^3 n^2 \log (a+b x) A}{3 b (b c-a d)^3}+\frac{5 B^2 d^3 n^2 \log (c+d x) A}{3 b (b c-a d)^3}-\frac{2 B^2 d^2 n (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) A}{(b c-a d)^3 (a+b x)}+\frac{2 B^2 d^3 n \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) A}{b (b c-a d)^3}-\frac{2 B^2 d^3 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) A}{b (b c-a d)^3}+\frac{B^2 d n \log \left(e (a+b x)^n (c+d x)^{-n}\right) A}{b (b c-a d) (a+b x)^2}-\frac{2 B^2 n \log \left(e (a+b x)^n (c+d x)^{-n}\right) A}{3 b (a+b x)^3}-\frac{2 B^2 d^3 n^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) A}{b (b c-a d)^3}-\frac{2 B^2 d^3 n^2 \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right) A}{b (b c-a d)^3}-\frac{11 B^2 d^2 n^2 A}{3 b (b c-a d)^2 (a+b x)}+\frac{5 B^2 d n^2 A}{6 b (b c-a d) (a+b x)^2}-\frac{2 B^2 n^2 A}{9 b (a+b x)^3}-\frac{B^3 \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b (a+b x)^3}+\frac{b B^3 d n^3 (c+d x)^2}{4 (b c-a d)^3 (a+b x)^2}+\frac{b B^3 d n (c+d x)^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 (b c-a d)^3 (a+b x)^2}-\frac{2 B^3 d^2 n (c+d x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{(b c-a d)^3 (a+b x)}+\frac{B^3 d^3 n \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{b (b c-a d)^3}-\frac{B^3 d^3 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{b (b c-a d)^3}-\frac{B^3 n \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b (a+b x)^3}-\frac{5 B^3 d^3 n^3 \log (a+b x)}{9 b (b c-a d)^3}+\frac{5 B^3 d^3 n^3 \log (c+d x)}{9 b (b c-a d)^3}+\frac{b B^3 d n^2 (c+d x)^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{2 (b c-a d)^3 (a+b x)^2}-\frac{14 B^3 d^2 n^2 (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 (b c-a d)^3 (a+b x)}+\frac{2 B^3 d^3 n^2 \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b (b c-a d)^3}-\frac{2 B^3 d^3 n^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b (b c-a d)^3}+\frac{B^3 d n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b (b c-a d) (a+b x)^2}-\frac{2 B^3 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{9 b (a+b x)^3}-\frac{2 B^3 d^3 n^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{3 b (b c-a d)^3}-\frac{2 B^3 d^3 n^3 \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{3 b (b c-a d)^3}-\frac{2 B^3 d^3 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{b (b c-a d)^3}-\frac{2 B^3 d^3 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right)}{b (b c-a d)^3}-\frac{2 B^3 d^3 n^3 \text{PolyLog}\left(3,\frac{b c-a d}{d (a+b x)}+1\right)}{b (b c-a d)^3}+\frac{2 B^3 d^3 n^3 \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right)}{b (b c-a d)^3}-\frac{47 B^3 d^2 n^3}{9 b (b c-a d)^2 (a+b x)}+\frac{5 B^3 d n^3}{18 b (b c-a d) (a+b x)^2}-\frac{2 B^3 n^3}{27 b (a+b x)^3}","-\frac{2 b^2 B^2 n^2 (c+d x)^3 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{9 (a+b x)^3 (b c-a d)^3}-\frac{b^2 B n (c+d x)^3 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{3 (a+b x)^3 (b c-a d)^3}-\frac{b^2 (c+d x)^3 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{3 (a+b x)^3 (b c-a d)^3}-\frac{6 B^2 d^2 n^2 (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{(a+b x) (b c-a d)^3}+\frac{3 b B^2 d n^2 (c+d x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{2 (a+b x)^2 (b c-a d)^3}-\frac{3 B d^2 n (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{(a+b x) (b c-a d)^3}-\frac{d^2 (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{(a+b x) (b c-a d)^3}+\frac{3 b B d n (c+d x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 (a+b x)^2 (b c-a d)^3}+\frac{b d (c+d x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{(a+b x)^2 (b c-a d)^3}-\frac{2 b^2 B^3 n^3 (c+d x)^3}{27 (a+b x)^3 (b c-a d)^3}-\frac{6 B^3 d^2 n^3 (c+d x)}{(a+b x) (b c-a d)^3}+\frac{3 b B^3 d n^3 (c+d x)^2}{4 (a+b x)^2 (b c-a d)^3}",1,"-A^3/(3*b*(a + b*x)^3) - (A^2*B*n)/(3*b*(a + b*x)^3) - (2*A*B^2*n^2)/(9*b*(a + b*x)^3) - (2*B^3*n^3)/(27*b*(a + b*x)^3) + (A^2*B*d*n)/(2*b*(b*c - a*d)*(a + b*x)^2) + (5*A*B^2*d*n^2)/(6*b*(b*c - a*d)*(a + b*x)^2) + (5*B^3*d*n^3)/(18*b*(b*c - a*d)*(a + b*x)^2) - (A^2*B*d^2*n)/(b*(b*c - a*d)^2*(a + b*x)) - (11*A*B^2*d^2*n^2)/(3*b*(b*c - a*d)^2*(a + b*x)) - (47*B^3*d^2*n^3)/(9*b*(b*c - a*d)^2*(a + b*x)) + (b*B^3*d*n^3*(c + d*x)^2)/(4*(b*c - a*d)^3*(a + b*x)^2) - (A^2*B*d^3*n*Log[a + b*x])/(b*(b*c - a*d)^3) - (5*A*B^2*d^3*n^2*Log[a + b*x])/(3*b*(b*c - a*d)^3) - (5*B^3*d^3*n^3*Log[a + b*x])/(9*b*(b*c - a*d)^3) + (A^2*B*d^3*n*Log[c + d*x])/(b*(b*c - a*d)^3) + (5*A*B^2*d^3*n^2*Log[c + d*x])/(3*b*(b*c - a*d)^3) + (5*B^3*d^3*n^3*Log[c + d*x])/(9*b*(b*c - a*d)^3) - (A^2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*(a + b*x)^3) - (2*A*B^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b*(a + b*x)^3) - (2*B^3*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(9*b*(a + b*x)^3) + (A*B^2*d*n*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*(b*c - a*d)*(a + b*x)^2) + (B^3*d*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b*(b*c - a*d)*(a + b*x)^2) - (2*A*B^2*d^2*n*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((b*c - a*d)^3*(a + b*x)) - (14*B^3*d^2*n^2*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*(b*c - a*d)^3*(a + b*x)) + (b*B^3*d*n^2*(c + d*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*(b*c - a*d)^3*(a + b*x)^2) + (2*A*B^2*d^3*n*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*(b*c - a*d)^3) + (2*B^3*d^3*n^2*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b*(b*c - a*d)^3) - (2*A*B^2*d^3*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*(b*c - a*d)^3) - (2*B^3*d^3*n^2*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b*(b*c - a*d)^3) - (A*B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(b*(a + b*x)^3) - (B^3*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(3*b*(a + b*x)^3) - (2*B^3*d^2*n*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/((b*c - a*d)^3*(a + b*x)) + (b*B^3*d*n*(c + d*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*(b*c - a*d)^3*(a + b*x)^2) + (B^3*d^3*n*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(b*(b*c - a*d)^3) - (B^3*d^3*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(b*(b*c - a*d)^3) - (B^3*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3)/(3*b*(a + b*x)^3) - (2*A*B^2*d^3*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(b*(b*c - a*d)^3) - (2*B^3*d^3*n^3*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(3*b*(b*c - a*d)^3) - (2*A*B^2*d^3*n^2*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(b*(b*c - a*d)^3) - (2*B^3*d^3*n^3*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(3*b*(b*c - a*d)^3) - (2*B^3*d^3*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(b*(b*c - a*d)^3) - (2*B^3*d^3*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*(b*c - a*d)^3) - (2*B^3*d^3*n^3*PolyLog[3, 1 + (b*c - a*d)/(d*(a + b*x))])/(b*(b*c - a*d)^3) + (2*B^3*d^3*n^3*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*(b*c - a*d)^3)","C",66,16,33,0.4848,1,"{6742, 2492, 44, 2514, 2490, 32, 2488, 2411, 2343, 2333, 2315, 2491, 2509, 37, 2506, 6610}"
171,1,2173,0,4.6749698,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(a+b x)^5} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(a + b*x)^5,x]","-\frac{3 B^3 n \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) d^4}{4 b (b c-a d)^4}+\frac{3 B^3 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) d^4}{4 b (b c-a d)^4}+\frac{79 B^3 n^3 \log (a+b x) d^4}{96 b (b c-a d)^4}+\frac{13 A B^2 n^2 \log (a+b x) d^4}{8 b (b c-a d)^4}+\frac{3 A^2 B n \log (a+b x) d^4}{4 b (b c-a d)^4}-\frac{79 B^3 n^3 \log (c+d x) d^4}{96 b (b c-a d)^4}-\frac{13 A B^2 n^2 \log (c+d x) d^4}{8 b (b c-a d)^4}-\frac{3 A^2 B n \log (c+d x) d^4}{4 b (b c-a d)^4}-\frac{7 B^3 n^2 \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) d^4}{8 b (b c-a d)^4}-\frac{3 A B^2 n \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) d^4}{2 b (b c-a d)^4}+\frac{7 B^3 n^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) d^4}{8 b (b c-a d)^4}+\frac{3 A B^2 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) d^4}{2 b (b c-a d)^4}+\frac{7 B^3 n^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) d^4}{8 b (b c-a d)^4}+\frac{3 A B^2 n^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) d^4}{2 b (b c-a d)^4}+\frac{7 B^3 n^3 \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right) d^4}{8 b (b c-a d)^4}+\frac{3 A B^2 n^2 \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right) d^4}{2 b (b c-a d)^4}+\frac{3 B^3 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right) d^4}{2 b (b c-a d)^4}+\frac{3 B^3 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) d^4}{2 b (b c-a d)^4}+\frac{3 B^3 n^3 \text{PolyLog}\left(3,\frac{b c-a d}{d (a+b x)}+1\right) d^4}{2 b (b c-a d)^4}-\frac{3 B^3 n^3 \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right) d^4}{2 b (b c-a d)^4}+\frac{3 B^3 n (c+d x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) d^3}{2 (b c-a d)^4 (a+b x)}+\frac{31 B^3 n^2 (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) d^3}{8 (b c-a d)^4 (a+b x)}+\frac{3 A B^2 n (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) d^3}{2 (b c-a d)^4 (a+b x)}+\frac{451 B^3 n^3 d^3}{96 b (b c-a d)^3 (a+b x)}+\frac{25 A B^2 n^2 d^3}{8 b (b c-a d)^3 (a+b x)}+\frac{3 A^2 B n d^3}{4 b (b c-a d)^3 (a+b x)}-\frac{3 b B^3 n^3 (c+d x)^2 d^2}{16 (b c-a d)^4 (a+b x)^2}-\frac{3 b B^3 n (c+d x)^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) d^2}{8 (b c-a d)^4 (a+b x)^2}-\frac{3 b B^3 n^2 (c+d x)^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) d^2}{8 (b c-a d)^4 (a+b x)^2}-\frac{7 B^3 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) d^2}{16 b (b c-a d)^2 (a+b x)^2}-\frac{3 A B^2 n \log \left(e (a+b x)^n (c+d x)^{-n}\right) d^2}{4 b (b c-a d)^2 (a+b x)^2}-\frac{79 B^3 n^3 d^2}{192 b (b c-a d)^2 (a+b x)^2}-\frac{13 A B^2 n^2 d^2}{16 b (b c-a d)^2 (a+b x)^2}-\frac{3 A^2 B n d^2}{8 b (b c-a d)^2 (a+b x)^2}+\frac{B^3 n \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) d}{4 b (b c-a d) (a+b x)^3}+\frac{7 B^3 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) d}{24 b (b c-a d) (a+b x)^3}+\frac{A B^2 n \log \left(e (a+b x)^n (c+d x)^{-n}\right) d}{2 b (b c-a d) (a+b x)^3}+\frac{37 B^3 n^3 d}{288 b (b c-a d) (a+b x)^3}+\frac{7 A B^2 n^2 d}{24 b (b c-a d) (a+b x)^3}+\frac{A^2 B n d}{4 b (b c-a d) (a+b x)^3}-\frac{B^3 \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)}{4 b (a+b x)^4}-\frac{3 A B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{4 b (a+b x)^4}-\frac{3 B^3 n \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{16 b (a+b x)^4}-\frac{3 B^3 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{32 b (a+b x)^4}-\frac{3 A^2 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{4 b (a+b x)^4}-\frac{3 A B^2 n \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{8 b (a+b x)^4}-\frac{3 B^3 n^3}{128 b (a+b x)^4}-\frac{3 A B^2 n^2}{32 b (a+b x)^4}-\frac{3 A^2 B n}{16 b (a+b x)^4}-\frac{A^3}{4 b (a+b x)^4}","-\frac{b^3 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 (c+d x)^4}{4 (b c-a d)^4 (a+b x)^4}-\frac{3 b^3 B n \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 (c+d x)^4}{16 (b c-a d)^4 (a+b x)^4}-\frac{3 b^3 B^2 n^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) (c+d x)^4}{32 (b c-a d)^4 (a+b x)^4}-\frac{3 b^3 B^3 n^3 (c+d x)^4}{128 (b c-a d)^4 (a+b x)^4}+\frac{b^2 d \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 (c+d x)^3}{(b c-a d)^4 (a+b x)^3}+\frac{b^2 B d n \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 (c+d x)^3}{(b c-a d)^4 (a+b x)^3}+\frac{2 b^2 B^2 d n^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) (c+d x)^3}{3 (b c-a d)^4 (a+b x)^3}+\frac{2 b^2 B^3 d n^3 (c+d x)^3}{9 (b c-a d)^4 (a+b x)^3}-\frac{3 b d^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 (c+d x)^2}{2 (b c-a d)^4 (a+b x)^2}-\frac{9 b B d^2 n \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 (c+d x)^2}{4 (b c-a d)^4 (a+b x)^2}-\frac{9 b B^2 d^2 n^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) (c+d x)^2}{4 (b c-a d)^4 (a+b x)^2}-\frac{9 b B^3 d^2 n^3 (c+d x)^2}{8 (b c-a d)^4 (a+b x)^2}+\frac{d^3 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 (c+d x)}{(b c-a d)^4 (a+b x)}+\frac{3 B d^3 n \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 (c+d x)}{(b c-a d)^4 (a+b x)}+\frac{6 B^2 d^3 n^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) (c+d x)}{(b c-a d)^4 (a+b x)}+\frac{6 B^3 d^3 n^3 (c+d x)}{(b c-a d)^4 (a+b x)}",1,"-A^3/(4*b*(a + b*x)^4) - (3*A^2*B*n)/(16*b*(a + b*x)^4) - (3*A*B^2*n^2)/(32*b*(a + b*x)^4) - (3*B^3*n^3)/(128*b*(a + b*x)^4) + (A^2*B*d*n)/(4*b*(b*c - a*d)*(a + b*x)^3) + (7*A*B^2*d*n^2)/(24*b*(b*c - a*d)*(a + b*x)^3) + (37*B^3*d*n^3)/(288*b*(b*c - a*d)*(a + b*x)^3) - (3*A^2*B*d^2*n)/(8*b*(b*c - a*d)^2*(a + b*x)^2) - (13*A*B^2*d^2*n^2)/(16*b*(b*c - a*d)^2*(a + b*x)^2) - (79*B^3*d^2*n^3)/(192*b*(b*c - a*d)^2*(a + b*x)^2) + (3*A^2*B*d^3*n)/(4*b*(b*c - a*d)^3*(a + b*x)) + (25*A*B^2*d^3*n^2)/(8*b*(b*c - a*d)^3*(a + b*x)) + (451*B^3*d^3*n^3)/(96*b*(b*c - a*d)^3*(a + b*x)) - (3*b*B^3*d^2*n^3*(c + d*x)^2)/(16*(b*c - a*d)^4*(a + b*x)^2) + (3*A^2*B*d^4*n*Log[a + b*x])/(4*b*(b*c - a*d)^4) + (13*A*B^2*d^4*n^2*Log[a + b*x])/(8*b*(b*c - a*d)^4) + (79*B^3*d^4*n^3*Log[a + b*x])/(96*b*(b*c - a*d)^4) - (3*A^2*B*d^4*n*Log[c + d*x])/(4*b*(b*c - a*d)^4) - (13*A*B^2*d^4*n^2*Log[c + d*x])/(8*b*(b*c - a*d)^4) - (79*B^3*d^4*n^3*Log[c + d*x])/(96*b*(b*c - a*d)^4) - (3*A^2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(4*b*(a + b*x)^4) - (3*A*B^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(8*b*(a + b*x)^4) - (3*B^3*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(32*b*(a + b*x)^4) + (A*B^2*d*n*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*b*(b*c - a*d)*(a + b*x)^3) + (7*B^3*d*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(24*b*(b*c - a*d)*(a + b*x)^3) - (3*A*B^2*d^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(4*b*(b*c - a*d)^2*(a + b*x)^2) - (7*B^3*d^2*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(16*b*(b*c - a*d)^2*(a + b*x)^2) + (3*A*B^2*d^3*n*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*(b*c - a*d)^4*(a + b*x)) + (31*B^3*d^3*n^2*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(8*(b*c - a*d)^4*(a + b*x)) - (3*b*B^3*d^2*n^2*(c + d*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(8*(b*c - a*d)^4*(a + b*x)^2) - (3*A*B^2*d^4*n*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*b*(b*c - a*d)^4) - (7*B^3*d^4*n^2*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(8*b*(b*c - a*d)^4) + (3*A*B^2*d^4*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*b*(b*c - a*d)^4) + (7*B^3*d^4*n^2*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(8*b*(b*c - a*d)^4) - (3*A*B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(4*b*(a + b*x)^4) - (3*B^3*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(16*b*(a + b*x)^4) + (B^3*d*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(4*b*(b*c - a*d)*(a + b*x)^3) + (3*B^3*d^3*n*(c + d*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*(b*c - a*d)^4*(a + b*x)) - (3*b*B^3*d^2*n*(c + d*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(8*(b*c - a*d)^4*(a + b*x)^2) - (3*B^3*d^4*n*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(4*b*(b*c - a*d)^4) + (3*B^3*d^4*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(4*b*(b*c - a*d)^4) - (B^3*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3)/(4*b*(a + b*x)^4) + (3*A*B^2*d^4*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(2*b*(b*c - a*d)^4) + (7*B^3*d^4*n^3*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(8*b*(b*c - a*d)^4) + (3*A*B^2*d^4*n^2*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(2*b*(b*c - a*d)^4) + (7*B^3*d^4*n^3*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(8*b*(b*c - a*d)^4) + (3*B^3*d^4*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(2*b*(b*c - a*d)^4) + (3*B^3*d^4*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/(2*b*(b*c - a*d)^4) + (3*B^3*d^4*n^3*PolyLog[3, 1 + (b*c - a*d)/(d*(a + b*x))])/(2*b*(b*c - a*d)^4) - (3*B^3*d^4*n^3*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/(2*b*(b*c - a*d)^4)","C",93,16,33,0.4848,1,"{6742, 2492, 44, 2514, 2490, 32, 2488, 2411, 2343, 2333, 2315, 2491, 2509, 37, 2506, 6610}"
172,0,0,0,0.0998305,"\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)} \, dx","Int[1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])),x]","\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)} \, dx","\frac{e^{\frac{A}{B n}} (c+d x) \left(e (a+b x)^n (c+d x)^{-n}\right)^{\frac{1}{n}} \text{Ei}\left(-\frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{B n}\right)}{B g^2 n (a+b x) (b c-a d)}",1,"Defer[Int][1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])), x]","F",0,0,0,0,-1,"{}"
173,1,180,0,0.1241987,"\int (a g+b g x)^4 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right) \, dx","Int[(a*g + b*g*x)^4*(A + B*Log[(e*(c + d*x))/(a + b*x)]),x]","\frac{g^4 (a+b x)^5 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{5 b}-\frac{B g^4 x (b c-a d)^4}{5 d^4}+\frac{B g^4 (a+b x)^2 (b c-a d)^3}{10 b d^3}-\frac{B g^4 (a+b x)^3 (b c-a d)^2}{15 b d^2}+\frac{B g^4 (b c-a d)^5 \log (c+d x)}{5 b d^5}+\frac{B g^4 (a+b x)^4 (b c-a d)}{20 b d}","\frac{g^4 (a+b x)^5 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{5 b}-\frac{B g^4 x (b c-a d)^4}{5 d^4}+\frac{B g^4 (a+b x)^2 (b c-a d)^3}{10 b d^3}-\frac{B g^4 (a+b x)^3 (b c-a d)^2}{15 b d^2}+\frac{B g^4 (b c-a d)^5 \log (c+d x)}{5 b d^5}+\frac{B g^4 (a+b x)^4 (b c-a d)}{20 b d}",1,"-(B*(b*c - a*d)^4*g^4*x)/(5*d^4) + (B*(b*c - a*d)^3*g^4*(a + b*x)^2)/(10*b*d^3) - (B*(b*c - a*d)^2*g^4*(a + b*x)^3)/(15*b*d^2) + (B*(b*c - a*d)*g^4*(a + b*x)^4)/(20*b*d) + (B*(b*c - a*d)^5*g^4*Log[c + d*x])/(5*b*d^5) + (g^4*(a + b*x)^5*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(5*b)","A",4,3,30,0.1000,1,"{2525, 12, 43}"
174,1,149,0,0.1010908,"\int (a g+b g x)^3 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right) \, dx","Int[(a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)]),x]","\frac{g^3 (a+b x)^4 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{4 b}+\frac{B g^3 x (b c-a d)^3}{4 d^3}-\frac{B g^3 (a+b x)^2 (b c-a d)^2}{8 b d^2}-\frac{B g^3 (b c-a d)^4 \log (c+d x)}{4 b d^4}+\frac{B g^3 (a+b x)^3 (b c-a d)}{12 b d}","\frac{g^3 (a+b x)^4 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{4 b}+\frac{B g^3 x (b c-a d)^3}{4 d^3}-\frac{B g^3 (a+b x)^2 (b c-a d)^2}{8 b d^2}-\frac{B g^3 (b c-a d)^4 \log (c+d x)}{4 b d^4}+\frac{B g^3 (a+b x)^3 (b c-a d)}{12 b d}",1,"(B*(b*c - a*d)^3*g^3*x)/(4*d^3) - (B*(b*c - a*d)^2*g^3*(a + b*x)^2)/(8*b*d^2) + (B*(b*c - a*d)*g^3*(a + b*x)^3)/(12*b*d) - (B*(b*c - a*d)^4*g^3*Log[c + d*x])/(4*b*d^4) + (g^3*(a + b*x)^4*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(4*b)","A",4,3,30,0.1000,1,"{2525, 12, 43}"
175,1,118,0,0.0806846,"\int (a g+b g x)^2 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right) \, dx","Int[(a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)]),x]","\frac{g^2 (a+b x)^3 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{3 b}-\frac{B g^2 x (b c-a d)^2}{3 d^2}+\frac{B g^2 (b c-a d)^3 \log (c+d x)}{3 b d^3}+\frac{B g^2 (a+b x)^2 (b c-a d)}{6 b d}","\frac{g^2 (a+b x)^3 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{3 b}-\frac{B g^2 x (b c-a d)^2}{3 d^2}+\frac{B g^2 (b c-a d)^3 \log (c+d x)}{3 b d^3}+\frac{B g^2 (a+b x)^2 (b c-a d)}{6 b d}",1,"-(B*(b*c - a*d)^2*g^2*x)/(3*d^2) + (B*(b*c - a*d)*g^2*(a + b*x)^2)/(6*b*d) + (B*(b*c - a*d)^3*g^2*Log[c + d*x])/(3*b*d^3) + (g^2*(a + b*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(3*b)","A",4,3,30,0.1000,1,"{2525, 12, 43}"
176,1,81,0,0.0547031,"\int (a g+b g x) \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right) \, dx","Int[(a*g + b*g*x)*(A + B*Log[(e*(c + d*x))/(a + b*x)]),x]","\frac{g (a+b x)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{2 b}-\frac{B g (b c-a d)^2 \log (c+d x)}{2 b d^2}+\frac{B g x (b c-a d)}{2 d}","\frac{g (a+b x)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{2 b}-\frac{B g (b c-a d)^2 \log (c+d x)}{2 b d^2}+\frac{B g x (b c-a d)}{2 d}",1,"(B*(b*c - a*d)*g*x)/(2*d) - (B*(b*c - a*d)^2*g*Log[c + d*x])/(2*b*d^2) + (g*(a + b*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(2*b)","A",4,3,28,0.1071,1,"{2525, 12, 43}"
177,1,122,0,0.211494,"\int \frac{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)}{a g+b g x} \, dx","Int[(A + B*Log[(e*(c + d*x))/(a + b*x)])/(a*g + b*g*x),x]","-\frac{B \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g}+\frac{\log (a g+b g x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{b g}-\frac{B \log (a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}+\frac{B \log ^2(g (a+b x))}{2 b g}","-\frac{B \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{b g}-\frac{\log \left(-\frac{b c-a d}{d (a+b x)}\right) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{b g}",1,"(B*Log[g*(a + b*x)]^2)/(2*b*g) - (B*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x])/(b*g) + ((A + B*Log[(e*(c + d*x))/(a + b*x)])*Log[a*g + b*g*x])/(b*g) - (B*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g)","A",10,8,30,0.2667,1,"{2524, 12, 2418, 2390, 2301, 2394, 2393, 2391}"
178,1,101,0,0.0767233,"\int \frac{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)}{(a g+b g x)^2} \, dx","Int[(A + B*Log[(e*(c + d*x))/(a + b*x)])/(a*g + b*g*x)^2,x]","-\frac{B \log \left(\frac{e (c+d x)}{a+b x}\right)+A}{b g^2 (a+b x)}+\frac{B d \log (a+b x)}{b g^2 (b c-a d)}-\frac{B d \log (c+d x)}{b g^2 (b c-a d)}+\frac{B}{b g^2 (a+b x)}","-\frac{A-B}{b g^2 (a+b x)}-\frac{B (c+d x) \log \left(\frac{e (c+d x)}{a+b x}\right)}{g^2 (a+b x) (b c-a d)}",1,"B/(b*g^2*(a + b*x)) + (B*d*Log[a + b*x])/(b*(b*c - a*d)*g^2) - (B*d*Log[c + d*x])/(b*(b*c - a*d)*g^2) - (A + B*Log[(e*(c + d*x))/(a + b*x)])/(b*g^2*(a + b*x))","A",4,3,30,0.1000,1,"{2525, 12, 44}"
179,1,144,0,0.1041021,"\int \frac{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)}{(a g+b g x)^3} \, dx","Int[(A + B*Log[(e*(c + d*x))/(a + b*x)])/(a*g + b*g*x)^3,x]","-\frac{B \log \left(\frac{e (c+d x)}{a+b x}\right)+A}{2 b g^3 (a+b x)^2}-\frac{B d^2 \log (a+b x)}{2 b g^3 (b c-a d)^2}+\frac{B d^2 \log (c+d x)}{2 b g^3 (b c-a d)^2}-\frac{B d}{2 b g^3 (a+b x) (b c-a d)}+\frac{B}{4 b g^3 (a+b x)^2}","-\frac{B \log \left(\frac{e (c+d x)}{a+b x}\right)+A}{2 b g^3 (a+b x)^2}-\frac{B d^2 \log (a+b x)}{2 b g^3 (b c-a d)^2}+\frac{B d^2 \log (c+d x)}{2 b g^3 (b c-a d)^2}-\frac{B d}{2 b g^3 (a+b x) (b c-a d)}+\frac{B}{4 b g^3 (a+b x)^2}",1,"B/(4*b*g^3*(a + b*x)^2) - (B*d)/(2*b*(b*c - a*d)*g^3*(a + b*x)) - (B*d^2*Log[a + b*x])/(2*b*(b*c - a*d)^2*g^3) + (B*d^2*Log[c + d*x])/(2*b*(b*c - a*d)^2*g^3) - (A + B*Log[(e*(c + d*x))/(a + b*x)])/(2*b*g^3*(a + b*x)^2)","A",4,3,30,0.1000,1,"{2525, 12, 44}"
180,1,175,0,0.1311358,"\int \frac{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)}{(a g+b g x)^4} \, dx","Int[(A + B*Log[(e*(c + d*x))/(a + b*x)])/(a*g + b*g*x)^4,x]","-\frac{B \log \left(\frac{e (c+d x)}{a+b x}\right)+A}{3 b g^4 (a+b x)^3}+\frac{B d^2}{3 b g^4 (a+b x) (b c-a d)^2}+\frac{B d^3 \log (a+b x)}{3 b g^4 (b c-a d)^3}-\frac{B d^3 \log (c+d x)}{3 b g^4 (b c-a d)^3}-\frac{B d}{6 b g^4 (a+b x)^2 (b c-a d)}+\frac{B}{9 b g^4 (a+b x)^3}","-\frac{B \log \left(\frac{e (c+d x)}{a+b x}\right)+A}{3 b g^4 (a+b x)^3}+\frac{B d^2}{3 b g^4 (a+b x) (b c-a d)^2}+\frac{B d^3 \log (a+b x)}{3 b g^4 (b c-a d)^3}-\frac{B d^3 \log (c+d x)}{3 b g^4 (b c-a d)^3}-\frac{B d}{6 b g^4 (a+b x)^2 (b c-a d)}+\frac{B}{9 b g^4 (a+b x)^3}",1,"B/(9*b*g^4*(a + b*x)^3) - (B*d)/(6*b*(b*c - a*d)*g^4*(a + b*x)^2) + (B*d^2)/(3*b*(b*c - a*d)^2*g^4*(a + b*x)) + (B*d^3*Log[a + b*x])/(3*b*(b*c - a*d)^3*g^4) - (B*d^3*Log[c + d*x])/(3*b*(b*c - a*d)^3*g^4) - (A + B*Log[(e*(c + d*x))/(a + b*x)])/(3*b*g^4*(a + b*x)^3)","A",4,3,30,0.1000,1,"{2525, 12, 44}"
181,1,206,0,0.1486404,"\int \frac{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)}{(a g+b g x)^5} \, dx","Int[(A + B*Log[(e*(c + d*x))/(a + b*x)])/(a*g + b*g*x)^5,x]","-\frac{B \log \left(\frac{e (c+d x)}{a+b x}\right)+A}{4 b g^5 (a+b x)^4}-\frac{B d^3}{4 b g^5 (a+b x) (b c-a d)^3}+\frac{B d^2}{8 b g^5 (a+b x)^2 (b c-a d)^2}-\frac{B d^4 \log (a+b x)}{4 b g^5 (b c-a d)^4}+\frac{B d^4 \log (c+d x)}{4 b g^5 (b c-a d)^4}-\frac{B d}{12 b g^5 (a+b x)^3 (b c-a d)}+\frac{B}{16 b g^5 (a+b x)^4}","-\frac{B \log \left(\frac{e (c+d x)}{a+b x}\right)+A}{4 b g^5 (a+b x)^4}-\frac{B d^3}{4 b g^5 (a+b x) (b c-a d)^3}+\frac{B d^2}{8 b g^5 (a+b x)^2 (b c-a d)^2}-\frac{B d^4 \log (a+b x)}{4 b g^5 (b c-a d)^4}+\frac{B d^4 \log (c+d x)}{4 b g^5 (b c-a d)^4}-\frac{B d}{12 b g^5 (a+b x)^3 (b c-a d)}+\frac{B}{16 b g^5 (a+b x)^4}",1,"B/(16*b*g^5*(a + b*x)^4) - (B*d)/(12*b*(b*c - a*d)*g^5*(a + b*x)^3) + (B*d^2)/(8*b*(b*c - a*d)^2*g^5*(a + b*x)^2) - (B*d^3)/(4*b*(b*c - a*d)^3*g^5*(a + b*x)) - (B*d^4*Log[a + b*x])/(4*b*(b*c - a*d)^4*g^5) + (B*d^4*Log[c + d*x])/(4*b*(b*c - a*d)^4*g^5) - (A + B*Log[(e*(c + d*x))/(a + b*x)])/(4*b*g^5*(a + b*x)^4)","A",4,3,30,0.1000,1,"{2525, 12, 44}"
182,1,557,0,0.8182759,"\int (a g+b g x)^4 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2 \, dx","Int[(a*g + b*g*x)^4*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2,x]","\frac{2 B^2 g^4 (b c-a d)^5 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{5 b d^5}+\frac{2 B g^4 (b c-a d)^5 \log (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{5 b d^5}+\frac{B g^4 (a+b x)^2 (b c-a d)^3 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{5 b d^3}-\frac{2 B g^4 (a+b x)^3 (b c-a d)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{15 b d^2}-\frac{2 A B g^4 x (b c-a d)^4}{5 d^4}+\frac{B g^4 (a+b x)^4 (b c-a d) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{10 b d}+\frac{g^4 (a+b x)^5 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{5 b}-\frac{2 B^2 g^4 (a+b x) (b c-a d)^4 \log \left(\frac{e (c+d x)}{a+b x}\right)}{5 b d^4}+\frac{13 B^2 g^4 x (b c-a d)^4}{30 d^4}-\frac{7 B^2 g^4 (a+b x)^2 (b c-a d)^3}{60 b d^3}+\frac{B^2 g^4 (a+b x)^3 (b c-a d)^2}{30 b d^2}-\frac{B^2 g^4 (b c-a d)^5 \log ^2(c+d x)}{5 b d^5}-\frac{5 B^2 g^4 (b c-a d)^5 \log (c+d x)}{6 b d^5}+\frac{2 B^2 g^4 (b c-a d)^5 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{5 b d^5}","\frac{2 B^2 g^4 (b c-a d)^5 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{5 b d^5}-\frac{2 B g^4 (b c-a d)^5 \log \left(1-\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{5 b d^5}-\frac{2 B g^4 (c+d x) (b c-a d)^4 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{5 d^5}+\frac{B g^4 (a+b x)^2 (b c-a d)^3 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{5 b d^3}-\frac{2 B g^4 (a+b x)^3 (b c-a d)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{15 b d^2}+\frac{B g^4 (a+b x)^4 (b c-a d) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{10 b d}+\frac{g^4 (a+b x)^5 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{5 b}+\frac{13 B^2 g^4 x (b c-a d)^4}{30 d^4}-\frac{7 B^2 g^4 (a+b x)^2 (b c-a d)^3}{60 b d^3}+\frac{B^2 g^4 (a+b x)^3 (b c-a d)^2}{30 b d^2}-\frac{5 B^2 g^4 (b c-a d)^5 \log (a+b x)}{6 b d^5}-\frac{13 B^2 g^4 (b c-a d)^5 \log \left(\frac{c+d x}{a+b x}\right)}{30 b d^5}",1,"(-2*A*B*(b*c - a*d)^4*g^4*x)/(5*d^4) + (13*B^2*(b*c - a*d)^4*g^4*x)/(30*d^4) - (7*B^2*(b*c - a*d)^3*g^4*(a + b*x)^2)/(60*b*d^3) + (B^2*(b*c - a*d)^2*g^4*(a + b*x)^3)/(30*b*d^2) - (5*B^2*(b*c - a*d)^5*g^4*Log[c + d*x])/(6*b*d^5) + (2*B^2*(b*c - a*d)^5*g^4*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(5*b*d^5) - (B^2*(b*c - a*d)^5*g^4*Log[c + d*x]^2)/(5*b*d^5) - (2*B^2*(b*c - a*d)^4*g^4*(a + b*x)*Log[(e*(c + d*x))/(a + b*x)])/(5*b*d^4) + (B*(b*c - a*d)^3*g^4*(a + b*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(5*b*d^3) - (2*B*(b*c - a*d)^2*g^4*(a + b*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(15*b*d^2) + (B*(b*c - a*d)*g^4*(a + b*x)^4*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(10*b*d) + (2*B*(b*c - a*d)^5*g^4*Log[c + d*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(5*b*d^5) + (g^4*(a + b*x)^5*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2)/(5*b) + (2*B^2*(b*c - a*d)^5*g^4*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(5*b*d^5)","A",28,13,32,0.4062,1,"{2525, 12, 2528, 2486, 31, 43, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
183,1,474,0,0.6481437,"\int (a g+b g x)^3 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2 \, dx","Int[(a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2,x]","-\frac{B^2 g^3 (b c-a d)^4 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{2 b d^4}-\frac{B g^3 (b c-a d)^4 \log (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{2 b d^4}-\frac{B g^3 (a+b x)^2 (b c-a d)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{4 b d^2}+\frac{A B g^3 x (b c-a d)^3}{2 d^3}+\frac{B g^3 (a+b x)^3 (b c-a d) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{6 b d}+\frac{g^3 (a+b x)^4 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{4 b}+\frac{B^2 g^3 (a+b x) (b c-a d)^3 \log \left(\frac{e (c+d x)}{a+b x}\right)}{2 b d^3}-\frac{5 B^2 g^3 x (b c-a d)^3}{12 d^3}+\frac{B^2 g^3 (a+b x)^2 (b c-a d)^2}{12 b d^2}+\frac{B^2 g^3 (b c-a d)^4 \log ^2(c+d x)}{4 b d^4}+\frac{11 B^2 g^3 (b c-a d)^4 \log (c+d x)}{12 b d^4}-\frac{B^2 g^3 (b c-a d)^4 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{2 b d^4}","-\frac{B^2 g^3 (b c-a d)^4 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{2 b d^4}+\frac{B g^3 (b c-a d)^4 \log \left(1-\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{2 b d^4}+\frac{B g^3 (c+d x) (b c-a d)^3 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{2 d^4}-\frac{B g^3 (a+b x)^2 (b c-a d)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{4 b d^2}+\frac{B g^3 (a+b x)^3 (b c-a d) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{6 b d}+\frac{g^3 (a+b x)^4 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{4 b}-\frac{5 B^2 g^3 x (b c-a d)^3}{12 d^3}+\frac{B^2 g^3 (a+b x)^2 (b c-a d)^2}{12 b d^2}+\frac{11 B^2 g^3 (b c-a d)^4 \log (a+b x)}{12 b d^4}+\frac{5 B^2 g^3 (b c-a d)^4 \log \left(\frac{c+d x}{a+b x}\right)}{12 b d^4}",1,"(A*B*(b*c - a*d)^3*g^3*x)/(2*d^3) - (5*B^2*(b*c - a*d)^3*g^3*x)/(12*d^3) + (B^2*(b*c - a*d)^2*g^3*(a + b*x)^2)/(12*b*d^2) + (11*B^2*(b*c - a*d)^4*g^3*Log[c + d*x])/(12*b*d^4) - (B^2*(b*c - a*d)^4*g^3*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(2*b*d^4) + (B^2*(b*c - a*d)^4*g^3*Log[c + d*x]^2)/(4*b*d^4) + (B^2*(b*c - a*d)^3*g^3*(a + b*x)*Log[(e*(c + d*x))/(a + b*x)])/(2*b*d^3) - (B*(b*c - a*d)^2*g^3*(a + b*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(4*b*d^2) + (B*(b*c - a*d)*g^3*(a + b*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(6*b*d) - (B*(b*c - a*d)^4*g^3*Log[c + d*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(2*b*d^4) + (g^3*(a + b*x)^4*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2)/(4*b) - (B^2*(b*c - a*d)^4*g^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*b*d^4)","A",24,13,32,0.4062,1,"{2525, 12, 2528, 2486, 31, 43, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
184,1,389,0,0.5559077,"\int (a g+b g x)^2 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2 \, dx","Int[(a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2,x]","\frac{2 B^2 g^2 (b c-a d)^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 b d^3}+\frac{2 B g^2 (b c-a d)^3 \log (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{3 b d^3}-\frac{2 A B g^2 x (b c-a d)^2}{3 d^2}+\frac{B g^2 (a+b x)^2 (b c-a d) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{3 b d}+\frac{g^2 (a+b x)^3 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{3 b}-\frac{2 B^2 g^2 (a+b x) (b c-a d)^2 \log \left(\frac{e (c+d x)}{a+b x}\right)}{3 b d^2}+\frac{B^2 g^2 x (b c-a d)^2}{3 d^2}-\frac{B^2 g^2 (b c-a d)^3 \log ^2(c+d x)}{3 b d^3}-\frac{B^2 g^2 (b c-a d)^3 \log (c+d x)}{b d^3}+\frac{2 B^2 g^2 (b c-a d)^3 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 b d^3}","\frac{2 B^2 g^2 (b c-a d)^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{3 b d^3}-\frac{2 B g^2 (b c-a d)^3 \log \left(1-\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{3 b d^3}-\frac{2 B g^2 (c+d x) (b c-a d)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{3 d^3}+\frac{B g^2 (a+b x)^2 (b c-a d) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{3 b d}+\frac{g^2 (a+b x)^3 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{3 b}+\frac{B^2 g^2 x (b c-a d)^2}{3 d^2}-\frac{B^2 g^2 (b c-a d)^3 \log (a+b x)}{b d^3}-\frac{B^2 g^2 (b c-a d)^3 \log \left(\frac{c+d x}{a+b x}\right)}{3 b d^3}",1,"(-2*A*B*(b*c - a*d)^2*g^2*x)/(3*d^2) + (B^2*(b*c - a*d)^2*g^2*x)/(3*d^2) - (B^2*(b*c - a*d)^3*g^2*Log[c + d*x])/(b*d^3) + (2*B^2*(b*c - a*d)^3*g^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*b*d^3) - (B^2*(b*c - a*d)^3*g^2*Log[c + d*x]^2)/(3*b*d^3) - (2*B^2*(b*c - a*d)^2*g^2*(a + b*x)*Log[(e*(c + d*x))/(a + b*x)])/(3*b*d^2) + (B*(b*c - a*d)*g^2*(a + b*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(3*b*d) + (2*B*(b*c - a*d)^3*g^2*Log[c + d*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(3*b*d^3) + (g^2*(a + b*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2)/(3*b) + (2*B^2*(b*c - a*d)^3*g^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*b*d^3)","A",20,13,32,0.4062,1,"{2525, 12, 2528, 2486, 31, 43, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
