1,1,146,188,0.1194849,"\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","Integrate[(a*g + b*g*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^4 \left((a+b x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-\frac{B n (b c-a d) \left(4 d^3 (a+b x)^3 (a d-b c)+6 d^2 (a+b x)^2 (b c-a d)^2-12 b d x (b c-a d)^3+12 (b c-a d)^4 \log (c+d x)+3 d^4 (a+b x)^4\right)}{12 d^5}\right)}{5 b}","\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 (b c-a d)^5 \log (c+d x)}{5 b d^5}+\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 (a+b x)^4 (b c-a d)}{20 b d}",1,"(g^4*((a + b*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - (B*(b*c - a*d)*n*(-12*b*d*(b*c - a*d)^3*x + 6*d^2*(b*c - a*d)^2*(a + b*x)^2 + 4*d^3*(-(b*c) + a*d)*(a + b*x)^3 + 3*d^4*(a + b*x)^4 + 12*(b*c - a*d)^4*Log[c + d*x]))/(12*d^5)))/(5*b)","A",1
2,1,124,156,0.1076257,"\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","Integrate[(a*g + b*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^3 \left((a+b x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-\frac{B n (b c-a d) \left(3 d^2 (a+b x)^2 (a d-b c)+6 b d x (b c-a d)^2-6 (b c-a d)^3 \log (c+d x)+2 d^3 (a+b x)^3\right)}{6 d^4}\right)}{4 b}","\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 (b c-a d)^4 \log (c+d x)}{4 b d^4}-\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 (a+b x)^3 (b c-a d)}{12 b d}",1,"(g^3*((a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - (B*(b*c - a*d)*n*(6*b*d*(b*c - a*d)^2*x + 3*d^2*(-(b*c) + a*d)*(a + b*x)^2 + 2*d^3*(a + b*x)^3 - 6*(b*c - a*d)^3*Log[c + d*x]))/(6*d^4)))/(4*b)","A",1
3,1,103,124,0.0579071,"\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","Integrate[(a*g + b*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^2 \left(\frac{B n (a d-b c) \left(d \left(a^2 d+4 a b d x+b^2 x (d x-2 c)\right)+2 (b c-a d)^2 \log (c+d x)\right)}{2 d^3}+(a+b x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)\right)}{3 b}","\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 (b c-a d)^3 \log (c+d x)}{3 b d^3}+\frac{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)}{6 b d}",1,"(g^2*((a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + (B*(-(b*c) + a*d)*n*(d*(a^2*d + 4*a*b*d*x + b^2*x*(-2*c + d*x)) + 2*(b*c - a*d)^2*Log[c + d*x]))/(2*d^3)))/(3*b)","A",1
4,1,73,86,0.0380339,"\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","Integrate[(a*g + b*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g \left((a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+\frac{B n (a d-b c) ((a d-b c) \log (c+d x)+b d x)}{d^2}\right)}{2 b}","\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,"(g*((a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + (B*(-(b*c) + a*d)*n*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]))/d^2))/(2*b)","A",1
5,1,101,84,0.0525087,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{a g+b g x} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(a*g + b*g*x),x]","\frac{\log (g (a+b x)) \left(2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B n \log \left(\frac{b (c+d x)}{b c-a d}\right)+A\right)-B n \log (g (a+b x))\right)+2 B n \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)}{2 b g}","\frac{B n \text{Li}_2\left(\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,"(Log[g*(a + b*x)]*(-(B*n*Log[g*(a + b*x)]) + 2*(A + B*Log[e*((a + b*x)/(c + d*x))^n] + B*n*Log[(b*(c + d*x))/(b*c - a*d)])) + 2*B*n*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(2*b*g)","A",1
6,1,115,67,0.061006,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(a*g + b*g*x)^2,x]","\frac{B n (b c-a d) \left(-\frac{1}{(a+b x) (b c-a d)}-\frac{d \log (a+b x)}{(b c-a d)^2}+\frac{d \log (c+d x)}{(b c-a d)^2}\right)}{b g^2}-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{b g (a g+b g 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,"-((A + B*Log[e*((a + b*x)/(c + d*x))^n])/(b*g*(a*g + b*g*x))) + (B*(b*c - a*d)*n*(-(1/((b*c - a*d)*(a + b*x))) - (d*Log[a + b*x])/(b*c - a*d)^2 + (d*Log[c + d*x])/(b*c - a*d)^2))/(b*g^2)","A",1
7,1,114,151,0.1520347,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(a*g + b*g*x)^3,x]","-\frac{2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+\frac{B n \left(2 d^2 (a+b x)^2 \log (c+d x)+(b c-a d) (b (c-2 d x)-3 a d)-2 d^2 (a+b x)^2 \log (a+b x)\right)}{(b c-a d)^2}}{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,"-1/4*(2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + (B*n*((b*c - a*d)*(-3*a*d + b*(c - 2*d*x)) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]))/(b*c - a*d)^2)/(b*g^3*(a + b*x)^2)","A",1
8,1,145,183,0.1738928,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(a*g + b*g*x)^4,x]","-\frac{\frac{B n \left((b c-a d) \left(11 a^2 d^2+a b d (15 d x-7 c)+b^2 \left(2 c^2-3 c d x+6 d^2 x^2\right)\right)-6 d^3 (a+b x)^3 \log (c+d x)+6 d^3 (a+b x)^3 \log (a+b x)\right)}{(b c-a d)^3}+6 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{18 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^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^2 n}{3 b g^4 (a+b x) (b c-a d)^2}+\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,"-1/18*(6*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + (B*n*((b*c - a*d)*(11*a^2*d^2 + a*b*d*(-7*c + 15*d*x) + b^2*(2*c^2 - 3*c*d*x + 6*d^2*x^2)) + 6*d^3*(a + b*x)^3*Log[a + b*x] - 6*d^3*(a + b*x)^3*Log[c + d*x]))/(b*c - a*d)^3)/(b*g^4*(a + b*x)^3)","A",1
9,1,162,215,0.2230157,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(a*g + b*g*x)^5,x]","\frac{\frac{B n \left(\frac{12 d^3 (b c-a d)}{a+b x}-\frac{6 d^2 (b c-a d)^2}{(a+b x)^2}+\frac{4 d (b c-a d)^3}{(a+b x)^3}-\frac{3 (b c-a d)^4}{(a+b x)^4}+12 d^4 \log (a+b x)-12 d^4 \log (c+d x)\right)}{12 (b c-a d)^4}-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{(a+b x)^4}}{4 b g^5}","-\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^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^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 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,"(-((A + B*Log[e*((a + b*x)/(c + d*x))^n])/(a + b*x)^4) + (B*n*((-3*(b*c - a*d)^4)/(a + b*x)^4 + (4*d*(b*c - a*d)^3)/(a + b*x)^3 - (6*d^2*(b*c - a*d)^2)/(a + b*x)^2 + (12*d^3*(b*c - a*d))/(a + b*x) + 12*d^4*Log[a + b*x] - 12*d^4*Log[c + d*x]))/(12*(b*c - a*d)^4))/(4*b*g^5)","A",1
10,1,535,396,0.5150812,"\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","Integrate[(a*g + b*g*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{g^4 \left(\frac{B n (b c-a d) \left(-6 d^4 (a+b x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+8 d^3 (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)-12 d^2 (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)-24 (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)+24 A b d x (b c-a d)^3+4 B n (b c-a d)^2 \left(2 b d x (b c-a d)-2 (b c-a d)^2 \log (c+d x)-d^2 (a+b x)^2\right)+B n (b c-a d) \left(3 d^2 (a+b x)^2 (a d-b c)+6 b d x (b c-a d)^2-6 (b c-a d)^3 \log (c+d x)+2 d^3 (a+b x)^3\right)+24 B d (a+b x) (b c-a d)^3 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+12 B n (b c-a d)^4 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-24 B n (b c-a d)^4 \log (c+d x)+12 B n (b c-a d)^3 ((a d-b c) \log (c+d x)+b d x)\right)}{12 d^5}+(a+b x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2\right)}{5 b}","\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}+\frac{2 B^2 g^4 n^2 (b c-a d)^5 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{5 b d^5}",1,"(g^4*((a + b*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (B*(b*c - a*d)*n*(24*A*b*d*(b*c - a*d)^3*x + 24*B*d*(b*c - a*d)^3*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] - 12*d^2*(b*c - a*d)^2*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 8*d^3*(b*c - a*d)*(a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 6*d^4*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 24*B*(b*c - a*d)^4*n*Log[c + d*x] - 24*(b*c - a*d)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + 4*B*(b*c - a*d)^2*n*(2*b*d*(b*c - a*d)*x - d^2*(a + b*x)^2 - 2*(b*c - a*d)^2*Log[c + d*x]) + B*(b*c - a*d)*n*(6*b*d*(b*c - a*d)^2*x + 3*d^2*(-(b*c) + a*d)*(a + b*x)^2 + 2*d^3*(a + b*x)^3 - 6*(b*c - a*d)^3*Log[c + d*x]) + 12*B*(b*c - a*d)^3*n*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 12*B*(b*c - a*d)^4*n*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(12*d^5)))/(5*b)","A",1
11,1,411,335,0.3488055,"\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","Integrate[(a*g + b*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{g^3 \left((a+b x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2-\frac{B n (b c-a d) \left(2 d^3 (a+b x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+3 d^2 (a+b x)^2 (a d-b c) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-6 (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)+6 A b d x (b c-a d)^2+B n (b c-a d) \left(2 b d x (b c-a d)-2 (b c-a d)^2 \log (c+d x)-d^2 (a+b x)^2\right)+6 B d (a+b x) (b c-a d)^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+3 B n (b c-a d)^3 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-6 B n (b c-a d)^3 \log (c+d x)+3 B n (b c-a d)^2 ((a d-b c) \log (c+d x)+b d x)\right)}{3 d^4}\right)}{4 b}","-\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}-\frac{B^2 g^3 n^2 (b c-a d)^4 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{2 b d^4}",1,"(g^3*((a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - (B*(b*c - a*d)*n*(6*A*b*d*(b*c - a*d)^2*x + 6*B*d*(b*c - a*d)^2*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] + 3*d^2*(-(b*c) + a*d)*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 2*d^3*(a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 6*B*(b*c - a*d)^3*n*Log[c + d*x] - 6*(b*c - a*d)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + B*(b*c - a*d)*n*(2*b*d*(b*c - a*d)*x - d^2*(a + b*x)^2 - 2*(b*c - a*d)^2*Log[c + d*x]) + 3*B*(b*c - a*d)^2*n*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 3*B*(b*c - a*d)^3*n*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(3*d^4)))/(4*b)","A",1
12,1,303,274,0.233041,"\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","Integrate[(a*g + b*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{g^2 \left(\frac{B n (b c-a d) \left(-d^2 (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-2 (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)+2 A b d x (b c-a d)+2 B d (a+b x) (b c-a d) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B n (b c-a d)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-2 B n (b c-a d)^2 \log (c+d x)+B n (b c-a d) ((a d-b c) \log (c+d x)+b d x)\right)}{d^3}+(a+b x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2\right)}{3 b}","\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}+\frac{2 B^2 g^2 n^2 (b c-a d)^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{3 b d^3}",1,"(g^2*((a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (B*(b*c - a*d)*n*(2*A*b*d*(b*c - a*d)*x + 2*B*d*(b*c - a*d)*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] - d^2*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 2*B*(b*c - a*d)^2*n*Log[c + d*x] - 2*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + B*(b*c - a*d)*n*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + B*(b*c - a*d)^2*n*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/d^3))/(3*b)","A",1
13,1,215,196,0.1952168,"\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","Integrate[(a*g + b*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{g \left((a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2-\frac{B n (b c-a d) \left(-2 (b c-a d) \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 (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B n (b c-a d) \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-2 B n (b c-a d) \log (c+d x)+2 A b d x\right)}{d^2}\right)}{2 b}","-\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}-\frac{B^2 g n^2 (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}",1,"(g*((a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - (B*(b*c - a*d)*n*(2*A*b*d*x + 2*B*d*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] - 2*B*(b*c - a*d)*n*Log[c + d*x] - 2*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + B*(b*c - a*d)*n*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/d^2))/(2*b)","A",1
14,1,537,138,0.4271814,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(a*g + b*g*x),x]","\frac{3 B n \left(-2 \left(\text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)\right)-2 \log (a+b x) \left(-\log \left(\frac{a+b x}{c+d x}\right)+\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)\right)+\log ^2\left(\frac{a}{b}+x\right)\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-B n \log \left(\frac{a+b x}{c+d x}\right)+A\right)+3 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-B n \log \left(\frac{a+b x}{c+d x}\right)+A\right)^2+B^2 n^2 \left(-6 \text{Li}_3\left(\frac{d (a+b x)}{a d-b c}\right)-6 \text{Li}_3\left(\frac{b (c+d x)}{b c-a d}\right)-3 \left(-\log \left(\frac{a+b x}{c+d x}\right)+\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)\right) \left(\log ^2\left(\frac{a}{b}+x\right)-2 \left(\text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)\right)\right)+6 \log \left(\frac{a}{b}+x\right) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)+6 \log \left(\frac{c}{d}+x\right) \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+3 \log ^2\left(\frac{a}{b}+x\right) \left(\log \left(\frac{b (c+d x)}{b c-a d}\right)-\log \left(\frac{c}{d}+x\right)\right)+3 \log ^2\left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)+3 \log (a+b x) \left(\log \left(\frac{a+b x}{c+d x}\right)-\log \left(\frac{a}{b}+x\right)+\log \left(\frac{c}{d}+x\right)\right)^2+\log ^3\left(\frac{a}{b}+x\right)\right)}{3 b g}","\frac{2 B n \text{Li}_2\left(\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{\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}+\frac{2 B^2 n^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b g}",1,"(3*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2 + 3*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])*(Log[a/b + x]^2 - 2*Log[a + b*x]*(Log[a/b + x] - Log[c/d + x] - Log[(a + b*x)/(c + d*x)]) - 2*(Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + PolyLog[2, (b*(c + d*x))/(b*c - a*d)])) + B^2*n^2*(Log[a/b + x]^3 + 3*Log[c/d + x]^2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 3*Log[a + b*x]*(-Log[a/b + x] + Log[c/d + x] + Log[(a + b*x)/(c + d*x)])^2 + 3*Log[a/b + x]^2*(-Log[c/d + x] + Log[(b*(c + d*x))/(b*c - a*d)]) + 6*Log[a/b + x]*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 6*Log[c/d + x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 3*(Log[a/b + x] - Log[c/d + x] - Log[(a + b*x)/(c + d*x)])*(Log[a/b + x]^2 - 2*(Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + PolyLog[2, (b*(c + d*x))/(b*c - a*d)])) - 6*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)] - 6*PolyLog[3, (b*(c + d*x))/(b*c - a*d)]))/(3*b*g)","B",1
15,1,330,136,0.5746869,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(a*g + b*g*x)^2,x]","-\frac{\frac{B n \left(2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+2 d (a+b x) \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-2 d (a+b x) \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-B d n (a+b x) \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+B d n (a+b x) \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+2 B n (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)\right)}{b c-a d}+\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{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,"-(((A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (B*n*(2*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 2*d*(a + b*x)*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 2*d*(a + b*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + 2*B*n*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - B*d*n*(a + b*x)*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + B*d*n*(a + b*x)*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d))/(b*g^2*(a + b*x)))","C",1
16,1,463,288,0.4943108,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(a*g + b*g*x)^3,x]","-\frac{\frac{B n \left(-4 d^2 (a+b x)^2 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+4 d^2 (a+b x)^2 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+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 d (a+b x) (a d-b c) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+2 B d^2 n (a+b x)^2 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)-2 B d^2 n (a+b x)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+B n \left(2 d^2 (a+b x)^2 \log (c+d x)+2 d (a+b x) (a d-b c)+(b c-a d)^2-2 d^2 (a+b x)^2 \log (a+b x)\right)-4 B d n (a+b x) (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)\right)}{(b c-a d)^2}+2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^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,"-1/4*(2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (B*n*(2*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 4*d*(-(b*c) + a*d)*(a + b*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 4*d^2*(a + b*x)^2*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 4*d^2*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - 4*B*d*n*(a + b*x)*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) + B*n*((b*c - a*d)^2 + 2*d*(-(b*c) + a*d)*(a + b*x) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]) + 2*B*d^2*n*(a + b*x)^2*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - 2*B*d^2*n*(a + b*x)^2*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^2)/(b*g^3*(a + b*x)^2)","C",1
17,1,609,448,0.7035972,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(a*g + b*g*x)^4,x]","-\frac{\frac{B n \left(36 d^3 (a+b x)^3 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-36 d^3 (a+b x)^3 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+36 d^2 (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)+12 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-18 d (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)-18 B d^3 n (a+b x)^3 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+18 B d^3 n (a+b x)^3 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+36 B d^2 n (a+b x)^2 (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)-9 B d n (a+b x) \left(2 d^2 (a+b x)^2 \log (c+d x)+2 d (a+b x) (a d-b c)+(b c-a d)^2-2 d^2 (a+b x)^2 \log (a+b x)\right)+2 B n \left(-6 d^3 (a+b x)^3 \log (c+d x)+6 d^2 (a+b x)^2 (b c-a d)-3 d (a+b x) (b c-a d)^2+2 (b c-a d)^3+6 d^3 (a+b x)^3 \log (a+b x)\right)\right)}{(b c-a d)^3}+18 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{54 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,"-1/54*(18*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (B*n*(12*(b*c - a*d)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 18*d*(b*c - a*d)^2*(a + b*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 36*d^2*(b*c - a*d)*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 36*d^3*(a + b*x)^3*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 36*d^3*(a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + 36*B*d^2*n*(a + b*x)^2*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - 9*B*d*n*(a + b*x)*((b*c - a*d)^2 + 2*d*(-(b*c) + a*d)*(a + b*x) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]) + 2*B*n*(2*(b*c - a*d)^3 - 3*d*(b*c - a*d)^2*(a + b*x) + 6*d^2*(b*c - a*d)*(a + b*x)^2 + 6*d^3*(a + b*x)^3*Log[a + b*x] - 6*d^3*(a + b*x)^3*Log[c + d*x]) - 18*B*d^3*n*(a + b*x)^3*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 18*B*d^3*n*(a + b*x)^3*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^3)/(b*g^4*(a + b*x)^3)","C",1
18,1,776,615,1.0245235,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(a*g + b*g*x)^5,x]","-\frac{\frac{B n \left(-144 d^4 (a+b x)^4 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+144 d^4 (a+b x)^4 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+144 d^3 (a+b x)^3 (a d-b c) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+72 d^2 (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)+36 (b c-a d)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+48 d (a+b x) (a d-b c)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+72 B d^4 n (a+b x)^4 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)-72 B d^4 n (a+b x)^4 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-144 B d^3 n (a+b x)^3 (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)+36 B d^2 n (a+b x)^2 \left(2 d^2 (a+b x)^2 \log (c+d x)+2 d (a+b x) (a d-b c)+(b c-a d)^2-2 d^2 (a+b x)^2 \log (a+b x)\right)-8 B d n (a+b x) \left(-6 d^3 (a+b x)^3 \log (c+d x)+6 d^2 (a+b x)^2 (b c-a d)-3 d (a+b x) (b c-a d)^2+2 (b c-a d)^3+6 d^3 (a+b x)^3 \log (a+b x)\right)+3 B n \left(12 d^4 (a+b x)^4 \log (c+d x)+12 d^3 (a+b x)^3 (a d-b c)+6 d^2 (a+b x)^2 (b c-a d)^2+4 d (a+b x) (a d-b c)^3+3 (b c-a d)^4-12 d^4 (a+b x)^4 \log (a+b x)\right)\right)}{(b c-a d)^4}+72 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{288 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{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{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{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{2 B^2 d^3 n^2 (c+d x)}{g^5 (a+b x) (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}",1,"-1/288*(72*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (B*n*(36*(b*c - a*d)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 48*d*(-(b*c) + a*d)^3*(a + b*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 72*d^2*(b*c - a*d)^2*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 144*d^3*(-(b*c) + a*d)*(a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 144*d^4*(a + b*x)^4*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 144*d^4*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - 144*B*d^3*n*(a + b*x)^3*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) + 36*B*d^2*n*(a + b*x)^2*((b*c - a*d)^2 + 2*d*(-(b*c) + a*d)*(a + b*x) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]) - 8*B*d*n*(a + b*x)*(2*(b*c - a*d)^3 - 3*d*(b*c - a*d)^2*(a + b*x) + 6*d^2*(b*c - a*d)*(a + b*x)^2 + 6*d^3*(a + b*x)^3*Log[a + b*x] - 6*d^3*(a + b*x)^3*Log[c + d*x]) + 3*B*n*(3*(b*c - a*d)^4 + 4*d*(-(b*c) + a*d)^3*(a + b*x) + 6*d^2*(b*c - a*d)^2*(a + b*x)^2 + 12*d^3*(-(b*c) + a*d)*(a + b*x)^3 - 12*d^4*(a + b*x)^4*Log[a + b*x] + 12*d^4*(a + b*x)^4*Log[c + d*x]) + 72*B*d^4*n*(a + b*x)^4*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - 72*B*d^4*n*(a + b*x)^4*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^4)/(b*g^5*(a + b*x)^4)","C",1
19,0,0,38,0.7713315,"\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","Integrate[(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,"Integrate[(a*g + b*g*x)^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x]","A",-1
20,0,0,36,0.2965577,"\int \frac{a g+b g x}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Integrate[(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,"Integrate[(a*g + b*g*x)/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x]","A",-1
21,0,0,38,0.1499912,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])), x]","A",-1
22,1,94,94,0.1663715,"\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","Integrate[1/((a*g + b*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])),x]","\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)}","\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,"(E^(A/(B*n))*(e*((a + b*x)/(c + d*x))^n)^n^(-1)*(c + d*x)*ExpIntegralEi[-((A + B*Log[e*((a + b*x)/(c + d*x))^n])/(B*n))])/(B*(b*c - a*d)*g^2*n*(a + b*x))","A",1
23,1,172,197,0.3276862,"\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","Integrate[1/((a*g + b*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])),x]","\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}} \left(b 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{2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{B n}\right)-d (a+b x) \text{Ei}\left(-\frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{B n}\right)\right)}{B g^3 n (a+b x)^2 (b c-a d)^2}","\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,"(E^(A/(B*n))*(e*((a + b*x)/(c + d*x))^n)^n^(-1)*(c + d*x)*(b*E^(A/(B*n))*(e*((a + b*x)/(c + d*x))^n)^n^(-1)*(c + d*x)*ExpIntegralEi[(-2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(B*n)] - d*(a + b*x)*ExpIntegralEi[-((A + B*Log[e*((a + b*x)/(c + d*x))^n])/(B*n))]))/(B*(b*c - a*d)^2*g^3*n*(a + b*x)^2)","A",1
24,0,0,38,1.0500063,"\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","Integrate[(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,"Integrate[(a*g + b*g*x)^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x]","A",-1
25,0,0,36,0.9871377,"\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","Integrate[(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,"Integrate[(a*g + b*g*x)/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x]","A",-1
26,0,0,38,0.5565475,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2), x]","A",-1
27,1,146,153,0.1856833,"\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","Integrate[1/((a*g + b*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2),x]","-\frac{(c+d x) \left(e^{\frac{A}{B n}} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{\frac{1}{n}} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right) \text{Ei}\left(-\frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{B n}\right)+B n\right)}{B^2 g^2 n^2 (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)}","-\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,"-(((c + d*x)*(B*n + E^(A/(B*n))*(e*((a + b*x)/(c + d*x))^n)^n^(-1)*ExpIntegralEi[-((A + B*Log[e*((a + b*x)/(c + d*x))^n])/(B*n))]*(A + B*Log[e*((a + b*x)/(c + d*x))^n])))/(B^2*(b*c - a*d)*g^2*n^2*(a + b*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])))","A",1
28,1,254,314,0.6159593,"\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","Integrate[1/((a*g + b*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2),x]","\frac{(c+d x) \left(-2 b e^{\frac{2 A}{B n}} (c+d x) \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{2/n} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right) \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)+d (a+b x) e^{\frac{A}{B n}} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{\frac{1}{n}} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right) \text{Ei}\left(-\frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{B n}\right)+B n (a d-b c)\right)}{B^2 g^3 n^2 (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{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,"((c + d*x)*(B*(-(b*c) + a*d)*n - 2*b*E^((2*A)/(B*n))*(e*((a + b*x)/(c + d*x))^n)^(2/n)*(c + d*x)*ExpIntegralEi[(-2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(B*n)]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + d*E^(A/(B*n))*(a + b*x)*(e*((a + b*x)/(c + d*x))^n)^n^(-1)*ExpIntegralEi[-((A + B*Log[e*((a + b*x)/(c + d*x))^n])/(B*n))]*(A + B*Log[e*((a + b*x)/(c + d*x))^n])))/(B^2*(b*c - a*d)^2*g^3*n^2*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))","A",1
29,1,146,188,0.1010389,"\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","Integrate[(c*g + d*g*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^4 \left((c+d x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-\frac{B n (b c-a d) \left(4 b^3 (c+d x)^3 (b c-a d)+6 b^2 (c+d x)^2 (b c-a d)^2+12 b d x (b c-a d)^3+12 (b c-a d)^4 \log (a+b x)+3 b^4 (c+d x)^4\right)}{12 b^5}\right)}{5 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 (b c-a d)^5 \log (a+b x)}{5 b^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 (c+d x)^4 (b c-a d)}{20 b d}",1,"(g^4*(-1/12*(B*(b*c - a*d)*n*(12*b*d*(b*c - a*d)^3*x + 6*b^2*(b*c - a*d)^2*(c + d*x)^2 + 4*b^3*(b*c - a*d)*(c + d*x)^3 + 3*b^4*(c + d*x)^4 + 12*(b*c - a*d)^4*Log[a + b*x]))/b^5 + (c + d*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n])))/(5*d)","A",1
30,1,124,156,0.0931916,"\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","Integrate[(c*g + d*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^3 \left((c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-\frac{B n (b c-a d) \left(3 b^2 (c+d x)^2 (b c-a d)+6 b d x (b c-a d)^2+6 (b c-a d)^3 \log (a+b x)+2 b^3 (c+d x)^3\right)}{6 b^4}\right)}{4 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 (b c-a d)^4 \log (a+b x)}{4 b^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 (c+d x)^3 (b c-a d)}{12 b d}",1,"(g^3*(-1/6*(B*(b*c - a*d)*n*(6*b*d*(b*c - a*d)^2*x + 3*b^2*(b*c - a*d)*(c + d*x)^2 + 2*b^3*(c + d*x)^3 + 6*(b*c - a*d)^3*Log[a + b*x]))/b^4 + (c + d*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])))/(4*d)","A",1
31,1,101,124,0.0607333,"\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","Integrate[(c*g + d*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^2 \left((c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-\frac{B n (b c-a d) \left(2 b d x (b c-a d)+2 (b c-a d)^2 \log (a+b x)+b^2 (c+d x)^2\right)}{2 b^3}\right)}{3 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 (b c-a d)^3 \log (a+b x)}{3 b^3 d}-\frac{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)}{6 b d}",1,"(g^2*(-1/2*(B*(b*c - a*d)*n*(2*b*d*(b*c - a*d)*x + b^2*(c + d*x)^2 + 2*(b*c - a*d)^2*Log[a + b*x]))/b^3 + (c + d*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])))/(3*d)","A",1
32,1,74,86,0.0387988,"\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","Integrate[(c*g + d*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g \left((c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-\frac{B n (b c-a d) ((b c-a d) \log (a+b x)+b d x)}{b^2}\right)}{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 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,"(g*(-((B*(b*c - a*d)*n*(b*d*x + (b*c - a*d)*Log[a + b*x]))/b^2) + (c + d*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])))/(2*d)","A",1
33,1,101,80,0.0438391,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{c g+d g x} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(c*g + d*g*x),x]","\frac{\log (g (c+d x)) \left(2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-2 B n \log \left(\frac{d (a+b x)}{a d-b c}\right)+2 A+B n \log (g (c+d x))\right)-2 B n \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)}{2 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}-\frac{B n \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d g}",1,"(Log[g*(c + d*x)]*(2*A - 2*B*n*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*B*Log[e*((a + b*x)/(c + d*x))^n] + B*n*Log[g*(c + d*x)]) - 2*B*n*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*d*g)","A",1
34,1,114,102,0.0585301,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(c*g + d*g*x)^2,x]","\frac{B n (b c-a d) \left(\frac{1}{(c+d x) (b c-a d)}+\frac{b \log (a+b x)}{(b c-a d)^2}-\frac{b \log (c+d x)}{(b c-a d)^2}\right)}{d g^2}-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{d g (c g+d g 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,"-((A + B*Log[e*((a + b*x)/(c + d*x))^n])/(d*g*(c*g + d*g*x))) + (B*(b*c - a*d)*n*(1/((b*c - a*d)*(c + d*x)) + (b*Log[a + b*x])/(b*c - a*d)^2 - (b*Log[c + d*x])/(b*c - a*d)^2))/(d*g^2)","A",1
35,1,115,151,0.1509714,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(c*g + d*g*x)^3,x]","\frac{\frac{B n \left(2 b^2 (c+d x)^2 \log (a+b x)+(b c-a d) (-a d+3 b c+2 b d x)-2 b^2 (c+d x)^2 \log (c+d x)\right)}{(b c-a d)^2}-2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{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,"(-2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + (B*n*((b*c - a*d)*(3*b*c - a*d + 2*b*d*x) + 2*b^2*(c + d*x)^2*Log[a + b*x] - 2*b^2*(c + d*x)^2*Log[c + d*x]))/(b*c - a*d)^2)/(4*d*g^3*(c + d*x)^2)","A",1
36,1,146,183,0.1702399,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(c*g + d*g*x)^4,x]","\frac{\frac{B n \left((b c-a d) \left(2 a^2 d^2-a b d (7 c+3 d x)+b^2 \left(11 c^2+15 c d x+6 d^2 x^2\right)\right)+6 b^3 (c+d x)^3 \log (a+b x)-6 b^3 (c+d x)^3 \log (c+d x)\right)}{(b c-a d)^3}-6 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{18 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^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^2 B n}{3 d g^4 (c+d x) (b c-a d)^2}+\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,"(-6*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + (B*n*((b*c - a*d)*(2*a^2*d^2 - a*b*d*(7*c + 3*d*x) + b^2*(11*c^2 + 15*c*d*x + 6*d^2*x^2)) + 6*b^3*(c + d*x)^3*Log[a + b*x] - 6*b^3*(c + d*x)^3*Log[c + d*x]))/(b*c - a*d)^3)/(18*d*g^4*(c + d*x)^3)","A",1
37,1,162,215,0.2312045,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(c*g + d*g*x)^5,x]","\frac{\frac{B n \left(12 b^4 \log (a+b x)+\frac{12 b^3 (b c-a d)}{c+d x}+\frac{6 b^2 (b c-a d)^2}{(c+d x)^2}+\frac{4 b (b c-a d)^3}{(c+d x)^3}+\frac{3 (b c-a d)^4}{(c+d x)^4}-12 b^4 \log (c+d x)\right)}{12 (b c-a d)^4}-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{(c+d x)^4}}{4 d g^5}","-\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^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^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 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,"(-((A + B*Log[e*((a + b*x)/(c + d*x))^n])/(c + d*x)^4) + (B*n*((3*(b*c - a*d)^4)/(c + d*x)^4 + (4*b*(b*c - a*d)^3)/(c + d*x)^3 + (6*b^2*(b*c - a*d)^2)/(c + d*x)^2 + (12*b^3*(b*c - a*d))/(c + d*x) + 12*b^4*Log[a + b*x] - 12*b^4*Log[c + d*x]))/(12*(b*c - a*d)^4))/(4*d*g^5)","A",1
38,1,533,544,0.5027008,"\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","Integrate[(c*g + d*g*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{g^4 \left((c+d x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2-\frac{B n (b c-a d) \left(6 b^4 (c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+8 b^3 (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)+12 b^2 (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)+24 (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)+24 A b d x (b c-a d)^3-4 B n (b c-a d)^2 \left(2 b d x (b c-a d)+2 (b c-a d)^2 \log (a+b x)+b^2 (c+d x)^2\right)-B n (b c-a d) \left(3 b^2 (c+d x)^2 (b c-a d)+6 b d x (b c-a d)^2+6 (b c-a d)^3 \log (a+b x)+2 b^3 (c+d x)^3\right)+24 B d (a+b x) (b c-a d)^3 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-12 B n (b c-a d)^4 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)-24 B n (b c-a d)^4 \log (c+d x)-12 B n (b c-a d)^3 ((b c-a d) \log (a+b x)+b d x)\right)}{12 b^5}\right)}{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{2 B^2 g^4 n^2 (b c-a d)^5 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{5 b^5 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}+\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}",1,"(g^4*((c + d*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - (B*(b*c - a*d)*n*(24*A*b*d*(b*c - a*d)^3*x - 12*B*(b*c - a*d)^3*n*(b*d*x + (b*c - a*d)*Log[a + b*x]) - 4*B*(b*c - a*d)^2*n*(2*b*d*(b*c - a*d)*x + b^2*(c + d*x)^2 + 2*(b*c - a*d)^2*Log[a + b*x]) - B*(b*c - a*d)*n*(6*b*d*(b*c - a*d)^2*x + 3*b^2*(b*c - a*d)*(c + d*x)^2 + 2*b^3*(c + d*x)^3 + 6*(b*c - a*d)^3*Log[a + b*x]) + 24*B*d*(b*c - a*d)^3*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] + 12*b^2*(b*c - a*d)^2*(c + d*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 8*b^3*(b*c - a*d)*(c + d*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 6*b^4*(c + d*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 24*(b*c - a*d)^4*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 24*B*(b*c - a*d)^4*n*Log[c + d*x] - 12*B*(b*c - a*d)^4*n*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])))/(12*b^5)))/(5*d)","A",1
39,1,409,454,0.3354401,"\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","Integrate[(c*g + d*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{g^3 \left((c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2-\frac{B n (b c-a d) \left(2 b^3 (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+3 b^2 (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)+6 (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)+6 A b d x (b c-a d)^2-B n (b c-a d) \left(2 b d x (b c-a d)+2 (b c-a d)^2 \log (a+b x)+b^2 (c+d x)^2\right)+6 B d (a+b x) (b c-a d)^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-3 B n (b c-a d)^3 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)-6 B n (b c-a d)^3 \log (c+d x)-3 B n (b c-a d)^2 ((b c-a d) \log (a+b x)+b d x)\right)}{3 b^4}\right)}{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{B^2 g^3 n^2 (b c-a d)^4 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{2 b^4 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}+\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}",1,"(g^3*((c + d*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - (B*(b*c - a*d)*n*(6*A*b*d*(b*c - a*d)^2*x - 3*B*(b*c - a*d)^2*n*(b*d*x + (b*c - a*d)*Log[a + b*x]) - B*(b*c - a*d)*n*(2*b*d*(b*c - a*d)*x + b^2*(c + d*x)^2 + 2*(b*c - a*d)^2*Log[a + b*x]) + 6*B*d*(b*c - a*d)^2*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] + 3*b^2*(b*c - a*d)*(c + d*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 2*b^3*(c + d*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 6*(b*c - a*d)^3*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 6*B*(b*c - a*d)^3*n*Log[c + d*x] - 3*B*(b*c - a*d)^3*n*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])))/(3*b^4)))/(4*d)","A",1
40,1,303,361,0.2391221,"\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","Integrate[(c*g + d*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{g^2 \left((c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2-\frac{B n (b c-a d) \left(b^2 (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+2 (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)+2 A b d x (b c-a d)+2 B d (a+b x) (b c-a d) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-B n (b c-a d)^2 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)-2 B n (b c-a d)^2 \log (c+d x)-B n (b c-a d) ((b c-a d) \log (a+b x)+b d x)\right)}{b^3}\right)}{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{2 B^2 g^2 n^2 (b c-a d)^3 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{3 b^3 d}+\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}+\frac{B^2 g^2 n^2 x (b c-a d)^2}{3 b^2}",1,"(g^2*((c + d*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - (B*(b*c - a*d)*n*(2*A*b*d*(b*c - a*d)*x - B*(b*c - a*d)*n*(b*d*x + (b*c - a*d)*Log[a + b*x]) + 2*B*d*(b*c - a*d)*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] + b^2*(c + d*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 2*(b*c - a*d)^2*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 2*B*(b*c - a*d)^2*n*Log[c + d*x] - B*(b*c - a*d)^2*n*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])))/b^3))/(3*d)","A",1
41,1,216,220,0.2054429,"\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","Integrate[(c*g + d*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{g \left(\frac{B n (b c-a d) \left(-2 (b c-a d) \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B n \log \left(\frac{b (c+d x)}{b c-a d}\right)+A\right)-2 \left(B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B n (a d-b c) \log (c+d x)+A b d x\right)+2 B n (a d-b c) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)+B n (b c-a d) \log ^2(a+b x)\right)}{b^2}+(c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2\right)}{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 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^2 d}+\frac{B^2 g n^2 (b c-a d)^2 \log (c+d x)}{b^2 d}",1,"(g*((c + d*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (B*(b*c - a*d)*n*(B*(b*c - a*d)*n*Log[a + b*x]^2 - 2*(A*b*d*x + B*d*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] + B*(-(b*c) + a*d)*n*Log[c + d*x]) - 2*(b*c - a*d)*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n] + B*n*Log[(b*(c + d*x))/(b*c - a*d)]) + 2*B*(-(b*c) + a*d)*n*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]))/b^2))/(2*d)","A",1
42,1,537,137,0.406822,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(c*g + d*g*x),x]","\frac{-3 B n \left(-2 \left(\text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)+\log \left(\frac{a}{b}+x\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)+2 \log (c+d x) \left(-\log \left(\frac{a+b x}{c+d x}\right)+\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)\right)+\log ^2\left(\frac{c}{d}+x\right)\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-B n \log \left(\frac{a+b x}{c+d x}\right)+A\right)+3 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-B n \log \left(\frac{a+b x}{c+d x}\right)+A\right)^2+B^2 n^2 \left(-6 \text{Li}_3\left(\frac{d (a+b x)}{a d-b c}\right)-6 \text{Li}_3\left(\frac{b (c+d x)}{b c-a d}\right)+3 \left(-\log \left(\frac{a+b x}{c+d x}\right)+\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)\right) \left(\log ^2\left(\frac{c}{d}+x\right)-2 \left(\text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)+\log \left(\frac{a}{b}+x\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)\right)+6 \log \left(\frac{c}{d}+x\right) \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+6 \log \left(\frac{a}{b}+x\right) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)+3 \log ^2\left(\frac{c}{d}+x\right) \left(\log \left(\frac{d (a+b x)}{a d-b c}\right)-\log \left(\frac{a}{b}+x\right)\right)+3 \log ^2\left(\frac{a}{b}+x\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)+3 \log (c+d x) \left(\log \left(\frac{a+b x}{c+d x}\right)-\log \left(\frac{a}{b}+x\right)+\log \left(\frac{c}{d}+x\right)\right)^2+\log ^3\left(\frac{c}{d}+x\right)\right)}{3 d g}","-\frac{2 B n \text{Li}_2\left(\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{\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}+\frac{2 B^2 n^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d g}",1,"(3*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2*Log[c + d*x] - 3*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])*(Log[c/d + x]^2 + 2*(Log[a/b + x] - Log[c/d + x] - Log[(a + b*x)/(c + d*x)])*Log[c + d*x] - 2*(Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])) + B^2*n^2*(Log[c/d + x]^3 + 3*Log[c/d + x]^2*(-Log[a/b + x] + Log[(d*(a + b*x))/(-(b*c) + a*d)]) + 3*(-Log[a/b + x] + Log[c/d + x] + Log[(a + b*x)/(c + d*x)])^2*Log[c + d*x] + 3*Log[a/b + x]^2*Log[(b*(c + d*x))/(b*c - a*d)] + 6*Log[a/b + x]*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 3*(Log[a/b + x] - Log[c/d + x] - Log[(a + b*x)/(c + d*x)])*(Log[c/d + x]^2 - 2*(Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])) + 6*Log[c/d + x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 6*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)] - 6*PolyLog[3, (b*(c + d*x))/(b*c - a*d)]))/(3*d*g)","B",1
43,1,331,163,0.4305634,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(c*g + d*g*x)^2,x]","\frac{\frac{B n \left(2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+2 b (c+d x) \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-2 b (c+d x) \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-b B n (c+d x) \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+b B n (c+d x) \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-2 B n (b (c+d x) \log (a+b x)-a d-b (c+d x) \log (c+d x)+b c)\right)}{b c-a d}-\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{(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,"(-(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (B*n*(2*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 2*b*(c + d*x)*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 2*b*(c + d*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - 2*B*n*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]) - b*B*n*(c + d*x)*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + b*B*n*(c + d*x)*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d))/(d*g^2*(c + d*x))","C",1
44,1,464,317,0.4436648,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(c*g + d*g*x)^3,x]","\frac{\frac{B n \left(4 b^2 (c+d x)^2 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-4 b^2 (c+d x)^2 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+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 (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)-2 b^2 B n (c+d x)^2 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+2 b^2 B n (c+d x)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-B n \left(2 b^2 (c+d x)^2 \log (a+b x)+2 b (c+d x) (b c-a d)+(b c-a d)^2-2 b^2 (c+d x)^2 \log (c+d x)\right)-4 b B n (c+d x) (b (c+d x) \log (a+b x)-a d-b (c+d x) \log (c+d x)+b c)\right)}{(b c-a d)^2}-2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^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,"(-2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (B*n*(2*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 4*b*(b*c - a*d)*(c + d*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 4*b^2*(c + d*x)^2*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 4*b^2*(c + d*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - 4*b*B*n*(c + d*x)*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]) - B*n*((b*c - a*d)^2 + 2*b*(b*c - a*d)*(c + d*x) + 2*b^2*(c + d*x)^2*Log[a + b*x] - 2*b^2*(c + d*x)^2*Log[c + d*x]) - 2*b^2*B*n*(c + d*x)^2*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 2*b^2*B*n*(c + d*x)^2*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^2)/(4*d*g^3*(c + d*x)^2)","C",1
