1,1,261,212,0.2205723,"\int (a g+b g x)^3 (c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(a*g + b*g*x)^3*(c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g^3 i \left(24 d (a+b x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+30 (a+b x)^4 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{5 B (b c-a d)^2 \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)}{d^4}+\frac{2 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)}{d^4}\right)}{120 b^2}","\frac{g^3 i (a+b x)^4 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A-B\right)}{20 b^2}+\frac{g^3 i (a+b x)^4 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{5 b}+\frac{B g^3 i (b c-a d)^5 \log (c+d x)}{20 b^2 d^4}+\frac{B g^3 i (a+b x)^2 (b c-a d)^3}{40 b^2 d^2}-\frac{B g^3 i (a+b x)^3 (b c-a d)^2}{60 b^2 d}-\frac{B g^3 i x (b c-a d)^4}{20 b d^3}",1,"(g^3*i*(30*(b*c - a*d)*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 24*d*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - (5*B*(b*c - a*d)^2*(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]))/d^4 + (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]))/d^4))/(120*b^2)","A",1
2,1,217,180,0.1588274,"\int (a g+b g x)^2 (c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(a*g + b*g*x)^2*(c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g^2 i \left(6 d (a+b x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+8 (a+b x)^3 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+\frac{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)}{d^3}-\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)}{d^3}\right)}{24 b^2}","\frac{g^2 i (a+b x)^3 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A-B\right)}{12 b^2}+\frac{g^2 i (a+b x)^3 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 b}-\frac{B g^2 i (b c-a d)^4 \log (c+d x)}{12 b^2 d^3}-\frac{B g^2 i (a+b x)^2 (b c-a d)^2}{24 b^2 d}+\frac{B g^2 i x (b c-a d)^3}{12 b d^2}",1,"(g^2*i*(8*(b*c - a*d)*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6*d*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(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]))/d^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]))/d^3))/(24*b^2)","A",1
3,1,181,140,0.2390458,"\int (a g+b g x) (c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(a*g + b*g*x)*(c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g i \left(b \left(d x \left(a^2 B d^2+a b d (6 A c+3 A d x+B d x)+A b^2 d x (3 c+2 d x)+b^2 (-B) c (c+d x)\right)+B c \left(6 a^2 d^2-3 a b c d+b^2 c^2\right) \log (c+d x)+B d^2 \left(6 a^2 c+3 a b x (2 c+d x)+b^2 x^2 (3 c+2 d x)\right) \log \left(\frac{e (a+b x)}{c+d x}\right)\right)-a^2 B d^2 (a d+3 b c) \log (a+b x)\right)}{6 b^2 d^2}","\frac{g i (a+b x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A-B\right)}{6 b^2}+\frac{g i (a+b x)^2 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b}+\frac{B g i (b c-a d)^3 \log (c+d x)}{6 b^2 d^2}-\frac{B g i x (b c-a d)^2}{6 b d}",1,"(g*i*(-(a^2*B*d^2*(3*b*c + a*d)*Log[a + b*x]) + b*(d*x*(a^2*B*d^2 - b^2*B*c*(c + d*x) + A*b^2*d*x*(3*c + 2*d*x) + a*b*d*(6*A*c + 3*A*d*x + B*d*x)) + B*d^2*(6*a^2*c + 3*a*b*x*(2*c + d*x) + b^2*x^2*(3*c + 2*d*x))*Log[(e*(a + b*x))/(c + d*x)] + B*c*(b^2*c^2 - 3*a*b*c*d + 6*a^2*d^2)*Log[c + d*x])))/(6*b^2*d^2)","A",1
4,1,70,81,0.0334191,"\int (c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{i \left((c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{B (b c-a d) ((b c-a d) \log (a+b x)+b d x)}{b^2}\right)}{2 d}","\frac{i (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 d}-\frac{B i (b c-a d)^2 \log (a+b x)}{2 b^2 d}-\frac{B i x (b c-a d)}{2 b}",1,"(i*(-((B*(b*c - a*d)*(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)])))/(2*d)","A",1
5,1,164,133,0.1171028,"\int \frac{(c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{a g+b g x} \, dx","Integrate[((c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x),x]","\frac{i \left(2 (b c-a d) \log (a+b x) \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)+2 \left(B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)+\log (c+d x) (a B d-b B c)+A b d x\right)+2 B (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)+\log ^2(a+b x) (a B d-b B c)\right)}{2 b^2 g}","-\frac{i (b c-a d) \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-B\right)}{b^2 g}+\frac{i (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b g}+\frac{B i (b c-a d) \text{Li}_2\left(\frac{b c-a d}{d (a+b x)}+1\right)}{b^2 g}",1,"(i*((-(b*B*c) + a*B*d)*Log[a + b*x]^2 + 2*(A*b*d*x + B*d*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] + (-(b*B*c) + a*B*d)*Log[c + d*x]) + 2*(b*c - a*d)*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)] + B*Log[(b*(c + d*x))/(b*c - a*d)]) + 2*B*(b*c - a*d)*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]))/(2*b^2*g)","A",1
6,1,175,142,0.1534651,"\int \frac{(c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(a g+b g x)^2} \, dx","Integrate[((c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x)^2,x]","\frac{i \left(2 d (a+b x) \log (a+b x) \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-B\right)-2 (A+B) (b c-a d)+2 (a B d-b B c) \log \left(\frac{e (a+b x)}{c+d x}\right)+2 B d (a+b x) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)+2 B d (a+b x) \log (c+d x)-B d (a+b x) \log ^2(a+b x)\right)}{2 b^2 g^2 (a+b x)}","-\frac{d i \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)}{b^2 g^2}-\frac{i (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b g^2 (a+b x)}+\frac{B d i \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^2 g^2}-\frac{B i (c+d x)}{b g^2 (a+b x)}",1,"(i*(-2*(A + B)*(b*c - a*d) - B*d*(a + b*x)*Log[a + b*x]^2 + 2*(-(b*B*c) + a*B*d)*Log[(e*(a + b*x))/(c + d*x)] + 2*B*d*(a + b*x)*Log[c + d*x] + 2*d*(a + b*x)*Log[a + b*x]*(A - B + B*Log[(e*(a + b*x))/(c + d*x)] + B*Log[(b*(c + d*x))/(b*c - a*d)]) + 2*B*d*(a + b*x)*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]))/(2*b^2*g^2*(a + b*x))","A",1
7,1,208,85,0.1530717,"\int \frac{(c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(a g+b g x)^3} \, dx","Integrate[((c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x)^3,x]","\frac{i \left(-\frac{d \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^2 (a+b x)}-\frac{(b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b^2 (a+b x)^2}-\frac{B \left(-\frac{2 d^2 \log (a+b x)}{b c-a d}+\frac{2 d^2 \log (c+d x)}{b c-a d}+\frac{b c-a d}{(a+b x)^2}-\frac{2 d}{a+b x}\right)}{4 b^2}-\frac{B d \left(\frac{d \log (a+b x)}{b c-a d}-\frac{d \log (c+d x)}{b c-a d}+\frac{1}{a+b x}\right)}{b^2}\right)}{g^3}","-\frac{i (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)}-\frac{B i (c+d x)^2}{4 g^3 (a+b x)^2 (b c-a d)}",1,"(i*(-1/2*((b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(b^2*(a + b*x)^2) - (d*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(b^2*(a + b*x)) - (B*d*((a + b*x)^(-1) + (d*Log[a + b*x])/(b*c - a*d) - (d*Log[c + d*x])/(b*c - a*d)))/b^2 - (B*((b*c - a*d)/(a + b*x)^2 - (2*d)/(a + b*x) - (2*d^2*Log[a + b*x])/(b*c - a*d) + (2*d^2*Log[c + d*x])/(b*c - a*d)))/(4*b^2)))/g^3","B",1
8,1,187,173,0.3936285,"\int \frac{(c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(a g+b g x)^4} \, dx","Integrate[((c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x)^4,x]","-\frac{i \left(\frac{12 A b c}{(a+b x)^3}+\frac{18 A d}{(a+b x)^2}-\frac{12 a A d}{(a+b x)^3}-\frac{6 B d^3 \log (a+b x)}{(b c-a d)^2}+\frac{6 B d^3 \log (c+d x)}{(b c-a d)^2}-\frac{6 B d^2}{(a+b x) (b c-a d)}+\frac{6 B (a d+2 b c+3 b d x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a+b x)^3}+\frac{4 b B c}{(a+b x)^3}+\frac{3 B d}{(a+b x)^2}-\frac{4 a B d}{(a+b x)^3}\right)}{36 b^2 g^4}","-\frac{b i (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 g^4 (a+b x)^3 (b c-a d)^2}+\frac{d i (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)^2}-\frac{b B i (c+d x)^3}{9 g^4 (a+b x)^3 (b c-a d)^2}+\frac{B d i (c+d x)^2}{4 g^4 (a+b x)^2 (b c-a d)^2}",1,"-1/36*(i*((12*A*b*c)/(a + b*x)^3 + (4*b*B*c)/(a + b*x)^3 - (12*a*A*d)/(a + b*x)^3 - (4*a*B*d)/(a + b*x)^3 + (18*A*d)/(a + b*x)^2 + (3*B*d)/(a + b*x)^2 - (6*B*d^2)/((b*c - a*d)*(a + b*x)) - (6*B*d^3*Log[a + b*x])/(b*c - a*d)^2 + (6*B*(2*b*c + a*d + 3*b*d*x)*Log[(e*(a + b*x))/(c + d*x)])/(a + b*x)^3 + (6*B*d^3*Log[c + d*x])/(b*c - a*d)^2))/(b^2*g^4)","A",1
9,1,210,269,0.4694472,"\int \frac{(c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(a g+b g x)^5} \, dx","Integrate[((c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x)^5,x]","-\frac{i \left(\frac{36 A b c}{(a+b x)^4}+\frac{48 A d}{(a+b x)^3}-\frac{36 a A d}{(a+b x)^4}+\frac{12 B d^4 \log (a+b x)}{(b c-a d)^3}-\frac{12 B d^4 \log (c+d x)}{(b c-a d)^3}+\frac{12 B d^3}{(a+b x) (b c-a d)^2}-\frac{6 B d^2}{(a+b x)^2 (b c-a d)}+\frac{12 B (a d+3 b c+4 b d x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a+b x)^4}+\frac{9 b B c}{(a+b x)^4}+\frac{4 B d}{(a+b x)^3}-\frac{9 a B d}{(a+b x)^4}\right)}{144 b^2 g^5}","-\frac{b^2 i (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 g^5 (a+b x)^4 (b c-a d)^3}-\frac{d^2 i (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)^3}+\frac{2 b d i (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)^3}-\frac{b^2 B i (c+d x)^4}{16 g^5 (a+b x)^4 (b c-a d)^3}-\frac{B d^2 i (c+d x)^2}{4 g^5 (a+b x)^2 (b c-a d)^3}+\frac{2 b B d i (c+d x)^3}{9 g^5 (a+b x)^3 (b c-a d)^3}",1,"-1/144*(i*((36*A*b*c)/(a + b*x)^4 + (9*b*B*c)/(a + b*x)^4 - (36*a*A*d)/(a + b*x)^4 - (9*a*B*d)/(a + b*x)^4 + (48*A*d)/(a + b*x)^3 + (4*B*d)/(a + b*x)^3 - (6*B*d^2)/((b*c - a*d)*(a + b*x)^2) + (12*B*d^3)/((b*c - a*d)^2*(a + b*x)) + (12*B*d^4*Log[a + b*x])/(b*c - a*d)^3 + (12*B*(3*b*c + a*d + 4*b*d*x)*Log[(e*(a + b*x))/(c + d*x)])/(a + b*x)^4 - (12*B*d^4*Log[c + d*x])/(b*c - a*d)^3))/(b^2*g^5)","A",1
10,1,429,423,0.3578795,"\int (a g+b g x)^3 (c i+d i x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(a*g + b*g*x)^3*(c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g^3 i^2 \left(60 d^6 (a+b x)^6 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+144 d^5 (a+b x)^5 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+90 d^4 (a+b x)^4 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-15 B (b c-a d)^3 \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 (b c-a d)^2 \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)-B (b c-a d) \left(15 d^4 (a+b x)^4 (a d-b c)+20 d^3 (a+b x)^3 (b c-a d)^2+30 d^2 (a+b x)^2 (a d-b c)^3+60 b d x (b c-a d)^4-60 (b c-a d)^5 \log (c+d x)+12 d^5 (a+b x)^5\right)\right)}{360 b^3 d^4}","\frac{b^3 g^3 i^2 (c+d x)^6 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{6 d^4}-\frac{3 b^2 g^3 i^2 (c+d x)^5 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{5 d^4}-\frac{g^3 i^2 (c+d x)^3 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 d^4}+\frac{3 b g^3 i^2 (c+d x)^4 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 d^4}+\frac{B g^3 i^2 (b c-a d)^6 \log \left(\frac{a+b x}{c+d x}\right)}{60 b^3 d^4}+\frac{B g^3 i^2 (b c-a d)^6 \log (c+d x)}{60 b^3 d^4}-\frac{b^2 B g^3 i^2 (c+d x)^5 (b c-a d)}{30 d^4}+\frac{B g^3 i^2 x (b c-a d)^5}{60 b^2 d^3}+\frac{B g^3 i^2 (c+d x)^2 (b c-a d)^4}{120 b d^4}-\frac{19 B g^3 i^2 (c+d x)^3 (b c-a d)^3}{180 d^4}+\frac{13 b B g^3 i^2 (c+d x)^4 (b c-a d)^2}{120 d^4}",1,"(g^3*i^2*(90*d^4*(b*c - a*d)^2*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 144*d^5*(b*c - a*d)*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 60*d^6*(a + b*x)^6*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 15*B*(b*c - a*d)^3*(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)^2*(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]) - B*(b*c - a*d)*(60*b*d*(b*c - a*d)^4*x + 30*d^2*(-(b*c) + a*d)^3*(a + b*x)^2 + 20*d^3*(b*c - a*d)^2*(a + b*x)^3 + 15*d^4*(-(b*c) + a*d)*(a + b*x)^4 + 12*d^5*(a + b*x)^5 - 60*(b*c - a*d)^5*Log[c + d*x])))/(360*b^3*d^4)","A",1
11,1,362,337,0.2517152,"\int (a g+b g x)^2 (c i+d i 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*(c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g^2 i^2 \left(12 d^5 (a+b x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+30 d^4 (a+b x)^4 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+20 d^3 (a+b x)^3 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+10 B (b c-a d)^3 \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)-5 B (b c-a d)^2 \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)+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)\right)}{60 b^3 d^3}","\frac{b^2 g^2 i^2 (c+d x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{5 d^3}+\frac{g^2 i^2 (c+d x)^3 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 d^3}-\frac{b g^2 i^2 (c+d x)^4 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 d^3}-\frac{B g^2 i^2 (b c-a d)^5 \log \left(\frac{a+b x}{c+d x}\right)}{30 b^3 d^3}-\frac{B g^2 i^2 (b c-a d)^5 \log (c+d x)}{30 b^3 d^3}-\frac{B g^2 i^2 x (b c-a d)^4}{30 b^2 d^2}-\frac{B g^2 i^2 (c+d x)^2 (b c-a d)^3}{60 b d^3}+\frac{B g^2 i^2 (c+d x)^3 (b c-a d)^2}{10 d^3}-\frac{b B g^2 i^2 (c+d x)^4 (b c-a d)}{20 d^3}",1,"(g^2*i^2*(20*d^3*(b*c - a*d)^2*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 30*d^4*(b*c - a*d)*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 12*d^5*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 10*B*(b*c - a*d)^3*(2*b*d*(b*c - a*d)*x - d^2*(a + b*x)^2 - 2*(b*c - a*d)^2*Log[c + d*x]) - 5*B*(b*c - a*d)^2*(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]) + 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])))/(60*b^3*d^3)","A",1
12,1,216,239,0.1836391,"\int (a g+b g x) (c i+d i x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(a*g + b*g*x)*(c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g i^2 \left(6 b (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-8 (c+d x)^3 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+\frac{4 B (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^3}-\frac{B (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)}{b^3}\right)}{24 d^2}","-\frac{g i^2 (c+d x)^3 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 d^2}+\frac{b g i^2 (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 d^2}+\frac{B g i^2 (b c-a d)^4 \log \left(\frac{a+b x}{c+d x}\right)}{12 b^3 d^2}+\frac{B g i^2 (b c-a d)^4 \log (c+d x)}{12 b^3 d^2}+\frac{B g i^2 x (b c-a d)^3}{12 b^2 d}+\frac{B g i^2 (c+d x)^2 (b c-a d)^2}{24 b d^2}-\frac{B g i^2 (c+d x)^3 (b c-a d)}{12 d^2}",1,"(g*i^2*((4*B*(b*c - a*d)^2*(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 - (B*(b*c - a*d)*(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^3 - 8*(b*c - a*d)*(c + d*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6*b*(c + d*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])))/(24*d^2)","A",1
13,1,97,118,0.040194,"\int (c i+d i x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{i^2 \left((c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{B (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{i^2 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 d}-\frac{B i^2 (b c-a d)^3 \log (a+b x)}{3 b^3 d}-\frac{B i^2 x (b c-a d)^2}{3 b^2}-\frac{B i^2 (c+d x)^2 (b c-a d)}{6 b d}",1,"(i^2*(-1/2*(B*(b*c - a*d)*(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)])))/(3*d)","A",1
14,1,252,276,0.1903443,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{a g+b g x} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x),x]","\frac{i^2 \left(b^2 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 (b c-a d)^2 \log (g (a+b 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{d (a+b x)}{a d-b c}\right)-\log (g (a+b x)) \left(\log (g (a+b x))-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)\right)-2 B (b c-a d)^2 \log (c+d x)-B (b c-a d) ((b c-a d) \log (a+b x)+b d x)\right)}{2 b^3 g}","\frac{d i^2 (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^3 g}-\frac{i^2 (b c-a d)^2 \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)}{b^3 g}+\frac{i^2 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b g}+\frac{B i^2 (b c-a d)^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^3 g}-\frac{B i^2 (b c-a d)^2 \log \left(\frac{a+b x}{c+d x}\right)}{2 b^3 g}-\frac{3 B i^2 (b c-a d)^2 \log (c+d x)}{2 b^3 g}-\frac{B d i^2 x (b c-a d)}{2 b^2 g}",1,"(i^2*(2*A*b*d*(b*c - a*d)*x - B*(b*c - a*d)*(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)] + b^2*(c + d*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*(b*c - a*d)^2*Log[g*(a + b*x)]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 2*B*(b*c - a*d)^2*Log[c + d*x] + B*(b*c - a*d)^2*(-(Log[g*(a + b*x)]*(Log[g*(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*g)","A",1
15,1,221,247,0.2295514,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(a g+b g x)^2} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x)^2,x]","\frac{i^2 \left(2 d (b c-a d) \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{(b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{a+b x}+B d^2 (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)+B d (a d-b c) \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)-\frac{B (b c-a d)^2}{a+b x}+B d (a d-b c) \log (a+b x)+A b d^2 x\right)}{b^3 g^2}","\frac{d^2 i^2 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^3 g^2}-\frac{2 d i^2 (b c-a d) \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)}{b^3 g^2}-\frac{i^2 (c+d x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^2 g^2 (a+b x)}+\frac{2 B d i^2 (b c-a d) \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^3 g^2}-\frac{B d i^2 (b c-a d) \log (c+d x)}{b^3 g^2}-\frac{B i^2 (c+d x) (b c-a d)}{b^2 g^2 (a+b x)}",1,"(i^2*(A*b*d^2*x - (B*(b*c - a*d)^2)/(a + b*x) + B*d*(-(b*c) + a*d)*Log[a + b*x] + B*d^2*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] - ((b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x) + 2*d*(b*c - a*d)*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + B*d*(-(b*c) + a*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^3*g^2)","A",1
16,1,244,230,0.3126855,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(a g+b g x)^3} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x)^3,x]","\frac{i^2 \left(4 d^2 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+\frac{8 d (a d-b c) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{a+b x}-\frac{2 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(a+b x)^2}-2 B 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)+\frac{6 B d (a d-b c)}{a+b x}-\frac{B (b c-a d)^2}{(a+b x)^2}-6 B d^2 \log (a+b x)+6 B d^2 \log (c+d x)\right)}{4 b^3 g^3}","-\frac{d^2 i^2 \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)}{b^3 g^3}-\frac{d i^2 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^2 g^3 (a+b x)}-\frac{i^2 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b g^3 (a+b x)^2}+\frac{B d^2 i^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^3 g^3}-\frac{B d i^2 (c+d x)}{b^2 g^3 (a+b x)}-\frac{B i^2 (c+d x)^2}{4 b g^3 (a+b x)^2}",1,"(i^2*(-((B*(b*c - a*d)^2)/(a + b*x)^2) + (6*B*d*(-(b*c) + a*d))/(a + b*x) - 6*B*d^2*Log[a + b*x] - (2*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x)^2 + (8*d*(-(b*c) + a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x) + 4*d^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6*B*d^2*Log[c + d*x] - 2*B*d^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)])))/(4*b^3*g^3)","A",1
17,1,315,89,0.2971369,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(a g+b g x)^4} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x)^4,x]","-\frac{i^2 \left(-3 a^3 A d^3-3 a^3 B d^3 \log (c+d x)-a^3 B d^3-9 a^2 A b d^3 x+3 B (b c-a d) \left(a^2 d^2+a b d (c+3 d x)+b^2 \left(c^2+3 c d x+3 d^2 x^2\right)\right) \log \left(\frac{e (a+b x)}{c+d x}\right)-9 a^2 b B d^3 x \log (c+d x)-3 a^2 b B d^3 x-9 a A b^2 d^3 x^2-9 a b^2 B d^3 x^2 \log (c+d x)-3 a b^2 B d^3 x^2+3 B d^3 (a+b x)^3 \log (a+b x)+3 A b^3 c^3+9 A b^3 c^2 d x+9 A b^3 c d^2 x^2+b^3 B c^3+3 b^3 B c^2 d x-3 b^3 B d^3 x^3 \log (c+d x)+3 b^3 B c d^2 x^2\right)}{9 b^3 g^4 (a+b x)^3 (b c-a d)}","-\frac{i^2 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 g^4 (a+b x)^3 (b c-a d)}-\frac{B i^2 (c+d x)^3}{9 g^4 (a+b x)^3 (b c-a d)}",1,"-1/9*(i^2*(3*A*b^3*c^3 + b^3*B*c^3 - 3*a^3*A*d^3 - a^3*B*d^3 + 9*A*b^3*c^2*d*x + 3*b^3*B*c^2*d*x - 9*a^2*A*b*d^3*x - 3*a^2*b*B*d^3*x + 9*A*b^3*c*d^2*x^2 + 3*b^3*B*c*d^2*x^2 - 9*a*A*b^2*d^3*x^2 - 3*a*b^2*B*d^3*x^2 + 3*B*d^3*(a + b*x)^3*Log[a + b*x] + 3*B*(b*c - a*d)*(a^2*d^2 + a*b*d*(c + 3*d*x) + b^2*(c^2 + 3*c*d*x + 3*d^2*x^2))*Log[(e*(a + b*x))/(c + d*x)] - 3*a^3*B*d^3*Log[c + d*x] - 9*a^2*b*B*d^3*x*Log[c + d*x] - 9*a*b^2*B*d^3*x^2*Log[c + d*x] - 3*b^3*B*d^3*x^3*Log[c + d*x]))/(b^3*(b*c - a*d)*g^4*(a + b*x)^3)","B",1