185,1,284,0,0.4176749,"\int (a g+b g x) \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2 \, dx","Int[(a*g + b*g*x)*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2,x]","-\frac{B^2 g (b c-a d)^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b d^2}-\frac{B g (b c-a d)^2 \log (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{b d^2}+\frac{g (a+b x)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{2 b}+\frac{A B g x (b c-a d)}{d}+\frac{B^2 g (b c-a d)^2 \log ^2(c+d x)}{2 b d^2}+\frac{B^2 g (b c-a d)^2 \log (c+d x)}{b d^2}-\frac{B^2 g (b c-a d)^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b d^2}+\frac{B^2 g (a+b x) (b c-a d) \log \left(\frac{e (c+d x)}{a+b x}\right)}{b d}","-\frac{B^2 g (b c-a d)^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}+\frac{B g (b c-a d)^2 \log \left(1-\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{b d^2}+\frac{B g (c+d x) (b c-a d) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{d^2}+\frac{g (a+b x)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{2 b}+\frac{B^2 g (b c-a d)^2 \log (a+b x)}{b d^2}",1,"(A*B*(b*c - a*d)*g*x)/d + (B^2*(b*c - a*d)^2*g*Log[c + d*x])/(b*d^2) - (B^2*(b*c - a*d)^2*g*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*d^2) + (B^2*(b*c - a*d)^2*g*Log[c + d*x]^2)/(2*b*d^2) + (B^2*(b*c - a*d)*g*(a + b*x)*Log[(e*(c + d*x))/(a + b*x)])/(b*d) - (B*(b*c - a*d)^2*g*Log[c + d*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(b*d^2) + (g*(a + b*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2)/(2*b) - (B^2*(b*c - a*d)^2*g*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*d^2)","A",16,12,30,0.4000,1,"{2525, 12, 2528, 2486, 31, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
186,1,719,0,4.42328,"\int \frac{\left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2}{a g+b g x} \, dx","Int[(A + B*Log[(e*(c + d*x))/(a + b*x)])^2/(a*g + b*g*x),x]","-\frac{2 A B \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g}+\frac{2 B^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) \left(-\log \left(\frac{e (c+d x)}{a+b x}\right)+\log \left(\frac{1}{a+b x}\right)+\log (c+d x)\right)}{b g}-\frac{2 B^2 \text{PolyLog}\left(3,-\frac{d (a+b x)}{b c-a d}\right)}{b g}-\frac{2 B^2 \text{PolyLog}\left(3,\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{2 B^2 \log \left(\frac{1}{a+b x}\right) \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g}+\frac{2 B^2 \log (c+d x) \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g}+\frac{\log (a g+b g x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{b g}-\frac{2 A B \log (a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}+\frac{A B \log ^2(g (a+b x))}{b g}+\frac{B^2 \log ^2(a g+b g x) \log \left(\frac{e (c+d x)}{a+b x}\right)}{b g}+\frac{2 B^2 \log (a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right) \left(-\log \left(\frac{e (c+d x)}{a+b x}\right)+\log \left(\frac{1}{a+b x}\right)+\log (c+d x)\right)}{b g}-\frac{B^2 \log (c+d x) \log ^2(g (a+b x))}{b g}+\frac{B^2 \log ^2(g (a+b x)) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{B^2 \log ^2(c+d x) \log (g (a+b x))}{b g}+\frac{B^2 \log ^2(c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g}-\frac{B^2 \log ^2(a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{B^2 \log ^2\left(\frac{1}{a+b x}\right) \log (c+d x)}{b g}+\frac{B^2 \log ^2\left(\frac{1}{a+b x}\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{2 B^2 \log \left(\frac{1}{a+b x}\right) \log (c+d x) \log (g (a+b x))}{b g}+\frac{B^2 \log ^3(g (a+b x))}{3 b g}","-\frac{2 B \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{b g}+\frac{2 B^2 \text{PolyLog}\left(3,\frac{b (c+d x)}{d (a+b x)}\right)}{b g}-\frac{\log \left(-\frac{b c-a d}{d (a+b x)}\right) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{b g}",1,"(A*B*Log[g*(a + b*x)]^2)/(b*g) + (B^2*Log[g*(a + b*x)]^3)/(3*b*g) - (B^2*Log[(a + b*x)^(-1)]^2*Log[c + d*x])/(b*g) - (2*B^2*Log[(a + b*x)^(-1)]*Log[g*(a + b*x)]*Log[c + d*x])/(b*g) - (B^2*Log[g*(a + b*x)]^2*Log[c + d*x])/(b*g) + (B^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x]^2)/(b*g) - (B^2*Log[g*(a + b*x)]*Log[c + d*x]^2)/(b*g) + (B^2*Log[(a + b*x)^(-1)]^2*Log[(b*(c + d*x))/(b*c - a*d)])/(b*g) + (B^2*Log[g*(a + b*x)]^2*Log[(b*(c + d*x))/(b*c - a*d)])/(b*g) - (2*A*B*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x])/(b*g) + (2*B^2*Log[(b*(c + d*x))/(b*c - a*d)]*(Log[(a + b*x)^(-1)] + Log[c + d*x] - Log[(e*(c + d*x))/(a + b*x)])*Log[a*g + b*g*x])/(b*g) + ((A + B*Log[(e*(c + d*x))/(a + b*x)])^2*Log[a*g + b*g*x])/(b*g) - (B^2*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x]^2)/(b*g) + (B^2*Log[(e*(c + d*x))/(a + b*x)]*Log[a*g + b*g*x]^2)/(b*g) - (2*A*B*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g) - (2*B^2*Log[(a + b*x)^(-1)]*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g) + (2*B^2*(Log[(a + b*x)^(-1)] + Log[c + d*x] - Log[(e*(c + d*x))/(a + b*x)])*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g) + (2*B^2*Log[c + d*x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*g) - (2*B^2*PolyLog[3, -((d*(a + b*x))/(b*c - a*d))])/(b*g) - (2*B^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])/(b*g)","B",47,24,32,0.7500,1,"{2524, 12, 2528, 2418, 2390, 2301, 2394, 2393, 2391, 6691, 6741, 6742, 2499, 2302, 30, 2396, 2433, 2374, 6589, 2500, 2440, 2434, 2375, 2317}"
187,1,470,0,0.7621864,"\int \frac{\left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2}{(a g+b g x)^2} \, dx","Int[(A + B*Log[(e*(c + d*x))/(a + b*x)])^2/(a*g + b*g*x)^2,x]","-\frac{2 B^2 d \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g^2 (b c-a d)}-\frac{2 B^2 d \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g^2 (b c-a d)}+\frac{2 B d \log (a+b x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{b g^2 (b c-a d)}-\frac{2 B d \log (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{b g^2 (b c-a d)}+\frac{2 B \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{b g^2 (a+b x)}-\frac{\left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{b g^2 (a+b x)}+\frac{B^2 d \log ^2(a+b x)}{b g^2 (b c-a d)}+\frac{B^2 d \log ^2(c+d x)}{b g^2 (b c-a d)}-\frac{2 B^2 d \log (a+b x)}{b g^2 (b c-a d)}-\frac{2 B^2 d \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g^2 (b c-a d)}+\frac{2 B^2 d \log (c+d x)}{b g^2 (b c-a d)}-\frac{2 B^2 d \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g^2 (b c-a d)}-\frac{2 B^2}{b g^2 (a+b x)}","-\frac{(c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{g^2 (a+b x) (b c-a d)}+\frac{2 A B (c+d x)}{g^2 (a+b x) (b c-a d)}+\frac{2 B^2 (c+d x) \log \left(\frac{e (c+d x)}{a+b x}\right)}{g^2 (a+b x) (b c-a d)}-\frac{2 B^2 (c+d x)}{g^2 (a+b x) (b c-a d)}",1,"(-2*B^2)/(b*g^2*(a + b*x)) - (2*B^2*d*Log[a + b*x])/(b*(b*c - a*d)*g^2) + (B^2*d*Log[a + b*x]^2)/(b*(b*c - a*d)*g^2) + (2*B^2*d*Log[c + d*x])/(b*(b*c - a*d)*g^2) - (2*B^2*d*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*(b*c - a*d)*g^2) + (B^2*d*Log[c + d*x]^2)/(b*(b*c - a*d)*g^2) - (2*B^2*d*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)*g^2) + (2*B*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(b*g^2*(a + b*x)) + (2*B*d*Log[a + b*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(b*(b*c - a*d)*g^2) - (2*B*d*Log[c + d*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(b*(b*c - a*d)*g^2) - (A + B*Log[(e*(c + d*x))/(a + b*x)])^2/(b*g^2*(a + b*x)) - (2*B^2*d*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*(b*c - a*d)*g^2) - (2*B^2*d*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)*g^2)","C",26,11,32,0.3438,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
188,1,578,0,0.9104128,"\int \frac{\left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2}{(a g+b g x)^3} \, dx","Int[(A + B*Log[(e*(c + d*x))/(a + b*x)])^2/(a*g + b*g*x)^3,x]","\frac{B^2 d^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}+\frac{B^2 d^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}-\frac{B d^2 \log (a+b x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{b g^3 (b c-a d)^2}+\frac{B d^2 \log (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{b g^3 (b c-a d)^2}-\frac{B d \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{b g^3 (a+b x) (b c-a d)}+\frac{B \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{2 b g^3 (a+b x)^2}-\frac{\left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{2 b g^3 (a+b x)^2}-\frac{B^2 d^2 \log ^2(a+b x)}{2 b g^3 (b c-a d)^2}-\frac{B^2 d^2 \log ^2(c+d x)}{2 b g^3 (b c-a d)^2}+\frac{3 B^2 d^2 \log (a+b x)}{2 b g^3 (b c-a d)^2}+\frac{B^2 d^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}-\frac{3 B^2 d^2 \log (c+d x)}{2 b g^3 (b c-a d)^2}+\frac{B^2 d^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}+\frac{3 B^2 d}{2 b g^3 (a+b x) (b c-a d)}-\frac{B^2}{4 b g^3 (a+b x)^2}","\frac{b B (c+d x)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{2 g^3 (a+b x)^2 (b c-a d)^2}-\frac{b (c+d x)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{2 g^3 (a+b x)^2 (b c-a d)^2}+\frac{d (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{g^3 (a+b x) (b c-a d)^2}-\frac{2 A B d (c+d x)}{g^3 (a+b x) (b c-a d)^2}-\frac{2 B^2 d (c+d x) \log \left(\frac{e (c+d x)}{a+b x}\right)}{g^3 (a+b x) (b c-a d)^2}-\frac{b B^2 (c+d x)^2}{4 g^3 (a+b x)^2 (b c-a d)^2}+\frac{2 B^2 d (c+d x)}{g^3 (a+b x) (b c-a d)^2}",1,"-B^2/(4*b*g^3*(a + b*x)^2) + (3*B^2*d)/(2*b*(b*c - a*d)*g^3*(a + b*x)) + (3*B^2*d^2*Log[a + b*x])/(2*b*(b*c - a*d)^2*g^3) - (B^2*d^2*Log[a + b*x]^2)/(2*b*(b*c - a*d)^2*g^3) - (3*B^2*d^2*Log[c + d*x])/(2*b*(b*c - a*d)^2*g^3) + (B^2*d^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*(b*c - a*d)^2*g^3) - (B^2*d^2*Log[c + d*x]^2)/(2*b*(b*c - a*d)^2*g^3) + (B^2*d^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)^2*g^3) + (B*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(2*b*g^3*(a + b*x)^2) - (B*d*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(b*(b*c - a*d)*g^3*(a + b*x)) - (B*d^2*Log[a + b*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(b*(b*c - a*d)^2*g^3) + (B*d^2*Log[c + d*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(b*(b*c - a*d)^2*g^3) - (A + B*Log[(e*(c + d*x))/(a + b*x)])^2/(2*b*g^3*(a + b*x)^2) + (B^2*d^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*(b*c - a*d)^2*g^3) + (B^2*d^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)^2*g^3)","C",30,11,32,0.3438,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
189,1,680,0,1.0740599,"\int \frac{\left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2}{(a g+b g x)^4} \, dx","Int[(A + B*Log[(e*(c + d*x))/(a + b*x)])^2/(a*g + b*g*x)^4,x]","-\frac{2 B^2 d^3 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}-\frac{2 B^2 d^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}+\frac{2 B d^3 \log (a+b x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{3 b g^4 (b c-a d)^3}-\frac{2 B d^3 \log (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{3 b g^4 (b c-a d)^3}+\frac{2 B d^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{3 b g^4 (a+b x) (b c-a d)^2}-\frac{B d \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{3 b g^4 (a+b x)^2 (b c-a d)}-\frac{\left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{3 b g^4 (a+b x)^3}+\frac{2 B \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{9 b g^4 (a+b x)^3}-\frac{11 B^2 d^2}{9 b g^4 (a+b x) (b c-a d)^2}+\frac{B^2 d^3 \log ^2(a+b x)}{3 b g^4 (b c-a d)^3}+\frac{B^2 d^3 \log ^2(c+d x)}{3 b g^4 (b c-a d)^3}-\frac{11 B^2 d^3 \log (a+b x)}{9 b g^4 (b c-a d)^3}-\frac{2 B^2 d^3 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}+\frac{11 B^2 d^3 \log (c+d x)}{9 b g^4 (b c-a d)^3}-\frac{2 B^2 d^3 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}+\frac{5 B^2 d}{18 b g^4 (a+b x)^2 (b c-a d)}-\frac{2 B^2}{27 b g^4 (a+b x)^3}","\frac{2 b^2 B (c+d x)^3 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{9 g^4 (a+b x)^3 (b c-a d)^3}-\frac{2 B d^3 \log \left(\frac{c+d x}{a+b x}\right) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{3 b g^4 (b c-a d)^3}+\frac{2 B d^2 (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{g^4 (a+b x) (b c-a d)^3}-\frac{b B d (c+d x)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{g^4 (a+b x)^2 (b c-a d)^3}-\frac{\left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{3 b g^4 (a+b x)^3}-\frac{2 b^2 B^2 (c+d x)^3}{27 g^4 (a+b x)^3 (b c-a d)^3}-\frac{2 B^2 d^2 (c+d x)}{g^4 (a+b x) (b c-a d)^3}+\frac{B^2 d^3 \log ^2\left(\frac{c+d x}{a+b x}\right)}{3 b g^4 (b c-a d)^3}+\frac{b B^2 d (c+d x)^2}{2 g^4 (a+b x)^2 (b c-a d)^3}",1,"(-2*B^2)/(27*b*g^4*(a + b*x)^3) + (5*B^2*d)/(18*b*(b*c - a*d)*g^4*(a + b*x)^2) - (11*B^2*d^2)/(9*b*(b*c - a*d)^2*g^4*(a + b*x)) - (11*B^2*d^3*Log[a + b*x])/(9*b*(b*c - a*d)^3*g^4) + (B^2*d^3*Log[a + b*x]^2)/(3*b*(b*c - a*d)^3*g^4) + (11*B^2*d^3*Log[c + d*x])/(9*b*(b*c - a*d)^3*g^4) - (2*B^2*d^3*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*b*(b*c - a*d)^3*g^4) + (B^2*d^3*Log[c + d*x]^2)/(3*b*(b*c - a*d)^3*g^4) - (2*B^2*d^3*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3*b*(b*c - a*d)^3*g^4) + (2*B*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(9*b*g^4*(a + b*x)^3) - (B*d*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(3*b*(b*c - a*d)*g^4*(a + b*x)^2) + (2*B*d^2*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(3*b*(b*c - a*d)^2*g^4*(a + b*x)) + (2*B*d^3*Log[a + b*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(3*b*(b*c - a*d)^3*g^4) - (2*B*d^3*Log[c + d*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(3*b*(b*c - a*d)^3*g^4) - (A + B*Log[(e*(c + d*x))/(a + b*x)])^2/(3*b*g^4*(a + b*x)^3) - (2*B^2*d^3*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(3*b*(b*c - a*d)^3*g^4) - (2*B^2*d^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*b*(b*c - a*d)^3*g^4)","C",34,11,32,0.3438,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
190,1,763,0,1.263717,"\int \frac{\left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2}{(a g+b g x)^5} \, dx","Int[(A + B*Log[(e*(c + d*x))/(a + b*x)])^2/(a*g + b*g*x)^5,x]","\frac{B^2 d^4 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{2 b g^5 (b c-a d)^4}+\frac{B^2 d^4 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{2 b g^5 (b c-a d)^4}-\frac{B d^4 \log (a+b x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{2 b g^5 (b c-a d)^4}+\frac{B d^4 \log (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{2 b g^5 (b c-a d)^4}-\frac{B d^3 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{2 b g^5 (a+b x) (b c-a d)^3}+\frac{B d^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{4 b g^5 (a+b x)^2 (b c-a d)^2}-\frac{B d \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{6 b g^5 (a+b x)^3 (b c-a d)}-\frac{\left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{4 b g^5 (a+b x)^4}+\frac{B \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{8 b g^5 (a+b x)^4}+\frac{25 B^2 d^3}{24 b g^5 (a+b x) (b c-a d)^3}-\frac{13 B^2 d^2}{48 b g^5 (a+b x)^2 (b c-a d)^2}-\frac{B^2 d^4 \log ^2(a+b x)}{4 b g^5 (b c-a d)^4}-\frac{B^2 d^4 \log ^2(c+d x)}{4 b g^5 (b c-a d)^4}+\frac{25 B^2 d^4 \log (a+b x)}{24 b g^5 (b c-a d)^4}+\frac{B^2 d^4 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{2 b g^5 (b c-a d)^4}-\frac{25 B^2 d^4 \log (c+d x)}{24 b g^5 (b c-a d)^4}+\frac{B^2 d^4 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{2 b g^5 (b c-a d)^4}+\frac{7 B^2 d}{72 b g^5 (a+b x)^3 (b c-a d)}-\frac{B^2}{32 b g^5 (a+b x)^4}","-\frac{2 b^2 B d (c+d x)^3 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{3 g^5 (a+b x)^3 (b c-a d)^4}+\frac{b^3 B (c+d x)^4 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{8 g^5 (a+b x)^4 (b c-a d)^4}+\frac{B d^4 \log \left(\frac{c+d x}{a+b x}\right) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{2 b g^5 (b c-a d)^4}-\frac{2 B d^3 (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{g^5 (a+b x) (b c-a d)^4}+\frac{3 b B d^2 (c+d x)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{2 g^5 (a+b x)^2 (b c-a d)^4}-\frac{\left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{4 b g^5 (a+b x)^4}+\frac{2 b^2 B^2 d (c+d x)^3}{9 g^5 (a+b x)^3 (b c-a d)^4}-\frac{b^3 B^2 (c+d x)^4}{32 g^5 (a+b x)^4 (b c-a d)^4}+\frac{2 B^2 d^3 (c+d x)}{g^5 (a+b x) (b c-a d)^4}-\frac{3 b B^2 d^2 (c+d x)^2}{4 g^5 (a+b x)^2 (b c-a d)^4}-\frac{B^2 d^4 \log ^2\left(\frac{c+d x}{a+b x}\right)}{4 b g^5 (b c-a d)^4}",1,"-B^2/(32*b*g^5*(a + b*x)^4) + (7*B^2*d)/(72*b*(b*c - a*d)*g^5*(a + b*x)^3) - (13*B^2*d^2)/(48*b*(b*c - a*d)^2*g^5*(a + b*x)^2) + (25*B^2*d^3)/(24*b*(b*c - a*d)^3*g^5*(a + b*x)) + (25*B^2*d^4*Log[a + b*x])/(24*b*(b*c - a*d)^4*g^5) - (B^2*d^4*Log[a + b*x]^2)/(4*b*(b*c - a*d)^4*g^5) - (25*B^2*d^4*Log[c + d*x])/(24*b*(b*c - a*d)^4*g^5) + (B^2*d^4*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(2*b*(b*c - a*d)^4*g^5) - (B^2*d^4*Log[c + d*x]^2)/(4*b*(b*c - a*d)^4*g^5) + (B^2*d^4*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(2*b*(b*c - a*d)^4*g^5) + (B*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(8*b*g^5*(a + b*x)^4) - (B*d*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(6*b*(b*c - a*d)*g^5*(a + b*x)^3) + (B*d^2*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(4*b*(b*c - a*d)^2*g^5*(a + b*x)^2) - (B*d^3*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(2*b*(b*c - a*d)^3*g^5*(a + b*x)) - (B*d^4*Log[a + b*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(2*b*(b*c - a*d)^4*g^5) + (B*d^4*Log[c + d*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(2*b*(b*c - a*d)^4*g^5) - (A + B*Log[(e*(c + d*x))/(a + b*x)])^2/(4*b*g^5*(a + b*x)^4) + (B^2*d^4*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(2*b*(b*c - a*d)^4*g^5) + (B^2*d^4*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*b*(b*c - a*d)^4*g^5)","C",38,11,32,0.3438,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
191,0,0,0,0.1956003,"\int \frac{(a g+b g x)^2}{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)} \, dx","Int[(a*g + b*g*x)^2/(A + B*Log[(e*(c + d*x))/(a + b*x)]),x]","\int \frac{(a g+b g x)^2}{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)} \, dx","\text{Int}\left(\frac{(a g+b g x)^2}{B \log \left(\frac{e (c+d x)}{a+b x}\right)+A},x\right)",0,"a^2*g^2*Defer[Int][(A + B*Log[(e*(c + d*x))/(a + b*x)])^(-1), x] + 2*a*b*g^2*Defer[Int][x/(A + B*Log[(e*(c + d*x))/(a + b*x)]), x] + b^2*g^2*Defer[Int][x^2/(A + B*Log[(e*(c + d*x))/(a + b*x)]), x]","A",0,0,0,0,-1,"{}"
192,0,0,0,0.1005702,"\int \frac{a g+b g x}{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)} \, dx","Int[(a*g + b*g*x)/(A + B*Log[(e*(c + d*x))/(a + b*x)]),x]","\int \frac{a g+b g x}{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)} \, dx","\text{Int}\left(\frac{a g+b g x}{B \log \left(\frac{e (c+d x)}{a+b x}\right)+A},x\right)",0,"a*g*Defer[Int][(A + B*Log[(e*(c + d*x))/(a + b*x)])^(-1), x] + b*g*Defer[Int][x/(A + B*Log[(e*(c + d*x))/(a + b*x)]), x]","A",0,0,0,0,-1,"{}"
193,0,0,0,0.0730861,"\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)} \, dx","Int[1/((a*g + b*g*x)*(A + B*Log[(e*(c + d*x))/(a + b*x)])),x]","\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{(a g+b g x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)},x\right)",0,"Defer[Int][1/((a*g + b*g*x)*(A + B*Log[(e*(c + d*x))/(a + b*x)])), x]","A",0,0,0,0,-1,"{}"
194,0,0,0,0.0858857,"\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)} \, dx","Int[1/((a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)])),x]","\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)} \, dx","-\frac{e^{-\frac{A}{B}} \text{Ei}\left(\frac{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)}{B}\right)}{B e g^2 (b c-a d)}",1,"Defer[Int][1/((a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)])), x]","F",0,0,0,0,-1,"{}"
195,0,0,0,0.0719976,"\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)} \, dx","Int[1/((a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)])),x]","\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)} \, dx","\frac{d e^{-\frac{A}{B}} \text{Ei}\left(\frac{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)}{B}\right)}{B e g^3 (b c-a d)^2}-\frac{b e^{-\frac{2 A}{B}} \text{Ei}\left(\frac{2 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)}{B}\right)}{B e^2 g^3 (b c-a d)^2}",1,"Defer[Int][1/((a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)])), x]","F",0,0,0,0,-1,"{}"
196,0,0,0,0.2063351,"\int \frac{(a g+b g x)^2}{\left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2} \, dx","Int[(a*g + b*g*x)^2/(A + B*Log[(e*(c + d*x))/(a + b*x)])^2,x]","\int \frac{(a g+b g x)^2}{\left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2} \, dx","\text{Int}\left(\frac{(a g+b g x)^2}{\left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2},x\right)",0,"a^2*g^2*Defer[Int][(A + B*Log[(e*(c + d*x))/(a + b*x)])^(-2), x] + 2*a*b*g^2*Defer[Int][x/(A + B*Log[(e*(c + d*x))/(a + b*x)])^2, x] + b^2*g^2*Defer[Int][x^2/(A + B*Log[(e*(c + d*x))/(a + b*x)])^2, x]","A",0,0,0,0,-1,"{}"
197,0,0,0,0.1060452,"\int \frac{a g+b g x}{\left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2} \, dx","Int[(a*g + b*g*x)/(A + B*Log[(e*(c + d*x))/(a + b*x)])^2,x]","\int \frac{a g+b g x}{\left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2} \, dx","\text{Int}\left(\frac{a g+b g x}{\left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2},x\right)",0,"a*g*Defer[Int][(A + B*Log[(e*(c + d*x))/(a + b*x)])^(-2), x] + b*g*Defer[Int][x/(A + B*Log[(e*(c + d*x))/(a + b*x)])^2, x]","A",0,0,0,0,-1,"{}"
198,0,0,0,0.0786841,"\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2} \, dx","Int[1/((a*g + b*g*x)*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2),x]","\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(a g+b g x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2},x\right)",0,"Defer[Int][1/((a*g + b*g*x)*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2), x]","A",0,0,0,0,-1,"{}"
199,0,0,0,0.0886496,"\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2} \, dx","Int[1/((a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2),x]","\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2} \, dx","\frac{c+d x}{B g^2 (a+b x) (b c-a d) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}-\frac{e^{-\frac{A}{B}} \text{Ei}\left(\frac{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)}{B}\right)}{B^2 e g^2 (b c-a d)}",1,"Defer[Int][1/((a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2), x]","F",0,0,0,0,-1,"{}"
200,0,0,0,0.0797503,"\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2} \, dx","Int[1/((a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2),x]","\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2} \, dx","-\frac{2 b e^{-\frac{2 A}{B}} \text{Ei}\left(\frac{2 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)}{B}\right)}{B^2 e^2 g^3 (b c-a d)^2}+\frac{d e^{-\frac{A}{B}} \text{Ei}\left(\frac{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)}{B}\right)}{B^2 e g^3 (b c-a d)^2}+\frac{c+d x}{B g^3 (a+b x)^2 (b c-a d) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}",1,"Defer[Int][1/((a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2), x]","F",0,0,0,0,-1,"{}"
201,1,182,0,0.1178559,"\int (a g+b g x)^4 \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right) \, dx","Int[(a*g + b*g*x)^4*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]),x]","\frac{g^4 (a+b x)^5 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{5 b}-\frac{2 B g^4 x (b c-a d)^4}{5 d^4}+\frac{B g^4 (a+b x)^2 (b c-a d)^3}{5 b d^3}-\frac{2 B g^4 (a+b x)^3 (b c-a d)^2}{15 b d^2}+\frac{2 B g^4 (b c-a d)^5 \log (c+d x)}{5 b d^5}+\frac{B g^4 (a+b x)^4 (b c-a d)}{10 b d}","\frac{g^4 (a+b x)^5 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{5 b}-\frac{2 B g^4 x (b c-a d)^4}{5 d^4}+\frac{B g^4 (a+b x)^2 (b c-a d)^3}{5 b d^3}-\frac{2 B g^4 (a+b x)^3 (b c-a d)^2}{15 b d^2}+\frac{2 B g^4 (b c-a d)^5 \log (c+d x)}{5 b d^5}+\frac{B g^4 (a+b x)^4 (b c-a d)}{10 b d}",1,"(-2*B*(b*c - a*d)^4*g^4*x)/(5*d^4) + (B*(b*c - a*d)^3*g^4*(a + b*x)^2)/(5*b*d^3) - (2*B*(b*c - a*d)^2*g^4*(a + b*x)^3)/(15*b*d^2) + (B*(b*c - a*d)*g^4*(a + b*x)^4)/(10*b*d) + (2*B*(b*c - a*d)^5*g^4*Log[c + d*x])/(5*b*d^5) + (g^4*(a + b*x)^5*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(5*b)","A",4,3,32,0.09375,1,"{2525, 12, 43}"
202,1,151,0,0.0982844,"\int (a g+b g x)^3 \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right) \, dx","Int[(a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]),x]","\frac{g^3 (a+b x)^4 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{4 b}+\frac{B g^3 x (b c-a d)^3}{2 d^3}-\frac{B g^3 (a+b x)^2 (b c-a d)^2}{4 b d^2}-\frac{B g^3 (b c-a d)^4 \log (c+d x)}{2 b d^4}+\frac{B g^3 (a+b x)^3 (b c-a d)}{6 b d}","\frac{g^3 (a+b x)^4 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{4 b}+\frac{B g^3 x (b c-a d)^3}{2 d^3}-\frac{B g^3 (a+b x)^2 (b c-a d)^2}{4 b d^2}-\frac{B g^3 (b c-a d)^4 \log (c+d x)}{2 b d^4}+\frac{B g^3 (a+b x)^3 (b c-a d)}{6 b d}",1,"(B*(b*c - a*d)^3*g^3*x)/(2*d^3) - (B*(b*c - a*d)^2*g^3*(a + b*x)^2)/(4*b*d^2) + (B*(b*c - a*d)*g^3*(a + b*x)^3)/(6*b*d) - (B*(b*c - a*d)^4*g^3*Log[c + d*x])/(2*b*d^4) + (g^3*(a + b*x)^4*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(4*b)","A",4,3,32,0.09375,1,"{2525, 12, 43}"
203,1,120,0,0.0783567,"\int (a g+b g x)^2 \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right) \, dx","Int[(a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]),x]","\frac{g^2 (a+b x)^3 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{3 b}-\frac{2 B g^2 x (b c-a d)^2}{3 d^2}+\frac{2 B g^2 (b c-a d)^3 \log (c+d x)}{3 b d^3}+\frac{B g^2 (a+b x)^2 (b c-a d)}{3 b d}","\frac{g^2 (a+b x)^3 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{3 b}-\frac{2 B g^2 x (b c-a d)^2}{3 d^2}+\frac{2 B g^2 (b c-a d)^3 \log (c+d x)}{3 b d^3}+\frac{B g^2 (a+b x)^2 (b c-a d)}{3 b d}",1,"(-2*B*(b*c - a*d)^2*g^2*x)/(3*d^2) + (B*(b*c - a*d)*g^2*(a + b*x)^2)/(3*b*d) + (2*B*(b*c - a*d)^3*g^2*Log[c + d*x])/(3*b*d^3) + (g^2*(a + b*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(3*b)","A",4,3,32,0.09375,1,"{2525, 12, 43}"
204,1,78,0,0.0523818,"\int (a g+b g x) \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right) \, dx","Int[(a*g + b*g*x)*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]),x]","\frac{g (a+b x)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{2 b}-\frac{B g (b c-a d)^2 \log (c+d x)}{b d^2}+\frac{B g x (b c-a d)}{d}","\frac{g (a+b x)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{2 b}-\frac{B g (b c-a d)^2 \log (c+d x)}{b d^2}+\frac{B g x (b c-a d)}{d}",1,"(B*(b*c - a*d)*g*x)/d - (B*(b*c - a*d)^2*g*Log[c + d*x])/(b*d^2) + (g*(a + b*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(2*b)","A",4,3,30,0.1000,1,"{2525, 12, 43}"
205,1,121,0,0.291895,"\int \frac{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{a g+b g x} \, dx","Int[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(a*g + b*g*x),x]","-\frac{2 B \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g}+\frac{\log (a g+b g x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b g}-\frac{2 B \log (a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}+\frac{B \log ^2(g (a+b x))}{b g}","-\frac{2 B \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{b g}-\frac{\log \left(-\frac{b c-a d}{d (a+b x)}\right) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b g}",1,"(B*Log[g*(a + b*x)]^2)/(b*g) - (2*B*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x])/(b*g) + ((A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])*Log[a*g + b*g*x])/(b*g) - (2*B*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g)","A",10,8,32,0.2500,1,"{2524, 12, 2418, 2390, 2301, 2394, 2393, 2391}"
206,1,105,0,0.07582,"\int \frac{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{(a g+b g x)^2} \, dx","Int[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(a*g + b*g*x)^2,x]","-\frac{B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A}{b g^2 (a+b x)}+\frac{2 B d \log (a+b x)}{b g^2 (b c-a d)}-\frac{2 B d \log (c+d x)}{b g^2 (b c-a d)}+\frac{2 B}{b g^2 (a+b x)}","-\frac{A (c+d x)}{g^2 (a+b x) (b c-a d)}-\frac{B (c+d x) \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{g^2 (a+b x) (b c-a d)}+\frac{2 B (c+d x)}{g^2 (a+b x) (b c-a d)}",1,"(2*B)/(b*g^2*(a + b*x)) + (2*B*d*Log[a + b*x])/(b*(b*c - a*d)*g^2) - (2*B*d*Log[c + d*x])/(b*(b*c - a*d)*g^2) - (A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(b*g^2*(a + b*x))","A",4,3,32,0.09375,1,"{2525, 12, 44}"
207,1,139,0,0.1005613,"\int \frac{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{(a g+b g x)^3} \, dx","Int[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(a*g + b*g*x)^3,x]","-\frac{B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A}{2 b g^3 (a+b x)^2}-\frac{B d^2 \log (a+b x)}{b g^3 (b c-a d)^2}+\frac{B d^2 \log (c+d x)}{b g^3 (b c-a d)^2}-\frac{B d}{b g^3 (a+b x) (b c-a d)}+\frac{B}{2 b g^3 (a+b x)^2}","-\frac{B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A}{2 b g^3 (a+b x)^2}-\frac{B d^2 \log (a+b x)}{b g^3 (b c-a d)^2}+\frac{B d^2 \log (c+d x)}{b g^3 (b c-a d)^2}-\frac{B d}{b g^3 (a+b x) (b c-a d)}+\frac{B}{2 b g^3 (a+b x)^2}",1,"B/(2*b*g^3*(a + b*x)^2) - (B*d)/(b*(b*c - a*d)*g^3*(a + b*x)) - (B*d^2*Log[a + b*x])/(b*(b*c - a*d)^2*g^3) + (B*d^2*Log[c + d*x])/(b*(b*c - a*d)^2*g^3) - (A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(2*b*g^3*(a + b*x)^2)","A",4,3,32,0.09375,1,"{2525, 12, 44}"
208,1,177,0,0.1208815,"\int \frac{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{(a g+b g x)^4} \, dx","Int[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(a*g + b*g*x)^4,x]","-\frac{B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A}{3 b g^4 (a+b x)^3}+\frac{2 B d^2}{3 b g^4 (a+b x) (b c-a d)^2}+\frac{2 B d^3 \log (a+b x)}{3 b g^4 (b c-a d)^3}-\frac{2 B d^3 \log (c+d x)}{3 b g^4 (b c-a d)^3}-\frac{B d}{3 b g^4 (a+b x)^2 (b c-a d)}+\frac{2 B}{9 b g^4 (a+b x)^3}","-\frac{B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A}{3 b g^4 (a+b x)^3}+\frac{2 B d^2}{3 b g^4 (a+b x) (b c-a d)^2}+\frac{2 B d^3 \log (a+b x)}{3 b g^4 (b c-a d)^3}-\frac{2 B d^3 \log (c+d x)}{3 b g^4 (b c-a d)^3}-\frac{B d}{3 b g^4 (a+b x)^2 (b c-a d)}+\frac{2 B}{9 b g^4 (a+b x)^3}",1,"(2*B)/(9*b*g^4*(a + b*x)^3) - (B*d)/(3*b*(b*c - a*d)*g^4*(a + b*x)^2) + (2*B*d^2)/(3*b*(b*c - a*d)^2*g^4*(a + b*x)) + (2*B*d^3*Log[a + b*x])/(3*b*(b*c - a*d)^3*g^4) - (2*B*d^3*Log[c + d*x])/(3*b*(b*c - a*d)^3*g^4) - (A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(3*b*g^4*(a + b*x)^3)","A",4,3,32,0.09375,1,"{2525, 12, 44}"
209,1,208,0,0.1427151,"\int \frac{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{(a g+b g x)^5} \, dx","Int[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(a*g + b*g*x)^5,x]","-\frac{B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A}{4 b g^5 (a+b x)^4}-\frac{B d^3}{2 b g^5 (a+b x) (b c-a d)^3}+\frac{B d^2}{4 b g^5 (a+b x)^2 (b c-a d)^2}-\frac{B d^4 \log (a+b x)}{2 b g^5 (b c-a d)^4}+\frac{B d^4 \log (c+d x)}{2 b g^5 (b c-a d)^4}-\frac{B d}{6 b g^5 (a+b x)^3 (b c-a d)}+\frac{B}{8 b g^5 (a+b x)^4}","-\frac{B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A}{4 b g^5 (a+b x)^4}-\frac{B d^3}{2 b g^5 (a+b x) (b c-a d)^3}+\frac{B d^2}{4 b g^5 (a+b x)^2 (b c-a d)^2}-\frac{B d^4 \log (a+b x)}{2 b g^5 (b c-a d)^4}+\frac{B d^4 \log (c+d x)}{2 b g^5 (b c-a d)^4}-\frac{B d}{6 b g^5 (a+b x)^3 (b c-a d)}+\frac{B}{8 b g^5 (a+b x)^4}",1,"B/(8*b*g^5*(a + b*x)^4) - (B*d)/(6*b*(b*c - a*d)*g^5*(a + b*x)^3) + (B*d^2)/(4*b*(b*c - a*d)^2*g^5*(a + b*x)^2) - (B*d^3)/(2*b*(b*c - a*d)^3*g^5*(a + b*x)) - (B*d^4*Log[a + b*x])/(2*b*(b*c - a*d)^4*g^5) + (B*d^4*Log[c + d*x])/(2*b*(b*c - a*d)^4*g^5) - (A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(4*b*g^5*(a + b*x)^4)","A",4,3,32,0.09375,1,"{2525, 12, 44}"
210,1,569,0,0.864275,"\int (a g+b g x)^4 \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2 \, dx","Int[(a*g + b*g*x)^4*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2,x]","\frac{8 B^2 g^4 (b c-a d)^5 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{5 b d^5}+\frac{4 B g^4 (b c-a d)^5 \log (c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{5 b d^5}+\frac{2 B g^4 (a+b x)^2 (b c-a d)^3 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{5 b d^3}-\frac{4 B g^4 (a+b x)^3 (b c-a d)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{15 b d^2}-\frac{4 A B g^4 x (b c-a d)^4}{5 d^4}+\frac{B g^4 (a+b x)^4 (b c-a d) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{5 b d}+\frac{g^4 (a+b x)^5 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{5 b}-\frac{4 B^2 g^4 (a+b x) (b c-a d)^4 \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{5 b d^4}+\frac{26 B^2 g^4 x (b c-a d)^4}{15 d^4}-\frac{7 B^2 g^4 (a+b x)^2 (b c-a d)^3}{15 b d^3}+\frac{2 B^2 g^4 (a+b x)^3 (b c-a d)^2}{15 b d^2}-\frac{4 B^2 g^4 (b c-a d)^5 \log ^2(c+d x)}{5 b d^5}-\frac{10 B^2 g^4 (b c-a d)^5 \log (c+d x)}{3 b d^5}+\frac{8 B^2 g^4 (b c-a d)^5 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{5 b d^5}","\frac{8 B^2 g^4 (b c-a d)^5 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{5 b d^5}-\frac{4 B g^4 (b c-a d)^5 \log \left(1-\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{5 b d^5}-\frac{4 B g^4 (c+d x) (b c-a d)^4 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{5 d^5}+\frac{2 B g^4 (a+b x)^2 (b c-a d)^3 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{5 b d^3}-\frac{4 B g^4 (a+b x)^3 (b c-a d)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{15 b d^2}+\frac{B g^4 (a+b x)^4 (b c-a d) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{5 b d}+\frac{g^4 (a+b x)^5 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{5 b}+\frac{26 B^2 g^4 x (b c-a d)^4}{15 d^4}-\frac{7 B^2 g^4 (a+b x)^2 (b c-a d)^3}{15 b d^3}+\frac{2 B^2 g^4 (a+b x)^3 (b c-a d)^2}{15 b d^2}-\frac{10 B^2 g^4 (b c-a d)^5 \log (a+b x)}{3 b d^5}-\frac{26 B^2 g^4 (b c-a d)^5 \log \left(\frac{c+d x}{a+b x}\right)}{15 b d^5}",1,"(-4*A*B*(b*c - a*d)^4*g^4*x)/(5*d^4) + (26*B^2*(b*c - a*d)^4*g^4*x)/(15*d^4) - (7*B^2*(b*c - a*d)^3*g^4*(a + b*x)^2)/(15*b*d^3) + (2*B^2*(b*c - a*d)^2*g^4*(a + b*x)^3)/(15*b*d^2) - (10*B^2*(b*c - a*d)^5*g^4*Log[c + d*x])/(3*b*d^5) + (8*B^2*(b*c - a*d)^5*g^4*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(5*b*d^5) - (4*B^2*(b*c - a*d)^5*g^4*Log[c + d*x]^2)/(5*b*d^5) - (4*B^2*(b*c - a*d)^4*g^4*(a + b*x)*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(5*b*d^4) + (2*B*(b*c - a*d)^3*g^4*(a + b*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(5*b*d^3) - (4*B*(b*c - a*d)^2*g^4*(a + b*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(15*b*d^2) + (B*(b*c - a*d)*g^4*(a + b*x)^4*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(5*b*d) + (4*B*(b*c - a*d)^5*g^4*Log[c + d*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(5*b*d^5) + (g^4*(a + b*x)^5*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2)/(5*b) + (8*B^2*(b*c - a*d)^5*g^4*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(5*b*d^5)","A",28,13,34,0.3824,1,"{2525, 12, 2528, 2486, 31, 43, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