45,1,609,429,0.6727249,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(c*g + d*g*x)^4,x]","\frac{\frac{B n \left(36 b^3 (c+d x)^3 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-36 b^3 (c+d x)^3 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+36 b^2 (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)+12 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+18 b (c+d x) (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-18 b^3 B n (c+d x)^3 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+18 b^3 B n (c+d x)^3 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-36 b^2 B n (c+d x)^2 (b (c+d x) \log (a+b x)-a d-b (c+d x) \log (c+d x)+b c)-9 b B n (c+d x) \left(2 b^2 (c+d x)^2 \log (a+b x)+2 b (c+d x) (b c-a d)+(b c-a d)^2-2 b^2 (c+d x)^2 \log (c+d x)\right)-2 B n \left(6 b^3 (c+d x)^3 \log (a+b x)+6 b^2 (c+d x)^2 (b c-a d)+3 b (c+d x) (b c-a d)^2+2 (b c-a d)^3-6 b^3 (c+d x)^3 \log (c+d x)\right)\right)}{(b c-a d)^3}-18 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{54 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{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 B^2 n^2 (a+b x)}{g^4 (c+d x) (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,"(-18*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (B*n*(12*(b*c - a*d)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 18*b*(b*c - a*d)^2*(c + d*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 36*b^2*(b*c - a*d)*(c + d*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 36*b^3*(c + d*x)^3*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 36*b^3*(c + d*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - 36*b^2*B*n*(c + d*x)^2*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]) - 9*b*B*n*(c + d*x)*((b*c - a*d)^2 + 2*b*(b*c - a*d)*(c + d*x) + 2*b^2*(c + d*x)^2*Log[a + b*x] - 2*b^2*(c + d*x)^2*Log[c + d*x]) - 2*B*n*(2*(b*c - a*d)^3 + 3*b*(b*c - a*d)^2*(c + d*x) + 6*b^2*(b*c - a*d)*(c + d*x)^2 + 6*b^3*(c + d*x)^3*Log[a + b*x] - 6*b^3*(c + d*x)^3*Log[c + d*x]) - 18*b^3*B*n*(c + d*x)^3*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 18*b^3*B*n*(c + d*x)^3*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^3)/(54*d*g^4*(c + d*x)^3)","C",1
46,1,776,536,0.9293329,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(c*g + d*g*x)^5,x]","\frac{\frac{B n \left(144 b^4 (c+d x)^4 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-144 b^4 (c+d x)^4 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+144 b^3 (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)+72 b^2 (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)+36 (b c-a d)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+48 b (c+d x) (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-72 b^4 B n (c+d x)^4 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+72 b^4 B n (c+d x)^4 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-144 b^3 B n (c+d x)^3 (b (c+d x) \log (a+b x)-a d-b (c+d x) \log (c+d x)+b c)-36 b^2 B n (c+d x)^2 \left(2 b^2 (c+d x)^2 \log (a+b x)+2 b (c+d x) (b c-a d)+(b c-a d)^2-2 b^2 (c+d x)^2 \log (c+d x)\right)-8 b B n (c+d x) \left(6 b^3 (c+d x)^3 \log (a+b x)+6 b^2 (c+d x)^2 (b c-a d)+3 b (c+d x) (b c-a d)^2+2 (b c-a d)^3-6 b^3 (c+d x)^3 \log (c+d x)\right)-3 B n \left(12 b^4 (c+d x)^4 \log (a+b x)+12 b^3 (c+d x)^3 (b c-a d)+6 b^2 (c+d x)^2 (b c-a d)^2+4 b (c+d x) (b c-a d)^3+3 (b c-a d)^4-12 b^4 (c+d x)^4 \log (c+d x)\right)\right)}{(b c-a d)^4}-72 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{288 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{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{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{\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{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^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^2 d^3 n^2 (a+b x)^4}{32 g^5 (c+d x)^4 (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}",1,"(-72*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (B*n*(36*(b*c - a*d)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 48*b*(b*c - a*d)^3*(c + d*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 72*b^2*(b*c - a*d)^2*(c + d*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 144*b^3*(b*c - a*d)*(c + d*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 144*b^4*(c + d*x)^4*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 144*b^4*(c + d*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - 144*b^3*B*n*(c + d*x)^3*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]) - 36*b^2*B*n*(c + d*x)^2*((b*c - a*d)^2 + 2*b*(b*c - a*d)*(c + d*x) + 2*b^2*(c + d*x)^2*Log[a + b*x] - 2*b^2*(c + d*x)^2*Log[c + d*x]) - 8*b*B*n*(c + d*x)*(2*(b*c - a*d)^3 + 3*b*(b*c - a*d)^2*(c + d*x) + 6*b^2*(b*c - a*d)*(c + d*x)^2 + 6*b^3*(c + d*x)^3*Log[a + b*x] - 6*b^3*(c + d*x)^3*Log[c + d*x]) - 3*B*n*(3*(b*c - a*d)^4 + 4*b*(b*c - a*d)^3*(c + d*x) + 6*b^2*(b*c - a*d)^2*(c + d*x)^2 + 12*b^3*(b*c - a*d)*(c + d*x)^3 + 12*b^4*(c + d*x)^4*Log[a + b*x] - 12*b^4*(c + d*x)^4*Log[c + d*x]) - 72*b^4*B*n*(c + d*x)^4*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 72*b^4*B*n*(c + d*x)^4*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^4)/(288*d*g^5*(c + d*x)^4)","C",1
47,0,0,38,0.4388892,"\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","Integrate[(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,"Integrate[(c*g + d*g*x)^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x]","A",-1
48,0,0,36,0.2977712,"\int \frac{c g+d g x}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Integrate[(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,"Integrate[(c*g + d*g*x)/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x]","A",-1
49,0,0,38,0.1784386,"\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","Integrate[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,"Integrate[1/((c*g + d*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])), x]","A",-1
50,1,96,96,0.1232213,"\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","Integrate[1/((c*g + d*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])),x]","\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)}","\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,"((a + b*x)*ExpIntegralEi[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(B*n)])/(B*(b*c - a*d)*E^(A/(B*n))*g^2*n*(e*((a + b*x)/(c + d*x))^n)^n^(-1)*(c + d*x))","A",1
51,1,174,199,0.285206,"\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","Integrate[1/((c*g + d*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])),x]","\frac{(a+b x) e^{-\frac{2 A}{B n}} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-2/n} \left(b 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)-d (a+b x) \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)\right)}{B g^3 n (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 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,"((a + b*x)*(b*E^(A/(B*n))*(e*((a + b*x)/(c + d*x))^n)^n^(-1)*(c + d*x)*ExpIntegralEi[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(B*n)] - d*(a + b*x)*ExpIntegralEi[(2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(B*n)]))/(B*(b*c - a*d)^2*E^((2*A)/(B*n))*g^3*n*(e*((a + b*x)/(c + d*x))^n)^(2/n)*(c + d*x)^2)","A",1
52,0,0,38,0.99566,"\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","Integrate[(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,"Integrate[(c*g + d*g*x)^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x]","A",-1
53,0,0,36,1.0036273,"\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","Integrate[(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,"Integrate[(c*g + d*g*x)/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x]","A",-1
54,0,0,38,0.5586746,"\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","Integrate[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,"Integrate[1/((c*g + d*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2), x]","A",-1
55,1,180,154,0.1712237,"\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","Integrate[1/((c*g + d*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2),x]","-\frac{(a+b x) e^{-\frac{A}{B n}} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-1/n} \left(B n e^{\frac{A}{B n}} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{\frac{1}{n}}-\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right) \text{Ei}\left(\frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{B n}\right)\right)}{B^2 g^2 n^2 (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)}","\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,"-(((a + b*x)*(B*E^(A/(B*n))*n*(e*((a + b*x)/(c + d*x))^n)^n^(-1) - ExpIntegralEi[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(B*n)]*(A + B*Log[e*((a + b*x)/(c + d*x))^n])))/(B^2*(b*c - a*d)*E^(A/(B*n))*g^2*n^2*(e*((a + b*x)/(c + d*x))^n)^n^(-1)*(c + d*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])))","A",1
56,1,288,256,0.5442523,"\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","Integrate[1/((c*g + d*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2),x]","\frac{(a+b x) e^{-\frac{2 A}{B n}} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-2/n} \left(b e^{\frac{A}{B n}} (c+d x) \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{\frac{1}{n}} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right) \text{Ei}\left(\frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{B n}\right)-2 d (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right) \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 n e^{\frac{2 A}{B n}} (b c-a d) \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{2/n}\right)}{B^2 g^3 n^2 (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)}","-\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,"((a + b*x)*(-(B*(b*c - a*d)*E^((2*A)/(B*n))*n*(e*((a + b*x)/(c + d*x))^n)^(2/n)) + b*E^(A/(B*n))*(e*((a + b*x)/(c + d*x))^n)^n^(-1)*(c + d*x)*ExpIntegralEi[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(B*n)]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 2*d*(a + b*x)*ExpIntegralEi[(2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(B*n)]*(A + B*Log[e*((a + b*x)/(c + d*x))^n])))/(B^2*(b*c - a*d)^2*E^((2*A)/(B*n))*g^3*n^2*(e*((a + b*x)/(c + d*x))^n)^(2/n)*(c + d*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))","A",1
57,1,285,364,0.6301328,"\int (f+g x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Integrate[(f + g*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{\frac{B g^2 n x (a d-b c) \left(-12 a^3 d^3 g^3+6 a^2 b d^2 g^2 (-2 c g+10 d f+d g x)-2 a b^2 d g \left(6 c^2 g^2-3 c d g (10 f+g x)+d^2 \left(60 f^2+15 f g x+2 g^2 x^2\right)\right)+b^3 \left(-12 c^3 g^3+6 c^2 d g^2 (10 f+g x)-2 c d^2 g \left(60 f^2+15 f g x+2 g^2 x^2\right)+d^3 \left(120 f^3+60 f^2 g x+20 f g^2 x^2+3 g^3 x^3\right)\right)\right)}{12 b^4 d^4}+(f+g x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-\frac{B n (b f-a g)^5 \log (a+b x)}{b^5}+\frac{B n (d f-c g)^5 \log (c+d x)}{d^5}}{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^3 d^3 g^3-a^2 b d^2 g^2 (5 d f-c g)+a b^2 d g \left(c^2 g^2-5 c d f g+10 d^2 f^2\right)-\left(b^3 \left(-c^3 g^3+5 c^2 d f g^2-10 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 n (b f-a g)^5 \log (a+b x)}{5 b^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 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*(-(b*c) + a*d)*g^2*n*x*(-12*a^3*d^3*g^3 + 6*a^2*b*d^2*g^2*(10*d*f - 2*c*g + d*g*x) - 2*a*b^2*d*g*(6*c^2*g^2 - 3*c*d*g*(10*f + g*x) + d^2*(60*f^2 + 15*f*g*x + 2*g^2*x^2)) + b^3*(-12*c^3*g^3 + 6*c^2*d*g^2*(10*f + g*x) - 2*c*d^2*g*(60*f^2 + 15*f*g*x + 2*g^2*x^2) + d^3*(120*f^3 + 60*f^2*g*x + 20*f*g^2*x^2 + 3*g^3*x^3))))/(12*b^4*d^4) - (B*(b*f - a*g)^5*n*Log[a + b*x])/b^5 + (f + g*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + (B*(d*f - c*g)^5*n*Log[c + d*x])/d^5)/(5*g)","A",1
58,1,219,235,0.2825807,"\int (f+g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Integrate[(f + g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{(f+g x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-\frac{B n \left(6 b d g^2 x (b c-a d) \left(a^2 d^2 g^2+a b d g (c g-4 d f)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right)+2 b^3 d^3 g^4 x^3 (b c-a d)+3 b^2 d^2 g^3 x^2 (b c-a d) (-a d g-b c g+4 b d f)+6 d^4 (b f-a g)^4 \log (a+b x)-6 b^4 (d f-c g)^4 \log (c+d x)\right)}{6 b^4 d^4}}{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 n (b f-a g)^4 \log (a+b x)}{4 b^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 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,"((f + g*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - (B*n*(6*b*d*(b*c - a*d)*g^2*(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 + 3*b^2*d^2*(b*c - a*d)*g^3*(4*b*d*f - b*c*g - a*d*g)*x^2 + 2*b^3*d^3*(b*c - a*d)*g^4*x^3 + 6*d^4*(b*f - a*g)^4*Log[a + b*x] - 6*b^4*(d*f - c*g)^4*Log[c + d*x]))/(6*b^4*d^4))/(4*g)","A",1
59,1,146,157,0.1463795,"\int (f+g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Integrate[(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)-\frac{B n \left(b^2 d^2 g^3 x^2 (b c-a d)+2 b d g^2 x (b c-a d) (-a d g-b c g+3 b d f)+2 d^3 (b f-a g)^3 \log (a+b x)-2 b^3 (d f-c g)^3 \log (c+d x)\right)}{2 b^3 d^3}}{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 n (b f-a g)^3 \log (a+b x)}{3 b^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 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,"((f + g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - (B*n*(2*b*d*(b*c - a*d)*g^2*(3*b*d*f - b*c*g - a*d*g)*x + b^2*d^2*(b*c - a*d)*g^3*x^2 + 2*d^3*(b*f - a*g)^3*Log[a + b*x] - 2*b^3*(d*f - c*g)^3*Log[c + d*x]))/(2*b^3*d^3))/(3*g)","A",1
60,1,120,115,0.1273479,"\int (f+g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Integrate[(f + g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{b \left(d \left(B g^2 n x (a d-b c)+A b d (f+g x)^2\right)+b B d^2 (f+g x)^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+b B n (d f-c g)^2 \log (c+d x)\right)-B d^2 n (b f-a g)^2 \log (a+b x)}{2 b^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*d^2*(b*f - a*g)^2*n*Log[a + b*x]) + b*(d*(B*(-(b*c) + a*d)*g^2*n*x + A*b*d*(f + g*x)^2) + b*B*d^2*(f + g*x)^2*Log[e*((a + b*x)/(c + d*x))^n] + b*B*(d*f - c*g)^2*n*Log[c + d*x]))/(2*b^2*d^2*g)","A",1
61,1,56,56,0.0097868,"\int \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Integrate[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",1
62,1,122,147,0.059593,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f+g x} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x),x]","\frac{\log (f+g x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-B n \log \left(\frac{g (a+b x)}{a g-b f}\right)+A+B n \log \left(\frac{g (c+d x)}{c g-d f}\right)\right)-B n \text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\right)+B n \text{Li}_2\left(\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 \text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\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 \text{Li}_2\left(\frac{d (f+g x)}{d f-c g}\right)}{g}+\frac{B n \log (f+g x) \log \left(-\frac{g (c+d x)}{d f-c g}\right)}{g}",1,"((A - B*n*Log[(g*(a + b*x))/(-(b*f) + a*g)] + B*Log[e*((a + b*x)/(c + d*x))^n] + B*n*Log[(g*(c + d*x))/(-(d*f) + c*g)])*Log[f + g*x] - B*n*PolyLog[2, (b*(f + g*x))/(b*f - a*g)] + B*n*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g","A",1
63,1,109,91,0.1472244,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(f+g x)^2} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x)^2,x]","\frac{\frac{B n (b \log (a+b x) (d f-c g)+\log (c+d x) (a d g-b d f)+g (b c-a d) \log (f+g x))}{(b f-a g) (d f-c g)}-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{f+g x}}{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,"(-((A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x)) + (B*n*(b*(d*f - c*g)*Log[a + b*x] + (-(b*d*f) + a*d*g)*Log[c + d*x] + (b*c - a*d)*g*Log[f + g*x]))/((b*f - a*g)*(d*f - c*g)))/g","A",1
64,1,173,190,0.5439698,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(f+g x)^3} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x)^3,x]","\frac{B n (b c-a d) \left(\frac{b^2 \log (a+b x)}{(b c-a d) (b f-a g)^2}+\frac{\frac{d^2 \log (c+d x)}{a d-b c}+\frac{g (c g-d f)}{(f+g x) (b f-a g)}-\frac{g \log (f+g x) (a d g+b c g-2 b d f)}{(b f-a g)^2}}{(d f-c g)^2}\right)-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{(f+g x)^2}}{2 g}","-\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,"(-((A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x)^2) + B*(b*c - a*d)*n*((b^2*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)^2) + ((g*(-(d*f) + c*g))/((b*f - a*g)*(f + g*x)) + (d^2*Log[c + d*x])/(-(b*c) + a*d) - (g*(-2*b*d*f + b*c*g + a*d*g)*Log[f + g*x])/(b*f - a*g)^2)/(d*f - c*g)^2))/(2*g)","A",1
65,1,264,283,0.8931805,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(f+g x)^4} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x)^4,x]","\frac{B n (b c-a d) \left(\frac{g \log (f+g x) \left(a^2 d^2 g^2+a b d g (c g-3 d f)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{(b f-a g)^3 (d f-c g)^3}+\frac{b^3 \log (a+b x)}{(b c-a d) (b f-a g)^3}+\frac{d^3 \log (c+d x)}{(b c-a d) (c g-d f)^3}+\frac{g (a d g+b c g-2 b d f)}{(f+g x) (b f-a g)^2 (d f-c g)^2}-\frac{g}{2 (f+g x)^2 (b f-a g) (d f-c g)}\right)-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{(f+g x)^3}}{3 g}","\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,"(-((A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x)^3) + B*(b*c - a*d)*n*(-1/2*g/((b*f - a*g)*(d*f - c*g)*(f + g*x)^2) + (g*(-2*b*d*f + b*c*g + a*d*g))/((b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)) + (b^3*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)^3) + (d^3*Log[c + d*x])/((b*c - a*d)*(-(d*f) + c*g)^3) + (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])/((b*f - a*g)^3*(d*f - c*g)^3)))/(3*g)","A",1
66,1,359,388,1.0702439,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(f+g x)^5} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x)^5,x]","\frac{B n (b c-a d) \left(-\frac{g \left(a^2 d^2 g^2+a b d g (c g-3 d f)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{(f+g x) (b f-a g)^3 (d f-c g)^3}-\frac{g \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(c^2 g^2-2 c d f g+2 d^2 f^2\right)\right)}{(b f-a g)^4 (d f-c g)^4}+\frac{b^4 \log (a+b x)}{(b c-a d) (b f-a g)^4}-\frac{d^4 \log (c+d x)}{(b c-a d) (d f-c g)^4}+\frac{g (a d g+b c g-2 b d f)}{2 (f+g x)^2 (b f-a g)^2 (d f-c g)^2}-\frac{g}{3 (f+g x)^3 (b f-a g) (d f-c g)}\right)-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{(f+g x)^4}}{4 g}","-\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-\left(b^2 \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,"(-((A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x)^4) + B*(b*c - a*d)*n*(-1/3*g/((b*f - a*g)*(d*f - c*g)*(f + g*x)^3) + (g*(-2*b*d*f + b*c*g + a*d*g))/(2*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)^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)))/((b*f - a*g)^3*(d*f - c*g)^3*(f + g*x)) + (b^4*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)^4) - (d^4*Log[c + d*x])/((b*c - a*d)*(d*f - c*g)^4) - (g*(-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])/((b*f - a*g)^4*(d*f - c*g)^4)))/(4*g)","A",1
67,1,757,923,1.0398019,"\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","Integrate[(f + g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{(f+g x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2-\frac{B n \left(B g^4 n (b c-a d) \left(2 a^3 d^3 \log (a+b x)+b d x (b c-a d) (2 a d+2 b c-b d x)-2 b^3 c^3 \log (c+d x)\right)+6 A b d g^2 x (b c-a d) \left(a^2 d^2 g^2+a b d g (c g-4 d f)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right)+6 B d g^2 (a+b x) (b c-a d) \left(a^2 d^2 g^2+a b d g (c g-4 d f)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-6 B g^2 n (b c-a d)^2 \log (c+d x) \left(a^2 d^2 g^2+a b d g (c g-4 d f)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right)-3 B g^3 n (b c-a d) (a d g+b c g-4 b d f) \left(b \left(d x (a d-b c)+b c^2 \log (c+d x)\right)-a^2 d^2 \log (a+b x)\right)-6 b^4 (d f-c g)^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^3 d^3 g^4 x^3 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+3 b^2 d^2 g^3 x^2 (b c-a d) (-a d g-b c g+4 b d f) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+6 d^4 (b f-a g)^4 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+3 b^4 B n (d f-c g)^4 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-3 B d^4 n (b f-a g)^4 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)\right)}{3 b^4 d^4}}{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(\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2\right)+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(\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2\right)+2 a d^2 f g b-a^2 d^2 g^2\right) n^2 \text{Li}_2\left(\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,"((f + g*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - (B*n*(6*A*b*d*(b*c - a*d)*g^2*(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 + 6*B*d*(b*c - a*d)*g^2*(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))^n] + 3*b^2*d^2*(b*c - a*d)*g^3*(4*b*d*f - b*c*g - a*d*g)*x^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 2*b^3*d^3*(b*c - a*d)*g^4*x^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 6*d^4*(b*f - a*g)^4*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 6*B*(b*c - a*d)^2*g^2*(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*Log[c + d*x] - 6*b^4*(d*f - c*g)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + B*(b*c - a*d)*g^4*n*(b*d*(b*c - a*d)*x*(2*b*c + 2*a*d - b*d*x) + 2*a^3*d^3*Log[a + b*x] - 2*b^3*c^3*Log[c + d*x]) - 3*B*(b*c - a*d)*g^3*(-4*b*d*f + b*c*g + a*d*g)*n*(-(a^2*d^2*Log[a + b*x]) + b*(d*(-(b*c) + a*d)*x + b*c^2*Log[c + d*x])) - 3*B*d^4*(b*f - a*g)^4*n*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 3*b^4*B*(d*f - c*g)^4*n*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(3*b^4*d^4))/(4*g)","A",1
68,1,506,565,0.5580358,"\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","Integrate[(f + g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{(f+g x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2-\frac{B n \left(-B g^3 n (b c-a d) \left(a^2 d^2 \log (a+b x)-b \left(d x (a d-b c)+b c^2 \log (c+d x)\right)\right)-2 b^3 (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)+b^2 d^2 g^3 x^2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+2 d^3 (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)+2 A b d g^2 x (b c-a d) (-a d g-b c g+3 b d f)+b^3 B n (d f-c g)^3 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-B d^3 n (b f-a g)^3 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+2 B d g^2 (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)+2 B g^2 n (b c-a d)^2 \log (c+d x) (a d g+b c g-3 b d f)\right)}{b^3 d^3}}{3 g}","\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^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{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\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 (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}+\frac{B^2 g^2 n^2 x (b c-a d)^2}{3 b^2 d^2}",1,"((f + g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - (B*n*(2*A*b*d*(b*c - a*d)*g^2*(3*b*d*f - b*c*g - a*d*g)*x + 2*B*d*(b*c - a*d)*g^2*(3*b*d*f - b*c*g - a*d*g)*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] + b^2*d^2*(b*c - a*d)*g^3*x^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 2*d^3*(b*f - a*g)^3*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 2*B*(b*c - a*d)^2*g^2*(-3*b*d*f + b*c*g + a*d*g)*n*Log[c + d*x] - 2*b^3*(d*f - c*g)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - B*(b*c - a*d)*g^3*n*(a^2*d^2*Log[a + b*x] - b*(d*(-(b*c) + a*d)*x + b*c^2*Log[c + d*x])) - B*d^3*(b*f - a*g)^3*n*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + b^3*B*(d*f - c*g)^3*n*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b^3*d^3))/(3*g)","A",1
69,1,362,290,0.3130336,"\int (f+g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Integrate[(f + g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,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-\frac{B n \left(-2 b^2 (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)+2 d^2 (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)+2 A b d g^2 x (b c-a d)+b^2 B n (d f-c g)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-B d^2 n (b f-a g)^2 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+2 B d g^2 (a+b x) (b c-a d) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-2 B g^2 n (b c-a d)^2 \log (c+d x)\right)}{b^2 d^2}}{2 g}","\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 n^2 (b c-a d) (-a d g-b c g+2 b d f) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^2 d^2}+\frac{B^2 g n^2 (b c-a d)^2 \log (c+d x)}{b^2 d^2}",1,"((f + g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - (B*n*(2*A*b*d*(b*c - a*d)*g^2*x + 2*B*d*(b*c - a*d)*g^2*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] + 2*d^2*(b*f - a*g)^2*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 2*B*(b*c - a*d)^2*g^2*n*Log[c + d*x] - 2*b^2*(d*f - c*g)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - B*d^2*(b*f - a*g)^2*n*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + b^2*B*(d*f - c*g)^2*n*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b^2*d^2))/(2*g)","A",1
70,1,226,135,0.1729068,"\int \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{B n \left(2 a d \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-2 b c \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-a B d n \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+b B c n \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)\right)}{b d}+x \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2","\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}+\frac{2 B^2 n^2 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b d}",1,"x*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (B*n*(2*a*d*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 2*b*c*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - a*B*d*n*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + b*B*c*n*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*d)","A",1
71,1,1441,297,0.4581685,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(f + g*x),x]","\frac{\log (f+g x) A^2-2 B n \log \left(\frac{a}{b}+x\right) \log (f+g x) A+2 B n \log \left(\frac{c}{d}+x\right) \log (f+g x) A+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log (f+g x) A+2 B n \log \left(\frac{a}{b}+x\right) \log \left(\frac{b (f+g x)}{b f-a g}\right) A-2 B n \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (f+g x)}{d f-c g}\right) A-B^2 n^2 \log \left(\frac{a d-b c}{d (a+b x)}\right) \log ^2\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right)+B^2 n^2 \log ^2\left(\frac{a}{b}+x\right) \log (f+g x)+B^2 n^2 \log ^2\left(\frac{c}{d}+x\right) \log (f+g x)+B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log (f+g x)-2 B^2 n^2 \log \left(\frac{a}{b}+x\right) \log \left(\frac{c}{d}+x\right) \log (f+g x)-2 B^2 n \log \left(\frac{a}{b}+x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log (f+g x)+2 B^2 n \log \left(\frac{c}{d}+x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log (f+g x)-B^2 n^2 \log ^2\left(\frac{a}{b}+x\right) \log \left(\frac{b (f+g x)}{b f-a g}\right)-B^2 n^2 \log ^2\left(\frac{g (c+d x)}{c g-d f}\right) \log \left(\frac{b (f+g x)}{b f-a g}\right)-B^2 n^2 \log ^2\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \log \left(\frac{b (f+g x)}{b f-a g}\right)+2 B^2 n \log \left(\frac{a}{b}+x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(\frac{b (f+g x)}{b f-a g}\right)+2 B^2 n^2 \log \left(\frac{a}{b}+x\right) \log \left(\frac{g (c+d x)}{c g-d f}\right) \log \left(\frac{b (f+g x)}{b f-a g}\right)+2 B^2 n^2 \log \left(\frac{g (c+d x)}{c g-d f}\right) \log \left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \log \left(\frac{b (f+g x)}{b f-a g}\right)-B^2 n^2 \log ^2\left(\frac{c}{d}+x\right) \log \left(\frac{d (f+g x)}{d f-c g}\right)+B^2 n^2 \log ^2\left(\frac{g (c+d x)}{c g-d f}\right) \log \left(\frac{d (f+g x)}{d f-c g}\right)+2 B^2 n^2 \log \left(\frac{a}{b}+x\right) \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (f+g x)}{d f-c g}\right)-2 B^2 n \log \left(\frac{c}{d}+x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(\frac{d (f+g x)}{d f-c g}\right)-2 B^2 n^2 \log \left(\frac{a}{b}+x\right) \log \left(\frac{g (c+d x)}{c g-d f}\right) \log \left(\frac{d (f+g x)}{d f-c g}\right)-2 B^2 n^2 \log \left(\frac{g (c+d x)}{c g-d f}\right) \log \left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \log \left(\frac{d (f+g x)}{d f-c g}\right)+B^2 n^2 \log ^2\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \log \left(\frac{(a d-b c) (f+g x)}{(d f-c g) (a+b x)}\right)+2 B n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B n \log \left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right)\right) \text{Li}_2\left(\frac{g (a+b x)}{a g-b f}\right)-2 B n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B n \log \left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right)\right) \text{Li}_2\left(\frac{g (c+d x)}{c g-d f}\right)-2 B^2 n^2 \log \left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)+2 B^2 n^2 \log \left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \text{Li}_2\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right)+2 B^2 n^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)-2 B^2 n^2 \text{Li}_3\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right)}{g}","\frac{2 B n \text{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\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{2 B n \text{Li}_2\left(\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{\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}-\frac{2 B^2 n^2 \text{Li}_3\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{g}+\frac{2 B^2 n^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{g}",1,"(-(B^2*n^2*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))]^2) + A^2*Log[f + g*x] - 2*A*B*n*Log[a/b + x]*Log[f + g*x] + B^2*n^2*Log[a/b + x]^2*Log[f + g*x] + 2*A*B*n*Log[c/d + x]*Log[f + g*x] - 2*B^2*n^2*Log[a/b + x]*Log[c/d + x]*Log[f + g*x] + B^2*n^2*Log[c/d + x]^2*Log[f + g*x] + 2*A*B*Log[e*((a + b*x)/(c + d*x))^n]*Log[f + g*x] - 2*B^2*n*Log[a/b + x]*Log[e*((a + b*x)/(c + d*x))^n]*Log[f + g*x] + 2*B^2*n*Log[c/d + x]*Log[e*((a + b*x)/(c + d*x))^n]*Log[f + g*x] + B^2*Log[e*((a + b*x)/(c + d*x))^n]^2*Log[f + g*x] + 2*A*B*n*Log[a/b + x]*Log[(b*(f + g*x))/(b*f - a*g)] - B^2*n^2*Log[a/b + x]^2*Log[(b*(f + g*x))/(b*f - a*g)] + 2*B^2*n*Log[a/b + x]*Log[e*((a + b*x)/(c + d*x))^n]*Log[(b*(f + g*x))/(b*f - a*g)] + 2*B^2*n^2*Log[a/b + x]*Log[(g*(c + d*x))/(-(d*f) + c*g)]*Log[(b*(f + g*x))/(b*f - a*g)] - B^2*n^2*Log[(g*(c + d*x))/(-(d*f) + c*g)]^2*Log[(b*(f + g*x))/(b*f - a*g)] + 2*B^2*n^2*Log[(g*(c + d*x))/(-(d*f) + c*g)]*Log[((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))]*Log[(b*(f + g*x))/(b*f - a*g)] - B^2*n^2*Log[((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))]^2*Log[(b*(f + g*x))/(b*f - a*g)] - 2*A*B*n*Log[c/d + x]*Log[(d*(f + g*x))/(d*f - c*g)] + 2*B^2*n^2*Log[a/b + x]*Log[c/d + x]*Log[(d*(f + g*x))/(d*f - c*g)] - B^2*n^2*Log[c/d + x]^2*Log[(d*(f + g*x))/(d*f - c*g)] - 2*B^2*n*Log[c/d + x]*Log[e*((a + b*x)/(c + d*x))^n]*Log[(d*(f + g*x))/(d*f - c*g)] - 2*B^2*n^2*Log[a/b + x]*Log[(g*(c + d*x))/(-(d*f) + c*g)]*Log[(d*(f + g*x))/(d*f - c*g)] + B^2*n^2*Log[(g*(c + d*x))/(-(d*f) + c*g)]^2*Log[(d*(f + g*x))/(d*f - c*g)] - 2*B^2*n^2*Log[(g*(c + d*x))/(-(d*f) + c*g)]*Log[((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))]*Log[(d*(f + g*x))/(d*f - c*g)] + B^2*n^2*Log[((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))]^2*Log[((-(b*c) + a*d)*(f + g*x))/((d*f - c*g)*(a + b*x))] + 2*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n] + B*n*Log[((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))])*PolyLog[2, (g*(a + b*x))/(-(b*f) + a*g)] - 2*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n] + B*n*Log[((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))])*PolyLog[2, (g*(c + d*x))/(-(d*f) + c*g)] - 2*B^2*n^2*Log[((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] + 2*B^2*n^2*Log[((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))]*PolyLog[2, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))] + 2*B^2*n^2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))] - 2*B^2*n^2*PolyLog[3, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))])/g","B",1
72,1,418,206,0.521022,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(f + g*x)^2,x]","\frac{\frac{B n \left(2 b \log (a+b x) (d f-c g) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-2 d (b f-a g) \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+2 g (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 B n (d f-c g) \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+B d n (b f-a g) \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-2 B g n (b c-a d) \left(\log (f+g x) \left(\log \left(\frac{g (a+b x)}{a g-b f}\right)-\log \left(\frac{g (c+d x)}{c g-d f}\right)\right)+\text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\right)-\text{Li}_2\left(\frac{d (f+g x)}{d f-c g}\right)\right)\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}{f+g x}}{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)}+\frac{2 B^2 n^2 (b c-a d) \text{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{(b f-a g) (d f-c g)}",1,"(-((A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(f + g*x)) + (B*n*(2*b*(d*f - c*g)*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 2*d*(b*f - a*g)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + 2*(b*c - a*d)*g*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[f + g*x] - b*B*(d*f - c*g)*n*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + B*d*(b*f - a*g)*n*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) - 2*B*(b*c - a*d)*g*n*((Log[(g*(a + b*x))/(-(b*f) + a*g)] - Log[(g*(c + d*x))/(-(d*f) + c*g)])*Log[f + g*x] + PolyLog[2, (b*(f + g*x))/(b*f - a*g)] - PolyLog[2, (d*(f + g*x))/(d*f - c*g)])))/((b*f - a*g)*(d*f - c*g)))/g","B",1
73,1,615,389,1.6522759,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(f + g*x)^3,x]","-\frac{\frac{B n (f+g x) \left(-2 b^2 (f+g x) \log (a+b x) (d f-c g)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+2 d^2 (f+g x) (b f-a g)^2 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+2 g (b c-a d) (b f-a g) (d f-c g) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+2 g (f+g x) (b c-a d) \log (f+g x) (a d g+b c g-2 b d f) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+b^2 B n (f+g x) (d f-c g)^2 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)-B d^2 n (f+g x) (b f-a g)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-2 B g n (f+g x) (b c-a d) (a d g+b c g-2 b d f) \left(\log (f+g x) \left(\log \left(\frac{g (a+b x)}{a g-b f}\right)-\log \left(\frac{g (c+d x)}{c g-d f}\right)\right)+\text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\right)-\text{Li}_2\left(\frac{d (f+g x)}{d f-c g}\right)\right)-2 B g n (f+g x) (b c-a d) (b \log (a+b x) (d f-c g)+\log (c+d x) (a d g-b d f)+g (b c-a d) \log (f+g x))\right)}{(b f-a g)^2 (d f-c g)^2}+\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 \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 n^2 (b c-a d) (-a d g-b c g+2 b d f) \text{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{(b f-a g)^2 (d f-c g)^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,"-1/2*((A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (B*n*(f + g*x)*(2*(b*c - a*d)*g*(b*f - a*g)*(d*f - c*g)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 2*b^2*(d*f - c*g)^2*(f + g*x)*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 2*d^2*(b*f - a*g)^2*(f + g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + 2*(b*c - a*d)*g*(-2*b*d*f + b*c*g + a*d*g)*(f + g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[f + g*x] - 2*B*(b*c - a*d)*g*n*(f + g*x)*(b*(d*f - c*g)*Log[a + b*x] + (-(b*d*f) + a*d*g)*Log[c + d*x] + (b*c - a*d)*g*Log[f + g*x]) + b^2*B*(d*f - c*g)^2*n*(f + g*x)*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - B*d^2*(b*f - a*g)^2*n*(f + g*x)*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) - 2*B*(b*c - a*d)*g*(-2*b*d*f + b*c*g + a*d*g)*n*(f + g*x)*((Log[(g*(a + b*x))/(-(b*f) + a*g)] - Log[(g*(c + d*x))/(-(d*f) + c*g)])*Log[f + g*x] + PolyLog[2, (b*(f + g*x))/(b*f - a*g)] - PolyLog[2, (d*(f + g*x))/(d*f - c*g)])))/((b*f - a*g)^2*(d*f - c*g)^2))/(g*(f + g*x)^2)","A",1
74,1,918,747,3.7127004,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(f + g*x)^4,x]","-\frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2+\frac{B n (f+g x) \left(2 d^3 (f+g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \log (c+d x) (b f-a g)^3-B d^3 n (f+g x)^2 \left(\left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right) \log (c+d x)+2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right) (b f-a g)^3+(b c-a d) g (d f-c g)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b f-a g)^2+2 (b c-a d) g (c g-d f) (-2 b d f+b c g+a d g) (f+g x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b f-a g)-2 b^3 (d f-c g)^3 (f+g x)^2 \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-2 (b c-a d) g \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2+a d g (c g-3 d f) b+a^2 d^2 g^2\right) (f+g x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \log (f+g x)-2 B (b c-a d) g (2 b d f-b c g-a d g) n (f+g x)^2 (b (d f-c g) \log (a+b x)+(a d g-b d f) \log (c+d x)+(b c-a d) g \log (f+g x))+B (b c-a d) g n (f+g x) \left(d^2 (f+g x) \log (c+d x) (b f-a g)^2+(b c-a d) g (d f-c g) (b f-a g)-b^2 (d f-c g)^2 (f+g x) \log (a+b x)+(b c-a d) g (-2 b d f+b c g+a d g) (f+g x) \log (f+g x)\right)+b^3 B (d f-c g)^3 n (f+g x)^2 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+2 B (b c-a d) g \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2+a d g (c g-3 d f) b+a^2 d^2 g^2\right) n (f+g x)^2 \left(\left(\log \left(\frac{g (a+b x)}{a g-b f}\right)-\log \left(\frac{g (c+d x)}{c g-d f}\right)\right) \log (f+g x)+\text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\right)-\text{Li}_2\left(\frac{d (f+g x)}{d f-c g}\right)\right)\right)}{(b f-a g)^3 (d f-c g)^3}}{3 g (f+g x)^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{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{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\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,"-1/3*((A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (B*n*(f + g*x)*((b*c - a*d)*g*(b*f - a*g)^2*(d*f - c*g)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 2*(b*c - a*d)*g*(b*f - a*g)*(-(d*f) + c*g)*(-2*b*d*f + b*c*g + a*d*g)*(f + g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 2*b^3*(d*f - c*g)^3*(f + g*x)^2*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 2*d^3*(b*f - a*g)^3*(f + g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - 2*(b*c - a*d)*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))*(f + g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[f + g*x] - 2*B*(b*c - a*d)*g*(2*b*d*f - b*c*g - a*d*g)*n*(f + g*x)^2*(b*(d*f - c*g)*Log[a + b*x] + (-(b*d*f) + a*d*g)*Log[c + d*x] + (b*c - a*d)*g*Log[f + g*x]) + B*(b*c - a*d)*g*n*(f + g*x)*((b*c - a*d)*g*(b*f - a*g)*(d*f - c*g) - b^2*(d*f - c*g)^2*(f + g*x)*Log[a + b*x] + d^2*(b*f - a*g)^2*(f + g*x)*Log[c + d*x] + (b*c - a*d)*g*(-2*b*d*f + b*c*g + a*d*g)*(f + g*x)*Log[f + g*x]) + b^3*B*(d*f - c*g)^3*n*(f + g*x)^2*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - B*d^3*(b*f - a*g)^3*n*(f + g*x)^2*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 2*B*(b*c - a*d)*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*(f + g*x)^2*((Log[(g*(a + b*x))/(-(b*f) + a*g)] - Log[(g*(c + d*x))/(-(d*f) + c*g)])*Log[f + g*x] + PolyLog[2, (b*(f + g*x))/(b*f - a*g)] - PolyLog[2, (d*(f + g*x))/(d*f - c*g)])))/((b*f - a*g)^3*(d*f - c*g)^3))/(g*(f + g*x)^3)","A",1
75,1,1476,1208,7.3220249,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(f + g*x)^5,x]","\frac{B (b c-a d) n \left(\frac{\log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) b^4}{(b c-a d) (b f-a g)^4}-\frac{B n \left(\log ^2(a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right) \log (a+b x)-2 \text{Li}_2\left(-\frac{d (a+b x)}{b c-a d}\right)\right) b^4}{2 (b c-a d) (b f-a g)^4}-\frac{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) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{(b f-a g)^3 (d f-c g)^3 (f+g x)}-\frac{g (2 b d f-b c g-a d g) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{2 (b f-a g)^2 (d f-c g)^2 (f+g x)^2}-\frac{g \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)^3}-\frac{d^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \log (c+d x)}{(b c-a d) (d f-c g)^4}+\frac{g (2 b d f-b c g-a d g) \left(2 d^2 f^2 b^2+c^2 g^2 b^2-2 c d f g b^2-2 a d^2 f g b+a^2 d^2 g^2\right) \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)^4 (d f-c g)^4}+\frac{B (b c-a d) 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 \left(\frac{b \log (a+b x)}{(b c-a d) (b f-a g)}-\frac{d \log (c+d x)}{(b c-a d) (d f-c g)}+\frac{g \log (f+g x)}{(b f-a g) (d f-c g)}\right)}{(b f-a g)^3 (d f-c g)^3}-\frac{B (b c-a d) g (2 b d f-b c g-a d g) n \left(-\frac{\log (a+b x) b^2}{(b c-a d) (b f-a g)^2}+\frac{d^2 \log (c+d x)}{(b c-a d) (d f-c g)^2}-\frac{g (2 b d f-b c g-a d g) \log (f+g x)}{(b f-a g)^2 (d f-c g)^2}+\frac{g}{(b f-a g) (d f-c g) (f+g x)}\right)}{2 (b f-a g)^2 (d f-c g)^2}-\frac{B (b c-a d) g n \left(-\frac{2 \log (a+b x) b^3}{(b c-a d) (b f-a g)^3}+\frac{2 d^3 \log (c+d x)}{(b c-a d) (d f-c g)^3}-\frac{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)}{(b f-a g)^3 (d f-c g)^3}+\frac{2 g (2 b d f-b c g-a d g)}{(b f-a g)^2 (d f-c g)^2 (f+g x)}+\frac{g}{(b f-a g) (d f-c g) (f+g x)^2}\right)}{6 (b f-a g) (d f-c g)}+\frac{B d^4 n \left(-\log ^2(c+d x)+2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x)+2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right)}{2 (b c-a d) (d f-c g)^4}-\frac{B g (2 b d f-b c g-a d g) \left(2 d^2 f^2 b^2+c^2 g^2 b^2-2 c d f g b^2-2 a d^2 f g b+a^2 d^2 g^2\right) n \left(\log \left(-\frac{g (a+b x)}{b f-a g}\right) \log (f+g x)-\log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x)+\text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\right)-\text{Li}_2\left(\frac{d (f+g x)}{d f-c g}\right)\right)}{(b f-a g)^4 (d f-c g)^4}\right)}{2 g}-\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{\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(\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2\right)+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(\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2\right)+2 a d^2 f g b-a^2 d^2 g^2\right) n^2 \text{Li}_2\left(\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,"-1/4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(g*(f + g*x)^4) + (B*(b*c - a*d)*n*(-1/3*(g*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/((b*f - a*g)*(d*f - c*g)*(f + g*x)^3) - (g*(2*b*d*f - b*c*g - a*d*g)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)^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))*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/((b*f - a*g)^3*(d*f - c*g)^3*(f + g*x)) + (b^4*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/((b*c - a*d)*(b*f - a*g)^4) - (d^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x])/((b*c - a*d)*(d*f - c*g)^4) + (g*(2*b*d*f - b*c*g - a*d*g)*(2*b^2*d^2*f^2 - 2*b^2*c*d*f*g - 2*a*b*d^2*f*g + b^2*c^2*g^2 + a^2*d^2*g^2)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[f + g*x])/((b*f - a*g)^4*(d*f - c*g)^4) + (B*(b*c - a*d)*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*((b*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)) - (d*Log[c + d*x])/((b*c - a*d)*(d*f - c*g)) + (g*Log[f + g*x])/((b*f - a*g)*(d*f - c*g))))/((b*f - a*g)^3*(d*f - c*g)^3) - (B*(b*c - a*d)*g*(2*b*d*f - b*c*g - a*d*g)*n*(g/((b*f - a*g)*(d*f - c*g)*(f + g*x)) - (b^2*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)^2) + (d^2*Log[c + d*x])/((b*c - a*d)*(d*f - c*g)^2) - (g*(2*b*d*f - b*c*g - a*d*g)*Log[f + g*x])/((b*f - a*g)^2*(d*f - c*g)^2)))/(2*(b*f - a*g)^2*(d*f - c*g)^2) - (B*(b*c - a*d)*g*n*(g/((b*f - a*g)*(d*f - c*g)*(f + g*x)^2) + (2*g*(2*b*d*f - b*c*g - a*d*g))/((b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)) - (2*b^3*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)^3) + (2*d^3*Log[c + d*x])/((b*c - a*d)*(d*f - c*g)^3) - (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])/((b*f - a*g)^3*(d*f - c*g)^3)))/(6*(b*f - a*g)*(d*f - c*g)) - (b^4*B*n*(Log[a + b*x]^2 - 2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] - 2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))]))/(2*(b*c - a*d)*(b*f - a*g)^4) + (B*d^4*n*(2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x] - Log[c + d*x]^2 + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]))/(2*(b*c - a*d)*(d*f - c*g)^4) - (B*g*(2*b*d*f - b*c*g - a*d*g)*(2*b^2*d^2*f^2 - 2*b^2*c*d*f*g - 2*a*b*d^2*f*g + b^2*c^2*g^2 + a^2*d^2*g^2)*n*(Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x] - Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x] + PolyLog[2, (b*(f + g*x))/(b*f - a*g)] - PolyLog[2, (d*(f + g*x))/(d*f - c*g)]))/((b*f - a*g)^4*(d*f - c*g)^4)))/(2*g)","A",1