18,1,454,181,0.3829711,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(a g+b g x)^5} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x)^5,x]","-\frac{i^2 \left(12 a^4 A d^4+12 a^4 B d^4 \log (c+d x)+7 a^4 B d^4+48 a^3 A b d^4 x+48 a^3 b B d^4 x \log (c+d x)+28 a^3 b B d^4 x+72 a^2 A b^2 d^4 x^2+12 B (b c-a d)^2 \left(a^2 d^2+2 a b d (c+2 d x)+b^2 \left(3 c^2+8 c d x+6 d^2 x^2\right)\right) \log \left(\frac{e (a+b x)}{c+d x}\right)+72 a^2 b^2 B d^4 x^2 \log (c+d x)+42 a^2 b^2 B d^4 x^2-48 a A b^3 c^3 d-144 a A b^3 c^2 d^2 x-144 a A b^3 c d^3 x^2-16 a b^3 B c^3 d-48 a b^3 B c^2 d^2 x+48 a b^3 B d^4 x^3 \log (c+d x)-48 a b^3 B c d^3 x^2+12 a b^3 B d^4 x^3-12 B d^4 (a+b x)^4 \log (a+b x)+36 A b^4 c^4+96 A b^4 c^3 d x+72 A b^4 c^2 d^2 x^2+9 b^4 B c^4+20 b^4 B c^3 d x+6 b^4 B c^2 d^2 x^2+12 b^4 B d^4 x^4 \log (c+d x)-12 b^4 B c d^3 x^3\right)}{144 b^3 g^5 (a+b x)^4 (b c-a d)^2}","-\frac{b i^2 (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 g^5 (a+b x)^4 (b c-a d)^2}+\frac{d i^2 (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)^2}-\frac{b B i^2 (c+d x)^4}{16 g^5 (a+b x)^4 (b c-a d)^2}+\frac{B d i^2 (c+d x)^3}{9 g^5 (a+b x)^3 (b c-a d)^2}",1,"-1/144*(i^2*(36*A*b^4*c^4 + 9*b^4*B*c^4 - 48*a*A*b^3*c^3*d - 16*a*b^3*B*c^3*d + 12*a^4*A*d^4 + 7*a^4*B*d^4 + 96*A*b^4*c^3*d*x + 20*b^4*B*c^3*d*x - 144*a*A*b^3*c^2*d^2*x - 48*a*b^3*B*c^2*d^2*x + 48*a^3*A*b*d^4*x + 28*a^3*b*B*d^4*x + 72*A*b^4*c^2*d^2*x^2 + 6*b^4*B*c^2*d^2*x^2 - 144*a*A*b^3*c*d^3*x^2 - 48*a*b^3*B*c*d^3*x^2 + 72*a^2*A*b^2*d^4*x^2 + 42*a^2*b^2*B*d^4*x^2 - 12*b^4*B*c*d^3*x^3 + 12*a*b^3*B*d^4*x^3 - 12*B*d^4*(a + b*x)^4*Log[a + b*x] + 12*B*(b*c - a*d)^2*(a^2*d^2 + 2*a*b*d*(c + 2*d*x) + b^2*(3*c^2 + 8*c*d*x + 6*d^2*x^2))*Log[(e*(a + b*x))/(c + d*x)] + 12*a^4*B*d^4*Log[c + d*x] + 48*a^3*b*B*d^4*x*Log[c + d*x] + 72*a^2*b^2*B*d^4*x^2*Log[c + d*x] + 48*a*b^3*B*d^4*x^3*Log[c + d*x] + 12*b^4*B*d^4*x^4*Log[c + d*x]))/(b^3*(b*c - a*d)^2*g^5*(a + b*x)^4)","B",1
19,1,344,281,0.8649435,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(a g+b g x)^6} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x)^6,x]","\frac{i^2 \left(-\frac{360 a^2 A d^2}{(a+b x)^5}-\frac{60 B \left(a^2 d^2+a b d (3 c+5 d x)+b^2 \left(6 c^2+15 c d x+10 d^2 x^2\right)\right) \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a+b x)^5}-\frac{72 a^2 B d^2}{(a+b x)^5}-\frac{360 A b^2 c^2}{(a+b x)^5}-\frac{900 A b c d}{(a+b x)^4}+\frac{720 a A b c d}{(a+b x)^5}-\frac{600 A d^2}{(a+b x)^3}+\frac{900 a A d^2}{(a+b x)^4}-\frac{72 b^2 B c^2}{(a+b x)^5}-\frac{60 B d^5 \log (a+b x)}{(b c-a d)^3}+\frac{60 B d^5 \log (c+d x)}{(b c-a d)^3}-\frac{60 B d^4}{(a+b x) (b c-a d)^2}+\frac{30 B d^3}{(a+b x)^2 (b c-a d)}-\frac{135 b B c d}{(a+b x)^4}+\frac{144 a b B c d}{(a+b x)^5}-\frac{20 B d^2}{(a+b x)^3}+\frac{135 a B d^2}{(a+b x)^4}\right)}{1800 b^3 g^6}","-\frac{b^2 i^2 (c+d x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{5 g^6 (a+b x)^5 (b c-a d)^3}-\frac{d^2 i^2 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 g^6 (a+b x)^3 (b c-a d)^3}+\frac{b d i^2 (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^6 (a+b x)^4 (b c-a d)^3}-\frac{b^2 B i^2 (c+d x)^5}{25 g^6 (a+b x)^5 (b c-a d)^3}-\frac{B d^2 i^2 (c+d x)^3}{9 g^6 (a+b x)^3 (b c-a d)^3}+\frac{b B d i^2 (c+d x)^4}{8 g^6 (a+b x)^4 (b c-a d)^3}",1,"(i^2*((-360*A*b^2*c^2)/(a + b*x)^5 - (72*b^2*B*c^2)/(a + b*x)^5 + (720*a*A*b*c*d)/(a + b*x)^5 + (144*a*b*B*c*d)/(a + b*x)^5 - (360*a^2*A*d^2)/(a + b*x)^5 - (72*a^2*B*d^2)/(a + b*x)^5 - (900*A*b*c*d)/(a + b*x)^4 - (135*b*B*c*d)/(a + b*x)^4 + (900*a*A*d^2)/(a + b*x)^4 + (135*a*B*d^2)/(a + b*x)^4 - (600*A*d^2)/(a + b*x)^3 - (20*B*d^2)/(a + b*x)^3 + (30*B*d^3)/((b*c - a*d)*(a + b*x)^2) - (60*B*d^4)/((b*c - a*d)^2*(a + b*x)) - (60*B*d^5*Log[a + b*x])/(b*c - a*d)^3 - (60*B*(a^2*d^2 + a*b*d*(3*c + 5*d*x) + b^2*(6*c^2 + 15*c*d*x + 10*d^2*x^2))*Log[(e*(a + b*x))/(c + d*x)])/(a + b*x)^5 + (60*B*d^5*Log[c + d*x])/(b*c - a*d)^3))/(1800*b^3*g^6)","A",1
20,1,586,457,0.589792,"\int (a g+b g x)^3 (c i+d i 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*(c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g^3 i^3 \left(120 d^3 (a+b x)^7 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+420 d^2 (a+b x)^6 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+210 (a+b x)^4 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+504 d (a+b x)^5 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+\frac{120 b^2 B c x (b c-a d)^5}{d^3}+\frac{126 B (b c-a d)^7 \log (c+d x)}{d^4}-\frac{120 b B c (b c-a d)^6 \log (c+d x)}{d^4}-\frac{126 b B x (b c-a d)^6}{d^3}+\frac{120 a B (b c-a d)^6 \log (c+d x)}{d^3}+\frac{63 B (a+b x)^2 (b c-a d)^5}{d^2}-\frac{60 b B c (a+b x)^2 (b c-a d)^4}{d^2}-20 b B c d^2 (a+b x)^6+24 a B d^2 (a+b x)^5 (a d-b c)+\frac{120 a b B x (a d-b c)^5}{d^2}-\frac{42 B (a+b x)^3 (b c-a d)^4}{d}+\frac{60 a B (a+b x)^2 (b c-a d)^4}{d}+\frac{40 b B c (a+b x)^3 (b c-a d)^3}{d}-84 B d (a+b x)^5 (b c-a d)^2-30 b B c (a+b x)^4 (b c-a d)^2+30 a B d (a+b x)^4 (b c-a d)^2+24 b B c d (a+b x)^5 (b c-a d)+21 B (a+b x)^4 (a d-b c)^3+40 a B (a+b x)^3 (a d-b c)^3+20 a B d^3 (a+b x)^6\right)}{840 b^4}","\frac{b^3 g^3 i^3 (c+d x)^7 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{7 d^4}-\frac{b^2 g^3 i^3 (c+d x)^6 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 d^4}-\frac{g^3 i^3 (c+d x)^4 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 d^4}+\frac{3 b g^3 i^3 (c+d x)^5 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{5 d^4}+\frac{B g^3 i^3 (b c-a d)^7 \log \left(\frac{a+b x}{c+d x}\right)}{140 b^4 d^4}+\frac{B g^3 i^3 (b c-a d)^7 \log (c+d x)}{140 b^4 d^4}+\frac{B g^3 i^3 x (b c-a d)^6}{140 b^3 d^3}+\frac{B g^3 i^3 (c+d x)^2 (b c-a d)^5}{280 b^2 d^4}-\frac{b^2 B g^3 i^3 (c+d x)^6 (b c-a d)}{42 d^4}+\frac{B g^3 i^3 (c+d x)^3 (b c-a d)^4}{420 b d^4}-\frac{17 B g^3 i^3 (c+d x)^4 (b c-a d)^3}{280 d^4}+\frac{b B g^3 i^3 (c+d x)^5 (b c-a d)^2}{14 d^4}",1,"(g^3*i^3*((120*b^2*B*c*(b*c - a*d)^5*x)/d^3 - (126*b*B*(b*c - a*d)^6*x)/d^3 + (120*a*b*B*(-(b*c) + a*d)^5*x)/d^2 - (60*b*B*c*(b*c - a*d)^4*(a + b*x)^2)/d^2 + (60*a*B*(b*c - a*d)^4*(a + b*x)^2)/d + (63*B*(b*c - a*d)^5*(a + b*x)^2)/d^2 + (40*b*B*c*(b*c - a*d)^3*(a + b*x)^3)/d - (42*B*(b*c - a*d)^4*(a + b*x)^3)/d + 40*a*B*(-(b*c) + a*d)^3*(a + b*x)^3 - 30*b*B*c*(b*c - a*d)^2*(a + b*x)^4 + 30*a*B*d*(b*c - a*d)^2*(a + b*x)^4 + 21*B*(-(b*c) + a*d)^3*(a + b*x)^4 + 24*b*B*c*d*(b*c - a*d)*(a + b*x)^5 - 84*B*d*(b*c - a*d)^2*(a + b*x)^5 + 24*a*B*d^2*(-(b*c) + a*d)*(a + b*x)^5 - 20*b*B*c*d^2*(a + b*x)^6 + 20*a*B*d^3*(a + b*x)^6 + 210*(b*c - a*d)^3*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 504*d*(b*c - a*d)^2*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 420*d^2*(b*c - a*d)*(a + b*x)^6*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 120*d^3*(a + b*x)^7*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - (120*b*B*c*(b*c - a*d)^6*Log[c + d*x])/d^4 + (120*a*B*(b*c - a*d)^6*Log[c + d*x])/d^3 + (126*B*(b*c - a*d)^7*Log[c + d*x])/d^4))/(840*b^4)","A",1
21,1,429,371,0.3196318,"\int (a g+b g x)^2 (c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(a*g + b*g*x)^2*(c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g^2 i^3 \left(60 b^6 (c+d x)^6 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-144 b^5 (c+d x)^5 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+90 b^4 (c+d x)^4 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-15 B (b c-a d)^3 \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)+12 B (b c-a d)^2 \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)-B (b c-a d) \left(15 b^4 (c+d x)^4 (b c-a d)+20 b^3 (c+d x)^3 (b c-a d)^2+30 b^2 (c+d x)^2 (b c-a d)^3+60 b d x (b c-a d)^4+60 (b c-a d)^5 \log (a+b x)+12 b^5 (c+d x)^5\right)\right)}{360 b^4 d^3}","\frac{b^2 g^2 i^3 (c+d x)^6 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{6 d^3}+\frac{g^2 i^3 (c+d x)^4 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 d^3}-\frac{2 b g^2 i^3 (c+d x)^5 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{5 d^3}-\frac{B g^2 i^3 (b c-a d)^6 \log \left(\frac{a+b x}{c+d x}\right)}{60 b^4 d^3}-\frac{B g^2 i^3 (b c-a d)^6 \log (c+d x)}{60 b^4 d^3}-\frac{B g^2 i^3 x (b c-a d)^5}{60 b^3 d^2}-\frac{B g^2 i^3 (c+d x)^2 (b c-a d)^4}{120 b^2 d^3}-\frac{B g^2 i^3 (c+d x)^3 (b c-a d)^3}{180 b d^3}+\frac{7 B g^2 i^3 (c+d x)^4 (b c-a d)^2}{120 d^3}-\frac{b B g^2 i^3 (c+d x)^5 (b c-a d)}{30 d^3}",1,"(g^2*i^3*(-15*B*(b*c - a*d)^3*(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]) + 12*B*(b*c - a*d)^2*(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*(b*c - a*d)*(60*b*d*(b*c - a*d)^4*x + 30*b^2*(b*c - a*d)^3*(c + d*x)^2 + 20*b^3*(b*c - a*d)^2*(c + d*x)^3 + 15*b^4*(b*c - a*d)*(c + d*x)^4 + 12*b^5*(c + d*x)^5 + 60*(b*c - a*d)^5*Log[a + b*x]) + 90*b^4*(b*c - a*d)^2*(c + d*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 144*b^5*(b*c - a*d)*(c + d*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 60*b^6*(c + d*x)^6*(A + B*Log[(e*(a + b*x))/(c + d*x)])))/(360*b^4*d^3)","A",1
22,1,261,271,0.1969641,"\int (a g+b g x) (c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(a*g + b*g*x)*(c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{g i^3 \left(24 b (c+d x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-30 (c+d x)^4 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+\frac{5 B (b c-a d)^2 \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)}{b^4}-\frac{2 B (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)}{b^4}\right)}{120 d^2}","-\frac{g i^3 (c+d x)^4 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 d^2}+\frac{b g i^3 (c+d x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{5 d^2}+\frac{B g i^3 (b c-a d)^5 \log \left(\frac{a+b x}{c+d x}\right)}{20 b^4 d^2}+\frac{B g i^3 (b c-a d)^5 \log (c+d x)}{20 b^4 d^2}+\frac{B g i^3 x (b c-a d)^4}{20 b^3 d}+\frac{B g i^3 (c+d x)^2 (b c-a d)^3}{40 b^2 d^2}+\frac{B g i^3 (c+d x)^3 (b c-a d)^2}{60 b d^2}-\frac{B g i^3 (c+d x)^4 (b c-a d)}{20 d^2}",1,"(g*i^3*((5*B*(b*c - a*d)^2*(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 - (2*B*(b*c - a*d)*(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^4 - 30*(b*c - a*d)*(c + d*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 24*b*(c + d*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])))/(120*d^2)","A",1
23,1,120,149,0.0580137,"\int (c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \, dx","Integrate[(c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]),x]","\frac{i^3 \left((c+d 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 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{i^3 (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 d}-\frac{B i^3 (b c-a d)^4 \log (a+b x)}{4 b^4 d}-\frac{B i^3 x (b c-a d)^3}{4 b^3}-\frac{B i^3 (c+d x)^2 (b c-a d)^2}{8 b^2 d}-\frac{B i^3 (c+d x)^3 (b c-a d)}{12 b d}",1,"(i^3*(-1/6*(B*(b*c - a*d)*(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)])))/(4*d)","A",1
24,1,352,356,0.2746604,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{a g+b g x} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x),x]","\frac{i^3 \left(2 b^3 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+3 b^2 (c+d x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+6 (b c-a d)^3 \log (g (a+b 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 (a+b x)+b^2 (c+d 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(\log (g (a+b x)) \left(\log (g (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 (b c-a d)^3 \log (c+d x)-3 B (b c-a d)^2 ((b c-a d) \log (a+b x)+b d x)\right)}{6 b^4 g}","\frac{d i^3 (a+b x) (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^4 g}-\frac{i^3 (b c-a d)^3 \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)}{b^4 g}+\frac{i^3 (c+d x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b^2 g}+\frac{i^3 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b g}+\frac{B i^3 (b c-a d)^3 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g}-\frac{5 B i^3 (b c-a d)^3 \log \left(\frac{a+b x}{c+d x}\right)}{6 b^4 g}-\frac{11 B i^3 (b c-a d)^3 \log (c+d x)}{6 b^4 g}-\frac{5 B d i^3 x (b c-a d)^2}{6 b^3 g}-\frac{B i^3 (c+d x)^2 (b c-a d)}{6 b^2 g}",1,"(i^3*(6*A*b*d*(b*c - a*d)^2*x - 3*B*(b*c - a*d)^2*(b*d*x + (b*c - a*d)*Log[a + b*x]) - B*(b*c - a*d)*(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)] + 3*b^2*(b*c - a*d)*(c + d*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*b^3*(c + d*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6*(b*c - a*d)^3*Log[g*(a + b*x)]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 6*B*(b*c - a*d)^3*Log[c + d*x] - 3*B*(b*c - a*d)^3*(Log[g*(a + b*x)]*(Log[g*(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*g)","A",1
25,1,374,373,0.390529,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(a g+b g x)^2} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x)^2,x]","\frac{i^3 \left(-a^2 B d^3 \log (a+b x)+b^2 d^3 x^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+6 d (b c-a d)^2 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{2 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{a+b x}+2 A b d^2 x (3 b c-2 a d)+2 B d^2 (a+b x) (3 b c-2 a d) \log \left(\frac{e (a+b x)}{c+d x}\right)-b B d^2 x (b c-a d)-3 B d (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)-\frac{2 B (b c-a d)^3}{a+b x}-2 B d (b c-a d)^2 \log (a+b x)+2 B d (b c-a d)^2 \log (c+d x)-2 B d (a d-b c) (2 a d-3 b c) \log (c+d x)+b^2 B c^2 d \log (c+d x)\right)}{2 b^4 g^2}","\frac{2 d^2 i^3 (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^4 g^2}-\frac{3 d i^3 (b c-a d)^2 \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)}{b^4 g^2}-\frac{i^3 (c+d x) (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^3 g^2 (a+b x)}+\frac{d i^3 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b^2 g^2}+\frac{3 B d i^3 (b c-a d)^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g^2}-\frac{B d i^3 (b c-a d)^2 \log \left(\frac{a+b x}{c+d x}\right)}{2 b^4 g^2}-\frac{5 B d i^3 (b c-a d)^2 \log (c+d x)}{2 b^4 g^2}-\frac{B d^2 i^3 x (b c-a d)}{2 b^3 g^2}-\frac{B i^3 (c+d x) (b c-a d)^2}{b^3 g^2 (a+b x)}",1,"(i^3*(2*A*b*d^2*(3*b*c - 2*a*d)*x - b*B*d^2*(b*c - a*d)*x - (2*B*(b*c - a*d)^3)/(a + b*x) - a^2*B*d^3*Log[a + b*x] - 2*B*d*(b*c - a*d)^2*Log[a + b*x] + 2*B*d^2*(3*b*c - 2*a*d)*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] + b^2*d^3*x^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - (2*(b*c - a*d)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x) + 6*d*(b*c - a*d)^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + b^2*B*c^2*d*Log[c + d*x] + 2*B*d*(b*c - a*d)^2*Log[c + d*x] - 2*B*d*(-(b*c) + a*d)*(-3*b*c + 2*a*d)*Log[c + d*x] - 3*B*d*(b*c - a*d)^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^4*g^2)","A",1
26,1,314,345,0.4056089,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(a g+b g x)^3} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x)^3,x]","\frac{i^3 \left(12 d^2 (b c-a d) \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{12 d (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{a+b x}-\frac{2 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(a+b x)^2}+4 B d^3 (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)+6 B d^2 (a d-b c) \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)+10 B d^2 (a d-b c) \log (a+b x)+6 B d^2 (b c-a d) \log (c+d x)-\frac{10 B d (b c-a d)^2}{a+b x}-\frac{B (b c-a d)^3}{(a+b x)^2}+4 A b d^3 x\right)}{4 b^4 g^3}","\frac{d^3 i^3 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^4 g^3}-\frac{3 d^2 i^3 (b c-a d) \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)}{b^4 g^3}-\frac{2 d i^3 (c+d x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^3 g^3 (a+b x)}-\frac{i^3 (c+d x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b^2 g^3 (a+b x)^2}+\frac{3 B d^2 i^3 (b c-a d) \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g^3}-\frac{B d^2 i^3 (b c-a d) \log (c+d x)}{b^4 g^3}-\frac{2 B d i^3 (c+d x) (b c-a d)}{b^3 g^3 (a+b x)}-\frac{B i^3 (c+d x)^2 (b c-a d)}{4 b^2 g^3 (a+b x)^2}",1,"(i^3*(4*A*b*d^3*x - (B*(b*c - a*d)^3)/(a + b*x)^2 - (10*B*d*(b*c - a*d)^2)/(a + b*x) + 10*B*d^2*(-(b*c) + a*d)*Log[a + b*x] + 4*B*d^3*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] - (2*(b*c - a*d)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x)^2 - (12*d*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x) + 12*d^2*(b*c - a*d)*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6*B*d^2*(b*c - a*d)*Log[c + d*x] + 6*B*d^2*(-(b*c) + a*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)])))/(4*b^4*g^3)","A",1
27,1,308,310,0.454867,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(a g+b g x)^4} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x)^4,x]","\frac{i^3 \left(36 d^3 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+\frac{108 d^2 (a d-b c) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{a+b x}-\frac{54 d (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(a+b x)^2}-\frac{12 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(a+b x)^3}-18 B 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)+\frac{66 B d^2 (a d-b c)}{a+b x}-\frac{21 B d (b c-a d)^2}{(a+b x)^2}-\frac{4 B (b c-a d)^3}{(a+b x)^3}-66 B d^3 \log (a+b x)+66 B d^3 \log (c+d x)\right)}{36 b^4 g^4}","-\frac{d^3 i^3 \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)}{b^4 g^4}-\frac{d^2 i^3 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^3 g^4 (a+b x)}-\frac{d i^3 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b^2 g^4 (a+b x)^2}-\frac{i^3 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b g^4 (a+b x)^3}+\frac{B d^3 i^3 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g^4}-\frac{B d^2 i^3 (c+d x)}{b^3 g^4 (a+b x)}-\frac{B d i^3 (c+d x)^2}{4 b^2 g^4 (a+b x)^2}-\frac{B i^3 (c+d x)^3}{9 b g^4 (a+b x)^3}",1,"(i^3*((-4*B*(b*c - a*d)^3)/(a + b*x)^3 - (21*B*d*(b*c - a*d)^2)/(a + b*x)^2 + (66*B*d^2*(-(b*c) + a*d))/(a + b*x) - 66*B*d^3*Log[a + b*x] - (12*(b*c - a*d)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x)^3 - (54*d*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x)^2 + (108*d^2*(-(b*c) + a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x) + 36*d^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 66*B*d^3*Log[c + d*x] - 18*B*d^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)])))/(36*b^4*g^4)","A",1
28,1,427,89,0.4932367,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(a g+b g x)^5} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x)^5,x]","-\frac{i^3 \left(-4 a^4 A d^4-4 a^4 B d^4 \log (c+d x)-a^4 B d^4-16 a^3 A b d^4 x-16 a^3 b B d^4 x \log (c+d x)-4 a^3 b B d^4 x-24 a^2 A b^2 d^4 x^2-24 a^2 b^2 B d^4 x^2 \log (c+d x)-6 a^2 b^2 B d^4 x^2+4 B \left(-a^4 d^4-4 a^3 b d^4 x-6 a^2 b^2 d^4 x^2-4 a b^3 d^4 x^3+b^4 c \left(c^3+4 c^2 d x+6 c d^2 x^2+4 d^3 x^3\right)\right) \log \left(\frac{e (a+b x)}{c+d x}\right)-16 a A b^3 d^4 x^3-16 a b^3 B d^4 x^3 \log (c+d x)-4 a b^3 B d^4 x^3+4 B d^4 (a+b x)^4 \log (a+b x)+4 A b^4 c^4+16 A b^4 c^3 d x+24 A b^4 c^2 d^2 x^2+16 A b^4 c d^3 x^3+b^4 B c^4+4 b^4 B c^3 d x+6 b^4 B c^2 d^2 x^2-4 b^4 B d^4 x^4 \log (c+d x)+4 b^4 B c d^3 x^3\right)}{16 b^4 g^5 (a+b x)^4 (b c-a d)}","-\frac{i^3 (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 g^5 (a+b x)^4 (b c-a d)}-\frac{B i^3 (c+d x)^4}{16 g^5 (a+b x)^4 (b c-a d)}",1,"-1/16*(i^3*(4*A*b^4*c^4 + b^4*B*c^4 - 4*a^4*A*d^4 - a^4*B*d^4 + 16*A*b^4*c^3*d*x + 4*b^4*B*c^3*d*x - 16*a^3*A*b*d^4*x - 4*a^3*b*B*d^4*x + 24*A*b^4*c^2*d^2*x^2 + 6*b^4*B*c^2*d^2*x^2 - 24*a^2*A*b^2*d^4*x^2 - 6*a^2*b^2*B*d^4*x^2 + 16*A*b^4*c*d^3*x^3 + 4*b^4*B*c*d^3*x^3 - 16*a*A*b^3*d^4*x^3 - 4*a*b^3*B*d^4*x^3 + 4*B*d^4*(a + b*x)^4*Log[a + b*x] + 4*B*(-(a^4*d^4) - 4*a^3*b*d^4*x - 6*a^2*b^2*d^4*x^2 - 4*a*b^3*d^4*x^3 + b^4*c*(c^3 + 4*c^2*d*x + 6*c*d^2*x^2 + 4*d^3*x^3))*Log[(e*(a + b*x))/(c + d*x)] - 4*a^4*B*d^4*Log[c + d*x] - 16*a^3*b*B*d^4*x*Log[c + d*x] - 24*a^2*b^2*B*d^4*x^2*Log[c + d*x] - 16*a*b^3*B*d^4*x^3*Log[c + d*x] - 4*b^4*B*d^4*x^4*Log[c + d*x]))/(b^4*(b*c - a*d)*g^5*(a + b*x)^4)","B",1
29,1,608,181,0.6024251,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(a g+b g x)^6} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x)^6,x]","-\frac{i^3 \left(20 a^5 A d^5+20 a^5 B d^5 \log (c+d x)+9 a^5 B d^5+100 a^4 A b d^5 x+100 a^4 b B d^5 x \log (c+d x)+45 a^4 b B d^5 x+200 a^3 A b^2 d^5 x^2+200 a^3 b^2 B d^5 x^2 \log (c+d x)+90 a^3 b^2 B d^5 x^2+200 a^2 A b^3 d^5 x^3+200 a^2 b^3 B d^5 x^3 \log (c+d x)+90 a^2 b^3 B d^5 x^3+20 B (b c-a d)^2 \left(a^3 d^3+a^2 b d^2 (2 c+5 d x)+a b^2 d \left(3 c^2+10 c d x+10 d^2 x^2\right)+b^3 \left(4 c^3+15 c^2 d x+20 c d^2 x^2+10 d^3 x^3\right)\right) \log \left(\frac{e (a+b x)}{c+d x}\right)-100 a A b^4 c^4 d-400 a A b^4 c^3 d^2 x-600 a A b^4 c^2 d^3 x^2-400 a A b^4 c d^4 x^3-25 a b^4 B c^4 d-100 a b^4 B c^3 d^2 x-150 a b^4 B c^2 d^3 x^2+100 a b^4 B d^5 x^4 \log (c+d x)-100 a b^4 B c d^4 x^3+20 a b^4 B d^5 x^4-20 B d^5 (a+b x)^5 \log (a+b x)+80 A b^5 c^5+300 A b^5 c^4 d x+400 A b^5 c^3 d^2 x^2+200 A b^5 c^2 d^3 x^3+16 b^5 B c^5+55 b^5 B c^4 d x+60 b^5 B c^3 d^2 x^2+10 b^5 B c^2 d^3 x^3+20 b^5 B d^5 x^5 \log (c+d x)-20 b^5 B c d^4 x^4\right)}{400 b^4 g^6 (a+b x)^5 (b c-a d)^2}","-\frac{b i^3 (c+d x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{5 g^6 (a+b x)^5 (b c-a d)^2}+\frac{d i^3 (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 g^6 (a+b x)^4 (b c-a d)^2}-\frac{b B i^3 (c+d x)^5}{25 g^6 (a+b x)^5 (b c-a d)^2}+\frac{B d i^3 (c+d x)^4}{16 g^6 (a+b x)^4 (b c-a d)^2}",1,"-1/400*(i^3*(80*A*b^5*c^5 + 16*b^5*B*c^5 - 100*a*A*b^4*c^4*d - 25*a*b^4*B*c^4*d + 20*a^5*A*d^5 + 9*a^5*B*d^5 + 300*A*b^5*c^4*d*x + 55*b^5*B*c^4*d*x - 400*a*A*b^4*c^3*d^2*x - 100*a*b^4*B*c^3*d^2*x + 100*a^4*A*b*d^5*x + 45*a^4*b*B*d^5*x + 400*A*b^5*c^3*d^2*x^2 + 60*b^5*B*c^3*d^2*x^2 - 600*a*A*b^4*c^2*d^3*x^2 - 150*a*b^4*B*c^2*d^3*x^2 + 200*a^3*A*b^2*d^5*x^2 + 90*a^3*b^2*B*d^5*x^2 + 200*A*b^5*c^2*d^3*x^3 + 10*b^5*B*c^2*d^3*x^3 - 400*a*A*b^4*c*d^4*x^3 - 100*a*b^4*B*c*d^4*x^3 + 200*a^2*A*b^3*d^5*x^3 + 90*a^2*b^3*B*d^5*x^3 - 20*b^5*B*c*d^4*x^4 + 20*a*b^4*B*d^5*x^4 - 20*B*d^5*(a + b*x)^5*Log[a + b*x] + 20*B*(b*c - a*d)^2*(a^3*d^3 + a^2*b*d^2*(2*c + 5*d*x) + a*b^2*d*(3*c^2 + 10*c*d*x + 10*d^2*x^2) + b^3*(4*c^3 + 15*c^2*d*x + 20*c*d^2*x^2 + 10*d^3*x^3))*Log[(e*(a + b*x))/(c + d*x)] + 20*a^5*B*d^5*Log[c + d*x] + 100*a^4*b*B*d^5*x*Log[c + d*x] + 200*a^3*b^2*B*d^5*x^2*Log[c + d*x] + 200*a^2*b^3*B*d^5*x^3*Log[c + d*x] + 100*a*b^4*B*d^5*x^4*Log[c + d*x] + 20*b^5*B*d^5*x^5*Log[c + d*x]))/(b^4*(b*c - a*d)^2*g^6*(a + b*x)^5)","B",1