211,1,469,0,0.7407158,"\int (a g+b g x)^3 \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2 \, dx","Int[(a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2,x]","-\frac{2 B^2 g^3 (b c-a d)^4 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b d^4}-\frac{B g^3 (b c-a d)^4 \log (c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b d^4}-\frac{B g^3 (a+b x)^2 (b c-a d)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{2 b d^2}+\frac{A B g^3 x (b c-a d)^3}{d^3}+\frac{B g^3 (a+b x)^3 (b c-a d) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{3 b d}+\frac{g^3 (a+b x)^4 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{4 b}+\frac{B^2 g^3 (a+b x) (b c-a d)^3 \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{b d^3}-\frac{5 B^2 g^3 x (b c-a d)^3}{3 d^3}+\frac{B^2 g^3 (a+b x)^2 (b c-a d)^2}{3 b d^2}+\frac{B^2 g^3 (b c-a d)^4 \log ^2(c+d x)}{b d^4}+\frac{11 B^2 g^3 (b c-a d)^4 \log (c+d x)}{3 b d^4}-\frac{2 B^2 g^3 (b c-a d)^4 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b d^4}","-\frac{2 B^2 g^3 (b c-a d)^4 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d^4}+\frac{B g^3 (b c-a d)^4 \log \left(1-\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b d^4}+\frac{B g^3 (c+d x) (b c-a d)^3 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{d^4}-\frac{B g^3 (a+b x)^2 (b c-a d)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{2 b d^2}+\frac{B g^3 (a+b x)^3 (b c-a d) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{3 b d}+\frac{g^3 (a+b x)^4 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{4 b}-\frac{5 B^2 g^3 x (b c-a d)^3}{3 d^3}+\frac{B^2 g^3 (a+b x)^2 (b c-a d)^2}{3 b d^2}+\frac{11 B^2 g^3 (b c-a d)^4 \log (a+b x)}{3 b d^4}+\frac{5 B^2 g^3 (b c-a d)^4 \log \left(\frac{c+d x}{a+b x}\right)}{3 b d^4}",1,"(A*B*(b*c - a*d)^3*g^3*x)/d^3 - (5*B^2*(b*c - a*d)^3*g^3*x)/(3*d^3) + (B^2*(b*c - a*d)^2*g^3*(a + b*x)^2)/(3*b*d^2) + (11*B^2*(b*c - a*d)^4*g^3*Log[c + d*x])/(3*b*d^4) - (2*B^2*(b*c - a*d)^4*g^3*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*d^4) + (B^2*(b*c - a*d)^4*g^3*Log[c + d*x]^2)/(b*d^4) + (B^2*(b*c - a*d)^3*g^3*(a + b*x)*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(b*d^3) - (B*(b*c - a*d)^2*g^3*(a + b*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(2*b*d^2) + (B*(b*c - a*d)*g^3*(a + b*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(3*b*d) - (B*(b*c - a*d)^4*g^3*Log[c + d*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(b*d^4) + (g^3*(a + b*x)^4*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2)/(4*b) - (2*B^2*(b*c - a*d)^4*g^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*d^4)","A",24,13,34,0.3824,1,"{2525, 12, 2528, 2486, 31, 43, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
212,1,397,0,0.625311,"\int (a g+b g x)^2 \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2 \, dx","Int[(a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2,x]","\frac{8 B^2 g^2 (b c-a d)^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 b d^3}+\frac{4 B g^2 (b c-a d)^3 \log (c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{3 b d^3}-\frac{4 A B g^2 x (b c-a d)^2}{3 d^2}+\frac{2 B g^2 (a+b x)^2 (b c-a d) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{3 b d}+\frac{g^2 (a+b x)^3 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{3 b}-\frac{4 B^2 g^2 (a+b x) (b c-a d)^2 \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{3 b d^2}+\frac{4 B^2 g^2 x (b c-a d)^2}{3 d^2}-\frac{4 B^2 g^2 (b c-a d)^3 \log ^2(c+d x)}{3 b d^3}-\frac{4 B^2 g^2 (b c-a d)^3 \log (c+d x)}{b d^3}+\frac{8 B^2 g^2 (b c-a d)^3 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 b d^3}","\frac{8 B^2 g^2 (b c-a d)^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{3 b d^3}-\frac{4 B g^2 (b c-a d)^3 \log \left(1-\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{3 b d^3}-\frac{4 B g^2 (c+d x) (b c-a d)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{3 d^3}+\frac{2 B g^2 (a+b x)^2 (b c-a d) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{3 b d}+\frac{g^2 (a+b x)^3 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{3 b}+\frac{4 B^2 g^2 x (b c-a d)^2}{3 d^2}-\frac{4 B^2 g^2 (b c-a d)^3 \log (a+b x)}{b d^3}-\frac{4 B^2 g^2 (b c-a d)^3 \log \left(\frac{c+d x}{a+b x}\right)}{3 b d^3}",1,"(-4*A*B*(b*c - a*d)^2*g^2*x)/(3*d^2) + (4*B^2*(b*c - a*d)^2*g^2*x)/(3*d^2) - (4*B^2*(b*c - a*d)^3*g^2*Log[c + d*x])/(b*d^3) + (8*B^2*(b*c - a*d)^3*g^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*b*d^3) - (4*B^2*(b*c - a*d)^3*g^2*Log[c + d*x]^2)/(3*b*d^3) - (4*B^2*(b*c - a*d)^2*g^2*(a + b*x)*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(3*b*d^2) + (2*B*(b*c - a*d)*g^2*(a + b*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(3*b*d) + (4*B*(b*c - a*d)^3*g^2*Log[c + d*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(3*b*d^3) + (g^2*(a + b*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2)/(3*b) + (8*B^2*(b*c - a*d)^3*g^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*b*d^3)","A",20,13,34,0.3824,1,"{2525, 12, 2528, 2486, 31, 43, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
213,1,291,0,0.5042354,"\int (a g+b g x) \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2 \, dx","Int[(a*g + b*g*x)*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2,x]","-\frac{4 B^2 g (b c-a d)^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b d^2}-\frac{2 B g (b c-a d)^2 \log (c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b d^2}+\frac{g (a+b x)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{2 b}+\frac{2 A B g x (b c-a d)}{d}+\frac{2 B^2 g (b c-a d)^2 \log ^2(c+d x)}{b d^2}+\frac{4 B^2 g (b c-a d)^2 \log (c+d x)}{b d^2}-\frac{4 B^2 g (b c-a d)^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b d^2}+\frac{2 B^2 g (a+b x) (b c-a d) \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{b d}","-\frac{4 B^2 g (b c-a d)^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}+\frac{2 B g (b c-a d)^2 \log \left(1-\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b d^2}+\frac{2 B g (c+d x) (b c-a d) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{d^2}+\frac{g (a+b x)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{2 b}+\frac{4 B^2 g (b c-a d)^2 \log (a+b x)}{b d^2}",1,"(2*A*B*(b*c - a*d)*g*x)/d + (4*B^2*(b*c - a*d)^2*g*Log[c + d*x])/(b*d^2) - (4*B^2*(b*c - a*d)^2*g*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*d^2) + (2*B^2*(b*c - a*d)^2*g*Log[c + d*x]^2)/(b*d^2) + (2*B^2*(b*c - a*d)*g*(a + b*x)*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(b*d) - (2*B*(b*c - a*d)^2*g*Log[c + d*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(b*d^2) + (g*(a + b*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2)/(2*b) - (4*B^2*(b*c - a*d)^2*g*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*d^2)","A",16,12,32,0.3750,1,"{2525, 12, 2528, 2486, 31, 2524, 2418, 2394, 2393, 2391, 2390, 2301}"
214,1,740,0,4.0795986,"\int \frac{\left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2}{a g+b g x} \, dx","Int[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2/(a*g + b*g*x),x]","-\frac{4 A B \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g}+\frac{4 B^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) \left(-\log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+\log \left(\frac{1}{(a+b x)^2}\right)+\log \left((c+d x)^2\right)\right)}{b g}-\frac{8 B^2 \text{PolyLog}\left(3,-\frac{d (a+b x)}{b c-a d}\right)}{b g}-\frac{8 B^2 \text{PolyLog}\left(3,\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{4 B^2 \log \left(\frac{1}{(a+b x)^2}\right) \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g}+\frac{4 B^2 \log \left((c+d x)^2\right) \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g}+\frac{\log (a g+b g x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{b g}-\frac{4 A B \log (a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}+\frac{2 A B \log ^2(g (a+b x))}{b g}+\frac{2 B^2 \log ^2(a g+b g x) \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{b g}+\frac{4 B^2 \log (a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right) \left(-\log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+\log \left(\frac{1}{(a+b x)^2}\right)+\log \left((c+d x)^2\right)\right)}{b g}-\frac{4 B^2 \log (c+d x) \log ^2(g (a+b x))}{b g}+\frac{4 B^2 \log ^2(g (a+b x)) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{B^2 \log ^2\left((c+d x)^2\right) \log (g (a+b x))}{b g}+\frac{B^2 \log ^2\left((c+d x)^2\right) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g}-\frac{4 B^2 \log ^2(a g+b g x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{B^2 \log ^2\left(\frac{1}{(a+b x)^2}\right) \log (c+d x)}{b g}+\frac{B^2 \log ^2\left(\frac{1}{(a+b x)^2}\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g}-\frac{4 B^2 \log \left(\frac{1}{(a+b x)^2}\right) \log (c+d x) \log (g (a+b x))}{b g}+\frac{4 B^2 \log ^3(g (a+b x))}{3 b g}","-\frac{4 B \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b g}+\frac{8 B^2 \text{PolyLog}\left(3,\frac{b (c+d x)}{d (a+b x)}\right)}{b g}-\frac{\log \left(-\frac{b c-a d}{d (a+b x)}\right) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{b g}",1,"(2*A*B*Log[g*(a + b*x)]^2)/(b*g) + (4*B^2*Log[g*(a + b*x)]^3)/(3*b*g) - (B^2*Log[(a + b*x)^(-2)]^2*Log[c + d*x])/(b*g) - (4*B^2*Log[(a + b*x)^(-2)]*Log[g*(a + b*x)]*Log[c + d*x])/(b*g) - (4*B^2*Log[g*(a + b*x)]^2*Log[c + d*x])/(b*g) + (B^2*Log[(a + b*x)^(-2)]^2*Log[(b*(c + d*x))/(b*c - a*d)])/(b*g) + (4*B^2*Log[g*(a + b*x)]^2*Log[(b*(c + d*x))/(b*c - a*d)])/(b*g) + (B^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[(c + d*x)^2]^2)/(b*g) - (B^2*Log[g*(a + b*x)]*Log[(c + d*x)^2]^2)/(b*g) - (4*A*B*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x])/(b*g) + (4*B^2*Log[(b*(c + d*x))/(b*c - a*d)]*(Log[(a + b*x)^(-2)] + Log[(c + d*x)^2] - Log[(e*(c + d*x)^2)/(a + b*x)^2])*Log[a*g + b*g*x])/(b*g) + ((A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2*Log[a*g + b*g*x])/(b*g) - (4*B^2*Log[(b*(c + d*x))/(b*c - a*d)]*Log[a*g + b*g*x]^2)/(b*g) + (2*B^2*Log[(e*(c + d*x)^2)/(a + b*x)^2]*Log[a*g + b*g*x]^2)/(b*g) - (4*A*B*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g) - (4*B^2*Log[(a + b*x)^(-2)]*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g) + (4*B^2*(Log[(a + b*x)^(-2)] + Log[(c + d*x)^2] - Log[(e*(c + d*x)^2)/(a + b*x)^2])*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*g) + (4*B^2*Log[(c + d*x)^2]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*g) - (8*B^2*PolyLog[3, -((d*(a + b*x))/(b*c - a*d))])/(b*g) - (8*B^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])/(b*g)","B",46,23,34,0.6765,1,"{2524, 12, 2528, 2418, 2390, 2301, 2394, 2393, 2391, 6688, 6742, 2499, 2302, 30, 2396, 2433, 2374, 6589, 2500, 2440, 2434, 2375, 2317}"
215,1,480,0,0.9237513,"\int \frac{\left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2}{(a g+b g x)^2} \, dx","Int[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2/(a*g + b*g*x)^2,x]","-\frac{8 B^2 d \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g^2 (b c-a d)}-\frac{8 B^2 d \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g^2 (b c-a d)}+\frac{4 B d \log (a+b x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b g^2 (b c-a d)}-\frac{4 B d \log (c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b g^2 (b c-a d)}+\frac{4 B \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b g^2 (a+b x)}-\frac{\left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{b g^2 (a+b x)}+\frac{4 B^2 d \log ^2(a+b x)}{b g^2 (b c-a d)}+\frac{4 B^2 d \log ^2(c+d x)}{b g^2 (b c-a d)}-\frac{8 B^2 d \log (a+b x)}{b g^2 (b c-a d)}-\frac{8 B^2 d \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g^2 (b c-a d)}+\frac{8 B^2 d \log (c+d x)}{b g^2 (b c-a d)}-\frac{8 B^2 d \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g^2 (b c-a d)}-\frac{8 B^2}{b g^2 (a+b x)}","-\frac{(c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{g^2 (a+b x) (b c-a d)}+\frac{4 A B (c+d x)}{g^2 (a+b x) (b c-a d)}+\frac{4 B^2 (c+d x) \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{g^2 (a+b x) (b c-a d)}-\frac{8 B^2 (c+d x)}{g^2 (a+b x) (b c-a d)}",1,"(-8*B^2)/(b*g^2*(a + b*x)) - (8*B^2*d*Log[a + b*x])/(b*(b*c - a*d)*g^2) + (4*B^2*d*Log[a + b*x]^2)/(b*(b*c - a*d)*g^2) + (8*B^2*d*Log[c + d*x])/(b*(b*c - a*d)*g^2) - (8*B^2*d*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*(b*c - a*d)*g^2) + (4*B^2*d*Log[c + d*x]^2)/(b*(b*c - a*d)*g^2) - (8*B^2*d*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)*g^2) + (4*B*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(b*g^2*(a + b*x)) + (4*B*d*Log[a + b*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(b*(b*c - a*d)*g^2) - (4*B*d*Log[c + d*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(b*(b*c - a*d)*g^2) - (A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2/(b*g^2*(a + b*x)) - (8*B^2*d*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*(b*c - a*d)*g^2) - (8*B^2*d*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)*g^2)","C",26,11,34,0.3235,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
216,1,578,0,1.080817,"\int \frac{\left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2}{(a g+b g x)^3} \, dx","Int[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2/(a*g + b*g*x)^3,x]","\frac{4 B^2 d^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}+\frac{4 B^2 d^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}-\frac{2 B d^2 \log (a+b x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b g^3 (b c-a d)^2}+\frac{2 B d^2 \log (c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b g^3 (b c-a d)^2}-\frac{2 B d \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b g^3 (a+b x) (b c-a d)}+\frac{B \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b g^3 (a+b x)^2}-\frac{\left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{2 b g^3 (a+b x)^2}-\frac{2 B^2 d^2 \log ^2(a+b x)}{b g^3 (b c-a d)^2}-\frac{2 B^2 d^2 \log ^2(c+d x)}{b g^3 (b c-a d)^2}+\frac{6 B^2 d^2 \log (a+b x)}{b g^3 (b c-a d)^2}+\frac{4 B^2 d^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}-\frac{6 B^2 d^2 \log (c+d x)}{b g^3 (b c-a d)^2}+\frac{4 B^2 d^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g^3 (b c-a d)^2}+\frac{6 B^2 d}{b g^3 (a+b x) (b c-a d)}-\frac{B^2}{b g^3 (a+b x)^2}","\frac{b B (c+d x)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{g^3 (a+b x)^2 (b c-a d)^2}-\frac{b (c+d x)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{2 g^3 (a+b x)^2 (b c-a d)^2}+\frac{d (c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{g^3 (a+b x) (b c-a d)^2}-\frac{4 A B d (c+d x)}{g^3 (a+b x) (b c-a d)^2}-\frac{4 B^2 d (c+d x) \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{g^3 (a+b x) (b c-a d)^2}-\frac{b B^2 (c+d x)^2}{g^3 (a+b x)^2 (b c-a d)^2}+\frac{8 B^2 d (c+d x)}{g^3 (a+b x) (b c-a d)^2}",1,"-(B^2/(b*g^3*(a + b*x)^2)) + (6*B^2*d)/(b*(b*c - a*d)*g^3*(a + b*x)) + (6*B^2*d^2*Log[a + b*x])/(b*(b*c - a*d)^2*g^3) - (2*B^2*d^2*Log[a + b*x]^2)/(b*(b*c - a*d)^2*g^3) - (6*B^2*d^2*Log[c + d*x])/(b*(b*c - a*d)^2*g^3) + (4*B^2*d^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*(b*c - a*d)^2*g^3) - (2*B^2*d^2*Log[c + d*x]^2)/(b*(b*c - a*d)^2*g^3) + (4*B^2*d^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)^2*g^3) + (B*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(b*g^3*(a + b*x)^2) - (2*B*d*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(b*(b*c - a*d)*g^3*(a + b*x)) - (2*B*d^2*Log[a + b*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(b*(b*c - a*d)^2*g^3) + (2*B*d^2*Log[c + d*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(b*(b*c - a*d)^2*g^3) - (A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2/(2*b*g^3*(a + b*x)^2) + (4*B^2*d^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*(b*c - a*d)^2*g^3) + (4*B^2*d^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)^2*g^3)","C",30,11,34,0.3235,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
217,1,692,0,1.2280793,"\int \frac{\left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2}{(a g+b g x)^4} \, dx","Int[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2/(a*g + b*g*x)^4,x]","-\frac{8 B^2 d^3 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}-\frac{8 B^2 d^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}+\frac{4 B d^3 \log (a+b x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{3 b g^4 (b c-a d)^3}-\frac{4 B d^3 \log (c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{3 b g^4 (b c-a d)^3}+\frac{4 B d^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{3 b g^4 (a+b x) (b c-a d)^2}-\frac{2 B d \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{3 b g^4 (a+b x)^2 (b c-a d)}-\frac{\left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{3 b g^4 (a+b x)^3}+\frac{4 B \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{9 b g^4 (a+b x)^3}-\frac{44 B^2 d^2}{9 b g^4 (a+b x) (b c-a d)^2}+\frac{4 B^2 d^3 \log ^2(a+b x)}{3 b g^4 (b c-a d)^3}+\frac{4 B^2 d^3 \log ^2(c+d x)}{3 b g^4 (b c-a d)^3}-\frac{44 B^2 d^3 \log (a+b x)}{9 b g^4 (b c-a d)^3}-\frac{8 B^2 d^3 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}+\frac{44 B^2 d^3 \log (c+d x)}{9 b g^4 (b c-a d)^3}-\frac{8 B^2 d^3 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{3 b g^4 (b c-a d)^3}+\frac{10 B^2 d}{9 b g^4 (a+b x)^2 (b c-a d)}-\frac{8 B^2}{27 b g^4 (a+b x)^3}","\frac{4 b^2 B (c+d x)^3 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{9 g^4 (a+b x)^3 (b c-a d)^3}-\frac{4 B d^3 \log \left(\frac{c+d x}{a+b x}\right) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{3 b g^4 (b c-a d)^3}+\frac{4 B d^2 (c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{g^4 (a+b x) (b c-a d)^3}-\frac{2 b B d (c+d x)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{g^4 (a+b x)^2 (b c-a d)^3}-\frac{\left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{3 b g^4 (a+b x)^3}-\frac{8 b^2 B^2 (c+d x)^3}{27 g^4 (a+b x)^3 (b c-a d)^3}-\frac{8 B^2 d^2 (c+d x)}{g^4 (a+b x) (b c-a d)^3}+\frac{4 B^2 d^3 \log ^2\left(\frac{c+d x}{a+b x}\right)}{3 b g^4 (b c-a d)^3}+\frac{2 b B^2 d (c+d x)^2}{g^4 (a+b x)^2 (b c-a d)^3}",1,"(-8*B^2)/(27*b*g^4*(a + b*x)^3) + (10*B^2*d)/(9*b*(b*c - a*d)*g^4*(a + b*x)^2) - (44*B^2*d^2)/(9*b*(b*c - a*d)^2*g^4*(a + b*x)) - (44*B^2*d^3*Log[a + b*x])/(9*b*(b*c - a*d)^3*g^4) + (4*B^2*d^3*Log[a + b*x]^2)/(3*b*(b*c - a*d)^3*g^4) + (44*B^2*d^3*Log[c + d*x])/(9*b*(b*c - a*d)^3*g^4) - (8*B^2*d^3*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*b*(b*c - a*d)^3*g^4) + (4*B^2*d^3*Log[c + d*x]^2)/(3*b*(b*c - a*d)^3*g^4) - (8*B^2*d^3*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3*b*(b*c - a*d)^3*g^4) + (4*B*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(9*b*g^4*(a + b*x)^3) - (2*B*d*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(3*b*(b*c - a*d)*g^4*(a + b*x)^2) + (4*B*d^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(3*b*(b*c - a*d)^2*g^4*(a + b*x)) + (4*B*d^3*Log[a + b*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(3*b*(b*c - a*d)^3*g^4) - (4*B*d^3*Log[c + d*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(3*b*(b*c - a*d)^3*g^4) - (A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2/(3*b*g^4*(a + b*x)^3) - (8*B^2*d^3*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(3*b*(b*c - a*d)^3*g^4) - (8*B^2*d^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*b*(b*c - a*d)^3*g^4)","C",34,11,34,0.3235,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
218,1,758,0,1.428864,"\int \frac{\left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2}{(a g+b g x)^5} \, dx","Int[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2/(a*g + b*g*x)^5,x]","\frac{2 B^2 d^4 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b g^5 (b c-a d)^4}+\frac{2 B^2 d^4 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b g^5 (b c-a d)^4}-\frac{B d^4 \log (a+b x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b g^5 (b c-a d)^4}+\frac{B d^4 \log (c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b g^5 (b c-a d)^4}-\frac{B d^3 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b g^5 (a+b x) (b c-a d)^3}+\frac{B d^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{2 b g^5 (a+b x)^2 (b c-a d)^2}-\frac{B d \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{3 b g^5 (a+b x)^3 (b c-a d)}-\frac{\left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{4 b g^5 (a+b x)^4}+\frac{B \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{4 b g^5 (a+b x)^4}+\frac{25 B^2 d^3}{6 b g^5 (a+b x) (b c-a d)^3}-\frac{13 B^2 d^2}{12 b g^5 (a+b x)^2 (b c-a d)^2}-\frac{B^2 d^4 \log ^2(a+b x)}{b g^5 (b c-a d)^4}-\frac{B^2 d^4 \log ^2(c+d x)}{b g^5 (b c-a d)^4}+\frac{25 B^2 d^4 \log (a+b x)}{6 b g^5 (b c-a d)^4}+\frac{2 B^2 d^4 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b g^5 (b c-a d)^4}-\frac{25 B^2 d^4 \log (c+d x)}{6 b g^5 (b c-a d)^4}+\frac{2 B^2 d^4 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b g^5 (b c-a d)^4}+\frac{7 B^2 d}{18 b g^5 (a+b x)^3 (b c-a d)}-\frac{B^2}{8 b g^5 (a+b x)^4}","-\frac{4 b^2 B d (c+d x)^3 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{3 g^5 (a+b x)^3 (b c-a d)^4}+\frac{b^3 B (c+d x)^4 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{4 g^5 (a+b x)^4 (b c-a d)^4}+\frac{B d^4 \log \left(\frac{c+d x}{a+b x}\right) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{b g^5 (b c-a d)^4}-\frac{4 B d^3 (c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{g^5 (a+b x) (b c-a d)^4}+\frac{3 b B d^2 (c+d x)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{g^5 (a+b x)^2 (b c-a d)^4}-\frac{\left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{4 b g^5 (a+b x)^4}+\frac{8 b^2 B^2 d (c+d x)^3}{9 g^5 (a+b x)^3 (b c-a d)^4}-\frac{b^3 B^2 (c+d x)^4}{8 g^5 (a+b x)^4 (b c-a d)^4}+\frac{8 B^2 d^3 (c+d x)}{g^5 (a+b x) (b c-a d)^4}-\frac{3 b B^2 d^2 (c+d x)^2}{g^5 (a+b x)^2 (b c-a d)^4}-\frac{B^2 d^4 \log ^2\left(\frac{c+d x}{a+b x}\right)}{b g^5 (b c-a d)^4}",1,"-B^2/(8*b*g^5*(a + b*x)^4) + (7*B^2*d)/(18*b*(b*c - a*d)*g^5*(a + b*x)^3) - (13*B^2*d^2)/(12*b*(b*c - a*d)^2*g^5*(a + b*x)^2) + (25*B^2*d^3)/(6*b*(b*c - a*d)^3*g^5*(a + b*x)) + (25*B^2*d^4*Log[a + b*x])/(6*b*(b*c - a*d)^4*g^5) - (B^2*d^4*Log[a + b*x]^2)/(b*(b*c - a*d)^4*g^5) - (25*B^2*d^4*Log[c + d*x])/(6*b*(b*c - a*d)^4*g^5) + (2*B^2*d^4*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*(b*c - a*d)^4*g^5) - (B^2*d^4*Log[c + d*x]^2)/(b*(b*c - a*d)^4*g^5) + (2*B^2*d^4*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)^4*g^5) + (B*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(4*b*g^5*(a + b*x)^4) - (B*d*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(3*b*(b*c - a*d)*g^5*(a + b*x)^3) + (B*d^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(2*b*(b*c - a*d)^2*g^5*(a + b*x)^2) - (B*d^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(b*(b*c - a*d)^3*g^5*(a + b*x)) - (B*d^4*Log[a + b*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(b*(b*c - a*d)^4*g^5) + (B*d^4*Log[c + d*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(b*(b*c - a*d)^4*g^5) - (A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2/(4*b*g^5*(a + b*x)^4) + (2*B^2*d^4*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*(b*c - a*d)^4*g^5) + (2*B^2*d^4*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)^4*g^5)","C",38,11,34,0.3235,1,"{2525, 12, 2528, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
219,0,0,0,0.2022011,"\int \frac{(a g+b g x)^2}{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)} \, dx","Int[(a*g + b*g*x)^2/(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]),x]","\int \frac{(a g+b g x)^2}{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)} \, dx","\text{Int}\left(\frac{(a g+b g x)^2}{B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A},x\right)",0,"a^2*g^2*Defer[Int][(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^(-1), x] + 2*a*b*g^2*Defer[Int][x/(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]), x] + b^2*g^2*Defer[Int][x^2/(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]), x]","A",0,0,0,0,-1,"{}"
220,0,0,0,0.1007777,"\int \frac{a g+b g x}{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)} \, dx","Int[(a*g + b*g*x)/(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]),x]","\int \frac{a g+b g x}{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)} \, dx","\text{Int}\left(\frac{a g+b g x}{B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A},x\right)",0,"a*g*Defer[Int][(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^(-1), x] + b*g*Defer[Int][x/(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]), x]","A",0,0,0,0,-1,"{}"
221,0,0,0,0.0731757,"\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)} \, dx","Int[1/((a*g + b*g*x)*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])),x]","\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)} \, dx","\text{Int}\left(\frac{1}{(a g+b g x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)},x\right)",0,"Defer[Int][1/((a*g + b*g*x)*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])), x]","A",0,0,0,0,-1,"{}"
222,0,0,0,0.0872545,"\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)} \, dx","Int[1/((a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])),x]","\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)} \, dx","-\frac{e^{-\frac{A}{2 B}} (c+d x) \text{Ei}\left(\frac{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{2 B}\right)}{2 B g^2 (a+b x) (b c-a d) \sqrt{\frac{e (c+d x)^2}{(a+b x)^2}}}",1,"Defer[Int][1/((a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])), x]","F",0,0,0,0,-1,"{}"
223,0,0,0,0.0736238,"\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)} \, dx","Int[1/((a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])),x]","\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)} \, dx","\frac{d e^{-\frac{A}{2 B}} (c+d x) \text{Ei}\left(\frac{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{2 B}\right)}{2 B g^3 (a+b x) (b c-a d)^2 \sqrt{\frac{e (c+d x)^2}{(a+b x)^2}}}-\frac{b e^{-\frac{A}{B}} \text{Ei}\left(\frac{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{B}\right)}{2 B e g^3 (b c-a d)^2}",1,"Defer[Int][1/((a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])), x]","F",0,0,0,0,-1,"{}"
224,0,0,0,0.2115949,"\int \frac{(a g+b g x)^2}{\left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2} \, dx","Int[(a*g + b*g*x)^2/(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2,x]","\int \frac{(a g+b g x)^2}{\left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2} \, dx","\text{Int}\left(\frac{(a g+b g x)^2}{\left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2},x\right)",0,"a^2*g^2*Defer[Int][(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^(-2), x] + 2*a*b*g^2*Defer[Int][x/(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2, x] + b^2*g^2*Defer[Int][x^2/(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2, x]","A",0,0,0,0,-1,"{}"
225,0,0,0,0.1095844,"\int \frac{a g+b g x}{\left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2} \, dx","Int[(a*g + b*g*x)/(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2,x]","\int \frac{a g+b g x}{\left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2} \, dx","\text{Int}\left(\frac{a g+b g x}{\left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2},x\right)",0,"a*g*Defer[Int][(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^(-2), x] + b*g*Defer[Int][x/(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2, x]","A",0,0,0,0,-1,"{}"
226,0,0,0,0.0821686,"\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2} \, dx","Int[1/((a*g + b*g*x)*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2),x]","\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(a g+b g x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2},x\right)",0,"Defer[Int][1/((a*g + b*g*x)*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2), x]","A",0,0,0,0,-1,"{}"
227,0,0,0,0.0930418,"\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2} \, dx","Int[1/((a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2),x]","\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2} \, dx","\frac{c+d x}{2 B g^2 (a+b x) (b c-a d) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}-\frac{e^{-\frac{A}{2 B}} (c+d x) \text{Ei}\left(\frac{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{2 B}\right)}{4 B^2 g^2 (a+b x) (b c-a d) \sqrt{\frac{e (c+d x)^2}{(a+b x)^2}}}",1,"Defer[Int][1/((a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2), x]","F",0,0,0,0,-1,"{}"
228,0,0,0,0.0850021,"\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2} \, dx","Int[1/((a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2),x]","\int \frac{1}{(a g+b g x)^3 \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right)^2} \, dx","\frac{d e^{-\frac{A}{2 B}} (c+d x) \text{Ei}\left(\frac{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{2 B}\right)}{4 B^2 g^3 (a+b x) (b c-a d)^2 \sqrt{\frac{e (c+d x)^2}{(a+b x)^2}}}-\frac{b e^{-\frac{A}{B}} \text{Ei}\left(\frac{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{B}\right)}{2 B^2 e g^3 (b c-a d)^2}+\frac{c+d x}{2 B g^3 (a+b x)^2 (b c-a d) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}",1,"Defer[Int][1/((a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2), x]","F",0,0,0,0,-1,"{}"
229,0,0,0,0.1024735,"\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)} \, dx","Int[1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])),x]","\int \frac{1}{(a g+b g x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)} \, dx","\frac{e^{\frac{A}{B n}} (c+d x) \left(e (a+b x)^n (c+d x)^{-n}\right)^{\frac{1}{n}} \text{Ei}\left(-\frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{B n}\right)}{B g^2 n (a+b x) (b c-a d)}",1,"Defer[Int][1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])), x]","F",0,0,0,0,-1,"{}"
230,1,339,0,0.5568747,"\int (f+g x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Int[(f + g*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","-\frac{B g^2 x^2 (b c-a d) \left(a^2 d^2 g^2-a b d g (5 d f-c g)+b^2 \left(c^2 g^2-5 c d f g+10 d^2 f^2\right)\right)}{10 b^3 d^3}+\frac{B g x \left(-10 a^2 b^2 d^4 f^2 g+5 a^3 b d^4 f g^2-a^4 d^4 g^3+10 a b^3 d^4 f^3+b^4 (-c) \left(5 c^2 d f g^2-c^3 g^3-10 c d^2 f^2 g+10 d^3 f^3\right)\right)}{5 b^4 d^4}+\frac{(f+g x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{5 g}-\frac{B g^3 x^3 (b c-a d) (-a d g-b c g+5 b d f)}{15 b^2 d^2}-\frac{B (b f-a g)^5 \log (a+b x)}{5 b^5 g}-\frac{B g^4 x^4 (b c-a d)}{20 b d}+\frac{B (d f-c g)^5 \log (c+d x)}{5 d^5 g}","-\frac{B g^2 x^2 (b c-a d) \left(a^2 d^2 g^2-a b d g (5 d f-c g)+b^2 \left(c^2 g^2-5 c d f g+10 d^2 f^2\right)\right)}{10 b^3 d^3}+\frac{B g x (b c-a d) \left(-a^2 b d^2 g^2 (5 d f-c g)+a^3 d^3 g^3+a b^2 d g \left(c^2 g^2-5 c d f g+10 d^2 f^2\right)+b^3 \left(-\left(5 c^2 d f g^2-c^3 g^3-10 c d^2 f^2 g+10 d^3 f^3\right)\right)\right)}{5 b^4 d^4}+\frac{(f+g x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{5 g}-\frac{B g^3 x^3 (b c-a d) (-a d g-b c g+5 b d f)}{15 b^2 d^2}-\frac{B (b f-a g)^5 \log (a+b x)}{5 b^5 g}-\frac{B g^4 x^4 (b c-a d)}{20 b d}+\frac{B (d f-c g)^5 \log (c+d x)}{5 d^5 g}",1,"(B*g*(10*a*b^3*d^4*f^3 - 10*a^2*b^2*d^4*f^2*g + 5*a^3*b*d^4*f*g^2 - a^4*d^4*g^3 - b^4*c*(10*d^3*f^3 - 10*c*d^2*f^2*g + 5*c^2*d*f*g^2 - c^3*g^3))*x)/(5*b^4*d^4) - (B*(b*c - a*d)*g^2*(a^2*d^2*g^2 - a*b*d*g*(5*d*f - c*g) + b^2*(10*d^2*f^2 - 5*c*d*f*g + c^2*g^2))*x^2)/(10*b^3*d^3) - (B*(b*c - a*d)*g^3*(5*b*d*f - b*c*g - a*d*g)*x^3)/(15*b^2*d^2) - (B*(b*c - a*d)*g^4*x^4)/(20*b*d) - (B*(b*f - a*g)^5*Log[a + b*x])/(5*b^5*g) + ((f + g*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(5*g) + (B*(d*f - c*g)^5*Log[c + d*x])/(5*d^5*g)","A",4,3,27,0.1111,1,"{2525, 12, 72}"
231,1,227,0,0.3411358,"\int (f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Int[(f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","-\frac{B g x (b c-a d) \left(a^2 d^2 g^2-a b d g (4 d f-c g)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right)}{4 b^3 d^3}+\frac{(f+g x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 g}-\frac{B g^2 x^2 (b c-a d) (-a d g-b c g+4 b d f)}{8 b^2 d^2}-\frac{B (b f-a g)^4 \log (a+b x)}{4 b^4 g}-\frac{B g^3 x^3 (b c-a d)}{12 b d}+\frac{B (d f-c g)^4 \log (c+d x)}{4 d^4 g}","-\frac{B g x (b c-a d) \left(a^2 d^2 g^2-a b d g (4 d f-c g)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right)}{4 b^3 d^3}+\frac{(f+g x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 g}-\frac{B g^2 x^2 (b c-a d) (-a d g-b c g+4 b d f)}{8 b^2 d^2}-\frac{B (b f-a g)^4 \log (a+b x)}{4 b^4 g}-\frac{B g^3 x^3 (b c-a d)}{12 b d}+\frac{B (d f-c g)^4 \log (c+d x)}{4 d^4 g}",1,"-(B*(b*c - a*d)*g*(a^2*d^2*g^2 - a*b*d*g*(4*d*f - c*g) + b^2*(6*d^2*f^2 - 4*c*d*f*g + c^2*g^2))*x)/(4*b^3*d^3) - (B*(b*c - a*d)*g^2*(4*b*d*f - b*c*g - a*d*g)*x^2)/(8*b^2*d^2) - (B*(b*c - a*d)*g^3*x^3)/(12*b*d) - (B*(b*f - a*g)^4*Log[a + b*x])/(4*b^4*g) + ((f + g*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(4*g) + (B*(d*f - c*g)^4*Log[c + d*x])/(4*d^4*g)","A",4,3,27,0.1111,1,"{2525, 12, 72}"
232,1,150,0,0.1694975,"\int (f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Int[(f + g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{(f+g x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 g}-\frac{B g x (b c-a d) (-a d g-b c g+3 b d f)}{3 b^2 d^2}-\frac{B (b f-a g)^3 \log (a+b x)}{3 b^3 g}-\frac{B g^2 x^2 (b c-a d)}{6 b d}+\frac{B (d f-c g)^3 \log (c+d x)}{3 d^3 g}","\frac{(f+g x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 g}-\frac{B g x (b c-a d) (-a d g-b c g+3 b d f)}{3 b^2 d^2}-\frac{B (b f-a g)^3 \log (a+b x)}{3 b^3 g}-\frac{B g^2 x^2 (b c-a d)}{6 b d}+\frac{B (d f-c g)^3 \log (c+d x)}{3 d^3 g}",1,"-(B*(b*c - a*d)*g*(3*b*d*f - b*c*g - a*d*g)*x)/(3*b^2*d^2) - (B*(b*c - a*d)*g^2*x^2)/(6*b*d) - (B*(b*f - a*g)^3*Log[a + b*x])/(3*b^3*g) + ((f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(3*g) + (B*(d*f - c*g)^3*Log[c + d*x])/(3*d^3*g)","A",4,3,27,0.1111,1,"{2525, 12, 72}"