76,0,0,35,0.4278923,"\int \frac{(f+g x)^2}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Integrate[(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,"Integrate[(f + g*x)^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x]","A",-1
77,0,0,33,0.2887053,"\int \frac{f+g x}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Integrate[(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,"Integrate[(f + g*x)/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x]","A",-1
78,0,0,27,0.0161255,"\int \frac{1}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Integrate[(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,"Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-1), x]","A",-1
79,0,0,35,0.9795004,"\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","Integrate[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,"Integrate[1/((f + g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])), x]","A",-1
80,0,0,35,1.1044598,"\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","Integrate[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,"Integrate[1/((f + g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])), x]","A",-1
81,0,0,35,11.8596008,"\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","Integrate[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,"Integrate[1/((f + g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])), x]","A",-1
82,0,0,35,0.9420892,"\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","Integrate[(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,"Integrate[(f + g*x)^2/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x]","A",-1
83,0,0,33,0.7411199,"\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","Integrate[(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,"Integrate[(f + g*x)/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x]","A",-1
84,0,0,27,0.665337,"\int \frac{1}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","Integrate[(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,"Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^(-2), x]","A",-1
85,0,0,35,1.7120667,"\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","Integrate[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,"Integrate[1/((f + g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2), x]","A",-1
86,0,0,35,3.822749,"\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","Integrate[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,"Integrate[1/((f + g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2), x]","A",-1
87,0,0,35,35.4621431,"\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","Integrate[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,"Integrate[1/((f + g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2), x]","A",-1
88,1,142,180,0.1049435,"\int (a g+b g x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(a*g + b*g*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g^4 \left((a+b x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{B (b c-a d) \left(4 d^3 (a+b x)^3 (a d-b c)+6 d^2 (a+b x)^2 (b c-a d)^2-12 b d x (b c-a d)^3+12 (b c-a d)^4 \log (c+d x)+3 d^4 (a+b x)^4\right)}{12 d^5}\right)}{5 b}","\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 (b c-a d)^5 \log (c+d x)}{5 b d^5}+\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 (a+b x)^4 (b c-a d)}{20 b d}",1,"(g^4*((a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - (B*(b*c - a*d)*(-12*b*d*(b*c - a*d)^3*x + 6*d^2*(b*c - a*d)^2*(a + b*x)^2 + 4*d^3*(-(b*c) + a*d)*(a + b*x)^3 + 3*d^4*(a + b*x)^4 + 12*(b*c - a*d)^4*Log[c + d*x]))/(12*d^5)))/(5*b)","A",1
89,1,120,149,0.0972203,"\int (a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g^3 \left((a+b x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{B (b c-a d) \left(3 d^2 (a+b x)^2 (a d-b c)+6 b d x (b c-a d)^2-6 (b c-a d)^3 \log (c+d x)+2 d^3 (a+b x)^3\right)}{6 d^4}\right)}{4 b}","\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 (b c-a d)^4 \log (c+d x)}{4 b d^4}-\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 (a+b x)^3 (b c-a d)}{12 b d}",1,"(g^3*((a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - (B*(b*c - a*d)*(6*b*d*(b*c - a*d)^2*x + 3*d^2*(-(b*c) + a*d)*(a + b*x)^2 + 2*d^3*(a + b*x)^3 - 6*(b*c - a*d)^3*Log[c + d*x]))/(6*d^4)))/(4*b)","A",1
90,1,99,118,0.0550723,"\int (a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g^2 \left(\frac{B (a d-b c) \left(d \left(a^2 d+4 a b d x+b^2 x (d x-2 c)\right)+2 (b c-a d)^2 \log (c+d x)\right)}{2 d^3}+(a+b x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)\right)}{3 b}","\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 (b c-a d)^3 \log (c+d x)}{3 b d^3}+\frac{B g^2 x (b c-a d)^2}{3 d^2}-\frac{B g^2 (a+b x)^2 (b c-a d)}{6 b d}",1,"(g^2*((a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + (B*(-(b*c) + a*d)*(d*(a^2*d + 4*a*b*d*x + b^2*x*(-2*c + d*x)) + 2*(b*c - a*d)^2*Log[c + d*x]))/(2*d^3)))/(3*b)","A",1
91,1,69,81,0.0345056,"\int (a g+b g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g \left((a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+\frac{B (a d-b c) ((a d-b c) \log (c+d x)+b d x)}{d^2}\right)}{2 b}","\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,"(g*((a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + (B*(-(b*c) + a*d)*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]))/d^2))/(2*b)","A",1
92,1,95,80,0.0446102,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{a g+b g x} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(a*g + b*g*x),x]","\frac{\log (g (a+b x)) \left(2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+B \log \left(\frac{b (c+d x)}{b c-a d}\right)+A\right)-B \log (g (a+b x))\right)+2 B \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)}{2 b g}","\frac{B \text{Li}_2\left(\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,"(Log[g*(a + b*x)]*(-(B*Log[g*(a + b*x)]) + 2*(A + B*Log[(e*(a + b*x))/(c + d*x)] + B*Log[(b*(c + d*x))/(b*c - a*d)])) + 2*B*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(2*b*g)","A",1
93,1,105,63,0.0580578,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(a*g + b*g*x)^2,x]","\frac{a A d+(a B d-b B c) \log \left(\frac{e (a+b x)}{c+d x}\right)-B d (a+b x) \log (a+b x)+a B d \log (c+d x)+a B d-A b c+b B d x \log (c+d x)-b B c}{b 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)}{g^2 (a+b x) (b c-a d)}-\frac{B}{b g^2 (a+b x)}",1,"(-(A*b*c) - b*B*c + a*A*d + a*B*d - B*d*(a + b*x)*Log[a + b*x] + (-(b*B*c) + a*B*d)*Log[(e*(a + b*x))/(c + d*x)] + a*B*d*Log[c + d*x] + b*B*d*x*Log[c + d*x])/(b*(b*c - a*d)*g^2*(a + b*x))","A",1
94,1,110,144,0.1292703,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(a*g + b*g*x)^3,x]","-\frac{2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+\frac{B \left(2 d^2 (a+b x)^2 \log (c+d x)+(b c-a d) (b (c-2 d x)-3 a d)-2 d^2 (a+b x)^2 \log (a+b x)\right)}{(b c-a d)^2}}{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,"-1/4*(2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + (B*((b*c - a*d)*(-3*a*d + b*(c - 2*d*x)) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]))/(b*c - a*d)^2)/(b*g^3*(a + b*x)^2)","A",1
95,1,141,175,0.1554652,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^4} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(a*g + b*g*x)^4,x]","-\frac{\frac{B \left((b c-a d) \left(11 a^2 d^2+a b d (15 d x-7 c)+b^2 \left(2 c^2-3 c d x+6 d^2 x^2\right)\right)-6 d^3 (a+b x)^3 \log (c+d x)+6 d^3 (a+b x)^3 \log (a+b x)\right)}{(b c-a d)^3}+6 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{18 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^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^2}{3 b g^4 (a+b x) (b c-a d)^2}+\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,"-1/18*(6*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + (B*((b*c - a*d)*(11*a^2*d^2 + a*b*d*(-7*c + 15*d*x) + b^2*(2*c^2 - 3*c*d*x + 6*d^2*x^2)) + 6*d^3*(a + b*x)^3*Log[a + b*x] - 6*d^3*(a + b*x)^3*Log[c + d*x]))/(b*c - a*d)^3)/(b*g^4*(a + b*x)^3)","A",1
96,1,158,206,0.2092771,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^5} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(a*g + b*g*x)^5,x]","\frac{\frac{B \left(\frac{12 d^3 (b c-a d)}{a+b x}-\frac{6 d^2 (b c-a d)^2}{(a+b x)^2}+\frac{4 d (b c-a d)^3}{(a+b x)^3}-\frac{3 (b c-a d)^4}{(a+b x)^4}+12 d^4 \log (a+b x)-12 d^4 \log (c+d x)\right)}{12 (b c-a d)^4}-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{(a+b x)^4}}{4 b g^5}","-\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^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^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}{12 b g^5 (a+b x)^3 (b c-a d)}-\frac{B}{16 b g^5 (a+b x)^4}",1,"(-((A + B*Log[(e*(a + b*x))/(c + d*x)])/(a + b*x)^4) + (B*((-3*(b*c - a*d)^4)/(a + b*x)^4 + (4*d*(b*c - a*d)^3)/(a + b*x)^3 - (6*d^2*(b*c - a*d)^2)/(a + b*x)^2 + (12*d^3*(b*c - a*d))/(a + b*x) + 12*d^4*Log[a + b*x] - 12*d^4*Log[c + d*x]))/(12*(b*c - a*d)^4))/(4*b*g^5)","A",1
97,1,511,365,0.4856275,"\int (a g+b g x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Integrate[(a*g + b*g*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{g^4 \left(\frac{B (b c-a d) \left(-6 d^4 (a+b x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+8 d^3 (a+b x)^3 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-12 d^2 (a+b x)^2 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-24 (b c-a d)^4 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+24 A b d x (b c-a d)^3+4 B (b c-a d)^2 \left(2 b d x (b c-a d)-2 (b c-a d)^2 \log (c+d x)-d^2 (a+b x)^2\right)+B (b c-a d) \left(3 d^2 (a+b x)^2 (a d-b c)+6 b d x (b c-a d)^2-6 (b c-a d)^3 \log (c+d x)+2 d^3 (a+b x)^3\right)+24 B d (a+b x) (b c-a d)^3 \log \left(\frac{e (a+b x)}{c+d x}\right)+12 B (b c-a d)^4 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-24 B (b c-a d)^4 \log (c+d x)+12 B (b c-a d)^3 ((a d-b c) \log (c+d x)+b d x)\right)}{12 d^5}+(a+b x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2\right)}{5 b}","\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}+\frac{2 B^2 g^4 (b c-a d)^5 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{5 b d^5}",1,"(g^4*((a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + (B*(b*c - a*d)*(24*A*b*d*(b*c - a*d)^3*x + 24*B*d*(b*c - a*d)^3*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] - 12*d^2*(b*c - a*d)^2*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 8*d^3*(b*c - a*d)*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 6*d^4*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 24*B*(b*c - a*d)^4*Log[c + d*x] - 24*(b*c - a*d)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 4*B*(b*c - a*d)^2*(2*b*d*(b*c - a*d)*x - d^2*(a + b*x)^2 - 2*(b*c - a*d)^2*Log[c + d*x]) + B*(b*c - a*d)*(6*b*d*(b*c - a*d)^2*x + 3*d^2*(-(b*c) + a*d)*(a + b*x)^2 + 2*d^3*(a + b*x)^3 - 6*(b*c - a*d)^3*Log[c + d*x]) + 12*B*(b*c - a*d)^3*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 12*B*(b*c - a*d)^4*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(12*d^5)))/(5*b)","A",1
98,1,391,309,0.3729296,"\int (a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Integrate[(a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{g^3 \left((a+b x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2-\frac{B (b c-a d) \left(2 d^3 (a+b x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+3 d^2 (a+b x)^2 (a d-b c) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-6 (b c-a d)^3 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+6 A b d x (b c-a d)^2+B (b c-a d) \left(2 b d x (b c-a d)-2 (b c-a d)^2 \log (c+d x)-d^2 (a+b x)^2\right)+6 B d (a+b x) (b c-a d)^2 \log \left(\frac{e (a+b x)}{c+d x}\right)+3 B (b c-a d)^3 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-6 B (b c-a d)^3 \log (c+d x)+3 B (b c-a d)^2 ((a d-b c) \log (c+d x)+b d x)\right)}{3 d^4}\right)}{4 b}","-\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}-\frac{B^2 g^3 (b c-a d)^4 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{2 b d^4}",1,"(g^3*((a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - (B*(b*c - a*d)*(6*A*b*d*(b*c - a*d)^2*x + 6*B*d*(b*c - a*d)^2*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] + 3*d^2*(-(b*c) + a*d)*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*d^3*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 6*B*(b*c - a*d)^3*Log[c + d*x] - 6*(b*c - a*d)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + B*(b*c - a*d)*(2*b*d*(b*c - a*d)*x - d^2*(a + b*x)^2 - 2*(b*c - a*d)^2*Log[c + d*x]) + 3*B*(b*c - a*d)^2*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 3*B*(b*c - a*d)^3*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(3*d^4)))/(4*b)","A",1
99,1,287,253,0.2874161,"\int (a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Integrate[(a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{g^2 \left(\frac{B (b c-a d) \left(-d^2 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-2 (b c-a d)^2 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 A b d x (b c-a d)+2 B d (a+b x) (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)+B (b c-a d)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-2 B (b c-a d)^2 \log (c+d x)+B (b c-a d) ((a d-b c) \log (c+d x)+b d x)\right)}{d^3}+(a+b x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2\right)}{3 b}","\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}+\frac{2 B^2 g^2 (b c-a d)^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{3 b d^3}",1,"(g^2*((a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + (B*(b*c - a*d)*(2*A*b*d*(b*c - a*d)*x + 2*B*d*(b*c - a*d)*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] - d^2*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 2*B*(b*c - a*d)^2*Log[c + d*x] - 2*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + B*(b*c - a*d)*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + B*(b*c - a*d)^2*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/d^3))/(3*b)","A",1
100,1,203,180,0.1729752,"\int (a g+b g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Integrate[(a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{g \left((a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2-\frac{B (b c-a d) \left(-2 (b c-a d) \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)+B (b c-a d) \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-2 B (b c-a d) \log (c+d x)+2 A b d x\right)}{d^2}\right)}{2 b}","-\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}-\frac{B^2 g (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}",1,"(g*((a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - (B*(b*c - a*d)*(2*A*b*d*x + 2*B*d*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] - 2*B*(b*c - a*d)*Log[c + d*x] - 2*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + B*(b*c - a*d)*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/d^2))/(2*b)","A",1
101,1,250,128,0.6132995,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{a g+b g x} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(a*g + b*g*x),x]","\frac{A^2 \log (a+b x)+2 A B \log (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 A B \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+2 A B \log (a+b x) \log \left(\frac{c}{d}+x\right)-2 A B \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)+A B \log ^2\left(\frac{a}{b}+x\right)-2 A B \log \left(\frac{a}{b}+x\right) \log (a+b x)+2 B^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right) \log \left(\frac{e (a+b x)}{c+d x}\right)-B^2 \log \left(\frac{a d-b c}{d (a+b x)}\right) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)+2 B^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b g}","\frac{2 B \text{Li}_2\left(\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{\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}+\frac{2 B^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b g}",1,"(A*B*Log[a/b + x]^2 + A^2*Log[a + b*x] - 2*A*B*Log[a/b + x]*Log[a + b*x] + 2*A*B*Log[c/d + x]*Log[a + b*x] - 2*A*B*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*A*B*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] - B^2*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(e*(a + b*x))/(c + d*x)]^2 - 2*A*B*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 2*B^2*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] + 2*B^2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))])/(b*g)","A",1
102,1,314,126,0.4544245,"\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","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(a*g + b*g*x)^2,x]","-\frac{\frac{B \left(2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 d (a+b x) \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-2 d (a+b x) \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-B d (a+b x) \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+B d (a+b x) \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+2 B (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)\right)}{b c-a d}+\left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^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,"-(((A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + (B*(2*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*d*(a + b*x)*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 2*d*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 2*B*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - B*d*(a + b*x)*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + B*d*(a + b*x)*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d))/(b*g^2*(a + b*x)))","C",1
103,1,443,268,0.4648678,"\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","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(a*g + b*g*x)^3,x]","-\frac{\frac{B \left(-4 d^2 (a+b x)^2 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+4 d^2 (a+b x)^2 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+4 d (a+b x) (a d-b c) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 B d^2 (a+b x)^2 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)-2 B d^2 (a+b x)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+B \left(2 d^2 (a+b x)^2 \log (c+d x)+2 d (a+b x) (a d-b c)+(b c-a d)^2-2 d^2 (a+b x)^2 \log (a+b x)\right)-4 B d (a+b x) (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)\right)}{(b c-a d)^2}+2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^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,"-1/4*(2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + (B*(2*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 4*d*(-(b*c) + a*d)*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 4*d^2*(a + b*x)^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 4*d^2*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 4*B*d*(a + b*x)*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) + B*((b*c - a*d)^2 + 2*d*(-(b*c) + a*d)*(a + b*x) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]) + 2*B*d^2*(a + b*x)^2*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - 2*B*d^2*(a + b*x)^2*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^2)/(b*g^3*(a + b*x)^2)","C",1
104,1,585,418,0.6905941,"\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","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(a*g + b*g*x)^4,x]","-\frac{\frac{B \left(36 d^3 (a+b x)^3 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-36 d^3 (a+b x)^3 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+36 d^2 (a+b x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+12 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-18 d (a+b x) (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-18 B d^3 (a+b x)^3 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+18 B d^3 (a+b x)^3 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+36 B d^2 (a+b x)^2 (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)-9 B d (a+b x) \left(2 d^2 (a+b x)^2 \log (c+d x)+2 d (a+b x) (a d-b c)+(b c-a d)^2-2 d^2 (a+b x)^2 \log (a+b x)\right)+2 B \left(-6 d^3 (a+b x)^3 \log (c+d x)+6 d^2 (a+b x)^2 (b c-a d)-3 d (a+b x) (b c-a d)^2+2 (b c-a d)^3+6 d^3 (a+b x)^3 \log (a+b x)\right)\right)}{(b c-a d)^3}+18 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{54 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,"-1/54*(18*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + (B*(12*(b*c - a*d)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 18*d*(b*c - a*d)^2*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 36*d^2*(b*c - a*d)*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 36*d^3*(a + b*x)^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 36*d^3*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 36*B*d^2*(a + b*x)^2*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - 9*B*d*(a + b*x)*((b*c - a*d)^2 + 2*d*(-(b*c) + a*d)*(a + b*x) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]) + 2*B*(2*(b*c - a*d)^3 - 3*d*(b*c - a*d)^2*(a + b*x) + 6*d^2*(b*c - a*d)*(a + b*x)^2 + 6*d^3*(a + b*x)^3*Log[a + b*x] - 6*d^3*(a + b*x)^3*Log[c + d*x]) - 18*B*d^3*(a + b*x)^3*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 18*B*d^3*(a + b*x)^3*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^3)/(b*g^4*(a + b*x)^3)","C",1
105,1,748,575,0.9672338,"\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","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(a*g + b*g*x)^5,x]","-\frac{\frac{B \left(-144 d^4 (a+b x)^4 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+144 d^4 (a+b x)^4 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+144 d^3 (a+b x)^3 (a d-b c) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+72 d^2 (a+b x)^2 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+36 (b c-a d)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+48 d (a+b x) (a d-b c)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+72 B d^4 (a+b x)^4 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)-72 B d^4 (a+b x)^4 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-144 B d^3 (a+b x)^3 (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)+36 B d^2 (a+b x)^2 \left(2 d^2 (a+b x)^2 \log (c+d x)+2 d (a+b x) (a d-b c)+(b c-a d)^2-2 d^2 (a+b x)^2 \log (a+b x)\right)-8 B d (a+b x) \left(-6 d^3 (a+b x)^3 \log (c+d x)+6 d^2 (a+b x)^2 (b c-a d)-3 d (a+b x) (b c-a d)^2+2 (b c-a d)^3+6 d^3 (a+b x)^3 \log (a+b x)\right)+3 B \left(12 d^4 (a+b x)^4 \log (c+d x)+12 d^3 (a+b x)^3 (a d-b c)+6 d^2 (a+b x)^2 (b c-a d)^2+4 d (a+b x) (a d-b c)^3+3 (b c-a d)^4-12 d^4 (a+b x)^4 \log (a+b x)\right)\right)}{(b c-a d)^4}+72 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{288 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{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{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{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{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}",1,"-1/288*(72*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + (B*(36*(b*c - a*d)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 48*d*(-(b*c) + a*d)^3*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 72*d^2*(b*c - a*d)^2*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 144*d^3*(-(b*c) + a*d)*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 144*d^4*(a + b*x)^4*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 144*d^4*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 144*B*d^3*(a + b*x)^3*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) + 36*B*d^2*(a + b*x)^2*((b*c - a*d)^2 + 2*d*(-(b*c) + a*d)*(a + b*x) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]) - 8*B*d*(a + b*x)*(2*(b*c - a*d)^3 - 3*d*(b*c - a*d)^2*(a + b*x) + 6*d^2*(b*c - a*d)*(a + b*x)^2 + 6*d^3*(a + b*x)^3*Log[a + b*x] - 6*d^3*(a + b*x)^3*Log[c + d*x]) + 3*B*(3*(b*c - a*d)^4 + 4*d*(-(b*c) + a*d)^3*(a + b*x) + 6*d^2*(b*c - a*d)^2*(a + b*x)^2 + 12*d^3*(-(b*c) + a*d)*(a + b*x)^3 - 12*d^4*(a + b*x)^4*Log[a + b*x] + 12*d^4*(a + b*x)^4*Log[c + d*x]) + 72*B*d^4*(a + b*x)^4*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - 72*B*d^4*(a + b*x)^4*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^4)/(b*g^5*(a + b*x)^4)","C",1
106,1,114,28,0.0504578,"\int \frac{\log \left(\frac{d (a+b x)}{b (c+d x)}\right)}{c f+d f x} \, dx","Integrate[Log[(d*(a + b*x))/(b*(c + d*x))]/(c*f + d*f*x),x]","\frac{\log \left(\frac{b c-a d}{b c+b d x}\right) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-2 \log \left(\frac{d (a+b x)}{b (c+d x)}\right)+\log \left(\frac{b c-a d}{b c+b d x}\right)\right)-2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)}{2 d f}","\frac{\text{Li}_2\left(\frac{b c-a d}{b (c+d x)}\right)}{d f}",1,"(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*Log[(d*(a + b*x))/(b*(c + d*x))] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*d*f)","B",1
107,1,140,15,0.0149127,"\int \frac{\log \left(1+\frac{1}{a+b x}\right)}{a+b x} \, dx","Integrate[Log[1 + (a + b*x)^(-1)]/(a + b*x),x]","-\frac{\text{Li}_2(-a-b x)}{b}+\frac{\log ^2\left(\frac{a b-(a+1) b}{b (a+b x)}\right)}{2 b}+\frac{\log \left(\frac{b (-a-b x-1)}{(-a-1) b+a b}\right) \log \left(\frac{a b-(a+1) b}{b (a+b x)}\right)}{b}-\frac{\log \left(\frac{a+b x+1}{a+b x}\right) \log \left(\frac{a b-(a+1) b}{b (a+b x)}\right)}{b}","\frac{\text{Li}_2\left(-\frac{1}{a+b x}\right)}{b}",1,"(Log[(b*(-1 - a - b*x))/((-1 - a)*b + a*b)]*Log[(a*b - (1 + a)*b)/(b*(a + b*x))])/b + Log[(a*b - (1 + a)*b)/(b*(a + b*x))]^2/(2*b) - (Log[(a*b - (1 + a)*b)/(b*(a + b*x))]*Log[(1 + a + b*x)/(a + b*x)])/b - PolyLog[2, -a - b*x]/b","B",1
108,1,133,13,0.0154357,"\int \frac{\log \left(1-\frac{1}{a+b x}\right)}{a+b x} \, dx","Integrate[Log[1 - (a + b*x)^(-1)]/(a + b*x),x]","-\frac{\text{Li}_2(a+b x)}{b}+\frac{\log ^2\left(\frac{a b-(a-1) b}{b (a+b x)}\right)}{2 b}+\frac{\log \left(\frac{b (a+b x-1)}{(a-1) b-a b}\right) \log \left(\frac{a b-(a-1) b}{b (a+b x)}\right)}{b}-\frac{\log \left(\frac{a+b x-1}{a+b x}\right) \log \left(\frac{a b-(a-1) b}{b (a+b x)}\right)}{b}","\frac{\text{Li}_2\left(\frac{1}{a+b x}\right)}{b}",1,"(Log[(b*(-1 + a + b*x))/((-1 + a)*b - a*b)]*Log[(-((-1 + a)*b) + a*b)/(b*(a + b*x))])/b + Log[(-((-1 + a)*b) + a*b)/(b*(a + b*x))]^2/(2*b) - (Log[(-((-1 + a)*b) + a*b)/(b*(a + b*x))]*Log[(-1 + a + b*x)/(a + b*x)])/b - PolyLog[2, a + b*x]/b","B",1
109,0,0,35,0.6164469,"\int \frac{(a g+b g x)^2}{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)} \, dx","Integrate[(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,"Integrate[(a*g + b*g*x)^2/(A + B*Log[(e*(a + b*x))/(c + d*x)]), x]","A",-1
110,0,0,33,0.2502874,"\int \frac{a g+b g x}{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)} \, dx","Integrate[(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,"Integrate[(a*g + b*g*x)/(A + B*Log[(e*(a + b*x))/(c + d*x)]), x]","A",-1
111,0,0,35,0.2281778,"\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)} \, dx","Integrate[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,"Integrate[1/((a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])), x]","A",-1
112,1,52,50,0.1041806,"\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","Integrate[1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])),x]","\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 B c g^2-a B d g^2}","\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,"(e*E^(A/B)*ExpIntegralEi[-((A + B*Log[(e*(a + b*x))/(c + d*x)])/B)])/(b*B*c*g^2 - a*B*d*g^2)","A",1
113,1,89,107,0.1712219,"\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","Integrate[1/((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])),x]","\frac{e e^{A/B} \left(b e e^{A/B} \text{Ei}\left(-\frac{2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{B}\right)-d \text{Ei}\left(-\frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{B}\right)\right)}{B g^3 (b c-a d)^2}","\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,"(e*E^(A/B)*(b*e*E^(A/B)*ExpIntegralEi[(-2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/B] - d*ExpIntegralEi[-((A + B*Log[(e*(a + b*x))/(c + d*x)])/B)]))/(B*(b*c - a*d)^2*g^3)","A",1
114,0,0,35,1.3499071,"\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","Integrate[(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,"Integrate[(a*g + b*g*x)^2/(A + B*Log[(e*(a + b*x))/(c + d*x)])^2, x]","A",-1
115,0,0,33,0.9300666,"\int \frac{a g+b g x}{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Integrate[(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,"Integrate[(a*g + b*g*x)/(A + B*Log[(e*(a + b*x))/(c + d*x)])^2, x]","A",-1
116,0,0,35,0.6348556,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2), x]","A",-1
117,1,87,103,0.1777327,"\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","Integrate[1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2),x]","\frac{e e^{A/B} \text{Ei}\left(-\frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{B}\right)+\frac{B (c+d x)}{(a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}}{B^2 g^2 (a d-b c)}","-\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,"(e*E^(A/B)*ExpIntegralEi[-((A + B*Log[(e*(a + b*x))/(c + d*x)])/B)] + (B*(c + d*x))/((a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])))/(B^2*(-(b*c) + a*d)*g^2)","A",1
118,1,136,212,0.6543071,"\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","Integrate[1/((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2),x]","\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)+d e e^{A/B} \text{Ei}\left(-\frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{B}\right)-\frac{B (c+d x) (b c-a d)}{(a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}}{B^2 g^3 (b c-a d)^2}","-\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,"(-2*b*e^2*E^((2*A)/B)*ExpIntegralEi[(-2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/B] + d*e*E^(A/B)*ExpIntegralEi[-((A + B*Log[(e*(a + b*x))/(c + d*x)])/B)] - (B*(b*c - a*d)*(c + d*x))/((a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])))/(B^2*(b*c - a*d)^2*g^3)","A",1
119,1,144,182,0.091488,"\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","Integrate[(a*g + b*g*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\frac{g^4 \left((a+b x)^5 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+\frac{B (b c-a d) \left(4 d^3 (a+b x)^3 (b c-a d)-6 d^2 (a+b x)^2 (b c-a d)^2+12 b d x (b c-a d)^3-12 (b c-a d)^4 \log (c+d x)-3 d^4 (a+b x)^4\right)}{6 d^5}\right)}{5 b}","\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 (b c-a d)^5 \log (c+d x)}{5 b d^5}+\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{B g^4 (a+b x)^4 (b c-a d)}{10 b d}",1,"(g^4*((a + b*x)^5*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + (B*(b*c - a*d)*(12*b*d*(b*c - a*d)^3*x - 6*d^2*(b*c - a*d)^2*(a + b*x)^2 + 4*d^3*(b*c - a*d)*(a + b*x)^3 - 3*d^4*(a + b*x)^4 - 12*(b*c - a*d)^4*Log[c + d*x]))/(6*d^5)))/(5*b)","A",1
120,1,122,151,0.0946656,"\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","Integrate[(a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\frac{g^3 \left((a+b x)^4 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)-\frac{B (b c-a d) \left(3 d^2 (a+b x)^2 (a d-b c)+6 b d x (b c-a d)^2-6 (b c-a d)^3 \log (c+d x)+2 d^3 (a+b x)^3\right)}{3 d^4}\right)}{4 b}","\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 (b c-a d)^4 \log (c+d x)}{2 b d^4}-\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 (a+b x)^3 (b c-a d)}{6 b d}",1,"(g^3*((a + b*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - (B*(b*c - a*d)*(6*b*d*(b*c - a*d)^2*x + 3*d^2*(-(b*c) + a*d)*(a + b*x)^2 + 2*d^3*(a + b*x)^3 - 6*(b*c - a*d)^3*Log[c + d*x]))/(3*d^4)))/(4*b)","A",1
121,1,98,120,0.064572,"\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","Integrate[(a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\frac{g^2 \left(\frac{B (a d-b c) \left(d \left(a^2 d+4 a b d x+b^2 x (d x-2 c)\right)+2 (b c-a d)^2 \log (c+d x)\right)}{d^3}+(a+b x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)\right)}{3 b}","\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 (b c-a d)^3 \log (c+d x)}{3 b d^3}+\frac{2 B g^2 x (b c-a d)^2}{3 d^2}-\frac{B g^2 (a+b x)^2 (b c-a d)}{3 b d}",1,"(g^2*((a + b*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + (B*(-(b*c) + a*d)*(d*(a^2*d + 4*a*b*d*x + b^2*x*(-2*c + d*x)) + 2*(b*c - a*d)^2*Log[c + d*x]))/d^3))/(3*b)","A",1
122,1,72,78,0.0456319,"\int (a g+b g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \, dx","Integrate[(a*g + b*g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\frac{g \left((a+b x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+\frac{2 B (a d-b c) ((a d-b c) \log (c+d x)+b d x)}{d^2}\right)}{2 b}","\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,"(g*((a + b*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + (2*B*(-(b*c) + a*d)*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]))/d^2))/(2*b)","A",1
123,1,88,83,0.0482327,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{a g+b g x} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(a*g + b*g*x),x]","\frac{\log (a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+2 B \log \left(\frac{b (c+d x)}{b c-a d}\right)-B \log (a+b x)+A\right)+2 B \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)}{b g}","\frac{2 B \text{Li}_2\left(\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,"(Log[a + b*x]*(A - B*Log[a + b*x] + B*Log[(e*(a + b*x)^2)/(c + d*x)^2] + 2*B*Log[(b*(c + d*x))/(b*c - a*d)]) + 2*B*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*g)","A",1
124,1,111,65,0.062831,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{(a g+b g x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(a*g + b*g*x)^2,x]","\frac{2 B (b c-a d) \left(-\frac{1}{(a+b x) (b c-a d)}-\frac{d \log (a+b x)}{(b c-a d)^2}+\frac{d \log (c+d x)}{(b c-a d)^2}\right)}{b g^2}-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{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,"-((A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(b*g^2*(a + b*x))) + (2*B*(b*c - a*d)*(-(1/((b*c - a*d)*(a + b*x))) - (d*Log[a + b*x])/(b*c - a*d)^2 + (d*Log[c + d*x])/(b*c - a*d)^2))/(b*g^2)","A",1
125,1,109,138,0.135669,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{(a g+b g x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(a*g + b*g*x)^3,x]","-\frac{\frac{B \left(2 d^2 (a+b x)^2 \log (c+d x)+(b c-a d) (b (c-2 d x)-3 a d)-2 d^2 (a+b x)^2 \log (a+b x)\right)}{(b c-a d)^2}+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 \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,"-1/2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2] + (B*((b*c - a*d)*(-3*a*d + b*(c - 2*d*x)) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]))/(b*c - a*d)^2)/(b*g^3*(a + b*x)^2)","A",1
126,1,140,177,0.1712128,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{(a g+b g x)^4} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(a*g + b*g*x)^4,x]","-\frac{3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+\frac{B \left(-6 d^3 (a+b x)^3 \log (c+d x)+6 d^2 (a+b x)^2 (b c-a d)-3 d (a+b x) (b c-a d)^2+2 (b c-a d)^3+6 d^3 (a+b x)^3 \log (a+b x)\right)}{(b c-a d)^3}}{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^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{2 B d^2}{3 b g^4 (a+b x) (b c-a d)^2}+\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,"-1/9*(3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + (B*(2*(b*c - a*d)^3 - 3*d*(b*c - a*d)^2*(a + b*x) + 6*d^2*(b*c - a*d)*(a + b*x)^2 + 6*d^3*(a + b*x)^3*Log[a + b*x] - 6*d^3*(a + b*x)^3*Log[c + d*x]))/(b*c - a*d)^3)/(b*g^4*(a + b*x)^3)","A",1
127,1,162,208,0.2218209,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{(a g+b g x)^5} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(a*g + b*g*x)^5,x]","-\frac{6 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+\frac{B \left(12 d^4 (a+b x)^4 \log (c+d x)+12 d^3 (a+b x)^3 (a d-b c)+6 d^2 (a+b x)^2 (b c-a d)^2+4 d (a+b x) (a d-b c)^3+3 (b c-a d)^4-12 d^4 (a+b x)^4 \log (a+b x)\right)}{(b c-a d)^4}}{24 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^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^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}{6 b g^5 (a+b x)^3 (b c-a d)}-\frac{B}{8 b g^5 (a+b x)^4}",1,"-1/24*(6*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + (B*(3*(b*c - a*d)^4 + 4*d*(-(b*c) + a*d)^3*(a + b*x) + 6*d^2*(b*c - a*d)^2*(a + b*x)^2 + 12*d^3*(-(b*c) + a*d)*(a + b*x)^3 - 12*d^4*(a + b*x)^4*Log[a + b*x] + 12*d^4*(a + b*x)^4*Log[c + d*x]))/(b*c - a*d)^4)/(b*g^5*(a + b*x)^4)","A",1
128,1,523,377,0.4620355,"\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","Integrate[(a*g + b*g*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","\frac{g^4 \left(\frac{B (b c-a d) \left(-3 d^4 (a+b x)^4 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+4 d^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)-6 d^2 (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)-12 (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)+12 A b d x (b c-a d)^3+4 B (b c-a d)^2 \left(2 b d x (b c-a d)-2 (b c-a d)^2 \log (c+d x)-d^2 (a+b x)^2\right)+B (b c-a d) \left(3 d^2 (a+b x)^2 (a d-b c)+6 b d x (b c-a d)^2-6 (b c-a d)^3 \log (c+d x)+2 d^3 (a+b x)^3\right)+12 B d (a+b x) (b c-a d)^3 \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+12 B (b c-a d)^4 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-24 B (b c-a d)^4 \log (c+d x)+12 B (b c-a d)^3 ((a d-b c) \log (c+d x)+b d x)\right)}{3 d^5}+(a+b x)^5 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2\right)}{5 b}","\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}+\frac{8 B^2 g^4 (b c-a d)^5 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{5 b d^5}",1,"(g^4*((a + b*x)^5*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2 + (B*(b*c - a*d)*(12*A*b*d*(b*c - a*d)^3*x + 12*B*d*(b*c - a*d)^3*(a + b*x)*Log[(e*(a + b*x)^2)/(c + d*x)^2] - 6*d^2*(b*c - a*d)^2*(a + b*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + 4*d^3*(b*c - a*d)*(a + b*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - 3*d^4*(a + b*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - 24*B*(b*c - a*d)^4*Log[c + d*x] - 12*(b*c - a*d)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x] + 4*B*(b*c - a*d)^2*(2*b*d*(b*c - a*d)*x - d^2*(a + b*x)^2 - 2*(b*c - a*d)^2*Log[c + d*x]) + B*(b*c - a*d)*(6*b*d*(b*c - a*d)^2*x + 3*d^2*(-(b*c) + a*d)*(a + b*x)^2 + 2*d^3*(a + b*x)^3 - 6*(b*c - a*d)^3*Log[c + d*x]) + 12*B*(b*c - a*d)^3*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 12*B*(b*c - a*d)^4*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(3*d^5)))/(5*b)","A",1
129,1,402,319,0.3175472,"\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","Integrate[(a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","\frac{g^3 \left((a+b x)^4 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2-\frac{2 B (b c-a d) \left(2 d^3 (a+b x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+3 d^2 (a+b x)^2 (a d-b c) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)-6 (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)+6 A b d x (b c-a d)^2+2 B (b c-a d) \left(2 b d x (b c-a d)-2 (b c-a d)^2 \log (c+d x)-d^2 (a+b x)^2\right)+6 B d (a+b x) (b c-a d)^2 \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+6 B (b c-a d)^3 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-12 B (b c-a d)^3 \log (c+d x)+6 B (b c-a d)^2 ((a d-b c) \log (c+d x)+b d x)\right)}{3 d^4}\right)}{4 b}","-\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}-\frac{2 B^2 g^3 (b c-a d)^4 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b d^4}",1,"(g^3*((a + b*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2 - (2*B*(b*c - a*d)*(6*A*b*d*(b*c - a*d)^2*x + 6*B*d*(b*c - a*d)^2*(a + b*x)*Log[(e*(a + b*x)^2)/(c + d*x)^2] + 3*d^2*(-(b*c) + a*d)*(a + b*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + 2*d^3*(a + b*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - 12*B*(b*c - a*d)^3*Log[c + d*x] - 6*(b*c - a*d)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x] + 2*B*(b*c - a*d)*(2*b*d*(b*c - a*d)*x - d^2*(a + b*x)^2 - 2*(b*c - a*d)^2*Log[c + d*x]) + 6*B*(b*c - a*d)^2*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 6*B*(b*c - a*d)^3*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(3*d^4)))/(4*b)","A",1
130,1,298,255,0.2168555,"\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","Integrate[(a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","\frac{g^2 \left(\frac{2 B (b c-a d) \left(-d^2 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)-2 (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)+2 A b d x (b c-a d)+2 B d (a+b x) (b c-a d) \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+2 B (b c-a d)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-4 B (b c-a d)^2 \log (c+d x)+2 B (b c-a d) ((a d-b c) \log (c+d x)+b d x)\right)}{d^3}+(a+b x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2\right)}{3 b}","\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}+\frac{8 B^2 g^2 (b c-a d)^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{3 b d^3}",1,"(g^2*((a + b*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2 + (2*B*(b*c - a*d)*(2*A*b*d*(b*c - a*d)*x + 2*B*d*(b*c - a*d)*(a + b*x)*Log[(e*(a + b*x)^2)/(c + d*x)^2] - d^2*(a + b*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - 4*B*(b*c - a*d)^2*Log[c + d*x] - 2*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x] + 2*B*(b*c - a*d)*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 2*B*(b*c - a*d)^2*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/d^3))/(3*b)","A",1
131,1,207,188,0.1701128,"\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","Integrate[(a*g + b*g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","\frac{g \left((a+b x)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2-\frac{4 B (b c-a d) \left(-(b c-a d) \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+B d (a+b x) \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+B (b c-a d) \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-2 B (b c-a d) \log (c+d x)+A b d x\right)}{d^2}\right)}{2 b}","-\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}-\frac{4 B^2 g (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}",1,"(g*((a + b*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2 - (4*B*(b*c - a*d)*(A*b*d*x + B*d*(a + b*x)*Log[(e*(a + b*x)^2)/(c + d*x)^2] - 2*B*(b*c - a*d)*Log[c + d*x] - (b*c - a*d)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x] + B*(b*c - a*d)*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/d^2))/(2*b)","A",1
132,1,257,132,0.3212792,"\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","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(a*g + b*g*x),x]","\frac{A^2 \log (a+b x)+2 A B \log (a+b x) \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)-4 A B \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+4 A B \log (a+b x) \log \left(\frac{c}{d}+x\right)-4 A B \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)+2 A B \log ^2\left(\frac{a}{b}+x\right)-4 A B \log \left(\frac{a}{b}+x\right) \log (a+b x)+4 B^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right) \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)-B^2 \log \left(\frac{a d-b c}{d (a+b x)}\right) \log ^2\left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+8 B^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b g}","\frac{4 B \text{Li}_2\left(\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{\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}+\frac{8 B^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b g}",1,"(2*A*B*Log[a/b + x]^2 + A^2*Log[a + b*x] - 4*A*B*Log[a/b + x]*Log[a + b*x] + 4*A*B*Log[c/d + x]*Log[a + b*x] - 4*A*B*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*A*B*Log[a + b*x]*Log[(e*(a + b*x)^2)/(c + d*x)^2] - B^2*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(e*(a + b*x)^2)/(c + d*x)^2]^2 - 4*A*B*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 4*B^2*Log[(e*(a + b*x)^2)/(c + d*x)^2]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] + 8*B^2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))])/(b*g)","A",1