30,1,642,281,1.0451361,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(a g+b g x)^7} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a*g + b*g*x)^7,x]","\frac{i^3 \left(1200 d^3 (a+b x)^3 (a d-b c)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-2700 d^2 (a+b x)^2 (b c-a d)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2160 d (a+b x) (a d-b c)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-600 (b c-a d)^6 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-2100 B d^6 (a+b x)^6 \log (c+d x)+2160 a B d^6 (a+b x)^5 \log (c+d x)+2160 b B d^6 x (a+b x)^5 \log (c+d x)+2100 B d^5 (a+b x)^5 (b c-a d)+2160 a B d^5 (a+b x)^4 (a d-b c)-2160 b B d^5 x (a+b x)^4 (b c-a d)-1050 B d^4 (a+b x)^4 (b c-a d)^2+1080 a B d^4 (a+b x)^3 (b c-a d)^2+1080 b B d^4 x (a+b x)^3 (b c-a d)^2+700 B d^3 (a+b x)^3 (b c-a d)^3+720 a B d^3 (a+b x)^2 (a d-b c)^3-720 b B d^3 x (a+b x)^2 (b c-a d)^3-825 B d^2 (a+b x)^2 (b c-a d)^4+540 a B d^2 (a+b x) (b c-a d)^4+540 b B d^2 x (a+b x) (b c-a d)^4-432 b B d x (b c-a d)^5+120 B d (a+b x) (b c-a d)^5+432 a B d (a d-b c)^5-100 B (b c-a d)^6+2100 B d^6 (a+b x)^6 \log (a+b x)-2160 a B d^6 (a+b x)^5 \log (a+b x)-2160 b B d^6 x (a+b x)^5 \log (a+b x)\right)}{3600 b^4 g^7 (a+b x)^6 (b c-a d)^3}","-\frac{b^2 i^3 (c+d x)^6 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{6 g^7 (a+b x)^6 (b c-a d)^3}-\frac{d^2 i^3 (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 g^7 (a+b x)^4 (b c-a d)^3}+\frac{2 b d i^3 (c+d x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{5 g^7 (a+b x)^5 (b c-a d)^3}-\frac{b^2 B i^3 (c+d x)^6}{36 g^7 (a+b x)^6 (b c-a d)^3}-\frac{B d^2 i^3 (c+d x)^4}{16 g^7 (a+b x)^4 (b c-a d)^3}+\frac{2 b B d i^3 (c+d x)^5}{25 g^7 (a+b x)^5 (b c-a d)^3}",1,"(i^3*(-100*B*(b*c - a*d)^6 + 432*a*B*d*(-(b*c) + a*d)^5 - 432*b*B*d*(b*c - a*d)^5*x + 540*a*B*d^2*(b*c - a*d)^4*(a + b*x) + 120*B*d*(b*c - a*d)^5*(a + b*x) + 540*b*B*d^2*(b*c - a*d)^4*x*(a + b*x) - 825*B*d^2*(b*c - a*d)^4*(a + b*x)^2 + 720*a*B*d^3*(-(b*c) + a*d)^3*(a + b*x)^2 - 720*b*B*d^3*(b*c - a*d)^3*x*(a + b*x)^2 + 1080*a*B*d^4*(b*c - a*d)^2*(a + b*x)^3 + 700*B*d^3*(b*c - a*d)^3*(a + b*x)^3 + 1080*b*B*d^4*(b*c - a*d)^2*x*(a + b*x)^3 - 1050*B*d^4*(b*c - a*d)^2*(a + b*x)^4 + 2160*a*B*d^5*(-(b*c) + a*d)*(a + b*x)^4 - 2160*b*B*d^5*(b*c - a*d)*x*(a + b*x)^4 + 2100*B*d^5*(b*c - a*d)*(a + b*x)^5 - 2160*a*B*d^6*(a + b*x)^5*Log[a + b*x] - 2160*b*B*d^6*x*(a + b*x)^5*Log[a + b*x] + 2100*B*d^6*(a + b*x)^6*Log[a + b*x] - 600*(b*c - a*d)^6*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2160*d*(-(b*c) + a*d)^5*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 2700*d^2*(b*c - a*d)^4*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 1200*d^3*(-(b*c) + a*d)^3*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2160*a*B*d^6*(a + b*x)^5*Log[c + d*x] + 2160*b*B*d^6*x*(a + b*x)^5*Log[c + d*x] - 2100*B*d^6*(a + b*x)^6*Log[c + d*x]))/(3600*b^4*(b*c - a*d)^3*g^7*(a + b*x)^6)","B",1
31,1,354,252,0.2933424,"\int \frac{(a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{c i+d i x} \, dx","Integrate[((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c*i + d*i*x),x]","\frac{g^3 \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 (i (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(\log (i (c+d x)) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (i (c+d x))\right)+2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\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)}{6 d^4 i}","\frac{g^3 (b c-a d)^3 \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)}{6 d^4 i}+\frac{g^3 (a+b x) (b c-a d)^2 \left(6 B \log \left(\frac{e (a+b x)}{c+d x}\right)+6 A+5 B\right)}{6 d^3 i}-\frac{g^3 (a+b x)^2 (b c-a d) \left(3 B \log \left(\frac{e (a+b x)}{c+d x}\right)+3 A+B\right)}{6 d^2 i}+\frac{g^3 (a+b x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 d i}+\frac{B g^3 (b c-a d)^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i}",1,"(g^3*(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] + 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*c - a*d)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[i*(c + d*x)] + 3*B*(b*c - a*d)^3*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[i*(c + d*x)])*Log[i*(c + d*x)] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(6*d^4*i)","A",1
32,1,254,198,0.1771794,"\int \frac{(a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{c i+d i x} \, dx","Integrate[((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c*i + d*i*x),x]","\frac{g^2 \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 (i (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) (a d-b c) \log \left(\frac{e (a+b x)}{c+d x}\right)-B (b c-a d)^2 \left(\log (i (c+d x)) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (i (c+d x))\right)+2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\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)}{2 d^3 i}","-\frac{g^2 (b c-a d)^2 \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)}{2 d^3 i}-\frac{g^2 (a+b x) (b c-a d) \left(2 B \log \left(\frac{e (a+b x)}{c+d x}\right)+2 A+B\right)}{2 d^2 i}+\frac{g^2 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 d i}-\frac{B g^2 (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^3 i}",1,"(g^2*(-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] - B*(b*c - a*d)*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 2*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[i*(c + d*x)] - B*(b*c - a*d)^2*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[i*(c + d*x)])*Log[i*(c + d*x)] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(2*d^3*i)","A",1
33,1,162,125,0.1106041,"\int \frac{(a g+b g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{c i+d i x} \, dx","Integrate[((a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c*i + d*i*x),x]","\frac{g \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)}{2 d^2 i}","\frac{g (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+B\right)}{d^2 i}+\frac{g (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{d i}+\frac{B g (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^2 i}",1,"(g*(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)])))/(2*d^2*i)","A",1
34,1,95,76,0.0324122,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{c i+d i x} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(c*i + d*i*x),x]","\frac{\log (i (c+d x)) \left(2 B \log \left(\frac{e (a+b x)}{c+d x}\right)-2 B \log \left(\frac{d (a+b x)}{a d-b c}\right)+2 A+B \log (i (c+d x))\right)-2 B \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)}{2 d i}","-\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)}{d i}-\frac{B \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d i}",1,"(Log[i*(c + d*x)]*(2*A - 2*B*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*B*Log[(e*(a + b*x))/(c + d*x)] + B*Log[i*(c + d*x)]) - 2*B*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*d*i)","A",1
35,1,207,44,0.1198755,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x) (c i+d i x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/((a*g + b*g*x)*(c*i + d*i*x)),x]","\frac{2 A \log (a+b x)+2 B \log (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 B \log (c+d x) \log \left(\frac{e (a+b x)}{c+d x}\right)+2 B \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)+2 B \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+2 B \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)+2 B \log (c+d x) \log \left(\frac{d (a+b x)}{a d-b c}\right)-B \log ^2(a+b x)-2 A \log (c+d x)-B \log ^2(c+d x)}{2 g i (b c-a d)}","\frac{\left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 B g i (b c-a d)}",1,"(2*A*Log[a + b*x] - B*Log[a + b*x]^2 + 2*B*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] - 2*A*Log[c + d*x] + 2*B*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] - 2*B*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] - B*Log[c + d*x]^2 + 2*B*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] + 2*B*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 2*B*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*(b*c - a*d)*g*i)","C",1
36,1,292,173,0.316795,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^2 (c i+d i x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/((a*g + b*g*x)^2*(c*i + d*i*x)),x]","-\frac{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)}{2 g^2 i (a+b x) (b c-a d)^2}","-\frac{d \log \left(\frac{a+b x}{c+d x}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^2 i (b c-a d)^2}-\frac{b (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^2 i (a+b x) (b c-a d)^2}-\frac{b B (c+d x)}{g^2 i (a+b x) (b c-a d)^2}+\frac{B d \log ^2\left(\frac{a+b x}{c+d x}\right)}{2 g^2 i (b c-a d)^2}",1,"-1/2*(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)^2*g^2*i*(a + b*x))","C",1
37,1,418,255,0.4295638,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^3 (c i+d i x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/((a*g + b*g*x)^3*(c*i + d*i*x)),x]","\frac{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) (b c-a d) \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)}{4 g^3 i (a+b x)^2 (b c-a d)^3}","-\frac{b^2 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^3 i (a+b x)^2 (b c-a d)^3}+\frac{d^2 \log \left(\frac{a+b x}{c+d x}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^3 i (b c-a d)^3}+\frac{2 b d (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^3 i (a+b x) (b c-a d)^3}-\frac{B d^2 \log ^2\left(\frac{a+b x}{c+d x}\right)}{2 g^3 i (b c-a d)^3}-\frac{B (c+d x)^2 \left(b-\frac{4 d (a+b x)}{c+d x}\right)^2}{4 g^3 i (a+b x)^2 (b c-a d)^3}",1,"(-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)]))/(4*(b*c - a*d)^3*g^3*i*(a + b*x)^2)","C",1
38,1,492,373,0.7070949,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^4 (c i+d i x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/((a*g + b*g*x)^4*(c*i + d*i*x)),x]","\frac{\frac{36 A d^2 (a d-b c)}{a+b x}+\frac{18 A d (b c-a d)^2}{(a+b x)^2}-\frac{12 A (b c-a d)^3}{(a+b x)^3}-36 A d^3 \log (a+b x)-36 B d^3 \log (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)+36 B d^3 \log (c+d x) \log \left(\frac{e (a+b x)}{c+d x}\right)-36 B d^3 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)-36 B d^3 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-36 B d^3 \log (c+d x) \log \left(\frac{d (a+b x)}{a d-b c}\right)-36 B d^3 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)+\frac{36 B d^2 (a d-b c) \log \left(\frac{e (a+b x)}{c+d x}\right)}{a+b x}+\frac{66 B d^2 (a d-b c)}{a+b x}+\frac{18 B d (b c-a d)^2 \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a+b x)^2}-\frac{12 B (b c-a d)^3 \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a+b x)^3}+\frac{15 B d (b c-a d)^2}{(a+b x)^2}-\frac{4 B (b c-a d)^3}{(a+b x)^3}+18 B d^3 \log ^2(a+b x)-66 B d^3 \log (a+b x)+36 A d^3 \log (c+d x)+18 B d^3 \log ^2(c+d x)+66 B d^3 \log (c+d x)}{36 g^4 i (b c-a d)^4}","-\frac{b^3 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 g^4 i (a+b x)^3 (b c-a d)^4}+\frac{3 b^2 d (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^4 i (a+b x)^2 (b c-a d)^4}-\frac{d^3 \log \left(\frac{a+b x}{c+d x}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^4 i (b c-a d)^4}-\frac{3 b d^2 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^4 i (a+b x) (b c-a d)^4}-\frac{b^3 B (c+d x)^3}{9 g^4 i (a+b x)^3 (b c-a d)^4}+\frac{3 b^2 B d (c+d x)^2}{4 g^4 i (a+b x)^2 (b c-a d)^4}+\frac{B d^3 \log ^2\left(\frac{a+b x}{c+d x}\right)}{2 g^4 i (b c-a d)^4}-\frac{3 b B d^2 (c+d x)}{g^4 i (a+b x) (b c-a d)^4}",1,"((-12*A*(b*c - a*d)^3)/(a + b*x)^3 - (4*B*(b*c - a*d)^3)/(a + b*x)^3 + (18*A*d*(b*c - a*d)^2)/(a + b*x)^2 + (15*B*d*(b*c - a*d)^2)/(a + b*x)^2 + (36*A*d^2*(-(b*c) + a*d))/(a + b*x) + (66*B*d^2*(-(b*c) + a*d))/(a + b*x) - 36*A*d^3*Log[a + b*x] - 66*B*d^3*Log[a + b*x] + 18*B*d^3*Log[a + b*x]^2 - (12*B*(b*c - a*d)^3*Log[(e*(a + b*x))/(c + d*x)])/(a + b*x)^3 + (18*B*d*(b*c - a*d)^2*Log[(e*(a + b*x))/(c + d*x)])/(a + b*x)^2 + (36*B*d^2*(-(b*c) + a*d)*Log[(e*(a + b*x))/(c + d*x)])/(a + b*x) - 36*B*d^3*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + 36*A*d^3*Log[c + d*x] + 66*B*d^3*Log[c + d*x] - 36*B*d^3*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] + 36*B*d^3*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] + 18*B*d^3*Log[c + d*x]^2 - 36*B*d^3*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] - 36*B*d^3*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] - 36*B*d^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(36*(b*c - a*d)^4*g^4*i)","C",1
39,1,359,341,0.4163469,"\int \frac{(a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(c i+d i x)^2} \, dx","Integrate[((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c*i + d*i*x)^2,x]","\frac{g^3 \left(b B \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)+b^3 d^2 x^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-2 A b^2 d x (2 b c-3 a d)+6 b (b c-a d)^2 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+\frac{2 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{c+d x}-2 b B d (a+b x) (2 b c-3 a d) \log \left(\frac{e (a+b x)}{c+d x}\right)-3 b 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 (2 b c-3 a d) (b c-a d) \log (c+d x)-2 B (b c-a d)^2 \left(\frac{b c-a d}{c+d x}+b \log (a+b x)-b \log (c+d x)\right)\right)}{2 d^4 i^2}","-\frac{b g^3 (b c-a d)^2 \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+5 B\right)}{2 d^4 i^2}-\frac{g^3 (6 A+5 B) (a+b x) (b c-a d)^2}{2 d^3 i^2 (c+d x)}-\frac{g^3 (a+b x)^2 (b c-a d) \left(3 B \log \left(\frac{e (a+b x)}{c+d x}\right)+3 A+B\right)}{2 d^2 i^2 (c+d x)}+\frac{g^3 (a+b x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 d i^2 (c+d x)}-\frac{3 b B g^3 (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i^2}-\frac{3 B g^3 (a+b x) (b c-a d)^2 \log \left(\frac{e (a+b x)}{c+d x}\right)}{d^3 i^2 (c+d x)}+\frac{3 B g^3 (a+b x) (b c-a d)^2}{d^3 i^2 (c+d x)}",1,"(g^3*(-2*A*b^2*d*(2*b*c - 3*a*d)*x - 2*b*B*d*(2*b*c - 3*a*d)*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] + b^3*d^2*x^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + (2*(b*c - a*d)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c + d*x) + 2*b*B*(2*b*c - 3*a*d)*(b*c - a*d)*Log[c + d*x] + 6*b*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 2*B*(b*c - a*d)^2*((b*c - a*d)/(c + d*x) + b*Log[a + b*x] - b*Log[c + d*x]) + b*B*(-(a^2*d^2*Log[a + b*x]) + b*(d*(-(b*c) + a*d)*x + b*c^2*Log[c + d*x])) - 3*b*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)])))/(2*d^4*i^2)","A",1
40,1,239,260,0.2367529,"\int \frac{(a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(c i+d i x)^2} \, dx","Integrate[((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c*i + d*i*x)^2,x]","\frac{g^2 \left(-2 b (b c-a d) \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{(b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{c+d x}+b B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)+b 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)+\frac{B (b c-a d)^2}{c+d x}+b B (b c-a d) \log (a+b x)-2 b B (b c-a d) \log (c+d x)+A b^2 d x\right)}{d^3 i^2}","\frac{b g^2 (b c-a d) \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+B\right)}{d^3 i^2}+\frac{g^2 (2 A+B) (a+b x) (b c-a d)}{d^2 i^2 (c+d x)}+\frac{g^2 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{d i^2 (c+d x)}+\frac{2 b B g^2 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^3 i^2}+\frac{2 B g^2 (a+b x) (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)}{d^2 i^2 (c+d x)}-\frac{2 B g^2 (a+b x) (b c-a d)}{d^2 i^2 (c+d x)}",1,"(g^2*(A*b^2*d*x + (B*(b*c - a*d)^2)/(c + d*x) + b*B*(b*c - a*d)*Log[a + b*x] + b*B*d*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] - ((b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c + d*x) - 2*b*B*(b*c - a*d)*Log[c + d*x] - 2*b*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + b*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^3*i^2)","A",1
41,1,175,160,0.1609802,"\int \frac{(a g+b g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(c i+d i x)^2} \, dx","Integrate[((a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c*i + d*i*x)^2,x]","\frac{g \left(2 b \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+\frac{2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{c+d x}-b B \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 \left(\frac{b c-a d}{c+d x}+b \log (a+b x)-b \log (c+d x)\right)\right)}{2 d^2 i^2}","-\frac{b g \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)}{d^2 i^2}-\frac{A g (a+b x)}{d i^2 (c+d x)}-\frac{b B g \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^2 i^2}-\frac{B g (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{d i^2 (c+d x)}+\frac{B g (a+b x)}{d i^2 (c+d x)}",1,"(g*((2*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c + d*x) + 2*b*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 2*B*((b*c - a*d)/(c + d*x) + b*Log[a + b*x] - b*Log[c + d*x]) - b*B*((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*d^2*i^2)","A",1
42,1,104,98,0.0451955,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(c i+d i x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(c*i + d*i*x)^2,x]","\frac{-a A d+B (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)-b B (c+d x) \log (a+b x)+a B d+A b c+b B c \log (c+d x)+b B d x \log (c+d x)-b B c}{d i^2 (c+d x) (a d-b c)}","\frac{A (a+b x)}{i^2 (c+d x) (b c-a d)}+\frac{B (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{i^2 (c+d x) (b c-a d)}-\frac{B (a+b x)}{i^2 (c+d x) (b c-a d)}",1,"(A*b*c - b*B*c - a*A*d + a*B*d - b*B*(c + d*x)*Log[a + b*x] + B*(b*c - a*d)*Log[(e*(a + b*x))/(c + d*x)] + b*B*c*Log[c + d*x] + b*B*d*x*Log[c + d*x])/(d*(-(b*c) + a*d)*i^2*(c + d*x))","A",1
43,1,292,156,0.2840359,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x) (c i+d i x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/((a*g + b*g*x)*(c*i + d*i*x)^2),x]","\frac{2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 b (c+d x) \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-2 b (c+d x) \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-b B (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 (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 (b (c+d x) \log (a+b x)-a d-b (c+d x) \log (c+d x)+b c)}{2 g i^2 (c+d x) (b c-a d)^2}","\frac{b \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 B g i^2 (b c-a d)^2}-\frac{A d (a+b x)}{g i^2 (c+d x) (b c-a d)^2}-\frac{B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{g i^2 (c+d x) (b c-a d)^2}+\frac{B d (a+b x)}{g i^2 (c+d x) (b c-a d)^2}",1,"(2*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*b*(c + d*x)*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 2*b*(c + d*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 2*B*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]) - b*B*(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*(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)]))/(2*(b*c - a*d)^2*g*i^2*(c + d*x))","C",1