233,1,109,0,0.0975082,"\int (f+g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Int[(f + g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{(f+g x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g}-\frac{B (b f-a g)^2 \log (a+b x)}{2 b^2 g}-\frac{B g x (b c-a d)}{2 b d}+\frac{B (d f-c g)^2 \log (c+d x)}{2 d^2 g}","\frac{(f+g x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g}-\frac{B (b f-a g)^2 \log (a+b x)}{2 b^2 g}-\frac{B g x (b c-a d)}{2 b d}+\frac{B (d f-c g)^2 \log (c+d x)}{2 d^2 g}",1,"-(B*(b*c - a*d)*g*x)/(2*b*d) - (B*(b*f - a*g)^2*Log[a + b*x])/(2*b^2*g) + ((f + g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(2*g) + (B*(d*f - c*g)^2*Log[c + d*x])/(2*d^2*g)","A",4,3,25,0.1200,1,"{2525, 12, 72}"
234,1,52,0,0.027389,"\int \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Int[A + B*Log[(e*(a + b*x))/(c + d*x)],x]","\frac{B (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{b}-\frac{B (b c-a d) \log (c+d x)}{b d}+A x","\frac{B (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{b}-\frac{B (b c-a d) \log (c+d x)}{b d}+A x",1,"A*x + (B*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)])/b - (B*(b*c - a*d)*Log[c + d*x])/(b*d)","A",3,2,19,0.1053,1,"{2486, 31}"
235,1,140,0,0.2469553,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{f+g x} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(f + g*x),x]","-\frac{B \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{g}+\frac{B \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{g}+\frac{\log (f+g x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g}-\frac{B \log (f+g x) \log \left(-\frac{g (a+b x)}{b f-a g}\right)}{g}+\frac{B \log (f+g x) \log \left(-\frac{g (c+d x)}{d f-c g}\right)}{g}","-\frac{B \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{g}+\frac{B \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{g}+\frac{\log (f+g x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g}-\frac{B \log (f+g x) \log \left(-\frac{g (a+b x)}{b f-a g}\right)}{g}+\frac{B \log (f+g x) \log \left(-\frac{g (c+d x)}{d f-c g}\right)}{g}",1,"-((B*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/g) + ((A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[f + g*x])/g + (B*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/g - (B*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/g + (B*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g","A",10,6,27,0.2222,1,"{2524, 12, 2418, 2394, 2393, 2391}"
236,1,113,0,0.1058289,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(f+g x)^2} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(f + g*x)^2,x]","-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{g (f+g x)}+\frac{B (b c-a d) \log (f+g x)}{(b f-a g) (d f-c g)}+\frac{b B \log (a+b x)}{g (b f-a g)}-\frac{B d \log (c+d x)}{g (d f-c g)}","\frac{(a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(f+g x) (b f-a g)}+\frac{B (b c-a d) \log \left(\frac{f+g x}{c+d x}\right)}{(b f-a g) (d f-c g)}",1,"(b*B*Log[a + b*x])/(g*(b*f - a*g)) - (A + B*Log[(e*(a + b*x))/(c + d*x)])/(g*(f + g*x)) - (B*d*Log[c + d*x])/(g*(d*f - c*g)) + (B*(b*c - a*d)*Log[f + g*x])/((b*f - a*g)*(d*f - c*g))","A",4,3,27,0.1111,1,"{2525, 12, 72}"
237,1,183,0,0.1854542,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(f+g x)^3} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(f + g*x)^3,x]","-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{2 g (f+g x)^2}+\frac{b^2 B \log (a+b x)}{2 g (b f-a g)^2}-\frac{B (b c-a d)}{2 (f+g x) (b f-a g) (d f-c g)}+\frac{B (b c-a d) \log (f+g x) (-a d g-b c g+2 b d f)}{2 (b f-a g)^2 (d f-c g)^2}-\frac{B d^2 \log (c+d x)}{2 g (d f-c g)^2}","-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{2 g (f+g x)^2}+\frac{b^2 B \log (a+b x)}{2 g (b f-a g)^2}-\frac{B (b c-a d)}{2 (f+g x) (b f-a g) (d f-c g)}+\frac{B (b c-a d) \log (f+g x) (-a d g-b c g+2 b d f)}{2 (b f-a g)^2 (d f-c g)^2}-\frac{B d^2 \log (c+d x)}{2 g (d f-c g)^2}",1,"-(B*(b*c - a*d))/(2*(b*f - a*g)*(d*f - c*g)*(f + g*x)) + (b^2*B*Log[a + b*x])/(2*g*(b*f - a*g)^2) - (A + B*Log[(e*(a + b*x))/(c + d*x)])/(2*g*(f + g*x)^2) - (B*d^2*Log[c + d*x])/(2*g*(d*f - c*g)^2) + (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*Log[f + g*x])/(2*(b*f - a*g)^2*(d*f - c*g)^2)","A",4,3,27,0.1111,1,"{2525, 12, 72}"
238,1,275,0,0.3960537,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(f+g x)^4} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(f + g*x)^4,x]","\frac{B (b c-a d) \log (f+g x) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{3 (b f-a g)^3 (d f-c g)^3}-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{3 g (f+g x)^3}+\frac{b^3 B \log (a+b x)}{3 g (b f-a g)^3}-\frac{B (b c-a d) (-a d g-b c g+2 b d f)}{3 (f+g x) (b f-a g)^2 (d f-c g)^2}-\frac{B (b c-a d)}{6 (f+g x)^2 (b f-a g) (d f-c g)}-\frac{B d^3 \log (c+d x)}{3 g (d f-c g)^3}","\frac{B (b c-a d) \log (f+g x) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{3 (b f-a g)^3 (d f-c g)^3}-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{3 g (f+g x)^3}+\frac{b^3 B \log (a+b x)}{3 g (b f-a g)^3}-\frac{B (b c-a d) (-a d g-b c g+2 b d f)}{3 (f+g x) (b f-a g)^2 (d f-c g)^2}-\frac{B (b c-a d)}{6 (f+g x)^2 (b f-a g) (d f-c g)}-\frac{B d^3 \log (c+d x)}{3 g (d f-c g)^3}",1,"-(B*(b*c - a*d))/(6*(b*f - a*g)*(d*f - c*g)*(f + g*x)^2) - (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g))/(3*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)) + (b^3*B*Log[a + b*x])/(3*g*(b*f - a*g)^3) - (A + B*Log[(e*(a + b*x))/(c + d*x)])/(3*g*(f + g*x)^3) - (B*d^3*Log[c + d*x])/(3*g*(d*f - c*g)^3) + (B*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*Log[f + g*x])/(3*(b*f - a*g)^3*(d*f - c*g)^3)","A",4,3,27,0.1111,1,"{2525, 12, 72}"
239,1,379,0,0.6177117,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(f+g x)^5} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(f + g*x)^5,x]","-\frac{B (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{4 (f+g x) (b f-a g)^3 (d f-c g)^3}-\frac{B (b c-a d) \log (f+g x) (-a d g-b c g+2 b d f) \left(-a^2 d^2 g^2+2 a b d^2 f g+b^2 \left(-\left(c^2 g^2-2 c d f g+2 d^2 f^2\right)\right)\right)}{4 (b f-a g)^4 (d f-c g)^4}-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{4 g (f+g x)^4}+\frac{b^4 B \log (a+b x)}{4 g (b f-a g)^4}-\frac{B (b c-a d) (-a d g-b c g+2 b d f)}{8 (f+g x)^2 (b f-a g)^2 (d f-c g)^2}-\frac{B (b c-a d)}{12 (f+g x)^3 (b f-a g) (d f-c g)}-\frac{B d^4 \log (c+d x)}{4 g (d f-c g)^4}","-\frac{B (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{4 (f+g x) (b f-a g)^3 (d f-c g)^3}-\frac{B (b c-a d) \log (f+g x) (-a d g-b c g+2 b d f) \left(-a^2 d^2 g^2+2 a b d^2 f g+b^2 \left(-\left(c^2 g^2-2 c d f g+2 d^2 f^2\right)\right)\right)}{4 (b f-a g)^4 (d f-c g)^4}-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{4 g (f+g x)^4}+\frac{b^4 B \log (a+b x)}{4 g (b f-a g)^4}-\frac{B (b c-a d) (-a d g-b c g+2 b d f)}{8 (f+g x)^2 (b f-a g)^2 (d f-c g)^2}-\frac{B (b c-a d)}{12 (f+g x)^3 (b f-a g) (d f-c g)}-\frac{B d^4 \log (c+d x)}{4 g (d f-c g)^4}",1,"-(B*(b*c - a*d))/(12*(b*f - a*g)*(d*f - c*g)*(f + g*x)^3) - (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g))/(8*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)^2) - (B*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2)))/(4*(b*f - a*g)^3*(d*f - c*g)^3*(f + g*x)) + (b^4*B*Log[a + b*x])/(4*g*(b*f - a*g)^4) - (A + B*Log[(e*(a + b*x))/(c + d*x)])/(4*g*(f + g*x)^4) - (B*d^4*Log[c + d*x])/(4*g*(d*f - c*g)^4) - (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*Log[f + g*x])/(4*(b*f - a*g)^4*(d*f - c*g)^4)","A",4,3,27,0.1111,1,"{2525, 12, 72}"
240,1,994,0,1.7439327,"\int (f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Int[(f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{B^2 \log ^2(a+b x) (b f-a g)^4}{4 b^4 g}-\frac{B \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b f-a g)^4}{2 b^4 g}-\frac{B^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) (b f-a g)^4}{2 b^4 g}-\frac{B^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) (b f-a g)^4}{2 b^4 g}+\frac{B^2 (b c-a d)^2 g^3 x^2}{12 b^2 d^2}+\frac{(f+g x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{4 g}+\frac{B^2 (d f-c g)^4 \log ^2(c+d x)}{4 d^4 g}-\frac{B^2 (b c-a d)^2 (b c+a d) g^3 x}{6 b^3 d^3}+\frac{B^2 (b c-a d)^2 g^2 (4 b d f-b c g-a d g) x}{4 b^3 d^3}-\frac{A B (b c-a d) g \left(\left(6 d^2 f^2-4 c d g f+c^2 g^2\right) b^2-a d g (4 d f-c g) b+a^2 d^2 g^2\right) x}{2 b^3 d^3}-\frac{a^3 B^2 (b c-a d) g^3 \log (a+b x)}{6 b^4 d}+\frac{a^2 B^2 (b c-a d) g^2 (4 b d f-b c g-a d g) \log (a+b x)}{4 b^4 d^2}-\frac{B^2 (b c-a d) g \left(\left(6 d^2 f^2-4 c d g f+c^2 g^2\right) b^2-a d g (4 d f-c g) b+a^2 d^2 g^2\right) (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{2 b^4 d^3}-\frac{B (b c-a d) g^3 x^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{6 b d}-\frac{B (b c-a d) g^2 (4 b d f-b c g-a d g) x^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{4 b^2 d^2}+\frac{B^2 c^3 (b c-a d) g^3 \log (c+d x)}{6 b d^4}-\frac{B^2 c^2 (b c-a d) g^2 (4 b d f-b c g-a d g) \log (c+d x)}{4 b^2 d^4}+\frac{B^2 (b c-a d)^2 g \left(\left(6 d^2 f^2-4 c d g f+c^2 g^2\right) b^2-a d g (4 d f-c g) b+a^2 d^2 g^2\right) \log (c+d x)}{2 b^4 d^4}-\frac{B^2 (d f-c g)^4 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x)}{2 d^4 g}+\frac{B (d f-c g)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x)}{2 d^4 g}-\frac{B^2 (d f-c g)^4 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{2 d^4 g}","\frac{B^2 g^3 \log \left(\frac{a+b x}{c+d x}\right) (b c-a d)^4}{6 b^4 d^4}+\frac{B^2 g^3 \log (c+d x) (b c-a d)^4}{6 b^4 d^4}+\frac{B^2 g^3 x (b c-a d)^3}{6 b^3 d^3}+\frac{B^2 g^2 (4 b d f-3 b c g-a d g) \log \left(\frac{a+b x}{c+d x}\right) (b c-a d)^3}{4 b^4 d^4}+\frac{B^2 g^2 (4 b d f-3 b c g-a d g) \log (c+d x) (b c-a d)^3}{4 b^4 d^4}+\frac{B^2 g^3 (c+d x)^2 (b c-a d)^2}{12 b^2 d^4}+\frac{B^2 g^2 (4 b d f-3 b c g-a d g) x (b c-a d)^2}{4 b^3 d^3}+\frac{B^2 g \left(\left(6 d^2 f^2-8 c d g f+3 c^2 g^2\right) b^2-2 a d g (2 d f-c g) b+a^2 d^2 g^2\right) \log (c+d x) (b c-a d)^2}{2 b^4 d^4}-\frac{B g^3 (c+d x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)}{6 b d^4}-\frac{B g^2 (4 b d f-3 b c g-a d g) (c+d x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)}{4 b^2 d^4}-\frac{B g \left(\left(6 d^2 f^2-8 c d g f+3 c^2 g^2\right) b^2-2 a d g (2 d f-c g) b+a^2 d^2 g^2\right) (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)}{2 b^4 d^3}-\frac{B (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)}{2 b^4 d^4}-\frac{B^2 (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) (b c-a d)}{2 b^4 d^4}-\frac{(b f-a g)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{4 b^4 g}+\frac{(f+g x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{4 g}",1,"-(B^2*(b*c - a*d)^2*(b*c + a*d)*g^3*x)/(6*b^3*d^3) + (B^2*(b*c - a*d)^2*g^2*(4*b*d*f - b*c*g - a*d*g)*x)/(4*b^3*d^3) - (A*B*(b*c - a*d)*g*(a^2*d^2*g^2 - a*b*d*g*(4*d*f - c*g) + b^2*(6*d^2*f^2 - 4*c*d*f*g + c^2*g^2))*x)/(2*b^3*d^3) + (B^2*(b*c - a*d)^2*g^3*x^2)/(12*b^2*d^2) - (a^3*B^2*(b*c - a*d)*g^3*Log[a + b*x])/(6*b^4*d) + (a^2*B^2*(b*c - a*d)*g^2*(4*b*d*f - b*c*g - a*d*g)*Log[a + b*x])/(4*b^4*d^2) + (B^2*(b*f - a*g)^4*Log[a + b*x]^2)/(4*b^4*g) - (B^2*(b*c - a*d)*g*(a^2*d^2*g^2 - a*b*d*g*(4*d*f - c*g) + b^2*(6*d^2*f^2 - 4*c*d*f*g + c^2*g^2))*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)])/(2*b^4*d^3) - (B*(b*c - a*d)*g^2*(4*b*d*f - b*c*g - a*d*g)*x^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(4*b^2*d^2) - (B*(b*c - a*d)*g^3*x^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(6*b*d) - (B*(b*f - a*g)^4*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(2*b^4*g) + ((f + g*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(4*g) + (B^2*c^3*(b*c - a*d)*g^3*Log[c + d*x])/(6*b*d^4) - (B^2*c^2*(b*c - a*d)*g^2*(4*b*d*f - b*c*g - a*d*g)*Log[c + d*x])/(4*b^2*d^4) + (B^2*(b*c - a*d)^2*g*(a^2*d^2*g^2 - a*b*d*g*(4*d*f - c*g) + b^2*(6*d^2*f^2 - 4*c*d*f*g + c^2*g^2))*Log[c + d*x])/(2*b^4*d^4) - (B^2*(d*f - c*g)^4*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(2*d^4*g) + (B*(d*f - c*g)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/(2*d^4*g) + (B^2*(d*f - c*g)^4*Log[c + d*x]^2)/(4*d^4*g) - (B^2*(b*f - a*g)^4*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(2*b^4*g) - (B^2*(b*f - a*g)^4*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(2*b^4*g) - (B^2*(d*f - c*g)^4*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*d^4*g)","A",33,13,29,0.4483,1,"{2525, 12, 2528, 2486, 31, 72, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
241,1,649,0,1.0935311,"\int (f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Int[(f + g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","-\frac{2 B^2 (b f-a g)^3 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{3 b^3 g}-\frac{2 B^2 (d f-c g)^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 d^3 g}+\frac{a^2 B^2 g^2 (b c-a d) \log (a+b x)}{3 b^3 d}-\frac{2 A B g x (b c-a d) (-a d g-b c g+3 b d f)}{3 b^2 d^2}-\frac{2 B (b f-a g)^3 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b^3 g}+\frac{2 B (d f-c g)^3 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 d^3 g}+\frac{(f+g x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 g}-\frac{B g^2 x^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b d}-\frac{2 B^2 g (a+b x) (b c-a d) (-a d g-b c g+3 b d f) \log \left(\frac{e (a+b x)}{c+d x}\right)}{3 b^3 d^2}+\frac{2 B^2 g (b c-a d)^2 \log (c+d x) (-a d g-b c g+3 b d f)}{3 b^3 d^3}+\frac{B^2 g^2 x (b c-a d)^2}{3 b^2 d^2}-\frac{2 B^2 (b f-a g)^3 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{3 b^3 g}+\frac{B^2 (b f-a g)^3 \log ^2(a+b x)}{3 b^3 g}-\frac{B^2 c^2 g^2 (b c-a d) \log (c+d x)}{3 b d^3}-\frac{2 B^2 (d f-c g)^3 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 d^3 g}+\frac{B^2 (d f-c g)^3 \log ^2(c+d x)}{3 d^3 g}","\frac{2 B^2 (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{3 b^3 d^3}+\frac{2 B (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b^3 d^3}-\frac{2 B g (a+b x) (b c-a d) (-a d g-2 b c g+3 b d f) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b^3 d^2}-\frac{(b f-a g)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 b^3 g}-\frac{B g^2 (c+d x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b d^3}+\frac{(f+g x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 g}+\frac{2 B^2 g (b c-a d)^2 \log (c+d x) (-a d g-2 b c g+3 b d f)}{3 b^3 d^3}+\frac{B^2 g^2 x (b c-a d)^2}{3 b^2 d^2}+\frac{B^2 g^2 (b c-a d)^3 \log \left(\frac{a+b x}{c+d x}\right)}{3 b^3 d^3}+\frac{B^2 g^2 (b c-a d)^3 \log (c+d x)}{3 b^3 d^3}",1,"(B^2*(b*c - a*d)^2*g^2*x)/(3*b^2*d^2) - (2*A*B*(b*c - a*d)*g*(3*b*d*f - b*c*g - a*d*g)*x)/(3*b^2*d^2) + (a^2*B^2*(b*c - a*d)*g^2*Log[a + b*x])/(3*b^3*d) + (B^2*(b*f - a*g)^3*Log[a + b*x]^2)/(3*b^3*g) - (2*B^2*(b*c - a*d)*g*(3*b*d*f - b*c*g - a*d*g)*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)])/(3*b^3*d^2) - (B*(b*c - a*d)*g^2*x^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(3*b*d) - (2*B*(b*f - a*g)^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(3*b^3*g) + ((f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(3*g) - (B^2*c^2*(b*c - a*d)*g^2*Log[c + d*x])/(3*b*d^3) + (2*B^2*(b*c - a*d)^2*g*(3*b*d*f - b*c*g - a*d*g)*Log[c + d*x])/(3*b^3*d^3) - (2*B^2*(d*f - c*g)^3*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*d^3*g) + (2*B*(d*f - c*g)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/(3*d^3*g) + (B^2*(d*f - c*g)^3*Log[c + d*x]^2)/(3*d^3*g) - (2*B^2*(b*f - a*g)^3*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3*b^3*g) - (2*B^2*(b*f - a*g)^3*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(3*b^3*g) - (2*B^2*(d*f - c*g)^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*d^3*g)","A",29,13,29,0.4483,1,"{2525, 12, 2528, 2486, 31, 72, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
242,1,444,0,0.8200354,"\int (f+g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Int[(f + g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","-\frac{B^2 (b f-a g)^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b^2 g}-\frac{B^2 (d f-c g)^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{d^2 g}-\frac{B (b f-a g)^2 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^2 g}+\frac{B (d f-c g)^2 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{d^2 g}+\frac{(f+g x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 g}-\frac{A B g x (b c-a d)}{b d}+\frac{B^2 g (b c-a d)^2 \log (c+d x)}{b^2 d^2}-\frac{B^2 g (a+b x) (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)}{b^2 d}-\frac{B^2 (b f-a g)^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b^2 g}+\frac{B^2 (b f-a g)^2 \log ^2(a+b x)}{2 b^2 g}-\frac{B^2 (d f-c g)^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{d^2 g}+\frac{B^2 (d f-c g)^2 \log ^2(c+d x)}{2 d^2 g}","\frac{B^2 (b c-a d) (-a d g-b c g+2 b d f) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b^2 d^2}+\frac{B (b c-a d) (-a d g-b c g+2 b d f) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^2 d^2}-\frac{(b f-a g)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 b^2 g}-\frac{B g (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^2 d}+\frac{(f+g x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 g}+\frac{B^2 g (b c-a d)^2 \log (c+d x)}{b^2 d^2}",1,"-((A*B*(b*c - a*d)*g*x)/(b*d)) + (B^2*(b*f - a*g)^2*Log[a + b*x]^2)/(2*b^2*g) - (B^2*(b*c - a*d)*g*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)])/(b^2*d) - (B*(b*f - a*g)^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(b^2*g) + ((f + g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(2*g) + (B^2*(b*c - a*d)^2*g*Log[c + d*x])/(b^2*d^2) - (B^2*(d*f - c*g)^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(d^2*g) + (B*(d*f - c*g)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/(d^2*g) + (B^2*(d*f - c*g)^2*Log[c + d*x]^2)/(2*d^2*g) - (B^2*(b*f - a*g)^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b^2*g) - (B^2*(b*f - a*g)^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b^2*g) - (B^2*(d*f - c*g)^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(d^2*g)","A",25,12,27,0.4444,1,"{2525, 12, 2528, 2486, 31, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
243,1,246,0,0.6371307,"\int \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{2 a B^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b}+\frac{2 B^2 c \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{d}+\frac{2 a B \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b}-\frac{2 B c \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{d}+x \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2+\frac{2 B^2 c \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{d}+\frac{2 a B^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b}-\frac{a B^2 \log ^2(a+b x)}{b}-\frac{B^2 c \log ^2(c+d x)}{d}","\frac{2 B^2 (b c-a d) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d}+\frac{2 B (b c-a d) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b d}+\frac{(a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{b}",1,"-((a*B^2*Log[a + b*x]^2)/b) + (2*a*B*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/b + x*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + (2*B^2*c*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/d - (2*B*c*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/d - (B^2*c*Log[c + d*x]^2)/d + (2*a*B^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/b + (2*a*B^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/b + (2*B^2*c*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/d","A",22,10,21,0.4762,1,"{2523, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
244,1,1998,0,4.9004799,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{f+g x} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(f + g*x),x]","\frac{\left(\log \left(\frac{b (c+d x)}{b c-a d}\right)+\log \left(\frac{b f-a g}{b (f+g x)}\right)-\log \left(\frac{(b f-a g) (c+d x)}{(b c-a d) (f+g x)}\right)\right) \log ^2\left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right) B^2}{g}-\frac{\left(\log \left(\frac{b (c+d x)}{b c-a d}\right)-\log \left(-\frac{g (c+d x)}{d f-c g}\right)\right) \left(\log (a+b x)+\log \left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right)\right)^2 B^2}{g}+\frac{\left(\log \left(-\frac{d (a+b x)}{b c-a d}\right)+\log \left(\frac{d f-c g}{d (f+g x)}\right)-\log \left(-\frac{(d f-c g) (a+b x)}{(b c-a d) (f+g x)}\right)\right) \log ^2\left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right) B^2}{g}-\frac{\left(\log \left(-\frac{d (a+b x)}{b c-a d}\right)-\log \left(-\frac{g (a+b x)}{b f-a g}\right)\right) \left(\log (c+d x)+\log \left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right)\right)^2 B^2}{g}-\frac{\log ^2(a+b x) \log (f+g x) B^2}{g}-\frac{\log ^2\left(\frac{1}{c+d x}\right) \log (f+g x) B^2}{g}+\frac{2 \log \left(-\frac{g (a+b x)}{b f-a g}\right) \left(\log (a+b x)+\log \left(\frac{1}{c+d x}\right)-\log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (f+g x) B^2}{g}+\frac{2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) \log (f+g x) B^2}{g}-\frac{2 \log \left(-\frac{g (a+b x)}{b f-a g}\right) \left(\log \left(\frac{1}{c+d x}\right)+\log (c+d x)\right) \log (f+g x) B^2}{g}+\frac{2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) \log (f+g x) B^2}{g}-\frac{2 \left(\log (a+b x)+\log \left(\frac{1}{c+d x}\right)-\log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x) B^2}{g}+\frac{\log ^2(a+b x) \log \left(\frac{b (f+g x)}{b f-a g}\right) B^2}{g}+\frac{\log ^2\left(\frac{1}{c+d x}\right) \log \left(\frac{d (f+g x)}{d f-c g}\right) B^2}{g}+\frac{2 \left(\log (f+g x)-\log \left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right)\right) \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) B^2}{g}+\frac{2 \log (a+b x) \text{PolyLog}\left(2,-\frac{g (a+b x)}{b f-a g}\right) B^2}{g}+\frac{2 \left(\log (f+g x)-\log \left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right)\right) \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) B^2}{g}-\frac{2 \log \left(\frac{1}{c+d x}\right) \text{PolyLog}\left(2,-\frac{g (c+d x)}{d f-c g}\right) B^2}{g}-\frac{2 \log \left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right) \text{PolyLog}\left(2,\frac{g (a+b x)}{b (f+g x)}\right) B^2}{g}+\frac{2 \log \left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right) \text{PolyLog}\left(2,-\frac{(d f-c g) (a+b x)}{(b c-a d) (f+g x)}\right) B^2}{g}-\frac{2 \log \left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right) \text{PolyLog}\left(2,\frac{g (c+d x)}{d (f+g x)}\right) B^2}{g}+\frac{2 \log \left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right) \text{PolyLog}\left(2,\frac{(b f-a g) (c+d x)}{(b c-a d) (f+g x)}\right) B^2}{g}+\frac{2 \left(\log (a+b x)+\log \left(\frac{1}{c+d x}\right)-\log \left(\frac{e (a+b x)}{c+d x}\right)\right) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right) B^2}{g}-\frac{2 \left(\log \left(\frac{1}{c+d x}\right)+\log (c+d x)\right) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right) B^2}{g}+\frac{2 \left(\log (c+d x)+\log \left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right)\right) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right) B^2}{g}-\frac{2 \left(\log (a+b x)+\log \left(\frac{1}{c+d x}\right)-\log \left(\frac{e (a+b x)}{c+d x}\right)\right) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right) B^2}{g}+\frac{2 \left(\log (a+b x)+\log \left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right)\right) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right) B^2}{g}-\frac{2 \text{PolyLog}\left(3,-\frac{d (a+b x)}{b c-a d}\right) B^2}{g}-\frac{2 \text{PolyLog}\left(3,-\frac{g (a+b x)}{b f-a g}\right) B^2}{g}-\frac{2 \text{PolyLog}\left(3,\frac{b (c+d x)}{b c-a d}\right) B^2}{g}-\frac{2 \text{PolyLog}\left(3,-\frac{g (c+d x)}{d f-c g}\right) B^2}{g}-\frac{2 \text{PolyLog}\left(3,\frac{g (a+b x)}{b (f+g x)}\right) B^2}{g}+\frac{2 \text{PolyLog}\left(3,-\frac{(d f-c g) (a+b x)}{(b c-a d) (f+g x)}\right) B^2}{g}-\frac{2 \text{PolyLog}\left(3,\frac{g (c+d x)}{d (f+g x)}\right) B^2}{g}+\frac{2 \text{PolyLog}\left(3,\frac{(b f-a g) (c+d x)}{(b c-a d) (f+g x)}\right) B^2}{g}-\frac{2 \text{PolyLog}\left(3,\frac{b (f+g x)}{b f-a g}\right) B^2}{g}-\frac{2 \text{PolyLog}\left(3,\frac{d (f+g x)}{d f-c g}\right) B^2}{g}-\frac{2 A \log \left(-\frac{g (a+b x)}{b f-a g}\right) \log (f+g x) B}{g}+\frac{2 A \log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x) B}{g}-\frac{2 A \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right) B}{g}+\frac{2 A \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right) B}{g}+\frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \log (f+g x)}{g}","\frac{2 B \text{PolyLog}\left(2,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g}-\frac{2 B \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g}-\frac{2 B^2 \text{PolyLog}\left(3,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{g}+\frac{2 B^2 \text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right)}{g}+\frac{\log \left(1-\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g}-\frac{\log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g}",1,"-((B^2*Log[a + b*x]^2*Log[f + g*x])/g) - (2*A*B*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/g - (B^2*Log[(c + d*x)^(-1)]^2*Log[f + g*x])/g + (2*B^2*Log[-((g*(a + b*x))/(b*f - a*g))]*(Log[a + b*x] + Log[(c + d*x)^(-1)] - Log[(e*(a + b*x))/(c + d*x)])*Log[f + g*x])/g + ((A + B*Log[(e*(a + b*x))/(c + d*x)])^2*Log[f + g*x])/g + (2*B^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x]*Log[f + g*x])/g - (2*B^2*Log[-((g*(a + b*x))/(b*f - a*g))]*(Log[(c + d*x)^(-1)] + Log[c + d*x])*Log[f + g*x])/g + (2*B^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)]*Log[f + g*x])/g + (2*A*B*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/g - (2*B^2*(Log[a + b*x] + Log[(c + d*x)^(-1)] - Log[(e*(a + b*x))/(c + d*x)])*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/g + (B^2*Log[a + b*x]^2*Log[(b*(f + g*x))/(b*f - a*g)])/g + (B^2*Log[(c + d*x)^(-1)]^2*Log[(d*(f + g*x))/(d*f - c*g)])/g + (B^2*(Log[(b*(c + d*x))/(b*c - a*d)] + Log[(b*f - a*g)/(b*(f + g*x))] - Log[((b*f - a*g)*(c + d*x))/((b*c - a*d)*(f + g*x))])*Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))]^2)/g - (B^2*(Log[(b*(c + d*x))/(b*c - a*d)] - Log[-((g*(c + d*x))/(d*f - c*g))])*(Log[a + b*x] + Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))])^2)/g + (B^2*(Log[-((d*(a + b*x))/(b*c - a*d))] + Log[(d*f - c*g)/(d*(f + g*x))] - Log[-(((d*f - c*g)*(a + b*x))/((b*c - a*d)*(f + g*x)))])*Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))]^2)/g - (B^2*(Log[-((d*(a + b*x))/(b*c - a*d))] - Log[-((g*(a + b*x))/(b*f - a*g))])*(Log[c + d*x] + Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])^2)/g + (2*B^2*(Log[f + g*x] - Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))])*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/g + (2*B^2*Log[a + b*x]*PolyLog[2, -((g*(a + b*x))/(b*f - a*g))])/g + (2*B^2*(Log[f + g*x] - Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/g - (2*B^2*Log[(c + d*x)^(-1)]*PolyLog[2, -((g*(c + d*x))/(d*f - c*g))])/g - (2*B^2*Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))]*PolyLog[2, (g*(a + b*x))/(b*(f + g*x))])/g + (2*B^2*Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))]*PolyLog[2, -(((d*f - c*g)*(a + b*x))/((b*c - a*d)*(f + g*x)))])/g - (2*B^2*Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))]*PolyLog[2, (g*(c + d*x))/(d*(f + g*x))])/g + (2*B^2*Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))]*PolyLog[2, ((b*f - a*g)*(c + d*x))/((b*c - a*d)*(f + g*x))])/g - (2*A*B*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/g + (2*B^2*(Log[a + b*x] + Log[(c + d*x)^(-1)] - Log[(e*(a + b*x))/(c + d*x)])*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/g - (2*B^2*(Log[(c + d*x)^(-1)] + Log[c + d*x])*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/g + (2*B^2*(Log[c + d*x] + Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/g + (2*A*B*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g - (2*B^2*(Log[a + b*x] + Log[(c + d*x)^(-1)] - Log[(e*(a + b*x))/(c + d*x)])*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g + (2*B^2*(Log[a + b*x] + Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))])*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g - (2*B^2*PolyLog[3, -((d*(a + b*x))/(b*c - a*d))])/g - (2*B^2*PolyLog[3, -((g*(a + b*x))/(b*f - a*g))])/g - (2*B^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])/g - (2*B^2*PolyLog[3, -((g*(c + d*x))/(d*f - c*g))])/g - (2*B^2*PolyLog[3, (g*(a + b*x))/(b*(f + g*x))])/g + (2*B^2*PolyLog[3, -(((d*f - c*g)*(a + b*x))/((b*c - a*d)*(f + g*x)))])/g - (2*B^2*PolyLog[3, (g*(c + d*x))/(d*(f + g*x))])/g + (2*B^2*PolyLog[3, ((b*f - a*g)*(c + d*x))/((b*c - a*d)*(f + g*x))])/g - (2*B^2*PolyLog[3, (b*(f + g*x))/(b*f - a*g)])/g - (2*B^2*PolyLog[3, (d*(f + g*x))/(d*f - c*g)])/g","B",41,21,29,0.7241,1,"{2524, 12, 2528, 2418, 2390, 2301, 2394, 2393, 2391, 6688, 6742, 2500, 2433, 2375, 2317, 2374, 6589, 2440, 2437, 2435, 2315}"
245,1,612,0,1.1193966,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(f+g x)^2} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(f + g*x)^2,x]","\frac{2 b B^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{g (b f-a g)}+\frac{2 B^2 d \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{g (d f-c g)}-\frac{2 B^2 (b c-a d) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{(b f-a g) (d f-c g)}+\frac{2 B^2 (b c-a d) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{(b f-a g) (d f-c g)}+\frac{2 b B \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g (b f-a g)}-\frac{2 B d \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g (d f-c g)}+\frac{2 B (b c-a d) \log (f+g x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(b f-a g) (d f-c g)}-\frac{\left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g (f+g x)}+\frac{2 B^2 d \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{g (d f-c g)}+\frac{2 b B^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{g (b f-a g)}-\frac{2 B^2 (b c-a d) \log (f+g x) \log \left(-\frac{g (a+b x)}{b f-a g}\right)}{(b f-a g) (d f-c g)}+\frac{2 B^2 (b c-a d) \log (f+g x) \log \left(-\frac{g (c+d x)}{d f-c g}\right)}{(b f-a g) (d f-c g)}-\frac{b B^2 \log ^2(a+b x)}{g (b f-a g)}-\frac{B^2 d \log ^2(c+d x)}{g (d f-c g)}","\frac{2 B^2 (b c-a d) \text{PolyLog}\left(2,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{(b f-a g) (d f-c g)}+\frac{2 B (b c-a d) \log \left(1-\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(b f-a g) (d f-c g)}+\frac{(a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{(f+g x) (b f-a g)}",1,"-((b*B^2*Log[a + b*x]^2)/(g*(b*f - a*g))) + (2*b*B*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(g*(b*f - a*g)) - (A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(g*(f + g*x)) + (2*B^2*d*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(g*(d*f - c*g)) - (2*B*d*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/(g*(d*f - c*g)) - (B^2*d*Log[c + d*x]^2)/(g*(d*f - c*g)) + (2*b*B^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(g*(b*f - a*g)) - (2*B^2*(b*c - a*d)*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/((b*f - a*g)*(d*f - c*g)) + (2*B*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[f + g*x])/((b*f - a*g)*(d*f - c*g)) + (2*B^2*(b*c - a*d)*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/((b*f - a*g)*(d*f - c*g)) + (2*b*B^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(g*(b*f - a*g)) + (2*B^2*d*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(g*(d*f - c*g)) - (2*B^2*(b*c - a*d)*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/((b*f - a*g)*(d*f - c*g)) + (2*B^2*(b*c - a*d)*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/((b*f - a*g)*(d*f - c*g))","B",32,10,29,0.3448,1,"{2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
246,1,883,0,1.4810358,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(f+g x)^3} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(f + g*x)^3,x]","-\frac{B^2 \log ^2(a+b x) b^2}{2 g (b f-a g)^2}+\frac{B \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) b^2}{g (b f-a g)^2}+\frac{B^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) b^2}{g (b f-a g)^2}+\frac{B^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) b^2}{g (b f-a g)^2}+\frac{B^2 (b c-a d) \log (a+b x) b}{(b f-a g)^2 (d f-c g)}-\frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{2 g (f+g x)^2}-\frac{B^2 d^2 \log ^2(c+d x)}{2 g (d f-c g)^2}-\frac{B (b c-a d) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(b f-a g) (d f-c g) (f+g x)}+\frac{B^2 d^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x)}{g (d f-c g)^2}-\frac{B d^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x)}{g (d f-c g)^2}-\frac{B^2 d (b c-a d) \log (c+d x)}{(b f-a g) (d f-c g)^2}-\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) \log \left(-\frac{g (a+b x)}{b f-a g}\right) \log (f+g x)}{(b f-a g)^2 (d f-c g)^2}+\frac{B (b c-a d) (2 b d f-b c g-a d g) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (f+g x)}{(b f-a g)^2 (d f-c g)^2}+\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) \log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x)}{(b f-a g)^2 (d f-c g)^2}+\frac{B^2 (b c-a d)^2 g \log (f+g x)}{(b f-a g)^2 (d f-c g)^2}+\frac{B^2 d^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{g (d f-c g)^2}-\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{(b f-a g)^2 (d f-c g)^2}+\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{(b f-a g)^2 (d f-c g)^2}","\frac{B^2 (b c-a d) (-a d g-b c g+2 b d f) \text{PolyLog}\left(2,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{(b f-a g)^2 (d f-c g)^2}+\frac{b^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 g (b f-a g)^2}+\frac{B g (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(f+g x) (b f-a g)^2 (d f-c g)}+\frac{B (b c-a d) (-a d g-b c g+2 b d f) \log \left(1-\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(b f-a g)^2 (d f-c g)^2}-\frac{\left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 g (f+g x)^2}+\frac{B^2 g (b c-a d)^2 \log \left(\frac{f+g x}{c+d x}\right)}{(b f-a g)^2 (d f-c g)^2}",1,"(b*B^2*(b*c - a*d)*Log[a + b*x])/((b*f - a*g)^2*(d*f - c*g)) - (b^2*B^2*Log[a + b*x]^2)/(2*g*(b*f - a*g)^2) - (B*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/((b*f - a*g)*(d*f - c*g)*(f + g*x)) + (b^2*B*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(g*(b*f - a*g)^2) - (A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(2*g*(f + g*x)^2) - (B^2*d*(b*c - a*d)*Log[c + d*x])/((b*f - a*g)*(d*f - c*g)^2) + (B^2*d^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(g*(d*f - c*g)^2) - (B*d^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/(g*(d*f - c*g)^2) - (B^2*d^2*Log[c + d*x]^2)/(2*g*(d*f - c*g)^2) + (b^2*B^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(g*(b*f - a*g)^2) + (B^2*(b*c - a*d)^2*g*Log[f + g*x])/((b*f - a*g)^2*(d*f - c*g)^2) - (B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/((b*f - a*g)^2*(d*f - c*g)^2) + (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[f + g*x])/((b*f - a*g)^2*(d*f - c*g)^2) + (B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/((b*f - a*g)^2*(d*f - c*g)^2) + (b^2*B^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(g*(b*f - a*g)^2) + (B^2*d^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(g*(d*f - c*g)^2) - (B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/((b*f - a*g)^2*(d*f - c*g)^2) + (B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/((b*f - a*g)^2*(d*f - c*g)^2)","B",36,11,29,0.3793,1,"{2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 72}"