133,1,321,130,0.428951,"\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","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(a*g + b*g*x)^2,x]","-\frac{\frac{4 B \left((b c-a d) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+d (a+b x) \log (a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)-d (a+b x) \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)-B d (a+b x) \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+B d (a+b x) \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+2 B (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)\right)}{b c-a d}+\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 (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,"-(((A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2 + (4*B*((b*c - a*d)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + d*(a + b*x)*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - d*(a + b*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x] + 2*B*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - B*d*(a + b*x)*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + B*d*(a + b*x)*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d))/(b*g^2*(a + b*x)))","C",1
134,1,451,272,0.4428979,"\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","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(a*g + b*g*x)^3,x]","-\frac{\frac{2 B \left(-2 d^2 (a+b x)^2 \log (a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+2 d^2 (a+b x)^2 \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+(b c-a d)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+2 d (a+b x) (a d-b c) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+2 B d^2 (a+b x)^2 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)-2 B d^2 (a+b x)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+B \left(2 d^2 (a+b x)^2 \log (c+d x)+2 d (a+b x) (a d-b c)+(b c-a d)^2-2 d^2 (a+b x)^2 \log (a+b x)\right)-4 B d (a+b x) (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)\right)}{(b c-a d)^2}+\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{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,"-1/2*((A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2 + (2*B*((b*c - a*d)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + 2*d*(-(b*c) + a*d)*(a + b*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - 2*d^2*(a + b*x)^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + 2*d^2*(a + b*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x] - 4*B*d*(a + b*x)*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) + B*((b*c - a*d)^2 + 2*d*(-(b*c) + a*d)*(a + b*x) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]) + 2*B*d^2*(a + b*x)^2*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - 2*B*d^2*(a + b*x)^2*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^2)/(b*g^3*(a + b*x)^2)","C",1
135,1,598,429,0.637597,"\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","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(a*g + b*g*x)^4,x]","-\frac{\frac{2 B \left(18 d^3 (a+b x)^3 \log (a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)-18 d^3 (a+b x)^3 \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+18 d^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)+6 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)-9 d (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)-18 B d^3 (a+b x)^3 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+18 B d^3 (a+b x)^3 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+36 B d^2 (a+b x)^2 (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)-9 B d (a+b x) \left(2 d^2 (a+b x)^2 \log (c+d x)+2 d (a+b x) (a d-b c)+(b c-a d)^2-2 d^2 (a+b x)^2 \log (a+b x)\right)+2 B \left(-6 d^3 (a+b x)^3 \log (c+d x)+6 d^2 (a+b x)^2 (b c-a d)-3 d (a+b x) (b c-a d)^2+2 (b c-a d)^3+6 d^3 (a+b x)^3 \log (a+b x)\right)\right)}{(b c-a d)^3}+9 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^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,"-1/27*(9*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2 + (2*B*(6*(b*c - a*d)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - 9*d*(b*c - a*d)^2*(a + b*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + 18*d^2*(b*c - a*d)*(a + b*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + 18*d^3*(a + b*x)^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - 18*d^3*(a + b*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x] + 36*B*d^2*(a + b*x)^2*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - 9*B*d*(a + b*x)*((b*c - a*d)^2 + 2*d*(-(b*c) + a*d)*(a + b*x) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]) + 2*B*(2*(b*c - a*d)^3 - 3*d*(b*c - a*d)^2*(a + b*x) + 6*d^2*(b*c - a*d)*(a + b*x)^2 + 6*d^3*(a + b*x)^3*Log[a + b*x] - 6*d^3*(a + b*x)^3*Log[c + d*x]) - 18*B*d^3*(a + b*x)^3*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 18*B*d^3*(a + b*x)^3*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^3)/(b*g^4*(a + b*x)^3)","C",1
136,1,762,587,0.9361319,"\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","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(a*g + b*g*x)^5,x]","-\frac{\frac{B \left(-72 d^4 (a+b x)^4 \log (a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+72 d^4 (a+b x)^4 \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+72 d^3 (a+b x)^3 (a d-b c) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+36 d^2 (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)+18 (b c-a d)^4 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+24 d (a+b x) (a d-b c)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+72 B d^4 (a+b x)^4 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)-72 B d^4 (a+b x)^4 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-144 B d^3 (a+b x)^3 (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)+36 B d^2 (a+b x)^2 \left(2 d^2 (a+b x)^2 \log (c+d x)+2 d (a+b x) (a d-b c)+(b c-a d)^2-2 d^2 (a+b x)^2 \log (a+b x)\right)-8 B d (a+b x) \left(-6 d^3 (a+b x)^3 \log (c+d x)+6 d^2 (a+b x)^2 (b c-a d)-3 d (a+b x) (b c-a d)^2+2 (b c-a d)^3+6 d^3 (a+b x)^3 \log (a+b x)\right)+3 B \left(12 d^4 (a+b x)^4 \log (c+d x)+12 d^3 (a+b x)^3 (a d-b c)+6 d^2 (a+b x)^2 (b c-a d)^2+4 d (a+b x) (a d-b c)^3+3 (b c-a d)^4-12 d^4 (a+b x)^4 \log (a+b x)\right)\right)}{(b c-a d)^4}+18 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2}{72 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{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{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{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{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}",1,"-1/72*(18*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2 + (B*(18*(b*c - a*d)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + 24*d*(-(b*c) + a*d)^3*(a + b*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + 36*d^2*(b*c - a*d)^2*(a + b*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + 72*d^3*(-(b*c) + a*d)*(a + b*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - 72*d^4*(a + b*x)^4*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + 72*d^4*(a + b*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x] - 144*B*d^3*(a + b*x)^3*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) + 36*B*d^2*(a + b*x)^2*((b*c - a*d)^2 + 2*d*(-(b*c) + a*d)*(a + b*x) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]) - 8*B*d*(a + b*x)*(2*(b*c - a*d)^3 - 3*d*(b*c - a*d)^2*(a + b*x) + 6*d^2*(b*c - a*d)*(a + b*x)^2 + 6*d^3*(a + b*x)^3*Log[a + b*x] - 6*d^3*(a + b*x)^3*Log[c + d*x]) + 3*B*(3*(b*c - a*d)^4 + 4*d*(-(b*c) + a*d)^3*(a + b*x) + 6*d^2*(b*c - a*d)^2*(a + b*x)^2 + 12*d^3*(-(b*c) + a*d)*(a + b*x)^3 - 12*d^4*(a + b*x)^4*Log[a + b*x] + 12*d^4*(a + b*x)^4*Log[c + d*x]) + 72*B*d^4*(a + b*x)^4*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - 72*B*d^4*(a + b*x)^4*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^4)/(b*g^5*(a + b*x)^4)","C",1
137,0,0,37,0.1622231,"\int \frac{(a g+b g x)^2}{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)} \, dx","Integrate[(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,"Integrate[(a*g + b*g*x)^2/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]), x]","A",-1
138,0,0,35,0.1158408,"\int \frac{a g+b g x}{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)} \, dx","Integrate[(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,"Integrate[(a*g + b*g*x)/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]), x]","A",-1
139,0,0,37,0.071157,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])), x]","A",-1
140,0,0,94,0.0748399,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])), x]","F",-1
141,0,0,152,0.0810618,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])), x]","F",-1
142,0,0,37,0.4673252,"\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","Integrate[(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,"Integrate[(a*g + b*g*x)^2/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2, x]","A",-1
143,0,0,35,0.3448141,"\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","Integrate[(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,"Integrate[(a*g + b*g*x)/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2, x]","A",-1
144,0,0,37,0.1444453,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2), x]","A",-1
145,0,0,150,0.1793591,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2), x]","F",-1
146,0,0,266,0.347803,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2), x]","F",-1
147,1,364,171,0.8062789,"\int (a+b x)^4 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Integrate[(a + b*x)^4*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]),x]","\frac{-48 a^5 B d^5 n \log (a+b x)+b d x \left(12 a^4 d^4 (5 A+4 B n)+12 a^3 b d^3 (10 A d x-10 B c n+3 B d n x)+4 a^2 b^2 d^2 \left(30 A d^2 x^2+B n \left(30 c^2-15 c d x+4 d^2 x^2\right)\right)+a b^3 d \left(60 A d^3 x^3+B n \left(-60 c^3+30 c^2 d x-20 c d^2 x^2+3 d^3 x^3\right)\right)+b^4 \left(12 A d^4 x^4+B c n \left(12 c^3-6 c^2 d x+4 c d^2 x^2-3 d^3 x^3\right)\right)\right)-12 B n \left(-5 a^5 d^5+5 a^4 b c d^4-10 a^3 b^2 c^2 d^3+10 a^2 b^3 c^3 d^2-5 a b^4 c^4 d+b^5 c^5\right) \log (c+d x)+12 B d^5 \left(5 a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{60 b d^5}","\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 (b c-a d)^5 \log (c+d x)}{5 b d^5}+\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 (a+b x)^4 (b c-a d)}{20 b d}",1,"(b*d*x*(12*a^4*d^4*(5*A + 4*B*n) + 12*a^3*b*d^3*(-10*B*c*n + 10*A*d*x + 3*B*d*n*x) + 4*a^2*b^2*d^2*(30*A*d^2*x^2 + B*n*(30*c^2 - 15*c*d*x + 4*d^2*x^2)) + b^4*(12*A*d^4*x^4 + B*c*n*(12*c^3 - 6*c^2*d*x + 4*c*d^2*x^2 - 3*d^3*x^3)) + a*b^3*d*(60*A*d^3*x^3 + B*n*(-60*c^3 + 30*c^2*d*x - 20*c*d^2*x^2 + 3*d^3*x^3))) - 48*a^5*B*d^5*n*Log[a + b*x] - 12*B*(b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - 5*a^5*d^5)*n*Log[c + d*x] + 12*B*d^5*(5*a^5 + 5*a^4*b*x + 10*a^3*b^2*x^2 + 10*a^2*b^3*x^3 + 5*a*b^4*x^4 + b^5*x^5)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(60*b*d^5)","B",1
148,1,273,142,0.4859072,"\int (a+b x)^3 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Integrate[(a + b*x)^3*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]),x]","\frac{-18 a^4 B d^4 n \log (a+b x)+b d x \left(6 a^3 d^3 (4 A+3 B n)+9 a^2 b d^2 (4 A d x-4 B c n+B d n x)+2 a b^2 d \left(12 A d^2 x^2+B n \left(12 c^2-6 c d x+d^2 x^2\right)\right)+b^3 \left(6 A d^3 x^3+B c n \left(-6 c^2+3 c d x-2 d^2 x^2\right)\right)\right)+6 B n \left(4 a^4 d^4-4 a^3 b c d^3+6 a^2 b^2 c^2 d^2-4 a b^3 c^3 d+b^4 c^4\right) \log (c+d x)+6 B d^4 \left(4 a^4+4 a^3 b x+6 a^2 b^2 x^2+4 a b^3 x^3+b^4 x^4\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{24 b d^4}","\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 (b c-a d)^4 \log (c+d x)}{4 b d^4}-\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 (a+b x)^3 (b c-a d)}{12 b d}",1,"(b*d*x*(6*a^3*d^3*(4*A + 3*B*n) + 9*a^2*b*d^2*(-4*B*c*n + 4*A*d*x + B*d*n*x) + b^3*(6*A*d^3*x^3 + B*c*n*(-6*c^2 + 3*c*d*x - 2*d^2*x^2)) + 2*a*b^2*d*(12*A*d^2*x^2 + B*n*(12*c^2 - 6*c*d*x + d^2*x^2))) - 18*a^4*B*d^4*n*Log[a + b*x] + 6*B*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + 4*a^4*d^4)*n*Log[c + d*x] + 6*B*d^4*(4*a^4 + 4*a^3*b*x + 6*a^2*b^2*x^2 + 4*a*b^3*x^3 + b^4*x^4)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(24*b*d^4)","A",1
149,1,194,113,0.2874697,"\int (a+b x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Integrate[(a + b*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]),x]","\frac{-4 a^3 B d^3 n \log (a+b x)+b d x \left(2 a^2 d^2 (3 A+2 B n)+a b d (6 A d x-6 B c n+B d n x)+b^2 \left(2 A d^2 x^2+B c n (2 c-d x)\right)\right)-2 B n \left(-3 a^3 d^3+3 a^2 b c d^2-3 a b^2 c^2 d+b^3 c^3\right) \log (c+d x)+2 B d^3 \left(3 a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{6 b d^3}","\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 (b c-a d)^3 \log (c+d x)}{3 b d^3}+\frac{B n x (b c-a d)^2}{3 d^2}-\frac{B n (a+b x)^2 (b c-a d)}{6 b d}",1,"(b*d*x*(2*a^2*d^2*(3*A + 2*B*n) + a*b*d*(-6*B*c*n + 6*A*d*x + B*d*n*x) + b^2*(2*A*d^2*x^2 + B*c*n*(2*c - d*x))) - 4*a^3*B*d^3*n*Log[a + b*x] - 2*B*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - 3*a^3*d^3)*n*Log[c + d*x] + 2*B*d^3*(3*a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(6*b*d^3)","A",1
150,1,126,84,0.1491797,"\int (a+b x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Integrate[(a + b*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]),x]","\frac{d \left(B d \left(2 a^2+2 a b x+b^2 x^2\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+b x (2 a A d+a B d n+A b d x-b B c n)\right)+B n \left(2 a^2 d^2-2 a b c d+b^2 c^2\right) \log (c+d x)-a^2 B d^2 n \log (a+b x)}{2 b d^2}","\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,"(-(a^2*B*d^2*n*Log[a + b*x]) + B*(b^2*c^2 - 2*a*b*c*d + 2*a^2*d^2)*n*Log[c + d*x] + d*(b*x*(2*a*A*d - b*B*c*n + a*B*d*n + A*b*d*x) + B*d*(2*a^2 + 2*a*b*x + b^2*x^2)*Log[(e*(a + b*x)^n)/(c + d*x)^n]))/(2*b*d^2)","A",1
151,1,129,79,0.0979045,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{a+b x} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(a + b*x),x]","\frac{2 A \log (a+b x)-2 B \log \left(\frac{a d-b c}{d (a+b x)}\right) \left(\log \left(e (a+b x)^n (c+d x)^{-n}\right)+n \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)+2 B n \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)-B n \log ^2\left(\frac{a d-b c}{d (a+b x)}\right)}{2 b}","\frac{B n \text{Li}_2\left(\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,"(-(B*n*Log[(-(b*c) + a*d)/(d*(a + b*x))]^2) + 2*A*Log[a + b*x] - 2*B*Log[(-(b*c) + a*d)/(d*(a + b*x))]*(n*Log[(b*(c + d*x))/(b*c - a*d)] + Log[(e*(a + b*x)^n)/(c + d*x)^n]) + 2*B*n*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(2*b)","A",1
152,1,89,97,0.0853765,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(a + b*x)^2,x]","\frac{-(b c-a d) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A+B n\right)+B d n (a+b x) \log (c+d x)-B d n (a+b x) \log (a+b x)}{b (a+b x) (b c-a d)}","-\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,"(-(B*d*n*(a + b*x)*Log[a + b*x]) + B*d*n*(a + b*x)*Log[c + d*x] - (b*c - a*d)*(A + B*n + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]))/(b*(b*c - a*d)*(a + b*x))","A",1
153,1,121,137,0.3106699,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(a + b*x)^3,x]","-\frac{\frac{2 A}{(a+b x)^2}+B n \left(-\frac{2 d^2 \log (a+b x)}{(b c-a d)^2}+\frac{2 d^2 \log (c+d x)}{(b c-a d)^2}+\frac{\frac{2 d (a+b x)}{a d-b c}+1}{(a+b x)^2}\right)+\frac{2 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x)^2}}{4 b}","-\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,"-1/4*((2*A)/(a + b*x)^2 + B*n*((1 + (2*d*(a + b*x))/(-(b*c) + a*d))/(a + b*x)^2 - (2*d^2*Log[a + b*x])/(b*c - a*d)^2 + (2*d^2*Log[c + d*x])/(b*c - a*d)^2) + (2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(a + b*x)^2)/b","A",1
154,1,143,166,0.376988,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x)^4} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(a + b*x)^4,x]","-\frac{\frac{6 A}{(a+b x)^3}+B n \left(\frac{6 d^3 \log (a+b x)}{(b c-a d)^3}-\frac{6 d^3 \log (c+d x)}{(b c-a d)^3}+\frac{\frac{6 d^2 (a+b x)^2}{(b c-a d)^2}+\frac{3 d (a+b x)}{a d-b c}+2}{(a+b x)^3}\right)+\frac{6 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x)^3}}{18 b}","-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A}{3 b (a+b x)^3}-\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^2 n}{3 b (a+b x) (b c-a d)^2}+\frac{B d n}{6 b (a+b x)^2 (b c-a d)}-\frac{B n}{9 b (a+b x)^3}",1,"-1/18*((6*A)/(a + b*x)^3 + B*n*((2 + (3*d*(a + b*x))/(-(b*c) + a*d) + (6*d^2*(a + b*x)^2)/(b*c - a*d)^2)/(a + b*x)^3 + (6*d^3*Log[a + b*x])/(b*c - a*d)^3 - (6*d^3*Log[c + d*x])/(b*c - a*d)^3) + (6*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(a + b*x)^3)/b","A",1
155,1,165,195,0.35762,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x)^5} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(a + b*x)^5,x]","-\frac{\frac{12 A}{(a+b x)^4}+B n \left(-\frac{12 d^4 \log (a+b x)}{(b c-a d)^4}+\frac{12 d^4 \log (c+d x)}{(b c-a d)^4}+\frac{-\frac{12 d^3 (a+b x)^3}{(b c-a d)^3}+\frac{6 d^2 (a+b x)^2}{(b c-a d)^2}+\frac{4 d (a+b x)}{a d-b c}+3}{(a+b x)^4}\right)+\frac{12 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x)^4}}{48 b}","-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A}{4 b (a+b x)^4}+\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^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 n}{12 b (a+b x)^3 (b c-a d)}-\frac{B n}{16 b (a+b x)^4}",1,"-1/48*((12*A)/(a + b*x)^4 + B*n*((3 + (4*d*(a + b*x))/(-(b*c) + a*d) + (6*d^2*(a + b*x)^2)/(b*c - a*d)^2 - (12*d^3*(a + b*x)^3)/(b*c - a*d)^3)/(a + b*x)^4 - (12*d^4*Log[a + b*x])/(b*c - a*d)^4 + (12*d^4*Log[c + d*x])/(b*c - a*d)^4) + (12*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(a + b*x)^4)/b","A",1
156,1,1709,322,1.7992318,"\int (a+b x)^3 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 \, dx","Integrate[(a + b*x)^3*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2,x]","\frac{3 A^2 d^4 x^4 b^4-2 A B c d^3 n x^3 b^4+B^2 c^2 d^2 n^2 x^2 b^4+3 A B c^2 d^2 n x^2 b^4+3 B^2 c^4 n^2 \log ^2(c+d x) b^4+3 B^2 d^4 x^4 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) b^4-5 B^2 c^3 d n^2 x b^4-6 A B c^3 d n x b^4+11 B^2 c^4 n^2 \log (c+d x) b^4+6 A B c^4 n \log (c+d x) b^4+6 A B d^4 x^4 \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^4-2 B^2 c d^3 n x^3 \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^4+3 B^2 c^2 d^2 n x^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^4-6 B^2 c^3 d n x \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^4+6 B^2 c^4 n \log (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^4+12 a A^2 d^4 x^3 b^3+2 a A B d^4 n x^3 b^3+6 a B^2 c^3 d n^2 b^3-2 a B^2 c d^3 n^2 x^2 b^3-12 a A B c d^3 n x^2 b^3-12 a B^2 c^3 d n^2 \log ^2(c+d x) b^3+12 a B^2 d^4 x^3 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) b^3+17 a B^2 c^2 d^2 n^2 x b^3+24 a A B c^2 d^2 n x b^3-38 a B^2 c^3 d n^2 \log (c+d x) b^3-24 a A B c^3 d n \log (c+d x) b^3+24 a A B d^4 x^3 \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^3+2 a B^2 d^4 n x^3 \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^3-12 a B^2 c d^3 n x^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^3+24 a B^2 c^2 d^2 n x \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^3-24 a B^2 c^3 d n \log (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^3-24 a^2 B^2 c^2 d^2 n^2 b^2+18 a^2 A^2 d^4 x^2 b^2+a^2 B^2 d^4 n^2 x^2 b^2+9 a^2 A B d^4 n x^2 b^2+18 a^2 B^2 c^2 d^2 n^2 \log ^2(c+d x) b^2+18 a^2 B^2 d^4 x^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) b^2-19 a^2 B^2 c d^3 n^2 x b^2-36 a^2 A B c d^3 n x b^2+45 a^2 B^2 c^2 d^2 n^2 \log (c+d x) b^2+36 a^2 A B c^2 d^2 n \log (c+d x) b^2+36 a^2 A B d^4 x^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^2+9 a^2 B^2 d^4 n x^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^2-36 a^2 B^2 c d^3 n x \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^2+36 a^2 B^2 c^2 d^2 n \log (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^2+36 a^3 B^2 c d^3 n^2 b-12 a^3 B^2 c d^3 n^2 \log ^2(c+d x) b+12 a^3 B^2 d^4 x \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) b+12 a^3 A^2 d^4 x b+7 a^3 B^2 d^4 n^2 x b+18 a^3 A B d^4 n x b-18 a^3 B^2 c d^3 n^2 \log (c+d x) b-24 a^3 A B c d^3 n \log (c+d x) b+24 a^3 A B d^4 x \log \left(e (a+b x)^n (c+d x)^{-n}\right) b+18 a^3 B^2 d^4 n x \log \left(e (a+b x)^n (c+d x)^{-n}\right) b-24 a^3 B^2 c d^3 n \log (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) b-24 a^4 B^2 d^4 n^2-3 a^4 B^2 d^4 n^2 \log ^2(a+b x)-24 a^4 A B d^4 n-24 a^4 B^2 d^4 n^2 \log (c+d x)-24 a^4 B^2 d^4 n \log \left(e (a+b x)^n (c+d x)^{-n}\right)+B n \log (a+b x) \left(6 B n \log \left(\frac{b (c+d x)}{b c-a d}\right) (b c-a d)^4-6 b B c \left(b^3 c^3-4 a b^2 d c^2+6 a^2 b d^2 c-4 a^3 d^3\right) n \log (c+d x)+a d \left(-6 b^3 B n c^3+21 a b^2 B d n c^2-26 a^2 b B d^2 n c+a^3 d^3 (6 A+35 B n)+6 a^3 B d^3 \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)\right)+6 B^2 (b c-a d)^4 n^2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)}{12 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}-\frac{B^2 n^2 (b c-a d)^4 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{2 b d^4}",1,"(-24*a^4*A*B*d^4*n + 6*a*b^3*B^2*c^3*d*n^2 - 24*a^2*b^2*B^2*c^2*d^2*n^2 + 36*a^3*b*B^2*c*d^3*n^2 - 24*a^4*B^2*d^4*n^2 + 12*a^3*A^2*b*d^4*x - 6*A*b^4*B*c^3*d*n*x + 24*a*A*b^3*B*c^2*d^2*n*x - 36*a^2*A*b^2*B*c*d^3*n*x + 18*a^3*A*b*B*d^4*n*x - 5*b^4*B^2*c^3*d*n^2*x + 17*a*b^3*B^2*c^2*d^2*n^2*x - 19*a^2*b^2*B^2*c*d^3*n^2*x + 7*a^3*b*B^2*d^4*n^2*x + 18*a^2*A^2*b^2*d^4*x^2 + 3*A*b^4*B*c^2*d^2*n*x^2 - 12*a*A*b^3*B*c*d^3*n*x^2 + 9*a^2*A*b^2*B*d^4*n*x^2 + b^4*B^2*c^2*d^2*n^2*x^2 - 2*a*b^3*B^2*c*d^3*n^2*x^2 + a^2*b^2*B^2*d^4*n^2*x^2 + 12*a*A^2*b^3*d^4*x^3 - 2*A*b^4*B*c*d^3*n*x^3 + 2*a*A*b^3*B*d^4*n*x^3 + 3*A^2*b^4*d^4*x^4 - 3*a^4*B^2*d^4*n^2*Log[a + b*x]^2 + 6*A*b^4*B*c^4*n*Log[c + d*x] - 24*a*A*b^3*B*c^3*d*n*Log[c + d*x] + 36*a^2*A*b^2*B*c^2*d^2*n*Log[c + d*x] - 24*a^3*A*b*B*c*d^3*n*Log[c + d*x] + 11*b^4*B^2*c^4*n^2*Log[c + d*x] - 38*a*b^3*B^2*c^3*d*n^2*Log[c + d*x] + 45*a^2*b^2*B^2*c^2*d^2*n^2*Log[c + d*x] - 18*a^3*b*B^2*c*d^3*n^2*Log[c + d*x] - 24*a^4*B^2*d^4*n^2*Log[c + d*x] + 3*b^4*B^2*c^4*n^2*Log[c + d*x]^2 - 12*a*b^3*B^2*c^3*d*n^2*Log[c + d*x]^2 + 18*a^2*b^2*B^2*c^2*d^2*n^2*Log[c + d*x]^2 - 12*a^3*b*B^2*c*d^3*n^2*Log[c + d*x]^2 - 24*a^4*B^2*d^4*n*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 24*a^3*A*b*B*d^4*x*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 6*b^4*B^2*c^3*d*n*x*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 24*a*b^3*B^2*c^2*d^2*n*x*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 36*a^2*b^2*B^2*c*d^3*n*x*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 18*a^3*b*B^2*d^4*n*x*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 36*a^2*A*b^2*B*d^4*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 3*b^4*B^2*c^2*d^2*n*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 12*a*b^3*B^2*c*d^3*n*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 9*a^2*b^2*B^2*d^4*n*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 24*a*A*b^3*B*d^4*x^3*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 2*b^4*B^2*c*d^3*n*x^3*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*a*b^3*B^2*d^4*n*x^3*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 6*A*b^4*B*d^4*x^4*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 6*b^4*B^2*c^4*n*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 24*a*b^3*B^2*c^3*d*n*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 36*a^2*b^2*B^2*c^2*d^2*n*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 24*a^3*b*B^2*c*d^3*n*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 12*a^3*b*B^2*d^4*x*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 18*a^2*b^2*B^2*d^4*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 12*a*b^3*B^2*d^4*x^3*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 3*b^4*B^2*d^4*x^4*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + B*n*Log[a + b*x]*(-6*b*B*c*(b^3*c^3 - 4*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 4*a^3*d^3)*n*Log[c + d*x] + 6*B*(b*c - a*d)^4*n*Log[(b*(c + d*x))/(b*c - a*d)] + a*d*(-6*b^3*B*c^3*n + 21*a*b^2*B*c^2*d*n - 26*a^2*b*B*c*d^2*n + a^3*d^3*(6*A + 35*B*n) + 6*a^3*B*d^3*Log[(e*(a + b*x)^n)/(c + d*x)^n])) + 6*B^2*(b*c - a*d)^4*n^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(12*b*d^4)","B",1
157,1,1149,263,1.0617658,"\int (a+b x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 \, dx","Integrate[(a + b*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2,x]","\frac{A^2 d^3 x^3 b^3-A B c d^2 n x^2 b^3-B^2 c^3 n^2 \log ^2(c+d x) b^3+B^2 d^3 x^3 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) b^3+B^2 c^2 d n^2 x b^3+2 A B c^2 d n x b^3-3 B^2 c^3 n^2 \log (c+d x) b^3-2 A B c^3 n \log (c+d x) b^3+2 A B d^3 x^3 \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^3-B^2 c d^2 n x^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^3+2 B^2 c^2 d n x \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^3-2 B^2 c^3 n \log (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^3-2 a B^2 c^2 d n^2 b^2+3 a A^2 d^3 x^2 b^2+a A B d^3 n x^2 b^2+3 a B^2 c^2 d n^2 \log ^2(c+d x) b^2+3 a B^2 d^3 x^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) b^2-2 a B^2 c d^2 n^2 x b^2-6 a A B c d^2 n x b^2+7 a B^2 c^2 d n^2 \log (c+d x) b^2+6 a A B c^2 d n \log (c+d x) b^2+6 a A B d^3 x^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^2+a B^2 d^3 n x^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^2-6 a B^2 c d^2 n x \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^2+6 a B^2 c^2 d n \log (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^2+6 a^2 B^2 c d^2 n^2 b-3 a^2 B^2 c d^2 n^2 \log ^2(c+d x) b+3 a^2 B^2 d^3 x \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) b+3 a^2 A^2 d^3 x b+a^2 B^2 d^3 n^2 x b+4 a^2 A B d^3 n x b-4 a^2 B^2 c d^2 n^2 \log (c+d x) b-6 a^2 A B c d^2 n \log (c+d x) b+6 a^2 A B d^3 x \log \left(e (a+b x)^n (c+d x)^{-n}\right) b+4 a^2 B^2 d^3 n x \log \left(e (a+b x)^n (c+d x)^{-n}\right) b-6 a^2 B^2 c d^2 n \log (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right) b-6 a^3 B^2 d^3 n^2-a^3 B^2 d^3 n^2 \log ^2(a+b x)-6 a^3 A B d^3 n-6 a^3 B^2 d^3 n^2 \log (c+d x)-6 a^3 B^2 d^3 n \log \left(e (a+b x)^n (c+d x)^{-n}\right)+B n \log (a+b x) \left(-2 B n \log \left(\frac{b (c+d x)}{b c-a d}\right) (b c-a d)^3+2 b B c \left(b^2 c^2-3 a b d c+3 a^2 d^2\right) n \log (c+d x)+a d \left(2 b^2 B n c^2-5 a b B d n c+a^2 d^2 (2 A+9 B n)+2 a^2 B d^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)\right)-2 B^2 (b c-a d)^3 n^2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\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}+\frac{2 B^2 n^2 (b c-a d)^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{3 b d^3}",1,"(-6*a^3*A*B*d^3*n - 2*a*b^2*B^2*c^2*d*n^2 + 6*a^2*b*B^2*c*d^2*n^2 - 6*a^3*B^2*d^3*n^2 + 3*a^2*A^2*b*d^3*x + 2*A*b^3*B*c^2*d*n*x - 6*a*A*b^2*B*c*d^2*n*x + 4*a^2*A*b*B*d^3*n*x + b^3*B^2*c^2*d*n^2*x - 2*a*b^2*B^2*c*d^2*n^2*x + a^2*b*B^2*d^3*n^2*x + 3*a*A^2*b^2*d^3*x^2 - A*b^3*B*c*d^2*n*x^2 + a*A*b^2*B*d^3*n*x^2 + A^2*b^3*d^3*x^3 - a^3*B^2*d^3*n^2*Log[a + b*x]^2 - 2*A*b^3*B*c^3*n*Log[c + d*x] + 6*a*A*b^2*B*c^2*d*n*Log[c + d*x] - 6*a^2*A*b*B*c*d^2*n*Log[c + d*x] - 3*b^3*B^2*c^3*n^2*Log[c + d*x] + 7*a*b^2*B^2*c^2*d*n^2*Log[c + d*x] - 4*a^2*b*B^2*c*d^2*n^2*Log[c + d*x] - 6*a^3*B^2*d^3*n^2*Log[c + d*x] - b^3*B^2*c^3*n^2*Log[c + d*x]^2 + 3*a*b^2*B^2*c^2*d*n^2*Log[c + d*x]^2 - 3*a^2*b*B^2*c*d^2*n^2*Log[c + d*x]^2 - 6*a^3*B^2*d^3*n*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 6*a^2*A*b*B*d^3*x*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*b^3*B^2*c^2*d*n*x*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 6*a*b^2*B^2*c*d^2*n*x*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 4*a^2*b*B^2*d^3*n*x*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 6*a*A*b^2*B*d^3*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] - b^3*B^2*c*d^2*n*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + a*b^2*B^2*d^3*n*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*A*b^3*B*d^3*x^3*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 2*b^3*B^2*c^3*n*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 6*a*b^2*B^2*c^2*d*n*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 6*a^2*b*B^2*c*d^2*n*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 3*a^2*b*B^2*d^3*x*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 3*a*b^2*B^2*d^3*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + b^3*B^2*d^3*x^3*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + B*n*Log[a + b*x]*(2*b*B*c*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2)*n*Log[c + d*x] - 2*B*(b*c - a*d)^3*n*Log[(b*(c + d*x))/(b*c - a*d)] + a*d*(2*b^2*B*c^2*n - 5*a*b*B*c*d*n + a^2*d^2*(2*A + 9*B*n) + 2*a^2*B*d^2*Log[(e*(a + b*x)^n)/(c + d*x)^n])) - 2*B^2*(b*c - a*d)^3*n^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*d^3)","B",1
158,1,656,195,0.7311992,"\int (a+b x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 \, dx","Integrate[(a + b*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2,x]","-\frac{2 a^2 A B n}{b}-\frac{2 a^2 B^2 n \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{b}-\frac{2 a^2 B^2 n^2 \log (c+d x)}{b}-\frac{a^2 B^2 n^2 \log ^2(a+b x)}{2 b}-\frac{2 a^2 B^2 n^2}{b}+a A^2 x+\frac{B n \log (a+b x) \left(a d \left(a d (A+3 B n)+a B d \log \left(e (a+b x)^n (c+d x)^{-n}\right)-b B c n\right)+B n (b c-a d)^2 \log \left(\frac{b (c+d x)}{b c-a d}\right)+b B c n (2 a d-b c) \log (c+d x)\right)}{b d^2}+A b B x^2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 a A B x \log \left(e (a+b x)^n (c+d x)^{-n}\right)-\frac{2 a A B c n \log (c+d x)}{d}+a A B n x+\frac{b B^2 c^2 n \log (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{d^2}+\frac{B^2 n^2 (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)}{b d^2}+\frac{1}{2} b B^2 x^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+a B^2 x \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+a B^2 n x \log \left(e (a+b x)^n (c+d x)^{-n}\right)-\frac{2 a B^2 c n \log (c+d x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{d}-\frac{b B^2 c n x \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{d}-\frac{a B^2 c n^2 \log ^2(c+d x)}{d}-\frac{a B^2 c n^2 \log (c+d x)}{d}+\frac{a B^2 c n^2}{d}+\frac{1}{2} A^2 b x^2+\frac{A b B c^2 n \log (c+d x)}{d^2}-\frac{A b B c n x}{d}+\frac{b B^2 c^2 n^2 \log ^2(c+d x)}{2 d^2}+\frac{b B^2 c^2 n^2 \log (c+d x)}{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}-\frac{B^2 n^2 (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}",1,"(-2*a^2*A*B*n)/b - (2*a^2*B^2*n^2)/b + (a*B^2*c*n^2)/d + a*A^2*x + a*A*B*n*x - (A*b*B*c*n*x)/d + (A^2*b*x^2)/2 - (a^2*B^2*n^2*Log[a + b*x]^2)/(2*b) + (A*b*B*c^2*n*Log[c + d*x])/d^2 - (2*a*A*B*c*n*Log[c + d*x])/d - (2*a^2*B^2*n^2*Log[c + d*x])/b + (b*B^2*c^2*n^2*Log[c + d*x])/d^2 - (a*B^2*c*n^2*Log[c + d*x])/d + (b*B^2*c^2*n^2*Log[c + d*x]^2)/(2*d^2) - (a*B^2*c*n^2*Log[c + d*x]^2)/d - (2*a^2*B^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n])/b + 2*a*A*B*x*Log[(e*(a + b*x)^n)/(c + d*x)^n] + a*B^2*n*x*Log[(e*(a + b*x)^n)/(c + d*x)^n] - (b*B^2*c*n*x*Log[(e*(a + b*x)^n)/(c + d*x)^n])/d + A*b*B*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + (b*B^2*c^2*n*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/d^2 - (2*a*B^2*c*n*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n])/d + a*B^2*x*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + (b*B^2*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)/2 + (B*n*Log[a + b*x]*(b*B*c*(-(b*c) + 2*a*d)*n*Log[c + d*x] + B*(b*c - a*d)^2*n*Log[(b*(c + d*x))/(b*c - a*d)] + a*d*(-(b*B*c*n) + a*d*(A + 3*B*n) + a*B*d*Log[(e*(a + b*x)^n)/(c + d*x)^n])))/(b*d^2) + (B^2*(b*c - a*d)^2*n^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*d^2)","B",1
159,1,269,131,0.1895622,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{a+b x} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(a + b*x),x]","\frac{A^2 \log (a+b x)-2 A B \log \left(\frac{a d-b c}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 A B n \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)-A B n \log ^2\left(\frac{a d-b c}{d (a+b x)}\right)-2 A B n \log \left(\frac{a d-b c}{d (a+b x)}\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)+2 B^2 n \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)-B^2 \log \left(\frac{a d-b c}{d (a+b x)}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+2 B^2 n^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b}","\frac{2 B n \text{Li}_2\left(\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{\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}+\frac{2 B^2 n^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b}",1,"(-(A*B*n*Log[(-(b*c) + a*d)/(d*(a + b*x))]^2) + A^2*Log[a + b*x] - 2*A*B*n*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(b*(c + d*x))/(b*c - a*d)] - 2*A*B*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - B^2*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 2*A*B*n*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 2*B^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] + 2*B^2*n^2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))])/b","B",1
160,1,236,129,0.3720521,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{(a+b x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(a + b*x)^2,x]","\frac{-(b c-a d) \left(2 B (A+B n) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+A^2+2 A B n+2 B^2 n^2\right)-2 B d n (a+b x) \log (a+b x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A+B n \log (c+d x)+B n\right)+2 B d n (a+b x) \log (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A+B n\right)+B^2 d n^2 (a+b x) \log ^2(c+d x)+B^2 d n^2 (a+b x) \log ^2(a+b x)}{b (a+b x) (b c-a d)}","-\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,"(B^2*d*n^2*(a + b*x)*Log[a + b*x]^2 + B^2*d*n^2*(a + b*x)*Log[c + d*x]^2 + 2*B*d*n*(a + b*x)*Log[c + d*x]*(A + B*n + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]) - 2*B*d*n*(a + b*x)*Log[a + b*x]*(A + B*n + B*n*Log[c + d*x] + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]) - (b*c - a*d)*(A^2 + 2*A*B*n + 2*B^2*n^2 + 2*B*(A + B*n)*Log[(e*(a + b*x)^n)/(c + d*x)^n] + B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2))/(b*(b*c - a*d)*(a + b*x))","A",1
161,1,332,274,0.5232381,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{(a+b x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(a + b*x)^3,x]","-\frac{(b c-a d) \left(2 A^2 (b c-a d)+2 B (2 A (b c-a d)+B n (-3 a d+b c-2 b d x)) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 A B n (-3 a d+b c-2 b d x)+2 B^2 (b c-a d) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+B^2 n^2 (-7 a d+b c-6 b d x)\right)+2 B d^2 n (a+b x)^2 \log (c+d x) \left(2 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 A+3 B n\right)-2 B d^2 n (a+b x)^2 \log (a+b x) \left(2 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 A+2 B n \log (c+d x)+3 B n\right)+2 B^2 d^2 n^2 (a+b x)^2 \log ^2(c+d x)+2 B^2 d^2 n^2 (a+b x)^2 \log ^2(a+b x)}{4 b (a+b x)^2 (b c-a d)^2}","-\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,"-1/4*(2*B^2*d^2*n^2*(a + b*x)^2*Log[a + b*x]^2 + 2*B^2*d^2*n^2*(a + b*x)^2*Log[c + d*x]^2 + 2*B*d^2*n*(a + b*x)^2*Log[c + d*x]*(2*A + 3*B*n + 2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n]) - 2*B*d^2*n*(a + b*x)^2*Log[a + b*x]*(2*A + 3*B*n + 2*B*n*Log[c + d*x] + 2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n]) + (b*c - a*d)*(2*A^2*(b*c - a*d) + B^2*n^2*(b*c - 7*a*d - 6*b*d*x) + 2*A*B*n*(b*c - 3*a*d - 2*b*d*x) + 2*B*(2*A*(b*c - a*d) + B*n*(b*c - 3*a*d - 2*b*d*x))*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*B^2*(b*c - a*d)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2))/(b*(b*c - a*d)^2*(a + b*x)^2)","A",1
162,1,432,427,0.7261366,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{(a+b x)^4} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(a + b*x)^4,x]","\frac{-(b c-a d) \left(6 B \left(B n \left(11 a^2 d^2+a b d (15 d x-7 c)+b^2 \left(2 c^2-3 c d x+6 d^2 x^2\right)\right)+6 A (b c-a d)^2\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+6 A B n \left(11 a^2 d^2+a b d (15 d x-7 c)+b^2 \left(2 c^2-3 c d x+6 d^2 x^2\right)\right)+B^2 n^2 \left(85 a^2 d^2+a b d (147 d x-23 c)+b^2 \left(4 c^2-15 c d x+66 d^2 x^2\right)\right)+18 A^2 (b c-a d)^2+18 B^2 (b c-a d)^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)\right)+6 B d^3 n (a+b x)^3 \log (c+d x) \left(6 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+6 A+11 B n\right)-6 B d^3 n (a+b x)^3 \log (a+b x) \left(6 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+6 A+6 B n \log (c+d x)+11 B n\right)+18 B^2 d^3 n^2 (a+b x)^3 \log ^2(c+d x)+18 B^2 d^3 n^2 (a+b x)^3 \log ^2(a+b x)}{54 b (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)^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,"(18*B^2*d^3*n^2*(a + b*x)^3*Log[a + b*x]^2 + 18*B^2*d^3*n^2*(a + b*x)^3*Log[c + d*x]^2 + 6*B*d^3*n*(a + b*x)^3*Log[c + d*x]*(6*A + 11*B*n + 6*B*Log[(e*(a + b*x)^n)/(c + d*x)^n]) - 6*B*d^3*n*(a + b*x)^3*Log[a + b*x]*(6*A + 11*B*n + 6*B*n*Log[c + d*x] + 6*B*Log[(e*(a + b*x)^n)/(c + d*x)^n]) - (b*c - a*d)*(18*A^2*(b*c - a*d)^2 + 6*A*B*n*(11*a^2*d^2 + a*b*d*(-7*c + 15*d*x) + b^2*(2*c^2 - 3*c*d*x + 6*d^2*x^2)) + B^2*n^2*(85*a^2*d^2 + a*b*d*(-23*c + 147*d*x) + b^2*(4*c^2 - 15*c*d*x + 66*d^2*x^2)) + 6*B*(6*A*(b*c - a*d)^2 + B*n*(11*a^2*d^2 + a*b*d*(-7*c + 15*d*x) + b^2*(2*c^2 - 3*c*d*x + 6*d^2*x^2)))*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 18*B^2*(b*c - a*d)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2))/(54*b*(b*c - a*d)^3*(a + b*x)^3)","A",1
163,1,1011,587,0.953958,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{(a+b x)^5} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(a + b*x)^5,x]","-\frac{9 \left(8 A^2+4 B n A+16 B \left(-n \log (a+b x)+n \log (c+d x)+\log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) A+B^2 n^2+8 B^2 \left(-n \log (a+b x)+n \log (c+d x)+\log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2+4 B^2 n \left(-n \log (a+b x)+n \log (c+d x)+\log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)\right) (b c-a d)^4-4 B d n (a+b x) \left(12 A+7 B n+12 B \left(-n \log (a+b x)+n \log (c+d x)+\log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)\right) (b c-a d)^3+6 B d^2 n (a+b x)^2 \left(12 A+13 B n+12 B \left(-n \log (a+b x)+n \log (c+d x)+\log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)\right) (b c-a d)^2-12 B d^3 n (a+b x)^3 \left(12 A+25 B n+12 B \left(-n \log (a+b x)+n \log (c+d x)+\log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)\right) (b c-a d)-12 B n \log (a+b x) \left(-3 \left(4 A+B n+4 B \left(-n \log (a+b x)+n \log (c+d x)+\log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)\right) (b c-a d)^3+4 B d n (a+b x) (b c-a d)^2+12 B d^3 n (a+b x)^3+6 B d^2 (a d-b c) n (a+b x)^2\right) (b c-a d)+72 b B^2 n^2 \left(\left(c^4-d^4 x^4\right) b^3-4 a d \left(c^3+d^3 x^3\right) b^2+6 a^2 d^2 \left(c^2-d^2 x^2\right) b-4 a^3 d^3 (c+d x)\right) \log ^2(a+b x)+72 b B^2 n^2 \left(\left(c^4-d^4 x^4\right) b^3-4 a d \left(c^3+d^3 x^3\right) b^2+6 a^2 d^2 \left(c^2-d^2 x^2\right) b-4 a^3 d^3 (c+d x)\right) \log ^2(c+d x)-12 B d^4 n (a+b x)^4 \log (a+b x) \left(12 A+25 B n+12 B \left(-n \log (a+b x)+n \log (c+d x)+\log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)\right)+12 B d^4 n (a+b x)^4 \log (c+d x) \left(12 A+25 B n+12 B \left(-n \log (a+b x)+n \log (c+d x)+\log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)\right)+12 B n \log (c+d x) \left(-12 B n \log (a+b x) (b c-a d)^4-3 \left(4 A+B n+4 B \left(-n \log (a+b x)+n \log (c+d x)+\log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)\right) (b c-a d)^4+4 B d n (a+b x) (b c-a d)^3-6 B d^2 n (a+b x)^2 (b c-a d)^2+12 B d^3 n (a+b x)^3 (b c-a d)+12 B d^4 n (a+b x)^4 \log (a+b x)\right)}{288 b (b c-a d)^4 (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{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{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{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{2 B^2 d^3 n^2 (c+d x)}{(a+b x) (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}",1,"-1/288*(72*b*B^2*n^2*(-4*a^3*d^3*(c + d*x) + 6*a^2*b*d^2*(c^2 - d^2*x^2) - 4*a*b^2*d*(c^3 + d^3*x^3) + b^3*(c^4 - d^4*x^4))*Log[a + b*x]^2 + 72*b*B^2*n^2*(-4*a^3*d^3*(c + d*x) + 6*a^2*b*d^2*(c^2 - d^2*x^2) - 4*a*b^2*d*(c^3 + d^3*x^3) + b^3*(c^4 - d^4*x^4))*Log[c + d*x]^2 - 4*B*d*(b*c - a*d)^3*n*(a + b*x)*(12*A + 7*B*n + 12*B*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n])) + 6*B*d^2*(b*c - a*d)^2*n*(a + b*x)^2*(12*A + 13*B*n + 12*B*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n])) - 12*B*d^3*(b*c - a*d)*n*(a + b*x)^3*(12*A + 25*B*n + 12*B*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n])) - 12*B*d^4*n*(a + b*x)^4*Log[a + b*x]*(12*A + 25*B*n + 12*B*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n])) + 12*B*d^4*n*(a + b*x)^4*Log[c + d*x]*(12*A + 25*B*n + 12*B*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n])) + 9*(b*c - a*d)^4*(8*A^2 + 4*A*B*n + B^2*n^2 + 16*A*B*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n]) + 4*B^2*n*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n]) + 8*B^2*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n])^2) - 12*B*(b*c - a*d)*n*Log[a + b*x]*(4*B*d*(b*c - a*d)^2*n*(a + b*x) + 6*B*d^2*(-(b*c) + a*d)*n*(a + b*x)^2 + 12*B*d^3*n*(a + b*x)^3 - 3*(b*c - a*d)^3*(4*A + B*n + 4*B*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n]))) + 12*B*n*Log[c + d*x]*(4*B*d*(b*c - a*d)^3*n*(a + b*x) - 6*B*d^2*(b*c - a*d)^2*n*(a + b*x)^2 + 12*B*d^3*(b*c - a*d)*n*(a + b*x)^3 - 12*B*(b*c - a*d)^4*n*Log[a + b*x] + 12*B*d^4*n*(a + b*x)^4*Log[a + b*x] - 3*(b*c - a*d)^4*(4*A + B*n + 4*B*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n]))))/(b*(b*c - a*d)^4*(a + b*x)^4)","A",1
164,1,9054,809,10.008281,"\int (a+b x)^3 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 \, dx","Integrate[(a + b*x)^3*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3,x]","\text{Result too large to show}","-\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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\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{Li}_3\left(\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,"Result too large to show","B",1
165,1,5668,614,4.2163545,"\int (a+b x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 \, dx","Integrate[(a + b*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3,x]","\text{Result too large to show}","\frac{2 B^2 n^2 (b c-a d)^3 \text{Li}_2\left(\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^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{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{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{(a+b x)^3 \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{3 b}+\frac{4 B^3 n^3 (b c-a d)^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b d^3}+\frac{B^3 n^3 (b c-a d)^3 \text{Li}_2\left(\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{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b d^3}-\frac{B^3 n^3 (b c-a d)^3 \log (c+d x)}{b d^3}",1,"Result too large to show","B",1