44,1,324,261,0.4278665,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^2 (c i+d i x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/((a*g + b*g*x)^2*(c*i + d*i*x)^2),x]","\frac{-2 b d \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{b (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{a+b x}+2 b d \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+\frac{d (a d-b c) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{c+d x}-\frac{b^2 B c}{a+b x}+b 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 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)+\frac{a b B d}{a+b x}-\frac{a B d^2}{c+d x}+\frac{b B c d}{c+d x}}{g^2 i^2 (b c-a d)^3}","-\frac{b^2 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^2 i^2 (a+b x) (b c-a d)^3}+\frac{d^2 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^2 i^2 (c+d x) (b c-a d)^3}-\frac{2 b d \log \left(\frac{a+b x}{c+d x}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^2 i^2 (b c-a d)^3}-\frac{b^2 B (c+d x)}{g^2 i^2 (a+b x) (b c-a d)^3}-\frac{B d^2 (a+b x)}{g^2 i^2 (c+d x) (b c-a d)^3}+\frac{b B d \log ^2\left(\frac{a+b x}{c+d x}\right)}{g^2 i^2 (b c-a d)^3}",1,"(-((b^2*B*c)/(a + b*x)) + (a*b*B*d)/(a + b*x) + (b*B*c*d)/(c + d*x) - (a*B*d^2)/(c + d*x) - (b*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x) + (d*(-(b*c) + a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c + d*x) - 2*b*d*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*b*d*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + b*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*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)]))/((b*c - a*d)^3*g^2*i^2)","C",1
45,1,453,364,0.730907,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^3 (c i+d i x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/((a*g + b*g*x)^3*(c*i + d*i*x)^2),x]","\frac{12 b d^2 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+\frac{4 d^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{c+d x}-12 b d^2 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+\frac{8 b d (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{a+b x}-\frac{2 b (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(a+b x)^2}+\frac{8 b^2 B c d}{a+b x}-6 b B 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)+6 b B 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)+\frac{2 b B d (b c-a d)}{a+b x}-\frac{b B (b c-a d)^2}{(a+b x)^2}-\frac{8 a b B d^2}{a+b x}+6 b B d^2 \log (a+b x)+\frac{4 a B d^3}{c+d x}-\frac{4 b B c d^2}{c+d x}-6 b B d^2 \log (c+d x)}{4 g^3 i^2 (b c-a d)^4}","-\frac{b^3 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^3 i^2 (a+b x)^2 (b c-a d)^4}+\frac{3 b^2 d (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^3 i^2 (a+b x) (b c-a d)^4}-\frac{d^3 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^3 i^2 (c+d x) (b c-a d)^4}+\frac{3 b d^2 \log \left(\frac{a+b x}{c+d x}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^3 i^2 (b c-a d)^4}-\frac{b^3 B (c+d x)^2}{4 g^3 i^2 (a+b x)^2 (b c-a d)^4}+\frac{3 b^2 B d (c+d x)}{g^3 i^2 (a+b x) (b c-a d)^4}+\frac{B d^3 (a+b x)}{g^3 i^2 (c+d x) (b c-a d)^4}-\frac{3 b B d^2 \log ^2\left(\frac{a+b x}{c+d x}\right)}{2 g^3 i^2 (b c-a d)^4}",1,"(-((b*B*(b*c - a*d)^2)/(a + b*x)^2) + (8*b^2*B*c*d)/(a + b*x) - (8*a*b*B*d^2)/(a + b*x) + (2*b*B*d*(b*c - a*d))/(a + b*x) - (4*b*B*c*d^2)/(c + d*x) + (4*a*B*d^3)/(c + d*x) + 6*b*B*d^2*Log[a + b*x] - (2*b*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x)^2 + (8*b*d*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x) + (4*d^2*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c + d*x) + 12*b*d^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 6*b*B*d^2*Log[c + d*x] - 12*b*d^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 6*b*B*d^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)]) + 6*b*B*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)]))/(4*(b*c - a*d)^4*g^3*i^2)","C",1
46,1,520,457,1.3399481,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^4 (c i+d i x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/((a*g + b*g*x)^4*(c*i + d*i*x)^2),x]","-\frac{36 b d^3 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{9 d^3 (a d-b c) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{c+d x}-36 b d^3 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+\frac{27 b d^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{a+b x}-\frac{9 b d (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(a+b x)^2}+\frac{3 b (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(a+b x)^3}+\frac{27 b^2 B c d^2}{a+b x}-18 b B 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)+18 b B 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)+\frac{12 b B d^2 (b c-a d)}{a+b x}-\frac{6 b B d (b c-a d)^2}{(a+b x)^2}+\frac{b B (b c-a d)^3}{(a+b x)^3}-\frac{27 a b B d^3}{a+b x}+30 b B d^3 \log (a+b x)+\frac{9 a B d^4}{c+d x}-\frac{9 b B c d^3}{c+d x}-30 b B d^3 \log (c+d x)}{9 g^4 i^2 (b c-a d)^5}","-\frac{b^4 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 g^4 i^2 (a+b x)^3 (b c-a d)^5}+\frac{2 b^3 d (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^4 i^2 (a+b x)^2 (b c-a d)^5}-\frac{6 b^2 d^2 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^4 i^2 (a+b x) (b c-a d)^5}+\frac{d^4 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^4 i^2 (c+d x) (b c-a d)^5}-\frac{4 b d^3 \log \left(\frac{a+b x}{c+d x}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^4 i^2 (b c-a d)^5}-\frac{b^4 B (c+d x)^3}{9 g^4 i^2 (a+b x)^3 (b c-a d)^5}+\frac{b^3 B d (c+d x)^2}{g^4 i^2 (a+b x)^2 (b c-a d)^5}-\frac{6 b^2 B d^2 (c+d x)}{g^4 i^2 (a+b x) (b c-a d)^5}-\frac{B d^4 (a+b x)}{g^4 i^2 (c+d x) (b c-a d)^5}+\frac{2 b B d^3 \log ^2\left(\frac{a+b x}{c+d x}\right)}{g^4 i^2 (b c-a d)^5}",1,"-1/9*((b*B*(b*c - a*d)^3)/(a + b*x)^3 - (6*b*B*d*(b*c - a*d)^2)/(a + b*x)^2 + (27*b^2*B*c*d^2)/(a + b*x) - (27*a*b*B*d^3)/(a + b*x) + (12*b*B*d^2*(b*c - a*d))/(a + b*x) - (9*b*B*c*d^3)/(c + d*x) + (9*a*B*d^4)/(c + d*x) + 30*b*B*d^3*Log[a + b*x] + (3*b*(b*c - a*d)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x)^3 - (9*b*d*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x)^2 + (27*b*d^2*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x) - (9*d^3*(-(b*c) + a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c + d*x) + 36*b*d^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 30*b*B*d^3*Log[c + d*x] - 36*b*d^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 18*b*B*d^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*B*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)]))/((b*c - a*d)^5*g^4*i^2)","C",1
47,1,317,361,0.4431482,"\int \frac{(a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(c i+d i x)^3} \, dx","Integrate[((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c*i + d*i*x)^3,x]","\frac{g^3 \left(-12 b^2 (b c-a d) \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{12 b (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{c+d x}+\frac{2 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(c+d x)^2}+4 b^2 B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)+6 b^2 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)+10 b^2 B (b c-a d) \log (a+b x)-14 b^2 B (b c-a d) \log (c+d x)+\frac{10 b B (b c-a d)^2}{c+d x}-\frac{B (b c-a d)^3}{(c+d x)^2}+4 A b^3 d x\right)}{4 d^4 i^3}","\frac{b^2 g^3 (b c-a d) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(3 B \log \left(\frac{e (a+b x)}{c+d x}\right)+3 A+B\right)}{d^4 i^3}+\frac{b g^3 (3 A+B) (a+b x) (b c-a d)}{d^3 i^3 (c+d x)}+\frac{g^3 (a+b x)^2 (b c-a d) \left(3 B \log \left(\frac{e (a+b x)}{c+d x}\right)+3 A+B\right)}{2 d^2 i^3 (c+d x)^2}+\frac{g^3 (a+b x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{d i^3 (c+d x)^2}+\frac{3 b^2 B g^3 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i^3}+\frac{3 b B g^3 (a+b x) (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)}{d^3 i^3 (c+d x)}-\frac{3 b B g^3 (a+b x) (b c-a d)}{d^3 i^3 (c+d x)}-\frac{3 B g^3 (a+b x)^2 (b c-a d)}{4 d^2 i^3 (c+d x)^2}",1,"(g^3*(4*A*b^3*d*x - (B*(b*c - a*d)^3)/(c + d*x)^2 + (10*b*B*(b*c - a*d)^2)/(c + d*x) + 10*b^2*B*(b*c - a*d)*Log[a + b*x] + 4*b^2*B*d*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] + (2*(b*c - a*d)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c + d*x)^2 - (12*b*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c + d*x) - 14*b^2*B*(b*c - a*d)*Log[c + d*x] - 12*b^2*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 6*b^2*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)])))/(4*d^4*i^3)","A",1
48,1,245,251,0.3363241,"\int \frac{(a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(c i+d i x)^3} \, dx","Integrate[((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c*i + d*i*x)^3,x]","\frac{g^2 \left(4 b^2 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+\frac{8 b (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{c+d x}-\frac{2 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(c+d x)^2}-2 b^2 B \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^2 B \log (a+b x)-\frac{6 b B (b c-a d)}{c+d x}+\frac{B (b c-a d)^2}{(c+d x)^2}+6 b^2 B \log (c+d x)\right)}{4 d^3 i^3}","-\frac{b^2 g^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\right)}{d^3 i^3}-\frac{g^2 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 d i^3 (c+d x)^2}-\frac{A b g^2 (a+b x)}{d^2 i^3 (c+d x)}-\frac{b^2 B g^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^3 i^3}-\frac{b B g^2 (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{d^2 i^3 (c+d x)}+\frac{b B g^2 (a+b x)}{d^2 i^3 (c+d x)}+\frac{B g^2 (a+b x)^2}{4 d i^3 (c+d x)^2}",1,"(g^2*((B*(b*c - a*d)^2)/(c + d*x)^2 - (6*b*B*(b*c - a*d))/(c + d*x) - 6*b^2*B*Log[a + b*x] - (2*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c + d*x)^2 + (8*b*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c + d*x) + 6*b^2*B*Log[c + d*x] + 4*b^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 2*b^2*B*((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*d^3*i^3)","A",1
49,1,207,85,0.1522169,"\int \frac{(a g+b g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{(c i+d i x)^3} \, dx","Integrate[((a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c*i + d*i*x)^3,x]","\frac{g \left(-\frac{b \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{d^2 (c+d x)}+\frac{(b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 d^2 (c+d x)^2}-\frac{B \left(\frac{2 b^2 \log (a+b x)}{b c-a d}-\frac{2 b^2 \log (c+d x)}{b c-a d}+\frac{b c-a d}{(c+d x)^2}+\frac{2 b}{c+d x}\right)}{4 d^2}+\frac{b B \left(\frac{b \log (a+b x)}{b c-a d}-\frac{b \log (c+d x)}{b c-a d}+\frac{1}{c+d x}\right)}{d^2}\right)}{i^3}","\frac{g (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 i^3 (c+d x)^2 (b c-a d)}-\frac{B g (a+b x)^2}{4 i^3 (c+d x)^2 (b c-a d)}",1,"(g*(((b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(2*d^2*(c + d*x)^2) - (b*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(d^2*(c + d*x)) + (b*B*((c + d*x)^(-1) + (b*Log[a + b*x])/(b*c - a*d) - (b*Log[c + d*x])/(b*c - a*d)))/d^2 - (B*((b*c - a*d)/(c + d*x)^2 + (2*b)/(c + d*x) + (2*b^2*Log[a + b*x])/(b*c - a*d) - (2*b^2*Log[c + d*x])/(b*c - a*d)))/(4*d^2)))/i^3","B",1
50,1,111,144,0.1184511,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(c i+d i x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/(c*i + d*i*x)^3,x]","\frac{\frac{B \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(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 d i^3 (c+d x)^2}","-\frac{B \log \left(\frac{e (a+b x)}{c+d x}\right)+A}{2 d i^3 (c+d x)^2}+\frac{b^2 B \log (a+b x)}{2 d i^3 (b c-a d)^2}-\frac{b^2 B \log (c+d x)}{2 d i^3 (b c-a d)^2}+\frac{b B}{2 d i^3 (c+d x) (b c-a d)}+\frac{B}{4 d i^3 (c+d x)^2}",1,"(-2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + (B*((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*i^3*(c + d*x)^2)","A",1
51,1,418,243,0.469701,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x) (c i+d i x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/((a*g + b*g*x)*(c*i + d*i*x)^3),x]","\frac{4 b^2 (c+d x)^2 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-4 b^2 (c+d 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 b (c+d x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-2 b^2 B (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 (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 \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 (c+d x) (b (c+d x) \log (a+b x)-a d-b (c+d x) \log (c+d x)+b c)}{4 g i^3 (c+d x)^2 (b c-a d)^3}","\frac{b^2 \log \left(\frac{a+b x}{c+d x}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g i^3 (b c-a d)^3}+\frac{d^2 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g i^3 (c+d x)^2 (b c-a d)^3}-\frac{2 b d (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g i^3 (c+d x) (b c-a d)^3}-\frac{b^2 B \log ^2\left(\frac{a+b x}{c+d x}\right)}{2 g i^3 (b c-a d)^3}-\frac{B \left(4 b-\frac{d (a+b x)}{c+d x}\right)^2}{4 g i^3 (b c-a d)^3}",1,"(2*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 4*b*(b*c - a*d)*(c + d*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 4*b^2*(c + d*x)^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 4*b^2*(c + d*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 4*b*B*(c + d*x)*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]) - B*((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*(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*(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)]))/(4*(b*c - a*d)^3*g*i^3*(c + d*x)^2)","C",1
52,1,452,365,0.7469664,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^2 (c i+d i x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/((a*g + b*g*x)^2*(c*i + d*i*x)^3),x]","\frac{-12 b^2 d \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{4 b^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{a+b x}+12 b^2 d \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{8 b d (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{c+d x}-\frac{2 d (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(c+d x)^2}-\frac{4 b^3 B c}{a+b x}+6 b^2 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)-6 b^2 B 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)+\frac{4 a b^2 B d}{a+b x}+6 b^2 B d \log (a+b x)-\frac{8 a b B d^2}{c+d x}+\frac{2 b B d (b c-a d)}{c+d x}+\frac{B d (b c-a d)^2}{(c+d x)^2}+\frac{8 b^2 B c d}{c+d x}-6 b^2 B d \log (c+d x)}{4 g^2 i^3 (b c-a d)^4}","-\frac{b^3 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^2 i^3 (a+b x) (b c-a d)^4}-\frac{3 b^2 d \log \left(\frac{a+b x}{c+d x}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^2 i^3 (b c-a d)^4}-\frac{d^3 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^2 i^3 (c+d x)^2 (b c-a d)^4}+\frac{3 b d^2 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^2 i^3 (c+d x) (b c-a d)^4}-\frac{b^3 B (c+d x)}{g^2 i^3 (a+b x) (b c-a d)^4}+\frac{3 b^2 B d \log ^2\left(\frac{a+b x}{c+d x}\right)}{2 g^2 i^3 (b c-a d)^4}+\frac{B d^3 (a+b x)^2}{4 g^2 i^3 (c+d x)^2 (b c-a d)^4}-\frac{3 b B d^2 (a+b x)}{g^2 i^3 (c+d x) (b c-a d)^4}",1,"((-4*b^3*B*c)/(a + b*x) + (4*a*b^2*B*d)/(a + b*x) + (B*d*(b*c - a*d)^2)/(c + d*x)^2 + (8*b^2*B*c*d)/(c + d*x) - (8*a*b*B*d^2)/(c + d*x) + (2*b*B*d*(b*c - a*d))/(c + d*x) + 6*b^2*B*d*Log[a + b*x] - (4*b^2*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x) - (2*d*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c + d*x)^2 - (8*b*d*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c + d*x) - 12*b^2*d*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 6*b^2*B*d*Log[c + d*x] + 12*b^2*d*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 6*b^2*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)]) - 6*b^2*B*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)]))/(4*(b*c - a*d)^4*g^2*i^3)","C",1
53,1,533,463,1.1762158,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^3 (c i+d i x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/((a*g + b*g*x)^3*(c*i + d*i*x)^3),x]","-\frac{-24 b^2 d^2 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+24 b^2 d^2 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-\frac{12 b^2 d (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{a+b x}+\frac{2 b^2 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(a+b x)^2}-\frac{12 b d^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{c+d x}-\frac{2 d^2 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(c+d x)^2}-\frac{12 b^3 B c d}{a+b x}+12 b^2 B 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)-12 b^2 B 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)-\frac{2 b^2 B d (b c-a d)}{a+b x}+\frac{b^2 B (b c-a d)^2}{(a+b x)^2}+\frac{12 a b^2 B d^2}{a+b x}-\frac{12 a b B d^3}{c+d x}+\frac{2 b B d^2 (b c-a d)}{c+d x}+\frac{B d^2 (b c-a d)^2}{(c+d x)^2}+\frac{12 b^2 B c d^2}{c+d x}}{4 g^3 i^3 (b c-a d)^5}","-\frac{b^4 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^3 i^3 (a+b x)^2 (b c-a d)^5}+\frac{4 b^3 d (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^3 i^3 (a+b x) (b c-a d)^5}+\frac{6 b^2 d^2 \log \left(\frac{a+b x}{c+d x}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^3 i^3 (b c-a d)^5}+\frac{d^4 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^3 i^3 (c+d x)^2 (b c-a d)^5}-\frac{4 b d^3 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^3 i^3 (c+d x) (b c-a d)^5}-\frac{b^4 B (c+d x)^2}{4 g^3 i^3 (a+b x)^2 (b c-a d)^5}+\frac{4 b^3 B d (c+d x)}{g^3 i^3 (a+b x) (b c-a d)^5}-\frac{3 b^2 B d^2 \log ^2\left(\frac{a+b x}{c+d x}\right)}{g^3 i^3 (b c-a d)^5}-\frac{B d^4 (a+b x)^2}{4 g^3 i^3 (c+d x)^2 (b c-a d)^5}+\frac{4 b B d^3 (a+b x)}{g^3 i^3 (c+d x) (b c-a d)^5}",1,"-1/4*((b^2*B*(b*c - a*d)^2)/(a + b*x)^2 - (12*b^3*B*c*d)/(a + b*x) + (12*a*b^2*B*d^2)/(a + b*x) - (2*b^2*B*d*(b*c - a*d))/(a + b*x) + (B*d^2*(b*c - a*d)^2)/(c + d*x)^2 + (12*b^2*B*c*d^2)/(c + d*x) - (12*a*b*B*d^3)/(c + d*x) + (2*b*B*d^2*(b*c - a*d))/(c + d*x) + (2*b^2*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x)^2 - (12*b^2*d*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x) - (2*d^2*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c + d*x)^2 - (12*b*d^2*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c + d*x) - 24*b^2*d^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 24*b^2*d^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 12*b^2*B*d^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)]) - 12*b^2*B*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)]))/((b*c - a*d)^5*g^3*i^3)","C",1
54,1,637,563,1.89339,"\int \frac{A+B \log \left(\frac{e (a+b x)}{c+d x}\right)}{(a g+b g x)^4 (c i+d i x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])/((a*g + b*g*x)^4*(c*i + d*i*x)^3),x]","-\frac{360 b^2 d^3 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-360 b^2 d^3 \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+\frac{216 b^2 d^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{a+b x}-\frac{54 b^2 d (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(a+b x)^2}+\frac{12 b^2 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(a+b x)^3}+\frac{144 b d^3 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{c+d x}+\frac{18 d^3 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{(c+d x)^2}+\frac{216 b^3 B c d^2}{a+b x}-180 b^2 B 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)+180 b^2 B 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)+\frac{66 b^2 B d^2 (b c-a d)}{a+b x}-\frac{33 b^2 B d (b c-a d)^2}{(a+b x)^2}+\frac{4 b^2 B (b c-a d)^3}{(a+b x)^3}-\frac{216 a b^2 B d^3}{a+b x}+120 b^2 B d^3 \log (a+b x)+\frac{144 a b B d^4}{c+d x}-\frac{18 b B d^3 (b c-a d)}{c+d x}-\frac{9 B d^3 (b c-a d)^2}{(c+d x)^2}-\frac{144 b^2 B c d^3}{c+d x}-120 b^2 B d^3 \log (c+d x)}{36 g^4 i^3 (b c-a d)^6}","-\frac{b^5 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 g^4 i^3 (a+b x)^3 (b c-a d)^6}+\frac{5 b^4 d (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^4 i^3 (a+b x)^2 (b c-a d)^6}-\frac{10 b^3 d^2 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^4 i^3 (a+b x) (b c-a d)^6}-\frac{10 b^2 d^3 \log \left(\frac{a+b x}{c+d x}\right) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^4 i^3 (b c-a d)^6}-\frac{d^5 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^4 i^3 (c+d x)^2 (b c-a d)^6}+\frac{5 b d^4 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^4 i^3 (c+d x) (b c-a d)^6}-\frac{b^5 B (c+d x)^3}{9 g^4 i^3 (a+b x)^3 (b c-a d)^6}+\frac{5 b^4 B d (c+d x)^2}{4 g^4 i^3 (a+b x)^2 (b c-a d)^6}-\frac{10 b^3 B d^2 (c+d x)}{g^4 i^3 (a+b x) (b c-a d)^6}+\frac{5 b^2 B d^3 \log ^2\left(\frac{a+b x}{c+d x}\right)}{g^4 i^3 (b c-a d)^6}+\frac{B d^5 (a+b x)^2}{4 g^4 i^3 (c+d x)^2 (b c-a d)^6}-\frac{5 b B d^4 (a+b x)}{g^4 i^3 (c+d x) (b c-a d)^6}",1,"-1/36*((4*b^2*B*(b*c - a*d)^3)/(a + b*x)^3 - (33*b^2*B*d*(b*c - a*d)^2)/(a + b*x)^2 + (216*b^3*B*c*d^2)/(a + b*x) - (216*a*b^2*B*d^3)/(a + b*x) + (66*b^2*B*d^2*(b*c - a*d))/(a + b*x) - (9*B*d^3*(b*c - a*d)^2)/(c + d*x)^2 - (144*b^2*B*c*d^3)/(c + d*x) + (144*a*b*B*d^4)/(c + d*x) - (18*b*B*d^3*(b*c - a*d))/(c + d*x) + 120*b^2*B*d^3*Log[a + b*x] + (12*b^2*(b*c - a*d)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x)^3 - (54*b^2*d*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x)^2 + (216*b^2*d^2*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(a + b*x) + (18*d^3*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c + d*x)^2 + (144*b*d^3*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(c + d*x) + 360*b^2*d^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 120*b^2*B*d^3*Log[c + d*x] - 360*b^2*d^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 180*b^2*B*d^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)]) + 180*b^2*B*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)]))/((b*c - a*d)^6*g^4*i^3)","C",1