247,1,1356,0,2.3812368,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(f+g x)^4} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(f + g*x)^4,x]","-\frac{B^2 \log ^2(a+b x) b^3}{3 g (b f-a g)^3}+\frac{2 B \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) b^3}{3 g (b f-a g)^3}+\frac{2 B^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) b^3}{3 g (b f-a g)^3}+\frac{2 B^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) b^3}{3 g (b f-a g)^3}+\frac{B^2 (b c-a d) \log (a+b x) b^2}{3 (b f-a g)^3 (d f-c g)}+\frac{2 B^2 (b c-a d) (2 b d f-b c g-a d g) \log (a+b x) b}{3 (b f-a g)^3 (d f-c g)^2}-\frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{3 g (f+g x)^3}-\frac{B^2 d^3 \log ^2(c+d x)}{3 g (d f-c g)^3}-\frac{2 B (b c-a d) (2 b d f-b c g-a d g) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{3 (b f-a g)^2 (d f-c g)^2 (f+g x)}-\frac{B (b c-a d) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{3 (b f-a g) (d f-c g) (f+g x)^2}-\frac{2 B^2 d (b c-a d) (2 b d f-b c g-a d g) \log (c+d x)}{3 (b f-a g)^2 (d f-c g)^3}+\frac{2 B^2 d^3 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x)}{3 g (d f-c g)^3}-\frac{2 B d^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x)}{3 g (d f-c g)^3}-\frac{B^2 d^2 (b c-a d) \log (c+d x)}{3 (b f-a g) (d f-c g)^3}+\frac{B^2 (b c-a d)^2 g (2 b d f-b c g-a d g) \log (f+g x)}{(b f-a g)^3 (d f-c g)^3}-\frac{2 B^2 (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \log \left(-\frac{g (a+b x)}{b f-a g}\right) \log (f+g x)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{2 B (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (f+g x)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{2 B^2 (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{2 B^2 d^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 g (d f-c g)^3}-\frac{2 B^2 (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{2 B^2 (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{3 (b f-a g)^3 (d f-c g)^3}-\frac{B^2 (b c-a d)^2 g}{3 (b f-a g)^2 (d f-c g)^2 (f+g x)}","\frac{2 B^2 (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right) \text{PolyLog}\left(2,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{2 B (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right) \log \left(1-\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{b^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 g (b f-a g)^3}-\frac{B g^2 (c+d x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 (f+g x)^2 (b f-a g) (d f-c g)^3}-\frac{\left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 g (f+g x)^3}+\frac{2 B g (a+b x) (b c-a d) (-2 a d g-b c g+3 b d f) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 (f+g x) (b f-a g)^3 (d f-c g)^2}+\frac{B^2 g^2 (c+d x) (b c-a d)^2}{3 (f+g x) (b f-a g)^2 (d f-c g)^3}+\frac{B^2 g^2 (b c-a d)^3 \log \left(\frac{a+b x}{c+d x}\right)}{3 (b f-a g)^3 (d f-c g)^3}-\frac{B^2 g^2 (b c-a d)^3 \log \left(\frac{f+g x}{c+d x}\right)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{2 B^2 g (b c-a d)^2 (-2 a d g-b c g+3 b d f) \log \left(\frac{f+g x}{c+d x}\right)}{3 (b f-a g)^3 (d f-c g)^3}",1,"-(B^2*(b*c - a*d)^2*g)/(3*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)) + (b^2*B^2*(b*c - a*d)*Log[a + b*x])/(3*(b*f - a*g)^3*(d*f - c*g)) + (2*b*B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*Log[a + b*x])/(3*(b*f - a*g)^3*(d*f - c*g)^2) - (b^3*B^2*Log[a + b*x]^2)/(3*g*(b*f - a*g)^3) - (B*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(3*(b*f - a*g)*(d*f - c*g)*(f + g*x)^2) - (2*B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(3*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)) + (2*b^3*B*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(3*g*(b*f - a*g)^3) - (A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(3*g*(f + g*x)^3) - (B^2*d^2*(b*c - a*d)*Log[c + d*x])/(3*(b*f - a*g)*(d*f - c*g)^3) - (2*B^2*d*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*Log[c + d*x])/(3*(b*f - a*g)^2*(d*f - c*g)^3) + (2*B^2*d^3*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*g*(d*f - c*g)^3) - (2*B*d^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/(3*g*(d*f - c*g)^3) - (B^2*d^3*Log[c + d*x]^2)/(3*g*(d*f - c*g)^3) + (2*b^3*B^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3*g*(b*f - a*g)^3) + (B^2*(b*c - a*d)^2*g*(2*b*d*f - b*c*g - a*d*g)*Log[f + g*x])/((b*f - a*g)^3*(d*f - c*g)^3) - (2*B^2*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/(3*(b*f - a*g)^3*(d*f - c*g)^3) + (2*B*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[f + g*x])/(3*(b*f - a*g)^3*(d*f - c*g)^3) + (2*B^2*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/(3*(b*f - a*g)^3*(d*f - c*g)^3) + (2*b^3*B^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(3*g*(b*f - a*g)^3) + (2*B^2*d^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*g*(d*f - c*g)^3) - (2*B^2*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/(3*(b*f - a*g)^3*(d*f - c*g)^3) + (2*B^2*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/(3*(b*f - a*g)^3*(d*f - c*g)^3)","A",40,11,29,0.3793,1,"{2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 72}"
248,1,1881,0,3.403103,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(f+g x)^5} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(f + g*x)^5,x]","-\frac{B^2 \log ^2(a+b x) b^4}{4 g (b f-a g)^4}+\frac{B \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) b^4}{2 g (b f-a g)^4}+\frac{B^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) b^4}{2 g (b f-a g)^4}+\frac{B^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) b^4}{2 g (b f-a g)^4}+\frac{B^2 (b c-a d) \log (a+b x) b^3}{6 (b f-a g)^4 (d f-c g)}+\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) \log (a+b x) b^2}{4 (b f-a g)^4 (d f-c g)^2}+\frac{B^2 (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \log (a+b x) b}{2 (b f-a g)^4 (d f-c g)^3}-\frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{4 g (f+g x)^4}-\frac{B^2 d^4 \log ^2(c+d x)}{4 g (d f-c g)^4}-\frac{B (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{2 (b f-a g)^3 (d f-c g)^3 (f+g x)}-\frac{B (b c-a d) (2 b d f-b c g-a d g) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{4 (b f-a g)^2 (d f-c g)^2 (f+g x)^2}-\frac{B (b c-a d) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{6 (b f-a g) (d f-c g) (f+g x)^3}-\frac{B^2 d^2 (b c-a d) (2 b d f-b c g-a d g) \log (c+d x)}{4 (b f-a g)^2 (d f-c g)^4}-\frac{B^2 d (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \log (c+d x)}{2 (b f-a g)^3 (d f-c g)^4}+\frac{B^2 d^4 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x)}{2 g (d f-c g)^4}-\frac{B d^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x)}{2 g (d f-c g)^4}-\frac{B^2 d^3 (b c-a d) \log (c+d x)}{6 (b f-a g) (d f-c g)^4}+\frac{B^2 (b c-a d)^2 g (2 b d f-b c g-a d g)^2 \log (f+g x)}{4 (b f-a g)^4 (d f-c g)^4}+\frac{2 B^2 (b c-a d)^2 g \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \log (f+g x)}{3 (b f-a g)^4 (d f-c g)^4}+\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \log \left(-\frac{g (a+b x)}{b f-a g}\right) \log (f+g x)}{2 (b f-a g)^4 (d f-c g)^4}-\frac{B (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (f+g x)}{2 (b f-a g)^4 (d f-c g)^4}-\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x)}{2 (b f-a g)^4 (d f-c g)^4}+\frac{B^2 d^4 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{2 g (d f-c g)^4}+\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{2 (b f-a g)^4 (d f-c g)^4}-\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{2 (b f-a g)^4 (d f-c g)^4}-\frac{5 B^2 (b c-a d)^2 g (2 b d f-b c g-a d g)}{12 (b f-a g)^3 (d f-c g)^3 (f+g x)}-\frac{B^2 (b c-a d)^2 g}{12 (b f-a g)^2 (d f-c g)^2 (f+g x)^2}","\frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 b^4}{4 g (b f-a g)^4}-\frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{4 g (f+g x)^4}+\frac{B^2 (b c-a d)^3 g^2 (4 b d f-b c g-3 a d g) \log \left(\frac{a+b x}{c+d x}\right)}{4 (b f-a g)^4 (d f-c g)^4}-\frac{B^2 (b c-a d)^4 g^3 \log \left(\frac{a+b x}{c+d x}\right)}{6 (b f-a g)^4 (d f-c g)^4}+\frac{B (b c-a d) g \left(\left(6 d^2 f^2-4 c d g f+c^2 g^2\right) b^2-2 a d g (4 d f-c g) b+3 a^2 d^2 g^2\right) (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{2 (b f-a g)^4 (d f-c g)^3 (f+g x)}-\frac{B (b c-a d) g^2 (4 b d f-b c g-3 a d g) (c+d x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{4 (b f-a g)^2 (d f-c g)^4 (f+g x)^2}+\frac{B (b c-a d) g^3 (c+d x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{6 (b f-a g) (d f-c g)^4 (f+g x)^3}-\frac{B^2 (b c-a d)^3 g^2 (4 b d f-b c g-3 a d g) \log \left(\frac{f+g x}{c+d x}\right)}{4 (b f-a g)^4 (d f-c g)^4}+\frac{B^2 (b c-a d)^2 g \left(\left(6 d^2 f^2-4 c d g f+c^2 g^2\right) b^2-2 a d g (4 d f-c g) b+3 a^2 d^2 g^2\right) \log \left(\frac{f+g x}{c+d x}\right)}{2 (b f-a g)^4 (d f-c g)^4}+\frac{B^2 (b c-a d)^4 g^3 \log \left(\frac{f+g x}{c+d x}\right)}{6 (b f-a g)^4 (d f-c g)^4}-\frac{B (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log \left(1-\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{2 (b f-a g)^4 (d f-c g)^4}-\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \text{PolyLog}\left(2,\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{2 (b f-a g)^4 (d f-c g)^4}+\frac{B^2 (b c-a d)^2 g^2 (4 b d f-b c g-3 a d g) (c+d x)}{4 (b f-a g)^3 (d f-c g)^4 (f+g x)}-\frac{B^2 (b c-a d)^3 g^3 (c+d x)}{6 (b f-a g)^3 (d f-c g)^4 (f+g x)}-\frac{B^2 (b c-a d)^2 g^3 (c+d x)^2}{12 (b f-a g)^2 (d f-c g)^4 (f+g x)^2}",1,"-(B^2*(b*c - a*d)^2*g)/(12*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)^2) - (5*B^2*(b*c - a*d)^2*g*(2*b*d*f - b*c*g - a*d*g))/(12*(b*f - a*g)^3*(d*f - c*g)^3*(f + g*x)) + (b^3*B^2*(b*c - a*d)*Log[a + b*x])/(6*(b*f - a*g)^4*(d*f - c*g)) + (b^2*B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*Log[a + b*x])/(4*(b*f - a*g)^4*(d*f - c*g)^2) + (b*B^2*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*Log[a + b*x])/(2*(b*f - a*g)^4*(d*f - c*g)^3) - (b^4*B^2*Log[a + b*x]^2)/(4*g*(b*f - a*g)^4) - (B*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(6*(b*f - a*g)*(d*f - c*g)*(f + g*x)^3) - (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(4*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)^2) - (B*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(2*(b*f - a*g)^3*(d*f - c*g)^3*(f + g*x)) + (b^4*B*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(2*g*(b*f - a*g)^4) - (A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(4*g*(f + g*x)^4) - (B^2*d^3*(b*c - a*d)*Log[c + d*x])/(6*(b*f - a*g)*(d*f - c*g)^4) - (B^2*d^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*Log[c + d*x])/(4*(b*f - a*g)^2*(d*f - c*g)^4) - (B^2*d*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*Log[c + d*x])/(2*(b*f - a*g)^3*(d*f - c*g)^4) + (B^2*d^4*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(2*g*(d*f - c*g)^4) - (B*d^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/(2*g*(d*f - c*g)^4) - (B^2*d^4*Log[c + d*x]^2)/(4*g*(d*f - c*g)^4) + (b^4*B^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(2*g*(b*f - a*g)^4) + (B^2*(b*c - a*d)^2*g*(2*b*d*f - b*c*g - a*d*g)^2*Log[f + g*x])/(4*(b*f - a*g)^4*(d*f - c*g)^4) + (2*B^2*(b*c - a*d)^2*g*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*Log[f + g*x])/(3*(b*f - a*g)^4*(d*f - c*g)^4) + (B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/(2*(b*f - a*g)^4*(d*f - c*g)^4) - (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[f + g*x])/(2*(b*f - a*g)^4*(d*f - c*g)^4) - (B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/(2*(b*f - a*g)^4*(d*f - c*g)^4) + (b^4*B^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(2*g*(b*f - a*g)^4) + (B^2*d^4*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*g*(d*f - c*g)^4) + (B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/(2*(b*f - a*g)^4*(d*f - c*g)^4) - (B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/(2*(b*f - a*g)^4*(d*f - c*g)^4)","A",44,11,29,0.3793,1,"{2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 72}"
249,1,34,0,0.0142757,"\int \frac{\log \left(\frac{1+x}{-1+x}\right)}{x^2} \, dx","Int[Log[(1 + x)/(-1 + x)]/x^2,x]","2 \log (x)-2 \log (x+1)-\frac{(1-x) \log \left(-\frac{x+1}{1-x}\right)}{x}","2 \log \left(-\frac{x}{1-x}\right)-\frac{(x+1) \log \left(-\frac{x+1}{1-x}\right)}{x}",1,"2*Log[x] - 2*Log[1 + x] - ((1 - x)*Log[-((1 + x)/(1 - x))])/x","A",4,4,14,0.2857,1,"{2490, 36, 29, 31}"
250,0,0,0,0.1683482,"\int \frac{(f+g x)^2}{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)} \, dx","Int[(f + g*x)^2/(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\int \frac{(f+g x)^2}{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)} \, dx","\text{Int}\left(\frac{(f+g x)^2}{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A},x\right)",0,"f^2*Defer[Int][(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-1), x] + 2*f*g*Defer[Int][x/(A + B*Log[(e*(a + b*x))/(c + d*x)]), x] + g^2*Defer[Int][x^2/(A + B*Log[(e*(a + b*x))/(c + d*x)]), x]","A",0,0,0,0,-1,"{}"
251,0,0,0,0.0903596,"\int \frac{f+g x}{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)} \, dx","Int[(f + g*x)/(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\int \frac{f+g x}{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)} \, dx","\text{Int}\left(\frac{f+g x}{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A},x\right)",0,"f*Defer[Int][(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-1), x] + g*Defer[Int][x/(A + B*Log[(e*(a + b*x))/(c + d*x)]), x]","A",0,0,0,0,-1,"{}"
252,0,0,0,0.0136068,"\int \frac{1}{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-1),x]","\int \frac{1}{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)} \, dx","\text{Int}\left(\frac{1}{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A},x\right)",0,"Defer[Int][(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-1), x]","A",0,0,0,0,-1,"{}"
253,0,0,0,0.0650778,"\int \frac{1}{(f+g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)} \, dx","Int[1/((f + g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])),x]","\int \frac{1}{(f+g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{(f+g x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)},x\right)",0,"Defer[Int][1/((f + g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])), x]","A",0,0,0,0,-1,"{}"
254,0,0,0,0.065483,"\int \frac{1}{(f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)} \, dx","Int[1/((f + g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])),x]","\int \frac{1}{(f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{(f+g x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)},x\right)",0,"Defer[Int][1/((f + g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])), x]","A",0,0,0,0,-1,"{}"
255,0,0,0,0.0614351,"\int \frac{1}{(f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)} \, dx","Int[1/((f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])),x]","\int \frac{1}{(f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{(f+g x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)},x\right)",0,"Defer[Int][1/((f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])), x]","A",0,0,0,0,-1,"{}"
256,0,0,0,0.1840679,"\int \frac{(f+g x)^2}{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Int[(f + g*x)^2/(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\int \frac{(f+g x)^2}{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","\text{Int}\left(\frac{(f+g x)^2}{\left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2},x\right)",0,"f^2*Defer[Int][(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-2), x] + 2*f*g*Defer[Int][x/(A + B*Log[(e*(a + b*x))/(c + d*x)])^2, x] + g^2*Defer[Int][x^2/(A + B*Log[(e*(a + b*x))/(c + d*x)])^2, x]","A",0,0,0,0,-1,"{}"
257,0,0,0,0.0996355,"\int \frac{f+g x}{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Int[(f + g*x)/(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\int \frac{f+g x}{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","\text{Int}\left(\frac{f+g x}{\left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2},x\right)",0,"f*Defer[Int][(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-2), x] + g*Defer[Int][x/(A + B*Log[(e*(a + b*x))/(c + d*x)])^2, x]","A",0,0,0,0,-1,"{}"
258,0,0,0,0.0141137,"\int \frac{1}{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-2),x]","\int \frac{1}{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2},x\right)",0,"Defer[Int][(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-2), x]","A",0,0,0,0,-1,"{}"
259,0,0,0,0.0696734,"\int \frac{1}{(f+g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Int[1/((f + g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2),x]","\int \frac{1}{(f+g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(f+g x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2},x\right)",0,"Defer[Int][1/((f + g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2), x]","A",0,0,0,0,-1,"{}"
260,0,0,0,0.0747316,"\int \frac{1}{(f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Int[1/((f + g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2),x]","\int \frac{1}{(f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(f+g x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2},x\right)",0,"Defer[Int][1/((f + g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2), x]","A",0,0,0,0,-1,"{}"
261,0,0,0,0.0697515,"\int \frac{1}{(f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Int[1/((f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2),x]","\int \frac{1}{(f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(f+g x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2},x\right)",0,"Defer[Int][1/((f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2), x]","A",0,0,0,0,-1,"{}"
262,1,341,0,0.5010096,"\int (f+g x)^4 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \, dx","Int[(f + g*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","-\frac{B g^2 x^2 (b c-a d) \left(a^2 d^2 g^2-a b d g (5 d f-c g)+b^2 \left(c^2 g^2-5 c d f g+10 d^2 f^2\right)\right)}{5 b^3 d^3}+\frac{2 B g x \left(-10 a^2 b^2 d^4 f^2 g+5 a^3 b d^4 f g^2-a^4 d^4 g^3+10 a b^3 d^4 f^3+b^4 (-c) \left(5 c^2 d f g^2-c^3 g^3-10 c d^2 f^2 g+10 d^3 f^3\right)\right)}{5 b^4 d^4}+\frac{(f+g x)^5 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{5 g}-\frac{2 B g^3 x^3 (b c-a d) (-a d g-b c g+5 b d f)}{15 b^2 d^2}-\frac{2 B (b f-a g)^5 \log (a+b x)}{5 b^5 g}-\frac{B g^4 x^4 (b c-a d)}{10 b d}+\frac{2 B (d f-c g)^5 \log (c+d x)}{5 d^5 g}","-\frac{B g^2 x^2 (b c-a d) \left(a^2 d^2 g^2-a b d g (5 d f-c g)+b^2 \left(c^2 g^2-5 c d f g+10 d^2 f^2\right)\right)}{5 b^3 d^3}+\frac{2 B g x (b c-a d) \left(-a^2 b d^2 g^2 (5 d f-c g)+a^3 d^3 g^3+a b^2 d g \left(c^2 g^2-5 c d f g+10 d^2 f^2\right)+b^3 \left(-\left(5 c^2 d f g^2-c^3 g^3-10 c d^2 f^2 g+10 d^3 f^3\right)\right)\right)}{5 b^4 d^4}+\frac{(f+g x)^5 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{5 g}-\frac{2 B g^3 x^3 (b c-a d) (-a d g-b c g+5 b d f)}{15 b^2 d^2}-\frac{2 B (b f-a g)^5 \log (a+b x)}{5 b^5 g}-\frac{B g^4 x^4 (b c-a d)}{10 b d}+\frac{2 B (d f-c g)^5 \log (c+d x)}{5 d^5 g}",1,"(2*B*g*(10*a*b^3*d^4*f^3 - 10*a^2*b^2*d^4*f^2*g + 5*a^3*b*d^4*f*g^2 - a^4*d^4*g^3 - b^4*c*(10*d^3*f^3 - 10*c*d^2*f^2*g + 5*c^2*d*f*g^2 - c^3*g^3))*x)/(5*b^4*d^4) - (B*(b*c - a*d)*g^2*(a^2*d^2*g^2 - a*b*d*g*(5*d*f - c*g) + b^2*(10*d^2*f^2 - 5*c*d*f*g + c^2*g^2))*x^2)/(5*b^3*d^3) - (2*B*(b*c - a*d)*g^3*(5*b*d*f - b*c*g - a*d*g)*x^3)/(15*b^2*d^2) - (B*(b*c - a*d)*g^4*x^4)/(10*b*d) - (2*B*(b*f - a*g)^5*Log[a + b*x])/(5*b^5*g) + ((f + g*x)^5*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(5*g) + (2*B*(d*f - c*g)^5*Log[c + d*x])/(5*d^5*g)","A",4,3,29,0.1034,1,"{2525, 12, 72}"
263,1,229,0,0.3235107,"\int (f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \, dx","Int[(f + g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","-\frac{B g x (b c-a d) \left(a^2 d^2 g^2-a b d g (4 d f-c g)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right)}{2 b^3 d^3}+\frac{(f+g x)^4 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{4 g}-\frac{B g^2 x^2 (b c-a d) (-a d g-b c g+4 b d f)}{4 b^2 d^2}-\frac{B (b f-a g)^4 \log (a+b x)}{2 b^4 g}-\frac{B g^3 x^3 (b c-a d)}{6 b d}+\frac{B (d f-c g)^4 \log (c+d x)}{2 d^4 g}","-\frac{B g x (b c-a d) \left(a^2 d^2 g^2-a b d g (4 d f-c g)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right)}{2 b^3 d^3}+\frac{(f+g x)^4 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{4 g}-\frac{B g^2 x^2 (b c-a d) (-a d g-b c g+4 b d f)}{4 b^2 d^2}-\frac{B (b f-a g)^4 \log (a+b x)}{2 b^4 g}-\frac{B g^3 x^3 (b c-a d)}{6 b d}+\frac{B (d f-c g)^4 \log (c+d x)}{2 d^4 g}",1,"-(B*(b*c - a*d)*g*(a^2*d^2*g^2 - a*b*d*g*(4*d*f - c*g) + b^2*(6*d^2*f^2 - 4*c*d*f*g + c^2*g^2))*x)/(2*b^3*d^3) - (B*(b*c - a*d)*g^2*(4*b*d*f - b*c*g - a*d*g)*x^2)/(4*b^2*d^2) - (B*(b*c - a*d)*g^3*x^3)/(6*b*d) - (B*(b*f - a*g)^4*Log[a + b*x])/(2*b^4*g) + ((f + g*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(4*g) + (B*(d*f - c*g)^4*Log[c + d*x])/(2*d^4*g)","A",4,3,29,0.1034,1,"{2525, 12, 72}"
264,1,152,0,0.1609028,"\int (f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \, dx","Int[(f + g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\frac{(f+g x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 g}-\frac{2 B g x (b c-a d) (-a d g-b c g+3 b d f)}{3 b^2 d^2}-\frac{2 B (b f-a g)^3 \log (a+b x)}{3 b^3 g}-\frac{B g^2 x^2 (b c-a d)}{3 b d}+\frac{2 B (d f-c g)^3 \log (c+d x)}{3 d^3 g}","\frac{(f+g x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 g}-\frac{2 B g x (b c-a d) (-a d g-b c g+3 b d f)}{3 b^2 d^2}-\frac{2 B (b f-a g)^3 \log (a+b x)}{3 b^3 g}-\frac{B g^2 x^2 (b c-a d)}{3 b d}+\frac{2 B (d f-c g)^3 \log (c+d x)}{3 d^3 g}",1,"(-2*B*(b*c - a*d)*g*(3*b*d*f - b*c*g - a*d*g)*x)/(3*b^2*d^2) - (B*(b*c - a*d)*g^2*x^2)/(3*b*d) - (2*B*(b*f - a*g)^3*Log[a + b*x])/(3*b^3*g) + ((f + g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(3*g) + (2*B*(d*f - c*g)^3*Log[c + d*x])/(3*d^3*g)","A",4,3,29,0.1034,1,"{2525, 12, 72}"
265,1,104,0,0.0870162,"\int (f+g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \, dx","Int[(f + g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\frac{(f+g x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{2 g}-\frac{B (b f-a g)^2 \log (a+b x)}{b^2 g}-\frac{B g x (b c-a d)}{b d}+\frac{B (d f-c g)^2 \log (c+d x)}{d^2 g}","\frac{(f+g x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{2 g}-\frac{B (b f-a g)^2 \log (a+b x)}{b^2 g}-\frac{B g x (b c-a d)}{b d}+\frac{B (d f-c g)^2 \log (c+d x)}{d^2 g}",1,"-((B*(b*c - a*d)*g*x)/(b*d)) - (B*(b*f - a*g)^2*Log[a + b*x])/(b^2*g) + ((f + g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(2*g) + (B*(d*f - c*g)^2*Log[c + d*x])/(d^2*g)","A",4,3,27,0.1111,1,"{2525, 12, 72}"
266,1,54,0,0.0271851,"\int \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \, dx","Int[A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2],x]","\frac{B (a+b x) \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{b}-\frac{2 B (b c-a d) \log (c+d x)}{b d}+A x","\frac{B (a+b x) \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{b}-\frac{2 B (b c-a d) \log (c+d x)}{b d}+A x",1,"A*x + (B*(a + b*x)*Log[(e*(a + b*x)^2)/(c + d*x)^2])/b - (2*B*(b*c - a*d)*Log[c + d*x])/(b*d)","A",3,2,21,0.09524,1,"{2486, 31}"
267,1,144,0,0.3088779,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{f+g x} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(f + g*x),x]","-\frac{2 B \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{g}+\frac{2 B \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{g}+\frac{\log (f+g x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{g}-\frac{2 B \log (f+g x) \log \left(-\frac{g (a+b x)}{b f-a g}\right)}{g}+\frac{2 B \log (f+g x) \log \left(-\frac{g (c+d x)}{d f-c g}\right)}{g}","-\frac{2 B \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{g}+\frac{2 B \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{g}+\frac{\log (f+g x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{g}-\frac{2 B \log (f+g x) \log \left(-\frac{g (a+b x)}{b f-a g}\right)}{g}+\frac{2 B \log (f+g x) \log \left(-\frac{g (c+d x)}{d f-c g}\right)}{g}",1,"(-2*B*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/g + ((A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[f + g*x])/g + (2*B*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/g - (2*B*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/g + (2*B*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g","A",10,6,29,0.2069,1,"{2524, 12, 2418, 2394, 2393, 2391}"
268,1,117,0,0.092491,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{(f+g x)^2} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(f + g*x)^2,x]","-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{g (f+g x)}+\frac{2 B (b c-a d) \log (f+g x)}{(b f-a g) (d f-c g)}+\frac{2 b B \log (a+b x)}{g (b f-a g)}-\frac{2 B d \log (c+d x)}{g (d f-c g)}","\frac{(a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{(f+g x) (b f-a g)}+\frac{2 B (b c-a d) \log \left(\frac{f+g x}{c+d x}\right)}{(b f-a g) (d f-c g)}",1,"(2*b*B*Log[a + b*x])/(g*(b*f - a*g)) - (A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(g*(f + g*x)) - (2*B*d*Log[c + d*x])/(g*(d*f - c*g)) + (2*B*(b*c - a*d)*Log[f + g*x])/((b*f - a*g)*(d*f - c*g))","A",4,3,29,0.1034,1,"{2525, 12, 72}"
269,1,175,0,0.1697619,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{(f+g x)^3} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(f + g*x)^3,x]","-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{2 g (f+g x)^2}+\frac{b^2 B \log (a+b x)}{g (b f-a g)^2}-\frac{B (b c-a d)}{(f+g x) (b f-a g) (d f-c g)}+\frac{B (b c-a d) \log (f+g x) (-a d g-b c g+2 b d f)}{(b f-a g)^2 (d f-c g)^2}-\frac{B d^2 \log (c+d x)}{g (d f-c g)^2}","-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{2 g (f+g x)^2}+\frac{b^2 B \log (a+b x)}{g (b f-a g)^2}-\frac{B (b c-a d)}{(f+g x) (b f-a g) (d f-c g)}+\frac{B (b c-a d) \log (f+g x) (-a d g-b c g+2 b d f)}{(b f-a g)^2 (d f-c g)^2}-\frac{B d^2 \log (c+d x)}{g (d f-c g)^2}",1,"-((B*(b*c - a*d))/((b*f - a*g)*(d*f - c*g)*(f + g*x))) + (b^2*B*Log[a + b*x])/(g*(b*f - a*g)^2) - (A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(2*g*(f + g*x)^2) - (B*d^2*Log[c + d*x])/(g*(d*f - c*g)^2) + (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*Log[f + g*x])/((b*f - a*g)^2*(d*f - c*g)^2)","A",4,3,29,0.1034,1,"{2525, 12, 72}"
270,1,277,0,0.3274429,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{(f+g x)^4} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(f + g*x)^4,x]","\frac{2 B (b c-a d) \log (f+g x) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{3 (b f-a g)^3 (d f-c g)^3}-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{3 g (f+g x)^3}+\frac{2 b^3 B \log (a+b x)}{3 g (b f-a g)^3}-\frac{2 B (b c-a d) (-a d g-b c g+2 b d f)}{3 (f+g x) (b f-a g)^2 (d f-c g)^2}-\frac{B (b c-a d)}{3 (f+g x)^2 (b f-a g) (d f-c g)}-\frac{2 B d^3 \log (c+d x)}{3 g (d f-c g)^3}","\frac{2 B (b c-a d) \log (f+g x) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{3 (b f-a g)^3 (d f-c g)^3}-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{3 g (f+g x)^3}+\frac{2 b^3 B \log (a+b x)}{3 g (b f-a g)^3}-\frac{2 B (b c-a d) (-a d g-b c g+2 b d f)}{3 (f+g x) (b f-a g)^2 (d f-c g)^2}-\frac{B (b c-a d)}{3 (f+g x)^2 (b f-a g) (d f-c g)}-\frac{2 B d^3 \log (c+d x)}{3 g (d f-c g)^3}",1,"-(B*(b*c - a*d))/(3*(b*f - a*g)*(d*f - c*g)*(f + g*x)^2) - (2*B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g))/(3*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)) + (2*b^3*B*Log[a + b*x])/(3*g*(b*f - a*g)^3) - (A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(3*g*(f + g*x)^3) - (2*B*d^3*Log[c + d*x])/(3*g*(d*f - c*g)^3) + (2*B*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*Log[f + g*x])/(3*(b*f - a*g)^3*(d*f - c*g)^3)","A",4,3,29,0.1034,1,"{2525, 12, 72}"
271,1,381,0,0.5532827,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{(f+g x)^5} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(f + g*x)^5,x]","-\frac{B (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{2 (f+g x) (b f-a g)^3 (d f-c g)^3}-\frac{B (b c-a d) \log (f+g x) (-a d g-b c g+2 b d f) \left(-a^2 d^2 g^2+2 a b d^2 f g+b^2 \left(-\left(c^2 g^2-2 c d f g+2 d^2 f^2\right)\right)\right)}{2 (b f-a g)^4 (d f-c g)^4}-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{4 g (f+g x)^4}+\frac{b^4 B \log (a+b x)}{2 g (b f-a g)^4}-\frac{B (b c-a d) (-a d g-b c g+2 b d f)}{4 (f+g x)^2 (b f-a g)^2 (d f-c g)^2}-\frac{B (b c-a d)}{6 (f+g x)^3 (b f-a g) (d f-c g)}-\frac{B d^4 \log (c+d x)}{2 g (d f-c g)^4}","-\frac{B (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{2 (f+g x) (b f-a g)^3 (d f-c g)^3}-\frac{B (b c-a d) \log (f+g x) (-a d g-b c g+2 b d f) \left(-a^2 d^2 g^2+2 a b d^2 f g+b^2 \left(-\left(c^2 g^2-2 c d f g+2 d^2 f^2\right)\right)\right)}{2 (b f-a g)^4 (d f-c g)^4}-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{4 g (f+g x)^4}+\frac{b^4 B \log (a+b x)}{2 g (b f-a g)^4}-\frac{B (b c-a d) (-a d g-b c g+2 b d f)}{4 (f+g x)^2 (b f-a g)^2 (d f-c g)^2}-\frac{B (b c-a d)}{6 (f+g x)^3 (b f-a g) (d f-c g)}-\frac{B d^4 \log (c+d x)}{2 g (d f-c g)^4}",1,"-(B*(b*c - a*d))/(6*(b*f - a*g)*(d*f - c*g)*(f + g*x)^3) - (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g))/(4*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)^2) - (B*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2)))/(2*(b*f - a*g)^3*(d*f - c*g)^3*(f + g*x)) + (b^4*B*Log[a + b*x])/(2*g*(b*f - a*g)^4) - (A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(4*g*(f + g*x)^4) - (B*d^4*Log[c + d*x])/(2*g*(d*f - c*g)^4) - (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*Log[f + g*x])/(2*(b*f - a*g)^4*(d*f - c*g)^4)","A",4,3,29,0.1034,1,"{2525, 12, 72}"
272,1,973,0,1.8080646,"\int (f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2 \, dx","Int[(f + g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","\frac{B^2 \log ^2(a+b x) (b f-a g)^4}{b^4 g}-\frac{B \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) (b f-a g)^4}{b^4 g}-\frac{2 B^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) (b f-a g)^4}{b^4 g}-\frac{2 B^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) (b f-a g)^4}{b^4 g}+\frac{B^2 (b c-a d)^2 g^3 x^2}{3 b^2 d^2}+\frac{(f+g x)^4 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{4 g}+\frac{B^2 (d f-c g)^4 \log ^2(c+d x)}{d^4 g}-\frac{2 B^2 (b c-a d)^2 (b c+a d) g^3 x}{3 b^3 d^3}+\frac{B^2 (b c-a d)^2 g^2 (4 b d f-b c g-a d g) x}{b^3 d^3}-\frac{A B (b c-a d) g \left(\left(6 d^2 f^2-4 c d g f+c^2 g^2\right) b^2-a d g (4 d f-c g) b+a^2 d^2 g^2\right) x}{b^3 d^3}-\frac{2 a^3 B^2 (b c-a d) g^3 \log (a+b x)}{3 b^4 d}+\frac{a^2 B^2 (b c-a d) g^2 (4 b d f-b c g-a d g) \log (a+b x)}{b^4 d^2}-\frac{B^2 (b c-a d) g \left(\left(6 d^2 f^2-4 c d g f+c^2 g^2\right) b^2-a d g (4 d f-c g) b+a^2 d^2 g^2\right) (a+b x) \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{b^4 d^3}-\frac{B (b c-a d) g^3 x^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)}{3 b d}-\frac{B (b c-a d) g^2 (4 b d f-b c g-a d g) x^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)}{2 b^2 d^2}+\frac{2 B^2 c^3 (b c-a d) g^3 \log (c+d x)}{3 b d^4}-\frac{B^2 c^2 (b c-a d) g^2 (4 b d f-b c g-a d g) \log (c+d x)}{b^2 d^4}+\frac{2 B^2 (b c-a d)^2 g \left(\left(6 d^2 f^2-4 c d g f+c^2 g^2\right) b^2-a d g (4 d f-c g) b+a^2 d^2 g^2\right) \log (c+d x)}{b^4 d^4}-\frac{2 B^2 (d f-c g)^4 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x)}{d^4 g}+\frac{B (d f-c g)^4 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \log (c+d x)}{d^4 g}-\frac{2 B^2 (d f-c g)^4 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{d^4 g}","\frac{2 B^2 g^3 \log \left(\frac{a+b x}{c+d x}\right) (b c-a d)^4}{3 b^4 d^4}+\frac{2 B^2 g^3 \log (c+d x) (b c-a d)^4}{3 b^4 d^4}+\frac{2 B^2 g^3 x (b c-a d)^3}{3 b^3 d^3}+\frac{B^2 g^2 (4 b d f-3 b c g-a d g) \log \left(\frac{a+b x}{c+d x}\right) (b c-a d)^3}{b^4 d^4}+\frac{B^2 g^2 (4 b d f-3 b c g-a d g) \log (c+d x) (b c-a d)^3}{b^4 d^4}+\frac{B^2 g^3 (c+d x)^2 (b c-a d)^2}{3 b^2 d^4}+\frac{B^2 g^2 (4 b d f-3 b c g-a d g) x (b c-a d)^2}{b^3 d^3}+\frac{2 B^2 g \left(\left(6 d^2 f^2-8 c d g f+3 c^2 g^2\right) b^2-2 a d g (2 d f-c g) b+a^2 d^2 g^2\right) \log (c+d x) (b c-a d)^2}{b^4 d^4}-\frac{B g^3 (c+d x)^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) (b c-a d)}{3 b d^4}-\frac{B g^2 (4 b d f-3 b c g-a d g) (c+d x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) (b c-a d)}{2 b^2 d^4}-\frac{B g \left(\left(6 d^2 f^2-8 c d g f+3 c^2 g^2\right) b^2-2 a d g (2 d f-c g) b+a^2 d^2 g^2\right) (a+b x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) (b c-a d)}{b^4 d^3}-\frac{B (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \log \left(\frac{b c-a d}{b (c+d x)}\right) (b c-a d)}{b^4 d^4}-\frac{2 B^2 (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) (b c-a d)}{b^4 d^4}-\frac{(b f-a g)^4 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{4 b^4 g}+\frac{(f+g x)^4 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{4 g}",1,"(-2*B^2*(b*c - a*d)^2*(b*c + a*d)*g^3*x)/(3*b^3*d^3) + (B^2*(b*c - a*d)^2*g^2*(4*b*d*f - b*c*g - a*d*g)*x)/(b^3*d^3) - (A*B*(b*c - a*d)*g*(a^2*d^2*g^2 - a*b*d*g*(4*d*f - c*g) + b^2*(6*d^2*f^2 - 4*c*d*f*g + c^2*g^2))*x)/(b^3*d^3) + (B^2*(b*c - a*d)^2*g^3*x^2)/(3*b^2*d^2) - (2*a^3*B^2*(b*c - a*d)*g^3*Log[a + b*x])/(3*b^4*d) + (a^2*B^2*(b*c - a*d)*g^2*(4*b*d*f - b*c*g - a*d*g)*Log[a + b*x])/(b^4*d^2) + (B^2*(b*f - a*g)^4*Log[a + b*x]^2)/(b^4*g) - (B^2*(b*c - a*d)*g*(a^2*d^2*g^2 - a*b*d*g*(4*d*f - c*g) + b^2*(6*d^2*f^2 - 4*c*d*f*g + c^2*g^2))*(a + b*x)*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(b^4*d^3) - (B*(b*c - a*d)*g^2*(4*b*d*f - b*c*g - a*d*g)*x^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(2*b^2*d^2) - (B*(b*c - a*d)*g^3*x^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(3*b*d) - (B*(b*f - a*g)^4*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(b^4*g) + ((f + g*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2)/(4*g) + (2*B^2*c^3*(b*c - a*d)*g^3*Log[c + d*x])/(3*b*d^4) - (B^2*c^2*(b*c - a*d)*g^2*(4*b*d*f - b*c*g - a*d*g)*Log[c + d*x])/(b^2*d^4) + (2*B^2*(b*c - a*d)^2*g*(a^2*d^2*g^2 - a*b*d*g*(4*d*f - c*g) + b^2*(6*d^2*f^2 - 4*c*d*f*g + c^2*g^2))*Log[c + d*x])/(b^4*d^4) - (2*B^2*(d*f - c*g)^4*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(d^4*g) + (B*(d*f - c*g)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/(d^4*g) + (B^2*(d*f - c*g)^4*Log[c + d*x]^2)/(d^4*g) - (2*B^2*(b*f - a*g)^4*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b^4*g) - (2*B^2*(b*f - a*g)^4*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b^4*g) - (2*B^2*(d*f - c*g)^4*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(d^4*g)","A",33,13,31,0.4194,1,"{2525, 12, 2528, 2486, 31, 72, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