166,1,3813,376,3.0882459,"\int (a+b x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 \, dx","Integrate[(a + b*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3,x]","\text{Result too large to show}","-\frac{3 B^2 n^2 (b c-a d)^2 \text{Li}_2\left(\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^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}-\frac{3 B^3 n^3 (b c-a d)^2 \text{Li}_2\left(\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{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}",1,"(4*a^2*B^3*d^2*n^3*Log[a + b*x]^3 - 6*a^2*B^2*d^2*n^2*Log[a + b*x]^2*(2*A - B*n + 2*B*n*Log[c + d*x] + 2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n]) + 6*a^2*B*d^2*n*Log[a + b*x]*(2*A^2 - 2*A*B*n + B^2*n^2 + 2*B^2*n^2*Log[c + d*x]^2 - 2*B*(-2*A + B*n)*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 2*B*n*Log[c + d*x]*(2*A - B*n + 2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])) + b*(4*B^3*c*(b*c - 2*a*d)*n^3*Log[c + d*x]^3 + 6*B^2*d^2*n^2*x*(2*a + b*x)*Log[c + d*x]^2*(2*A - B*n + 2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n]) + 6*B*d^2*n*x*(2*a + b*x)*Log[c + d*x]*(2*A^2 - 2*A*B*n + B^2*n^2 - 2*B*(-2*A + B*n)*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2) + d^2*x*(2*a + b*x)*(4*A^3 - 6*A^2*B*n + 6*A*B^2*n^2 - 3*B^3*n^3 + 6*B*(2*A^2 - 2*A*B*n + B^2*n^2)*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 6*B^2*(-2*A + B*n)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 4*B^3*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3)))/(8*b*d^2) - (3*B*n*(-8*a*A*b*B*c*d*n + 16*a^2*A*B*d^2*n - 8*b^2*B^2*c^2*n^2 + 16*a*b*B^2*c*d*n^2 - 8*a^2*B^2*d^2*n^2 + 4*A^2*b^2*c*d*x - 8*a*A^2*b*d^2*x + 4*a*A*b*B*d^2*n*x - 2*a*b*B^2*d^2*n^2*x - 2*A^2*b^2*d^2*x^2 + 2*A*b^2*B*d^2*n*x^2 - b^2*B^2*d^2*n^2*x^2 + 8*a*A*b*B*c*d*n*Log[a + b*x] - 12*a^2*A*B*d^2*n*Log[a + b*x] + 8*a*b*B^2*c*d*n^2*Log[a + b*x] - 14*a^2*B^2*d^2*n^2*Log[a + b*x] - 4*a*b*B^2*c*d*n^2*Log[a + b*x]^2 + 6*a^2*B^2*d^2*n^2*Log[a + b*x]^2 - 4*A^2*b^2*c^2*Log[c + d*x] + 8*a*A^2*b*c*d*Log[c + d*x] - 8*A*b^2*B*c^2*n*Log[c + d*x] + 8*a*A*b*B*c*d*n*Log[c + d*x] - 8*a*b*B^2*c*d*n^2*Log[c + d*x] + 16*a^2*B^2*d^2*n^2*Log[c + d*x] + 8*a*A^2*b*d^2*x*Log[c + d*x] - 8*a*A*b*B*d^2*n*x*Log[c + d*x] + 4*a*b*B^2*d^2*n^2*x*Log[c + d*x] + 4*A^2*b^2*d^2*x^2*Log[c + d*x] - 4*A*b^2*B*d^2*n*x^2*Log[c + d*x] + 2*b^2*B^2*d^2*n^2*x^2*Log[c + d*x] + 8*A*b^2*B*c^2*n*Log[a + b*x]*Log[c + d*x] - 16*a*A*b*B*c*d*n*Log[a + b*x]*Log[c + d*x] + 8*a^2*A*B*d^2*n*Log[a + b*x]*Log[c + d*x] - 4*b^2*B^2*c^2*n^2*Log[a + b*x]*Log[c + d*x] + 16*a*b*B^2*c*d*n^2*Log[a + b*x]*Log[c + d*x] - 16*a^2*B^2*d^2*n^2*Log[a + b*x]*Log[c + d*x] - 4*b^2*B^2*c^2*n^2*Log[a + b*x]^2*Log[c + d*x] + 8*a*b*B^2*c*d*n^2*Log[a + b*x]^2*Log[c + d*x] - 4*a^2*B^2*d^2*n^2*Log[a + b*x]^2*Log[c + d*x] + 12*b^2*B^2*c^2*n^2*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] - 24*a*b*B^2*c*d*n^2*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] + 12*a^2*B^2*d^2*n^2*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] - 4*A*b^2*B*c^2*n*Log[c + d*x]^2 + 8*a*A*b*B*c*d*n*Log[c + d*x]^2 - 4*b^2*B^2*c^2*n^2*Log[c + d*x]^2 + 4*a*b*B^2*c*d*n^2*Log[c + d*x]^2 + 8*a*A*b*B*d^2*n*x*Log[c + d*x]^2 - 4*a*b*B^2*d^2*n^2*x*Log[c + d*x]^2 + 4*A*b^2*B*d^2*n*x^2*Log[c + d*x]^2 - 2*b^2*B^2*d^2*n^2*x^2*Log[c + d*x]^2 + 8*b^2*B^2*c^2*n^2*Log[a + b*x]*Log[c + d*x]^2 - 16*a*b*B^2*c*d*n^2*Log[a + b*x]*Log[c + d*x]^2 + 8*a^2*B^2*d^2*n^2*Log[a + b*x]*Log[c + d*x]^2 - 4*b^2*B^2*c^2*n^2*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x]^2 + 8*a*b*B^2*c*d*n^2*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x]^2 - 4*a^2*B^2*d^2*n^2*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x]^2 - 8*A*b^2*B*c^2*n*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] + 16*a*A*b*B*c*d*n*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] - 8*a^2*A*B*d^2*n*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] + 4*b^2*B^2*c^2*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] - 8*a*b*B^2*c*d*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] + 4*a^2*B^2*d^2*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] + 4*b^2*B^2*c^2*n^2*Log[a + b*x]^2*Log[(b*(c + d*x))/(b*c - a*d)] - 8*a*b*B^2*c*d*n^2*Log[a + b*x]^2*Log[(b*(c + d*x))/(b*c - a*d)] + 4*a^2*B^2*d^2*n^2*Log[a + b*x]^2*Log[(b*(c + d*x))/(b*c - a*d)] - 8*b^2*B^2*c^2*n^2*Log[a + b*x]*Log[c + d*x]*Log[(b*(c + d*x))/(b*c - a*d)] + 16*a*b*B^2*c*d*n^2*Log[a + b*x]*Log[c + d*x]*Log[(b*(c + d*x))/(b*c - a*d)] - 8*a^2*B^2*d^2*n^2*Log[a + b*x]*Log[c + d*x]*Log[(b*(c + d*x))/(b*c - a*d)] - 8*a*b*B^2*c*d*n*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 16*a^2*B^2*d^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 8*A*b^2*B*c*d*x*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 16*a*A*b*B*d^2*x*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 4*a*b*B^2*d^2*n*x*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 4*A*b^2*B*d^2*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*b^2*B^2*d^2*n*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 8*a*b*B^2*c*d*n*Log[a + b*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 12*a^2*B^2*d^2*n*Log[a + b*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 8*A*b^2*B*c^2*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 16*a*A*b*B*c*d*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 8*b^2*B^2*c^2*n*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 8*a*b*B^2*c*d*n*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 16*a*A*b*B*d^2*x*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 8*a*b*B^2*d^2*n*x*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 8*A*b^2*B*d^2*x^2*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 4*b^2*B^2*d^2*n*x^2*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 8*b^2*B^2*c^2*n*Log[a + b*x]*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 16*a*b*B^2*c*d*n*Log[a + b*x]*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 8*a^2*B^2*d^2*n*Log[a + b*x]*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 4*b^2*B^2*c^2*n*Log[c + d*x]^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 8*a*b*B^2*c*d*n*Log[c + d*x]^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 8*a*b*B^2*d^2*n*x*Log[c + d*x]^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 4*b^2*B^2*d^2*n*x^2*Log[c + d*x]^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 8*b^2*B^2*c^2*n*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 16*a*b*B^2*c*d*n*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 8*a^2*B^2*d^2*n*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 4*b^2*B^2*c*d*x*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 - 8*a*b*B^2*d^2*x*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 - 2*b^2*B^2*d^2*x^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 - 4*b^2*B^2*c^2*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 8*a*b*B^2*c*d*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 8*a*b*B^2*d^2*x*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 4*b^2*B^2*d^2*x^2*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 - 4*B*(b*c - a*d)^2*n*(2*A - B*n + 2*B*n*Log[c + d*x] + 2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] - 4*B^2*(b*c - a*d)^2*n^2*(-3 + 2*Log[c + d*x])*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 8*b^2*B^2*c^2*n^2*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)] - 16*a*b*B^2*c*d*n^2*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)] + 8*a^2*B^2*d^2*n^2*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)] + 8*b^2*B^2*c^2*n^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)] - 16*a*b*B^2*c*d*n^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)] + 8*a^2*B^2*d^2*n^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)]))/(8*b*d^2)","B",1
167,1,2513,186,0.9860365,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{a+b x} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(a + b*x),x]","\text{Result too large to show}","\frac{6 B^2 n^2 \text{Li}_3\left(\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{Li}_2\left(\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{\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}+\frac{6 B^3 n^3 \text{Li}_4\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b}",1,"(4*A^3*Log[a + b*x] - 6*A^2*B*n*Log[a + b*x]^2 + 4*A*B^2*n^2*Log[a + b*x]^3 - B^3*n^3*Log[a + b*x]^4 + B^3*n^3*Log[(d*(a + b*x))/(-(b*c) + a*d)]^4 - 4*B^3*n^3*Log[(d*(a + b*x))/(-(b*c) + a*d)]^3*Log[-((d*(a + b*x))/(b*(c + d*x)))] + 6*B^3*n^3*Log[(d*(a + b*x))/(-(b*c) + a*d)]^2*Log[-((d*(a + b*x))/(b*(c + d*x)))]^2 - 4*B^3*n^3*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[-((d*(a + b*x))/(b*(c + d*x)))]^3 + B^3*n^3*Log[-((d*(a + b*x))/(b*(c + d*x)))]^4 - 12*A*B^2*n^2*Log[a + b*x]*Log[c + d*x]^2 + 12*B^3*n^3*Log[a + b*x]^2*Log[c + d*x]^2 + 12*A*B^2*n^2*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x]^2 - 12*B^3*n^3*Log[a + b*x]*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x]^2 - 8*B^3*n^3*Log[a + b*x]*Log[c + d*x]^3 + 8*B^3*n^3*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x]^3 + 12*A^2*B*n*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] - 12*A*B^2*n^2*Log[a + b*x]^2*Log[(b*(c + d*x))/(b*c - a*d)] + 4*B^3*n^3*Log[a + b*x]^3*Log[(b*(c + d*x))/(b*c - a*d)] + 8*B^3*n^3*Log[(d*(a + b*x))/(-(b*c) + a*d)]^3*Log[(b*(c + d*x))/(b*c - a*d)] - 12*B^3*n^3*Log[(d*(a + b*x))/(-(b*c) + a*d)]^2*Log[-((d*(a + b*x))/(b*(c + d*x)))]*Log[(b*(c + d*x))/(b*c - a*d)] + 24*A*B^2*n^2*Log[a + b*x]*Log[c + d*x]*Log[(b*(c + d*x))/(b*c - a*d)] - 24*B^3*n^3*Log[a + b*x]^2*Log[c + d*x]*Log[(b*(c + d*x))/(b*c - a*d)] + 12*B^3*n^3*Log[a + b*x]*Log[c + d*x]^2*Log[(b*(c + d*x))/(b*c - a*d)] + 6*B^3*n^3*Log[a + b*x]^2*Log[(b*(c + d*x))/(b*c - a*d)]^2 + 12*B^3*n^3*Log[a + b*x]*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[(b*(c + d*x))/(b*c - a*d)]^2 - 18*B^3*n^3*Log[(d*(a + b*x))/(-(b*c) + a*d)]^2*Log[(b*(c + d*x))/(b*c - a*d)]^2 + 12*A^2*B*Log[a + b*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 12*A*B^2*n*Log[a + b*x]^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 4*B^3*n^2*Log[a + b*x]^3*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 12*B^3*n^2*Log[a + b*x]*Log[c + d*x]^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 12*B^3*n^2*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x]^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 24*A*B^2*n*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 12*B^3*n^2*Log[a + b*x]^2*Log[(b*(c + d*x))/(b*c - a*d)]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 24*B^3*n^2*Log[a + b*x]*Log[c + d*x]*Log[(b*(c + d*x))/(b*c - a*d)]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 12*A*B^2*Log[a + b*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 - 6*B^3*n*Log[a + b*x]^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 12*B^3*n*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 4*B^3*Log[a + b*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3 - 4*B^3*n^3*Log[-((d*(a + b*x))/(b*(c + d*x)))]^3*Log[(b*c - a*d)/(b*c + b*d*x)] + 12*B*n*(A^2 + B^2*n^2*Log[(d*(a + b*x))/(-(b*c) + a*d)]^2 + B^2*n^2*Log[c + d*x]^2 + 2*B^2*n^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] - 2*B^2*n^2*Log[(d*(a + b*x))/(-(b*c) + a*d)]*(Log[-((d*(a + b*x))/(b*(c + d*x)))] + Log[(b*(c + d*x))/(b*c - a*d)]) + 2*A*B*Log[(e*(a + b*x)^n)/(c + d*x)^n] + B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 2*B*n*Log[c + d*x]*(A - B*n*Log[a + b*x] + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]))*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] - 12*B^3*n^3*Log[-((d*(a + b*x))/(b*(c + d*x)))]^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] + 12*B^3*n^3*Log[(d*(a + b*x))/(-(b*c) + a*d)]^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 24*B^3*n^3*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[-((d*(a + b*x))/(b*(c + d*x)))]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 12*B^3*n^3*Log[-((d*(a + b*x))/(b*(c + d*x)))]^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 24*A*B^2*n^2*Log[c + d*x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 24*B^3*n^3*Log[a + b*x]*Log[c + d*x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 12*B^3*n^3*Log[c + d*x]^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 24*B^3*n^3*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 24*B^3*n^3*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[(b*(c + d*x))/(b*c - a*d)]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 24*B^3*n^2*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 24*A*B^2*n^2*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)] + 24*B^3*n^3*Log[-((d*(a + b*x))/(b*(c + d*x)))]*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)] - 24*B^3*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)] + 24*B^3*n^3*Log[-((d*(a + b*x))/(b*(c + d*x)))]*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] - 24*A*B^2*n^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)] + 24*B^3*n^3*Log[-((d*(a + b*x))/(b*(c + d*x)))]*PolyLog[3, (b*(c + d*x))/(b*c - a*d)] - 24*B^3*n^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[3, (b*(c + d*x))/(b*c - a*d)] - 24*B^3*n^3*PolyLog[4, (d*(a + b*x))/(b*(c + d*x))])/(4*b)","B",1
168,1,524,184,0.7880921,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(a+b x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(a + b*x)^2,x]","\frac{-3 B d n (a+b x) \log (a+b x) \left(2 B (A+B n) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 B n \log (c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A+B n\right)+B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+A^2+2 A B n+B^2 n^2 \log ^2(c+d x)+2 B^2 n^2\right)+3 B d n (a+b x) \log (c+d x) \left(2 B (A+B n) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+A^2+2 A B n+2 B^2 n^2\right)-(b c-a d) \left(3 B \left(A^2+2 A B n+2 B^2 n^2\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+3 B^2 (A+B n) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+B^3 \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)+A^3+3 A^2 B n+6 A B^2 n^2+6 B^3 n^3\right)+3 B^2 d n^2 (a+b x) \log ^2(a+b x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A+B n \log (c+d x)+B n\right)+3 B^2 d n^2 (a+b x) \log ^2(c+d x) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A+B n\right)+B^3 d n^3 (a+b x) \log ^3(c+d x)-B^3 d n^3 (a+b x) \log ^3(a+b x)}{b (a+b x) (b c-a d)}","-\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,"(-(B^3*d*n^3*(a + b*x)*Log[a + b*x]^3) + B^3*d*n^3*(a + b*x)*Log[c + d*x]^3 + 3*B^2*d*n^2*(a + b*x)*Log[c + d*x]^2*(A + B*n + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]) + 3*B^2*d*n^2*(a + b*x)*Log[a + b*x]^2*(A + B*n + B*n*Log[c + d*x] + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]) + 3*B*d*n*(a + b*x)*Log[c + d*x]*(A^2 + 2*A*B*n + 2*B^2*n^2 + 2*B*(A + B*n)*Log[(e*(a + b*x)^n)/(c + d*x)^n] + B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2) - (b*c - a*d)*(A^3 + 3*A^2*B*n + 6*A*B^2*n^2 + 6*B^3*n^3 + 3*B*(A^2 + 2*A*B*n + 2*B^2*n^2)*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 3*B^2*(A + B*n)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + B^3*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3) - 3*B*d*n*(a + b*x)*Log[a + b*x]*(A^2 + 2*A*B*n + 2*B^2*n^2 + B^2*n^2*Log[c + d*x]^2 + 2*B*(A + B*n)*Log[(e*(a + b*x)^n)/(c + d*x)^n] + B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 2*B*n*Log[c + d*x]*(A + B*n + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])))/(b*(b*c - a*d)*(a + b*x))","B",1
169,1,693,390,1.1840233,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(a+b x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(a + b*x)^3,x]","-\frac{-6 B d^2 n (a+b x)^2 \log (a+b x) \left(2 B (2 A+3 B n) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 B n \log (c+d x) \left(2 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 A+3 B n\right)+2 B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+2 A^2+6 A B n+2 B^2 n^2 \log ^2(c+d x)+7 B^2 n^2\right)+6 B d^2 n (a+b x)^2 \log (c+d x) \left(2 B (2 A+3 B n) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+2 A^2+6 A B n+7 B^2 n^2\right)+(b c-a d) \left(4 A^3 (b c-a d)+6 B \left(2 A^2 (b c-a d)+2 A B n (b (c-2 d x)-3 a d)+B^2 n^2 (b (c-6 d x)-7 a d)\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+6 A^2 B n (b (c-2 d x)-3 a d)+6 B^2 (2 A (b c-a d)+B n (b (c-2 d x)-3 a d)) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+6 A B^2 n^2 (b (c-6 d x)-7 a d)+4 B^3 (b c-a d) \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)+3 B^3 n^3 (b (c-14 d x)-15 a d)\right)+6 B^2 d^2 n^2 (a+b x)^2 \log ^2(a+b x) \left(2 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 A+2 B n \log (c+d x)+3 B n\right)+6 B^2 d^2 n^2 (a+b x)^2 \log ^2(c+d x) \left(2 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 A+3 B n\right)+4 B^3 d^2 n^3 (a+b x)^2 \log ^3(c+d x)-4 B^3 d^2 n^3 (a+b x)^2 \log ^3(a+b x)}{8 b (a+b x)^2 (b c-a d)^2}","-\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,"-1/8*(-4*B^3*d^2*n^3*(a + b*x)^2*Log[a + b*x]^3 + 4*B^3*d^2*n^3*(a + b*x)^2*Log[c + d*x]^3 + 6*B^2*d^2*n^2*(a + b*x)^2*Log[c + d*x]^2*(2*A + 3*B*n + 2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n]) + 6*B^2*d^2*n^2*(a + b*x)^2*Log[a + b*x]^2*(2*A + 3*B*n + 2*B*n*Log[c + d*x] + 2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n]) + 6*B*d^2*n*(a + b*x)^2*Log[c + d*x]*(2*A^2 + 6*A*B*n + 7*B^2*n^2 + 2*B*(2*A + 3*B*n)*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2) + (b*c - a*d)*(4*A^3*(b*c - a*d) + 3*B^3*n^3*(-15*a*d + b*(c - 14*d*x)) + 6*A*B^2*n^2*(-7*a*d + b*(c - 6*d*x)) + 6*A^2*B*n*(-3*a*d + b*(c - 2*d*x)) + 6*B*(2*A^2*(b*c - a*d) + B^2*n^2*(-7*a*d + b*(c - 6*d*x)) + 2*A*B*n*(-3*a*d + b*(c - 2*d*x)))*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 6*B^2*(2*A*(b*c - a*d) + B*n*(-3*a*d + b*(c - 2*d*x)))*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 4*B^3*(b*c - a*d)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3) - 6*B*d^2*n*(a + b*x)^2*Log[a + b*x]*(2*A^2 + 6*A*B*n + 7*B^2*n^2 + 2*B^2*n^2*Log[c + d*x]^2 + 2*B*(2*A + 3*B*n)*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 2*B*n*Log[c + d*x]*(2*A + 3*B*n + 2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])))/(b*(b*c - a*d)^2*(a + b*x)^2)","A",1
170,1,1003,611,1.5032038,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(a+b x)^4} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(a + b*x)^4,x]","\frac{-36 B^3 d^3 n^3 \log ^3(a+b x) (a+b x)^3+36 B^3 d^3 n^3 \log ^3(c+d x) (a+b x)^3+18 B^2 d^3 n^2 \log ^2(c+d x) \left(6 A+11 B n+6 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) (a+b x)^3+18 B^2 d^3 n^2 \log ^2(a+b x) \left(6 A+11 B n+6 B n \log (c+d x)+6 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) (a+b x)^3+6 B d^3 n \log (c+d x) \left(18 A^2+66 B n A+85 B^2 n^2+18 B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+6 B (6 A+11 B n) \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) (a+b x)^3-6 B d^3 n \log (a+b x) \left(18 A^2+66 B n A+85 B^2 n^2+18 B^2 n^2 \log ^2(c+d x)+18 B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+6 B (6 A+11 B n) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+6 B n \log (c+d x) \left(6 A+11 B n+6 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)\right) (a+b x)^3-(b c-a d) \left(36 b^2 c^2 A^3+36 a^2 d^2 A^3-72 a b c d A^3+108 b^2 B d^2 n x^2 A^2+36 b^2 B c^2 n A^2+198 a^2 B d^2 n A^2-126 a b B c d n A^2+270 a b B d^2 n x A^2-54 b^2 B c d n x A^2+24 b^2 B^2 c^2 n^2 A+510 a^2 B^2 d^2 n^2 A-138 a b B^2 c d n^2 A+396 b^2 B^2 d^2 n^2 x^2 A+882 a b B^2 d^2 n^2 x A-90 b^2 B^2 c d n^2 x A+8 b^2 B^3 c^2 n^3+575 a^2 B^3 d^2 n^3-73 a b B^3 c d n^3+36 B^3 (b c-a d)^2 \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)+510 b^2 B^3 d^2 n^3 x^2+18 B^2 \left(6 A (b c-a d)^2+B n \left(\left(2 c^2-3 d x c+6 d^2 x^2\right) b^2+a d (15 d x-7 c) b+11 a^2 d^2\right)\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+1077 a b B^3 d^2 n^3 x-57 b^2 B^3 c d n^3 x+6 B \left(18 A^2 (b c-a d)^2+6 A B n \left(\left(2 c^2-3 d x c+6 d^2 x^2\right) b^2+a d (15 d x-7 c) b+11 a^2 d^2\right)+B^2 n^2 \left(\left(4 c^2-15 d x c+66 d^2 x^2\right) b^2+a d (147 d x-23 c) b+85 a^2 d^2\right)\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)}{108 b (b c-a d)^3 (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,"(-36*B^3*d^3*n^3*(a + b*x)^3*Log[a + b*x]^3 + 36*B^3*d^3*n^3*(a + b*x)^3*Log[c + d*x]^3 + 18*B^2*d^3*n^2*(a + b*x)^3*Log[c + d*x]^2*(6*A + 11*B*n + 6*B*Log[(e*(a + b*x)^n)/(c + d*x)^n]) + 18*B^2*d^3*n^2*(a + b*x)^3*Log[a + b*x]^2*(6*A + 11*B*n + 6*B*n*Log[c + d*x] + 6*B*Log[(e*(a + b*x)^n)/(c + d*x)^n]) + 6*B*d^3*n*(a + b*x)^3*Log[c + d*x]*(18*A^2 + 66*A*B*n + 85*B^2*n^2 + 6*B*(6*A + 11*B*n)*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 18*B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2) - (b*c - a*d)*(36*A^3*b^2*c^2 - 72*a*A^3*b*c*d + 36*a^2*A^3*d^2 + 36*A^2*b^2*B*c^2*n - 126*a*A^2*b*B*c*d*n + 198*a^2*A^2*B*d^2*n + 24*A*b^2*B^2*c^2*n^2 - 138*a*A*b*B^2*c*d*n^2 + 510*a^2*A*B^2*d^2*n^2 + 8*b^2*B^3*c^2*n^3 - 73*a*b*B^3*c*d*n^3 + 575*a^2*B^3*d^2*n^3 - 54*A^2*b^2*B*c*d*n*x + 270*a*A^2*b*B*d^2*n*x - 90*A*b^2*B^2*c*d*n^2*x + 882*a*A*b*B^2*d^2*n^2*x - 57*b^2*B^3*c*d*n^3*x + 1077*a*b*B^3*d^2*n^3*x + 108*A^2*b^2*B*d^2*n*x^2 + 396*A*b^2*B^2*d^2*n^2*x^2 + 510*b^2*B^3*d^2*n^3*x^2 + 6*B*(18*A^2*(b*c - a*d)^2 + 6*A*B*n*(11*a^2*d^2 + a*b*d*(-7*c + 15*d*x) + b^2*(2*c^2 - 3*c*d*x + 6*d^2*x^2)) + B^2*n^2*(85*a^2*d^2 + a*b*d*(-23*c + 147*d*x) + b^2*(4*c^2 - 15*c*d*x + 66*d^2*x^2)))*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 18*B^2*(6*A*(b*c - a*d)^2 + B*n*(11*a^2*d^2 + a*b*d*(-7*c + 15*d*x) + b^2*(2*c^2 - 3*c*d*x + 6*d^2*x^2)))*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 36*B^3*(b*c - a*d)^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3) - 6*B*d^3*n*(a + b*x)^3*Log[a + b*x]*(18*A^2 + 66*A*B*n + 85*B^2*n^2 + 18*B^2*n^2*Log[c + d*x]^2 + 6*B*(6*A + 11*B*n)*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 18*B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 6*B*n*Log[c + d*x]*(6*A + 11*B*n + 6*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])))/(108*b*(b*c - a*d)^3*(a + b*x)^3)","A",1
171,1,1370,830,2.2178563,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(a+b x)^5} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(a + b*x)^5,x]","-\frac{-288 B^3 d^4 n^3 \log ^3(a+b x) (a+b x)^4+288 B^3 d^4 n^3 \log ^3(c+d x) (a+b x)^4+72 B^2 d^4 n^2 \log ^2(c+d x) \left(12 A+25 B n+12 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) (a+b x)^4+72 B^2 d^4 n^2 \log ^2(a+b x) \left(12 A+25 B n+12 B n \log (c+d x)+12 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) (a+b x)^4+12 B d^4 n \log (c+d x) \left(72 A^2+300 B n A+415 B^2 n^2+72 B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+12 B (12 A+25 B n) \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) (a+b x)^4-12 B d^4 n \log (a+b x) \left(72 A^2+300 B n A+415 B^2 n^2+72 B^2 n^2 \log ^2(c+d x)+72 B^2 \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+12 B (12 A+25 B n) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+12 B n \log (c+d x) \left(12 A+25 B n+12 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)\right) (a+b x)^4+(b c-a d) \left(288 b^3 c^3 A^3-288 a^3 d^3 A^3+864 a^2 b c d^2 A^3-864 a b^2 c^2 d A^3-864 b^3 B d^3 n x^3 A^2-3024 a b^2 B d^3 n x^2 A^2+432 b^3 B c d^2 n x^2 A^2+216 b^3 B c^3 n A^2-1800 a^3 B d^3 n A^2+1656 a^2 b B c d^2 n A^2-936 a b^2 B c^2 d n A^2-3744 a^2 b B d^3 n x A^2+1440 a b^2 B c d^2 n x A^2-288 b^3 B c^2 d n x A^2-3600 b^3 B^2 d^3 n^2 x^3 A+108 b^3 B^2 c^3 n^2 A-4980 a^3 B^2 d^3 n^2 A+1932 a^2 b B^2 c d^2 n^2 A-660 a b^2 B^2 c^2 d n^2 A-11736 a b^2 B^2 d^3 n^2 x^2 A+936 b^3 B^2 c d^2 n^2 x^2 A-13008 a^2 b B^2 d^3 n^2 x A+2544 a b^2 B^2 c d^2 n^2 x A-336 b^3 B^2 c^2 d n^2 x A+27 b^3 B^3 c^3 n^3-5845 a^3 B^3 d^3 n^3+1067 a^2 b B^3 c d^2 n^3-229 a b^2 B^3 c^2 d n^3-4980 b^3 B^3 d^3 n^3 x^3+288 B^3 (b c-a d)^3 \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)-15630 a b^2 B^3 d^3 n^3 x^2+690 b^3 B^3 c d^2 n^3 x^2+72 B^2 \left(12 A (b c-a d)^3+B n \left(\left(3 c^3-4 d x c^2+6 d^2 x^2 c-12 d^3 x^3\right) b^3+a d \left(-13 c^2+20 d x c-42 d^2 x^2\right) b^2+a^2 d^2 (23 c-52 d x) b-25 a^3 d^3\right)\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)-16468 a^2 b B^3 d^3 n^3 x+1676 a b^2 B^3 c d^2 n^3 x-148 b^3 B^3 c^2 d n^3 x+12 B \left(72 A^2 (b c-a d)^3+B^2 n^2 \left(\left(9 c^3-28 d x c^2+78 d^2 x^2 c-300 d^3 x^3\right) b^3+a d \left(-55 c^2+212 d x c-978 d^2 x^2\right) b^2+a^2 d^2 (161 c-1084 d x) b-415 a^3 d^3\right)+12 A B n \left(\left(3 c^3-4 d x c^2+6 d^2 x^2 c-12 d^3 x^3\right) b^3+a d \left(-13 c^2+20 d x c-42 d^2 x^2\right) b^2+a^2 d^2 (23 c-52 d x) b-25 a^3 d^3\right)\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)}{1152 b (b c-a d)^4 (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,"-1/1152*(-288*B^3*d^4*n^3*(a + b*x)^4*Log[a + b*x]^3 + 288*B^3*d^4*n^3*(a + b*x)^4*Log[c + d*x]^3 + 72*B^2*d^4*n^2*(a + b*x)^4*Log[c + d*x]^2*(12*A + 25*B*n + 12*B*Log[(e*(a + b*x)^n)/(c + d*x)^n]) + 72*B^2*d^4*n^2*(a + b*x)^4*Log[a + b*x]^2*(12*A + 25*B*n + 12*B*n*Log[c + d*x] + 12*B*Log[(e*(a + b*x)^n)/(c + d*x)^n]) + 12*B*d^4*n*(a + b*x)^4*Log[c + d*x]*(72*A^2 + 300*A*B*n + 415*B^2*n^2 + 12*B*(12*A + 25*B*n)*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 72*B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2) + (b*c - a*d)*(288*A^3*b^3*c^3 - 864*a*A^3*b^2*c^2*d + 864*a^2*A^3*b*c*d^2 - 288*a^3*A^3*d^3 + 216*A^2*b^3*B*c^3*n - 936*a*A^2*b^2*B*c^2*d*n + 1656*a^2*A^2*b*B*c*d^2*n - 1800*a^3*A^2*B*d^3*n + 108*A*b^3*B^2*c^3*n^2 - 660*a*A*b^2*B^2*c^2*d*n^2 + 1932*a^2*A*b*B^2*c*d^2*n^2 - 4980*a^3*A*B^2*d^3*n^2 + 27*b^3*B^3*c^3*n^3 - 229*a*b^2*B^3*c^2*d*n^3 + 1067*a^2*b*B^3*c*d^2*n^3 - 5845*a^3*B^3*d^3*n^3 - 288*A^2*b^3*B*c^2*d*n*x + 1440*a*A^2*b^2*B*c*d^2*n*x - 3744*a^2*A^2*b*B*d^3*n*x - 336*A*b^3*B^2*c^2*d*n^2*x + 2544*a*A*b^2*B^2*c*d^2*n^2*x - 13008*a^2*A*b*B^2*d^3*n^2*x - 148*b^3*B^3*c^2*d*n^3*x + 1676*a*b^2*B^3*c*d^2*n^3*x - 16468*a^2*b*B^3*d^3*n^3*x + 432*A^2*b^3*B*c*d^2*n*x^2 - 3024*a*A^2*b^2*B*d^3*n*x^2 + 936*A*b^3*B^2*c*d^2*n^2*x^2 - 11736*a*A*b^2*B^2*d^3*n^2*x^2 + 690*b^3*B^3*c*d^2*n^3*x^2 - 15630*a*b^2*B^3*d^3*n^3*x^2 - 864*A^2*b^3*B*d^3*n*x^3 - 3600*A*b^3*B^2*d^3*n^2*x^3 - 4980*b^3*B^3*d^3*n^3*x^3 + 12*B*(72*A^2*(b*c - a*d)^3 + B^2*n^2*(-415*a^3*d^3 + a^2*b*d^2*(161*c - 1084*d*x) + a*b^2*d*(-55*c^2 + 212*c*d*x - 978*d^2*x^2) + b^3*(9*c^3 - 28*c^2*d*x + 78*c*d^2*x^2 - 300*d^3*x^3)) + 12*A*B*n*(-25*a^3*d^3 + a^2*b*d^2*(23*c - 52*d*x) + a*b^2*d*(-13*c^2 + 20*c*d*x - 42*d^2*x^2) + b^3*(3*c^3 - 4*c^2*d*x + 6*c*d^2*x^2 - 12*d^3*x^3)))*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 72*B^2*(12*A*(b*c - a*d)^3 + B*n*(-25*a^3*d^3 + a^2*b*d^2*(23*c - 52*d*x) + a*b^2*d*(-13*c^2 + 20*c*d*x - 42*d^2*x^2) + b^3*(3*c^3 - 4*c^2*d*x + 6*c*d^2*x^2 - 12*d^3*x^3)))*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 288*B^3*(b*c - a*d)^3*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3) - 12*B*d^4*n*(a + b*x)^4*Log[a + b*x]*(72*A^2 + 300*A*B*n + 415*B^2*n^2 + 72*B^2*n^2*Log[c + d*x]^2 + 12*B*(12*A + 25*B*n)*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 72*B^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + 12*B*n*Log[c + d*x]*(12*A + 25*B*n + 12*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])))/(b*(b*c - a*d)^4*(a + b*x)^4)","A",1
172,0,0,96,0.086779,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])), x]","F",-1
173,1,142,180,0.1027576,"\int (a g+b g x)^4 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right) \, dx","Integrate[(a*g + b*g*x)^4*(A + B*Log[(e*(c + d*x))/(a + b*x)]),x]","\frac{g^4 \left((a+b x)^5 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)-\frac{B (a d-b c) \left(4 d^3 (a+b x)^3 (a d-b c)+6 d^2 (a+b x)^2 (b c-a d)^2-12 b d x (b c-a d)^3+12 (b c-a d)^4 \log (c+d x)+3 d^4 (a+b x)^4\right)}{12 d^5}\right)}{5 b}","\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 (b c-a d)^5 \log (c+d x)}{5 b d^5}-\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 (a+b x)^4 (b c-a d)}{20 b d}",1,"(g^4*(-1/12*(B*(-(b*c) + a*d)*(-12*b*d*(b*c - a*d)^3*x + 6*d^2*(b*c - a*d)^2*(a + b*x)^2 + 4*d^3*(-(b*c) + a*d)*(a + b*x)^3 + 3*d^4*(a + b*x)^4 + 12*(b*c - a*d)^4*Log[c + d*x]))/d^5 + (a + b*x)^5*(A + B*Log[(e*(c + d*x))/(a + b*x)])))/(5*b)","A",1
174,1,120,149,0.0810404,"\int (a g+b g x)^3 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right) \, dx","Integrate[(a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)]),x]","\frac{g^3 \left((a+b x)^4 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+\frac{B (b c-a d) \left(3 d^2 (a+b x)^2 (a d-b c)+6 b d x (b c-a d)^2-6 (b c-a d)^3 \log (c+d x)+2 d^3 (a+b x)^3\right)}{6 d^4}\right)}{4 b}","\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 (b c-a d)^4 \log (c+d x)}{4 b d^4}+\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 (a+b x)^3 (b c-a d)}{12 b d}",1,"(g^3*((B*(b*c - a*d)*(6*b*d*(b*c - a*d)^2*x + 3*d^2*(-(b*c) + a*d)*(a + b*x)^2 + 2*d^3*(a + b*x)^3 - 6*(b*c - a*d)^3*Log[c + d*x]))/(6*d^4) + (a + b*x)^4*(A + B*Log[(e*(c + d*x))/(a + b*x)])))/(4*b)","A",1
175,1,99,118,0.0518302,"\int (a g+b g x)^2 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right) \, dx","Integrate[(a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)]),x]","\frac{g^2 \left(\frac{B (b c-a d) \left(d \left(a^2 d+4 a b d x+b^2 x (d x-2 c)\right)+2 (b c-a d)^2 \log (c+d x)\right)}{2 d^3}+(a+b x)^3 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)\right)}{3 b}","\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 (b c-a d)^3 \log (c+d x)}{3 b d^3}-\frac{B g^2 x (b c-a d)^2}{3 d^2}+\frac{B g^2 (a+b x)^2 (b c-a d)}{6 b d}",1,"(g^2*((B*(b*c - a*d)*(d*(a^2*d + 4*a*b*d*x + b^2*x*(-2*c + d*x)) + 2*(b*c - a*d)^2*Log[c + d*x]))/(2*d^3) + (a + b*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)])))/(3*b)","A",1
176,1,69,81,0.0382548,"\int (a g+b g x) \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right) \, dx","Integrate[(a*g + b*g*x)*(A + B*Log[(e*(c + d*x))/(a + b*x)]),x]","\frac{g \left((a+b x)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+\frac{B (b c-a d) ((a d-b c) \log (c+d x)+b d x)}{d^2}\right)}{2 b}","\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,"(g*((B*(b*c - a*d)*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]))/d^2 + (a + b*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)])))/(2*b)","A",1
177,1,95,81,0.0433575,"\int \frac{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)}{a g+b g x} \, dx","Integrate[(A + B*Log[(e*(c + d*x))/(a + b*x)])/(a*g + b*g*x),x]","\frac{\log (g (a+b x)) \left(2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)-B \log \left(\frac{b (c+d x)}{b c-a d}\right)+A\right)+B \log (g (a+b x))\right)-2 B \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)}{2 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}-\frac{B \text{Li}_2\left(\frac{b c-a d}{d (a+b x)}+1\right)}{b g}",1,"(Log[g*(a + b*x)]*(B*Log[g*(a + b*x)] + 2*(A - B*Log[(b*(c + d*x))/(b*c - a*d)] + B*Log[(e*(c + d*x))/(a + b*x)])) - 2*B*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(2*b*g)","A",1
178,1,86,64,0.0541256,"\int \frac{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)}{(a g+b g x)^2} \, dx","Integrate[(A + B*Log[(e*(c + d*x))/(a + b*x)])/(a*g + b*g*x)^2,x]","\frac{-(b c-a d) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A-B\right)-B d (a+b x) \log (c+d x)+B d (a+b x) \log (a+b x)}{b g^2 (a+b x) (b c-a d)}","-\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*d*(a + b*x)*Log[a + b*x] - B*d*(a + b*x)*Log[c + d*x] - (b*c - a*d)*(A - B + B*Log[(e*(c + d*x))/(a + b*x)]))/(b*(b*c - a*d)*g^2*(a + b*x))","A",1
179,1,128,144,0.0952011,"\int \frac{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)}{(a g+b g x)^3} \, dx","Integrate[(A + B*Log[(e*(c + d*x))/(a + b*x)])/(a*g + b*g*x)^3,x]","-\frac{(b c-a d) \left(-2 a A d+2 B (b c-a d) \log \left(\frac{e (c+d x)}{a+b x}\right)+3 a B d+2 A b c-b B c+2 b B d x\right)-2 B d^2 (a+b x)^2 \log (c+d x)+2 B d^2 (a+b x)^2 \log (a+b x)}{4 b g^3 (a+b x)^2 (b c-a d)^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,"-1/4*(2*B*d^2*(a + b*x)^2*Log[a + b*x] - 2*B*d^2*(a + b*x)^2*Log[c + d*x] + (b*c - a*d)*(2*A*b*c - b*B*c - 2*a*A*d + 3*a*B*d + 2*b*B*d*x + 2*B*(b*c - a*d)*Log[(e*(c + d*x))/(a + b*x)]))/(b*(b*c - a*d)^2*g^3*(a + b*x)^2)","A",1
180,1,141,175,0.1413932,"\int \frac{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)}{(a g+b g x)^4} \, dx","Integrate[(A + B*Log[(e*(c + d*x))/(a + b*x)])/(a*g + b*g*x)^4,x]","\frac{\frac{B \left((b c-a d) \left(11 a^2 d^2+a b d (15 d x-7 c)+b^2 \left(2 c^2-3 c d x+6 d^2 x^2\right)\right)-6 d^3 (a+b x)^3 \log (c+d x)+6 d^3 (a+b x)^3 \log (a+b x)\right)}{(b c-a d)^3}-6 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}{18 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^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^2}{3 b g^4 (a+b x) (b c-a d)^2}-\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*((b*c - a*d)*(11*a^2*d^2 + a*b*d*(-7*c + 15*d*x) + b^2*(2*c^2 - 3*c*d*x + 6*d^2*x^2)) + 6*d^3*(a + b*x)^3*Log[a + b*x] - 6*d^3*(a + b*x)^3*Log[c + d*x]))/(b*c - a*d)^3 - 6*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/(18*b*g^4*(a + b*x)^3)","A",1
181,1,166,206,0.19182,"\int \frac{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)}{(a g+b g x)^5} \, dx","Integrate[(A + B*Log[(e*(c + d*x))/(a + b*x)])/(a*g + b*g*x)^5,x]","\frac{\frac{B (a d-b c) \left(\frac{12 d^3 (b c-a d)}{a+b x}-\frac{6 d^2 (b c-a d)^2}{(a+b x)^2}+\frac{4 d (b c-a d)^3}{(a+b x)^3}-\frac{3 (b c-a d)^4}{(a+b x)^4}+12 d^4 \log (a+b x)-12 d^4 \log (c+d x)\right)}{12 (b c-a d)^5}-\frac{B \log \left(\frac{e (c+d x)}{a+b x}\right)+A}{(a+b x)^4}}{4 b g^5}","-\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^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^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}{12 b g^5 (a+b x)^3 (b c-a d)}+\frac{B}{16 b g^5 (a+b x)^4}",1,"((B*(-(b*c) + a*d)*((-3*(b*c - a*d)^4)/(a + b*x)^4 + (4*d*(b*c - a*d)^3)/(a + b*x)^3 - (6*d^2*(b*c - a*d)^2)/(a + b*x)^2 + (12*d^3*(b*c - a*d))/(a + b*x) + 12*d^4*Log[a + b*x] - 12*d^4*Log[c + d*x]))/(12*(b*c - a*d)^5) - (A + B*Log[(e*(c + d*x))/(a + b*x)])/(a + b*x)^4)/(4*b*g^5)","A",1
182,1,512,503,0.5056342,"\int (a g+b g x)^4 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2 \, dx","Integrate[(a*g + b*g*x)^4*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2,x]","\frac{g^4 \left((a+b x)^5 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2-\frac{B (b c-a d) \left(-6 d^4 (a+b x)^4 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+8 d^3 (a+b x)^3 (b c-a d) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)-12 d^2 (a+b x)^2 (b c-a d)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)-24 (b c-a d)^4 \log (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+24 A b d x (b c-a d)^3-4 B (b c-a d)^2 \left(2 b d x (b c-a d)-2 (b c-a d)^2 \log (c+d x)-d^2 (a+b x)^2\right)-B (b c-a d) \left(3 d^2 (a+b x)^2 (a d-b c)+6 b d x (b c-a d)^2-6 (b c-a d)^3 \log (c+d x)+2 d^3 (a+b x)^3\right)+24 b B (c+d x) (b c-a d)^3 \log \left(\frac{e (c+d x)}{a+b x}\right)-12 B (b c-a d)^4 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+24 B (b c-a d)^4 \log (a+b x)-12 B (b c-a d)^3 ((a d-b c) \log (c+d x)+b d x)\right)}{12 d^5}\right)}{5 b}","-\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{2 B^2 g^4 (b c-a d)^5 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{5 b d^5}-\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}+\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}",1,"(g^4*((a + b*x)^5*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2 - (B*(b*c - a*d)*(24*A*b*d*(b*c - a*d)^3*x + 24*B*(b*c - a*d)^4*Log[a + b*x] - 4*B*(b*c - a*d)^2*(2*b*d*(b*c - a*d)*x - d^2*(a + b*x)^2 - 2*(b*c - a*d)^2*Log[c + d*x]) - B*(b*c - a*d)*(6*b*d*(b*c - a*d)^2*x + 3*d^2*(-(b*c) + a*d)*(a + b*x)^2 + 2*d^3*(a + b*x)^3 - 6*(b*c - a*d)^3*Log[c + d*x]) - 12*B*(b*c - a*d)^3*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 24*b*B*(b*c - a*d)^3*(c + d*x)*Log[(e*(c + d*x))/(a + b*x)] - 12*d^2*(b*c - a*d)^2*(a + b*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)]) + 8*d^3*(b*c - a*d)*(a + b*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)]) - 6*d^4*(a + b*x)^4*(A + B*Log[(e*(c + d*x))/(a + b*x)]) - 24*(b*c - a*d)^4*Log[c + d*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]) - 12*B*(b*c - a*d)^4*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(12*d^5)))/(5*b)","A",1
183,1,392,420,0.3458947,"\int (a g+b g x)^3 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2 \, dx","Integrate[(a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2,x]","\frac{g^3 \left(\frac{B (b c-a d) \left(2 d^3 (a+b x)^3 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+3 d^2 (a+b x)^2 (a d-b c) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)-6 (b c-a d)^3 \log (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+6 A b d x (b c-a d)^2-B (b c-a d) \left(2 b d x (b c-a d)-2 (b c-a d)^2 \log (c+d x)-d^2 (a+b x)^2\right)+6 b B (c+d x) (b c-a d)^2 \log \left(\frac{e (c+d x)}{a+b x}\right)-3 B (b c-a d)^3 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+6 B (b c-a d)^3 \log (a+b x)-3 B (b c-a d)^2 ((a d-b c) \log (c+d x)+b d x)\right)}{3 d^4}+(a+b x)^4 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2\right)}{4 b}","\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{B^2 g^3 (b c-a d)^4 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{2 b d^4}+\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}-\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}",1,"(g^3*((a + b*x)^4*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2 + (B*(b*c - a*d)*(6*A*b*d*(b*c - a*d)^2*x + 6*B*(b*c - a*d)^3*Log[a + b*x] - B*(b*c - a*d)*(2*b*d*(b*c - a*d)*x - d^2*(a + b*x)^2 - 2*(b*c - a*d)^2*Log[c + d*x]) - 3*B*(b*c - a*d)^2*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 6*b*B*(b*c - a*d)^2*(c + d*x)*Log[(e*(c + d*x))/(a + b*x)] + 3*d^2*(-(b*c) + a*d)*(a + b*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)]) + 2*d^3*(a + b*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)]) - 6*(b*c - a*d)^3*Log[c + d*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]) - 3*B*(b*c - a*d)^3*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(3*d^4)))/(4*b)","A",1
184,1,290,335,0.2382344,"\int (a g+b g x)^2 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2 \, dx","Integrate[(a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2,x]","\frac{g^2 \left((a+b x)^3 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2-\frac{B (b c-a d) \left(-d^2 (a+b x)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)-2 (b c-a d)^2 \log (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+2 A b d x (b c-a d)+2 b B (c+d x) (b c-a d) \log \left(\frac{e (c+d x)}{a+b x}\right)-B (b c-a d)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+2 B (b c-a d)^2 \log (a+b x)-B (b c-a d) ((a d-b c) \log (c+d x)+b d x)\right)}{d^3}\right)}{3 b}","-\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{2 B^2 g^2 (b c-a d)^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{3 b d^3}-\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}+\frac{B^2 g^2 x (b c-a d)^2}{3 d^2}",1,"(g^2*((a + b*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2 - (B*(b*c - a*d)*(2*A*b*d*(b*c - a*d)*x + 2*B*(b*c - a*d)^2*Log[a + b*x] - B*(b*c - a*d)*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 2*b*B*(b*c - a*d)*(c + d*x)*Log[(e*(c + d*x))/(a + b*x)] - d^2*(a + b*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)]) - 2*(b*c - a*d)^2*Log[c + d*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]) - B*(b*c - a*d)^2*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/d^3))/(3*b)","A",1
185,1,203,202,0.179824,"\int (a g+b g x) \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2 \, dx","Integrate[(a*g + b*g*x)*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2,x]","\frac{g \left(\frac{B (b c-a d) \left(-2 (b c-a d) \log (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+2 b B (c+d x) \log \left(\frac{e (c+d x)}{a+b x}\right)-B (b c-a d) \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+2 B (b c-a d) \log (a+b x)+2 A b d x\right)}{d^2}+(a+b x)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2\right)}{2 b}","\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 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}+\frac{B^2 g (b c-a d)^2 \log (a+b x)}{b d^2}",1,"(g*((a + b*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2 + (B*(b*c - a*d)*(2*A*b*d*x + 2*B*(b*c - a*d)*Log[a + b*x] + 2*b*B*(c + d*x)*Log[(e*(c + d*x))/(a + b*x)] - 2*(b*c - a*d)*Log[c + d*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]) - B*(b*c - a*d)*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/d^2))/(2*b)","A",1
186,1,251,128,0.2860447,"\int \frac{\left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2}{a g+b g x} \, dx","Integrate[(A + B*Log[(e*(c + d*x))/(a + b*x)])^2/(a*g + b*g*x),x]","\frac{A^2 \log (a+b x)+2 A B \log (a+b x) \log \left(\frac{e (c+d x)}{a+b x}\right)+2 A B \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-2 A B \log (a+b x) \log \left(\frac{c}{d}+x\right)+2 A B \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)-A B \log ^2\left(\frac{a}{b}+x\right)+2 A B \log \left(\frac{a}{b}+x\right) \log (a+b x)-2 B^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right) \log \left(\frac{e (c+d x)}{a+b x}\right)-B^2 \log \left(\frac{a d-b c}{d (a+b x)}\right) \log ^2\left(\frac{e (c+d x)}{a+b x}\right)+2 B^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b g}","-\frac{2 B \text{Li}_2\left(\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{\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}+\frac{2 B^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b g}",1,"(-(A*B*Log[a/b + x]^2) + A^2*Log[a + b*x] + 2*A*B*Log[a/b + x]*Log[a + b*x] - 2*A*B*Log[c/d + x]*Log[a + b*x] + 2*A*B*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*A*B*Log[a + b*x]*Log[(e*(c + d*x))/(a + b*x)] - B^2*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(e*(c + d*x))/(a + b*x)]^2 + 2*A*B*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 2*B^2*Log[(e*(c + d*x))/(a + b*x)]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] + 2*B^2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))])/(b*g)","A",1
187,1,314,153,0.4760834,"\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","Integrate[(A + B*Log[(e*(c + d*x))/(a + b*x)])^2/(a*g + b*g*x)^2,x]","-\frac{\frac{B \left(-2 (b c-a d) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)-2 d (a+b x) \log (a+b x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+2 d (a+b x) \log (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)-B d (a+b x) \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+B d (a+b x) \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+2 B (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)\right)}{b c-a d}+\left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^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,"-(((A + B*Log[(e*(c + d*x))/(a + b*x)])^2 + (B*(2*B*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - 2*(b*c - a*d)*(A + B*Log[(e*(c + d*x))/(a + b*x)]) - 2*d*(a + b*x)*Log[a + b*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]) + 2*d*(a + b*x)*Log[c + d*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]) - B*d*(a + b*x)*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + B*d*(a + b*x)*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d))/(b*g^2*(a + b*x)))","C",1
188,1,444,296,0.4365423,"\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","Integrate[(A + B*Log[(e*(c + d*x))/(a + b*x)])^2/(a*g + b*g*x)^3,x]","\frac{\frac{B \left(-4 d^2 (a+b x)^2 \log (a+b x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+4 d^2 (a+b x)^2 \log (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+2 (b c-a d)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+4 d (a+b x) (a d-b c) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)-2 B d^2 (a+b x)^2 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+2 B d^2 (a+b x)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-B \left(2 d^2 (a+b x)^2 \log (c+d x)+2 d (a+b x) (a d-b c)+(b c-a d)^2-2 d^2 (a+b x)^2 \log (a+b x)\right)+4 B d (a+b x) (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)\right)}{(b c-a d)^2}-2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^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,"(-2*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2 + (B*(4*B*d*(a + b*x)*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - B*((b*c - a*d)^2 + 2*d*(-(b*c) + a*d)*(a + b*x) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]) + 2*(b*c - a*d)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)]) + 4*d*(-(b*c) + a*d)*(a + b*x)*(A + B*Log[(e*(c + d*x))/(a + b*x)]) - 4*d^2*(a + b*x)^2*Log[a + b*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]) + 4*d^2*(a + b*x)^2*Log[c + d*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]) - 2*B*d^2*(a + b*x)^2*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 2*B*d^2*(a + b*x)^2*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^2)/(4*b*g^3*(a + b*x)^2)","C",1
189,1,585,399,0.6845395,"\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","Integrate[(A + B*Log[(e*(c + d*x))/(a + b*x)])^2/(a*g + b*g*x)^4,x]","-\frac{\frac{B \left(-36 d^3 (a+b x)^3 \log (a+b x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+36 d^3 (a+b x)^3 \log (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+36 d^2 (a+b x)^2 (a d-b c) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)-12 (b c-a d)^3 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+18 d (a+b x) (b c-a d)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)-18 B d^3 (a+b x)^3 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+18 B d^3 (a+b x)^3 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+36 B d^2 (a+b x)^2 (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)-9 B d (a+b x) \left(2 d^2 (a+b x)^2 \log (c+d x)+2 d (a+b x) (a d-b c)+(b c-a d)^2-2 d^2 (a+b x)^2 \log (a+b x)\right)+2 B \left(-6 d^3 (a+b x)^3 \log (c+d x)+6 d^2 (a+b x)^2 (b c-a d)-3 d (a+b x) (b c-a d)^2+2 (b c-a d)^3+6 d^3 (a+b x)^3 \log (a+b x)\right)\right)}{(b c-a d)^3}+18 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{54 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{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^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,"-1/54*(18*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2 + (B*(36*B*d^2*(a + b*x)^2*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - 9*B*d*(a + b*x)*((b*c - a*d)^2 + 2*d*(-(b*c) + a*d)*(a + b*x) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]) + 2*B*(2*(b*c - a*d)^3 - 3*d*(b*c - a*d)^2*(a + b*x) + 6*d^2*(b*c - a*d)*(a + b*x)^2 + 6*d^3*(a + b*x)^3*Log[a + b*x] - 6*d^3*(a + b*x)^3*Log[c + d*x]) - 12*(b*c - a*d)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)]) + 18*d*(b*c - a*d)^2*(a + b*x)*(A + B*Log[(e*(c + d*x))/(a + b*x)]) + 36*d^2*(-(b*c) + a*d)*(a + b*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)]) - 36*d^3*(a + b*x)^3*Log[a + b*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]) + 36*d^3*(a + b*x)^3*Log[c + d*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]) - 18*B*d^3*(a + b*x)^3*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 18*B*d^3*(a + b*x)^3*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^3)/(b*g^4*(a + b*x)^3)","C",1