55,1,905,539,0.7640447,"\int (a g+b g x)^3 (c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Integrate[(a*g + b*g*x)^3*(c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{g^3 i \left(4 d \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (a+b x)^5+5 (b c-a d) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (a+b x)^4-\frac{5 B (b c-a d)^2 \left(-6 B \log (c+d x) (b c-a d)^3-6 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x) (b c-a d)^3+3 B \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 c-a d)^3+6 A b d x (b c-a d)^2+6 B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right) (b c-a d)^2+3 B (b d x+(a d-b c) \log (c+d x)) (b c-a d)^2+B \left(-2 \log (c+d x) (b c-a d)^2+2 b d x (b c-a d)-d^2 (a+b x)^2\right) (b c-a d)+2 d^3 (a+b x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)+3 d^2 (a d-b c) (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)\right)}{3 d^4}+\frac{B (b c-a d) \left(-24 B \log (c+d x) (b c-a d)^4-24 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x) (b c-a d)^4+12 B \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 c-a d)^4+24 A b d x (b c-a d)^3+24 B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right) (b c-a d)^3+12 B (b d x+(a d-b c) \log (c+d x)) (b c-a d)^3-12 d^2 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2+4 B \left(-2 \log (c+d x) (b c-a d)^2+2 b d x (b c-a d)-d^2 (a+b x)^2\right) (b c-a d)^2+8 d^3 (a+b x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)+B \left(-6 \log (c+d x) (b c-a d)^3+6 b d x (b c-a d)^2+2 d^3 (a+b x)^3+3 d^2 (a d-b c) (a+b x)^2\right) (b c-a d)-6 d^4 (a+b x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)\right)}{3 d^4}\right)}{20 b^2}","-\frac{B g^3 i (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)}{c+d x}\right)+6 A+11 B\right)}{60 b^2 d^4}-\frac{B g^3 i (a+b x) (b c-a d)^4 \left(6 B \log \left(\frac{e (a+b x)}{c+d x}\right)+6 A+5 B\right)}{60 b^2 d^3}+\frac{B g^3 i (a+b x)^2 (b c-a d)^3 \left(3 B \log \left(\frac{e (a+b x)}{c+d x}\right)+3 A+B\right)}{60 b^2 d^2}-\frac{B g^3 i (a+b x)^3 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{30 b^2 d}+\frac{g^3 i (a+b x)^4 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{20 b^2}-\frac{B g^3 i (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^2}+\frac{g^3 i (a+b x)^4 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{5 b}-\frac{B^2 g^3 i (b c-a d)^5 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{10 b^2 d^4}-\frac{B^2 g^3 i (b c-a d)^5 \log (c+d x)}{10 b^2 d^4}-\frac{3 B^2 g^3 i (c+d x)^2 (b c-a d)^3}{20 d^4}+\frac{b B^2 g^3 i (c+d x)^3 (b c-a d)^2}{30 d^4}+\frac{3 B^2 g^3 i x (b c-a d)^4}{10 b d^3}",1,"(g^3*i*(5*(b*c - a*d)*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 4*d*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - (5*B*(b*c - a*d)^2*(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) + (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)])))/(3*d^4)))/(20*b^2)","A",1
56,1,680,450,0.541447,"\int (a g+b g x)^2 (c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Integrate[(a*g + b*g*x)^2*(c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{g^2 i \left(\frac{4 B (b c-a d)^2 \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}-\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)}{d^3}+3 d (a+b x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2+4 (a+b x)^3 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2\right)}{12 b^2}","\frac{B g^2 i (b c-a d)^4 \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)}{12 b^2 d^3}+\frac{B g^2 i (a+b x) (b c-a d)^3 \left(2 B \log \left(\frac{e (a+b x)}{c+d x}\right)+2 A+B\right)}{12 b^2 d^2}-\frac{B g^2 i (a+b x)^2 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{12 b^2 d}+\frac{g^2 i (a+b x)^3 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{12 b^2}-\frac{B g^2 i (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^2}+\frac{g^2 i (a+b x)^3 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{4 b}+\frac{B^2 g^2 i (b c-a d)^4 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{6 b^2 d^3}+\frac{B^2 g^2 i (b c-a d)^4 \log (c+d x)}{6 b^2 d^3}+\frac{B^2 g^2 i (c+d x)^2 (b c-a d)^2}{12 d^3}-\frac{B^2 g^2 i x (b c-a d)^3}{3 b d^2}",1,"(g^2*i*(4*(b*c - a*d)*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 3*d*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + (4*B*(b*c - a*d)^2*(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 - (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)])))/d^3))/(12*b^2)","A",1
57,1,869,343,0.7319368,"\int (a g+b g x) (c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Integrate[(a*g + b*g*x)*(c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{g i \left(2 b^3 B \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x) c^3-b^3 B^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) c^3-6 a b^2 B d \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x) c^2+3 a b^2 B^2 d \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) c^2+6 a b^2 d^2 x \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 c-6 A b^2 B d (b c-a d) x c-6 b B^2 d (b c-a d) (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right) c+6 a^2 b B d^2 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) c+6 b B^2 (b c-a d)^2 \log (c+d x) c-3 a^2 b B^2 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) c+2 b^3 d^3 x^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2+3 b^2 d^2 (b c+a d) x^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2+6 a A b B d^2 (a d-b c) x+4 A b B d (b c-a d) (b c+a d) x+6 a B^2 d^2 (a d-b c) (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)+4 B^2 d (b c-a d) (b c+a d) (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 b^2 B d^2 (b c-a d) x^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)-2 a^3 B d^3 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)+6 a B^2 d (b c-a d)^2 \log (c+d x)-4 B^2 (b c-a d)^2 (b c+a d) \log (c+d x)+2 B^2 (b c-a d) \left(a^2 d^2 \log (a+b x)-b \left(b \log (c+d x) c^2+d (a d-b c) x\right)\right)+a^3 B^2 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)\right)}{6 b^2 d^2}","-\frac{B g i (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)}{c+d x}\right)+A+B\right)}{3 b^2 d^2}-\frac{B g i (a+b x) (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b^2 d}+\frac{g i (a+b x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{6 b^2}-\frac{B g i (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^2}+\frac{g i (a+b x)^2 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 b}-\frac{B^2 g i (b c-a d)^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{3 b^2 d^2}-\frac{B^2 g i (b c-a d)^3 \log (c+d x)}{3 b^2 d^2}+\frac{B^2 g i x (b c-a d)^2}{3 b d}",1,"(g*i*(-6*A*b^2*B*c*d*(b*c - a*d)*x + 6*a*A*b*B*d^2*(-(b*c) + a*d)*x + 4*A*b*B*d*(b*c - a*d)*(b*c + a*d)*x - 6*b*B^2*c*d*(b*c - a*d)*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] + 6*a*B^2*d^2*(-(b*c) + a*d)*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] + 4*B^2*d*(b*c - a*d)*(b*c + a*d)*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] - 2*b^2*B*d^2*(b*c - a*d)*x^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6*a^2*b*B*c*d^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 2*a^3*B*d^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6*a*b^2*c*d^2*x*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 3*b^2*d^2*(b*c + a*d)*x^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 2*b^3*d^3*x^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 6*b*B^2*c*(b*c - a*d)^2*Log[c + d*x] + 6*a*B^2*d*(b*c - a*d)^2*Log[c + d*x] - 4*B^2*(b*c - a*d)^2*(b*c + a*d)*Log[c + d*x] + 2*b^3*B*c^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 6*a*b^2*B*c^2*d*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 2*B^2*(b*c - a*d)*(a^2*d^2*Log[a + b*x] - b*(d*(-(b*c) + a*d)*x + b*c^2*Log[c + d*x])) - 3*a^2*b*B^2*c*d^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)]) + a^3*B^2*d^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^2*c^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*a*b^2*B^2*c^2*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)])))/(6*b^2*d^2)","B",1
58,1,205,203,0.1966849,"\int (c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Integrate[(c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{i \left((c+d 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 (a+b x) \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)+2 \left(B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)+\log (c+d x) (a B d-b B c)+A b d x\right)+2 B (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)+\log ^2(a+b x) (a B d-b B c)\right)}{b^2}\right)}{2 d}","\frac{B i (b c-a d)^2 \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)}{b^2 d}-\frac{B i (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^2}+\frac{i (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 d}-\frac{B^2 i (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 i (b c-a d)^2 \log (c+d x)}{b^2 d}",1,"(i*((c + d*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - (B*(b*c - a*d)*((-(b*B*c) + a*B*d)*Log[a + b*x]^2 + 2*(A*b*d*x + B*d*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] + (-(b*B*c) + a*B*d)*Log[c + d*x]) + 2*(b*c - a*d)*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)] + B*Log[(b*(c + d*x))/(b*c - a*d)]) + 2*B*(b*c - a*d)*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]))/b^2))/(2*d)","A",1
59,1,987,286,1.3007931,"\int \frac{(c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{a g+b g x} \, dx","Integrate[((c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x),x]","\frac{i \left(3 b d x A^2+3 (b c-a d) \log (a+b x) A^2-3 B \left(a d \log ^2\left(\frac{a}{b}+x\right)-2 a d (\log (a+b x)+1) \log \left(\frac{a}{b}+x\right)+2 \left(-b c+a d+\log \left(\frac{c}{d}+x\right) \left(b c+a d \log (a+b x)-a d \log \left(\frac{d (a+b x)}{a d-b c}\right)\right)+(a d \log (a+b x)-b d x) \log \left(\frac{e (a+b x)}{c+d x}\right)\right)-2 a d \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right) A+3 b B c \left(\log ^2\left(\frac{a}{b}+x\right)-2 \log (a+b x) \left(\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)-\log \left(\frac{e (a+b x)}{c+d x}\right)\right)-2 \left(\log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)+\text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right)\right) A-B^2 \left(a d \log ^3\left(\frac{a}{b}+x\right)-3 d (b x-a \log (a+b x)) \left(-\log \left(\frac{a}{b}+x\right)+\log \left(\frac{c}{d}+x\right)+\log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2-3 d \left((a+b x) \log ^2\left(\frac{a}{b}+x\right)-2 (a+b x) \log \left(\frac{a}{b}+x\right)+2 b x\right)-3 b \left((c+d x) \log ^2\left(\frac{c}{d}+x\right)-2 (c+d x) \log \left(\frac{c}{d}+x\right)+2 d x\right)+6 \left(a d+2 b x d-b x \log \left(\frac{c}{d}+x\right) d-b c \log (c+d x)+\log \left(\frac{a}{b}+x\right) \left(-d (a+b x)+d \log \left(\frac{c}{d}+x\right) (a+b x)+(b c-a d) \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)+(b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)-3 \left(\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)-\log \left(\frac{e (a+b x)}{c+d x}\right)\right) \left(a d \log ^2\left(\frac{a}{b}+x\right)-2 d (a+b x) \log \left(\frac{a}{b}+x\right)-2 b c+2 a d+2 \log \left(\frac{c}{d}+x\right) \left(b (c+d x)-a d \log \left(\frac{d (a+b x)}{a d-b c}\right)\right)-2 a d \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right)-3 a d \left(\left(\log \left(\frac{c}{d}+x\right)-\log \left(\frac{b (c+d x)}{b c-a d}\right)\right) \log ^2\left(\frac{a}{b}+x\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right) \log \left(\frac{a}{b}+x\right)+2 \text{Li}_3\left(\frac{d (a+b x)}{a d-b c}\right)\right)+3 a d \left(\log \left(\frac{d (a+b x)}{a d-b c}\right) \log ^2\left(\frac{c}{d}+x\right)+2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right) \log \left(\frac{c}{d}+x\right)-2 \text{Li}_3\left(\frac{b (c+d x)}{b c-a d}\right)\right)\right)-3 b B^2 c \left(\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 \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)-2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)\right)\right)}{3 b^2 g}","\frac{2 B i (b c-a d) \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^2 g}+\frac{2 B i (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^2 g}+\frac{d i (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{b^2 g}-\frac{i (b c-a d) \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^2 g}+\frac{2 B^2 i (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^2 g}+\frac{2 B^2 i (b c-a d) \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^2 g}",1,"(i*(3*A^2*b*d*x + 3*A^2*(b*c - a*d)*Log[a + b*x] - 3*A*B*(a*d*Log[a/b + x]^2 - 2*a*d*Log[a/b + x]*(1 + Log[a + b*x]) + 2*(-(b*c) + a*d + Log[c/d + x]*(b*c + a*d*Log[a + b*x] - a*d*Log[(d*(a + b*x))/(-(b*c) + a*d)]) + (-(b*d*x) + a*d*Log[a + b*x])*Log[(e*(a + b*x))/(c + d*x)]) - 2*a*d*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 3*A*b*B*c*(Log[a/b + x]^2 - 2*Log[a + b*x]*(Log[a/b + x] - Log[c/d + x] - Log[(e*(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*(a*d*Log[a/b + x]^3 - 3*d*(2*b*x - 2*(a + b*x)*Log[a/b + x] + (a + b*x)*Log[a/b + x]^2) - 3*b*(2*d*x - 2*(c + d*x)*Log[c/d + x] + (c + d*x)*Log[c/d + x]^2) - 3*d*(b*x - a*Log[a + b*x])*(-Log[a/b + x] + Log[c/d + x] + Log[(e*(a + b*x))/(c + d*x)])^2 + 6*(a*d + 2*b*d*x - b*d*x*Log[c/d + x] - b*c*Log[c + d*x] + Log[a/b + x]*(-(d*(a + b*x)) + d*(a + b*x)*Log[c/d + x] + (b*c - a*d)*Log[(b*(c + d*x))/(b*c - a*d)]) + (b*c - a*d)*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - 3*(Log[a/b + x] - Log[c/d + x] - Log[(e*(a + b*x))/(c + d*x)])*(-2*b*c + 2*a*d - 2*d*(a + b*x)*Log[a/b + x] + a*d*Log[a/b + x]^2 + 2*Log[c/d + x]*(b*(c + d*x) - a*d*Log[(d*(a + b*x))/(-(b*c) + a*d)]) - 2*a*d*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) - 3*a*d*(Log[a/b + x]^2*(Log[c/d + x] - Log[(b*(c + d*x))/(b*c - a*d)]) - 2*Log[a/b + x]*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 2*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)]) + 3*a*d*(Log[c/d + x]^2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*Log[c/d + x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])) - 3*b*B^2*c*(Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(e*(a + b*x))/(c + d*x)]^2 - 2*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))])))/(3*b^2*g)","B",1
60,1,1407,241,2.0515831,"\int \frac{(c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^2} \, dx","Integrate[((c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x)^2,x]","\frac{i \left(3 d \log (a+b x) A^2+\frac{3 (a d-b c) A^2}{a+b x}-\frac{6 b B c \left(-d (a+b x) \log \left(\frac{c}{d}+x\right)+d (a+b x) \log \left(\frac{d (a+b x)}{a d-b c}\right)+(b c-a d) \left(\log \left(\frac{e (a+b x)}{c+d x}\right)+1\right)\right) A}{(b c-a d) (a+b x)}+3 B d \left(\log ^2\left(\frac{a}{b}+x\right)-2 \log (a+b x) \log \left(\frac{a}{b}+x\right)-2 \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)+2 \log (a+b x) \left(\frac{a d}{b c-a d}+\log \left(\frac{c}{d}+x\right)+\log \left(\frac{e (a+b x)}{c+d x}\right)\right)+2 a \left(\frac{\log \left(\frac{e (a+b x)}{c+d x}\right)}{a+b x}+\frac{d \log (c+d x)}{a d-b c}+\frac{1}{a+b x}\right)-2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right) A+\frac{3 b B^2 c \left(-\left((b c-a d) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)\right)-2 (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 d (a+b x) \log (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 d (a+b x) \log \left(\frac{b c-a d}{b c+b d x}\right) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 b c+2 a d-2 d (a+b x) \log (a+b x)+2 d (a+b x) \log (c+d x)+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)+d (a+b x) \left(\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)+\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)\right)\right)}{(b c-a d) (a+b x)}+\frac{B^2 d \left((b c-a d) (a+b x) \log ^3\left(\frac{a}{b}+x\right)+3 (b c-a d) (a+(a+b x) \log (a+b x)) \left(-\log \left(\frac{a}{b}+x\right)+\log \left(\frac{c}{d}+x\right)+\log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2+3 a (b c-a d) \left(\log ^2\left(\frac{a}{b}+x\right)+2 \log \left(\frac{a}{b}+x\right)+2\right)+3 a \left(d (a+b x) \log ^2\left(\frac{a}{b}+x\right)-2 \left((b c-a d) \log \left(\frac{c}{d}+x\right)+d (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)\right) \log \left(\frac{a}{b}+x\right)+2 \left((a d-b c) \log \left(\frac{c}{d}+x\right)+d (a+b x) (\log (a+b x)-\log (c+d x))\right)-2 d (a+b x) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)+3 a \left(\log \left(\frac{c}{d}+x\right) \left(b (c+d x) \log \left(\frac{c}{d}+x\right)-2 d (a+b x) \log \left(\frac{d (a+b x)}{a d-b c}\right)\right)-2 d (a+b x) \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right)-3 \left(\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)-\log \left(\frac{e (a+b x)}{c+d x}\right)\right) \left((b c-a d) (a+b x) \log ^2\left(\frac{a}{b}+x\right)+2 a (b c-a d) \left(\log \left(\frac{a}{b}+x\right)+1\right)+2 a (a d-b c) \log \left(\frac{c}{d}+x\right)+2 a d (a+b x) (\log (a+b x)-\log (c+d x))-2 (b c-a d) (a+b x) \left(\log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)+\text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right)\right)-3 (b c-a d) (a+b x) \left(\left(\log \left(\frac{c}{d}+x\right)-\log \left(\frac{b (c+d x)}{b c-a d}\right)\right) \log ^2\left(\frac{a}{b}+x\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right) \log \left(\frac{a}{b}+x\right)+2 \text{Li}_3\left(\frac{d (a+b x)}{a d-b c}\right)\right)+3 (b c-a d) (a+b x) \left(\log \left(\frac{d (a+b x)}{a d-b c}\right) \log ^2\left(\frac{c}{d}+x\right)+2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right) \log \left(\frac{c}{d}+x\right)-2 \text{Li}_3\left(\frac{b (c+d x)}{b c-a d}\right)\right)\right)}{(b c-a d) (a+b x)}\right)}{3 b^2 g^2}","\frac{2 B d i \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^2 g^2}-\frac{d i \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^2 g^2}-\frac{2 B i (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b g^2 (a+b x)}-\frac{i (c+d x) \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^2 d i \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^2 g^2}-\frac{2 B^2 i (c+d x)}{b g^2 (a+b x)}",1,"(i*((3*A^2*(-(b*c) + a*d))/(a + b*x) + 3*A^2*d*Log[a + b*x] - (6*A*b*B*c*(-(d*(a + b*x)*Log[c/d + x]) + d*(a + b*x)*Log[(d*(a + b*x))/(-(b*c) + a*d)] + (b*c - a*d)*(1 + Log[(e*(a + b*x))/(c + d*x)])))/((b*c - a*d)*(a + b*x)) + (3*b*B^2*c*(-2*b*c + 2*a*d - 2*d*(a + b*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(e*(a + b*x))/(c + d*x)] - 2*d*(a + b*x)*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] - (b*c - a*d)*Log[(e*(a + b*x))/(c + d*x)]^2 + 2*d*(a + b*x)*Log[c + d*x] - 2*d*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 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)]) + d*(a + b*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(a + b*x)) + 3*A*B*d*(Log[a/b + x]^2 - 2*Log[a/b + x]*Log[a + b*x] - 2*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*Log[a + b*x]*((a*d)/(b*c - a*d) + Log[c/d + x] + Log[(e*(a + b*x))/(c + d*x)]) + 2*a*((a + b*x)^(-1) + Log[(e*(a + b*x))/(c + d*x)]/(a + b*x) + (d*Log[c + d*x])/(-(b*c) + a*d)) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + (B^2*d*((b*c - a*d)*(a + b*x)*Log[a/b + x]^3 + 3*a*(b*c - a*d)*(2 + 2*Log[a/b + x] + Log[a/b + x]^2) + 3*(b*c - a*d)*(a + (a + b*x)*Log[a + b*x])*(-Log[a/b + x] + Log[c/d + x] + Log[(e*(a + b*x))/(c + d*x)])^2 + 3*a*(d*(a + b*x)*Log[a/b + x]^2 + 2*((-(b*c) + a*d)*Log[c/d + x] + d*(a + b*x)*(Log[a + b*x] - Log[c + d*x])) - 2*Log[a/b + x]*((b*c - a*d)*Log[c/d + x] + d*(a + b*x)*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*d*(a + b*x)*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 3*a*(Log[c/d + x]*(b*(c + d*x)*Log[c/d + x] - 2*d*(a + b*x)*Log[(d*(a + b*x))/(-(b*c) + a*d)]) - 2*d*(a + b*x)*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) - 3*(Log[a/b + x] - Log[c/d + x] - Log[(e*(a + b*x))/(c + d*x)])*((b*c - a*d)*(a + b*x)*Log[a/b + x]^2 + 2*a*(b*c - a*d)*(1 + Log[a/b + x]) + 2*a*(-(b*c) + a*d)*Log[c/d + x] + 2*a*d*(a + b*x)*(Log[a + b*x] - Log[c + d*x]) - 2*(b*c - a*d)*(a + b*x)*(Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + PolyLog[2, (b*(c + d*x))/(b*c - a*d)])) - 3*(b*c - a*d)*(a + b*x)*(Log[a/b + x]^2*(Log[c/d + x] - Log[(b*(c + d*x))/(b*c - a*d)]) - 2*Log[a/b + x]*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 2*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)]) + 3*(b*c - a*d)*(a + b*x)*(Log[c/d + x]^2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*Log[c/d + x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(a + b*x))))/(3*b^2*g^2)","B",1