273,1,659,0,1.1986683,"\int (f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2 \, dx","Int[(f + g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","-\frac{8 B^2 (b f-a g)^3 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{3 b^3 g}-\frac{8 B^2 (d f-c g)^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 d^3 g}+\frac{4 a^2 B^2 g^2 (b c-a d) \log (a+b x)}{3 b^3 d}-\frac{4 A B g x (b c-a d) (-a d g-b c g+3 b d f)}{3 b^2 d^2}-\frac{4 B (b f-a g)^3 \log (a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b^3 g}+\frac{4 B (d f-c g)^3 \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 d^3 g}+\frac{(f+g x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{3 g}-\frac{2 B g^2 x^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b d}-\frac{4 B^2 g (a+b x) (b c-a d) (-a d g-b c g+3 b d f) \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{3 b^3 d^2}+\frac{8 B^2 g (b c-a d)^2 \log (c+d x) (-a d g-b c g+3 b d f)}{3 b^3 d^3}+\frac{4 B^2 g^2 x (b c-a d)^2}{3 b^2 d^2}-\frac{8 B^2 (b f-a g)^3 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{3 b^3 g}+\frac{4 B^2 (b f-a g)^3 \log ^2(a+b x)}{3 b^3 g}-\frac{4 B^2 c^2 g^2 (b c-a d) \log (c+d x)}{3 b d^3}-\frac{8 B^2 (d f-c g)^3 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 d^3 g}+\frac{4 B^2 (d f-c g)^3 \log ^2(c+d x)}{3 d^3 g}","\frac{8 B^2 (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{3 b^3 d^3}+\frac{4 B (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b^3 d^3}-\frac{4 B g (a+b x) (b c-a d) (-a d g-2 b c g+3 b d f) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b^3 d^2}-\frac{(b f-a g)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{3 b^3 g}-\frac{2 B g^2 (c+d x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 b d^3}+\frac{(f+g x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{3 g}+\frac{8 B^2 g (b c-a d)^2 \log (c+d x) (-a d g-2 b c g+3 b d f)}{3 b^3 d^3}+\frac{4 B^2 g^2 x (b c-a d)^2}{3 b^2 d^2}+\frac{4 B^2 g^2 (b c-a d)^3 \log \left(\frac{a+b x}{c+d x}\right)}{3 b^3 d^3}+\frac{4 B^2 g^2 (b c-a d)^3 \log (c+d x)}{3 b^3 d^3}",1,"(4*B^2*(b*c - a*d)^2*g^2*x)/(3*b^2*d^2) - (4*A*B*(b*c - a*d)*g*(3*b*d*f - b*c*g - a*d*g)*x)/(3*b^2*d^2) + (4*a^2*B^2*(b*c - a*d)*g^2*Log[a + b*x])/(3*b^3*d) + (4*B^2*(b*f - a*g)^3*Log[a + b*x]^2)/(3*b^3*g) - (4*B^2*(b*c - a*d)*g*(3*b*d*f - b*c*g - a*d*g)*(a + b*x)*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(3*b^3*d^2) - (2*B*(b*c - a*d)*g^2*x^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(3*b*d) - (4*B*(b*f - a*g)^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(3*b^3*g) + ((f + g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2)/(3*g) - (4*B^2*c^2*(b*c - a*d)*g^2*Log[c + d*x])/(3*b*d^3) + (8*B^2*(b*c - a*d)^2*g*(3*b*d*f - b*c*g - a*d*g)*Log[c + d*x])/(3*b^3*d^3) - (8*B^2*(d*f - c*g)^3*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*d^3*g) + (4*B*(d*f - c*g)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/(3*d^3*g) + (4*B^2*(d*f - c*g)^3*Log[c + d*x]^2)/(3*d^3*g) - (8*B^2*(b*f - a*g)^3*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3*b^3*g) - (8*B^2*(b*f - a*g)^3*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(3*b^3*g) - (8*B^2*(d*f - c*g)^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*d^3*g)","A",29,13,31,0.4194,1,"{2525, 12, 2528, 2486, 31, 72, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
274,1,450,0,0.9594113,"\int (f+g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2 \, dx","Int[(f + g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","-\frac{4 B^2 (b f-a g)^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b^2 g}-\frac{4 B^2 (d f-c g)^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{d^2 g}-\frac{2 B (b f-a g)^2 \log (a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b^2 g}+\frac{2 B (d f-c g)^2 \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{d^2 g}+\frac{(f+g x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{2 g}-\frac{2 A B g x (b c-a d)}{b d}+\frac{4 B^2 g (b c-a d)^2 \log (c+d x)}{b^2 d^2}-\frac{2 B^2 g (a+b x) (b c-a d) \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{b^2 d}-\frac{4 B^2 (b f-a g)^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b^2 g}+\frac{2 B^2 (b f-a g)^2 \log ^2(a+b x)}{b^2 g}-\frac{4 B^2 (d f-c g)^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{d^2 g}+\frac{2 B^2 (d f-c g)^2 \log ^2(c+d x)}{d^2 g}","\frac{4 B^2 (b c-a d) (-a d g-b c g+2 b d f) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b^2 d^2}+\frac{2 B (b c-a d) (-a d g-b c g+2 b d f) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b^2 d^2}-\frac{(b f-a g)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{2 b^2 g}-\frac{2 B g (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b^2 d}+\frac{(f+g x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{2 g}+\frac{4 B^2 g (b c-a d)^2 \log (c+d x)}{b^2 d^2}",1,"(-2*A*B*(b*c - a*d)*g*x)/(b*d) + (2*B^2*(b*f - a*g)^2*Log[a + b*x]^2)/(b^2*g) - (2*B^2*(b*c - a*d)*g*(a + b*x)*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(b^2*d) - (2*B*(b*f - a*g)^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(b^2*g) + ((f + g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2)/(2*g) + (4*B^2*(b*c - a*d)^2*g*Log[c + d*x])/(b^2*d^2) - (4*B^2*(d*f - c*g)^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(d^2*g) + (2*B*(d*f - c*g)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/(d^2*g) + (2*B^2*(d*f - c*g)^2*Log[c + d*x]^2)/(d^2*g) - (4*B^2*(b*f - a*g)^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b^2*g) - (4*B^2*(b*f - a*g)^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b^2*g) - (4*B^2*(d*f - c*g)^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(d^2*g)","A",25,12,29,0.4138,1,"{2525, 12, 2528, 2486, 31, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
275,1,252,0,0.7739033,"\int \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2 \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","\frac{8 a B^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b}+\frac{8 B^2 c \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{d}+\frac{4 a B \log (a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b}-\frac{4 B c \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{d}+x \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2+\frac{8 B^2 c \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{d}+\frac{8 a B^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b}-\frac{4 a B^2 \log ^2(a+b x)}{b}-\frac{4 B^2 c \log ^2(c+d x)}{d}","\frac{8 B^2 (b c-a d) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d}+\frac{4 B (b c-a d) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{b d}+\frac{(a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{b}",1,"(-4*a*B^2*Log[a + b*x]^2)/b + (4*a*B*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/b + x*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2 + (8*B^2*c*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/d - (4*B*c*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/d - (4*B^2*c*Log[c + d*x]^2)/d + (8*a*B^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/b + (8*a*B^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/b + (8*B^2*c*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/d","A",22,10,23,0.4348,1,"{2523, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
276,1,2126,0,5.8460757,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{f+g x} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(f + g*x),x]","\frac{4 \left(\log \left(\frac{b (c+d x)}{b c-a d}\right)+\log \left(\frac{b f-a g}{b (f+g x)}\right)-\log \left(\frac{(b f-a g) (c+d x)}{(b c-a d) (f+g x)}\right)\right) \log ^2\left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right) B^2}{g}-\frac{4 \left(\log \left(\frac{b (c+d x)}{b c-a d}\right)-\log \left(-\frac{g (c+d x)}{d f-c g}\right)\right) \left(\log (a+b x)+\log \left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right)\right)^2 B^2}{g}+\frac{4 \left(\log \left(-\frac{d (a+b x)}{b c-a d}\right)+\log \left(\frac{d f-c g}{d (f+g x)}\right)-\log \left(-\frac{(d f-c g) (a+b x)}{(b c-a d) (f+g x)}\right)\right) \log ^2\left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right) B^2}{g}-\frac{4 \left(\log \left(-\frac{d (a+b x)}{b c-a d}\right)-\log \left(-\frac{g (a+b x)}{b f-a g}\right)\right) \left(\log (c+d x)+\log \left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right)\right)^2 B^2}{g}-\frac{\log ^2\left((a+b x)^2\right) \log (f+g x) B^2}{g}-\frac{\log ^2\left(\frac{1}{(c+d x)^2}\right) \log (f+g x) B^2}{g}+\frac{4 \log \left(-\frac{g (a+b x)}{b f-a g}\right) \left(\log \left((a+b x)^2\right)+\log \left(\frac{1}{(c+d x)^2}\right)-\log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \log (f+g x) B^2}{g}+\frac{8 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) \log (f+g x) B^2}{g}-\frac{4 \log \left(-\frac{g (a+b x)}{b f-a g}\right) \left(\log \left(\frac{1}{(c+d x)^2}\right)+2 \log (c+d x)\right) \log (f+g x) B^2}{g}+\frac{8 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) \log (f+g x) B^2}{g}-\frac{4 \left(2 \log (a+b x)-\log \left((a+b x)^2\right)\right) \log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x) B^2}{g}-\frac{4 \left(\log \left((a+b x)^2\right)+\log \left(\frac{1}{(c+d x)^2}\right)-\log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x) B^2}{g}+\frac{\log ^2\left((a+b x)^2\right) \log \left(\frac{b (f+g x)}{b f-a g}\right) B^2}{g}+\frac{\log ^2\left(\frac{1}{(c+d x)^2}\right) \log \left(\frac{d (f+g x)}{d f-c g}\right) B^2}{g}+\frac{8 \left(\log (f+g x)-\log \left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right)\right) \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) B^2}{g}+\frac{4 \log \left((a+b x)^2\right) \text{PolyLog}\left(2,-\frac{g (a+b x)}{b f-a g}\right) B^2}{g}+\frac{8 \left(\log (f+g x)-\log \left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right)\right) \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) B^2}{g}-\frac{4 \log \left(\frac{1}{(c+d x)^2}\right) \text{PolyLog}\left(2,-\frac{g (c+d x)}{d f-c g}\right) B^2}{g}-\frac{8 \log \left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right) \text{PolyLog}\left(2,\frac{g (a+b x)}{b (f+g x)}\right) B^2}{g}+\frac{8 \log \left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right) \text{PolyLog}\left(2,-\frac{(d f-c g) (a+b x)}{(b c-a d) (f+g x)}\right) B^2}{g}-\frac{8 \log \left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right) \text{PolyLog}\left(2,\frac{g (c+d x)}{d (f+g x)}\right) B^2}{g}+\frac{8 \log \left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right) \text{PolyLog}\left(2,\frac{(b f-a g) (c+d x)}{(b c-a d) (f+g x)}\right) B^2}{g}+\frac{4 \left(\log \left((a+b x)^2\right)+\log \left(\frac{1}{(c+d x)^2}\right)-\log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right) B^2}{g}-\frac{4 \left(\log \left(\frac{1}{(c+d x)^2}\right)+2 \log (c+d x)\right) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right) B^2}{g}+\frac{8 \left(\log (c+d x)+\log \left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right)\right) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right) B^2}{g}-\frac{4 \left(2 \log (a+b x)-\log \left((a+b x)^2\right)\right) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right) B^2}{g}-\frac{4 \left(\log \left((a+b x)^2\right)+\log \left(\frac{1}{(c+d x)^2}\right)-\log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right) B^2}{g}+\frac{8 \left(\log (a+b x)+\log \left(-\frac{(b c-a d) (f+g x)}{(d f-c g) (a+b x)}\right)\right) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right) B^2}{g}-\frac{8 \text{PolyLog}\left(3,-\frac{d (a+b x)}{b c-a d}\right) B^2}{g}-\frac{8 \text{PolyLog}\left(3,-\frac{g (a+b x)}{b f-a g}\right) B^2}{g}-\frac{8 \text{PolyLog}\left(3,\frac{b (c+d x)}{b c-a d}\right) B^2}{g}-\frac{8 \text{PolyLog}\left(3,-\frac{g (c+d x)}{d f-c g}\right) B^2}{g}-\frac{8 \text{PolyLog}\left(3,\frac{g (a+b x)}{b (f+g x)}\right) B^2}{g}+\frac{8 \text{PolyLog}\left(3,-\frac{(d f-c g) (a+b x)}{(b c-a d) (f+g x)}\right) B^2}{g}-\frac{8 \text{PolyLog}\left(3,\frac{g (c+d x)}{d (f+g x)}\right) B^2}{g}+\frac{8 \text{PolyLog}\left(3,\frac{(b f-a g) (c+d x)}{(b c-a d) (f+g x)}\right) B^2}{g}-\frac{8 \text{PolyLog}\left(3,\frac{b (f+g x)}{b f-a g}\right) B^2}{g}-\frac{8 \text{PolyLog}\left(3,\frac{d (f+g x)}{d f-c g}\right) B^2}{g}-\frac{4 A \log \left(-\frac{g (a+b x)}{b f-a g}\right) \log (f+g x) B}{g}+\frac{4 A \log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x) B}{g}-\frac{4 A \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right) B}{g}+\frac{4 A \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right) B}{g}+\frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2 \log (f+g x)}{g}","\frac{4 B \text{PolyLog}\left(2,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{g}-\frac{4 B \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{g}-\frac{8 B^2 \text{PolyLog}\left(3,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{g}+\frac{8 B^2 \text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right)}{g}+\frac{\log \left(1-\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{g}-\frac{\log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{g}",1,"(-4*A*B*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/g - (B^2*Log[(a + b*x)^2]^2*Log[f + g*x])/g - (B^2*Log[(c + d*x)^(-2)]^2*Log[f + g*x])/g + (4*B^2*Log[-((g*(a + b*x))/(b*f - a*g))]*(Log[(a + b*x)^2] + Log[(c + d*x)^(-2)] - Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[f + g*x])/g + ((A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2*Log[f + g*x])/g + (8*B^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x]*Log[f + g*x])/g - (4*B^2*Log[-((g*(a + b*x))/(b*f - a*g))]*(Log[(c + d*x)^(-2)] + 2*Log[c + d*x])*Log[f + g*x])/g + (8*B^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)]*Log[f + g*x])/g + (4*A*B*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/g - (4*B^2*(2*Log[a + b*x] - Log[(a + b*x)^2])*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/g - (4*B^2*(Log[(a + b*x)^2] + Log[(c + d*x)^(-2)] - Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/g + (B^2*Log[(a + b*x)^2]^2*Log[(b*(f + g*x))/(b*f - a*g)])/g + (B^2*Log[(c + d*x)^(-2)]^2*Log[(d*(f + g*x))/(d*f - c*g)])/g + (4*B^2*(Log[(b*(c + d*x))/(b*c - a*d)] + Log[(b*f - a*g)/(b*(f + g*x))] - Log[((b*f - a*g)*(c + d*x))/((b*c - a*d)*(f + g*x))])*Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))]^2)/g - (4*B^2*(Log[(b*(c + d*x))/(b*c - a*d)] - Log[-((g*(c + d*x))/(d*f - c*g))])*(Log[a + b*x] + Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))])^2)/g + (4*B^2*(Log[-((d*(a + b*x))/(b*c - a*d))] + Log[(d*f - c*g)/(d*(f + g*x))] - Log[-(((d*f - c*g)*(a + b*x))/((b*c - a*d)*(f + g*x)))])*Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))]^2)/g - (4*B^2*(Log[-((d*(a + b*x))/(b*c - a*d))] - Log[-((g*(a + b*x))/(b*f - a*g))])*(Log[c + d*x] + Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])^2)/g + (8*B^2*(Log[f + g*x] - Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))])*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/g + (4*B^2*Log[(a + b*x)^2]*PolyLog[2, -((g*(a + b*x))/(b*f - a*g))])/g + (8*B^2*(Log[f + g*x] - Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/g - (4*B^2*Log[(c + d*x)^(-2)]*PolyLog[2, -((g*(c + d*x))/(d*f - c*g))])/g - (8*B^2*Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))]*PolyLog[2, (g*(a + b*x))/(b*(f + g*x))])/g + (8*B^2*Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))]*PolyLog[2, -(((d*f - c*g)*(a + b*x))/((b*c - a*d)*(f + g*x)))])/g - (8*B^2*Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))]*PolyLog[2, (g*(c + d*x))/(d*(f + g*x))])/g + (8*B^2*Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))]*PolyLog[2, ((b*f - a*g)*(c + d*x))/((b*c - a*d)*(f + g*x))])/g - (4*A*B*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/g + (4*B^2*(Log[(a + b*x)^2] + Log[(c + d*x)^(-2)] - Log[(e*(a + b*x)^2)/(c + d*x)^2])*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/g - (4*B^2*(Log[(c + d*x)^(-2)] + 2*Log[c + d*x])*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/g + (8*B^2*(Log[c + d*x] + Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/g + (4*A*B*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g - (4*B^2*(2*Log[a + b*x] - Log[(a + b*x)^2])*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g - (4*B^2*(Log[(a + b*x)^2] + Log[(c + d*x)^(-2)] - Log[(e*(a + b*x)^2)/(c + d*x)^2])*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g + (8*B^2*(Log[a + b*x] + Log[-(((b*c - a*d)*(f + g*x))/((d*f - c*g)*(a + b*x)))])*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g - (8*B^2*PolyLog[3, -((d*(a + b*x))/(b*c - a*d))])/g - (8*B^2*PolyLog[3, -((g*(a + b*x))/(b*f - a*g))])/g - (8*B^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])/g - (8*B^2*PolyLog[3, -((g*(c + d*x))/(d*f - c*g))])/g - (8*B^2*PolyLog[3, (g*(a + b*x))/(b*(f + g*x))])/g + (8*B^2*PolyLog[3, -(((d*f - c*g)*(a + b*x))/((b*c - a*d)*(f + g*x)))])/g - (8*B^2*PolyLog[3, (g*(c + d*x))/(d*(f + g*x))])/g + (8*B^2*PolyLog[3, ((b*f - a*g)*(c + d*x))/((b*c - a*d)*(f + g*x))])/g - (8*B^2*PolyLog[3, (b*(f + g*x))/(b*f - a*g)])/g - (8*B^2*PolyLog[3, (d*(f + g*x))/(d*f - c*g)])/g","B",44,21,31,0.6774,1,"{2524, 12, 2528, 2418, 2390, 2301, 2394, 2393, 2391, 6688, 6742, 2500, 2433, 2375, 2317, 2374, 6589, 2440, 2437, 2435, 2315}"
277,1,620,0,1.3013622,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{(f+g x)^2} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(f + g*x)^2,x]","\frac{8 b B^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{g (b f-a g)}+\frac{8 B^2 d \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{g (d f-c g)}-\frac{8 B^2 (b c-a d) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{(b f-a g) (d f-c g)}+\frac{8 B^2 (b c-a d) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{(b f-a g) (d f-c g)}+\frac{4 b B \log (a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{g (b f-a g)}-\frac{4 B d \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{g (d f-c g)}+\frac{4 B (b c-a d) \log (f+g x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{(b f-a g) (d f-c g)}-\frac{\left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{g (f+g x)}+\frac{8 B^2 d \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{g (d f-c g)}+\frac{8 b B^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{g (b f-a g)}-\frac{8 B^2 (b c-a d) \log (f+g x) \log \left(-\frac{g (a+b x)}{b f-a g}\right)}{(b f-a g) (d f-c g)}+\frac{8 B^2 (b c-a d) \log (f+g x) \log \left(-\frac{g (c+d x)}{d f-c g}\right)}{(b f-a g) (d f-c g)}-\frac{4 b B^2 \log ^2(a+b x)}{g (b f-a g)}-\frac{4 B^2 d \log ^2(c+d x)}{g (d f-c g)}","\frac{8 B^2 (b c-a d) \text{PolyLog}\left(2,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{(b f-a g) (d f-c g)}+\frac{4 B (b c-a d) \log \left(1-\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{(b f-a g) (d f-c g)}+\frac{(a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{(f+g x) (b f-a g)}",1,"(-4*b*B^2*Log[a + b*x]^2)/(g*(b*f - a*g)) + (4*b*B*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(g*(b*f - a*g)) - (A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(g*(f + g*x)) + (8*B^2*d*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(g*(d*f - c*g)) - (4*B*d*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/(g*(d*f - c*g)) - (4*B^2*d*Log[c + d*x]^2)/(g*(d*f - c*g)) + (8*b*B^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(g*(b*f - a*g)) - (8*B^2*(b*c - a*d)*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/((b*f - a*g)*(d*f - c*g)) + (4*B*(b*c - a*d)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[f + g*x])/((b*f - a*g)*(d*f - c*g)) + (8*B^2*(b*c - a*d)*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/((b*f - a*g)*(d*f - c*g)) + (8*b*B^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(g*(b*f - a*g)) + (8*B^2*d*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(g*(d*f - c*g)) - (8*B^2*(b*c - a*d)*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/((b*f - a*g)*(d*f - c*g)) + (8*B^2*(b*c - a*d)*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/((b*f - a*g)*(d*f - c*g))","B",32,10,31,0.3226,1,"{2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
278,1,899,0,1.6441597,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{(f+g x)^3} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(f + g*x)^3,x]","-\frac{2 B^2 \log ^2(a+b x) b^2}{g (b f-a g)^2}+\frac{2 B \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) b^2}{g (b f-a g)^2}+\frac{4 B^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) b^2}{g (b f-a g)^2}+\frac{4 B^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) b^2}{g (b f-a g)^2}+\frac{4 B^2 (b c-a d) \log (a+b x) b}{(b f-a g)^2 (d f-c g)}-\frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{2 g (f+g x)^2}-\frac{2 B^2 d^2 \log ^2(c+d x)}{g (d f-c g)^2}-\frac{2 B (b c-a d) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)}{(b f-a g) (d f-c g) (f+g x)}+\frac{4 B^2 d^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x)}{g (d f-c g)^2}-\frac{2 B d^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \log (c+d x)}{g (d f-c g)^2}-\frac{4 B^2 d (b c-a d) \log (c+d x)}{(b f-a g) (d f-c g)^2}-\frac{4 B^2 (b c-a d) (2 b d f-b c g-a d g) \log \left(-\frac{g (a+b x)}{b f-a g}\right) \log (f+g x)}{(b f-a g)^2 (d f-c g)^2}+\frac{2 B (b c-a d) (2 b d f-b c g-a d g) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \log (f+g x)}{(b f-a g)^2 (d f-c g)^2}+\frac{4 B^2 (b c-a d) (2 b d f-b c g-a d g) \log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x)}{(b f-a g)^2 (d f-c g)^2}+\frac{4 B^2 (b c-a d)^2 g \log (f+g x)}{(b f-a g)^2 (d f-c g)^2}+\frac{4 B^2 d^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{g (d f-c g)^2}-\frac{4 B^2 (b c-a d) (2 b d f-b c g-a d g) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{(b f-a g)^2 (d f-c g)^2}+\frac{4 B^2 (b c-a d) (2 b d f-b c g-a d g) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{(b f-a g)^2 (d f-c g)^2}","\frac{4 B^2 (b c-a d) (-a d g-b c g+2 b d f) \text{PolyLog}\left(2,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{(b f-a g)^2 (d f-c g)^2}+\frac{b^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{2 g (b f-a g)^2}+\frac{2 B g (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{(f+g x) (b f-a g)^2 (d f-c g)}+\frac{2 B (b c-a d) (-a d g-b c g+2 b d f) \log \left(1-\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{(b f-a g)^2 (d f-c g)^2}-\frac{\left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{2 g (f+g x)^2}+\frac{4 B^2 g (b c-a d)^2 \log \left(\frac{f+g x}{c+d x}\right)}{(b f-a g)^2 (d f-c g)^2}",1,"(4*b*B^2*(b*c - a*d)*Log[a + b*x])/((b*f - a*g)^2*(d*f - c*g)) - (2*b^2*B^2*Log[a + b*x]^2)/(g*(b*f - a*g)^2) - (2*B*(b*c - a*d)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/((b*f - a*g)*(d*f - c*g)*(f + g*x)) + (2*b^2*B*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(g*(b*f - a*g)^2) - (A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(2*g*(f + g*x)^2) - (4*B^2*d*(b*c - a*d)*Log[c + d*x])/((b*f - a*g)*(d*f - c*g)^2) + (4*B^2*d^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(g*(d*f - c*g)^2) - (2*B*d^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/(g*(d*f - c*g)^2) - (2*B^2*d^2*Log[c + d*x]^2)/(g*(d*f - c*g)^2) + (4*b^2*B^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(g*(b*f - a*g)^2) + (4*B^2*(b*c - a*d)^2*g*Log[f + g*x])/((b*f - a*g)^2*(d*f - c*g)^2) - (4*B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/((b*f - a*g)^2*(d*f - c*g)^2) + (2*B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[f + g*x])/((b*f - a*g)^2*(d*f - c*g)^2) + (4*B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/((b*f - a*g)^2*(d*f - c*g)^2) + (4*b^2*B^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(g*(b*f - a*g)^2) + (4*B^2*d^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(g*(d*f - c*g)^2) - (4*B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/((b*f - a*g)^2*(d*f - c*g)^2) + (4*B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/((b*f - a*g)^2*(d*f - c*g)^2)","B",36,11,31,0.3548,1,"{2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 72}"
279,1,1369,0,2.5397512,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{(f+g x)^4} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(f + g*x)^4,x]","-\frac{4 B^2 \log ^2(a+b x) b^3}{3 g (b f-a g)^3}+\frac{4 B \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) b^3}{3 g (b f-a g)^3}+\frac{8 B^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) b^3}{3 g (b f-a g)^3}+\frac{8 B^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) b^3}{3 g (b f-a g)^3}+\frac{4 B^2 (b c-a d) \log (a+b x) b^2}{3 (b f-a g)^3 (d f-c g)}+\frac{8 B^2 (b c-a d) (2 b d f-b c g-a d g) \log (a+b x) b}{3 (b f-a g)^3 (d f-c g)^2}-\frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{3 g (f+g x)^3}-\frac{4 B^2 d^3 \log ^2(c+d x)}{3 g (d f-c g)^3}-\frac{4 B (b c-a d) (2 b d f-b c g-a d g) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)}{3 (b f-a g)^2 (d f-c g)^2 (f+g x)}-\frac{2 B (b c-a d) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)}{3 (b f-a g) (d f-c g) (f+g x)^2}-\frac{8 B^2 d (b c-a d) (2 b d f-b c g-a d g) \log (c+d x)}{3 (b f-a g)^2 (d f-c g)^3}+\frac{8 B^2 d^3 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x)}{3 g (d f-c g)^3}-\frac{4 B d^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \log (c+d x)}{3 g (d f-c g)^3}-\frac{4 B^2 d^2 (b c-a d) \log (c+d x)}{3 (b f-a g) (d f-c g)^3}+\frac{4 B^2 (b c-a d)^2 g (2 b d f-b c g-a d g) \log (f+g x)}{(b f-a g)^3 (d f-c g)^3}-\frac{8 B^2 (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \log \left(-\frac{g (a+b x)}{b f-a g}\right) \log (f+g x)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{4 B (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \log (f+g x)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{8 B^2 (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{8 B^2 d^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 g (d f-c g)^3}-\frac{8 B^2 (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{8 B^2 (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{3 (b f-a g)^3 (d f-c g)^3}-\frac{4 B^2 (b c-a d)^2 g}{3 (b f-a g)^2 (d f-c g)^2 (f+g x)}","\frac{8 B^2 (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right) \text{PolyLog}\left(2,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{4 B (b c-a d) \left(a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right) \log \left(1-\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{b^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{3 g (b f-a g)^3}-\frac{2 B g^2 (c+d x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 (f+g x)^2 (b f-a g) (d f-c g)^3}-\frac{\left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{3 g (f+g x)^3}+\frac{4 B g (a+b x) (b c-a d) (-2 a d g-b c g+3 b d f) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)}{3 (f+g x) (b f-a g)^3 (d f-c g)^2}+\frac{4 B^2 g^2 (c+d x) (b c-a d)^2}{3 (f+g x) (b f-a g)^2 (d f-c g)^3}+\frac{4 B^2 g^2 (b c-a d)^3 \log \left(\frac{a+b x}{c+d x}\right)}{3 (b f-a g)^3 (d f-c g)^3}-\frac{4 B^2 g^2 (b c-a d)^3 \log \left(\frac{f+g x}{c+d x}\right)}{3 (b f-a g)^3 (d f-c g)^3}+\frac{8 B^2 g (b c-a d)^2 (-2 a d g-b c g+3 b d f) \log \left(\frac{f+g x}{c+d x}\right)}{3 (b f-a g)^3 (d f-c g)^3}",1,"(-4*B^2*(b*c - a*d)^2*g)/(3*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)) + (4*b^2*B^2*(b*c - a*d)*Log[a + b*x])/(3*(b*f - a*g)^3*(d*f - c*g)) + (8*b*B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*Log[a + b*x])/(3*(b*f - a*g)^3*(d*f - c*g)^2) - (4*b^3*B^2*Log[a + b*x]^2)/(3*g*(b*f - a*g)^3) - (2*B*(b*c - a*d)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(3*(b*f - a*g)*(d*f - c*g)*(f + g*x)^2) - (4*B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(3*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)) + (4*b^3*B*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(3*g*(b*f - a*g)^3) - (A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(3*g*(f + g*x)^3) - (4*B^2*d^2*(b*c - a*d)*Log[c + d*x])/(3*(b*f - a*g)*(d*f - c*g)^3) - (8*B^2*d*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*Log[c + d*x])/(3*(b*f - a*g)^2*(d*f - c*g)^3) + (8*B^2*d^3*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*g*(d*f - c*g)^3) - (4*B*d^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/(3*g*(d*f - c*g)^3) - (4*B^2*d^3*Log[c + d*x]^2)/(3*g*(d*f - c*g)^3) + (8*b^3*B^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3*g*(b*f - a*g)^3) + (4*B^2*(b*c - a*d)^2*g*(2*b*d*f - b*c*g - a*d*g)*Log[f + g*x])/((b*f - a*g)^3*(d*f - c*g)^3) - (8*B^2*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/(3*(b*f - a*g)^3*(d*f - c*g)^3) + (4*B*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[f + g*x])/(3*(b*f - a*g)^3*(d*f - c*g)^3) + (8*B^2*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/(3*(b*f - a*g)^3*(d*f - c*g)^3) + (8*b^3*B^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(3*g*(b*f - a*g)^3) + (8*B^2*d^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*g*(d*f - c*g)^3) - (8*B^2*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/(3*(b*f - a*g)^3*(d*f - c*g)^3) + (8*B^2*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/(3*(b*f - a*g)^3*(d*f - c*g)^3)","A",40,11,31,0.3548,1,"{2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 72}"