190,1,748,498,0.9197472,"\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","Integrate[(A + B*Log[(e*(c + d*x))/(a + b*x)])^2/(a*g + b*g*x)^5,x]","\frac{\frac{B \left(-144 d^4 (a+b x)^4 \log (a+b x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+144 d^4 (a+b x)^4 \log (c+d x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+144 d^3 (a+b x)^3 (a d-b c) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+72 d^2 (a+b x)^2 (b c-a d)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+36 (b c-a d)^4 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)+48 d (a+b x) (a d-b c)^3 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)-72 B d^4 (a+b x)^4 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+72 B d^4 (a+b x)^4 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+144 B d^3 (a+b x)^3 (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)-36 B d^2 (a+b x)^2 \left(2 d^2 (a+b x)^2 \log (c+d x)+2 d (a+b x) (a d-b c)+(b c-a d)^2-2 d^2 (a+b x)^2 \log (a+b x)\right)+8 B d (a+b x) \left(-6 d^3 (a+b x)^3 \log (c+d x)+6 d^2 (a+b x)^2 (b c-a d)-3 d (a+b x) (b c-a d)^2+2 (b c-a d)^3+6 d^3 (a+b x)^3 \log (a+b x)\right)-3 B \left(12 d^4 (a+b x)^4 \log (c+d x)+12 d^3 (a+b x)^3 (a d-b c)+6 d^2 (a+b x)^2 (b c-a d)^2+4 d (a+b x) (a d-b c)^3+3 (b c-a d)^4-12 d^4 (a+b x)^4 \log (a+b x)\right)\right)}{(b c-a d)^4}-72 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)^2}{288 b g^5 (a+b x)^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{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 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{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{B^2 d^4 \log ^2\left(\frac{c+d x}{a+b x}\right)}{4 b g^5 (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}",1,"(-72*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2 + (B*(144*B*d^3*(a + b*x)^3*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - 36*B*d^2*(a + b*x)^2*((b*c - a*d)^2 + 2*d*(-(b*c) + a*d)*(a + b*x) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]) + 8*B*d*(a + b*x)*(2*(b*c - a*d)^3 - 3*d*(b*c - a*d)^2*(a + b*x) + 6*d^2*(b*c - a*d)*(a + b*x)^2 + 6*d^3*(a + b*x)^3*Log[a + b*x] - 6*d^3*(a + b*x)^3*Log[c + d*x]) - 3*B*(3*(b*c - a*d)^4 + 4*d*(-(b*c) + a*d)^3*(a + b*x) + 6*d^2*(b*c - a*d)^2*(a + b*x)^2 + 12*d^3*(-(b*c) + a*d)*(a + b*x)^3 - 12*d^4*(a + b*x)^4*Log[a + b*x] + 12*d^4*(a + b*x)^4*Log[c + d*x]) + 36*(b*c - a*d)^4*(A + B*Log[(e*(c + d*x))/(a + b*x)]) + 48*d*(-(b*c) + a*d)^3*(a + b*x)*(A + B*Log[(e*(c + d*x))/(a + b*x)]) + 72*d^2*(b*c - a*d)^2*(a + b*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)]) + 144*d^3*(-(b*c) + a*d)*(a + b*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)]) - 144*d^4*(a + b*x)^4*Log[a + b*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]) + 144*d^4*(a + b*x)^4*Log[c + d*x]*(A + B*Log[(e*(c + d*x))/(a + b*x)]) - 72*B*d^4*(a + b*x)^4*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 72*B*d^4*(a + b*x)^4*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^4)/(288*b*g^5*(a + b*x)^4)","C",1
191,0,0,35,0.6014865,"\int \frac{(a g+b g x)^2}{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)} \, dx","Integrate[(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,"Integrate[(a*g + b*g*x)^2/(A + B*Log[(e*(c + d*x))/(a + b*x)]), x]","A",-1
192,0,0,33,0.2467835,"\int \frac{a g+b g x}{A+B \log \left(\frac{e (c+d x)}{a+b x}\right)} \, dx","Integrate[(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,"Integrate[(a*g + b*g*x)/(A + B*Log[(e*(c + d*x))/(a + b*x)]), x]","A",-1
193,0,0,35,0.2456099,"\int \frac{1}{(a g+b g x) \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)} \, dx","Integrate[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,"Integrate[1/((a*g + b*g*x)*(A + B*Log[(e*(c + d*x))/(a + b*x)])), x]","A",-1
194,1,50,53,0.0678262,"\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","Integrate[1/((a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)])),x]","\frac{e^{-\frac{A}{B}} \text{Ei}\left(\frac{A}{B}+\log \left(\frac{e (c+d x)}{a+b x}\right)\right)}{B e g^2 (a d-b c)}","-\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,"ExpIntegralEi[A/B + Log[(e*(c + d*x))/(a + b*x)]]/(B*(-(b*c) + a*d)*e*E^(A/B)*g^2)","A",1
195,1,89,109,0.1619636,"\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","Integrate[1/((a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)])),x]","\frac{e^{-\frac{2 A}{B}} \left(d e e^{A/B} \text{Ei}\left(\frac{A}{B}+\log \left(\frac{e (c+d x)}{a+b x}\right)\right)-b \text{Ei}\left(\frac{2 \left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)}{B}\right)\right)}{B 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 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,"(d*e*E^(A/B)*ExpIntegralEi[A/B + Log[(e*(c + d*x))/(a + b*x)]] - b*ExpIntegralEi[(2*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/B])/(B*(b*c - a*d)^2*e^2*E^((2*A)/B)*g^3)","A",1
196,0,0,35,1.3976267,"\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","Integrate[(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,"Integrate[(a*g + b*g*x)^2/(A + B*Log[(e*(c + d*x))/(a + b*x)])^2, x]","A",-1
197,0,0,33,0.9701436,"\int \frac{a g+b g x}{\left(A+B \log \left(\frac{e (c+d x)}{a+b x}\right)\right)^2} \, dx","Integrate[(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,"Integrate[(a*g + b*g*x)/(A + B*Log[(e*(c + d*x))/(a + b*x)])^2, x]","A",-1
198,0,0,35,0.5231476,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2), x]","A",-1
199,1,88,104,0.118972,"\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","Integrate[1/((a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2),x]","\frac{\frac{e^{-\frac{A}{B}} \text{Ei}\left(\frac{A}{B}+\log \left(\frac{e (c+d x)}{a+b x}\right)\right)}{e}-\frac{B (c+d x)}{(a+b x) \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}}{B^2 g^2 (a d-b c)}","\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,"(ExpIntegralEi[A/B + Log[(e*(c + d*x))/(a + b*x)]]/(e*E^(A/B)) - (B*(c + d*x))/((a + b*x)*(A + B*Log[(e*(c + d*x))/(a + b*x)])))/(B^2*(-(b*c) + a*d)*g^2)","A",1
200,1,135,159,0.4146467,"\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","Integrate[1/((a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x))/(a + b*x)])^2),x]","\frac{-\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)}{e^2}+\frac{d e^{-\frac{A}{B}} \text{Ei}\left(\frac{A}{B}+\log \left(\frac{e (c+d x)}{a+b x}\right)\right)}{e}+\frac{B (c+d x) (b c-a d)}{(a+b x)^2 \left(B \log \left(\frac{e (c+d x)}{a+b x}\right)+A\right)}}{B^2 g^3 (b c-a d)^2}","-\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,"((d*ExpIntegralEi[A/B + Log[(e*(c + d*x))/(a + b*x)]])/(e*E^(A/B)) - (2*b*ExpIntegralEi[(2*(A + B*Log[(e*(c + d*x))/(a + b*x)]))/B])/(e^2*E^((2*A)/B)) + (B*(b*c - a*d)*(c + d*x))/((a + b*x)^2*(A + B*Log[(e*(c + d*x))/(a + b*x)])))/(B^2*(b*c - a*d)^2*g^3)","A",1
201,1,144,182,0.1011876,"\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","Integrate[(a*g + b*g*x)^4*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]),x]","\frac{g^4 \left((a+b x)^5 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)-\frac{B (a d-b c) \left(4 d^3 (a+b x)^3 (a d-b c)+6 d^2 (a+b x)^2 (b c-a d)^2-12 b d x (b c-a d)^3+12 (b c-a d)^4 \log (c+d x)+3 d^4 (a+b x)^4\right)}{6 d^5}\right)}{5 b}","\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 (b c-a d)^5 \log (c+d x)}{5 b d^5}-\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{B g^4 (a+b x)^4 (b c-a d)}{10 b d}",1,"(g^4*(-1/6*(B*(-(b*c) + a*d)*(-12*b*d*(b*c - a*d)^3*x + 6*d^2*(b*c - a*d)^2*(a + b*x)^2 + 4*d^3*(-(b*c) + a*d)*(a + b*x)^3 + 3*d^4*(a + b*x)^4 + 12*(b*c - a*d)^4*Log[c + d*x]))/d^5 + (a + b*x)^5*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])))/(5*b)","A",1
202,1,122,151,0.0752223,"\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","Integrate[(a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]),x]","\frac{g^3 \left((a+b x)^4 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)+\frac{B (b c-a d) \left(3 d^2 (a+b x)^2 (a d-b c)+6 b d x (b c-a d)^2-6 (b c-a d)^3 \log (c+d x)+2 d^3 (a+b x)^3\right)}{3 d^4}\right)}{4 b}","\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 (b c-a d)^4 \log (c+d x)}{2 b d^4}+\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 (a+b x)^3 (b c-a d)}{6 b d}",1,"(g^3*((B*(b*c - a*d)*(6*b*d*(b*c - a*d)^2*x + 3*d^2*(-(b*c) + a*d)*(a + b*x)^2 + 2*d^3*(a + b*x)^3 - 6*(b*c - a*d)^3*Log[c + d*x]))/(3*d^4) + (a + b*x)^4*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])))/(4*b)","A",1
203,1,98,120,0.0511818,"\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","Integrate[(a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]),x]","\frac{g^2 \left(\frac{B (b c-a d) \left(d \left(a^2 d+4 a b d x+b^2 x (d x-2 c)\right)+2 (b c-a d)^2 \log (c+d x)\right)}{d^3}+(a+b x)^3 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)\right)}{3 b}","\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 (b c-a d)^3 \log (c+d x)}{3 b d^3}-\frac{2 B g^2 x (b c-a d)^2}{3 d^2}+\frac{B g^2 (a+b x)^2 (b c-a d)}{3 b d}",1,"(g^2*((B*(b*c - a*d)*(d*(a^2*d + 4*a*b*d*x + b^2*x*(-2*c + d*x)) + 2*(b*c - a*d)^2*Log[c + d*x]))/d^3 + (a + b*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])))/(3*b)","A",1
204,1,72,78,0.0380501,"\int (a g+b g x) \left(A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)\right) \, dx","Integrate[(a*g + b*g*x)*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]),x]","\frac{g \left((a+b x)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)-\frac{2 B (a d-b c) ((a d-b c) \log (c+d x)+b d x)}{d^2}\right)}{2 b}","\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,"(g*((-2*B*(-(b*c) + a*d)*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]))/d^2 + (a + b*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])))/(2*b)","A",1
205,1,87,83,0.0383348,"\int \frac{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{a g+b g x} \, dx","Integrate[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(a*g + b*g*x),x]","\frac{\log (a+b x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)-2 B \log \left(\frac{b (c+d x)}{b c-a d}\right)+B \log (a+b x)+A\right)-2 B \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\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}-\frac{2 B \text{Li}_2\left(\frac{b c-a d}{d (a+b x)}+1\right)}{b g}",1,"(Log[a + b*x]*(A + B*Log[a + b*x] - 2*B*Log[(b*(c + d*x))/(b*c - a*d)] + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) - 2*B*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*g)","A",1
206,1,89,102,0.0515555,"\int \frac{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{(a g+b g x)^2} \, dx","Integrate[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(a*g + b*g*x)^2,x]","\frac{-(b c-a d) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A-2 B\right)-2 B d (a+b x) \log (c+d x)+2 B d (a+b x) \log (a+b x)}{b g^2 (a+b x) (b c-a d)}","-\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*d*(a + b*x)*Log[a + b*x] - 2*B*d*(a + b*x)*Log[c + d*x] - (b*c - a*d)*(A - 2*B + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(b*(b*c - a*d)*g^2*(a + b*x))","A",1
207,1,128,139,0.092096,"\int \frac{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{(a g+b g x)^3} \, dx","Integrate[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(a*g + b*g*x)^3,x]","-\frac{(b c-a d) \left(-a A d+B (b c-a d) \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+3 a B d+A b c-b B c+2 b B d x\right)-2 B d^2 (a+b x)^2 \log (c+d x)+2 B d^2 (a+b x)^2 \log (a+b x)}{2 b g^3 (a+b x)^2 (b c-a d)^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,"-1/2*(2*B*d^2*(a + b*x)^2*Log[a + b*x] - 2*B*d^2*(a + b*x)^2*Log[c + d*x] + (b*c - a*d)*(A*b*c - b*B*c - a*A*d + 3*a*B*d + 2*b*B*d*x + B*(b*c - a*d)*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(b*(b*c - a*d)^2*g^3*(a + b*x)^2)","A",1
208,1,140,177,0.1037108,"\int \frac{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{(a g+b g x)^4} \, dx","Integrate[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(a*g + b*g*x)^4,x]","\frac{\frac{B \left(-6 d^3 (a+b x)^3 \log (c+d x)+6 d^2 (a+b x)^2 (b c-a d)-3 d (a+b x) (b c-a d)^2+2 (b c-a d)^3+6 d^3 (a+b x)^3 \log (a+b x)\right)}{(b c-a d)^3}-3 \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{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^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{2 B d^2}{3 b g^4 (a+b x) (b c-a d)^2}-\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,"((B*(2*(b*c - a*d)^3 - 3*d*(b*c - a*d)^2*(a + b*x) + 6*d^2*(b*c - a*d)*(a + b*x)^2 + 6*d^3*(a + b*x)^3*Log[a + b*x] - 6*d^3*(a + b*x)^3*Log[c + d*x]))/(b*c - a*d)^3 - 3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(9*b*g^4*(a + b*x)^3)","A",1
209,1,162,208,0.1691121,"\int \frac{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)}{(a g+b g x)^5} \, dx","Integrate[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])/(a*g + b*g*x)^5,x]","\frac{\frac{B \left(12 d^4 (a+b x)^4 \log (c+d x)+12 d^3 (a+b x)^3 (a d-b c)+6 d^2 (a+b x)^2 (b c-a d)^2+4 d (a+b x) (a d-b c)^3+3 (b c-a d)^4-12 d^4 (a+b x)^4 \log (a+b x)\right)}{(b c-a d)^4}-6 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)}{24 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^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^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}{6 b g^5 (a+b x)^3 (b c-a d)}+\frac{B}{8 b g^5 (a+b x)^4}",1,"((B*(3*(b*c - a*d)^4 + 4*d*(-(b*c) + a*d)^3*(a + b*x) + 6*d^2*(b*c - a*d)^2*(a + b*x)^2 + 12*d^3*(-(b*c) + a*d)*(a + b*x)^3 - 12*d^4*(a + b*x)^4*Log[a + b*x] + 12*d^4*(a + b*x)^4*Log[c + d*x]))/(b*c - a*d)^4 - 6*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]))/(24*b*g^5*(a + b*x)^4)","A",1
210,1,524,515,0.4684495,"\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","Integrate[(a*g + b*g*x)^4*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2,x]","\frac{g^4 \left((a+b x)^5 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2-\frac{B (b c-a d) \left(-3 d^4 (a+b x)^4 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)+4 d^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)-6 d^2 (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)-12 (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)+12 A b d x (b c-a d)^3-4 B (b c-a d)^2 \left(2 b d x (b c-a d)-2 (b c-a d)^2 \log (c+d x)-d^2 (a+b x)^2\right)-B (b c-a d) \left(3 d^2 (a+b x)^2 (a d-b c)+6 b d x (b c-a d)^2-6 (b c-a d)^3 \log (c+d x)+2 d^3 (a+b x)^3\right)+12 B d (a+b x) (b c-a d)^3 \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)-12 B (b c-a d)^4 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+24 B (b c-a d)^4 \log (c+d x)-12 B (b c-a d)^3 ((a d-b c) \log (c+d x)+b d x)\right)}{3 d^5}\right)}{5 b}","-\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{8 B^2 g^4 (b c-a d)^5 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{5 b d^5}-\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}+\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}",1,"(g^4*((a + b*x)^5*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2 - (B*(b*c - a*d)*(12*A*b*d*(b*c - a*d)^3*x + 24*B*(b*c - a*d)^4*Log[c + d*x] - 4*B*(b*c - a*d)^2*(2*b*d*(b*c - a*d)*x - d^2*(a + b*x)^2 - 2*(b*c - a*d)^2*Log[c + d*x]) - B*(b*c - a*d)*(6*b*d*(b*c - a*d)^2*x + 3*d^2*(-(b*c) + a*d)*(a + b*x)^2 + 2*d^3*(a + b*x)^3 - 6*(b*c - a*d)^3*Log[c + d*x]) - 12*B*(b*c - a*d)^3*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 12*B*d*(b*c - a*d)^3*(a + b*x)*Log[(e*(c + d*x)^2)/(a + b*x)^2] - 6*d^2*(b*c - a*d)^2*(a + b*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) + 4*d^3*(b*c - a*d)*(a + b*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) - 3*d^4*(a + b*x)^4*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) - 12*(b*c - a*d)^4*Log[c + d*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) - 12*B*(b*c - a*d)^4*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(3*d^5)))/(5*b)","A",1
211,1,402,422,0.3234516,"\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","Integrate[(a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2,x]","\frac{g^3 \left(\frac{2 B (b c-a d) \left(2 d^3 (a+b x)^3 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)+3 d^2 (a+b x)^2 (a d-b c) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)-6 (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)+6 A b d x (b c-a d)^2-2 B (b c-a d) \left(2 b d x (b c-a d)-2 (b c-a d)^2 \log (c+d x)-d^2 (a+b x)^2\right)+6 B d (a+b x) (b c-a d)^2 \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)-6 B (b c-a d)^3 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+12 B (b c-a d)^3 \log (c+d x)-6 B (b c-a d)^2 ((a d-b c) \log (c+d x)+b d x)\right)}{3 d^4}+(a+b x)^4 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2\right)}{4 b}","\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{2 B^2 g^3 (b c-a d)^4 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b d^4}+\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}-\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}",1,"(g^3*((a + b*x)^4*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2 + (2*B*(b*c - a*d)*(6*A*b*d*(b*c - a*d)^2*x + 12*B*(b*c - a*d)^3*Log[c + d*x] - 2*B*(b*c - a*d)*(2*b*d*(b*c - a*d)*x - d^2*(a + b*x)^2 - 2*(b*c - a*d)^2*Log[c + d*x]) - 6*B*(b*c - a*d)^2*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 6*B*d*(b*c - a*d)^2*(a + b*x)*Log[(e*(c + d*x)^2)/(a + b*x)^2] + 3*d^2*(-(b*c) + a*d)*(a + b*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) + 2*d^3*(a + b*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) - 6*(b*c - a*d)^3*Log[c + d*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) - 6*B*(b*c - a*d)^3*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(3*d^4)))/(4*b)","A",1
212,1,298,343,0.2252506,"\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","Integrate[(a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2,x]","\frac{g^2 \left((a+b x)^3 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2-\frac{2 B (b c-a d) \left(-d^2 (a+b x)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)-2 (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)+2 A b d x (b c-a d)+2 B d (a+b x) (b c-a d) \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)-2 B (b c-a d)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+4 B (b c-a d)^2 \log (c+d x)-2 B (b c-a d) ((a d-b c) \log (c+d x)+b d x)\right)}{d^3}\right)}{3 b}","-\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{8 B^2 g^2 (b c-a d)^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{3 b d^3}-\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}+\frac{4 B^2 g^2 x (b c-a d)^2}{3 d^2}",1,"(g^2*((a + b*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2 - (2*B*(b*c - a*d)*(2*A*b*d*(b*c - a*d)*x + 4*B*(b*c - a*d)^2*Log[c + d*x] - 2*B*(b*c - a*d)*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 2*B*d*(b*c - a*d)*(a + b*x)*Log[(e*(c + d*x)^2)/(a + b*x)^2] - d^2*(a + b*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) - 2*(b*c - a*d)^2*Log[c + d*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) - 2*B*(b*c - a*d)^2*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/d^3))/(3*b)","A",1
213,1,195,211,0.171759,"\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","Integrate[(a*g + b*g*x)*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2,x]","\frac{g \left(\frac{4 B (b c-a d) \left(-(b c-a d) \log (c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+2 B \log \left(\frac{d (a+b x)}{a d-b c}\right)+A-2 B\right)+B d (a+b x) \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+(2 a B d-2 b B c) \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+B (b c-a d) \log ^2(c+d x)+A b d x\right)}{d^2}+(a+b x)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2\right)}{2 b}","\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 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b d^2}+\frac{4 B^2 g (b c-a d)^2 \log (a+b x)}{b d^2}",1,"(g*((a + b*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2 + (4*B*(b*c - a*d)*(A*b*d*x + B*(b*c - a*d)*Log[c + d*x]^2 + B*d*(a + b*x)*Log[(e*(c + d*x)^2)/(a + b*x)^2] - (b*c - a*d)*Log[c + d*x]*(A - 2*B + 2*B*Log[(d*(a + b*x))/(-(b*c) + a*d)] + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) + (-2*b*B*c + 2*a*B*d)*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]))/d^2))/(2*b)","A",1
214,1,257,132,0.3345868,"\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","Integrate[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2/(a*g + b*g*x),x]","\frac{A^2 \log (a+b x)+2 A B \log (a+b x) \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+4 A B \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-4 A B \log (a+b x) \log \left(\frac{c}{d}+x\right)+4 A B \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)-2 A B \log ^2\left(\frac{a}{b}+x\right)+4 A B \log \left(\frac{a}{b}+x\right) \log (a+b x)-4 B^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right) \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)-B^2 \log \left(\frac{a d-b c}{d (a+b x)}\right) \log ^2\left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+8 B^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b g}","-\frac{4 B \text{Li}_2\left(\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{\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}+\frac{8 B^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b g}",1,"(-2*A*B*Log[a/b + x]^2 + A^2*Log[a + b*x] + 4*A*B*Log[a/b + x]*Log[a + b*x] - 4*A*B*Log[c/d + x]*Log[a + b*x] + 4*A*B*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*A*B*Log[a + b*x]*Log[(e*(c + d*x)^2)/(a + b*x)^2] - B^2*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(e*(c + d*x)^2)/(a + b*x)^2]^2 + 4*A*B*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 4*B^2*Log[(e*(c + d*x)^2)/(a + b*x)^2]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] + 8*B^2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))])/(b*g)","A",1
215,1,322,157,0.4613797,"\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","Integrate[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2/(a*g + b*g*x)^2,x]","-\frac{\frac{4 B \left(-(b c-a d) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)-d (a+b x) \log (a+b x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)+d (a+b x) \log (c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)-B d (a+b x) \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+B d (a+b x) \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+2 B (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)\right)}{b c-a d}+\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{(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,"-(((A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2 + (4*B*(2*B*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - (b*c - a*d)*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) - d*(a + b*x)*Log[a + b*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) + d*(a + b*x)*Log[c + d*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) - B*d*(a + b*x)*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + B*d*(a + b*x)*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d))/(b*g^2*(a + b*x)))","C",1
216,1,452,299,0.4583834,"\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","Integrate[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2/(a*g + b*g*x)^3,x]","-\frac{\left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2-\frac{2 B \left(-2 d^2 (a+b x)^2 \log (a+b x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)+2 d^2 (a+b x)^2 \log (c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)+(b c-a d)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)+2 d (a+b x) (a d-b c) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)-2 B d^2 (a+b x)^2 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+2 B d^2 (a+b x)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-B \left(2 d^2 (a+b x)^2 \log (c+d x)+2 d (a+b x) (a d-b c)+(b c-a d)^2-2 d^2 (a+b x)^2 \log (a+b x)\right)+4 B d (a+b x) (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)\right)}{(b c-a d)^2}}{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,"-1/2*((A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2 - (2*B*(4*B*d*(a + b*x)*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - B*((b*c - a*d)^2 + 2*d*(-(b*c) + a*d)*(a + b*x) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]) + (b*c - a*d)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) + 2*d*(-(b*c) + a*d)*(a + b*x)*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) - 2*d^2*(a + b*x)^2*Log[a + b*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) + 2*d^2*(a + b*x)^2*Log[c + d*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) - 2*B*d^2*(a + b*x)^2*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 2*B*d^2*(a + b*x)^2*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^2)/(b*g^3*(a + b*x)^2)","C",1
217,1,598,407,0.7600497,"\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","Integrate[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2/(a*g + b*g*x)^4,x]","-\frac{\frac{2 B \left(-18 d^3 (a+b x)^3 \log (a+b x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)+18 d^3 (a+b x)^3 \log (c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)+18 d^2 (a+b x)^2 (a d-b c) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)-6 (b c-a d)^3 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)+9 d (a+b x) (b c-a d)^2 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)-18 B d^3 (a+b x)^3 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+18 B d^3 (a+b x)^3 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+36 B d^2 (a+b x)^2 (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)-9 B d (a+b x) \left(2 d^2 (a+b x)^2 \log (c+d x)+2 d (a+b x) (a d-b c)+(b c-a d)^2-2 d^2 (a+b x)^2 \log (a+b x)\right)+2 B \left(-6 d^3 (a+b x)^3 \log (c+d x)+6 d^2 (a+b x)^2 (b c-a d)-3 d (a+b x) (b c-a d)^2+2 (b c-a d)^3+6 d^3 (a+b x)^3 \log (a+b x)\right)\right)}{(b c-a d)^3}+9 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^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{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{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,"-1/27*(9*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2 + (2*B*(36*B*d^2*(a + b*x)^2*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - 9*B*d*(a + b*x)*((b*c - a*d)^2 + 2*d*(-(b*c) + a*d)*(a + b*x) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]) + 2*B*(2*(b*c - a*d)^3 - 3*d*(b*c - a*d)^2*(a + b*x) + 6*d^2*(b*c - a*d)*(a + b*x)^2 + 6*d^3*(a + b*x)^3*Log[a + b*x] - 6*d^3*(a + b*x)^3*Log[c + d*x]) - 6*(b*c - a*d)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) + 9*d*(b*c - a*d)^2*(a + b*x)*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) + 18*d^2*(-(b*c) + a*d)*(a + b*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) - 18*d^3*(a + b*x)^3*Log[a + b*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) + 18*d^3*(a + b*x)^3*Log[c + d*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) - 18*B*d^3*(a + b*x)^3*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 18*B*d^3*(a + b*x)^3*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^3)/(b*g^4*(a + b*x)^3)","C",1
218,1,762,501,0.872708,"\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","Integrate[(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2/(a*g + b*g*x)^5,x]","\frac{\frac{B \left(-72 d^4 (a+b x)^4 \log (a+b x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)+72 d^4 (a+b x)^4 \log (c+d x) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)+72 d^3 (a+b x)^3 (a d-b c) \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)+36 d^2 (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)+18 (b c-a d)^4 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)+24 d (a+b x) (a d-b c)^3 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)-72 B d^4 (a+b x)^4 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+72 B d^4 (a+b x)^4 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)+144 B d^3 (a+b x)^3 (-d (a+b x) \log (c+d x)+d (a+b x) \log (a+b x)-a d+b c)-36 B d^2 (a+b x)^2 \left(2 d^2 (a+b x)^2 \log (c+d x)+2 d (a+b x) (a d-b c)+(b c-a d)^2-2 d^2 (a+b x)^2 \log (a+b x)\right)+8 B d (a+b x) \left(-6 d^3 (a+b x)^3 \log (c+d x)+6 d^2 (a+b x)^2 (b c-a d)-3 d (a+b x) (b c-a d)^2+2 (b c-a d)^3+6 d^3 (a+b x)^3 \log (a+b x)\right)-3 B \left(12 d^4 (a+b x)^4 \log (c+d x)+12 d^3 (a+b x)^3 (a d-b c)+6 d^2 (a+b x)^2 (b c-a d)^2+4 d (a+b x) (a d-b c)^3+3 (b c-a d)^4-12 d^4 (a+b x)^4 \log (a+b x)\right)\right)}{(b c-a d)^4}-18 \left(B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)+A\right)^2}{72 b g^5 (a+b x)^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{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 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{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{B^2 d^4 \log ^2\left(\frac{c+d x}{a+b x}\right)}{b g^5 (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}",1,"(-18*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2 + (B*(144*B*d^3*(a + b*x)^3*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - 36*B*d^2*(a + b*x)^2*((b*c - a*d)^2 + 2*d*(-(b*c) + a*d)*(a + b*x) - 2*d^2*(a + b*x)^2*Log[a + b*x] + 2*d^2*(a + b*x)^2*Log[c + d*x]) + 8*B*d*(a + b*x)*(2*(b*c - a*d)^3 - 3*d*(b*c - a*d)^2*(a + b*x) + 6*d^2*(b*c - a*d)*(a + b*x)^2 + 6*d^3*(a + b*x)^3*Log[a + b*x] - 6*d^3*(a + b*x)^3*Log[c + d*x]) - 3*B*(3*(b*c - a*d)^4 + 4*d*(-(b*c) + a*d)^3*(a + b*x) + 6*d^2*(b*c - a*d)^2*(a + b*x)^2 + 12*d^3*(-(b*c) + a*d)*(a + b*x)^3 - 12*d^4*(a + b*x)^4*Log[a + b*x] + 12*d^4*(a + b*x)^4*Log[c + d*x]) + 18*(b*c - a*d)^4*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) + 24*d*(-(b*c) + a*d)^3*(a + b*x)*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) + 36*d^2*(b*c - a*d)^2*(a + b*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) + 72*d^3*(-(b*c) + a*d)*(a + b*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) - 72*d^4*(a + b*x)^4*Log[a + b*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) + 72*d^4*(a + b*x)^4*Log[c + d*x]*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]) - 72*B*d^4*(a + b*x)^4*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 72*B*d^4*(a + b*x)^4*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^4)/(72*b*g^5*(a + b*x)^4)","C",1
219,0,0,37,0.1592642,"\int \frac{(a g+b g x)^2}{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)} \, dx","Integrate[(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,"Integrate[(a*g + b*g*x)^2/(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]), x]","A",-1
220,0,0,35,0.1176989,"\int \frac{a g+b g x}{A+B \log \left(\frac{e (c+d x)^2}{(a+b x)^2}\right)} \, dx","Integrate[(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,"Integrate[(a*g + b*g*x)/(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2]), x]","A",-1
221,0,0,37,0.0730779,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])), x]","A",-1
222,0,0,91,0.0775496,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])), x]","F",-1
223,0,0,151,0.0819994,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])), x]","F",-1
224,0,0,37,0.4690027,"\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","Integrate[(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,"Integrate[(a*g + b*g*x)^2/(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2, x]","A",-1
225,0,0,35,0.3478239,"\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","Integrate[(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,"Integrate[(a*g + b*g*x)/(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2, x]","A",-1
226,0,0,37,0.1464358,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2), x]","A",-1
227,0,0,147,0.18621,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)^2*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2), x]","F",-1
228,0,0,206,0.3536328,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)^3*(A + B*Log[(e*(c + d*x)^2)/(a + b*x)^2])^2), x]","F",-1
229,0,0,96,0.0641386,"\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","Integrate[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,"Integrate[1/((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])), x]","F",-1
230,1,279,355,0.587857,"\int (f+g x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(f + g*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{\frac{B g^2 x (a d-b c) \left(-12 a^3 d^3 g^3+6 a^2 b d^2 g^2 (-2 c g+10 d f+d g x)-2 a b^2 d g \left(6 c^2 g^2-3 c d g (10 f+g x)+d^2 \left(60 f^2+15 f g x+2 g^2 x^2\right)\right)+b^3 \left(-12 c^3 g^3+6 c^2 d g^2 (10 f+g x)-2 c d^2 g \left(60 f^2+15 f g x+2 g^2 x^2\right)+d^3 \left(120 f^3+60 f^2 g x+20 f g^2 x^2+3 g^3 x^3\right)\right)\right)}{12 b^4 d^4}+(f+g x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{B (b f-a g)^5 \log (a+b x)}{b^5}+\frac{B (d f-c g)^5 \log (c+d x)}{d^5}}{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^3 d^3 g^3-a^2 b d^2 g^2 (5 d f-c g)+a b^2 d g \left(c^2 g^2-5 c d f g+10 d^2 f^2\right)-\left(b^3 \left(-c^3 g^3+5 c^2 d f g^2-10 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 (b f-a g)^5 \log (a+b x)}{5 b^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 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*(-(b*c) + a*d)*g^2*x*(-12*a^3*d^3*g^3 + 6*a^2*b*d^2*g^2*(10*d*f - 2*c*g + d*g*x) - 2*a*b^2*d*g*(6*c^2*g^2 - 3*c*d*g*(10*f + g*x) + d^2*(60*f^2 + 15*f*g*x + 2*g^2*x^2)) + b^3*(-12*c^3*g^3 + 6*c^2*d*g^2*(10*f + g*x) - 2*c*d^2*g*(60*f^2 + 15*f*g*x + 2*g^2*x^2) + d^3*(120*f^3 + 60*f^2*g*x + 20*f*g^2*x^2 + 3*g^3*x^3))))/(12*b^4*d^4) - (B*(b*f - a*g)^5*Log[a + b*x])/b^5 + (f + g*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + (B*(d*f - c*g)^5*Log[c + d*x])/d^5)/(5*g)","A",1
231,1,215,227,0.2656002,"\int (f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{(f+g x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{B \left(6 b d g^2 x (b c-a d) \left(a^2 d^2 g^2+a b d g (c g-4 d f)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right)+2 b^3 d^3 g^4 x^3 (b c-a d)+3 b^2 d^2 g^3 x^2 (b c-a d) (-a d g-b c g+4 b d f)+6 d^4 (b f-a g)^4 \log (a+b x)-6 b^4 (d f-c g)^4 \log (c+d x)\right)}{6 b^4 d^4}}{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 (b f-a g)^4 \log (a+b x)}{4 b^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 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,"((f + g*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - (B*(6*b*d*(b*c - a*d)*g^2*(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 + 3*b^2*d^2*(b*c - a*d)*g^3*(4*b*d*f - b*c*g - a*d*g)*x^2 + 2*b^3*d^3*(b*c - a*d)*g^4*x^3 + 6*d^4*(b*f - a*g)^4*Log[a + b*x] - 6*b^4*(d*f - c*g)^4*Log[c + d*x]))/(6*b^4*d^4))/(4*g)","A",1
232,1,142,150,0.1312636,"\int (f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(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)-\frac{B \left(b^2 d^2 g^3 x^2 (b c-a d)+2 b d g^2 x (b c-a d) (-a d g-b c g+3 b d f)+2 d^3 (b f-a g)^3 \log (a+b x)-2 b^3 (d f-c g)^3 \log (c+d x)\right)}{2 b^3 d^3}}{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 (b f-a g)^3 \log (a+b x)}{3 b^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 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,"((f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - (B*(2*b*d*(b*c - a*d)*g^2*(3*b*d*f - b*c*g - a*d*g)*x + b^2*d^2*(b*c - a*d)*g^3*x^2 + 2*d^3*(b*f - a*g)^3*Log[a + b*x] - 2*b^3*(d*f - c*g)^3*Log[c + d*x]))/(2*b^3*d^3))/(3*g)","A",1
233,1,114,109,0.1100605,"\int (f+g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(f + g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{b \left(d \left(B g^2 x (a d-b c)+A b d (f+g x)^2\right)+b B d^2 (f+g x)^2 \log \left(\frac{e (a+b x)}{c+d x}\right)+b B (d f-c g)^2 \log (c+d x)\right)-B d^2 (b f-a g)^2 \log (a+b x)}{2 b^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*d^2*(b*f - a*g)^2*Log[a + b*x]) + b*(d*(B*(-(b*c) + a*d)*g^2*x + A*b*d*(f + g*x)^2) + b*B*d^2*(f + g*x)^2*Log[(e*(a + b*x))/(c + d*x)] + b*B*(d*f - c*g)^2*Log[c + d*x]))/(2*b^2*d^2*g)","A",1
234,1,52,52,0.0079745,"\int \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[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",1
235,1,115,140,0.060368,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{f+g x} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(f + g*x),x]","\frac{\log (f+g x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)-B \log \left(\frac{g (a+b x)}{a g-b f}\right)+A+B \log \left(\frac{g (c+d x)}{c g-d f}\right)\right)-B \text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\right)+B \text{Li}_2\left(\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 \text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\right)}{g}-\frac{B \log (f+g x) \log \left(-\frac{g (a+b x)}{b f-a g}\right)}{g}+\frac{B \text{Li}_2\left(\frac{d (f+g x)}{d f-c g}\right)}{g}+\frac{B \log (f+g x) \log \left(-\frac{g (c+d x)}{d f-c g}\right)}{g}",1,"((A - B*Log[(g*(a + b*x))/(-(b*f) + a*g)] + B*Log[(e*(a + b*x))/(c + d*x)] + B*Log[(g*(c + d*x))/(-(d*f) + c*g)])*Log[f + g*x] - B*PolyLog[2, (b*(f + g*x))/(b*f - a*g)] + B*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g","A",1
236,1,105,87,0.1295461,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(f+g x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(f + g*x)^2,x]","\frac{\frac{B (b \log (a+b x) (d f-c g)+\log (c+d x) (a d g-b d f)+g (b c-a d) \log (f+g x))}{(b f-a g) (d f-c g)}-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{f+g x}}{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,"(-((A + B*Log[(e*(a + b*x))/(c + d*x)])/(f + g*x)) + (B*(b*(d*f - c*g)*Log[a + b*x] + (-(b*d*f) + a*d*g)*Log[c + d*x] + (b*c - a*d)*g*Log[f + g*x]))/((b*f - a*g)*(d*f - c*g)))/g","A",1
237,1,169,183,0.5049633,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(f+g x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(f + g*x)^3,x]","\frac{B (b c-a d) \left(\frac{b^2 \log (a+b x)}{(b c-a d) (b f-a g)^2}+\frac{\frac{d^2 \log (c+d x)}{a d-b c}+\frac{g (c g-d f)}{(f+g x) (b f-a g)}-\frac{g \log (f+g x) (a d g+b c g-2 b d f)}{(b f-a g)^2}}{(d f-c g)^2}\right)-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{(f+g x)^2}}{2 g}","-\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,"(-((A + B*Log[(e*(a + b*x))/(c + d*x)])/(f + g*x)^2) + B*(b*c - a*d)*((b^2*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)^2) + ((g*(-(d*f) + c*g))/((b*f - a*g)*(f + g*x)) + (d^2*Log[c + d*x])/(-(b*c) + a*d) - (g*(-2*b*d*f + b*c*g + a*d*g)*Log[f + g*x])/(b*f - a*g)^2)/(d*f - c*g)^2))/(2*g)","A",1
238,1,260,275,0.7160886,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(f+g x)^4} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(f + g*x)^4,x]","\frac{B (b c-a d) \left(\frac{g \log (f+g x) \left(a^2 d^2 g^2+a b d g (c g-3 d f)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{(b f-a g)^3 (d f-c g)^3}+\frac{b^3 \log (a+b x)}{(b c-a d) (b f-a g)^3}+\frac{d^3 \log (c+d x)}{(b c-a d) (c g-d f)^3}+\frac{g (a d g+b c g-2 b d f)}{(f+g x) (b f-a g)^2 (d f-c g)^2}-\frac{g}{2 (f+g x)^2 (b f-a g) (d f-c g)}\right)-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{(f+g x)^3}}{3 g}","\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,"(-((A + B*Log[(e*(a + b*x))/(c + d*x)])/(f + g*x)^3) + B*(b*c - a*d)*(-1/2*g/((b*f - a*g)*(d*f - c*g)*(f + g*x)^2) + (g*(-2*b*d*f + b*c*g + a*d*g))/((b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)) + (b^3*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)^3) + (d^3*Log[c + d*x])/((b*c - a*d)*(-(d*f) + c*g)^3) + (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])/((b*f - a*g)^3*(d*f - c*g)^3)))/(3*g)","A",1
239,1,355,379,0.9311898,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(f+g x)^5} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(f + g*x)^5,x]","\frac{B (b c-a d) \left(-\frac{g \left(a^2 d^2 g^2+a b d g (c g-3 d f)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{(f+g x) (b f-a g)^3 (d f-c g)^3}-\frac{g \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(c^2 g^2-2 c d f g+2 d^2 f^2\right)\right)}{(b f-a g)^4 (d f-c g)^4}+\frac{b^4 \log (a+b x)}{(b c-a d) (b f-a g)^4}-\frac{d^4 \log (c+d x)}{(b c-a d) (d f-c g)^4}+\frac{g (a d g+b c g-2 b d f)}{2 (f+g x)^2 (b f-a g)^2 (d f-c g)^2}-\frac{g}{3 (f+g x)^3 (b f-a g) (d f-c g)}\right)-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{(f+g x)^4}}{4 g}","-\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-\left(b^2 \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,"(-((A + B*Log[(e*(a + b*x))/(c + d*x)])/(f + g*x)^4) + B*(b*c - a*d)*(-1/3*g/((b*f - a*g)*(d*f - c*g)*(f + g*x)^3) + (g*(-2*b*d*f + b*c*g + a*d*g))/(2*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)^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)))/((b*f - a*g)^3*(d*f - c*g)^3*(f + g*x)) + (b^4*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)^4) - (d^4*Log[c + d*x])/((b*c - a*d)*(d*f - c*g)^4) - (g*(-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])/((b*f - a*g)^4*(d*f - c*g)^4)))/(4*g)","A",1
240,1,733,874,0.9793385,"\int (f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Integrate[(f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{(f+g x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2-\frac{B \left(B g^4 (b c-a d) \left(2 a^3 d^3 \log (a+b x)+b d x (b c-a d) (2 a d+2 b c-b d x)-2 b^3 c^3 \log (c+d x)\right)+6 A b d g^2 x (b c-a d) \left(a^2 d^2 g^2+a b d g (c g-4 d f)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right)+6 B d g^2 (a+b x) (b c-a d) \left(a^2 d^2 g^2+a b d g (c g-4 d f)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right) \log \left(\frac{e (a+b x)}{c+d x}\right)-6 B g^2 (b c-a d)^2 \log (c+d x) \left(a^2 d^2 g^2+a b d g (c g-4 d f)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right)-3 B g^3 (b c-a d) (a d g+b c g-4 b d f) \left(b \left(d x (a d-b c)+b c^2 \log (c+d x)\right)-a^2 d^2 \log (a+b x)\right)-6 b^4 (d f-c g)^4 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 b^3 d^3 g^4 x^3 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+3 b^2 d^2 g^3 x^2 (b c-a d) (-a d g-b c g+4 b d f) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+6 d^4 (b f-a g)^4 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+3 b^4 B (d f-c g)^4 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-3 B d^4 (b f-a g)^4 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)\right)}{3 b^4 d^4}}{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(\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2\right)+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(\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2\right)+2 a d^2 f g b-a^2 d^2 g^2\right) \text{Li}_2\left(\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,"((f + g*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - (B*(6*A*b*d*(b*c - a*d)*g^2*(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 + 6*B*d*(b*c - a*d)*g^2*(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)] + 3*b^2*d^2*(b*c - a*d)*g^3*(4*b*d*f - b*c*g - a*d*g)*x^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*b^3*d^3*(b*c - a*d)*g^4*x^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6*d^4*(b*f - a*g)^4*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 6*B*(b*c - a*d)^2*g^2*(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] - 6*b^4*(d*f - c*g)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + B*(b*c - a*d)*g^4*(b*d*(b*c - a*d)*x*(2*b*c + 2*a*d - b*d*x) + 2*a^3*d^3*Log[a + b*x] - 2*b^3*c^3*Log[c + d*x]) - 3*B*(b*c - a*d)*g^3*(-4*b*d*f + b*c*g + a*d*g)*(-(a^2*d^2*Log[a + b*x]) + b*(d*(-(b*c) + a*d)*x + b*c^2*Log[c + d*x])) - 3*B*d^4*(b*f - a*g)^4*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 3*b^4*B*(d*f - c*g)^4*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(3*b^4*d^4))/(4*g)","A",1
241,1,486,532,0.5307732,"\int (f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Integrate[(f + g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{(f+g x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2-\frac{B \left(-B g^3 (b c-a d) \left(a^2 d^2 \log (a+b x)-b \left(d x (a d-b c)+b c^2 \log (c+d x)\right)\right)-2 b^3 (d f-c g)^3 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+b^2 d^2 g^3 x^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 d^3 (b f-a g)^3 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 A b d g^2 x (b c-a d) (-a d g-b c g+3 b d f)+b^3 B (d f-c g)^3 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-B d^3 (b f-a g)^3 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+2 B d g^2 (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)+2 B g^2 (b c-a d)^2 \log (c+d x) (a d g+b c g-3 b d f)\right)}{b^3 d^3}}{3 g}","\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^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{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\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 (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}+\frac{B^2 g^2 x (b c-a d)^2}{3 b^2 d^2}",1,"((f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - (B*(2*A*b*d*(b*c - a*d)*g^2*(3*b*d*f - b*c*g - a*d*g)*x + 2*B*d*(b*c - a*d)*g^2*(3*b*d*f - b*c*g - a*d*g)*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] + b^2*d^2*(b*c - a*d)*g^3*x^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*d^3*(b*f - a*g)^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*B*(b*c - a*d)^2*g^2*(-3*b*d*f + b*c*g + a*d*g)*Log[c + d*x] - 2*b^3*(d*f - c*g)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - B*(b*c - a*d)*g^3*(a^2*d^2*Log[a + b*x] - b*(d*(-(b*c) + a*d)*x + b*c^2*Log[c + d*x])) - B*d^3*(b*f - a*g)^3*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + b^3*B*(d*f - c*g)^3*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b^3*d^3))/(3*g)","A",1