61,1,765,141,0.9107124,"\int \frac{(c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^3} \, dx","Integrate[((c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x)^3,x]","-\frac{i \left(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)+4 B d (a+b x) \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)+2 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2-4 d (a+b x) (a d-b c) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2\right)}{4 b^2 g^3 (a+b x)^2 (b c-a d)}","-\frac{i (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)}-\frac{B i (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)}-\frac{B^2 i (c+d x)^2}{4 g^3 (a+b x)^2 (b c-a d)}",1,"-1/4*(i*(2*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - 4*d*(-(b*c) + a*d)*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 4*B*d*(a + b*x)*(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*(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^2*(b*c - a*d)*g^3*(a + b*x)^2)","C",1
62,1,1035,287,1.0413605,"\int \frac{(c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^4} \, dx","Integrate[((c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x)^4,x]","-\frac{i \left(36 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (b c-a d)^3+54 d (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (b c-a d)^2+27 B d (a+b x) \left(2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2+4 d (a d-b c) (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)-4 d^2 (a+b x)^2 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)+4 d^2 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \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 \left((b c-a d)^2+2 d (a d-b c) (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)\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(\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)\right)+2 B \left(12 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^3-18 d (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2+36 d^2 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)+36 d^3 (a+b x)^3 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)-36 d^3 (a+b x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \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) \left((b c-a d)^2+2 d (a d-b c) (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)\right)+2 B \left(2 (b c-a d)^3-3 d (a+b x) (b c-a d)^2+6 d^2 (a+b x)^2 (b c-a d)+6 d^3 (a+b x)^3 \log (a+b x)-6 d^3 (a+b x)^3 \log (c+d x)\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(\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)\right)\right)}{108 b^2 (b c-a d)^2 g^4 (a+b x)^3}","-\frac{b i (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)^2}-\frac{2 b B i (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)^2}+\frac{d i (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 g^4 (a+b x)^2 (b c-a d)^2}+\frac{B d i (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)^2}-\frac{2 b B^2 i (c+d x)^3}{27 g^4 (a+b x)^3 (b c-a d)^2}+\frac{B^2 d i (c+d x)^2}{4 g^4 (a+b x)^2 (b c-a d)^2}",1,"-1/108*(i*(36*(b*c - a*d)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 54*d*(b*c - a*d)^2*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 27*B*d*(a + b*x)*(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)])) + 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^2*(b*c - a*d)^2*g^4*(a + b*x)^3)","C",1
63,1,1340,445,1.6276993,"\int \frac{(c i+d i x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^5} \, dx","Integrate[((c*i + d*i*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x)^5,x]","-\frac{i \left(216 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (b c-a d)^4-288 d (a d-b c)^3 (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2+16 B d (a+b x) \left(12 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^3-18 d (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2+36 d^2 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)+36 d^3 (a+b x)^3 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)-36 d^3 (a+b x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \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) \left((b c-a d)^2+2 d (a d-b c) (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)\right)+2 B \left(2 (b c-a d)^3-3 d (a+b x) (b c-a d)^2+6 d^2 (a+b x)^2 (b c-a d)+6 d^3 (a+b x)^3 \log (a+b x)-6 d^3 (a+b x)^3 \log (c+d x)\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(\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)\right)+3 B \left(36 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^4+72 d^2 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2+144 d^3 (a d-b c) (a+b x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)+48 d (a d-b c)^3 (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)-144 d^4 (a+b x)^4 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)+144 d^4 (a+b x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \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 \left((b c-a d)^2+2 d (a d-b c) (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)\right)-8 B d (a+b x) \left(2 (b c-a d)^3-3 d (a+b x) (b c-a d)^2+6 d^2 (a+b x)^2 (b c-a d)+6 d^3 (a+b x)^3 \log (a+b x)-6 d^3 (a+b x)^3 \log (c+d x)\right)+3 B \left(3 (b c-a d)^4+6 d^2 (a+b x)^2 (b c-a d)^2+12 d^3 (a d-b c) (a+b x)^3+4 d (a d-b c)^3 (a+b x)-12 d^4 (a+b x)^4 \log (a+b x)+12 d^4 (a+b x)^4 \log (c+d x)\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(\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)\right)\right)}{864 b^2 (b c-a d)^3 g^5 (a+b x)^4}","-\frac{b^2 i (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)^3}-\frac{b^2 B i (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)^3}-\frac{d^2 i (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)^3}-\frac{B d^2 i (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)^3}+\frac{2 b d i (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 g^5 (a+b x)^3 (b c-a d)^3}+\frac{4 b B d i (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{9 g^5 (a+b x)^3 (b c-a d)^3}-\frac{b^2 B^2 i (c+d x)^4}{32 g^5 (a+b x)^4 (b c-a d)^3}-\frac{B^2 d^2 i (c+d x)^2}{4 g^5 (a+b x)^2 (b c-a d)^3}+\frac{4 b B^2 d i (c+d x)^3}{27 g^5 (a+b x)^3 (b c-a d)^3}",1,"-1/864*(i*(216*(b*c - a*d)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - 288*d*(-(b*c) + a*d)^3*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 16*B*d*(a + b*x)*(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)])) + 3*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^2*(b*c - a*d)^3*g^5*(a + b*x)^4)","C",1
64,1,1559,711,1.3747273,"\int (a g+b g x)^3 (c i+d i 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)^3*(c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{g^3 i^2 \left(10 d^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (a+b x)^6+24 d (b c-a d) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (a+b x)^5+15 (b c-a d)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (a+b x)^4-\frac{5 B (b c-a d)^3 \left(-6 B \log (c+d x) (b c-a d)^3-6 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x) (b c-a d)^3+3 B \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 c-a d)^3+6 A b d x (b c-a d)^2+6 B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right) (b c-a d)^2+3 B (b d x+(a d-b c) \log (c+d x)) (b c-a d)^2+B \left(-2 \log (c+d x) (b c-a d)^2+2 b d x (b c-a d)-d^2 (a+b x)^2\right) (b c-a d)+2 d^3 (a+b x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)+3 d^2 (a d-b c) (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)\right)}{d^4}+\frac{2 B (b c-a d)^2 \left(-24 B \log (c+d x) (b c-a d)^4-24 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x) (b c-a d)^4+12 B \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 c-a d)^4+24 A b d x (b c-a d)^3+24 B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right) (b c-a d)^3+12 B (b d x+(a d-b c) \log (c+d x)) (b c-a d)^3-12 d^2 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2+4 B \left(-2 \log (c+d x) (b c-a d)^2+2 b d x (b c-a d)-d^2 (a+b x)^2\right) (b c-a d)^2+8 d^3 (a+b x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)+B \left(-6 \log (c+d x) (b c-a d)^3+6 b d x (b c-a d)^2+2 d^3 (a+b x)^3+3 d^2 (a d-b c) (a+b x)^2\right) (b c-a d)-6 d^4 (a+b x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)\right)}{d^4}-\frac{B (b c-a d) \left(6 a B (a+b x)^4 d^5+24 (a+b x)^5 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) d^5-6 b B c (a+b x)^4 d^4+8 a B (a d-b c) (a+b x)^3 d^4+30 (a d-b c) (a+b x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) d^4+10 B (b c-a d)^2 (a+b x)^3 d^3+8 b B c (b c-a d) (a+b x)^3 d^3+12 a B (b c-a d)^2 (a+b x)^2 d^3+40 (b c-a d)^2 (a+b x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) d^3+35 B (a d-b c)^3 (a+b x)^2 d^2-12 b B c (b c-a d)^2 (a+b x)^2 d^2+24 a b B (a d-b c)^3 x d^2+60 (a d-b c)^3 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) d^2+120 A b (b c-a d)^4 x d+130 b B (b c-a d)^4 x d+24 b^2 B c (b c-a d)^3 x d+120 B (b c-a d)^4 (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right) d+24 a B (b c-a d)^4 \log (c+d x) d-250 B (b c-a d)^5 \log (c+d x)-24 b B c (b c-a d)^4 \log (c+d x)-120 (b c-a d)^5 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x)+60 B (b c-a d)^5 \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)\right)}{6 d^4}\right)}{60 b^3}","-\frac{B g^3 i^2 (b c-a d)^6 \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)}{180 b^3 d^4}-\frac{B g^3 i^2 (a+b x) (b c-a d)^5 \left(6 B \log \left(\frac{e (a+b x)}{c+d x}\right)+6 A+5 B\right)}{180 b^3 d^3}+\frac{B g^3 i^2 (a+b x)^2 (b c-a d)^4 \left(3 B \log \left(\frac{e (a+b x)}{c+d x}\right)+3 A+B\right)}{180 b^3 d^2}-\frac{B g^3 i^2 (a+b x)^3 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{90 b^3 d}+\frac{g^3 i^2 (a+b x)^4 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{60 b^3}-\frac{B g^3 i^2 (a+b x)^4 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{20 b^3}+\frac{g^3 i^2 (a+b x)^4 (c+d x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{15 b^2}-\frac{B g^3 i^2 (a+b x)^4 (c+d x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{15 b^2}+\frac{g^3 i^2 (a+b x)^4 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{6 b}-\frac{B^2 g^3 i^2 (b c-a d)^6 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{30 b^3 d^4}-\frac{B^2 g^3 i^2 (b c-a d)^6 \log (c+d x)}{20 b^3 d^4}+\frac{B^2 g^3 i^2 (a+b x)^4 (b c-a d)^2}{60 b^3}+\frac{3 B^2 g^3 i^2 x (b c-a d)^5}{20 b^2 d^3}-\frac{3 B^2 g^3 i^2 (c+d x)^2 (b c-a d)^4}{40 b d^4}+\frac{B^2 g^3 i^2 (c+d x)^3 (b c-a d)^3}{60 d^4}",1,"(g^3*i^2*(15*(b*c - a*d)^2*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 24*d*(b*c - a*d)*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 10*d^2*(a + b*x)^6*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - (5*B*(b*c - a*d)^3*(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)])))/d^4 + (2*B*(b*c - a*d)^2*(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)])))/d^4 - (B*(b*c - a*d)*(24*b^2*B*c*d*(b*c - a*d)^3*x + 120*A*b*d*(b*c - a*d)^4*x + 130*b*B*d*(b*c - a*d)^4*x + 24*a*b*B*d^2*(-(b*c) + a*d)^3*x - 12*b*B*c*d^2*(b*c - a*d)^2*(a + b*x)^2 + 12*a*B*d^3*(b*c - a*d)^2*(a + b*x)^2 + 35*B*d^2*(-(b*c) + a*d)^3*(a + b*x)^2 + 8*b*B*c*d^3*(b*c - a*d)*(a + b*x)^3 + 10*B*d^3*(b*c - a*d)^2*(a + b*x)^3 + 8*a*B*d^4*(-(b*c) + a*d)*(a + b*x)^3 - 6*b*B*c*d^4*(a + b*x)^4 + 6*a*B*d^5*(a + b*x)^4 + 120*B*d*(b*c - a*d)^4*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] + 60*d^2*(-(b*c) + a*d)^3*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 40*d^3*(b*c - a*d)^2*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 30*d^4*(-(b*c) + a*d)*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 24*d^5*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 24*b*B*c*(b*c - a*d)^4*Log[c + d*x] + 24*a*B*d*(b*c - a*d)^4*Log[c + d*x] - 250*B*(b*c - a*d)^5*Log[c + d*x] - 120*(b*c - a*d)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 60*B*(b*c - a*d)^5*((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)])))/(6*d^4)))/(60*b^3)","B",1
65,1,1194,761,0.9504602,"\int (a g+b g x)^2 (c i+d i 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*(c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{g^2 i^2 \left(12 d^5 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (a+b x)^5+30 d^4 (b c-a d) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (a+b x)^4+20 d^3 (b c-a d)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (a+b x)^3+20 B (b c-a d)^3 \left(-2 B \log (c+d x) (b c-a d)^2-2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x) (b c-a d)^2+B \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 c-a d)^2+2 A b d x (b c-a d)+2 B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right) (b c-a d)+B (b d x+(a d-b c) \log (c+d x)) (b c-a d)-d^2 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)\right)-10 B (b c-a d)^2 \left(-6 B \log (c+d x) (b c-a d)^3-6 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x) (b c-a d)^3+3 B \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 c-a d)^3+6 A b d x (b c-a d)^2+6 B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right) (b c-a d)^2+3 B (b d x+(a d-b c) \log (c+d x)) (b c-a d)^2+B \left(-2 \log (c+d x) (b c-a d)^2+2 b d x (b c-a d)-d^2 (a+b x)^2\right) (b c-a d)+2 d^3 (a+b x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)+3 d^2 (a d-b c) (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)\right)+B (b c-a d) \left(-24 B \log (c+d x) (b c-a d)^4-24 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x) (b c-a d)^4+12 B \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 c-a d)^4+24 A b d x (b c-a d)^3+24 B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right) (b c-a d)^3+12 B (b d x+(a d-b c) \log (c+d x)) (b c-a d)^3-12 d^2 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2+4 B \left(-2 \log (c+d x) (b c-a d)^2+2 b d x (b c-a d)-d^2 (a+b x)^2\right) (b c-a d)^2+8 d^3 (a+b x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)+B \left(-6 \log (c+d x) (b c-a d)^3+6 b d x (b c-a d)^2+2 d^3 (a+b x)^3+3 d^2 (a d-b c) (a+b x)^2\right) (b c-a d)-6 d^4 (a+b x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)\right)\right)}{60 b^3 d^3}","\frac{B g^2 i^2 (b c-a d)^5 \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)}{30 b^3 d^3}+\frac{B g^2 i^2 (a+b x) (b c-a d)^4 \left(2 B \log \left(\frac{e (a+b x)}{c+d x}\right)+2 A+B\right)}{30 b^3 d^2}-\frac{B g^2 i^2 (a+b x)^2 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{30 b^3 d}+\frac{g^2 i^2 (a+b x)^3 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{30 b^3}-\frac{B g^2 i^2 (a+b x)^3 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{15 b^3}+\frac{g^2 i^2 (a+b x)^3 (c+d x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{10 b^2}-\frac{B g^2 i^2 (c+d x)^2 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{5 b d^3}+\frac{4 B g^2 i^2 (c+d x)^3 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{15 d^3}-\frac{b B g^2 i^2 (c+d x)^4 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{10 d^3}+\frac{g^2 i^2 (a+b x)^3 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{5 b}+\frac{B^2 g^2 i^2 (b c-a d)^5 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{15 b^3 d^3}+\frac{B^2 g^2 i^2 (b c-a d)^5 \log \left(\frac{a+b x}{c+d x}\right)}{30 b^3 d^3}+\frac{B^2 g^2 i^2 (b c-a d)^5 \log (c+d x)}{10 b^3 d^3}-\frac{B^2 g^2 i^2 x (b c-a d)^4}{10 b^2 d^2}-\frac{B^2 g^2 i^2 (c+d x)^2 (b c-a d)^3}{20 b d^3}+\frac{B^2 g^2 i^2 (c+d x)^3 (b c-a d)^2}{30 d^3}",1,"(g^2*i^2*(20*d^3*(b*c - a*d)^2*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 30*d^4*(b*c - a*d)*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 12*d^5*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 20*B*(b*c - a*d)^3*(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)])) - 10*B*(b*c - a*d)^2*(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)])) + 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)]))))/(60*b^3*d^3)","A",1
66,1,677,589,0.5945698,"\int (a g+b g x) (c i+d i 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)*(c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{g i^2 \left(\frac{4 B (b c-a d)^2 \left(b^2 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 (b c-a d)^2 \log (a+b 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(\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)^2 \log (c+d x)-B (b c-a d) ((b c-a d) \log (a+b x)+b d x)\right)}{b^3}-\frac{B (b c-a d) \left(2 b^3 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+3 b^2 (c+d x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+6 (b c-a d)^3 \log (a+b 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 (a+b x)+b^2 (c+d 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(\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 (b c-a d)^3 \log (c+d x)-3 B (b c-a d)^2 ((b c-a d) \log (a+b x)+b d x)\right)}{b^3}+3 b (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2-4 (c+d x)^3 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2\right)}{12 d^2}","-\frac{B g i^2 (b c-a d)^4 \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)}{6 b^3 d^2}-\frac{B g i^2 (a+b x) (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{6 b^3 d}+\frac{g i^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)^2}{12 b^3}-\frac{B g i^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)}{6 b^3}+\frac{g i^2 (a+b x)^2 (c+d x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{6 b^2}+\frac{B g i^2 (c+d x)^2 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 b d^2}-\frac{B g i^2 (c+d x)^3 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{6 d^2}+\frac{g i^2 (a+b x)^2 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{4 b}-\frac{B^2 g i^2 (b c-a d)^4 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{6 b^3 d^2}-\frac{B^2 g i^2 (b c-a d)^4 \log \left(\frac{a+b x}{c+d x}\right)}{12 b^3 d^2}-\frac{B^2 g i^2 (b c-a d)^4 \log (c+d x)}{4 b^3 d^2}+\frac{B^2 g i^2 x (b c-a d)^3}{12 b^2 d}+\frac{B^2 g i^2 (c+d x)^2 (b c-a d)^2}{12 b d^2}",1,"(g*i^2*(-4*(b*c - a*d)*(c + d*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 3*b*(c + d*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + (4*B*(b*c - a*d)^2*(2*A*b*d*(b*c - a*d)*x - B*(b*c - a*d)*(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)] + b^2*(c + d*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*(b*c - a*d)^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 2*B*(b*c - a*d)^2*Log[c + d*x] - B*(b*c - a*d)^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^3 - (B*(b*c - a*d)*(6*A*b*d*(b*c - a*d)^2*x - 3*B*(b*c - a*d)^2*(b*d*x + (b*c - a*d)*Log[a + b*x]) - B*(b*c - a*d)*(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)] + 3*b^2*(b*c - a*d)*(c + d*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*b^3*(c + d*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6*(b*c - a*d)^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 6*B*(b*c - a*d)^3*Log[c + d*x] - 3*B*(b*c - a*d)^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))/(12*d^2)","A",1
67,1,287,334,0.2199797,"\int (c i+d i x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Integrate[(c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{i^2 \left((c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2-\frac{B (b c-a d) \left(b^2 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 (b c-a d)^2 \log (a+b 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(\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)^2 \log (c+d x)-B (b c-a d) ((b c-a d) \log (a+b x)+b d x)\right)}{b^3}\right)}{3 d}","\frac{2 B i^2 (b c-a d)^3 \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)}{3 b^3 d}-\frac{2 B i^2 (a+b x) (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b^3}-\frac{B i^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}+\frac{i^2 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 d}-\frac{2 B^2 i^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 i^2 (b c-a d)^3 \log \left(\frac{a+b x}{c+d x}\right)}{3 b^3 d}+\frac{B^2 i^2 (b c-a d)^3 \log (c+d x)}{b^3 d}+\frac{B^2 i^2 x (b c-a d)^2}{3 b^2}",1,"(i^2*((c + d*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 - B*(b*c - a*d)*(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)] + b^2*(c + d*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*(b*c - a*d)^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 2*B*(b*c - a*d)^2*Log[c + d*x] - B*(b*c - a*d)^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^3))/(3*d)","A",1