280,1,1854,0,3.5430597,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{(f+g x)^5} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(f + g*x)^5,x]","-\frac{B^2 \log ^2(a+b x) b^4}{g (b f-a g)^4}+\frac{B \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) b^4}{g (b f-a g)^4}+\frac{2 B^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) b^4}{g (b f-a g)^4}+\frac{2 B^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) b^4}{g (b f-a g)^4}+\frac{2 B^2 (b c-a d) \log (a+b x) b^3}{3 (b f-a g)^4 (d f-c g)}+\frac{B^2 (b c-a d) (2 b d f-b c g-a d g) \log (a+b x) b^2}{(b f-a g)^4 (d f-c g)^2}+\frac{2 B^2 (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \log (a+b x) b}{(b f-a g)^4 (d f-c g)^3}-\frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{4 g (f+g x)^4}-\frac{B^2 d^4 \log ^2(c+d x)}{g (d f-c g)^4}-\frac{B (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)}{(b f-a g)^3 (d f-c g)^3 (f+g x)}-\frac{B (b c-a d) (2 b d f-b c g-a d g) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)}{2 (b f-a g)^2 (d f-c g)^2 (f+g x)^2}-\frac{B (b c-a d) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)}{3 (b f-a g) (d f-c g) (f+g x)^3}-\frac{B^2 d^2 (b c-a d) (2 b d f-b c g-a d g) \log (c+d x)}{(b f-a g)^2 (d f-c g)^4}-\frac{2 B^2 d (b c-a d) \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \log (c+d x)}{(b f-a g)^3 (d f-c g)^4}+\frac{2 B^2 d^4 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x)}{g (d f-c g)^4}-\frac{B d^4 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \log (c+d x)}{g (d f-c g)^4}-\frac{2 B^2 d^3 (b c-a d) \log (c+d x)}{3 (b f-a g) (d f-c g)^4}+\frac{B^2 (b c-a d)^2 g (2 b d f-b c g-a d g)^2 \log (f+g x)}{(b f-a g)^4 (d f-c g)^4}+\frac{8 B^2 (b c-a d)^2 g \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2-a d g (3 d f-c g) b+a^2 d^2 g^2\right) \log (f+g x)}{3 (b f-a g)^4 (d f-c g)^4}+\frac{2 B^2 (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \log \left(-\frac{g (a+b x)}{b f-a g}\right) \log (f+g x)}{(b f-a g)^4 (d f-c g)^4}-\frac{B (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \log (f+g x)}{(b f-a g)^4 (d f-c g)^4}-\frac{2 B^2 (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x)}{(b f-a g)^4 (d f-c g)^4}+\frac{2 B^2 d^4 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{g (d f-c g)^4}+\frac{2 B^2 (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \text{PolyLog}\left(2,\frac{b (f+g x)}{b f-a g}\right)}{(b f-a g)^4 (d f-c g)^4}-\frac{2 B^2 (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \text{PolyLog}\left(2,\frac{d (f+g x)}{d f-c g}\right)}{(b f-a g)^4 (d f-c g)^4}-\frac{5 B^2 (b c-a d)^2 g (2 b d f-b c g-a d g)}{3 (b f-a g)^3 (d f-c g)^3 (f+g x)}-\frac{B^2 (b c-a d)^2 g}{3 (b f-a g)^2 (d f-c g)^2 (f+g x)^2}","\frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2 b^4}{4 g (b f-a g)^4}-\frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{4 g (f+g x)^4}+\frac{B (b c-a d) g \left(\left(6 d^2 f^2-4 c d g f+c^2 g^2\right) b^2-2 a d g (4 d f-c g) b+3 a^2 d^2 g^2\right) (a+b x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)}{(b f-a g)^4 (d f-c g)^3 (f+g x)}-\frac{B (b c-a d) g^2 (4 b d f-b c g-3 a d g) (c+d x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)}{2 (b f-a g)^2 (d f-c g)^4 (f+g x)^2}+\frac{B (b c-a d) g^3 (c+d x)^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)}{3 (b f-a g) (d f-c g)^4 (f+g x)^3}+\frac{B^2 (b c-a d)^3 g^2 (4 b d f-b c g-3 a d g) \log \left(\frac{a+b x}{c+d x}\right)}{(b f-a g)^4 (d f-c g)^4}-\frac{2 B^2 (b c-a d)^4 g^3 \log \left(\frac{a+b x}{c+d x}\right)}{3 (b f-a g)^4 (d f-c g)^4}-\frac{B^2 (b c-a d)^3 g^2 (4 b d f-b c g-3 a d g) \log \left(\frac{f+g x}{c+d x}\right)}{(b f-a g)^4 (d f-c g)^4}+\frac{2 B^2 (b c-a d)^2 g \left(\left(6 d^2 f^2-4 c d g f+c^2 g^2\right) b^2-2 a d g (4 d f-c g) b+3 a^2 d^2 g^2\right) \log \left(\frac{f+g x}{c+d x}\right)}{(b f-a g)^4 (d f-c g)^4}+\frac{2 B^2 (b c-a d)^4 g^3 \log \left(\frac{f+g x}{c+d x}\right)}{3 (b f-a g)^4 (d f-c g)^4}-\frac{B (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \log \left(1-\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{(b f-a g)^4 (d f-c g)^4}-\frac{2 B^2 (b c-a d) (2 b d f-b c g-a d g) \left(-\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2+2 a d^2 f g b-a^2 d^2 g^2\right) \text{PolyLog}\left(2,\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{(b f-a g)^4 (d f-c g)^4}+\frac{B^2 (b c-a d)^2 g^2 (4 b d f-b c g-3 a d g) (c+d x)}{(b f-a g)^3 (d f-c g)^4 (f+g x)}-\frac{2 B^2 (b c-a d)^3 g^3 (c+d x)}{3 (b f-a g)^3 (d f-c g)^4 (f+g x)}-\frac{B^2 (b c-a d)^2 g^3 (c+d x)^2}{3 (b f-a g)^2 (d f-c g)^4 (f+g x)^2}",1,"-(B^2*(b*c - a*d)^2*g)/(3*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)^2) - (5*B^2*(b*c - a*d)^2*g*(2*b*d*f - b*c*g - a*d*g))/(3*(b*f - a*g)^3*(d*f - c*g)^3*(f + g*x)) + (2*b^3*B^2*(b*c - a*d)*Log[a + b*x])/(3*(b*f - a*g)^4*(d*f - c*g)) + (b^2*B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*Log[a + b*x])/((b*f - a*g)^4*(d*f - c*g)^2) + (2*b*B^2*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*Log[a + b*x])/((b*f - a*g)^4*(d*f - c*g)^3) - (b^4*B^2*Log[a + b*x]^2)/(g*(b*f - a*g)^4) - (B*(b*c - a*d)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(3*(b*f - a*g)*(d*f - c*g)*(f + g*x)^3) - (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(2*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)^2) - (B*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/((b*f - a*g)^3*(d*f - c*g)^3*(f + g*x)) + (b^4*B*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/(g*(b*f - a*g)^4) - (A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(4*g*(f + g*x)^4) - (2*B^2*d^3*(b*c - a*d)*Log[c + d*x])/(3*(b*f - a*g)*(d*f - c*g)^4) - (B^2*d^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*Log[c + d*x])/((b*f - a*g)^2*(d*f - c*g)^4) - (2*B^2*d*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*Log[c + d*x])/((b*f - a*g)^3*(d*f - c*g)^4) + (2*B^2*d^4*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(g*(d*f - c*g)^4) - (B*d^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/(g*(d*f - c*g)^4) - (B^2*d^4*Log[c + d*x]^2)/(g*(d*f - c*g)^4) + (2*b^4*B^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(g*(b*f - a*g)^4) + (B^2*(b*c - a*d)^2*g*(2*b*d*f - b*c*g - a*d*g)^2*Log[f + g*x])/((b*f - a*g)^4*(d*f - c*g)^4) + (8*B^2*(b*c - a*d)^2*g*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2))*Log[f + g*x])/(3*(b*f - a*g)^4*(d*f - c*g)^4) + (2*B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x])/((b*f - a*g)^4*(d*f - c*g)^4) - (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[f + g*x])/((b*f - a*g)^4*(d*f - c*g)^4) - (2*B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x])/((b*f - a*g)^4*(d*f - c*g)^4) + (2*b^4*B^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(g*(b*f - a*g)^4) + (2*B^2*d^4*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(g*(d*f - c*g)^4) + (2*B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*PolyLog[2, (b*(f + g*x))/(b*f - a*g)])/((b*f - a*g)^4*(d*f - c*g)^4) - (2*B^2*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/((b*f - a*g)^4*(d*f - c*g)^4)","A",44,11,31,0.3548,1,"{2525, 12, 2528, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 72}"
281,0,0,0,0.1743908,"\int \frac{(f+g x)^2}{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)} \, dx","Int[(f + g*x)^2/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\int \frac{(f+g x)^2}{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)} \, dx","\text{Int}\left(\frac{(f+g x)^2}{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A},x\right)",0,"f^2*Defer[Int][(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^(-1), x] + 2*f*g*Defer[Int][x/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]), x] + g^2*Defer[Int][x^2/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]), x]","A",0,0,0,0,-1,"{}"
282,0,0,0,0.0918307,"\int \frac{f+g x}{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)} \, dx","Int[(f + g*x)/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\int \frac{f+g x}{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)} \, dx","\text{Int}\left(\frac{f+g x}{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A},x\right)",0,"f*Defer[Int][(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^(-1), x] + g*Defer[Int][x/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]), x]","A",0,0,0,0,-1,"{}"
283,0,0,0,0.0141488,"\int \frac{1}{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^(-1),x]","\int \frac{1}{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)} \, dx","\text{Int}\left(\frac{1}{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A},x\right)",0,"Defer[Int][(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^(-1), x]","A",0,0,0,0,-1,"{}"
284,0,0,0,0.0643133,"\int \frac{1}{(f+g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)} \, dx","Int[1/((f + g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])),x]","\int \frac{1}{(f+g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)} \, dx","\text{Int}\left(\frac{1}{(f+g x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)},x\right)",0,"Defer[Int][1/((f + g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])), x]","A",0,0,0,0,-1,"{}"
285,0,0,0,0.0678718,"\int \frac{1}{(f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)} \, dx","Int[1/((f + g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])),x]","\int \frac{1}{(f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)} \, dx","\text{Int}\left(\frac{1}{(f+g x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)},x\right)",0,"Defer[Int][1/((f + g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])), x]","A",0,0,0,0,-1,"{}"
286,0,0,0,0.0615744,"\int \frac{1}{(f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)} \, dx","Int[1/((f + g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])),x]","\int \frac{1}{(f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)} \, dx","\text{Int}\left(\frac{1}{(f+g x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)},x\right)",0,"Defer[Int][1/((f + g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])), x]","A",0,0,0,0,-1,"{}"
287,0,0,0,0.191497,"\int \frac{(f+g x)^2}{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","Int[(f + g*x)^2/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","\int \frac{(f+g x)^2}{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","\text{Int}\left(\frac{(f+g x)^2}{\left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2},x\right)",0,"f^2*Defer[Int][(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^(-2), x] + 2*f*g*Defer[Int][x/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2, x] + g^2*Defer[Int][x^2/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2, x]","A",0,0,0,0,-1,"{}"
288,0,0,0,0.1027344,"\int \frac{f+g x}{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","Int[(f + g*x)/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","\int \frac{f+g x}{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","\text{Int}\left(\frac{f+g x}{\left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2},x\right)",0,"f*Defer[Int][(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^(-2), x] + g*Defer[Int][x/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2, x]","A",0,0,0,0,-1,"{}"
289,0,0,0,0.0139057,"\int \frac{1}{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","Int[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^(-2),x]","\int \frac{1}{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2},x\right)",0,"Defer[Int][(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^(-2), x]","A",0,0,0,0,-1,"{}"
290,0,0,0,0.071707,"\int \frac{1}{(f+g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","Int[1/((f + g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2),x]","\int \frac{1}{(f+g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(f+g x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2},x\right)",0,"Defer[Int][1/((f + g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2), x]","A",0,0,0,0,-1,"{}"
291,0,0,0,0.0757691,"\int \frac{1}{(f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","Int[1/((f + g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2),x]","\int \frac{1}{(f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(f+g x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2},x\right)",0,"Defer[Int][1/((f + g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2), x]","A",0,0,0,0,-1,"{}"
292,0,0,0,0.0713971,"\int \frac{1}{(f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","Int[1/((f + g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2),x]","\int \frac{1}{(f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{(f+g x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2},x\right)",0,"Defer[Int][1/((f + g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2), x]","A",0,0,0,0,-1,"{}"
293,1,377,0,0.7122624,"\int (g+h x)^4 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Int[(g + h*x)^4*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]),x]","-\frac{B h^2 n x^2 (b c-a d) \left(a^2 d^2 h^2-a b d h (5 d g-c h)+b^2 \left(c^2 h^2-5 c d g h+10 d^2 g^2\right)\right)}{10 b^3 d^3}+\frac{B h n x (b c-a d) \left(-a^2 b d^2 h^2 (5 d g-c h)+a^3 d^3 h^3+a b^2 d h \left(c^2 h^2-5 c d g h+10 d^2 g^2\right)+b^3 \left(-\left(5 c^2 d g h^2-c^3 h^3-10 c d^2 g^2 h+10 d^3 g^3\right)\right)\right)}{5 b^4 d^4}-\frac{B h^3 n x^3 (b c-a d) (-a d h-b c h+5 b d g)}{15 b^2 d^2}-\frac{B n (b g-a h)^5 \log (a+b x)}{5 b^5 h}+\frac{B (g+h x)^5 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{5 h}-\frac{B h^4 n x^4 (b c-a d)}{20 b d}+\frac{A (g+h x)^5}{5 h}+\frac{B n (d g-c h)^5 \log (c+d x)}{5 d^5 h}","-\frac{B h^2 n x^2 (b c-a d) \left(a^2 d^2 h^2-a b d h (5 d g-c h)+b^2 \left(c^2 h^2-5 c d g h+10 d^2 g^2\right)\right)}{10 b^3 d^3}+\frac{B h n x (b c-a d) \left(-a^2 b d^2 h^2 (5 d g-c h)+a^3 d^3 h^3+a b^2 d h \left(c^2 h^2-5 c d g h+10 d^2 g^2\right)+b^3 \left(-\left(5 c^2 d g h^2-c^3 h^3-10 c d^2 g^2 h+10 d^3 g^3\right)\right)\right)}{5 b^4 d^4}+\frac{(g+h x)^5 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{5 h}-\frac{B h^3 n x^3 (b c-a d) (-a d h-b c h+5 b d g)}{15 b^2 d^2}-\frac{B n (b g-a h)^5 \log (a+b x)}{5 b^5 h}-\frac{B h^4 n x^4 (b c-a d)}{20 b d}+\frac{B n (d g-c h)^5 \log (c+d x)}{5 d^5 h}",1,"(B*(b*c - a*d)*h*(a^3*d^3*h^3 - a^2*b*d^2*h^2*(5*d*g - c*h) + a*b^2*d*h*(10*d^2*g^2 - 5*c*d*g*h + c^2*h^2) - b^3*(10*d^3*g^3 - 10*c*d^2*g^2*h + 5*c^2*d*g*h^2 - c^3*h^3))*n*x)/(5*b^4*d^4) - (B*(b*c - a*d)*h^2*(a^2*d^2*h^2 - a*b*d*h*(5*d*g - c*h) + b^2*(10*d^2*g^2 - 5*c*d*g*h + c^2*h^2))*n*x^2)/(10*b^3*d^3) - (B*(b*c - a*d)*h^3*(5*b*d*g - b*c*h - a*d*h)*n*x^3)/(15*b^2*d^2) - (B*(b*c - a*d)*h^4*n*x^4)/(20*b*d) + (A*(g + h*x)^5)/(5*h) - (B*(b*g - a*h)^5*n*Log[a + b*x])/(5*b^5*h) + (B*(d*g - c*h)^5*n*Log[c + d*x])/(5*d^5*h) + (B*(g + h*x)^5*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(5*h)","A",5,3,31,0.09677,1,"{6742, 2492, 72}"
294,1,248,0,0.4556436,"\int (g+h x)^3 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Int[(g + h*x)^3*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]),x]","-\frac{B h n x (b c-a d) \left(a^2 d^2 h^2-a b d h (4 d g-c h)+b^2 \left(c^2 h^2-4 c d g h+6 d^2 g^2\right)\right)}{4 b^3 d^3}-\frac{B h^2 n x^2 (b c-a d) (-a d h-b c h+4 b d g)}{8 b^2 d^2}-\frac{B n (b g-a h)^4 \log (a+b x)}{4 b^4 h}+\frac{B (g+h x)^4 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{4 h}-\frac{B h^3 n x^3 (b c-a d)}{12 b d}+\frac{A (g+h x)^4}{4 h}+\frac{B n (d g-c h)^4 \log (c+d x)}{4 d^4 h}","-\frac{B h n x (b c-a d) \left(a^2 d^2 h^2-a b d h (4 d g-c h)+b^2 \left(c^2 h^2-4 c d g h+6 d^2 g^2\right)\right)}{4 b^3 d^3}+\frac{(g+h x)^4 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{4 h}-\frac{B h^2 n x^2 (b c-a d) (-a d h-b c h+4 b d g)}{8 b^2 d^2}-\frac{B n (b g-a h)^4 \log (a+b x)}{4 b^4 h}-\frac{B h^3 n x^3 (b c-a d)}{12 b d}+\frac{B n (d g-c h)^4 \log (c+d x)}{4 d^4 h}",1,"-(B*(b*c - a*d)*h*(a^2*d^2*h^2 - a*b*d*h*(4*d*g - c*h) + b^2*(6*d^2*g^2 - 4*c*d*g*h + c^2*h^2))*n*x)/(4*b^3*d^3) - (B*(b*c - a*d)*h^2*(4*b*d*g - b*c*h - a*d*h)*n*x^2)/(8*b^2*d^2) - (B*(b*c - a*d)*h^3*n*x^3)/(12*b*d) + (A*(g + h*x)^4)/(4*h) - (B*(b*g - a*h)^4*n*Log[a + b*x])/(4*b^4*h) + (B*(d*g - c*h)^4*n*Log[c + d*x])/(4*d^4*h) + (B*(g + h*x)^4*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(4*h)","A",5,3,31,0.09677,1,"{6742, 2492, 72}"
295,1,170,0,0.2402667,"\int (g+h x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Int[(g + h*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]),x]","-\frac{B h n x (b c-a d) (-a d h-b c h+3 b d g)}{3 b^2 d^2}-\frac{B n (b g-a h)^3 \log (a+b x)}{3 b^3 h}+\frac{B (g+h x)^3 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 h}-\frac{B h^2 n x^2 (b c-a d)}{6 b d}+\frac{A (g+h x)^3}{3 h}+\frac{B n (d g-c h)^3 \log (c+d x)}{3 d^3 h}","\frac{(g+h x)^3 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{3 h}-\frac{B h n x (b c-a d) (-a d h-b c h+3 b d g)}{3 b^2 d^2}-\frac{B n (b g-a h)^3 \log (a+b x)}{3 b^3 h}-\frac{B h^2 n x^2 (b c-a d)}{6 b d}+\frac{B n (d g-c h)^3 \log (c+d x)}{3 d^3 h}",1,"-(B*(b*c - a*d)*h*(3*b*d*g - b*c*h - a*d*h)*n*x)/(3*b^2*d^2) - (B*(b*c - a*d)*h^2*n*x^2)/(6*b*d) + (A*(g + h*x)^3)/(3*h) - (B*(b*g - a*h)^3*n*Log[a + b*x])/(3*b^3*h) + (B*(d*g - c*h)^3*n*Log[c + d*x])/(3*d^3*h) + (B*(g + h*x)^3*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*h)","A",5,3,31,0.09677,1,"{6742, 2492, 72}"
296,1,128,0,0.1488686,"\int (g+h x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Int[(g + h*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]),x]","-\frac{B n (b g-a h)^2 \log (a+b x)}{2 b^2 h}+\frac{B (g+h x)^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{2 h}-\frac{B h n x (b c-a d)}{2 b d}+\frac{A (g+h x)^2}{2 h}+\frac{B n (d g-c h)^2 \log (c+d x)}{2 d^2 h}","\frac{(g+h x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{2 h}-\frac{B n (b g-a h)^2 \log (a+b x)}{2 b^2 h}-\frac{B h n x (b c-a d)}{2 b d}+\frac{B n (d g-c h)^2 \log (c+d x)}{2 d^2 h}",1,"-(B*(b*c - a*d)*h*n*x)/(2*b*d) + (A*(g + h*x)^2)/(2*h) - (B*(b*g - a*h)^2*n*Log[a + b*x])/(2*b^2*h) + (B*(d*g - c*h)^2*n*Log[c + d*x])/(2*d^2*h) + (B*(g + h*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*h)","A",5,3,29,0.1034,1,"{6742, 2492, 72}"
297,1,57,0,0.0299171,"\int \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Int[A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n],x]","\frac{B (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b}-\frac{B n (b c-a d) \log (c+d x)}{b d}+A x","\frac{B (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b}-\frac{B n (b c-a d) \log (c+d x)}{b d}+A x",1,"A*x - (B*(b*c - a*d)*n*Log[c + d*x])/(b*d) + (B*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/b","A",3,2,23,0.08696,1,"{2486, 31}"
298,1,156,0,0.1889282,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{g+h x} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(g + h*x),x]","-\frac{B n \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right)}{h}+\frac{B n \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right)}{h}+\frac{B \log (g+h x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{h}-\frac{B n \log (g+h x) \log \left(-\frac{h (a+b x)}{b g-a h}\right)}{h}+\frac{A \log (g+h x)}{h}+\frac{B n \log (g+h x) \log \left(-\frac{h (c+d x)}{d g-c h}\right)}{h}","-\frac{B n \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right)}{h}+\frac{B n \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right)}{h}+\frac{\log (g+h x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{h}-\frac{B n \log (g+h x) \log \left(-\frac{h (a+b x)}{b g-a h}\right)}{h}+\frac{B n \log (g+h x) \log \left(-\frac{h (c+d x)}{d g-c h}\right)}{h}",1,"(A*Log[g + h*x])/h - (B*n*Log[-((h*(a + b*x))/(b*g - a*h))]*Log[g + h*x])/h + (B*n*Log[-((h*(c + d*x))/(d*g - c*h))]*Log[g + h*x])/h + (B*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[g + h*x])/h - (B*n*PolyLog[2, (b*(g + h*x))/(b*g - a*h)])/h + (B*n*PolyLog[2, (d*(g + h*x))/(d*g - c*h)])/h","A",9,5,31,0.1613,1,"{6742, 2494, 2394, 2393, 2391}"
299,1,132,0,0.1198286,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x)^2} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(g + h*x)^2,x]","\frac{B (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x) (b g-a h)}-\frac{B n (b c-a d) \log (c+d x)}{(b g-a h) (d g-c h)}+\frac{B n (b c-a d) \log (g+h x)}{(b g-a h) (d g-c h)}-\frac{A}{h (g+h x)}","-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A}{h (g+h x)}+\frac{B n (b c-a d) \log (g+h x)}{(b g-a h) (d g-c h)}+\frac{b B n \log (a+b x)}{h (b g-a h)}-\frac{B d n \log (c+d x)}{h (d g-c h)}",1,"-(A/(h*(g + h*x))) - (B*(b*c - a*d)*n*Log[c + d*x])/((b*g - a*h)*(d*g - c*h)) + (B*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((b*g - a*h)*(g + h*x)) + (B*(b*c - a*d)*n*Log[g + h*x])/((b*g - a*h)*(d*g - c*h))","A",6,4,31,0.1290,1,"{6742, 2490, 36, 31}"
300,1,203,0,0.3008384,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x)^3} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(g + h*x)^3,x]","\frac{b^2 B n \log (a+b x)}{2 h (b g-a h)^2}-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{2 h (g+h x)^2}-\frac{B n (b c-a d)}{2 (g+h x) (b g-a h) (d g-c h)}+\frac{B n (b c-a d) \log (g+h x) (-a d h-b c h+2 b d g)}{2 (b g-a h)^2 (d g-c h)^2}-\frac{A}{2 h (g+h x)^2}-\frac{B d^2 n \log (c+d x)}{2 h (d g-c h)^2}","-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A}{2 h (g+h x)^2}+\frac{b^2 B n \log (a+b x)}{2 h (b g-a h)^2}-\frac{B n (b c-a d)}{2 (g+h x) (b g-a h) (d g-c h)}+\frac{B n (b c-a d) \log (g+h x) (-a d h-b c h+2 b d g)}{2 (b g-a h)^2 (d g-c h)^2}-\frac{B d^2 n \log (c+d x)}{2 h (d g-c h)^2}",1,"-A/(2*h*(g + h*x)^2) - (B*(b*c - a*d)*n)/(2*(b*g - a*h)*(d*g - c*h)*(g + h*x)) + (b^2*B*n*Log[a + b*x])/(2*h*(b*g - a*h)^2) - (B*d^2*n*Log[c + d*x])/(2*h*(d*g - c*h)^2) - (B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*h*(g + h*x)^2) + (B*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n*Log[g + h*x])/(2*(b*g - a*h)^2*(d*g - c*h)^2)","A",5,3,31,0.09677,1,"{6742, 2492, 72}"
301,1,296,0,0.5361167,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x)^4} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(g + h*x)^4,x]","\frac{B n (b c-a d) \log (g+h x) \left(a^2 d^2 h^2-a b d h (3 d g-c h)+b^2 \left(c^2 h^2-3 c d g h+3 d^2 g^2\right)\right)}{3 (b g-a h)^3 (d g-c h)^3}+\frac{b^3 B n \log (a+b x)}{3 h (b g-a h)^3}-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 h (g+h x)^3}-\frac{B n (b c-a d) (-a d h-b c h+2 b d g)}{3 (g+h x) (b g-a h)^2 (d g-c h)^2}-\frac{B n (b c-a d)}{6 (g+h x)^2 (b g-a h) (d g-c h)}-\frac{A}{3 h (g+h x)^3}-\frac{B d^3 n \log (c+d x)}{3 h (d g-c h)^3}","\frac{B n (b c-a d) \log (g+h x) \left(a^2 d^2 h^2-a b d h (3 d g-c h)+b^2 \left(c^2 h^2-3 c d g h+3 d^2 g^2\right)\right)}{3 (b g-a h)^3 (d g-c h)^3}-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A}{3 h (g+h x)^3}+\frac{b^3 B n \log (a+b x)}{3 h (b g-a h)^3}-\frac{B n (b c-a d) (-a d h-b c h+2 b d g)}{3 (g+h x) (b g-a h)^2 (d g-c h)^2}-\frac{B n (b c-a d)}{6 (g+h x)^2 (b g-a h) (d g-c h)}-\frac{B d^3 n \log (c+d x)}{3 h (d g-c h)^3}",1,"-A/(3*h*(g + h*x)^3) - (B*(b*c - a*d)*n)/(6*(b*g - a*h)*(d*g - c*h)*(g + h*x)^2) - (B*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n)/(3*(b*g - a*h)^2*(d*g - c*h)^2*(g + h*x)) + (b^3*B*n*Log[a + b*x])/(3*h*(b*g - a*h)^3) - (B*d^3*n*Log[c + d*x])/(3*h*(d*g - c*h)^3) - (B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*h*(g + h*x)^3) + (B*(b*c - a*d)*(a^2*d^2*h^2 - a*b*d*h*(3*d*g - c*h) + b^2*(3*d^2*g^2 - 3*c*d*g*h + c^2*h^2))*n*Log[g + h*x])/(3*(b*g - a*h)^3*(d*g - c*h)^3)","A",5,3,31,0.09677,1,"{6742, 2492, 72}"
302,1,401,0,0.8209676,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x)^5} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(g + h*x)^5,x]","-\frac{B n (b c-a d) \left(a^2 d^2 h^2-a b d h (3 d g-c h)+b^2 \left(c^2 h^2-3 c d g h+3 d^2 g^2\right)\right)}{4 (g+h x) (b g-a h)^3 (d g-c h)^3}-\frac{B n (b c-a d) \log (g+h x) (-a d h-b c h+2 b d g) \left(-a^2 d^2 h^2+2 a b d^2 g h+b^2 \left(-\left(c^2 h^2-2 c d g h+2 d^2 g^2\right)\right)\right)}{4 (b g-a h)^4 (d g-c h)^4}+\frac{b^4 B n \log (a+b x)}{4 h (b g-a h)^4}-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{4 h (g+h x)^4}-\frac{B n (b c-a d) (-a d h-b c h+2 b d g)}{8 (g+h x)^2 (b g-a h)^2 (d g-c h)^2}-\frac{B n (b c-a d)}{12 (g+h x)^3 (b g-a h) (d g-c h)}-\frac{A}{4 h (g+h x)^4}-\frac{B d^4 n \log (c+d x)}{4 h (d g-c h)^4}","-\frac{B n (b c-a d) \left(a^2 d^2 h^2-a b d h (3 d g-c h)+b^2 \left(c^2 h^2-3 c d g h+3 d^2 g^2\right)\right)}{4 (g+h x) (b g-a h)^3 (d g-c h)^3}-\frac{B n (b c-a d) \log (g+h x) (-a d h-b c h+2 b d g) \left(-a^2 d^2 h^2+2 a b d^2 g h+b^2 \left(-\left(c^2 h^2-2 c d g h+2 d^2 g^2\right)\right)\right)}{4 (b g-a h)^4 (d g-c h)^4}-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A}{4 h (g+h x)^4}+\frac{b^4 B n \log (a+b x)}{4 h (b g-a h)^4}-\frac{B n (b c-a d) (-a d h-b c h+2 b d g)}{8 (g+h x)^2 (b g-a h)^2 (d g-c h)^2}-\frac{B n (b c-a d)}{12 (g+h x)^3 (b g-a h) (d g-c h)}-\frac{B d^4 n \log (c+d x)}{4 h (d g-c h)^4}",1,"-A/(4*h*(g + h*x)^4) - (B*(b*c - a*d)*n)/(12*(b*g - a*h)*(d*g - c*h)*(g + h*x)^3) - (B*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n)/(8*(b*g - a*h)^2*(d*g - c*h)^2*(g + h*x)^2) - (B*(b*c - a*d)*(a^2*d^2*h^2 - a*b*d*h*(3*d*g - c*h) + b^2*(3*d^2*g^2 - 3*c*d*g*h + c^2*h^2))*n)/(4*(b*g - a*h)^3*(d*g - c*h)^3*(g + h*x)) + (b^4*B*n*Log[a + b*x])/(4*h*(b*g - a*h)^4) - (B*d^4*n*Log[c + d*x])/(4*h*(d*g - c*h)^4) - (B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(4*h*(g + h*x)^4) - (B*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*(2*a*b*d^2*g*h - a^2*d^2*h^2 - b^2*(2*d^2*g^2 - 2*c*d*g*h + c^2*h^2))*n*Log[g + h*x])/(4*(b*g - a*h)^4*(d*g - c*h)^4)","A",5,3,31,0.09677,1,"{6742, 2492, 72}"
303,1,697,0,1.2938529,"\int (g+h x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 \, dx","Int[(g + h*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2,x]","-\frac{2 B^2 n^2 (b g-a h)^3 \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{3 b^3 h}-\frac{2 B^2 n^2 (d g-c h)^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{3 d^3 h}+\frac{a^2 B^2 h^2 n^2 (b c-a d) \log (a+b x)}{3 b^3 d}-\frac{2 A B h n x (b c-a d) (-a d h-b c h+3 b d g)}{3 b^2 d^2}-\frac{2 A B n (b g-a h)^3 \log (a+b x)}{3 b^3 h}+\frac{2 A B (g+h x)^3 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 h}-\frac{A B h^2 n x^2 (b c-a d)}{3 b d}-\frac{2 B^2 h n (a+b x) (b c-a d) (-a d h-b c h+3 b d g) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b^3 d^2}+\frac{2 B^2 h n^2 (b c-a d)^2 \log (c+d x) (-a d h-b c h+3 b d g)}{3 b^3 d^3}+\frac{B^2 h^2 n^2 x (b c-a d)^2}{3 b^2 d^2}+\frac{2 B^2 n (b g-a h)^3 \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b^3 h}-\frac{B^2 c^2 h^2 n^2 (b c-a d) \log (c+d x)}{3 b d^3}-\frac{2 B^2 n (d g-c h)^3 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 d^3 h}+\frac{B^2 (g+h x)^3 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{3 h}-\frac{B^2 h^2 n x^2 (b c-a d) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{3 b d}+\frac{A^2 (g+h x)^3}{3 h}+\frac{2 A B n (d g-c h)^3 \log (c+d x)}{3 d^3 h}","\frac{2 B^2 n^2 (b c-a d) \left(a^2 d^2 h^2-a b d h (3 d g-c h)+b^2 \left(c^2 h^2-3 c d g h+3 d^2 g^2\right)\right) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{3 b^3 d^3}+\frac{2 B n (b c-a d) \left(a^2 d^2 h^2-a b d h (3 d g-c h)+b^2 \left(c^2 h^2-3 c d g h+3 d^2 g^2\right)\right) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{3 b^3 d^3}-\frac{2 B h n (a+b x) (b c-a d) (-a d h-2 b c h+3 b d g) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{3 b^3 d^2}-\frac{(b g-a h)^3 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{3 b^3 h}-\frac{B h^2 n (c+d x)^2 (b c-a d) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{3 b d^3}+\frac{(g+h x)^3 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{3 h}+\frac{2 B^2 h n^2 (b c-a d)^2 \log (c+d x) (-a d h-2 b c h+3 b d g)}{3 b^3 d^3}+\frac{B^2 h^2 n^2 x (b c-a d)^2}{3 b^2 d^2}+\frac{B^2 h^2 n^2 (b c-a d)^3 \log \left(\frac{a+b x}{c+d x}\right)}{3 b^3 d^3}+\frac{B^2 h^2 n^2 (b c-a d)^3 \log (c+d x)}{3 b^3 d^3}",1,"(-2*A*B*(b*c - a*d)*h*(3*b*d*g - b*c*h - a*d*h)*n*x)/(3*b^2*d^2) + (B^2*(b*c - a*d)^2*h^2*n^2*x)/(3*b^2*d^2) - (A*B*(b*c - a*d)*h^2*n*x^2)/(3*b*d) + (A^2*(g + h*x)^3)/(3*h) - (2*A*B*(b*g - a*h)^3*n*Log[a + b*x])/(3*b^3*h) + (a^2*B^2*(b*c - a*d)*h^2*n^2*Log[a + b*x])/(3*b^3*d) + (2*A*B*(d*g - c*h)^3*n*Log[c + d*x])/(3*d^3*h) - (B^2*c^2*(b*c - a*d)*h^2*n^2*Log[c + d*x])/(3*b*d^3) + (2*B^2*(b*c - a*d)^2*h*(3*b*d*g - b*c*h - a*d*h)*n^2*Log[c + d*x])/(3*b^3*d^3) - (B^2*(b*c - a*d)*h^2*n*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b*d) - (2*B^2*(b*c - a*d)*h*(3*b*d*g - b*c*h - a*d*h)*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b^3*d^2) + (2*A*B*(g + h*x)^3*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*h) + (2*B^2*(b*g - a*h)^3*n*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*b^3*h) - (2*B^2*(d*g - c*h)^3*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(3*d^3*h) + (B^2*(g + h*x)^3*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(3*h) - (2*B^2*(d*g - c*h)^3*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(3*d^3*h) - (2*B^2*(b*g - a*h)^3*n^2*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(3*b^3*h)","A",23,11,33,0.3333,1,"{6742, 2492, 72, 2514, 2486, 31, 2488, 2411, 2343, 2333, 2315}"
304,1,449,0,0.9551474,"\int (g+h x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 \, dx","Int[(g + h*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2,x]","-\frac{B^2 n^2 (b g-a h)^2 \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{b^2 h}-\frac{B^2 n^2 (d g-c h)^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{d^2 h}-\frac{A B n (b g-a h)^2 \log (a+b x)}{b^2 h}+\frac{A B (g+h x)^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{h}-\frac{A B h n x (b c-a d)}{b d}+\frac{B^2 h n^2 (b c-a d)^2 \log (c+d x)}{b^2 d^2}+\frac{B^2 n (b g-a h)^2 \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b^2 h}-\frac{B^2 h n (a+b x) (b c-a d) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b^2 d}-\frac{B^2 n (d g-c h)^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{d^2 h}+\frac{B^2 (g+h x)^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 h}+\frac{A^2 (g+h x)^2}{2 h}+\frac{A B n (d g-c h)^2 \log (c+d x)}{d^2 h}","\frac{B^2 n^2 (b c-a d) (-a d h-b c h+2 b d g) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b^2 d^2}+\frac{B n (b c-a d) (-a d h-b c h+2 b d g) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b^2 d^2}-\frac{(b g-a h)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 b^2 h}-\frac{B h n (a+b x) (b c-a d) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b^2 d}+\frac{(g+h x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 h}+\frac{B^2 h n^2 (b c-a d)^2 \log (c+d x)}{b^2 d^2}",1,"-((A*B*(b*c - a*d)*h*n*x)/(b*d)) + (A^2*(g + h*x)^2)/(2*h) - (A*B*(b*g - a*h)^2*n*Log[a + b*x])/(b^2*h) + (A*B*(d*g - c*h)^2*n*Log[c + d*x])/(d^2*h) + (B^2*(b*c - a*d)^2*h*n^2*Log[c + d*x])/(b^2*d^2) - (B^2*(b*c - a*d)*h*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b^2*d) + (A*B*(g + h*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/h + (B^2*(b*g - a*h)^2*n*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b^2*h) - (B^2*(d*g - c*h)^2*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(d^2*h) + (B^2*(g + h*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*h) - (B^2*(d*g - c*h)^2*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(d^2*h) - (B^2*(b*g - a*h)^2*n^2*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(b^2*h)","A",20,11,31,0.3548,1,"{6742, 2492, 72, 2514, 2486, 31, 2488, 2411, 2343, 2333, 2315}"
305,1,195,0,0.3207972,"\int \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2,x]","\frac{2 B^2 n^2 (b c-a d) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d}+\frac{2 A B (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b}-\frac{2 A B n (b c-a d) \log (c+d x)}{b d}+\frac{B^2 (a+b x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{b}+\frac{2 B^2 n (b c-a d) \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b d}+A^2 x","\frac{2 B^2 n^2 (b c-a d) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d}+\frac{2 B n (b c-a d) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b d}+\frac{(a+b x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{b}",1,"A^2*x - (2*A*B*(b*c - a*d)*n*Log[c + d*x])/(b*d) + (2*A*B*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/b + (2*B^2*(b*c - a*d)*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*d) + (B^2*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/b + (2*B^2*(b*c - a*d)*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(b*d)","A",10,8,25,0.3200,1,"{6742, 2486, 31, 2488, 2411, 2343, 2333, 2315}"
306,1,473,0,0.8152562,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{g+h x} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(g + h*x),x]","-\frac{2 A B n \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right)}{h}+\frac{2 B^2 n \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,1-\frac{(g+h x) (b c-a d)}{(c+d x) (b g-a h)}\right)}{h}-\frac{2 B^2 n \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{h}-\frac{2 B^2 n^2 \text{PolyLog}\left(3,1-\frac{(g+h x) (b c-a d)}{(c+d x) (b g-a h)}\right)}{h}+\frac{2 B^2 n^2 \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right)}{h}+\frac{2 A B n \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right)}{h}+\frac{2 A B \log (g+h x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{h}-\frac{2 A B n \log (g+h x) \log \left(-\frac{h (a+b x)}{b g-a h}\right)}{h}+\frac{B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) \log \left(\frac{(g+h x) (b c-a d)}{(c+d x) (b g-a h)}\right)}{h}-\frac{B^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{h}+\frac{A^2 \log (g+h x)}{h}+\frac{2 A B n \log (g+h x) \log \left(-\frac{h (c+d x)}{d g-c h}\right)}{h}","\frac{2 B n \text{PolyLog}\left(2,\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{h}-\frac{2 B n \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{h}-\frac{2 B^2 n^2 \text{PolyLog}\left(3,\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right)}{h}+\frac{2 B^2 n^2 \text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right)}{h}+\frac{\log \left(1-\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{h}-\frac{\log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{h}",1,"-((B^2*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/h) + (A^2*Log[g + h*x])/h - (2*A*B*n*Log[-((h*(a + b*x))/(b*g - a*h))]*Log[g + h*x])/h + (2*A*B*n*Log[-((h*(c + d*x))/(d*g - c*h))]*Log[g + h*x])/h + (2*A*B*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[g + h*x])/h + (B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2*Log[((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/h - (2*A*B*n*PolyLog[2, (b*(g + h*x))/(b*g - a*h)])/h + (2*A*B*n*PolyLog[2, (d*(g + h*x))/(d*g - c*h)])/h - (2*B^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/h + (2*B^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 - ((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/h + (2*B^2*n^2*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/h - (2*B^2*n^2*PolyLog[3, 1 - ((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/h","A",16,10,33,0.3030,1,"{6742, 2494, 2394, 2393, 2391, 2489, 2488, 2506, 6610, 2503}"
307,1,343,0,0.406977,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{(g+h x)^2} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(g + h*x)^2,x]","\frac{2 B^2 n^2 (b c-a d) \text{PolyLog}\left(2,1-\frac{(g+h x) (b c-a d)}{(c+d x) (b g-a h)}\right)}{(b g-a h) (d g-c h)}+\frac{2 A B (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x) (b g-a h)}-\frac{2 A B n (b c-a d) \log (c+d x)}{(b g-a h) (d g-c h)}+\frac{2 A B n (b c-a d) \log (g+h x)}{(b g-a h) (d g-c h)}+\frac{B^2 (a+b x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x) (b g-a h)}+\frac{2 B^2 n (b c-a d) \log \left(e (a+b x)^n (c+d x)^{-n}\right) \log \left(\frac{(g+h x) (b c-a d)}{(c+d x) (b g-a h)}\right)}{(b g-a h) (d g-c h)}-\frac{A^2}{h (g+h x)}","\frac{2 B^2 n^2 (b c-a d) \text{PolyLog}\left(2,\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right)}{(b g-a h) (d g-c h)}+\frac{2 B n (b c-a d) \log \left(1-\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{(b g-a h) (d g-c h)}+\frac{(a+b x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{(g+h x) (b g-a h)}",1,"-(A^2/(h*(g + h*x))) - (2*A*B*(b*c - a*d)*n*Log[c + d*x])/((b*g - a*h)*(d*g - c*h)) + (2*A*B*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((b*g - a*h)*(g + h*x)) + (B^2*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/((b*g - a*h)*(g + h*x)) + (2*A*B*(b*c - a*d)*n*Log[g + h*x])/((b*g - a*h)*(d*g - c*h)) + (2*B^2*(b*c - a*d)*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/((b*g - a*h)*(d*g - c*h)) + (2*B^2*(b*c - a*d)*n^2*PolyLog[2, 1 - ((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/((b*g - a*h)*(d*g - c*h))","A",10,7,33,0.2121,1,"{6742, 2490, 36, 31, 2503, 2502, 2315}"