242,1,346,270,0.3522916,"\int (f+g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Integrate[(f + g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{(f+g x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2-\frac{B \left(-2 b^2 (d f-c g)^2 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 d^2 (b f-a g)^2 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 A b d g^2 x (b c-a d)+b^2 B (d f-c g)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-B d^2 (b f-a g)^2 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+2 B d g^2 (a+b x) (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 B g^2 (b c-a d)^2 \log (c+d x)\right)}{b^2 d^2}}{2 g}","\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 (b c-a d) (-a d g-b c g+2 b d f) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^2 d^2}+\frac{B^2 g (b c-a d)^2 \log (c+d x)}{b^2 d^2}",1,"((f + g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - (B*(2*A*b*d*(b*c - a*d)*g^2*x + 2*B*d*(b*c - a*d)*g^2*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] + 2*d^2*(b*f - a*g)^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 2*B*(b*c - a*d)^2*g^2*Log[c + d*x] - 2*b^2*(d*f - c*g)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - B*d^2*(b*f - a*g)^2*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + b^2*B*(d*f - c*g)^2*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b^2*d^2))/(2*g)","A",1
243,1,214,125,0.2057021,"\int \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{B \left(2 a d \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-2 b c \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-a B d \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+b B c \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)\right)}{b d}+x \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2","\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}+\frac{2 B^2 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b d}",1,"x*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + (B*(2*a*d*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 2*b*c*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - a*B*d*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + b*B*c*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*d)","A",1
244,1,431,277,0.8498614,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{f+g x} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(f + g*x),x]","\frac{2 A B \log (f+g x) \log \left(\frac{e (a+b x)}{c+d x}\right)+2 A B \text{Li}_2\left(\frac{g (a+b x)}{a g-b f}\right)-2 A B \log \left(\frac{a}{b}+x\right) \log (f+g x)+2 A B \log \left(\frac{a}{b}+x\right) \log \left(\frac{b (f+g x)}{b f-a g}\right)+2 B^2 \log \left(\frac{e (a+b x)}{c+d x}\right) \text{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)+B^2 \log ^2\left(\frac{e (a+b x)}{c+d x}\right) \log \left(\frac{(f+g x) (b c-a d)}{(c+d x) (b f-a g)}\right)-2 B^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right) \log \left(\frac{e (a+b x)}{c+d x}\right)-B^2 \log \left(\frac{b c-a d}{b c+b d x}\right) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)-2 B^2 \text{Li}_3\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)+2 B^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)+A^2 \log (f+g x)-2 A B \text{Li}_2\left(\frac{g (c+d x)}{c g-d f}\right)+2 A B \log \left(\frac{c}{d}+x\right) \log (f+g x)-2 A B \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (f+g x)}{d f-c g}\right)}{g}","\frac{2 B \text{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\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{2 B \text{Li}_2\left(\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{\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}-\frac{2 B^2 \text{Li}_3\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{g}+\frac{2 B^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{g}",1,"(-(B^2*Log[(e*(a + b*x))/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)]) + A^2*Log[f + g*x] - 2*A*B*Log[a/b + x]*Log[f + g*x] + 2*A*B*Log[c/d + x]*Log[f + g*x] + 2*A*B*Log[(e*(a + b*x))/(c + d*x)]*Log[f + g*x] + 2*A*B*Log[a/b + x]*Log[(b*(f + g*x))/(b*f - a*g)] - 2*A*B*Log[c/d + x]*Log[(d*(f + g*x))/(d*f - c*g)] + B^2*Log[(e*(a + b*x))/(c + d*x)]^2*Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))] + 2*A*B*PolyLog[2, (g*(a + b*x))/(-(b*f) + a*g)] - 2*B^2*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] + 2*B^2*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, ((d*f - c*g)*(a + b*x))/((b*f - a*g)*(c + d*x))] - 2*A*B*PolyLog[2, (g*(c + d*x))/(-(d*f) + c*g)] + 2*B^2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] - 2*B^2*PolyLog[3, ((d*f - c*g)*(a + b*x))/((b*f - a*g)*(c + d*x))])/g","A",1
245,1,402,196,0.5787361,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(f+g x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(f + g*x)^2,x]","\frac{\frac{B \left(2 b \log (a+b x) (d f-c g) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-2 d (b f-a g) \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 g (b c-a d) \log (f+g x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-b B (d f-c g) \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+B d (b f-a g) \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-2 B g (b c-a d) \left(\log (f+g x) \left(\log \left(\frac{g (a+b x)}{a g-b f}\right)-\log \left(\frac{g (c+d x)}{c g-d f}\right)\right)+\text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\right)-\text{Li}_2\left(\frac{d (f+g x)}{d f-c g}\right)\right)\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}{f+g x}}{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)}+\frac{2 B^2 (b c-a d) \text{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{(b f-a g) (d f-c g)}",1,"(-((A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(f + g*x)) + (B*(2*b*(d*f - c*g)*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 2*d*(b*f - a*g)*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 2*(b*c - a*d)*g*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[f + g*x] - b*B*(d*f - c*g)*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + B*d*(b*f - a*g)*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) - 2*B*(b*c - a*d)*g*((Log[(g*(a + b*x))/(-(b*f) + a*g)] - Log[(g*(c + d*x))/(-(d*f) + c*g)])*Log[f + g*x] + PolyLog[2, (b*(f + g*x))/(b*f - a*g)] - PolyLog[2, (d*(f + g*x))/(d*f - c*g)])))/((b*f - a*g)*(d*f - c*g)))/g","B",1
246,1,595,369,1.5354008,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(f+g x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(f + g*x)^3,x]","-\frac{\frac{B (f+g x) \left(-2 b^2 (f+g x) \log (a+b x) (d f-c g)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 d^2 (f+g x) (b f-a g)^2 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 g (b c-a d) (b f-a g) (d f-c g) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 g (f+g x) (b c-a d) \log (f+g x) (a d g+b c g-2 b d f) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+b^2 B (f+g x) (d f-c g)^2 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)-B d^2 (f+g x) (b f-a g)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-2 B g (f+g x) (b c-a d) (a d g+b c g-2 b d f) \left(\log (f+g x) \left(\log \left(\frac{g (a+b x)}{a g-b f}\right)-\log \left(\frac{g (c+d x)}{c g-d f}\right)\right)+\text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\right)-\text{Li}_2\left(\frac{d (f+g x)}{d f-c g}\right)\right)-2 B g (f+g x) (b c-a d) (b \log (a+b x) (d f-c g)+\log (c+d x) (a d g-b d f)+g (b c-a d) \log (f+g x))\right)}{(b f-a g)^2 (d f-c g)^2}+\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 \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 (b c-a d) (-a d g-b c g+2 b d f) \text{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{(b f-a g)^2 (d f-c g)^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,"-1/2*((A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + (B*(f + g*x)*(2*(b*c - a*d)*g*(b*f - a*g)*(d*f - c*g)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 2*b^2*(d*f - c*g)^2*(f + g*x)*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*d^2*(b*f - a*g)^2*(f + g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 2*(b*c - a*d)*g*(-2*b*d*f + b*c*g + a*d*g)*(f + g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[f + g*x] - 2*B*(b*c - a*d)*g*(f + g*x)*(b*(d*f - c*g)*Log[a + b*x] + (-(b*d*f) + a*d*g)*Log[c + d*x] + (b*c - a*d)*g*Log[f + g*x]) + b^2*B*(d*f - c*g)^2*(f + g*x)*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - B*d^2*(b*f - a*g)^2*(f + g*x)*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) - 2*B*(b*c - a*d)*g*(-2*b*d*f + b*c*g + a*d*g)*(f + g*x)*((Log[(g*(a + b*x))/(-(b*f) + a*g)] - Log[(g*(c + d*x))/(-(d*f) + c*g)])*Log[f + g*x] + PolyLog[2, (b*(f + g*x))/(b*f - a*g)] - PolyLog[2, (d*(f + g*x))/(d*f - c*g)])))/((b*f - a*g)^2*(d*f - c*g)^2))/(g*(f + g*x)^2)","A",1
247,1,894,714,3.1824501,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(f+g x)^4} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(f + g*x)^4,x]","-\frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2+\frac{B (f+g x) \left(2 d^3 (f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x) (b f-a g)^3-B d^3 (f+g x)^2 \left(\left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right) \log (c+d x)+2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right) (b f-a g)^3+(b c-a d) g (d f-c g)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b f-a g)^2+2 (b c-a d) g (c g-d f) (-2 b d f+b c g+a d g) (f+g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b f-a g)-2 b^3 (d f-c g)^3 (f+g x)^2 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)-2 (b c-a d) g \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2+a d g (c g-3 d f) b+a^2 d^2 g^2\right) (f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (f+g x)-2 B (b c-a d) g (2 b d f-b c g-a d g) (f+g x)^2 (b (d f-c g) \log (a+b x)+(a d g-b d f) \log (c+d x)+(b c-a d) g \log (f+g x))+B (b c-a d) g (f+g x) \left(d^2 (f+g x) \log (c+d x) (b f-a g)^2+(b c-a d) g (d f-c g) (b f-a g)-b^2 (d f-c g)^2 (f+g x) \log (a+b x)+(b c-a d) g (-2 b d f+b c g+a d g) (f+g x) \log (f+g x)\right)+b^3 B (d f-c g)^3 (f+g x)^2 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+2 B (b c-a d) g \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2+a d g (c g-3 d f) b+a^2 d^2 g^2\right) (f+g x)^2 \left(\left(\log \left(\frac{g (a+b x)}{a g-b f}\right)-\log \left(\frac{g (c+d x)}{c g-d f}\right)\right) \log (f+g x)+\text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\right)-\text{Li}_2\left(\frac{d (f+g x)}{d f-c g}\right)\right)\right)}{(b f-a g)^3 (d f-c g)^3}}{3 g (f+g x)^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{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{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\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,"-1/3*((A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + (B*(f + g*x)*((b*c - a*d)*g*(b*f - a*g)^2*(d*f - c*g)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*(b*c - a*d)*g*(b*f - a*g)*(-(d*f) + c*g)*(-2*b*d*f + b*c*g + a*d*g)*(f + g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 2*b^3*(d*f - c*g)^3*(f + g*x)^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*d^3*(b*f - a*g)^3*(f + g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 2*(b*c - a*d)*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))*(f + g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[f + g*x] - 2*B*(b*c - a*d)*g*(2*b*d*f - b*c*g - a*d*g)*(f + g*x)^2*(b*(d*f - c*g)*Log[a + b*x] + (-(b*d*f) + a*d*g)*Log[c + d*x] + (b*c - a*d)*g*Log[f + g*x]) + B*(b*c - a*d)*g*(f + g*x)*((b*c - a*d)*g*(b*f - a*g)*(d*f - c*g) - b^2*(d*f - c*g)^2*(f + g*x)*Log[a + b*x] + d^2*(b*f - a*g)^2*(f + g*x)*Log[c + d*x] + (b*c - a*d)*g*(-2*b*d*f + b*c*g + a*d*g)*(f + g*x)*Log[f + g*x]) + b^3*B*(d*f - c*g)^3*(f + g*x)^2*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - B*d^3*(b*f - a*g)^3*(f + g*x)^2*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 2*B*(b*c - a*d)*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))*(f + g*x)^2*((Log[(g*(a + b*x))/(-(b*f) + a*g)] - Log[(g*(c + d*x))/(-(d*f) + c*g)])*Log[f + g*x] + PolyLog[2, (b*(f + g*x))/(b*f - a*g)] - PolyLog[2, (d*(f + g*x))/(d*f - c*g)])))/((b*f - a*g)^3*(d*f - c*g)^3))/(g*(f + g*x)^3)","A",1
248,1,1448,1159,7.4185534,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(f+g x)^5} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(f + g*x)^5,x]","\frac{B (b c-a d) \left(\frac{\log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) b^4}{(b c-a d) (b f-a g)^4}-\frac{B \left(\log ^2(a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right) \log (a+b x)-2 \text{Li}_2\left(-\frac{d (a+b x)}{b c-a d}\right)\right) b^4}{2 (b c-a d) (b f-a g)^4}-\frac{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) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(b f-a g)^3 (d f-c g)^3 (f+g x)}-\frac{g (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)}{2 (b f-a g)^2 (d f-c g)^2 (f+g x)^2}-\frac{g \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)^3}-\frac{d^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x)}{(b c-a d) (d f-c g)^4}+\frac{g (2 b d f-b c g-a d g) \left(2 d^2 f^2 b^2+c^2 g^2 b^2-2 c d f g 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)}{(b f-a g)^4 (d f-c g)^4}+\frac{B (b c-a d) 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) \left(\frac{b \log (a+b x)}{(b c-a d) (b f-a g)}-\frac{d \log (c+d x)}{(b c-a d) (d f-c g)}+\frac{g \log (f+g x)}{(b f-a g) (d f-c g)}\right)}{(b f-a g)^3 (d f-c g)^3}-\frac{B (b c-a d) g (2 b d f-b c g-a d g) \left(-\frac{\log (a+b x) b^2}{(b c-a d) (b f-a g)^2}+\frac{d^2 \log (c+d x)}{(b c-a d) (d f-c g)^2}-\frac{g (2 b d f-b c g-a d g) \log (f+g x)}{(b f-a g)^2 (d f-c g)^2}+\frac{g}{(b f-a g) (d f-c g) (f+g x)}\right)}{2 (b f-a g)^2 (d f-c g)^2}-\frac{B (b c-a d) g \left(-\frac{2 \log (a+b x) b^3}{(b c-a d) (b f-a g)^3}+\frac{2 d^3 \log (c+d x)}{(b c-a d) (d f-c g)^3}-\frac{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)}{(b f-a g)^3 (d f-c g)^3}+\frac{2 g (2 b d f-b c g-a d g)}{(b f-a g)^2 (d f-c g)^2 (f+g x)}+\frac{g}{(b f-a g) (d f-c g) (f+g x)^2}\right)}{6 (b f-a g) (d f-c g)}+\frac{B d^4 \left(-\log ^2(c+d x)+2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x)+2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right)}{2 (b c-a d) (d f-c g)^4}-\frac{B g (2 b d f-b c g-a d g) \left(2 d^2 f^2 b^2+c^2 g^2 b^2-2 c d f g b^2-2 a d^2 f g b+a^2 d^2 g^2\right) \left(\log \left(-\frac{g (a+b x)}{b f-a g}\right) \log (f+g x)-\log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x)+\text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\right)-\text{Li}_2\left(\frac{d (f+g x)}{d f-c g}\right)\right)}{(b f-a g)^4 (d f-c g)^4}\right)}{2 g}-\frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{4 g (f+g x)^4}","\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(\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2\right)+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(\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2\right)+2 a d^2 f g b-a^2 d^2 g^2\right) \text{Li}_2\left(\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,"-1/4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(g*(f + g*x)^4) + (B*(b*c - a*d)*(-1/3*(g*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/((b*f - a*g)*(d*f - c*g)*(f + g*x)^3) - (g*(2*b*d*f - b*c*g - a*d*g)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(2*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)^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))*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/((b*f - a*g)^3*(d*f - c*g)^3*(f + g*x)) + (b^4*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/((b*c - a*d)*(b*f - a*g)^4) - (d^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/((b*c - a*d)*(d*f - c*g)^4) + (g*(2*b*d*f - b*c*g - a*d*g)*(2*b^2*d^2*f^2 - 2*b^2*c*d*f*g - 2*a*b*d^2*f*g + b^2*c^2*g^2 + a^2*d^2*g^2)*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[f + g*x])/((b*f - a*g)^4*(d*f - c*g)^4) + (B*(b*c - a*d)*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))*((b*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)) - (d*Log[c + d*x])/((b*c - a*d)*(d*f - c*g)) + (g*Log[f + g*x])/((b*f - a*g)*(d*f - c*g))))/((b*f - a*g)^3*(d*f - c*g)^3) - (B*(b*c - a*d)*g*(2*b*d*f - b*c*g - a*d*g)*(g/((b*f - a*g)*(d*f - c*g)*(f + g*x)) - (b^2*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)^2) + (d^2*Log[c + d*x])/((b*c - a*d)*(d*f - c*g)^2) - (g*(2*b*d*f - b*c*g - a*d*g)*Log[f + g*x])/((b*f - a*g)^2*(d*f - c*g)^2)))/(2*(b*f - a*g)^2*(d*f - c*g)^2) - (B*(b*c - a*d)*g*(g/((b*f - a*g)*(d*f - c*g)*(f + g*x)^2) + (2*g*(2*b*d*f - b*c*g - a*d*g))/((b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)) - (2*b^3*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)^3) + (2*d^3*Log[c + d*x])/((b*c - a*d)*(d*f - c*g)^3) - (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])/((b*f - a*g)^3*(d*f - c*g)^3)))/(6*(b*f - a*g)*(d*f - c*g)) - (b^4*B*(Log[a + b*x]^2 - 2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] - 2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))]))/(2*(b*c - a*d)*(b*f - a*g)^4) + (B*d^4*(2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x] - Log[c + d*x]^2 + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]))/(2*(b*c - a*d)*(d*f - c*g)^4) - (B*g*(2*b*d*f - b*c*g - a*d*g)*(2*b^2*d^2*f^2 - 2*b^2*c*d*f*g - 2*a*b*d^2*f*g + b^2*c^2*g^2 + a^2*d^2*g^2)*(Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x] - Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x] + PolyLog[2, (b*(f + g*x))/(b*f - a*g)] - PolyLog[2, (d*(f + g*x))/(d*f - c*g)]))/((b*f - a*g)^4*(d*f - c*g)^4)))/(2*g)","A",1
249,1,30,35,0.0057892,"\int \frac{\log \left(\frac{1+x}{-1+x}\right)}{x^2} \, dx","Integrate[Log[(1 + x)/(-1 + x)]/x^2,x]","-\log \left(1-x^2\right)+2 \log (x)-\frac{\log \left(\frac{x+1}{x-1}\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] - Log[(1 + x)/(-1 + x)]/x - Log[1 - x^2]","A",1
250,0,0,32,0.4286456,"\int \frac{(f+g x)^2}{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)} \, dx","Integrate[(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,"Integrate[(f + g*x)^2/(A + B*Log[(e*(a + b*x))/(c + d*x)]), x]","A",-1
251,0,0,30,0.2517406,"\int \frac{f+g x}{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)} \, dx","Integrate[(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,"Integrate[(f + g*x)/(A + B*Log[(e*(a + b*x))/(c + d*x)]), x]","A",-1
252,0,0,24,0.0232151,"\int \frac{1}{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)} \, dx","Integrate[(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,"Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-1), x]","A",-1
253,0,0,32,0.8969445,"\int \frac{1}{(f+g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)} \, dx","Integrate[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,"Integrate[1/((f + g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])), x]","A",-1
254,0,0,32,0.8802546,"\int \frac{1}{(f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)} \, dx","Integrate[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,"Integrate[1/((f + g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])), x]","A",-1
255,0,0,32,8.1457063,"\int \frac{1}{(f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)} \, dx","Integrate[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,"Integrate[1/((f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])), x]","A",-1
256,0,0,32,1.3660979,"\int \frac{(f+g x)^2}{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Integrate[(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,"Integrate[(f + g*x)^2/(A + B*Log[(e*(a + b*x))/(c + d*x)])^2, x]","A",-1
257,0,0,30,0.9465612,"\int \frac{f+g x}{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Integrate[(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,"Integrate[(f + g*x)/(A + B*Log[(e*(a + b*x))/(c + d*x)])^2, x]","A",-1
258,0,0,24,0.5874024,"\int \frac{1}{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Integrate[(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,"Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-2), x]","A",-1
259,0,0,32,2.6027486,"\int \frac{1}{(f+g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Integrate[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,"Integrate[1/((f + g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2), x]","A",-1
260,0,0,32,3.9310355,"\int \frac{1}{(f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Integrate[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,"Integrate[1/((f + g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2), x]","A",-1
261,0,0,32,30.0059049,"\int \frac{1}{(f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2} \, dx","Integrate[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,"Integrate[1/((f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2), x]","A",-1
262,1,282,357,0.5978542,"\int (f+g x)^4 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \, dx","Integrate[(f + g*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\frac{\frac{B g^2 x (a d-b c) \left(-12 a^3 d^3 g^3+6 a^2 b d^2 g^2 (-2 c g+10 d f+d g x)-2 a b^2 d g \left(6 c^2 g^2-3 c d g (10 f+g x)+d^2 \left(60 f^2+15 f g x+2 g^2 x^2\right)\right)+b^3 \left(-12 c^3 g^3+6 c^2 d g^2 (10 f+g x)-2 c d^2 g \left(60 f^2+15 f g x+2 g^2 x^2\right)+d^3 \left(120 f^3+60 f^2 g x+20 f g^2 x^2+3 g^3 x^3\right)\right)\right)}{6 b^4 d^4}+(f+g x)^5 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)-\frac{2 B (b f-a g)^5 \log (a+b x)}{b^5}+\frac{2 B (d f-c g)^5 \log (c+d x)}{d^5}}{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^3 d^3 g^3-a^2 b d^2 g^2 (5 d f-c g)+a b^2 d g \left(c^2 g^2-5 c d f g+10 d^2 f^2\right)-\left(b^3 \left(-c^3 g^3+5 c^2 d f g^2-10 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 (b f-a g)^5 \log (a+b x)}{5 b^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{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,"((B*(-(b*c) + a*d)*g^2*x*(-12*a^3*d^3*g^3 + 6*a^2*b*d^2*g^2*(10*d*f - 2*c*g + d*g*x) - 2*a*b^2*d*g*(6*c^2*g^2 - 3*c*d*g*(10*f + g*x) + d^2*(60*f^2 + 15*f*g*x + 2*g^2*x^2)) + b^3*(-12*c^3*g^3 + 6*c^2*d*g^2*(10*f + g*x) - 2*c*d^2*g*(60*f^2 + 15*f*g*x + 2*g^2*x^2) + d^3*(120*f^3 + 60*f^2*g*x + 20*f*g^2*x^2 + 3*g^3*x^3))))/(6*b^4*d^4) - (2*B*(b*f - a*g)^5*Log[a + b*x])/b^5 + (f + g*x)^5*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + (2*B*(d*f - c*g)^5*Log[c + d*x])/d^5)/(5*g)","A",1
263,1,217,229,0.25669,"\int (f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \, dx","Integrate[(f + g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\frac{(f+g x)^4 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)-\frac{B \left(6 b d g^2 x (b c-a d) \left(a^2 d^2 g^2+a b d g (c g-4 d f)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right)+2 b^3 d^3 g^4 x^3 (b c-a d)+3 b^2 d^2 g^3 x^2 (b c-a d) (-a d g-b c g+4 b d f)+6 d^4 (b f-a g)^4 \log (a+b x)-6 b^4 (d f-c g)^4 \log (c+d x)\right)}{3 b^4 d^4}}{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 (b f-a g)^4 \log (a+b x)}{2 b^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 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,"((f + g*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - (B*(6*b*d*(b*c - a*d)*g^2*(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 + 3*b^2*d^2*(b*c - a*d)*g^3*(4*b*d*f - b*c*g - a*d*g)*x^2 + 2*b^3*d^3*(b*c - a*d)*g^4*x^3 + 6*d^4*(b*f - a*g)^4*Log[a + b*x] - 6*b^4*(d*f - c*g)^4*Log[c + d*x]))/(3*b^4*d^4))/(4*g)","A",1
264,1,142,152,0.1377136,"\int (f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \, dx","Integrate[(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)-\frac{B \left(b^2 d^2 g^3 x^2 (b c-a d)+2 b d g^2 x (b c-a d) (-a d g-b c g+3 b d f)+2 d^3 (b f-a g)^3 \log (a+b x)-2 b^3 (d f-c g)^3 \log (c+d x)\right)}{b^3 d^3}}{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 (b f-a g)^3 \log (a+b x)}{3 b^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{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,"((f + g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - (B*(2*b*d*(b*c - a*d)*g^2*(3*b*d*f - b*c*g - a*d*g)*x + b^2*d^2*(b*c - a*d)*g^3*x^2 + 2*d^3*(b*f - a*g)^3*Log[a + b*x] - 2*b^3*(d*f - c*g)^3*Log[c + d*x]))/(b^3*d^3))/(3*g)","A",1
265,1,118,104,0.1069265,"\int (f+g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \, dx","Integrate[(f + g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]),x]","\frac{b \left(d \left(2 B g^2 x (a d-b c)+A b d (f+g x)^2\right)+b B d^2 (f+g x)^2 \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+2 b B (d f-c g)^2 \log (c+d x)\right)-2 B d^2 (b f-a g)^2 \log (a+b x)}{2 b^2 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,"(-2*B*d^2*(b*f - a*g)^2*Log[a + b*x] + b*(d*(2*B*(-(b*c) + a*d)*g^2*x + A*b*d*(f + g*x)^2) + b*B*d^2*(f + g*x)^2*Log[(e*(a + b*x)^2)/(c + d*x)^2] + 2*b*B*(d*f - c*g)^2*Log[c + d*x]))/(2*b^2*d^2*g)","A",1
266,1,54,54,0.0244684,"\int \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \, dx","Integrate[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",1
267,1,119,144,0.0613042,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{f+g x} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(f + g*x),x]","\frac{\log (f+g x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)-2 B \log \left(\frac{g (a+b x)}{a g-b f}\right)+A+2 B \log \left(\frac{g (c+d x)}{c g-d f}\right)\right)-2 B \text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\right)+2 B \text{Li}_2\left(\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 \text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\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 \text{Li}_2\left(\frac{d (f+g x)}{d f-c g}\right)}{g}+\frac{2 B \log (f+g x) \log \left(-\frac{g (c+d x)}{d f-c g}\right)}{g}",1,"((A - 2*B*Log[(g*(a + b*x))/(-(b*f) + a*g)] + B*Log[(e*(a + b*x)^2)/(c + d*x)^2] + 2*B*Log[(g*(c + d*x))/(-(d*f) + c*g)])*Log[f + g*x] - 2*B*PolyLog[2, (b*(f + g*x))/(b*f - a*g)] + 2*B*PolyLog[2, (d*(f + g*x))/(d*f - c*g)])/g","A",1
268,1,108,90,0.1342935,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{(f+g x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(f + g*x)^2,x]","\frac{\frac{2 B (b \log (a+b x) (d f-c g)+\log (c+d x) (a d g-b d f)+g (b c-a d) \log (f+g x))}{(b f-a g) (d f-c g)}-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{f+g x}}{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,"(-((A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(f + g*x)) + (2*B*(b*(d*f - c*g)*Log[a + b*x] + (-(b*d*f) + a*d*g)*Log[c + d*x] + (b*c - a*d)*g*Log[f + g*x]))/((b*f - a*g)*(d*f - c*g)))/g","A",1
269,1,172,175,0.5473682,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{(f+g x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(f + g*x)^3,x]","\frac{2 B (b c-a d) \left(\frac{b^2 \log (a+b x)}{(b c-a d) (b f-a g)^2}+\frac{\frac{d^2 \log (c+d x)}{a d-b c}+\frac{g (c g-d f)}{(f+g x) (b f-a g)}-\frac{g \log (f+g x) (a d g+b c g-2 b d f)}{(b f-a g)^2}}{(d f-c g)^2}\right)-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{(f+g x)^2}}{2 g}","-\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,"(-((A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(f + g*x)^2) + 2*B*(b*c - a*d)*((b^2*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)^2) + ((g*(-(d*f) + c*g))/((b*f - a*g)*(f + g*x)) + (d^2*Log[c + d*x])/(-(b*c) + a*d) - (g*(-2*b*d*f + b*c*g + a*d*g)*Log[f + g*x])/(b*f - a*g)^2)/(d*f - c*g)^2))/(2*g)","A",1
270,1,263,277,0.7378928,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{(f+g x)^4} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(f + g*x)^4,x]","\frac{2 B (b c-a d) \left(\frac{g \log (f+g x) \left(a^2 d^2 g^2+a b d g (c g-3 d f)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{(b f-a g)^3 (d f-c g)^3}+\frac{b^3 \log (a+b x)}{(b c-a d) (b f-a g)^3}+\frac{d^3 \log (c+d x)}{(b c-a d) (c g-d f)^3}+\frac{g (a d g+b c g-2 b d f)}{(f+g x) (b f-a g)^2 (d f-c g)^2}-\frac{g}{2 (f+g x)^2 (b f-a g) (d f-c g)}\right)-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{(f+g x)^3}}{3 g}","\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,"(-((A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(f + g*x)^3) + 2*B*(b*c - a*d)*(-1/2*g/((b*f - a*g)*(d*f - c*g)*(f + g*x)^2) + (g*(-2*b*d*f + b*c*g + a*d*g))/((b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)) + (b^3*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)^3) + (d^3*Log[c + d*x])/((b*c - a*d)*(-(d*f) + c*g)^3) + (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])/((b*f - a*g)^3*(d*f - c*g)^3)))/(3*g)","A",1
271,1,358,381,0.9673946,"\int \frac{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)}{(f+g x)^5} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(f + g*x)^5,x]","\frac{2 B (b c-a d) \left(-\frac{g \left(a^2 d^2 g^2+a b d g (c g-3 d f)+b^2 \left(c^2 g^2-3 c d f g+3 d^2 f^2\right)\right)}{(f+g x) (b f-a g)^3 (d f-c g)^3}-\frac{g \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(c^2 g^2-2 c d f g+2 d^2 f^2\right)\right)}{(b f-a g)^4 (d f-c g)^4}+\frac{b^4 \log (a+b x)}{(b c-a d) (b f-a g)^4}-\frac{d^4 \log (c+d x)}{(b c-a d) (d f-c g)^4}+\frac{g (a d g+b c g-2 b d f)}{2 (f+g x)^2 (b f-a g)^2 (d f-c g)^2}-\frac{g}{3 (f+g x)^3 (b f-a g) (d f-c g)}\right)-\frac{B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A}{(f+g x)^4}}{4 g}","-\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-\left(b^2 \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,"(-((A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])/(f + g*x)^4) + 2*B*(b*c - a*d)*(-1/3*g/((b*f - a*g)*(d*f - c*g)*(f + g*x)^3) + (g*(-2*b*d*f + b*c*g + a*d*g))/(2*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)^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)))/((b*f - a*g)^3*(d*f - c*g)^3*(f + g*x)) + (b^4*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)^4) - (d^4*Log[c + d*x])/((b*c - a*d)*(d*f - c*g)^4) - (g*(-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])/((b*f - a*g)^4*(d*f - c*g)^4)))/(4*g)","A",1
272,1,746,869,0.9984123,"\int (f+g x)^3 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2 \, dx","Integrate[(f + g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","\frac{(f+g x)^4 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2-\frac{2 B \left(2 B g^4 (b c-a d) \left(2 a^3 d^3 \log (a+b x)+b d x (b c-a d) (2 a d+2 b c-b d x)-2 b^3 c^3 \log (c+d x)\right)+6 A b d g^2 x (b c-a d) \left(a^2 d^2 g^2+a b d g (c g-4 d f)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right)+6 B d g^2 (a+b x) (b c-a d) \left(a^2 d^2 g^2+a b d g (c g-4 d f)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right) \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)-12 B g^2 (b c-a d)^2 \log (c+d x) \left(a^2 d^2 g^2+a b d g (c g-4 d f)+b^2 \left(c^2 g^2-4 c d f g+6 d^2 f^2\right)\right)-6 B g^3 (b c-a d) (a d g+b c g-4 b d f) \left(b \left(d x (a d-b c)+b c^2 \log (c+d x)\right)-a^2 d^2 \log (a+b x)\right)-6 b^4 (d f-c g)^4 \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+2 b^3 d^3 g^4 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^2 d^2 g^3 x^2 (b c-a d) (-a d g-b c g+4 b d f) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+6 d^4 (b f-a g)^4 \log (a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+6 b^4 B (d f-c g)^4 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-6 B d^4 (b f-a g)^4 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)\right)}{3 b^4 d^4}}{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(\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2\right)+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(\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2\right)+2 a d^2 f g b-a^2 d^2 g^2\right) \text{Li}_2\left(\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,"((f + g*x)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2 - (2*B*(6*A*b*d*(b*c - a*d)*g^2*(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 + 6*B*d*(b*c - a*d)*g^2*(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] + 3*b^2*d^2*(b*c - a*d)*g^3*(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^3*d^3*(b*c - a*d)*g^4*x^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + 6*d^4*(b*f - a*g)^4*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - 12*B*(b*c - a*d)^2*g^2*(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] - 6*b^4*(d*f - c*g)^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x] + 2*B*(b*c - a*d)*g^4*(b*d*(b*c - a*d)*x*(2*b*c + 2*a*d - b*d*x) + 2*a^3*d^3*Log[a + b*x] - 2*b^3*c^3*Log[c + d*x]) - 6*B*(b*c - a*d)*g^3*(-4*b*d*f + b*c*g + a*d*g)*(-(a^2*d^2*Log[a + b*x]) + b*(d*(-(b*c) + a*d)*x + b*c^2*Log[c + d*x])) - 6*B*d^4*(b*f - a*g)^4*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 6*b^4*B*(d*f - c*g)^4*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(3*b^4*d^4))/(4*g)","A",1
273,1,497,542,0.5455599,"\int (f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2 \, dx","Integrate[(f + g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","\frac{(f+g x)^3 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2-\frac{2 B \left(-2 B g^3 (b c-a d) \left(a^2 d^2 \log (a+b x)-b \left(d x (a d-b c)+b c^2 \log (c+d x)\right)\right)-2 b^3 (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)+b^2 d^2 g^3 x^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+2 d^3 (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)+2 A b d g^2 x (b c-a d) (-a d g-b c g+3 b d f)+2 b^3 B (d f-c g)^3 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-2 B d^3 (b f-a g)^3 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+2 B d g^2 (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)+4 B g^2 (b c-a d)^2 \log (c+d x) (a d g+b c g-3 b d f)\right)}{b^3 d^3}}{3 g}","\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{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{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\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 (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}+\frac{4 B^2 g^2 x (b c-a d)^2}{3 b^2 d^2}",1,"((f + g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2 - (2*B*(2*A*b*d*(b*c - a*d)*g^2*(3*b*d*f - b*c*g - a*d*g)*x + 2*B*d*(b*c - a*d)*g^2*(3*b*d*f - b*c*g - a*d*g)*(a + b*x)*Log[(e*(a + b*x)^2)/(c + d*x)^2] + b^2*d^2*(b*c - a*d)*g^3*x^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + 2*d^3*(b*f - a*g)^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + 4*B*(b*c - a*d)^2*g^2*(-3*b*d*f + b*c*g + a*d*g)*Log[c + d*x] - 2*b^3*(d*f - c*g)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x] - 2*B*(b*c - a*d)*g^3*(a^2*d^2*Log[a + b*x] - b*(d*(-(b*c) + a*d)*x + b*c^2*Log[c + d*x])) - 2*B*d^3*(b*f - a*g)^3*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 2*b^3*B*(d*f - c*g)^3*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b^3*d^3))/(3*g)","A",1
274,1,351,281,0.3052716,"\int (f+g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2 \, dx","Integrate[(f + g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^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-\frac{4 B \left(-b^2 (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 (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)+A b d g^2 x (b c-a d)+b^2 B (d f-c g)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-B d^2 (b f-a g)^2 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+B d g^2 (a+b x) (b c-a d) \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)-2 B g^2 (b c-a d)^2 \log (c+d x)\right)}{b^2 d^2}}{2 g}","\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 (b c-a d) (-a d g-b c g+2 b d f) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^2 d^2}+\frac{4 B^2 g (b c-a d)^2 \log (c+d x)}{b^2 d^2}",1,"((f + g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2 - (4*B*(A*b*d*(b*c - a*d)*g^2*x + B*d*(b*c - a*d)*g^2*(a + b*x)*Log[(e*(a + b*x)^2)/(c + d*x)^2] + d^2*(b*f - a*g)^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - 2*B*(b*c - a*d)^2*g^2*Log[c + d*x] - b^2*(d*f - c*g)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x] - B*d^2*(b*f - a*g)^2*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + b^2*B*(d*f - c*g)^2*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b^2*d^2))/(2*g)","A",1
275,1,220,129,0.1734869,"\int \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2 \, dx","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2,x]","\frac{4 B \left(a d \log (a+b x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)-b c \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)-a B d \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+b B c \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)\right)}{b d}+x \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)^2","\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}+\frac{8 B^2 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b d}",1,"x*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2 + (4*B*(a*d*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - b*c*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x] - a*B*d*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + b*B*c*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*d)","A",1
276,0,0,285,2.3021323,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{f+g x} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(f + g*x),x]","\int \frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2}{f+g x} \, dx","\frac{4 B \text{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\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{4 B \text{Li}_2\left(\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{\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}-\frac{8 B^2 \text{Li}_3\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{g}+\frac{8 B^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{g}",1,"Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(f + g*x), x]","F",-1
277,1,409,200,0.5878732,"\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","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(f + g*x)^2,x]","\frac{\frac{4 B \left(b \log (a+b x) (d f-c g) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)-d (b f-a g) \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+g (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 B (d f-c g) \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+B d (b f-a g) \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-2 B g (b c-a d) \left(\log (f+g x) \left(\log \left(\frac{g (a+b x)}{a g-b f}\right)-\log \left(\frac{g (c+d x)}{c g-d f}\right)\right)+\text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\right)-\text{Li}_2\left(\frac{d (f+g x)}{d f-c g}\right)\right)\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}{f+g x}}{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)}+\frac{8 B^2 (b c-a d) \text{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{(b f-a g) (d f-c g)}",1,"(-((A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(f + g*x)) + (4*B*(b*(d*f - c*g)*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - d*(b*f - a*g)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x] + (b*c - a*d)*g*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[f + g*x] - b*B*(d*f - c*g)*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + B*d*(b*f - a*g)*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) - 2*B*(b*c - a*d)*g*((Log[(g*(a + b*x))/(-(b*f) + a*g)] - Log[(g*(c + d*x))/(-(d*f) + c*g)])*Log[f + g*x] + PolyLog[2, (b*(f + g*x))/(b*f - a*g)] - PolyLog[2, (d*(f + g*x))/(d*f - c*g)])))/((b*f - a*g)*(d*f - c*g)))/g","B",1
278,1,603,381,1.5757606,"\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","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(f + g*x)^3,x]","-\frac{\frac{4 B (f+g x) \left(-b^2 (f+g x) \log (a+b x) (d f-c g)^2 \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+d^2 (f+g x) (b f-a g)^2 \log (c+d x) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+g (b c-a d) (b f-a g) (d f-c g) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+g (f+g x) (b c-a d) \log (f+g x) (a d g+b c g-2 b d f) \left(B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)+A\right)+b^2 B (f+g x) (d f-c g)^2 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)-B d^2 (f+g x) (b f-a g)^2 \left(2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right)\right)-2 B g (f+g x) (b c-a d) (a d g+b c g-2 b d f) \left(\log (f+g x) \left(\log \left(\frac{g (a+b x)}{a g-b f}\right)-\log \left(\frac{g (c+d x)}{c g-d f}\right)\right)+\text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\right)-\text{Li}_2\left(\frac{d (f+g x)}{d f-c g}\right)\right)-2 B g (f+g x) (b c-a d) (b \log (a+b x) (d f-c g)+\log (c+d x) (a d g-b d f)+g (b c-a d) \log (f+g x))\right)}{(b f-a g)^2 (d f-c g)^2}+\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{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 (b c-a d) (-a d g-b c g+2 b d f) \text{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{(b f-a g)^2 (d f-c g)^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,"-1/2*((A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2 + (4*B*(f + g*x)*((b*c - a*d)*g*(b*f - a*g)*(d*f - c*g)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - b^2*(d*f - c*g)^2*(f + g*x)*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + d^2*(b*f - a*g)^2*(f + g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x] + (b*c - a*d)*g*(-2*b*d*f + b*c*g + a*d*g)*(f + g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[f + g*x] - 2*B*(b*c - a*d)*g*(f + g*x)*(b*(d*f - c*g)*Log[a + b*x] + (-(b*d*f) + a*d*g)*Log[c + d*x] + (b*c - a*d)*g*Log[f + g*x]) + b^2*B*(d*f - c*g)^2*(f + g*x)*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - B*d^2*(b*f - a*g)^2*(f + g*x)*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) - 2*B*(b*c - a*d)*g*(-2*b*d*f + b*c*g + a*d*g)*(f + g*x)*((Log[(g*(a + b*x))/(-(b*f) + a*g)] - Log[(g*(c + d*x))/(-(d*f) + c*g)])*Log[f + g*x] + PolyLog[2, (b*(f + g*x))/(b*f - a*g)] - PolyLog[2, (d*(f + g*x))/(d*f - c*g)])))/((b*f - a*g)^2*(d*f - c*g)^2))/(g*(f + g*x)^2)","A",1
279,1,909,724,3.3700895,"\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","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(f + g*x)^4,x]","-\frac{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2+\frac{2 B (f+g x) \left(2 d^3 (f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \log (c+d x) (b f-a g)^3-2 B d^3 (f+g x)^2 \left(\left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (c+d x)\right) \log (c+d x)+2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right) (b f-a g)^3+(b c-a d) g (d f-c g)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) (b f-a g)^2+2 (b c-a d) g (c g-d f) (-2 b d f+b c g+a d g) (f+g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) (b f-a g)-2 b^3 (d f-c g)^3 (f+g x)^2 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)-2 (b c-a d) g \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2+a d g (c g-3 d f) b+a^2 d^2 g^2\right) (f+g x)^2 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \log (f+g x)-4 B (b c-a d) g (2 b d f-b c g-a d g) (f+g x)^2 (b (d f-c g) \log (a+b x)+(a d g-b d f) \log (c+d x)+(b c-a d) g \log (f+g x))+2 B (b c-a d) g (f+g x) \left(d^2 (f+g x) \log (c+d x) (b f-a g)^2+(b c-a d) g (d f-c g) (b f-a g)-b^2 (d f-c g)^2 (f+g x) \log (a+b x)+(b c-a d) g (-2 b d f+b c g+a d g) (f+g x) \log (f+g x)\right)+2 b^3 B (d f-c g)^3 (f+g x)^2 \left(\log (a+b x) \left(\log (a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+4 B (b c-a d) g \left(\left(3 d^2 f^2-3 c d g f+c^2 g^2\right) b^2+a d g (c g-3 d f) b+a^2 d^2 g^2\right) (f+g x)^2 \left(\left(\log \left(\frac{g (a+b x)}{a g-b f}\right)-\log \left(\frac{g (c+d x)}{c g-d f}\right)\right) \log (f+g x)+\text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\right)-\text{Li}_2\left(\frac{d (f+g x)}{d f-c g}\right)\right)\right)}{(b f-a g)^3 (d f-c g)^3}}{3 g (f+g x)^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{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{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\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,"-1/3*((A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2 + (2*B*(f + g*x)*((b*c - a*d)*g*(b*f - a*g)^2*(d*f - c*g)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + 2*(b*c - a*d)*g*(b*f - a*g)*(-(d*f) + c*g)*(-2*b*d*f + b*c*g + a*d*g)*(f + g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) - 2*b^3*(d*f - c*g)^3*(f + g*x)^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]) + 2*d^3*(b*f - a*g)^3*(f + g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x] - 2*(b*c - a*d)*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))*(f + g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[f + g*x] - 4*B*(b*c - a*d)*g*(2*b*d*f - b*c*g - a*d*g)*(f + g*x)^2*(b*(d*f - c*g)*Log[a + b*x] + (-(b*d*f) + a*d*g)*Log[c + d*x] + (b*c - a*d)*g*Log[f + g*x]) + 2*B*(b*c - a*d)*g*(f + g*x)*((b*c - a*d)*g*(b*f - a*g)*(d*f - c*g) - b^2*(d*f - c*g)^2*(f + g*x)*Log[a + b*x] + d^2*(b*f - a*g)^2*(f + g*x)*Log[c + d*x] + (b*c - a*d)*g*(-2*b*d*f + b*c*g + a*d*g)*(f + g*x)*Log[f + g*x]) + 2*b^3*B*(d*f - c*g)^3*(f + g*x)^2*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - 2*B*d^3*(b*f - a*g)^3*(f + g*x)^2*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 4*B*(b*c - a*d)*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))*(f + g*x)^2*((Log[(g*(a + b*x))/(-(b*f) + a*g)] - Log[(g*(c + d*x))/(-(d*f) + c*g)])*Log[f + g*x] + PolyLog[2, (b*(f + g*x))/(b*f - a*g)] - PolyLog[2, (d*(f + g*x))/(d*f - c*g)])))/((b*f - a*g)^3*(d*f - c*g)^3))/(g*(f + g*x)^3)","A",1