68,1,1987,535,3.6737498,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{a g+b g x} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x),x]","\frac{i^2 \left(6 b^2 d^2 x^2 A^2+12 b d (2 b c-a d) x A^2+12 (b c-a d)^2 \log (a+b x) A^2-24 b B c \left(a d \log ^2\left(\frac{a}{b}+x\right)-2 a d (\log (a+b x)+1) \log \left(\frac{a}{b}+x\right)+2 \left(-b c+a d+\log \left(\frac{c}{d}+x\right) \left(b c+a d \log (a+b x)-a d \log \left(\frac{d (a+b x)}{a d-b c}\right)\right)+(a d \log (a+b x)-b d x) \log \left(\frac{e (a+b x)}{c+d x}\right)\right)-2 a d \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right) A+12 b^2 B c^2 \left(\log ^2\left(\frac{a}{b}+x\right)-2 \log (a+b x) \left(\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)-\log \left(\frac{e (a+b x)}{c+d x}\right)\right)-2 \left(\log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)+\text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right)\right) A+6 B \left(\left(2 \log (c+d x) c^2+d x (d x-2 c)-2 d^2 x^2 \log \left(\frac{c}{d}+x\right)\right) b^2+4 a d (c+d x) \left(\log \left(\frac{c}{d}+x\right)-1\right) b+2 a^2 d^2 \log ^2\left(\frac{a}{b}+x\right)-4 a d^2 (a+b x) \left(\log \left(\frac{a}{b}+x\right)-1\right)+d^2 \left(-2 \log (a+b x) a^2+b x (2 a-b x)+2 b^2 x^2 \log \left(\frac{a}{b}+x\right)\right)-2 d^2 \left(2 \log (a+b x) a^2+b x (b x-2 a)\right) \left(\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)-\log \left(\frac{e (a+b x)}{c+d x}\right)\right)-4 a^2 d^2 \left(\log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)+\text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right)\right) A+8 b B^2 c \left(\log \left(\frac{e (a+b x)}{c+d x}\right) \left(-a d \log ^2\left(\frac{e (a+b x)}{c+d x}\right)+3 d \left(\log \left(\frac{b c-a d}{b c+b d x}\right) a+a+b x\right) \log \left(\frac{e (a+b x)}{c+d x}\right)+6 (b c-a d) \log \left(\frac{b c-a d}{b c+b d x}\right)\right)+6 \left(b c-a d+a d \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)-6 a d \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right)+B^2 \left(4 a^2 d^2 \log ^3\left(\frac{a}{b}+x\right)+6 d^2 \left(2 \log (a+b x) a^2+b x (b x-2 a)\right) \left(-\log \left(\frac{a}{b}+x\right)+\log \left(\frac{c}{d}+x\right)+\log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2-12 a d^2 \left((a+b x) \log ^2\left(\frac{a}{b}+x\right)-2 (a+b x) \log \left(\frac{a}{b}+x\right)+2 b x\right)-3 d^2 \left(2 \left(a^2-b^2 x^2\right) \log ^2\left(\frac{a}{b}+x\right)+\left(-6 a^2-4 b x a+2 b^2 x^2\right) \log \left(\frac{a}{b}+x\right)+b x (6 a-b x)\right)-12 a b d \left((c+d x) \log ^2\left(\frac{c}{d}+x\right)-2 (c+d x) \log \left(\frac{c}{d}+x\right)+2 d x\right)-3 b^2 \left(2 \left(c^2-d^2 x^2\right) \log ^2\left(\frac{c}{d}+x\right)+\left(-6 c^2-4 d x c+2 d^2 x^2\right) \log \left(\frac{c}{d}+x\right)+d x (6 c-d x)\right)-6 \left(\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)-\log \left(\frac{e (a+b x)}{c+d x}\right)\right) \left(\left(2 \log (c+d x) c^2+d x (d x-2 c)-2 d^2 x^2 \log \left(\frac{c}{d}+x\right)\right) b^2+4 a d (c+d x) \left(\log \left(\frac{c}{d}+x\right)-1\right) b+2 a^2 d^2 \log ^2\left(\frac{a}{b}+x\right)-4 a d^2 (a+b x) \left(\log \left(\frac{a}{b}+x\right)-1\right)+d^2 \left(-2 \log (a+b x) a^2+b x (2 a-b x)+2 b^2 x^2 \log \left(\frac{a}{b}+x\right)\right)-4 a^2 d^2 \left(\log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)+\text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right)\right)+6 \left(-d^2 x^2 b^2+3 c d x b^2+d^2 x^2 \log \left(\frac{c}{d}+x\right) b^2-c^2 \log (c+d x) b^2+2 a c d b+3 a d^2 x b-2 a d^2 x \log \left(\frac{c}{d}+x\right) b-2 a c d \log (c+d x) b-a^2 d^2 \log (a+b x)-\log \left(\frac{a}{b}+x\right) \left(-2 \left(a^2-b^2 x^2\right) \log \left(\frac{c}{d}+x\right) d^2+b (2 a c+b x (2 c-d x)) d+\left(2 a^2 d^2-2 b^2 c^2\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)+2 \left(b^2 c^2-a^2 d^2\right) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)+4 a d \left(a d+2 b x d-b x \log \left(\frac{c}{d}+x\right) d-b c \log (c+d x)+\log \left(\frac{a}{b}+x\right) \left(-d (a+b x)+d \log \left(\frac{c}{d}+x\right) (a+b x)+(b c-a d) \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)+(b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)-2 a^2 d^2 \left(\left(\log \left(\frac{c}{d}+x\right)-\log \left(\frac{b (c+d x)}{b c-a d}\right)\right) \log ^2\left(\frac{a}{b}+x\right)-2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right) \log \left(\frac{a}{b}+x\right)+2 \text{Li}_3\left(\frac{d (a+b x)}{a d-b c}\right)\right)\right)+12 a^2 d^2 \left(\log \left(\frac{d (a+b x)}{a d-b c}\right) \log ^2\left(\frac{c}{d}+x\right)+2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right) \log \left(\frac{c}{d}+x\right)-2 \text{Li}_3\left(\frac{b (c+d x)}{b c-a d}\right)\right)\right)-12 b^2 B^2 c^2 \left(\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 \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)-2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)\right)\right)}{12 b^3 g}","\frac{2 B i^2 (b c-a d)^2 \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^3 g}+\frac{d i^2 (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{b^3 g}-\frac{B d i^2 (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^3 g}+\frac{2 B i^2 (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\right)}{b^3 g}-\frac{i^2 (b c-a d)^2 \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^3 g}+\frac{B i^2 (b c-a d)^2 \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)}{b^3 g}+\frac{i^2 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 b g}+\frac{2 B^2 i^2 (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^3 g}-\frac{B^2 i^2 (b c-a d)^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^3 g}+\frac{2 B^2 i^2 (b c-a d)^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^3 g}+\frac{B^2 i^2 (b c-a d)^2 \log (c+d x)}{b^3 g}",1,"(i^2*(12*A^2*b*d*(2*b*c - a*d)*x + 6*A^2*b^2*d^2*x^2 + 12*A^2*(b*c - a*d)^2*Log[a + b*x] - 24*A*b*B*c*(a*d*Log[a/b + x]^2 - 2*a*d*Log[a/b + x]*(1 + Log[a + b*x]) + 2*(-(b*c) + a*d + Log[c/d + x]*(b*c + a*d*Log[a + b*x] - a*d*Log[(d*(a + b*x))/(-(b*c) + a*d)]) + (-(b*d*x) + a*d*Log[a + b*x])*Log[(e*(a + b*x))/(c + d*x)]) - 2*a*d*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 12*A*b^2*B*c^2*(Log[a/b + x]^2 - 2*Log[a + b*x]*(Log[a/b + x] - Log[c/d + x] - Log[(e*(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)])) + 6*A*B*(-4*a*d^2*(a + b*x)*(-1 + Log[a/b + x]) + 2*a^2*d^2*Log[a/b + x]^2 + 4*a*b*d*(c + d*x)*(-1 + Log[c/d + x]) + d^2*(b*x*(2*a - b*x) + 2*b^2*x^2*Log[a/b + x] - 2*a^2*Log[a + b*x]) - 2*d^2*(b*x*(-2*a + b*x) + 2*a^2*Log[a + b*x])*(Log[a/b + x] - Log[c/d + x] - Log[(e*(a + b*x))/(c + d*x)]) + b^2*(d*x*(-2*c + d*x) - 2*d^2*x^2*Log[c/d + x] + 2*c^2*Log[c + d*x]) - 4*a^2*d^2*(Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + PolyLog[2, (b*(c + d*x))/(b*c - a*d)])) + 8*b*B^2*c*(Log[(e*(a + b*x))/(c + d*x)]*(-(a*d*Log[(e*(a + b*x))/(c + d*x)]^2) + 6*(b*c - a*d)*Log[(b*c - a*d)/(b*c + b*d*x)] + 3*d*Log[(e*(a + b*x))/(c + d*x)]*(a + b*x + a*Log[(b*c - a*d)/(b*c + b*d*x)])) + 6*(b*c - a*d + a*d*Log[(e*(a + b*x))/(c + d*x)])*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 6*a*d*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))]) + B^2*(4*a^2*d^2*Log[a/b + x]^3 - 12*a*d^2*(2*b*x - 2*(a + b*x)*Log[a/b + x] + (a + b*x)*Log[a/b + x]^2) - 3*d^2*(b*x*(6*a - b*x) + (-6*a^2 - 4*a*b*x + 2*b^2*x^2)*Log[a/b + x] + 2*(a^2 - b^2*x^2)*Log[a/b + x]^2) - 12*a*b*d*(2*d*x - 2*(c + d*x)*Log[c/d + x] + (c + d*x)*Log[c/d + x]^2) - 3*b^2*(d*x*(6*c - d*x) + (-6*c^2 - 4*c*d*x + 2*d^2*x^2)*Log[c/d + x] + 2*(c^2 - d^2*x^2)*Log[c/d + x]^2) + 6*d^2*(b*x*(-2*a + b*x) + 2*a^2*Log[a + b*x])*(-Log[a/b + x] + Log[c/d + x] + Log[(e*(a + b*x))/(c + d*x)])^2 - 6*(Log[a/b + x] - Log[c/d + x] - Log[(e*(a + b*x))/(c + d*x)])*(-4*a*d^2*(a + b*x)*(-1 + Log[a/b + x]) + 2*a^2*d^2*Log[a/b + x]^2 + 4*a*b*d*(c + d*x)*(-1 + Log[c/d + x]) + d^2*(b*x*(2*a - b*x) + 2*b^2*x^2*Log[a/b + x] - 2*a^2*Log[a + b*x]) + b^2*(d*x*(-2*c + d*x) - 2*d^2*x^2*Log[c/d + x] + 2*c^2*Log[c + d*x]) - 4*a^2*d^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*(2*a*b*c*d + 3*b^2*c*d*x + 3*a*b*d^2*x - b^2*d^2*x^2 - 2*a*b*d^2*x*Log[c/d + x] + b^2*d^2*x^2*Log[c/d + x] - a^2*d^2*Log[a + b*x] - b^2*c^2*Log[c + d*x] - 2*a*b*c*d*Log[c + d*x] - Log[a/b + x]*(b*d*(2*a*c + b*x*(2*c - d*x)) - 2*d^2*(a^2 - b^2*x^2)*Log[c/d + x] + (-2*b^2*c^2 + 2*a^2*d^2)*Log[(b*(c + d*x))/(b*c - a*d)]) + 2*(b^2*c^2 - a^2*d^2)*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 4*a*d*(a*d + 2*b*d*x - b*d*x*Log[c/d + x] - b*c*Log[c + d*x] + Log[a/b + x]*(-(d*(a + b*x)) + d*(a + b*x)*Log[c/d + x] + (b*c - a*d)*Log[(b*(c + d*x))/(b*c - a*d)]) + (b*c - a*d)*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - 2*a^2*d^2*(Log[a/b + x]^2*(Log[c/d + x] - Log[(b*(c + d*x))/(b*c - a*d)]) - 2*Log[a/b + x]*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 2*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)])) + 12*a^2*d^2*(Log[c/d + x]^2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*Log[c/d + x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])) - 12*b^2*B^2*c^2*(Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(e*(a + b*x))/(c + d*x)]^2 - 2*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))])))/(12*b^3*g)","B",1
69,1,2652,442,6.9154991,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^2} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x)^2,x]","\text{Result too large to show}","\frac{d^2 i^2 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{b^3 g^2}+\frac{4 B d i^2 (b c-a d) \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^3 g^2}+\frac{2 B d i^2 (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^3 g^2}-\frac{2 d i^2 (b c-a d) \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^3 g^2}-\frac{i^2 (c+d x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{b^2 g^2 (a+b x)}-\frac{2 B i^2 (c+d x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^2 g^2 (a+b x)}+\frac{2 B^2 d i^2 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^3 g^2}+\frac{4 B^2 d i^2 (b c-a d) \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^3 g^2}-\frac{2 B^2 i^2 (c+d x) (b c-a d)}{b^2 g^2 (a+b x)}",1,"(i^2*(3*A^2*b*d^2*x - (3*A^2*(b*c - a*d)^2)/(a + b*x) + 6*A^2*d*(b*c - a*d)*Log[a + b*x] - (6*A*b^2*B*c^2*(-(d*(a + b*x)*Log[c/d + x]) + d*(a + b*x)*Log[(d*(a + b*x))/(-(b*c) + a*d)] + (b*c - a*d)*(1 + Log[(e*(a + b*x))/(c + d*x)])))/((b*c - a*d)*(a + b*x)) + (3*b^2*B^2*c^2*(-2*b*c + 2*a*d - 2*d*(a + b*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(e*(a + b*x))/(c + d*x)] - 2*d*(a + b*x)*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] - (b*c - a*d)*Log[(e*(a + b*x))/(c + d*x)]^2 + 2*d*(a + b*x)*Log[c + d*x] - 2*d*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 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)]) + d*(a + b*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(a + b*x)) + 6*A*b*B*c*d*(Log[a/b + x]^2 - 2*Log[a/b + x]*Log[a + b*x] - 2*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*Log[a + b*x]*((a*d)/(b*c - a*d) + Log[c/d + x] + Log[(e*(a + b*x))/(c + d*x)]) + 2*a*((a + b*x)^(-1) + Log[(e*(a + b*x))/(c + d*x)]/(a + b*x) + (d*Log[c + d*x])/(-(b*c) + a*d)) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 6*A*B*d^2*((a + b*x)*(-1 + Log[a/b + x]) - a*Log[a/b + x]^2 - (a^2*(1 + Log[a/b + x]))/(a + b*x) - b*(c/d + x)*(-1 + Log[c/d + x]) + (a^2*Log[c/d + x])/(a + b*x) + (b*x - a^2/(a + b*x) - 2*a*Log[a + b*x])*(-Log[a/b + x] + Log[c/d + x] + Log[(e*(a + b*x))/(c + d*x)]) + (a^2*d*(Log[a + b*x] - Log[c + d*x]))/(-(b*c) + a*d) + 2*a*(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*d^2*(6*b*x - 6*(a + b*x)*Log[a/b + x] + 3*(a + b*x)*Log[a/b + x]^2 - 2*a*Log[a/b + x]^3 - (3*a^2*(2 + 2*Log[a/b + x] + Log[a/b + x]^2))/(a + b*x) + (3*b*(2*d*x - 2*(c + d*x)*Log[c/d + x] + (c + d*x)*Log[c/d + x]^2))/d + 3*(b*x - a^2/(a + b*x) - 2*a*Log[a + b*x])*(-Log[a/b + x] + Log[c/d + x] + Log[(e*(a + b*x))/(c + d*x)])^2 - (6*(a*d + 2*b*d*x - b*d*x*Log[c/d + x] - b*c*Log[c + d*x] + Log[a/b + x]*(-(d*(a + b*x)) + d*(a + b*x)*Log[c/d + x] + (b*c - a*d)*Log[(b*(c + d*x))/(b*c - a*d)]) + (b*c - a*d)*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]))/d + (3*a^2*(d*(a + b*x)*Log[a/b + x]^2 + 2*((-(b*c) + a*d)*Log[c/d + x] + d*(a + b*x)*(Log[a + b*x] - Log[c + d*x])) - 2*Log[a/b + x]*((b*c - a*d)*Log[c/d + x] + d*(a + b*x)*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*d*(a + b*x)*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]))/((-(b*c) + a*d)*(a + b*x)) + (3*a^2*(-(b*(c + d*x)*Log[c/d + x]^2) + 2*d*(a + b*x)*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*d*(a + b*x)*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]))/((b*c - a*d)*(a + b*x)) + 6*(-Log[a/b + x] + Log[c/d + x] + Log[(e*(a + b*x))/(c + d*x)])*((a + b*x)*(-1 + Log[a/b + x]) - a*Log[a/b + x]^2 - (a^2*(1 + Log[a/b + x]))/(a + b*x) - b*(c/d + x)*(-1 + Log[c/d + x]) + (a^2*Log[c/d + x])/(a + b*x) + (a^2*d*(Log[a + b*x] - Log[c + d*x]))/(-(b*c) + a*d) + 2*a*(Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + PolyLog[2, (b*(c + d*x))/(b*c - a*d)])) + 6*a*(Log[a/b + x]^2*(Log[c/d + x] - Log[(b*(c + d*x))/(b*c - a*d)]) - 2*Log[a/b + x]*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 2*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)]) - 6*a*(Log[c/d + x]^2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*Log[c/d + x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])) + (2*b*B^2*c*d*(6*b*c - 6*a*d - (6*b^2*c*x)/(a + b*x) + (6*a*b*d*x)/(a + b*x) + 6*a*d*Log[a/b + x] + 3*b*c*Log[a/b + x]^2 - 3*a*d*Log[a/b + x]^2 - 6*b*c*Log[c/d + x] + 6*b*c*Log[a + b*x] - 6*a*d*Log[a + b*x] - 6*b*c*Log[a/b + x]*Log[a + b*x] + 6*a*d*Log[a/b + x]*Log[a + b*x] + 6*b*c*Log[c/d + x]*Log[a + b*x] - 6*a*d*Log[c/d + x]*Log[a + b*x] - 6*b*c*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 6*a*d*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] - (6*b*(b*c - a*d)*x*Log[(e*(a + b*x))/(c + d*x)])/(a + b*x) + 6*b*c*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] - 6*a*d*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + 3*a*d*Log[(e*(a + b*x))/(c + d*x)]^2 + 3*b*d*x*Log[(e*(a + b*x))/(c + d*x)]^2 - (3*b^2*x*(c + d*x)*Log[(e*(a + b*x))/(c + d*x)]^2)/(a + b*x) - 3*b*c*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(e*(a + b*x))/(c + d*x)]^2 - a*d*Log[(e*(a + b*x))/(c + d*x)]^3 + 6*b*c*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 6*a*d*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 3*a*d*Log[(e*(a + b*x))/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*(b*c - a*d + a*d*Log[(e*(a + b*x))/(c + d*x)])*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 6*(b*c - a*d)*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 6*b*c*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 6*a*d*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] + 6*b*c*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))]))/(b*c - a*d)))/(3*b^3*g^2)","B",1
70,1,3582,387,7.1292376,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^3} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x)^3,x]","\text{Result too large to show}","\frac{2 B d^2 i^2 \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^3 g^3}-\frac{d^2 i^2 \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^3 g^3}-\frac{d i^2 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{b^2 g^3 (a+b x)}-\frac{2 B d i^2 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^2 g^3 (a+b x)}-\frac{i^2 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 b g^3 (a+b x)^2}-\frac{B i^2 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b g^3 (a+b x)^2}+\frac{2 B^2 d^2 i^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^3 g^3}-\frac{2 B^2 d i^2 (c+d x)}{b^2 g^3 (a+b x)}-\frac{B^2 i^2 (c+d x)^2}{4 b g^3 (a+b x)^2}",1,"(i^2*(-6*A^2*(b*c - a*d)^4 + 24*A^2*d*(-(b*c) + a*d)^3*(a + b*x) + 12*A^2*d^2*(b*c - a*d)^2*(a + b*x)^2*Log[a + b*x] - 6*A*b^2*B*c^2*(b^2*c^2 - 4*a*b*c*d + a^2*d^2 - 2*b^2*c*d*x - 2*a*b*d^2*x - 2*b^2*d^2*x^2 + 2*d^2*(a + b*x)^2*Log[c/d + x] - 2*d^2*(a + b*x)^2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*b^2*c^2*Log[(e*(a + b*x))/(c + d*x)] - 4*a*b*c*d*Log[(e*(a + b*x))/(c + d*x)] + 2*a^2*d^2*Log[(e*(a + b*x))/(c + d*x)]) - 12*A*b*B*c*d*(3*a*b^2*c^2 - 4*a^2*b*c*d + a^3*d^2 + 4*b^3*c^2*x - 6*a*b^2*c*d*x + 2*a^2*b*d^2*x - 2*d*(-2*b*c + a*d)*(a + b*x)^2*Log[a + b*x] + 2*(b*c - a*d)^2*(a + 2*b*x)*Log[(e*(a + b*x))/(c + d*x)] - 4*a^2*b*c*d*Log[c + d*x] + 2*a^3*d^2*Log[c + d*x] - 8*a*b^2*c*d*x*Log[c + d*x] + 4*a^2*b*d^2*x*Log[c + d*x] - 4*b^3*c*d*x^2*Log[c + d*x] + 2*a*b^2*d^2*x^2*Log[c + d*x]) - 3*b^2*B^2*c^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*(b*c - a*d)^2*Log[(e*(a + b*x))/(c + d*x)] + 4*d*(-(b*c) + a*d)*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] - 4*d^2*(a + b*x)^2*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + 2*(b*c - a*d)^2*Log[(e*(a + b*x))/(c + d*x)]^2 + 2*d^2*(a + b*x)^2*Log[c + d*x] - 4*d*(a + b*x)*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - 4*d^2*(a + b*x)^2*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*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*d^2*(a + b*x)^2*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])) + 6*A*B*d^2*(2*(b*c - a*d)^2*(a + b*x)^2*Log[a/b + x]^2 + 8*a*(b*c - a*d)^2*(a + b*x)*(1 + Log[a/b + x]) - a^2*(b*c - a*d)^2*(1 + 2*Log[a/b + x]) - 2*(b*c - a*d)^2*(a*(3*a + 4*b*x) + 2*(a + b*x)^2*Log[a + b*x])*(Log[a/b + x] - Log[c/d + x] - Log[(e*(a + b*x))/(c + d*x)]) + 8*a*(b*c - a*d)*(a + b*x)*((-(b*c) + a*d)*Log[c/d + x] + d*(a + b*x)*(Log[a + b*x] - Log[c + d*x])) + 2*a^2*((b*c - a*d)^2*Log[c/d + x] + d*(a + b*x)*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x])) - 4*(b*c - a*d)^2*(a + b*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)])) - 6*b*B^2*c*d*(4*(b*c - a*d)^2*(a + b*x)*(2 + 2*Log[a/b + x] + Log[a/b + x]^2) - a*(b*c - a*d)^2*(1 + 2*Log[a/b + x] + 2*Log[a/b + x]^2) + 2*(b*c - a*d)^2*(a + 2*b*x)*(-Log[a/b + x] + Log[c/d + x] + Log[(e*(a + b*x))/(c + d*x)])^2 - 2*(Log[a/b + x] - Log[c/d + x] - Log[(e*(a + b*x))/(c + d*x)])*(4*(b*c - a*d)^2*(a + b*x)*(1 + Log[a/b + x]) - a*(b*c - a*d)^2*(1 + 2*Log[a/b + x]) - 4*(b*c - a*d)*(a + b*x)*((b*c - a*d)*Log[c/d + x] - d*(a + b*x)*(Log[a + b*x] - Log[c + d*x])) + 2*a*((b*c - a*d)^2*Log[c/d + x] + d*(a + b*x)*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]))) + 4*(b*c - a*d)*(a + b*x)*(d*(a + b*x)*Log[a/b + x]^2 + 2*((-(b*c) + a*d)*Log[c/d + x] + d*(a + b*x)*(Log[a + b*x] - Log[c + d*x])) - 2*Log[a/b + x]*((b*c - a*d)*Log[c/d + x] + d*(a + b*x)*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*d*(a + b*x)*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - 2*a*(d*(-(b*c) + a*d)*(a + b*x) - (b*c - a*d)^2*(1 + 2*Log[a/b + x])*Log[c/d + x] - d^2*(a + b*x)^2*Log[a + b*x] + d^2*(a + b*x)^2*Log[c + d*x] - d*(a + b*x)*(d*(a + b*x)*Log[a/b + x]^2 + 2*(b*c - a*d)*(1 + Log[a/b + x]) - 2*d*(a + b*x)*(Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]))) + 4*(b*c - a*d)*(a + b*x)*(Log[c/d + x]*(b*(c + d*x)*Log[c/d + x] - 2*d*(a + b*x)*Log[(d*(a + b*x))/(-(b*c) + a*d)]) - 2*d*(a + b*x)*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 2*a*(2*d*(-(b*c) + a*d)*(a + b*x)*Log[c/d + x] - (b*c - a*d)^2*Log[c/d + x]^2 + d^2*(a + b*x)^2*Log[c/d + x]^2 + 2*d^2*(a + b*x)^2*Log[a + b*x] - 2*d^2*(a + b*x)^2*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*d^2*(a + b*x)^2*Log[c + d*x] - 2*d^2*(a + b*x)^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])) + B^2*d^2*(4*(b*c - a*d)^2*(a + b*x)^2*Log[a/b + x]^3 + 24*a*(b*c - a*d)^2*(a + b*x)*(2 + 2*Log[a/b + x] + Log[a/b + x]^2) - 3*a^2*(b*c - a*d)^2*(1 + 2*Log[a/b + x] + 2*Log[a/b + x]^2) + 6*(b*c - a*d)^2*(a*(3*a + 4*b*x) + 2*(a + b*x)^2*Log[a + b*x])*(-Log[a/b + x] + Log[c/d + x] + Log[(e*(a + b*x))/(c + d*x)])^2 + 24*a*(b*c - a*d)*(a + b*x)*(Log[c/d + x]*(b*(c + d*x)*Log[c/d + x] - 2*d*(a + b*x)*Log[(d*(a + b*x))/(-(b*c) + a*d)]) - 2*d*(a + b*x)*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 6*a^2*(2*d*(-(b*c) + a*d)*(a + b*x)*Log[c/d + x] - (b*c - a*d)^2*Log[c/d + x]^2 + d^2*(a + b*x)^2*Log[c/d + x]^2 + 2*d^2*(a + b*x)^2*Log[a + b*x] - 2*d^2*(a + b*x)^2*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*d^2*(a + b*x)^2*Log[c + d*x] - 2*d^2*(a + b*x)^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) - 6*(Log[a/b + x] - Log[c/d + x] - Log[(e*(a + b*x))/(c + d*x)])*(2*(b*c - a*d)^2*(a + b*x)^2*Log[a/b + x]^2 + 8*a*(b*c - a*d)^2*(a + b*x)*(1 + Log[a/b + x]) - a^2*(b*c - a*d)^2*(1 + 2*Log[a/b + x]) - 8*a*(b*c - a*d)*(a + b*x)*((b*c - a*d)*Log[c/d + x] - d*(a + b*x)*(Log[a + b*x] - Log[c + d*x])) + 2*a^2*((b*c - a*d)^2*Log[c/d + x] + d*(a + b*x)*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x])) - 4*(b*c - a*d)^2*(a + b*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)])) + 6*(4*a*(b*c - a*d)*(a + b*x)*(d*(a + b*x)*Log[a/b + x]^2 + 2*((-(b*c) + a*d)*Log[c/d + x] + d*(a + b*x)*(Log[a + b*x] - Log[c + d*x])) - 2*Log[a/b + x]*((b*c - a*d)*Log[c/d + x] + d*(a + b*x)*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*d*(a + b*x)*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - a^2*(d*(-(b*c) + a*d)*(a + b*x) - (b*c - a*d)^2*(1 + 2*Log[a/b + x])*Log[c/d + x] - d^2*(a + b*x)^2*Log[a + b*x] + d^2*(a + b*x)^2*Log[c + d*x] - d*(a + b*x)*(d*(a + b*x)*Log[a/b + x]^2 + 2*(b*c - a*d)*(1 + Log[a/b + x]) - 2*d*(a + b*x)*(Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]))) - 2*(b*c - a*d)^2*(a + b*x)^2*(Log[a/b + x]^2*(Log[c/d + x] - Log[(b*(c + d*x))/(b*c - a*d)]) - 2*Log[a/b + x]*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 2*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)])) + 12*(b*c - a*d)^2*(a + b*x)^2*(Log[c/d + x]^2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*Log[c/d + x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)]))))/(12*b^3*(b*c - a*d)^2*g^3*(a + b*x)^2)","B",1