308,1,968,0,1.6305731,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{(g+h x)^3} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(g + h*x)^3,x]","-\frac{A^2}{2 h (g+h x)^2}+\frac{b^2 B n \log (a+b x) A}{h (b g-a h)^2}-\frac{B d^2 n \log (c+d x) A}{h (d g-c h)^2}-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right) A}{h (g+h x)^2}+\frac{B (b c-a d) (2 b d g-b c h-a d h) n \log (g+h x) A}{(b g-a h)^2 (d g-c h)^2}-\frac{B (b c-a d) n A}{(b g-a h) (d g-c h) (g+h x)}-\frac{B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 h (g+h x)^2}-\frac{B^2 (b c-a d)^2 h n^2 \log (c+d x)}{(b g-a h)^2 (d g-c h)^2}-\frac{b^2 B^2 n \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{h (b g-a h)^2}+\frac{B^2 d^2 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{h (d g-c h)^2}+\frac{B^2 (b c-a d) h n (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(b g-a h)^2 (d g-c h) (g+h x)}+\frac{B^2 (b c-a d)^2 h n^2 \log (g+h x)}{(b g-a h)^2 (d g-c h)^2}-\frac{B^2 (b c-a d) (2 b d g-b c h-a d h) n^2 \log \left(-\frac{h (a+b x)}{b g-a h}\right) \log (g+h x)}{(b g-a h)^2 (d g-c h)^2}+\frac{B^2 (b c-a d) (2 b d g-b c h-a d h) n^2 \log \left(-\frac{h (c+d x)}{d g-c h}\right) \log (g+h x)}{(b g-a h)^2 (d g-c h)^2}+\frac{B^2 (b c-a d) (2 b d g-b c h-a d h) n \log \left(e (a+b x)^n (c+d x)^{-n}\right) \log (g+h x)}{(b g-a h)^2 (d g-c h)^2}+\frac{B^2 d^2 n^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{h (d g-c h)^2}-\frac{B^2 (b c-a d) (2 b d g-b c h-a d h) n^2 \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right)}{(b g-a h)^2 (d g-c h)^2}+\frac{B^2 (b c-a d) (2 b d g-b c h-a d h) n^2 \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right)}{(b g-a h)^2 (d g-c h)^2}+\frac{b^2 B^2 n^2 \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{h (b g-a h)^2}","\frac{B^2 n^2 (b c-a d) (-a d h-b c h+2 b d g) \text{PolyLog}\left(2,\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right)}{(b g-a h)^2 (d g-c h)^2}+\frac{b^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 h (b g-a h)^2}+\frac{B h n (a+b x) (b c-a d) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{(g+h x) (b g-a h)^2 (d g-c h)}+\frac{B n (b c-a d) (-a d h-b c h+2 b d g) \log \left(1-\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{(b g-a h)^2 (d g-c h)^2}-\frac{\left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 h (g+h x)^2}+\frac{B^2 h n^2 (b c-a d)^2 \log \left(\frac{g+h x}{c+d x}\right)}{(b g-a h)^2 (d g-c h)^2}",1,"-A^2/(2*h*(g + h*x)^2) - (A*B*(b*c - a*d)*n)/((b*g - a*h)*(d*g - c*h)*(g + h*x)) + (A*b^2*B*n*Log[a + b*x])/(h*(b*g - a*h)^2) - (A*B*d^2*n*Log[c + d*x])/(h*(d*g - c*h)^2) - (B^2*(b*c - a*d)^2*h*n^2*Log[c + d*x])/((b*g - a*h)^2*(d*g - c*h)^2) - (A*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(h*(g + h*x)^2) + (B^2*(b*c - a*d)*h*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((b*g - a*h)^2*(d*g - c*h)*(g + h*x)) - (b^2*B^2*n*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(h*(b*g - a*h)^2) + (B^2*d^2*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(h*(d*g - c*h)^2) - (B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*h*(g + h*x)^2) + (A*B*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n*Log[g + h*x])/((b*g - a*h)^2*(d*g - c*h)^2) + (B^2*(b*c - a*d)^2*h*n^2*Log[g + h*x])/((b*g - a*h)^2*(d*g - c*h)^2) - (B^2*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n^2*Log[-((h*(a + b*x))/(b*g - a*h))]*Log[g + h*x])/((b*g - a*h)^2*(d*g - c*h)^2) + (B^2*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n^2*Log[-((h*(c + d*x))/(d*g - c*h))]*Log[g + h*x])/((b*g - a*h)^2*(d*g - c*h)^2) + (B^2*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[g + h*x])/((b*g - a*h)^2*(d*g - c*h)^2) + (B^2*d^2*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(h*(d*g - c*h)^2) - (B^2*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n^2*PolyLog[2, (b*(g + h*x))/(b*g - a*h)])/((b*g - a*h)^2*(d*g - c*h)^2) + (B^2*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n^2*PolyLog[2, (d*(g + h*x))/(d*g - c*h)])/((b*g - a*h)^2*(d*g - c*h)^2) + (b^2*B^2*n^2*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(h*(b*g - a*h)^2)","B",29,16,33,0.4848,1,"{6742, 2492, 72, 2514, 2488, 2411, 2343, 2333, 2315, 2490, 36, 31, 2494, 2394, 2393, 2391}"
309,1,1640,0,3.4812403,"\int (g+h x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 \, dx","Int[(g + h*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3,x]","\frac{(g+h x)^3 \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right) B^3}{3 h}-\frac{(b c-a d) h^2 n x^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) B^3}{2 b d}-\frac{(b c-a d) h (3 b d g-b c h-a d h) n (a+b x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) B^3}{b^3 d^2}+\frac{(b g-a h)^3 n \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) B^3}{b^3 h}-\frac{(d g-c h)^3 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) B^3}{d^3 h}-\frac{(b c-a d)^3 h^2 n^3 \log (c+d x) B^3}{b^3 d^3}+\frac{(b c-a d)^2 h^2 n^2 (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) B^3}{b^3 d^2}-\frac{a^2 (b c-a d) h^2 n^2 \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) B^3}{b^3 d}+\frac{c^2 (b c-a d) h^2 n^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) B^3}{b d^3}-\frac{2 (b c-a d)^2 h (3 b d g-b c h-a d h) n^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) B^3}{b^3 d^3}+\frac{c^2 (b c-a d) h^2 n^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) B^3}{b d^3}-\frac{2 (b c-a d)^2 h (3 b d g-b c h-a d h) n^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) B^3}{b^3 d^3}+\frac{a^2 (b c-a d) h^2 n^3 \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right) B^3}{b^3 d}-\frac{2 (b g-a h)^3 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right) B^3}{b^3 h}-\frac{2 (d g-c h)^3 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) B^3}{d^3 h}-\frac{2 (b g-a h)^3 n^3 \text{PolyLog}\left(3,\frac{b c-a d}{d (a+b x)}+1\right) B^3}{b^3 h}+\frac{2 (d g-c h)^3 n^3 \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right) B^3}{d^3 h}+\frac{A (g+h x)^3 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) B^2}{h}+\frac{A (b c-a d)^2 h^2 n^2 x B^2}{b^2 d^2}+\frac{a^2 A (b c-a d) h^2 n^2 \log (a+b x) B^2}{b^3 d}-\frac{A c^2 (b c-a d) h^2 n^2 \log (c+d x) B^2}{b d^3}+\frac{2 A (b c-a d)^2 h (3 b d g-b c h-a d h) n^2 \log (c+d x) B^2}{b^3 d^3}-\frac{A (b c-a d) h^2 n x^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) B^2}{b d}-\frac{2 A (b c-a d) h (3 b d g-b c h-a d h) n (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) B^2}{b^3 d^2}+\frac{2 A (b g-a h)^3 n \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) B^2}{b^3 h}-\frac{2 A (d g-c h)^3 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) B^2}{d^3 h}-\frac{2 A (d g-c h)^3 n^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) B^2}{d^3 h}-\frac{2 A (b g-a h)^3 n^2 \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right) B^2}{b^3 h}-\frac{A^2 (b c-a d) h^2 n x^2 B}{2 b d}-\frac{A^2 (b c-a d) h (3 b d g-b c h-a d h) n x B}{b^2 d^2}-\frac{A^2 (b g-a h)^3 n \log (a+b x) B}{b^3 h}+\frac{A^2 (d g-c h)^3 n \log (c+d x) B}{d^3 h}+\frac{A^2 (g+h x)^3 \log \left(e (a+b x)^n (c+d x)^{-n}\right) B}{h}+\frac{A^3 (g+h x)^3}{3 h}","-\frac{B^3 h^2 n^3 \log (c+d x) (b c-a d)^3}{b^3 d^3}-\frac{B^2 h^2 n^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \log \left(1-\frac{b (c+d x)}{d (a+b x)}\right) (b c-a d)^3}{b^3 d^3}+\frac{B^3 h^2 n^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right) (b c-a d)^3}{b^3 d^3}+\frac{B^2 h^2 n^2 (a+b x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) (b c-a d)^2}{b^3 d^2}-\frac{2 B^2 h (3 b d g-2 b c h-a d h) n^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) (b c-a d)^2}{b^3 d^3}-\frac{2 B^3 h (3 b d g-2 b c h-a d h) n^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) (b c-a d)^2}{b^3 d^3}-\frac{B h^2 n (c+d x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 (b c-a d)}{2 b d^3}-\frac{B h (3 b d g-2 b c h-a d h) n (a+b x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 (b c-a d)}{b^3 d^2}+\frac{B \left(\left(3 d^2 g^2-3 c d h g+c^2 h^2\right) b^2-a d h (3 d g-c h) b+a^2 d^2 h^2\right) n \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 (b c-a d)}{b^3 d^3}+\frac{2 B^2 \left(\left(3 d^2 g^2-3 c d h g+c^2 h^2\right) b^2-a d h (3 d g-c h) b+a^2 d^2 h^2\right) n^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) (b c-a d)}{b^3 d^3}-\frac{2 B^3 \left(\left(3 d^2 g^2-3 c d h g+c^2 h^2\right) b^2-a d h (3 d g-c h) b+a^2 d^2 h^2\right) n^3 \text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right) (b c-a d)}{b^3 d^3}-\frac{(b g-a h)^3 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{3 b^3 h}+\frac{(g+h x)^3 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{3 h}",1,"-((A^2*B*(b*c - a*d)*h*(3*b*d*g - b*c*h - a*d*h)*n*x)/(b^2*d^2)) + (A*B^2*(b*c - a*d)^2*h^2*n^2*x)/(b^2*d^2) - (A^2*B*(b*c - a*d)*h^2*n*x^2)/(2*b*d) + (A^3*(g + h*x)^3)/(3*h) - (A^2*B*(b*g - a*h)^3*n*Log[a + b*x])/(b^3*h) + (a^2*A*B^2*(b*c - a*d)*h^2*n^2*Log[a + b*x])/(b^3*d) + (A^2*B*(d*g - c*h)^3*n*Log[c + d*x])/(d^3*h) - (A*B^2*c^2*(b*c - a*d)*h^2*n^2*Log[c + d*x])/(b*d^3) + (2*A*B^2*(b*c - a*d)^2*h*(3*b*d*g - b*c*h - a*d*h)*n^2*Log[c + d*x])/(b^3*d^3) - (B^3*(b*c - a*d)^3*h^2*n^3*Log[c + d*x])/(b^3*d^3) - (A*B^2*(b*c - a*d)*h^2*n*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*d) - (2*A*B^2*(b*c - a*d)*h*(3*b*d*g - b*c*h - a*d*h)*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b^3*d^2) + (B^3*(b*c - a*d)^2*h^2*n^2*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b^3*d^2) + (A^2*B*(g + h*x)^3*Log[(e*(a + b*x)^n)/(c + d*x)^n])/h + (2*A*B^2*(b*g - a*h)^3*n*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b^3*h) - (a^2*B^3*(b*c - a*d)*h^2*n^2*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b^3*d) - (2*A*B^2*(d*g - c*h)^3*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(d^3*h) + (B^3*c^2*(b*c - a*d)*h^2*n^2*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*d^3) - (2*B^3*(b*c - a*d)^2*h*(3*b*d*g - b*c*h - a*d*h)*n^2*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b^3*d^3) - (B^3*(b*c - a*d)*h^2*n*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*b*d) - (B^3*(b*c - a*d)*h*(3*b*d*g - b*c*h - a*d*h)*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(b^3*d^2) + (A*B^2*(g + h*x)^3*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/h + (B^3*(b*g - a*h)^3*n*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(b^3*h) - (B^3*(d*g - c*h)^3*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(d^3*h) + (B^3*(g + h*x)^3*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3)/(3*h) - (2*A*B^2*(d*g - c*h)^3*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(d^3*h) + (B^3*c^2*(b*c - a*d)*h^2*n^3*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(b*d^3) - (2*B^3*(b*c - a*d)^2*h*(3*b*d*g - b*c*h - a*d*h)*n^3*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(b^3*d^3) - (2*A*B^2*(b*g - a*h)^3*n^2*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(b^3*h) + (a^2*B^3*(b*c - a*d)*h^2*n^3*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(b^3*d) - (2*B^3*(b*g - a*h)^3*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(b^3*h) - (2*B^3*(d*g - c*h)^3*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/(d^3*h) - (2*B^3*(b*g - a*h)^3*n^3*PolyLog[3, 1 + (b*c - a*d)/(d*(a + b*x))])/(b^3*h) + (2*B^3*(d*g - c*h)^3*n^3*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/(d^3*h)","A",53,13,33,0.3939,1,"{6742, 2492, 72, 2514, 2486, 31, 2488, 2411, 2343, 2333, 2315, 2506, 6610}"
310,1,1030,0,2.1123729,"\int (g+h x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 \, dx","Int[(g + h*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3,x]","\frac{(g+h x)^2 A^3}{2 h}-\frac{3 B (b c-a d) h n x A^2}{2 b d}-\frac{3 B (b g-a h)^2 n \log (a+b x) A^2}{2 b^2 h}+\frac{3 B (d g-c h)^2 n \log (c+d x) A^2}{2 d^2 h}+\frac{3 B (g+h x)^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) A^2}{2 h}+\frac{3 B^2 (g+h x)^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) A}{2 h}+\frac{3 B^2 (b c-a d)^2 h n^2 \log (c+d x) A}{b^2 d^2}-\frac{3 B^2 (b c-a d) h n (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) A}{b^2 d}+\frac{3 B^2 (b g-a h)^2 n \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) A}{b^2 h}-\frac{3 B^2 (d g-c h)^2 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) A}{d^2 h}-\frac{3 B^2 (d g-c h)^2 n^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) A}{d^2 h}-\frac{3 B^2 (b g-a h)^2 n^2 \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right) A}{b^2 h}+\frac{B^3 (g+h x)^2 \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 h}-\frac{3 B^3 (b c-a d) h n (a+b x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 b^2 d}+\frac{3 B^3 (b g-a h)^2 n \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 b^2 h}-\frac{3 B^3 (d g-c h)^2 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 d^2 h}-\frac{3 B^3 (b c-a d)^2 h n^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b^2 d^2}-\frac{3 B^3 (b c-a d)^2 h n^3 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b^2 d^2}-\frac{3 B^3 (b g-a h)^2 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{b^2 h}-\frac{3 B^3 (d g-c h)^2 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right)}{d^2 h}-\frac{3 B^3 (b g-a h)^2 n^3 \text{PolyLog}\left(3,\frac{b c-a d}{d (a+b x)}+1\right)}{b^2 h}+\frac{3 B^3 (d g-c h)^2 n^3 \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right)}{d^2 h}","\frac{3 B^2 n^2 (b c-a d) (-a d h-b c h+2 b d g) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b^2 d^2}-\frac{3 B^3 n^3 (b c-a d) (-a d h-b c h+2 b d g) \text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right)}{b^2 d^2}-\frac{3 B^3 h n^3 (b c-a d)^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b^2 d^2}-\frac{3 B^2 h n^2 (b c-a d)^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b^2 d^2}+\frac{3 B n (b c-a d) (-a d h-b c h+2 b d g) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 b^2 d^2}-\frac{(b g-a h)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{2 b^2 h}-\frac{3 B h n (a+b x) (b c-a d) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 b^2 d}+\frac{(g+h x)^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{2 h}",1,"(-3*A^2*B*(b*c - a*d)*h*n*x)/(2*b*d) + (A^3*(g + h*x)^2)/(2*h) - (3*A^2*B*(b*g - a*h)^2*n*Log[a + b*x])/(2*b^2*h) + (3*A^2*B*(d*g - c*h)^2*n*Log[c + d*x])/(2*d^2*h) + (3*A*B^2*(b*c - a*d)^2*h*n^2*Log[c + d*x])/(b^2*d^2) - (3*A*B^2*(b*c - a*d)*h*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b^2*d) + (3*A^2*B*(g + h*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*h) + (3*A*B^2*(b*g - a*h)^2*n*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b^2*h) - (3*A*B^2*(d*g - c*h)^2*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(d^2*h) - (3*B^3*(b*c - a*d)^2*h*n^2*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b^2*d^2) - (3*B^3*(b*c - a*d)*h*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*b^2*d) + (3*A*B^2*(g + h*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*h) + (3*B^3*(b*g - a*h)^2*n*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*b^2*h) - (3*B^3*(d*g - c*h)^2*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*d^2*h) + (B^3*(g + h*x)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3)/(2*h) - (3*A*B^2*(d*g - c*h)^2*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(d^2*h) - (3*B^3*(b*c - a*d)^2*h*n^3*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(b^2*d^2) - (3*A*B^2*(b*g - a*h)^2*n^2*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(b^2*h) - (3*B^3*(b*g - a*h)^2*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(b^2*h) - (3*B^3*(d*g - c*h)^2*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/(d^2*h) - (3*B^3*(b*g - a*h)^2*n^3*PolyLog[3, 1 + (b*c - a*d)/(d*(a + b*x))])/(b^2*h) + (3*B^3*(d*g - c*h)^2*n^3*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/(d^2*h)","B",35,13,31,0.4194,1,"{6742, 2492, 72, 2514, 2486, 31, 2488, 2411, 2343, 2333, 2315, 2506, 6610}"
311,1,408,0,0.5901358,"\int \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3,x]","\frac{6 A B^2 n^2 (b c-a d) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right)}{b d}+\frac{6 B^3 n^2 (b c-a d) \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b d}-\frac{6 B^3 n^3 (b c-a d) \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right)}{b d}+\frac{3 A^2 B (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b}-\frac{3 A^2 B n (b c-a d) \log (c+d x)}{b d}+\frac{3 A B^2 (a+b x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{b}+\frac{6 A B^2 n (b c-a d) \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b d}+\frac{B^3 (a+b x) \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)}{b}+\frac{3 B^3 n (b c-a d) \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{b d}+A^3 x","\frac{6 B^2 n^2 (b c-a d) \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b d}-\frac{6 B^3 n^3 (b c-a d) \text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right)}{b d}+\frac{3 B n (b c-a d) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{b d}+\frac{(a+b x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{b}",1,"A^3*x - (3*A^2*B*(b*c - a*d)*n*Log[c + d*x])/(b*d) + (3*A^2*B*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/b + (6*A*B^2*(b*c - a*d)*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(b*d) + (3*A*B^2*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/b + (3*B^3*(b*c - a*d)*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(b*d) + (B^3*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3)/b + (6*A*B^2*(b*c - a*d)*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(b*d) + (6*B^3*(b*c - a*d)*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*d) - (6*B^3*(b*c - a*d)*n^3*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*d)","B",14,10,25,0.4000,1,"{6742, 2486, 31, 2488, 2411, 2343, 2333, 2315, 2506, 6610}"
312,1,921,0,1.6418267,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{g+h x} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(g + h*x),x]","\frac{\log (g+h x) A^3}{h}-\frac{3 B n \log \left(-\frac{h (a+b x)}{b g-a h}\right) \log (g+h x) A^2}{h}+\frac{3 B n \log \left(-\frac{h (c+d x)}{d g-c h}\right) \log (g+h x) A^2}{h}+\frac{3 B \log \left(e (a+b x)^n (c+d x)^{-n}\right) \log (g+h x) A^2}{h}-\frac{3 B n \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right) A^2}{h}+\frac{3 B n \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right) A^2}{h}-\frac{3 B^2 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) A}{h}+\frac{3 B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) \log \left(\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right) A}{h}-\frac{6 B^2 n \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) A}{h}+\frac{6 B^2 n \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,1-\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right) A}{h}+\frac{6 B^2 n^2 \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right) A}{h}-\frac{6 B^2 n^2 \text{PolyLog}\left(3,1-\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right) A}{h}-\frac{B^3 \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)}{h}+\frac{B^3 \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right) \log \left(\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right)}{h}-\frac{3 B^3 n \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right)}{h}+\frac{3 B^3 n \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,1-\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right)}{h}+\frac{6 B^3 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right)}{h}-\frac{6 B^3 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(3,1-\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right)}{h}-\frac{6 B^3 n^3 \text{PolyLog}\left(4,1-\frac{b c-a d}{b (c+d x)}\right)}{h}+\frac{6 B^3 n^3 \text{PolyLog}\left(4,1-\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right)}{h}","-\frac{6 B^2 n^2 \text{PolyLog}\left(3,\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{h}+\frac{6 B^2 n^2 \text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{h}+\frac{3 B n \text{PolyLog}\left(2,\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{h}-\frac{3 B n \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{h}+\frac{6 B^3 n^3 \text{PolyLog}\left(4,\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right)}{h}-\frac{6 B^3 n^3 \text{PolyLog}\left(4,\frac{d (a+b x)}{b (c+d x)}\right)}{h}+\frac{\log \left(1-\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{h}-\frac{\log \left(\frac{b c-a d}{b (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{h}",1,"(-3*A*B^2*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/h - (B^3*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3)/h + (A^3*Log[g + h*x])/h - (3*A^2*B*n*Log[-((h*(a + b*x))/(b*g - a*h))]*Log[g + h*x])/h + (3*A^2*B*n*Log[-((h*(c + d*x))/(d*g - c*h))]*Log[g + h*x])/h + (3*A^2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[g + h*x])/h + (3*A*B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2*Log[((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/h + (B^3*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3*Log[((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/h - (3*A^2*B*n*PolyLog[2, (b*(g + h*x))/(b*g - a*h)])/h + (3*A^2*B*n*PolyLog[2, (d*(g + h*x))/(d*g - c*h)])/h - (6*A*B^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/h - (3*B^3*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/h + (6*A*B^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 - ((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/h + (3*B^3*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2*PolyLog[2, 1 - ((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/h + (6*A*B^2*n^2*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/h + (6*B^3*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/h - (6*A*B^2*n^2*PolyLog[3, 1 - ((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/h - (6*B^3*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[3, 1 - ((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/h - (6*B^3*n^3*PolyLog[4, 1 - (b*c - a*d)/(b*(c + d*x))])/h + (6*B^3*n^3*PolyLog[4, 1 - ((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/h","B",25,11,33,0.3333,1,"{6742, 2494, 2394, 2393, 2391, 2489, 2488, 2506, 6610, 2503, 2508}"
313,1,650,0,0.8074123,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(g+h x)^2} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(g + h*x)^2,x]","\frac{6 A B^2 n^2 (b c-a d) \text{PolyLog}\left(2,1-\frac{(g+h x) (b c-a d)}{(c+d x) (b g-a h)}\right)}{(b g-a h) (d g-c h)}+\frac{6 B^3 n^2 (b c-a d) \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,1-\frac{(g+h x) (b c-a d)}{(c+d x) (b g-a h)}\right)}{(b g-a h) (d g-c h)}-\frac{6 B^3 n^3 (b c-a d) \text{PolyLog}\left(3,1-\frac{(g+h x) (b c-a d)}{(c+d x) (b g-a h)}\right)}{(b g-a h) (d g-c h)}+\frac{3 A^2 B (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x) (b g-a h)}-\frac{3 A^2 B n (b c-a d) \log (c+d x)}{(b g-a h) (d g-c h)}+\frac{3 A^2 B n (b c-a d) \log (g+h x)}{(b g-a h) (d g-c h)}+\frac{3 A B^2 (a+b x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x) (b g-a h)}+\frac{6 A B^2 n (b c-a d) \log \left(e (a+b x)^n (c+d x)^{-n}\right) \log \left(\frac{(g+h x) (b c-a d)}{(c+d x) (b g-a h)}\right)}{(b g-a h) (d g-c h)}+\frac{B^3 (a+b x) \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x) (b g-a h)}+\frac{3 B^3 n (b c-a d) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) \log \left(\frac{(g+h x) (b c-a d)}{(c+d x) (b g-a h)}\right)}{(b g-a h) (d g-c h)}-\frac{A^3}{h (g+h x)}","\frac{6 B^2 n^2 (b c-a d) \text{PolyLog}\left(2,\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{(b g-a h) (d g-c h)}-\frac{6 B^3 n^3 (b c-a d) \text{PolyLog}\left(3,\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right)}{(b g-a h) (d g-c h)}+\frac{3 B n (b c-a d) \log \left(1-\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{(b g-a h) (d g-c h)}+\frac{(a+b x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{(g+h x) (b g-a h)}",1,"-(A^3/(h*(g + h*x))) - (3*A^2*B*(b*c - a*d)*n*Log[c + d*x])/((b*g - a*h)*(d*g - c*h)) + (3*A^2*B*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((b*g - a*h)*(g + h*x)) + (3*A*B^2*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/((b*g - a*h)*(g + h*x)) + (B^3*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3)/((b*g - a*h)*(g + h*x)) + (3*A^2*B*(b*c - a*d)*n*Log[g + h*x])/((b*g - a*h)*(d*g - c*h)) + (6*A*B^2*(b*c - a*d)*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/((b*g - a*h)*(d*g - c*h)) + (3*B^3*(b*c - a*d)*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2*Log[((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/((b*g - a*h)*(d*g - c*h)) + (6*A*B^2*(b*c - a*d)*n^2*PolyLog[2, 1 - ((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/((b*g - a*h)*(d*g - c*h)) + (6*B^3*(b*c - a*d)*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 - ((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/((b*g - a*h)*(d*g - c*h)) - (6*B^3*(b*c - a*d)*n^3*PolyLog[3, 1 - ((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/((b*g - a*h)*(d*g - c*h))","B",14,9,33,0.2727,1,"{6742, 2490, 36, 31, 2503, 2502, 2315, 2506, 6610}"
314,1,2207,0,3.7450984,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(g+h x)^3} \, dx","Int[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(g + h*x)^3,x]","-\frac{A^3}{2 h (g+h x)^2}+\frac{3 b^2 B n \log (a+b x) A^2}{2 h (b g-a h)^2}-\frac{3 B d^2 n \log (c+d x) A^2}{2 h (d g-c h)^2}-\frac{3 B \log \left(e (a+b x)^n (c+d x)^{-n}\right) A^2}{2 h (g+h x)^2}+\frac{3 B (b c-a d) (2 b d g-b c h-a d h) n \log (g+h x) A^2}{2 (b g-a h)^2 (d g-c h)^2}-\frac{3 B (b c-a d) n A^2}{2 (b g-a h) (d g-c h) (g+h x)}-\frac{3 B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) A}{2 h (g+h x)^2}-\frac{3 B^2 (b c-a d)^2 h n^2 \log (c+d x) A}{(b g-a h)^2 (d g-c h)^2}-\frac{3 b^2 B^2 n \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) A}{h (b g-a h)^2}+\frac{3 B^2 d^2 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) A}{h (d g-c h)^2}+\frac{3 B^2 (b c-a d) h n (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) A}{(b g-a h)^2 (d g-c h) (g+h x)}+\frac{3 B^2 (b c-a d)^2 h n^2 \log (g+h x) A}{(b g-a h)^2 (d g-c h)^2}-\frac{3 B^2 (b c-a d) (2 b d g-b c h-a d h) n^2 \log \left(-\frac{h (a+b x)}{b g-a h}\right) \log (g+h x) A}{(b g-a h)^2 (d g-c h)^2}+\frac{3 B^2 (b c-a d) (2 b d g-b c h-a d h) n^2 \log \left(-\frac{h (c+d x)}{d g-c h}\right) \log (g+h x) A}{(b g-a h)^2 (d g-c h)^2}+\frac{3 B^2 (b c-a d) (2 b d g-b c h-a d h) n \log \left(e (a+b x)^n (c+d x)^{-n}\right) \log (g+h x) A}{(b g-a h)^2 (d g-c h)^2}+\frac{3 B^2 d^2 n^2 \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) A}{h (d g-c h)^2}-\frac{3 B^2 (b c-a d) (2 b d g-b c h-a d h) n^2 \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right) A}{(b g-a h)^2 (d g-c h)^2}+\frac{3 B^2 (b c-a d) (2 b d g-b c h-a d h) n^2 \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right) A}{(b g-a h)^2 (d g-c h)^2}+\frac{3 b^2 B^2 n^2 \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right) A}{h (b g-a h)^2}-\frac{B^3 \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 h (g+h x)^2}-\frac{3 b^2 B^3 n \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 h (b g-a h)^2}-\frac{3 B^3 (b c-a d) (2 b d g-b c h-a d h) n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 (b g-a h)^2 (d g-c h)^2}+\frac{3 B^3 d^2 n \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 h (d g-c h)^2}+\frac{3 B^3 (b c-a d) h n (a+b x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)}{2 (b g-a h)^2 (d g-c h) (g+h x)}+\frac{3 B^3 (b c-a d) (2 b d g-b c h-a d h) n \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) \log \left(\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right)}{2 (b g-a h)^2 (d g-c h)^2}+\frac{3 B^3 (b c-a d)^2 h n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \log \left(\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right)}{(b g-a h)^2 (d g-c h)^2}+\frac{3 b^2 B^3 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right)}{h (b g-a h)^2}-\frac{3 B^3 (b c-a d) (2 b d g-b c h-a d h) n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right)}{(b g-a h)^2 (d g-c h)^2}+\frac{3 B^3 d^2 n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right)}{h (d g-c h)^2}+\frac{3 B^3 (b c-a d)^2 h n^3 \text{PolyLog}\left(2,1-\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right)}{(b g-a h)^2 (d g-c h)^2}+\frac{3 B^3 (b c-a d) (2 b d g-b c h-a d h) n^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) \text{PolyLog}\left(2,1-\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right)}{(b g-a h)^2 (d g-c h)^2}+\frac{3 b^2 B^3 n^3 \text{PolyLog}\left(3,\frac{b c-a d}{d (a+b x)}+1\right)}{h (b g-a h)^2}+\frac{3 B^3 (b c-a d) (2 b d g-b c h-a d h) n^3 \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right)}{(b g-a h)^2 (d g-c h)^2}-\frac{3 B^3 d^2 n^3 \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right)}{h (d g-c h)^2}-\frac{3 B^3 (b c-a d) (2 b d g-b c h-a d h) n^3 \text{PolyLog}\left(3,1-\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right)}{(b g-a h)^2 (d g-c h)^2}","\frac{3 B^2 n^2 (b c-a d) (-a d h-b c h+2 b d g) \text{PolyLog}\left(2,\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{(b g-a h)^2 (d g-c h)^2}+\frac{3 B^3 h n^3 (b c-a d)^2 \text{PolyLog}\left(2,\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right)}{(b g-a h)^2 (d g-c h)^2}-\frac{3 B^3 n^3 (b c-a d) (-a d h-b c h+2 b d g) \text{PolyLog}\left(3,\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right)}{(b g-a h)^2 (d g-c h)^2}+\frac{b^2 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{2 h (b g-a h)^2}+\frac{3 B^2 h n^2 (b c-a d)^2 \log \left(1-\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{(b g-a h)^2 (d g-c h)^2}+\frac{3 B h n (a+b x) (b c-a d) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 (g+h x) (b g-a h)^2 (d g-c h)}+\frac{3 B n (b c-a d) (-a d h-b c h+2 b d g) \log \left(1-\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 (b g-a h)^2 (d g-c h)^2}-\frac{\left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{2 h (g+h x)^2}",1,"-A^3/(2*h*(g + h*x)^2) - (3*A^2*B*(b*c - a*d)*n)/(2*(b*g - a*h)*(d*g - c*h)*(g + h*x)) + (3*A^2*b^2*B*n*Log[a + b*x])/(2*h*(b*g - a*h)^2) - (3*A^2*B*d^2*n*Log[c + d*x])/(2*h*(d*g - c*h)^2) - (3*A*B^2*(b*c - a*d)^2*h*n^2*Log[c + d*x])/((b*g - a*h)^2*(d*g - c*h)^2) - (3*A^2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(2*h*(g + h*x)^2) + (3*A*B^2*(b*c - a*d)*h*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((b*g - a*h)^2*(d*g - c*h)*(g + h*x)) - (3*A*b^2*B^2*n*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(h*(b*g - a*h)^2) + (3*A*B^2*d^2*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(h*(d*g - c*h)^2) - (3*A*B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*h*(g + h*x)^2) + (3*B^3*(b*c - a*d)*h*n*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*(b*g - a*h)^2*(d*g - c*h)*(g + h*x)) - (3*b^2*B^3*n*Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*h*(b*g - a*h)^2) + (3*B^3*d^2*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*h*(d*g - c*h)^2) - (3*B^3*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n*Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/(2*(b*g - a*h)^2*(d*g - c*h)^2) - (B^3*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3)/(2*h*(g + h*x)^2) + (3*A^2*B*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n*Log[g + h*x])/(2*(b*g - a*h)^2*(d*g - c*h)^2) + (3*A*B^2*(b*c - a*d)^2*h*n^2*Log[g + h*x])/((b*g - a*h)^2*(d*g - c*h)^2) - (3*A*B^2*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n^2*Log[-((h*(a + b*x))/(b*g - a*h))]*Log[g + h*x])/((b*g - a*h)^2*(d*g - c*h)^2) + (3*A*B^2*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n^2*Log[-((h*(c + d*x))/(d*g - c*h))]*Log[g + h*x])/((b*g - a*h)^2*(d*g - c*h)^2) + (3*A*B^2*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[g + h*x])/((b*g - a*h)^2*(d*g - c*h)^2) + (3*B^3*(b*c - a*d)^2*h*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/((b*g - a*h)^2*(d*g - c*h)^2) + (3*B^3*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2*Log[((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/(2*(b*g - a*h)^2*(d*g - c*h)^2) + (3*A*B^2*d^2*n^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(h*(d*g - c*h)^2) - (3*A*B^2*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n^2*PolyLog[2, (b*(g + h*x))/(b*g - a*h)])/((b*g - a*h)^2*(d*g - c*h)^2) + (3*A*B^2*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n^2*PolyLog[2, (d*(g + h*x))/(d*g - c*h)])/((b*g - a*h)^2*(d*g - c*h)^2) + (3*A*b^2*B^2*n^2*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(h*(b*g - a*h)^2) + (3*b^2*B^3*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(h*(b*g - a*h)^2) + (3*B^3*d^2*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/(h*(d*g - c*h)^2) - (3*B^3*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/((b*g - a*h)^2*(d*g - c*h)^2) + (3*B^3*(b*c - a*d)^2*h*n^3*PolyLog[2, 1 - ((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/((b*g - a*h)^2*(d*g - c*h)^2) + (3*B^3*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, 1 - ((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/((b*g - a*h)^2*(d*g - c*h)^2) + (3*b^2*B^3*n^3*PolyLog[3, 1 + (b*c - a*d)/(d*(a + b*x))])/(h*(b*g - a*h)^2) - (3*B^3*d^2*n^3*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/(h*(d*g - c*h)^2) + (3*B^3*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n^3*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/((b*g - a*h)^2*(d*g - c*h)^2) - (3*B^3*(b*c - a*d)*(2*b*d*g - b*c*h - a*d*h)*n^3*PolyLog[3, 1 - ((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])/((b*g - a*h)^2*(d*g - c*h)^2)","B",49,21,33,0.6364,1,"{6742, 2492, 72, 2514, 2488, 2411, 2343, 2333, 2315, 2490, 36, 31, 2494, 2394, 2393, 2391, 2506, 6610, 2503, 2502, 2489}"