280,1,1453,1154,7.3447704,"\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","Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(f + g*x)^5,x]","\frac{B (b c-a d) \left(\frac{\log (a+b x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) b^4}{(b c-a d) (b f-a g)^4}-\frac{B \left(\log ^2(a+b x)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right) \log (a+b x)-2 \text{Li}_2\left(-\frac{d (a+b x)}{b c-a d}\right)\right) b^4}{(b c-a d) (b f-a g)^4}-\frac{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) \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{g (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{g \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{d^4 \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right) \log (c+d x)}{(b c-a d) (d f-c g)^4}+\frac{g (2 b d f-b c g-a d g) \left(2 d^2 f^2 b^2+c^2 g^2 b^2-2 c d f g 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 (b c-a d) 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) \left(\frac{b \log (a+b x)}{(b c-a d) (b f-a g)}-\frac{d \log (c+d x)}{(b c-a d) (d f-c g)}+\frac{g \log (f+g x)}{(b f-a g) (d f-c g)}\right)}{(b f-a g)^3 (d f-c g)^3}-\frac{B (b c-a d) g (2 b d f-b c g-a d g) \left(-\frac{\log (a+b x) b^2}{(b c-a d) (b f-a g)^2}+\frac{d^2 \log (c+d x)}{(b c-a d) (d f-c g)^2}-\frac{g (2 b d f-b c g-a d g) \log (f+g x)}{(b f-a g)^2 (d f-c g)^2}+\frac{g}{(b f-a g) (d f-c g) (f+g x)}\right)}{(b f-a g)^2 (d f-c g)^2}-\frac{B (b c-a d) g \left(-\frac{2 \log (a+b x) b^3}{(b c-a d) (b f-a g)^3}+\frac{2 d^3 \log (c+d x)}{(b c-a d) (d f-c g)^3}-\frac{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)}{(b f-a g)^3 (d f-c g)^3}+\frac{2 g (2 b d f-b c g-a d g)}{(b f-a g)^2 (d f-c g)^2 (f+g x)}+\frac{g}{(b f-a g) (d f-c g) (f+g x)^2}\right)}{3 (b f-a g) (d f-c g)}+\frac{B d^4 \left(-\log ^2(c+d x)+2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x)+2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right)}{(b c-a d) (d f-c g)^4}-\frac{2 B g (2 b d f-b c g-a d g) \left(2 d^2 f^2 b^2+c^2 g^2 b^2-2 c d f g b^2-2 a d^2 f g b+a^2 d^2 g^2\right) \left(\log \left(-\frac{g (a+b x)}{b f-a g}\right) \log (f+g x)-\log \left(-\frac{g (c+d x)}{d f-c g}\right) \log (f+g x)+\text{Li}_2\left(\frac{b (f+g x)}{b f-a g}\right)-\text{Li}_2\left(\frac{d (f+g x)}{d f-c g}\right)\right)}{(b f-a g)^4 (d f-c g)^4}\right)}{g}-\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{\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(\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2\right)+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(\left(2 d^2 f^2-2 c d g f+c^2 g^2\right) b^2\right)+2 a d^2 f g b-a^2 d^2 g^2\right) \text{Li}_2\left(\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,"-1/4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2/(g*(f + g*x)^4) + (B*(b*c - a*d)*(-1/3*(g*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/((b*f - a*g)*(d*f - c*g)*(f + g*x)^3) - (g*(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) - (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))*(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*Log[a + b*x]*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]))/((b*c - a*d)*(b*f - a*g)^4) - (d^4*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])*Log[c + d*x])/((b*c - a*d)*(d*f - c*g)^4) + (g*(2*b*d*f - b*c*g - a*d*g)*(2*b^2*d^2*f^2 - 2*b^2*c*d*f*g - 2*a*b*d^2*f*g + b^2*c^2*g^2 + a^2*d^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*(b*c - a*d)*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))*((b*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)) - (d*Log[c + d*x])/((b*c - a*d)*(d*f - c*g)) + (g*Log[f + g*x])/((b*f - a*g)*(d*f - c*g))))/((b*f - a*g)^3*(d*f - c*g)^3) - (B*(b*c - a*d)*g*(2*b*d*f - b*c*g - a*d*g)*(g/((b*f - a*g)*(d*f - c*g)*(f + g*x)) - (b^2*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)^2) + (d^2*Log[c + d*x])/((b*c - a*d)*(d*f - c*g)^2) - (g*(2*b*d*f - b*c*g - a*d*g)*Log[f + g*x])/((b*f - a*g)^2*(d*f - c*g)^2)))/((b*f - a*g)^2*(d*f - c*g)^2) - (B*(b*c - a*d)*g*(g/((b*f - a*g)*(d*f - c*g)*(f + g*x)^2) + (2*g*(2*b*d*f - b*c*g - a*d*g))/((b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)) - (2*b^3*Log[a + b*x])/((b*c - a*d)*(b*f - a*g)^3) + (2*d^3*Log[c + d*x])/((b*c - a*d)*(d*f - c*g)^3) - (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])/((b*f - a*g)^3*(d*f - c*g)^3)))/(3*(b*f - a*g)*(d*f - c*g)) - (b^4*B*(Log[a + b*x]^2 - 2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] - 2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))]))/((b*c - a*d)*(b*f - a*g)^4) + (B*d^4*(2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x] - Log[c + d*x]^2 + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]))/((b*c - a*d)*(d*f - c*g)^4) - (2*B*g*(2*b*d*f - b*c*g - a*d*g)*(2*b^2*d^2*f^2 - 2*b^2*c*d*f*g - 2*a*b*d^2*f*g + b^2*c^2*g^2 + a^2*d^2*g^2)*(Log[-((g*(a + b*x))/(b*f - a*g))]*Log[f + g*x] - Log[-((g*(c + d*x))/(d*f - c*g))]*Log[f + g*x] + PolyLog[2, (b*(f + g*x))/(b*f - a*g)] - PolyLog[2, (d*(f + g*x))/(d*f - c*g)]))/((b*f - a*g)^4*(d*f - c*g)^4)))/g","A",1
281,0,0,34,0.1798482,"\int \frac{(f+g x)^2}{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)} \, dx","Integrate[(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,"Integrate[(f + g*x)^2/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]), x]","A",-1
282,0,0,32,0.1463559,"\int \frac{f+g x}{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)} \, dx","Integrate[(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,"Integrate[(f + g*x)/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2]), x]","A",-1
283,0,0,26,0.0418687,"\int \frac{1}{A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)} \, dx","Integrate[(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,"Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^(-1), x]","A",-1
284,0,0,34,0.0902917,"\int \frac{1}{(f+g x) \left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)} \, dx","Integrate[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,"Integrate[1/((f + g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])), x]","A",-1
285,0,0,34,0.0938429,"\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","Integrate[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,"Integrate[1/((f + g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])), x]","A",-1
286,0,0,34,0.095532,"\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","Integrate[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,"Integrate[1/((f + g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])), x]","A",-1
287,0,0,34,0.7154522,"\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","Integrate[(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,"Integrate[(f + g*x)^2/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2, x]","A",-1
288,0,0,32,0.4332666,"\int \frac{f+g x}{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","Integrate[(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,"Integrate[(f + g*x)/(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2, x]","A",-1
289,0,0,26,0.2320878,"\int \frac{1}{\left(A+B \log \left(\frac{e (a+b x)^2}{(c+d x)^2}\right)\right)^2} \, dx","Integrate[(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,"Integrate[(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^(-2), x]","A",-1
290,0,0,34,0.4980785,"\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","Integrate[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,"Integrate[1/((f + g*x)*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2), x]","A",-1
291,0,0,34,0.6063527,"\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","Integrate[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,"Integrate[1/((f + g*x)^2*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2), x]","A",-1
292,0,0,34,0.6410702,"\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","Integrate[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,"Integrate[1/((f + g*x)^3*(A + B*Log[(e*(a + b*x)^2)/(c + d*x)^2])^2), x]","A",-1
293,1,463,365,1.0087735,"\int (g+h x)^4 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Integrate[(g + h*x)^4*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]),x]","\frac{b d x \left(B h n (b c-a d) \left(12 a^3 d^3 h^3-6 a^2 b d^2 h^2 (-2 c h+10 d g+d h x)+2 a b^2 d h \left(6 c^2 h^2-3 c d h (10 g+h x)+d^2 \left(60 g^2+15 g h x+2 h^2 x^2\right)\right)-\left(b^3 \left(-12 c^3 h^3+6 c^2 d h^2 (10 g+h x)-2 c d^2 h \left(60 g^2+15 g h x+2 h^2 x^2\right)+d^3 \left(120 g^3+60 g^2 h x+20 g h^2 x^2+3 h^3 x^3\right)\right)\right)\right)+12 A b^4 d^4 \left(5 g^4+10 g^3 h x+10 g^2 h^2 x^2+5 g h^3 x^3+h^4 x^4\right)\right)+12 a^2 B d^5 h n \left(a^3 h^3-5 a^2 b g h^2+10 a b^2 g^2 h-10 b^3 g^3\right) \log (a+b x)-12 b^4 B n \log (c+d x) \left(b c \left(c^4 h^4-5 c^3 d g h^3+10 c^2 d^2 g^2 h^2-10 c d^3 g^3 h+5 d^4 g^4\right)-5 a d^5 g^4\right)+12 b^4 B d^5 \left(5 a g^4+b x \left(5 g^4+10 g^3 h x+10 g^2 h^2 x^2+5 g h^3 x^3+h^4 x^4\right)\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{60 b^5 d^5}","-\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^3 d^3 h^3-a^2 b d^2 h^2 (5 d g-c h)+a b^2 d h \left(c^2 h^2-5 c d g h+10 d^2 g^2\right)-\left(b^3 \left(-c^3 h^3+5 c^2 d g h^2-10 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 n (b g-a h)^5 \log (a+b x)}{5 b^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 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*d*x*(12*A*b^4*d^4*(5*g^4 + 10*g^3*h*x + 10*g^2*h^2*x^2 + 5*g*h^3*x^3 + h^4*x^4) + B*(b*c - a*d)*h*n*(12*a^3*d^3*h^3 - 6*a^2*b*d^2*h^2*(10*d*g - 2*c*h + d*h*x) + 2*a*b^2*d*h*(6*c^2*h^2 - 3*c*d*h*(10*g + h*x) + d^2*(60*g^2 + 15*g*h*x + 2*h^2*x^2)) - b^3*(-12*c^3*h^3 + 6*c^2*d*h^2*(10*g + h*x) - 2*c*d^2*h*(60*g^2 + 15*g*h*x + 2*h^2*x^2) + d^3*(120*g^3 + 60*g^2*h*x + 20*g*h^2*x^2 + 3*h^3*x^3)))) + 12*a^2*B*d^5*h*(-10*b^3*g^3 + 10*a*b^2*g^2*h - 5*a^2*b*g*h^2 + a^3*h^3)*n*Log[a + b*x] - 12*b^4*B*(-5*a*d^5*g^4 + b*c*(5*d^4*g^4 - 10*c*d^3*g^3*h + 10*c^2*d^2*g^2*h^2 - 5*c^3*d*g*h^3 + c^4*h^4))*n*Log[c + d*x] + 12*b^4*B*d^5*(5*a*g^4 + b*x*(5*g^4 + 10*g^3*h*x + 10*g^2*h^2*x^2 + 5*g*h^3*x^3 + h^4*x^4))*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(60*b^5*d^5)","A",1
294,1,314,236,0.6104076,"\int (g+h x)^3 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Integrate[(g + h*x)^3*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]),x]","\frac{b d x \left(6 A b^3 d^3 \left(4 g^3+6 g^2 h x+4 g h^2 x^2+h^3 x^3\right)-B h n (b c-a d) \left(6 a^2 d^2 h^2-3 a b d h (-2 c h+8 d g+d h x)+b^2 \left(6 c^2 h^2-3 c d h (8 g+h x)+2 d^2 \left(18 g^2+6 g h x+h^2 x^2\right)\right)\right)\right)-6 a^2 B d^4 h n \left(a^2 h^2-4 a b g h+6 b^2 g^2\right) \log (a+b x)+6 b^3 B n \log (c+d x) \left(4 a d^4 g^3+b c \left(c^3 h^3-4 c^2 d g h^2+6 c d^2 g^2 h-4 d^3 g^3\right)\right)+6 b^3 B d^4 \left(4 a g^3+b x \left(4 g^3+6 g^2 h x+4 g h^2 x^2+h^3 x^3\right)\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{24 b^4 d^4}","-\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 n (b g-a h)^4 \log (a+b x)}{4 b^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 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*d*x*(6*A*b^3*d^3*(4*g^3 + 6*g^2*h*x + 4*g*h^2*x^2 + h^3*x^3) - B*(b*c - a*d)*h*n*(6*a^2*d^2*h^2 - 3*a*b*d*h*(8*d*g - 2*c*h + d*h*x) + b^2*(6*c^2*h^2 - 3*c*d*h*(8*g + h*x) + 2*d^2*(18*g^2 + 6*g*h*x + h^2*x^2)))) - 6*a^2*B*d^4*h*(6*b^2*g^2 - 4*a*b*g*h + a^2*h^2)*n*Log[a + b*x] + 6*b^3*B*(4*a*d^4*g^3 + b*c*(-4*d^3*g^3 + 6*c*d^2*g^2*h - 4*c^2*d*g*h^2 + c^3*h^3))*n*Log[c + d*x] + 6*b^3*B*d^4*(4*a*g^3 + b*x*(4*g^3 + 6*g^2*h*x + 4*g*h^2*x^2 + h^3*x^3))*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(24*b^4*d^4)","A",1
295,1,204,158,0.3925345,"\int (g+h x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Integrate[(g + h*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]),x]","\frac{2 a^2 B d^3 h n (a h-3 b g) \log (a+b x)+b \left(d x \left(B h n (b c-a d) (2 a d h+2 b c h-6 b d g-b d h x)+2 A b^2 d^2 \left(3 g^2+3 g h x+h^2 x^2\right)\right)-2 b B n \log (c+d x) \left(b c \left(c^2 h^2-3 c d g h+3 d^2 g^2\right)-3 a d^3 g^2\right)+2 b B d^3 \left(3 a g^2+b x \left(3 g^2+3 g h x+h^2 x^2\right)\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)}{6 b^3 d^3}","\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 n (b g-a h)^3 \log (a+b x)}{3 b^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 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,"(2*a^2*B*d^3*h*(-3*b*g + a*h)*n*Log[a + b*x] + b*(d*x*(B*(b*c - a*d)*h*n*(-6*b*d*g + 2*b*c*h + 2*a*d*h - b*d*h*x) + 2*A*b^2*d^2*(3*g^2 + 3*g*h*x + h^2*x^2)) - 2*b*B*(-3*a*d^3*g^2 + b*c*(3*d^2*g^2 - 3*c*d*g*h + c^2*h^2))*n*Log[c + d*x] + 2*b*B*d^3*(3*a*g^2 + b*x*(3*g^2 + 3*g*h*x + h^2*x^2))*Log[(e*(a + b*x)^n)/(c + d*x)^n]))/(6*b^3*d^3)","A",1
296,1,124,116,0.1939952,"\int (g+h x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Integrate[(g + h*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]),x]","\frac{-a^2 B d^2 h n \log (a+b x)+b d \left(x (B h n (a d-b c)+A b d (2 g+h x))+B d (2 a g+b x (2 g+h x)) \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)+b B n \log (c+d x) \left(2 a d^2 g+b c (c h-2 d g)\right)}{2 b^2 d^2}","\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,"(-(a^2*B*d^2*h*n*Log[a + b*x]) + b*B*(2*a*d^2*g + b*c*(-2*d*g + c*h))*n*Log[c + d*x] + b*d*(x*(B*(-(b*c) + a*d)*h*n + A*b*d*(2*g + h*x)) + B*d*(2*a*g + b*x*(2*g + h*x))*Log[(e*(a + b*x)^n)/(c + d*x)^n]))/(2*b^2*d^2)","A",1
297,1,57,57,0.0125606,"\int \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \, dx","Integrate[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",1
298,1,150,148,0.1111354,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{g+h x} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(g + h*x),x]","\frac{\log (g+h x) \left(B \left(\log \left(e (a+b x)^n (c+d x)^{-n}\right)-n \log (a+b x)+n \log (c+d x)\right)+A\right)+B n \left(\text{Li}_2\left(\frac{h (a+b x)}{a h-b g}\right)+\log (a+b x) \log \left(\frac{b (g+h x)}{b g-a h}\right)\right)-B n \left(\text{Li}_2\left(\frac{h (c+d x)}{c h-d g}\right)+\log (c+d x) \log \left(\frac{d (g+h x)}{d g-c h}\right)\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 \text{Li}_2\left(\frac{b (g+h x)}{b g-a h}\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 \text{Li}_2\left(\frac{d (g+h x)}{d g-c 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 + B*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n]))*Log[g + h*x] + B*n*(Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)] + PolyLog[2, (h*(a + b*x))/(-(b*g) + a*h)]) - B*n*(Log[c + d*x]*Log[(d*(g + h*x))/(d*g - c*h)] + PolyLog[2, (h*(c + d*x))/(-(d*g) + c*h)]))/h","A",1
299,1,117,120,0.2029288,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(g + h*x)^2,x]","\frac{-\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{g+h x}+\frac{B n (b \log (a+b x) (d g-c h)+\log (c+d x) (a d h-b d g)+h (b c-a d) \log (g+h x))}{(b g-a h) (d g-c h)}-\frac{A}{g+h x}}{h}","-\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/(g + h*x)) - (B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(g + h*x) + (B*n*(b*(d*g - c*h)*Log[a + b*x] + (-(b*d*g) + a*d*h)*Log[c + d*x] + (b*c - a*d)*h*Log[g + h*x]))/((b*g - a*h)*(d*g - c*h)))/h","A",1
300,1,178,191,0.6173545,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(g + h*x)^3,x]","-\frac{B n (b c-a d) \left(\frac{\frac{d^2 \log (c+d x)}{b c-a d}+\frac{h \left(\frac{(b g-a h) (d g-c h)}{g+h x}+\log (g+h x) (a d h+b c h-2 b d g)\right)}{(b g-a h)^2}}{(d g-c h)^2}-\frac{b^2 \log (a+b x)}{(b c-a d) (b g-a h)^2}\right)+\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x)^2}+\frac{A}{(g+h x)^2}}{2 h}","-\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,"-1/2*(A/(g + h*x)^2 + (B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(g + h*x)^2 + B*(b*c - a*d)*n*(-((b^2*Log[a + b*x])/((b*c - a*d)*(b*g - a*h)^2)) + ((d^2*Log[c + d*x])/(b*c - a*d) + (h*(((b*g - a*h)*(d*g - c*h))/(g + h*x) + (-2*b*d*g + b*c*h + a*d*h)*Log[g + h*x]))/(b*g - a*h)^2)/(d*g - c*h)^2))/h","A",1
301,1,273,284,1.1387489,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x)^4} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(g + h*x)^4,x]","-\frac{B n (b c-a d) \left(-\frac{2 h \log (g+h x) \left(a^2 d^2 h^2+a b d h (c h-3 d g)+b^2 \left(c^2 h^2-3 c d g h+3 d^2 g^2\right)\right)}{(b g-a h)^3 (d g-c h)^3}-\frac{2 b^3 \log (a+b x)}{(b c-a d) (b g-a h)^3}+\frac{2 d^3 \log (c+d x)}{(b c-a d) (d g-c h)^3}-\frac{2 h (a d h+b c h-2 b d g)}{(g+h x) (b g-a h)^2 (d g-c h)^2}+\frac{h}{(g+h x)^2 (b g-a h) (d g-c h)}\right)+\frac{2 B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x)^3}+\frac{2 A}{(g+h x)^3}}{6 h}","\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,"-1/6*((2*A)/(g + h*x)^3 + (2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(g + h*x)^3 + B*(b*c - a*d)*n*(h/((b*g - a*h)*(d*g - c*h)*(g + h*x)^2) - (2*h*(-2*b*d*g + b*c*h + a*d*h))/((b*g - a*h)^2*(d*g - c*h)^2*(g + h*x)) - (2*b^3*Log[a + b*x])/((b*c - a*d)*(b*g - a*h)^3) + (2*d^3*Log[c + d*x])/((b*c - a*d)*(d*g - c*h)^3) - (2*h*(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))*Log[g + h*x])/((b*g - a*h)^3*(d*g - c*h)^3)))/h","A",1
302,1,366,389,1.2089731,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x)^5} \, dx","Integrate[(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(-\frac{h \left(a^2 d^2 h^2+a b d h (c h-3 d g)+b^2 \left(c^2 h^2-3 c d g h+3 d^2 g^2\right)\right)}{(g+h x) (b g-a h)^3 (d g-c h)^3}-\frac{h \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(c^2 h^2-2 c d g h+2 d^2 g^2\right)\right)}{(b g-a h)^4 (d g-c h)^4}+\frac{b^4 \log (a+b x)}{(b c-a d) (b g-a h)^4}-\frac{d^4 \log (c+d x)}{(b c-a d) (d g-c h)^4}+\frac{h (a d h+b c h-2 b d g)}{2 (g+h x)^2 (b g-a h)^2 (d g-c h)^2}-\frac{h}{3 (g+h x)^3 (b g-a h) (d g-c h)}\right)+\frac{B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(g+h x)^4}+\frac{A}{(g+h x)^4}}{4 h}","-\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-\left(b^2 \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,"-1/4*(A/(g + h*x)^4 + (B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(g + h*x)^4 - B*(b*c - a*d)*n*(-1/3*h/((b*g - a*h)*(d*g - c*h)*(g + h*x)^3) + (h*(-2*b*d*g + b*c*h + a*d*h))/(2*(b*g - a*h)^2*(d*g - c*h)^2*(g + h*x)^2) - (h*(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)))/((b*g - a*h)^3*(d*g - c*h)^3*(g + h*x)) + (b^4*Log[a + b*x])/((b*c - a*d)*(b*g - a*h)^4) - (d^4*Log[c + d*x])/((b*c - a*d)*(d*g - c*h)^4) - (h*(-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))*Log[g + h*x])/((b*g - a*h)^4*(d*g - c*h)^4)))/h","A",1
303,1,906,570,1.8436429,"\int (g+h x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 \, dx","Integrate[(g + h*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2,x]","\frac{-a B^2 \left(3 b^2 g^2-3 a b h g+a^2 h^2\right) n^2 \log ^2(a+b x) d^3+B n \log (a+b x) \left(2 B c \left(3 d^2 g^2-3 c d h g+c^2 h^2\right) n \log (c+d x) b^3+2 B \left(-c \left(3 d^2 g^2-3 c d h g+c^2 h^2\right) b^3+3 a d^3 g^2 b^2-3 a^2 d^3 g h b+a^3 d^3 h^2\right) n \log \left(\frac{b (c+d x)}{b c-a d}\right)+a d \left(2 A \left(3 b^2 g^2-3 a b h g+a^2 h^2\right) d^2+2 B \left(3 b^2 g^2-3 a b h g+a^2 h^2\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) d^2+B \left(2 \left(3 d^2 g^2-3 c d h g+c^2 h^2\right) b^2+a d h (6 d g+c h) b-3 a^2 d^2 h^2\right) n\right)\right)+b \left(-b^2 B^2 c \left(3 d^2 g^2-3 c d h g+c^2 h^2\right) n^2 \log ^2(c+d x)+B n \left(-2 A c \left(3 d^2 g^2-3 c d h g+c^2 h^2\right) b^2-2 B c \left(3 d^2 g^2-3 c d h g+c^2 h^2\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right) b^2+B \left(-3 b^2 h (c h-2 d g) c^2+2 a^2 d^2 h^2 c+a b d \left(-6 d^2 g^2-6 c d h g+c^2 h^2\right)\right) n\right) \log (c+d x)+d \left(B^2 d^2 x \left(3 g^2+3 h x g+h^2 x^2\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right) b^2+x \left(A^2 \left(3 g^2+3 h x g+h^2 x^2\right) d^2+B^2 c^2 h^2 n^2+A B c h n (2 c h-d (6 g+h x))\right) b^2+a B n \left(A d^2 \left(-6 g^2+6 h x g+h^2 x^2\right)-2 B n \left(3 d^2 g^2+c^2 h^2+c d h (h x-3 g)\right)\right) b+a^2 B d^2 h^2 n (B n-2 A) x+B \left(x \left(2 A \left(3 g^2+3 h x g+h^2 x^2\right) d^2+B c h n (-6 d g+2 c h-d h x)\right) b^2+a B d^2 n \left(-6 g^2+6 h x g+h^2 x^2\right) b-2 a^2 B d^2 h^2 n x\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)\right)+2 B^2 \left(-c \left(3 d^2 g^2-3 c d h g+c^2 h^2\right) b^3+3 a d^3 g^2 b^2-3 a^2 d^3 g h b+a^3 d^3 h^2\right) n^2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\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^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{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\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 (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}+\frac{B^2 h^2 n^2 x (b c-a d)^2}{3 b^2 d^2}",1,"(-(a*B^2*d^3*(3*b^2*g^2 - 3*a*b*g*h + a^2*h^2)*n^2*Log[a + b*x]^2) + B*n*Log[a + b*x]*(2*b^3*B*c*(3*d^2*g^2 - 3*c*d*g*h + c^2*h^2)*n*Log[c + d*x] + 2*B*(3*a*b^2*d^3*g^2 - 3*a^2*b*d^3*g*h + a^3*d^3*h^2 - b^3*c*(3*d^2*g^2 - 3*c*d*g*h + c^2*h^2))*n*Log[(b*(c + d*x))/(b*c - a*d)] + a*d*(2*A*d^2*(3*b^2*g^2 - 3*a*b*g*h + a^2*h^2) + B*(-3*a^2*d^2*h^2 + a*b*d*h*(6*d*g + c*h) + 2*b^2*(3*d^2*g^2 - 3*c*d*g*h + c^2*h^2))*n + 2*B*d^2*(3*b^2*g^2 - 3*a*b*g*h + a^2*h^2)*Log[(e*(a + b*x)^n)/(c + d*x)^n])) + b*(-(b^2*B^2*c*(3*d^2*g^2 - 3*c*d*g*h + c^2*h^2)*n^2*Log[c + d*x]^2) + B*n*Log[c + d*x]*(-2*A*b^2*c*(3*d^2*g^2 - 3*c*d*g*h + c^2*h^2) + B*(2*a^2*c*d^2*h^2 - 3*b^2*c^2*h*(-2*d*g + c*h) + a*b*d*(-6*d^2*g^2 - 6*c*d*g*h + c^2*h^2))*n - 2*b^2*B*c*(3*d^2*g^2 - 3*c*d*g*h + c^2*h^2)*Log[(e*(a + b*x)^n)/(c + d*x)^n]) + d*(a^2*B*d^2*h^2*n*(-2*A + B*n)*x + a*b*B*n*(A*d^2*(-6*g^2 + 6*g*h*x + h^2*x^2) - 2*B*n*(3*d^2*g^2 + c^2*h^2 + c*d*h*(-3*g + h*x))) + b^2*x*(B^2*c^2*h^2*n^2 + A^2*d^2*(3*g^2 + 3*g*h*x + h^2*x^2) + A*B*c*h*n*(2*c*h - d*(6*g + h*x))) + B*(-2*a^2*B*d^2*h^2*n*x + a*b*B*d^2*n*(-6*g^2 + 6*g*h*x + h^2*x^2) + b^2*x*(B*c*h*n*(-6*d*g + 2*c*h - d*h*x) + 2*A*d^2*(3*g^2 + 3*g*h*x + h^2*x^2)))*Log[(e*(a + b*x)^n)/(c + d*x)^n] + b^2*B^2*d^2*x*(3*g^2 + 3*g*h*x + h^2*x^2)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)) + 2*B^2*(3*a*b^2*d^3*g^2 - 3*a^2*b*d^3*g*h + a^3*d^3*h^2 - b^3*c*(3*d^2*g^2 - 3*c*d*g*h + c^2*h^2))*n^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b^3*d^3)","A",1
304,1,472,294,0.9745426,"\int (g+h x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 \, dx","Integrate[(g + h*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2,x]","\frac{-2 B n \log (a+b x) \left(a d \left(A (a d h-2 b d g)+B d (a h-2 b g) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+B n (-a d h+b c h-2 b d g)\right)-B n (b c-a d) (a d h+b c h-2 b d g) \log \left(\frac{b (c+d x)}{b c-a d}\right)+b^2 B c n (c h-2 d g) \log (c+d x)\right)+b \left(d \left(2 B \log \left(e (a+b x)^n (c+d x)^{-n}\right) (a B d n (h x-2 g)+b x (2 A d g+A d h x-B c h n))+2 a B n (-2 A d g+A d h x+B c h n-2 B d g n)+b B^2 d x (2 g+h x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+A b x (2 A d g+A d h x-2 B c h n)\right)+2 B n \log (c+d x) \left(B n \left(b c^2 h-a d (c h+2 d g)\right)+b B c (c h-2 d g) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A b c (c h-2 d g)\right)+b B^2 c n^2 (c h-2 d g) \log ^2(c+d x)\right)+2 B^2 n^2 (b c-a d) (a d h+b c h-2 b d g) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)+a B^2 d^2 n^2 (a h-2 b g) \log ^2(a+b x)}{2 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 n^2 (b c-a d) (-a d h-b c h+2 b d g) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^2 d^2}+\frac{B^2 h n^2 (b c-a d)^2 \log (c+d x)}{b^2 d^2}",1,"(a*B^2*d^2*(-2*b*g + a*h)*n^2*Log[a + b*x]^2 - 2*B*n*Log[a + b*x]*(b^2*B*c*(-2*d*g + c*h)*n*Log[c + d*x] - B*(b*c - a*d)*(-2*b*d*g + b*c*h + a*d*h)*n*Log[(b*(c + d*x))/(b*c - a*d)] + a*d*(A*(-2*b*d*g + a*d*h) + B*(-2*b*d*g + b*c*h - a*d*h)*n + B*d*(-2*b*g + a*h)*Log[(e*(a + b*x)^n)/(c + d*x)^n])) + b*(b*B^2*c*(-2*d*g + c*h)*n^2*Log[c + d*x]^2 + 2*B*n*Log[c + d*x]*(A*b*c*(-2*d*g + c*h) + B*(b*c^2*h - a*d*(2*d*g + c*h))*n + b*B*c*(-2*d*g + c*h)*Log[(e*(a + b*x)^n)/(c + d*x)^n]) + d*(A*b*x*(2*A*d*g - 2*B*c*h*n + A*d*h*x) + 2*a*B*n*(-2*A*d*g - 2*B*d*g*n + B*c*h*n + A*d*h*x) + 2*B*(a*B*d*n*(-2*g + h*x) + b*x*(2*A*d*g - B*c*h*n + A*d*h*x))*Log[(e*(a + b*x)^n)/(c + d*x)^n] + b*B^2*d*x*(2*g + h*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2)) + 2*B^2*(b*c - a*d)*(-2*b*d*g + b*c*h + a*d*h)*n^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(2*b^2*d^2)","A",1
305,1,217,137,0.1565344,"\int \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2 \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2,x]","\frac{2 A B d (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)-2 A B n (b c-a d) \log (c+d x)+B^2 n (b c-a d) \left(2 n \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-\log \left(\frac{b c-a d}{b c+b d x}\right) \left(-2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 n \log \left(\frac{d (a+b x)}{a d-b c}\right)+n \log \left(\frac{b c-a d}{b c+b d x}\right)\right)\right)+B^2 d (a+b x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+A^2 b d x}{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}+\frac{2 B^2 n^2 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b d}",1,"(A^2*b*d*x - 2*A*B*(b*c - a*d)*n*Log[c + d*x] + 2*A*B*d*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n] + B^2*d*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + B^2*(b*c - a*d)*n*(-(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*n*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + n*Log[(b*c - a*d)/(b*c + b*d*x)])) + 2*n*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]))/(b*d)","A",1
306,1,1082,301,0.4878719,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{g+h x} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(g + h*x),x]","\frac{-2 n \left(-n \log (a+b x)+n \log (c+d x)+\log \left(e (a+b x)^n (c+d x)^{-n}\right)\right) \left(\log (c+d x) \log \left(\frac{d (g+h x)}{d g-c h}\right)+\text{Li}_2\left(\frac{h (c+d x)}{c h-d g}\right)\right) B^2+n^2 \left(\log \left(\frac{b (g+h x)}{b g-a h}\right) \log ^2(a+b x)+2 \text{Li}_2\left(\frac{h (a+b x)}{a h-b g}\right) \log (a+b x)-2 \text{Li}_3\left(\frac{h (a+b x)}{a h-b g}\right)\right) B^2+n^2 \left(\log \left(\frac{d (g+h x)}{d g-c h}\right) \log ^2(c+d x)+2 \text{Li}_2\left(\frac{h (c+d x)}{c h-d g}\right) \log (c+d x)-2 \text{Li}_3\left(\frac{h (c+d x)}{c h-d g}\right)\right) B^2-2 n^2 \left(\frac{1}{2} \left(\log \left(\frac{a d-b c}{d (a+b x)}\right)+\log \left(\frac{b (g+h x)}{b g-a h}\right)-\log \left(\frac{(a d-b c) (g+h x)}{(d g-c h) (a+b x)}\right)\right) \log ^2\left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right)+\log \left(\frac{h (c+d x)}{c h-d g}\right) \left(\log \left(\frac{d (g+h x)}{d g-c h}\right)-\log \left(\frac{b (g+h x)}{b g-a h}\right)\right) \log \left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right)+\left(\text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)-\text{Li}_2\left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right)\right) \log \left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right)+\log (a+b x) \log (c+d x) \log \left(\frac{b (g+h x)}{b g-a h}\right)+\frac{1}{2} \log \left(\frac{h (c+d x)}{c h-d g}\right) \left(\log \left(\frac{h (c+d x)}{c h-d g}\right)-2 \log (a+b x)\right) \left(\log \left(\frac{b (g+h x)}{b g-a h}\right)-\log \left(\frac{d (g+h x)}{d g-c h}\right)\right)+\left(\log (c+d x)-\log \left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right)\right) \text{Li}_2\left(\frac{h (a+b x)}{a h-b g}\right)+\left(\log (a+b x)+\log \left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right)\right) \text{Li}_2\left(\frac{h (c+d x)}{c h-d g}\right)-\text{Li}_3\left(\frac{h (a+b x)}{a h-b g}\right)-\text{Li}_3\left(\frac{h (c+d x)}{c h-d g}\right)-\text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)+\text{Li}_3\left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right)\right) B^2+2 n \left(A+B \left(-n \log (a+b x)+n \log (c+d x)+\log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)\right) \left(\log (a+b x) \log \left(\frac{b (g+h x)}{b g-a h}\right)+\text{Li}_2\left(\frac{h (a+b x)}{a h-b g}\right)\right) B-2 A n \left(\log (c+d x) \log \left(\frac{d (g+h x)}{d g-c h}\right)+\text{Li}_2\left(\frac{h (c+d x)}{c h-d g}\right)\right) B+\left(A+B \left(-n \log (a+b x)+n \log (c+d x)+\log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)\right)^2 \log (g+h x)}{h}","\frac{2 B n \text{Li}_2\left(\frac{(d g-c h) (a+b x)}{(b g-a h) (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\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{2 B n \text{Li}_2\left(\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{\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}-\frac{2 B^2 n^2 \text{Li}_3\left(\frac{(d g-c h) (a+b x)}{(b g-a h) (c+d x)}\right)}{h}+\frac{2 B^2 n^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{h}",1,"((A + B*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n]))^2*Log[g + h*x] + 2*B*n*(A + B*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n]))*(Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)] + PolyLog[2, (h*(a + b*x))/(-(b*g) + a*h)]) - 2*A*B*n*(Log[c + d*x]*Log[(d*(g + h*x))/(d*g - c*h)] + PolyLog[2, (h*(c + d*x))/(-(d*g) + c*h)]) - 2*B^2*n*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n])*(Log[c + d*x]*Log[(d*(g + h*x))/(d*g - c*h)] + PolyLog[2, (h*(c + d*x))/(-(d*g) + c*h)]) + B^2*n^2*(Log[a + b*x]^2*Log[(b*(g + h*x))/(b*g - a*h)] + 2*Log[a + b*x]*PolyLog[2, (h*(a + b*x))/(-(b*g) + a*h)] - 2*PolyLog[3, (h*(a + b*x))/(-(b*g) + a*h)]) + B^2*n^2*(Log[c + d*x]^2*Log[(d*(g + h*x))/(d*g - c*h)] + 2*Log[c + d*x]*PolyLog[2, (h*(c + d*x))/(-(d*g) + c*h)] - 2*PolyLog[3, (h*(c + d*x))/(-(d*g) + c*h)]) - 2*B^2*n^2*(Log[a + b*x]*Log[c + d*x]*Log[(b*(g + h*x))/(b*g - a*h)] + (Log[(h*(c + d*x))/(-(d*g) + c*h)]*(-2*Log[a + b*x] + Log[(h*(c + d*x))/(-(d*g) + c*h)])*(Log[(b*(g + h*x))/(b*g - a*h)] - Log[(d*(g + h*x))/(d*g - c*h)]))/2 + Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*(-Log[(b*(g + h*x))/(b*g - a*h)] + Log[(d*(g + h*x))/(d*g - c*h)]) + (Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]^2*(Log[(-(b*c) + a*d)/(d*(a + b*x))] + Log[(b*(g + h*x))/(b*g - a*h)] - Log[((-(b*c) + a*d)*(g + h*x))/((d*g - c*h)*(a + b*x))]))/2 + (Log[c + d*x] - Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))])*PolyLog[2, (h*(a + b*x))/(-(b*g) + a*h)] + (Log[a + b*x] + Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))])*PolyLog[2, (h*(c + d*x))/(-(d*g) + c*h)] + Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*(PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - PolyLog[2, ((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]) - PolyLog[3, (h*(a + b*x))/(-(b*g) + a*h)] - PolyLog[3, (h*(c + d*x))/(-(d*g) + c*h)] - PolyLog[3, (b*(c + d*x))/(d*(a + b*x))] + PolyLog[3, ((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]))/h","B",1
307,1,3460,208,1.3015542,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{(g+h x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(g + h*x)^2,x]","\text{Result too large to show}","\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)}+\frac{2 B^2 n^2 (b c-a d) \text{Li}_2\left(\frac{(d g-c h) (a+b x)}{(b g-a h) (c+d x)}\right)}{(b g-a h) (d g-c h)}",1,"(-(A^2*b*d*g^2) + A^2*b*c*g*h + a*A^2*d*g*h - a*A^2*c*h^2 + 2*A*b*B*d*g^2*n*Log[a + b*x] - 2*A*b*B*c*g*h*n*Log[a + b*x] + 2*A*b*B*d*g*h*n*x*Log[a + b*x] - 2*A*b*B*c*h^2*n*x*Log[a + b*x] - b*B^2*d*g^2*n^2*Log[a + b*x]^2 + b*B^2*c*g*h*n^2*Log[a + b*x]^2 - b*B^2*d*g*h*n^2*x*Log[a + b*x]^2 + b*B^2*c*h^2*n^2*x*Log[a + b*x]^2 - 2*A*b*B*d*g^2*n*Log[c + d*x] + 2*a*A*B*d*g*h*n*Log[c + d*x] - 2*A*b*B*d*g*h*n*x*Log[c + d*x] + 2*a*A*B*d*h^2*n*x*Log[c + d*x] + 2*b*B^2*d*g^2*n^2*Log[a + b*x]*Log[c + d*x] - 2*a*B^2*d*g*h*n^2*Log[a + b*x]*Log[c + d*x] + 2*b*B^2*d*g*h*n^2*x*Log[a + b*x]*Log[c + d*x] - 2*a*B^2*d*h^2*n^2*x*Log[a + b*x]*Log[c + d*x] - b*B^2*d*g^2*n^2*Log[c + d*x]^2 + a*B^2*d*g*h*n^2*Log[c + d*x]^2 - b*B^2*d*g*h*n^2*x*Log[c + d*x]^2 + a*B^2*d*h^2*n^2*x*Log[c + d*x]^2 - 2*b*B^2*c*g*h*n^2*Log[a + b*x]*Log[(h*(c + d*x))/(-(d*g) + c*h)] + 2*a*B^2*d*g*h*n^2*Log[a + b*x]*Log[(h*(c + d*x))/(-(d*g) + c*h)] - 2*b*B^2*c*h^2*n^2*x*Log[a + b*x]*Log[(h*(c + d*x))/(-(d*g) + c*h)] + 2*a*B^2*d*h^2*n^2*x*Log[a + b*x]*Log[(h*(c + d*x))/(-(d*g) + c*h)] + b*B^2*c*g*h*n^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]^2 - a*B^2*d*g*h*n^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]^2 + b*B^2*c*h^2*n^2*x*Log[(h*(c + d*x))/(-(d*g) + c*h)]^2 - a*B^2*d*h^2*n^2*x*Log[(h*(c + d*x))/(-(d*g) + c*h)]^2 - 2*b*B^2*c*g*h*n^2*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] + 2*a*B^2*d*g*h*n^2*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] - 2*b*B^2*c*h^2*n^2*x*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] + 2*a*B^2*d*h^2*n^2*x*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] - 2*b*B^2*c*g*h*n^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] + 2*a*B^2*d*g*h*n^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] - 2*b*B^2*c*h^2*n^2*x*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] + 2*a*B^2*d*h^2*n^2*x*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] + b*B^2*c*g*h*n^2*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]^2 - a*B^2*d*g*h*n^2*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]^2 + b*B^2*c*h^2*n^2*x*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]^2 - a*B^2*d*h^2*n^2*x*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]^2 - 2*A*b*B*d*g^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*A*b*B*c*g*h*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*a*A*B*d*g*h*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 2*a*A*B*c*h^2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*b*B^2*d*g^2*n*Log[a + b*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 2*b*B^2*c*g*h*n*Log[a + b*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*b*B^2*d*g*h*n*x*Log[a + b*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 2*b*B^2*c*h^2*n*x*Log[a + b*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 2*b*B^2*d*g^2*n*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*a*B^2*d*g*h*n*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - 2*b*B^2*d*g*h*n*x*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*a*B^2*d*h^2*n*x*Log[c + d*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] - b*B^2*d*g^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + b*B^2*c*g*h*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + a*B^2*d*g*h*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 - a*B^2*c*h^2*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 - 2*A*b*B*d*g^2*n*Log[(b*(g + h*x))/(b*g - a*h)] + 2*A*b*B*c*g*h*n*Log[(b*(g + h*x))/(b*g - a*h)] - 2*A*b*B*d*g*h*n*x*Log[(b*(g + h*x))/(b*g - a*h)] + 2*A*b*B*c*h^2*n*x*Log[(b*(g + h*x))/(b*g - a*h)] + 2*b*B^2*d*g^2*n^2*Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)] - 2*a*B^2*d*g*h*n^2*Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)] + 2*b*B^2*d*g*h*n^2*x*Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)] - 2*a*B^2*d*h^2*n^2*x*Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)] - 2*b*B^2*d*g^2*n^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(b*(g + h*x))/(b*g - a*h)] + 2*b*B^2*c*g*h*n^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(b*(g + h*x))/(b*g - a*h)] - 2*b*B^2*d*g*h*n^2*x*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(b*(g + h*x))/(b*g - a*h)] + 2*b*B^2*c*h^2*n^2*x*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(b*(g + h*x))/(b*g - a*h)] - 2*b*B^2*d*g^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[(b*(g + h*x))/(b*g - a*h)] + 2*b*B^2*c*g*h*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[(b*(g + h*x))/(b*g - a*h)] - 2*b*B^2*d*g*h*n*x*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[(b*(g + h*x))/(b*g - a*h)] + 2*b*B^2*c*h^2*n*x*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[(b*(g + h*x))/(b*g - a*h)] + 2*A*b*B*d*g^2*n*Log[(d*(g + h*x))/(d*g - c*h)] - 2*a*A*B*d*g*h*n*Log[(d*(g + h*x))/(d*g - c*h)] + 2*A*b*B*d*g*h*n*x*Log[(d*(g + h*x))/(d*g - c*h)] - 2*a*A*B*d*h^2*n*x*Log[(d*(g + h*x))/(d*g - c*h)] - 2*b*B^2*d*g^2*n^2*Log[a + b*x]*Log[(d*(g + h*x))/(d*g - c*h)] + 2*a*B^2*d*g*h*n^2*Log[a + b*x]*Log[(d*(g + h*x))/(d*g - c*h)] - 2*b*B^2*d*g*h*n^2*x*Log[a + b*x]*Log[(d*(g + h*x))/(d*g - c*h)] + 2*a*B^2*d*h^2*n^2*x*Log[a + b*x]*Log[(d*(g + h*x))/(d*g - c*h)] + 2*b*B^2*d*g^2*n^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(d*(g + h*x))/(d*g - c*h)] - 2*b*B^2*c*g*h*n^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(d*(g + h*x))/(d*g - c*h)] + 2*b*B^2*d*g*h*n^2*x*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(d*(g + h*x))/(d*g - c*h)] - 2*b*B^2*c*h^2*n^2*x*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(d*(g + h*x))/(d*g - c*h)] + 2*b*B^2*d*g^2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[(d*(g + h*x))/(d*g - c*h)] - 2*a*B^2*d*g*h*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[(d*(g + h*x))/(d*g - c*h)] + 2*b*B^2*d*g*h*n*x*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[(d*(g + h*x))/(d*g - c*h)] - 2*a*B^2*d*h^2*n*x*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[(d*(g + h*x))/(d*g - c*h)] + 2*B^2*(b*c - a*d)*h*n^2*(g + h*x)*PolyLog[2, (h*(a + b*x))/(-(b*g) + a*h)] - 2*B^2*(b*c - a*d)*h*n^2*(g + h*x)*PolyLog[2, (h*(c + d*x))/(-(d*g) + c*h)] - 2*b*B^2*c*g*h*n^2*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] + 2*a*B^2*d*g*h*n^2*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 2*b*B^2*c*h^2*n^2*x*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] + 2*a*B^2*d*h^2*n^2*x*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))])/(h*(-(b*g) + a*h)*(-(d*g) + c*h)*(g + h*x))","B",1
308,1,15406,393,6.4601762,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{(g+h x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(g + h*x)^3,x]","\text{Result too large to show}","\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 n^2 (b c-a d) (-a d h-b c h+2 b d g) \text{Li}_2\left(\frac{(d g-c h) (a+b x)}{(b g-a h) (c+d x)}\right)}{(b g-a h)^2 (d g-c h)^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,"Result too large to show","B",1
309,0,0,875,6.0215064,"\int (g+h x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 \, dx","Integrate[(g + h*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3,x]","\int (g+h x)^2 \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 \, dx","-\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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\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{Li}_3\left(\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,"Integrate[(g + h*x)^2*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3, x]","F",-1
310,0,0,466,3.2921368,"\int (g+h x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 \, dx","Integrate[(g + h*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3,x]","\int (g+h x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 \, dx","\frac{3 B^2 n^2 (b c-a d) (-a d h-b c h+2 b d g) \text{Li}_2\left(\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^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}-\frac{3 B^3 n^3 (b c-a d) (-a d h-b c h+2 b d g) \text{Li}_3\left(\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{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^2 d^2}",1,"Integrate[(g + h*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3, x]","F",-1
311,1,378,203,0.3104673,"\int \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3 \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3,x]","\frac{3 A^2 B d (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)-3 A^2 B n (b c-a d) \log (c+d x)+3 A B^2 n (b c-a d) \left(2 n \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-\log \left(\frac{b c-a d}{b c+b d x}\right) \left(-2 \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 n \log \left(\frac{d (a+b x)}{a d-b c}\right)+n \log \left(\frac{b c-a d}{b c+b d x}\right)\right)\right)+3 A B^2 d (a+b x) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)+3 B^3 n (b c-a d) \left(2 n \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+\log \left(\frac{b c-a d}{b c+b d x}\right) \log ^2\left(e (a+b x)^n (c+d x)^{-n}\right)-2 n^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right)+B^3 d (a+b x) \log ^3\left(e (a+b x)^n (c+d x)^{-n}\right)+A^3 b d x}{b d}","\frac{6 B^2 n^2 (b c-a d) \text{Li}_2\left(\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{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}-\frac{6 B^3 n^3 (b c-a d) \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b d}",1,"(A^3*b*d*x - 3*A^2*B*(b*c - a*d)*n*Log[c + d*x] + 3*A^2*B*d*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 3*A*B^2*d*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^2 + B^3*d*(a + b*x)*Log[(e*(a + b*x)^n)/(c + d*x)^n]^3 + 3*A*B^2*(b*c - a*d)*n*(-(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*n*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*Log[(e*(a + b*x)^n)/(c + d*x)^n] + n*Log[(b*c - a*d)/(b*c + b*d*x)])) + 2*n*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 3*B^3*(b*c - a*d)*n*(Log[(e*(a + b*x)^n)/(c + d*x)^n]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*n*Log[(e*(a + b*x)^n)/(c + d*x)^n]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 2*n^2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))]))/(b*d)","A",1
312,0,0,425,1.5277055,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{g+h x} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(g + h*x),x]","\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{g+h x} \, dx","-\frac{6 B^2 n^2 \text{Li}_3\left(\frac{(d g-c h) (a+b x)}{(b g-a h) (c+d x)}\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{Li}_3\left(\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{Li}_2\left(\frac{(d g-c h) (a+b x)}{(b g-a h) (c+d x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{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{3 B n \text{Li}_2\left(\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{\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}+\frac{6 B^3 n^3 \text{Li}_4\left(\frac{(d g-c h) (a+b x)}{(b g-a h) (c+d x)}\right)}{h}-\frac{6 B^3 n^3 \text{Li}_4\left(\frac{d (a+b x)}{b (c+d x)}\right)}{h}",1,"Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(g + h*x), x]","F",-1
313,0,0,302,3.1284029,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(g+h x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(g + h*x)^2,x]","\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(g+h x)^2} \, dx","\frac{6 B^2 n^2 (b c-a d) \text{Li}_2\left(\frac{(d g-c h) (a+b x)}{(b g-a h) (c+d x)}\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{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)}-\frac{6 B^3 n^3 (b c-a d) \text{Li}_3\left(\frac{(d g-c h) (a+b x)}{(b g-a h) (c+d x)}\right)}{(b g-a h) (d g-c h)}",1,"Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(g + h*x)^2, x]","F",-1
314,0,0,629,6.3716718,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(g+h x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(g + h*x)^3,x]","\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(g+h x)^3} \, dx","\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 n^2 (b c-a d) (-a d h-b c h+2 b d g) \text{Li}_2\left(\frac{(d g-c h) (a+b x)}{(b g-a h) (c+d x)}\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^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}+\frac{3 B^3 h n^3 (b c-a d)^2 \text{Li}_2\left(\frac{(d g-c h) (a+b x)}{(b g-a h) (c+d x)}\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{Li}_3\left(\frac{(d g-c h) (a+b x)}{(b g-a h) (c+d x)}\right)}{(b g-a h)^2 (d g-c h)^2}",1,"Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(g + h*x)^3, x]","F",-1