71,1,1355,147,2.2547359,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^4} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x)^4,x]","-\frac{i^2 \left(18 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (b c-a d)^3+54 d (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (b c-a d)^2-54 d^2 (a d-b c) (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2+54 B d^2 (a+b x)^2 \left(2 (b c-a d) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)+2 d (a+b x) \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)-2 d (a+b x) \log (c+d x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)+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) \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(\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)\right)+27 B d (a+b x) \left(2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2+4 d (a d-b c) (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)-4 d^2 (a+b x)^2 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)+4 d^2 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \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 \left((b c-a d)^2+2 d (a d-b c) (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)\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(\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)\right)+B \left(12 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^3-18 d (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2+36 d^2 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)+36 d^3 (a+b x)^3 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)-36 d^3 (a+b x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \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) \left((b c-a d)^2+2 d (a d-b c) (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)\right)+2 B \left(2 (b c-a d)^3-3 d (a+b x) (b c-a d)^2+6 d^2 (a+b x)^2 (b c-a d)+6 d^3 (a+b x)^3 \log (a+b x)-6 d^3 (a+b x)^3 \log (c+d x)\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(\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)\right)\right)}{54 b^3 (b c-a d) g^4 (a+b x)^3}","-\frac{i^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)}-\frac{2 B i^2 (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)}-\frac{2 B^2 i^2 (c+d x)^3}{27 g^4 (a+b x)^3 (b c-a d)}",1,"-1/54*(i^2*(18*(b*c - a*d)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 54*d*(b*c - a*d)^2*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - 54*d^2*(-(b*c) + a*d)*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 54*B*d^2*(a + b*x)^2*(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)])) + 27*B*d*(a + b*x)*(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*(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^3*(b*c - a*d)*g^4*(a + b*x)^3)","C",1
72,1,1788,299,3.1044569,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^5} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x)^5,x]","-\frac{i^2 \left(216 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (b c-a d)^4+432 d^2 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (b c-a d)^2-576 d (a d-b c)^3 (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2+216 B d^2 (a+b x)^2 \left(2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2+4 d (a d-b c) (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)-4 d^2 (a+b x)^2 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)+4 d^2 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \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 \left((b c-a d)^2+2 d (a d-b c) (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)\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(\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)\right)+32 B d (a+b x) \left(12 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^3-18 d (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2+36 d^2 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)+36 d^3 (a+b x)^3 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)-36 d^3 (a+b x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \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) \left((b c-a d)^2+2 d (a d-b c) (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)\right)+2 B \left(2 (b c-a d)^3-3 d (a+b x) (b c-a d)^2+6 d^2 (a+b x)^2 (b c-a d)+6 d^3 (a+b x)^3 \log (a+b x)-6 d^3 (a+b x)^3 \log (c+d x)\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(\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)\right)+3 B \left(36 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^4+72 d^2 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2+144 d^3 (a d-b c) (a+b x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)+48 d (a d-b c)^3 (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)-144 d^4 (a+b x)^4 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)+144 d^4 (a+b x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) \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 \left((b c-a d)^2+2 d (a d-b c) (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)\right)-8 B d (a+b x) \left(2 (b c-a d)^3-3 d (a+b x) (b c-a d)^2+6 d^2 (a+b x)^2 (b c-a d)+6 d^3 (a+b x)^3 \log (a+b x)-6 d^3 (a+b x)^3 \log (c+d x)\right)+3 B \left(3 (b c-a d)^4+6 d^2 (a+b x)^2 (b c-a d)^2+12 d^3 (a d-b c) (a+b x)^3+4 d (a d-b c)^3 (a+b x)-12 d^4 (a+b x)^4 \log (a+b x)+12 d^4 (a+b x)^4 \log (c+d x)\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(\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)\right)\right)}{864 b^3 (b c-a d)^2 g^5 (a+b x)^4}","-\frac{b i^2 (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)^2}-\frac{b B i^2 (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)^2}+\frac{d i^2 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 g^5 (a+b x)^3 (b c-a d)^2}+\frac{2 B d i^2 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{9 g^5 (a+b x)^3 (b c-a d)^2}-\frac{b B^2 i^2 (c+d x)^4}{32 g^5 (a+b x)^4 (b c-a d)^2}+\frac{2 B^2 d i^2 (c+d x)^3}{27 g^5 (a+b x)^3 (b c-a d)^2}",1,"-1/864*(i^2*(216*(b*c - a*d)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - 576*d*(-(b*c) + a*d)^3*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 432*d^2*(b*c - a*d)^2*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 216*B*d^2*(a + b*x)^2*(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)])) + 32*B*d*(a + b*x)*(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)])) + 3*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^3*(b*c - a*d)^2*g^5*(a + b*x)^4)","C",1
73,1,2220,463,4.6967942,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^6} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x)^6,x]","\text{Result too large to show}","-\frac{b^2 i^2 (c+d x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{5 g^6 (a+b x)^5 (b c-a d)^3}-\frac{2 b^2 B i^2 (c+d x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{25 g^6 (a+b x)^5 (b c-a d)^3}-\frac{d^2 i^2 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 g^6 (a+b x)^3 (b c-a d)^3}-\frac{2 B d^2 i^2 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{9 g^6 (a+b x)^3 (b c-a d)^3}+\frac{b d i^2 (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 g^6 (a+b x)^4 (b c-a d)^3}+\frac{b B d i^2 (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 g^6 (a+b x)^4 (b c-a d)^3}-\frac{2 b^2 B^2 i^2 (c+d x)^5}{125 g^6 (a+b x)^5 (b c-a d)^3}-\frac{2 B^2 d^2 i^2 (c+d x)^3}{27 g^6 (a+b x)^3 (b c-a d)^3}+\frac{b B^2 d i^2 (c+d x)^4}{16 g^6 (a+b x)^4 (b c-a d)^3}",1,"-1/54000*(i^2*(10800*(b*c - a*d)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 27000*d*(b*c - a*d)^4*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - 18000*d^2*(-(b*c) + a*d)^3*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 1000*B*d^2*(a + b*x)^2*(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)])) + 375*B*d*(a + b*x)*(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)])) + 6*B*(-225*a*B*d*(b*c - a*d)^4 + 144*B*(b*c - a*d)^5 - 225*b*B*d*(b*c - a*d)^4*x + 300*a*B*d^2*(b*c - a*d)^3*(a + b*x) - 180*B*d*(b*c - a*d)^4*(a + b*x) + 300*b*B*d^2*(b*c - a*d)^3*x*(a + b*x) - 450*a*B*d^3*(b*c - a*d)^2*(a + b*x)^2 + 640*B*d^2*(b*c - a*d)^3*(a + b*x)^2 - 450*b*B*d^3*(b*c - a*d)^2*x*(a + b*x)^2 + 900*a*B*d^4*(b*c - a*d)*(a + b*x)^3 - 1860*B*d^3*(b*c - a*d)^2*(a + b*x)^3 + 900*b*B*d^4*(b*c - a*d)*x*(a + b*x)^3 + 3600*b*B*c*d^4*(a + b*x)^4 - 3600*a*B*d^5*(a + b*x)^4 + 3720*B*d^4*(b*c - a*d)*(a + b*x)^4 + 900*a*B*d^5*(a + b*x)^4*Log[a + b*x] + 900*b*B*d^5*x*(a + b*x)^4*Log[a + b*x] + 7320*B*d^5*(a + b*x)^5*Log[a + b*x] + 720*(b*c - a*d)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 900*d*(b*c - a*d)^4*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 1200*d^2*(b*c - a*d)^3*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 1800*d^3*(b*c - a*d)^2*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 3600*d^4*(b*c - a*d)*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 3600*d^5*(a + b*x)^5*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 900*a*B*d^5*(a + b*x)^4*Log[c + d*x] - 900*b*B*d^5*x*(a + b*x)^4*Log[c + d*x] - 7320*B*d^5*(a + b*x)^5*Log[c + d*x] - 3600*d^5*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 1800*B*d^5*(a + b*x)^5*(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)]) + 1800*B*d^5*(a + b*x)^5*((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*(b*c - a*d)^3*g^6*(a + b*x)^5)","C",1
74,1,2330,1089,3.5986375,"\int (a g+b g x)^3 (c i+d i 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*(c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\text{Result too large to show}","-\frac{B^2 g^3 i^3 \log \left(\frac{a+b x}{c+d x}\right) (b c-a d)^7}{210 b^4 d^4}-\frac{B g^3 i^3 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(6 A+11 B+6 B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^7}{420 b^4 d^4}-\frac{11 B^2 g^3 i^3 \log (c+d x) (b c-a d)^7}{420 b^4 d^4}-\frac{B^2 g^3 i^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right) (b c-a d)^7}{70 b^4 d^4}+\frac{5 B^2 g^3 i^3 x (b c-a d)^6}{84 b^3 d^3}-\frac{B g^3 i^3 (a+b x) \left(6 A+5 B+6 B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^6}{420 b^4 d^3}-\frac{29 B^2 g^3 i^3 (c+d x)^2 (b c-a d)^5}{840 b^2 d^4}+\frac{B g^3 i^3 (a+b x)^2 \left(3 A+B+3 B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^5}{420 b^4 d^2}+\frac{47 B^2 g^3 i^3 (c+d x)^3 (b c-a d)^4}{1260 b d^4}-\frac{B g^3 i^3 (a+b x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^4}{210 b^4 d}+\frac{2 B g^3 i^3 (c+d x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^4}{21 b d^4}+\frac{B^2 g^3 i^3 (a+b x)^4 (b c-a d)^3}{140 b^4}-\frac{13 B^2 g^3 i^3 (c+d x)^4 (b c-a d)^3}{420 d^4}+\frac{g^3 i^3 (a+b x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (b c-a d)^3}{140 b^4}-\frac{3 B g^3 i^3 (a+b x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^3}{140 b^4}-\frac{3 B g^3 i^3 (c+d x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^3}{14 d^4}+\frac{b B^2 g^3 i^3 (c+d x)^5 (b c-a d)^2}{105 d^4}+\frac{g^3 i^3 (a+b x)^4 (c+d x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (b c-a d)^2}{35 b^3}+\frac{6 b B g^3 i^3 (c+d x)^5 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2}{35 d^4}-\frac{B g^3 i^3 (a+b x)^4 (c+d x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2}{35 b^3}+\frac{g^3 i^3 (a+b x)^4 (c+d x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (b c-a d)}{14 b^2}-\frac{b^2 B g^3 i^3 (c+d x)^6 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)}{21 d^4}+\frac{g^3 i^3 (a+b x)^4 (c+d x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{7 b}",1,"(g^3*i^3*(35*(b*c - a*d)^3*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 84*d*(b*c - a*d)^2*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 70*d^2*(b*c - a*d)*(a + b*x)^6*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 20*d^3*(a + b*x)^7*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - (35*B*(b*c - a*d)^4*(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) + (7*B*(b*c - a*d)^3*(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)])))/d^4 - (7*B*(b*c - a*d)^2*(24*b^2*B*c*d*(b*c - a*d)^3*x + 120*A*b*d*(b*c - a*d)^4*x + 130*b*B*d*(b*c - a*d)^4*x + 24*a*b*B*d^2*(-(b*c) + a*d)^3*x - 12*b*B*c*d^2*(b*c - a*d)^2*(a + b*x)^2 + 12*a*B*d^3*(b*c - a*d)^2*(a + b*x)^2 + 35*B*d^2*(-(b*c) + a*d)^3*(a + b*x)^2 + 8*b*B*c*d^3*(b*c - a*d)*(a + b*x)^3 + 10*B*d^3*(b*c - a*d)^2*(a + b*x)^3 + 8*a*B*d^4*(-(b*c) + a*d)*(a + b*x)^3 - 6*b*B*c*d^4*(a + b*x)^4 + 6*a*B*d^5*(a + b*x)^4 + 120*B*d*(b*c - a*d)^4*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] + 60*d^2*(-(b*c) + a*d)^3*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 40*d^3*(b*c - a*d)^2*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 30*d^4*(-(b*c) + a*d)*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 24*d^5*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 24*b*B*c*(b*c - a*d)^4*Log[c + d*x] + 24*a*B*d*(b*c - a*d)^4*Log[c + d*x] - 250*B*(b*c - a*d)^5*Log[c + d*x] - 120*(b*c - a*d)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 60*B*(b*c - a*d)^5*((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)])))/(6*d^4) + (B*(b*c - a*d)*(60*b^2*B*c*d*(b*c - a*d)^4*x - 60*a*b*B*d^2*(b*c - a*d)^4*x + 360*A*b*d*(b*c - a*d)^5*x + 462*b*B*d*(b*c - a*d)^5*x - 30*b*B*c*d^2*(b*c - a*d)^3*(a + b*x)^2 + 30*a*B*d^3*(b*c - a*d)^3*(a + b*x)^2 - 141*B*d^2*(b*c - a*d)^4*(a + b*x)^2 + 20*b*B*c*d^3*(b*c - a*d)^2*(a + b*x)^3 - 20*a*B*d^4*(b*c - a*d)^2*(a + b*x)^3 + 54*B*d^3*(b*c - a*d)^3*(a + b*x)^3 - 15*b*B*c*d^4*(b*c - a*d)*(a + b*x)^4 + 15*a*B*d^5*(b*c - a*d)*(a + b*x)^4 - 18*B*d^4*(b*c - a*d)^2*(a + b*x)^4 + 12*b*B*c*d^5*(a + b*x)^5 - 12*a*B*d^6*(a + b*x)^5 + 360*B*d*(b*c - a*d)^5*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] - 180*d^2*(b*c - a*d)^4*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 120*d^3*(b*c - a*d)^3*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 90*d^4*(b*c - a*d)^2*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 72*d^5*(b*c - a*d)*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 60*d^6*(a + b*x)^6*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 60*b*B*c*(b*c - a*d)^5*Log[c + d*x] + 60*a*B*d*(b*c - a*d)^5*Log[c + d*x] - 822*B*(b*c - a*d)^6*Log[c + d*x] - 360*(b*c - a*d)^6*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 180*B*(b*c - a*d)^6*((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)])))/(9*d^4)))/(140*b^4)","B",1
75,1,1555,908,1.3807227,"\int (a g+b g x)^2 (c i+d i 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)^2*(c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{g^2 i^3 \left(10 b^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (c+d x)^6-24 b (b c-a d) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (c+d x)^5+15 (b c-a d)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (c+d x)^4-\frac{5 B (b c-a d)^3 \left(6 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^3-6 B \log (c+d x) (b c-a d)^3-3 B \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 c-a d)^3+6 A b d x (b c-a d)^2-3 B (b d x+(b c-a d) \log (a+b x)) (b c-a d)^2+6 B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right) (b c-a d)^2-B \left(2 \log (a+b x) (b c-a d)^2+2 b d x (b c-a d)+b^2 (c+d x)^2\right) (b c-a d)+3 b^2 (c+d x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)+2 b^3 (c+d x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)\right)}{b^4}+\frac{2 B (b c-a d)^2 \left(24 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^4-24 B \log (c+d x) (b c-a d)^4-12 B \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 c-a d)^4+24 A b d x (b c-a d)^3-12 B (b d x+(b c-a d) \log (a+b x)) (b c-a d)^3+24 B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right) (b c-a d)^3-4 B \left(2 \log (a+b x) (b c-a d)^2+2 b d x (b c-a d)+b^2 (c+d x)^2\right) (b c-a d)^2+12 b^2 (c+d x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2-B \left(6 \log (a+b x) (b c-a d)^3+6 b d x (b c-a d)^2+3 b^2 (c+d x)^2 (b c-a d)+2 b^3 (c+d x)^3\right) (b c-a d)+8 b^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^4 (c+d x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)\right)}{b^4}-\frac{B (b c-a d) \left(120 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^5-120 B \log (c+d x) (b c-a d)^5-60 B \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 c-a d)^5+120 A b d x (b c-a d)^4-60 B (b d x+(b c-a d) \log (a+b x)) (b c-a d)^4+120 B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right) (b c-a d)^4-20 B \left(2 \log (a+b x) (b c-a d)^2+2 b d x (b c-a d)+b^2 (c+d x)^2\right) (b c-a d)^3+60 b^2 (c+d x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^3-5 B \left(6 \log (a+b x) (b c-a d)^3+6 b d x (b c-a d)^2+3 b^2 (c+d x)^2 (b c-a d)+2 b^3 (c+d x)^3\right) (b c-a d)^2+40 b^3 (c+d x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2-2 B \left(12 \log (a+b x) (b c-a d)^4+12 b d x (b c-a d)^3+6 b^2 (c+d x)^2 (b c-a d)^2+4 b^3 (c+d x)^3 (b c-a d)+3 b^4 (c+d x)^4\right) (b c-a d)+30 b^4 (c+d x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)+24 b^5 (c+d x)^5 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)\right)}{6 b^4}\right)}{60 d^3}","\frac{B^2 g^2 i^3 \log \left(\frac{a+b x}{c+d x}\right) (b c-a d)^6}{36 b^4 d^3}+\frac{B g^2 i^3 \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(2 A+3 B+2 B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^6}{60 b^4 d^3}+\frac{11 B^2 g^2 i^3 \log (c+d x) (b c-a d)^6}{180 b^4 d^3}+\frac{B^2 g^2 i^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right) (b c-a d)^6}{30 b^4 d^3}-\frac{7 B^2 g^2 i^3 x (b c-a d)^5}{180 b^3 d^2}+\frac{B g^2 i^3 (a+b x) \left(2 A+B+2 B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^5}{60 b^4 d^2}-\frac{7 B^2 g^2 i^3 (c+d x)^2 (b c-a d)^4}{360 b^2 d^3}-\frac{B g^2 i^3 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^4}{60 b^4 d}-\frac{B g^2 i^3 (c+d x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^4}{10 b^2 d^3}-\frac{B^2 g^2 i^3 (c+d x)^3 (b c-a d)^3}{60 b d^3}+\frac{g^2 i^3 (a+b x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (b c-a d)^3}{60 b^4}-\frac{B g^2 i^3 (a+b x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^3}{30 b^4}+\frac{B g^2 i^3 (c+d x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^3}{45 b d^3}+\frac{B^2 g^2 i^3 (c+d x)^4 (b c-a d)^2}{60 d^3}+\frac{g^2 i^3 (a+b x)^3 (c+d x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (b c-a d)^2}{20 b^3}+\frac{7 B g^2 i^3 (c+d x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2}{60 d^3}+\frac{g^2 i^3 (a+b x)^3 (c+d x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (b c-a d)}{10 b^2}-\frac{b B g^2 i^3 (c+d x)^5 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)}{15 d^3}+\frac{g^2 i^3 (a+b x)^3 (c+d x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{6 b}",1,"(g^2*i^3*(15*(b*c - a*d)^2*(c + d*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - 24*b*(b*c - a*d)*(c + d*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 10*b^2*(c + d*x)^6*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - (5*B*(b*c - a*d)^3*(6*A*b*d*(b*c - a*d)^2*x - 3*B*(b*c - a*d)^2*(b*d*x + (b*c - a*d)*Log[a + b*x]) - B*(b*c - a*d)*(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)] + 3*b^2*(b*c - a*d)*(c + d*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*b^3*(c + d*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6*(b*c - a*d)^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 6*B*(b*c - a*d)^3*Log[c + d*x] - 3*B*(b*c - a*d)^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^4 + (2*B*(b*c - a*d)^2*(24*A*b*d*(b*c - a*d)^3*x - 12*B*(b*c - a*d)^3*(b*d*x + (b*c - a*d)*Log[a + b*x]) - 4*B*(b*c - a*d)^2*(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)*(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)] + 12*b^2*(b*c - a*d)^2*(c + d*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 8*b^3*(b*c - a*d)*(c + d*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6*b^4*(c + d*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 24*(b*c - a*d)^4*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 24*B*(b*c - a*d)^4*Log[c + d*x] - 12*B*(b*c - a*d)^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)])))/b^4 - (B*(b*c - a*d)*(120*A*b*d*(b*c - a*d)^4*x - 60*B*(b*c - a*d)^4*(b*d*x + (b*c - a*d)*Log[a + b*x]) - 20*B*(b*c - a*d)^3*(2*b*d*(b*c - a*d)*x + b^2*(c + d*x)^2 + 2*(b*c - a*d)^2*Log[a + b*x]) - 5*B*(b*c - a*d)^2*(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]) - 2*B*(b*c - a*d)*(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]) + 120*B*d*(b*c - a*d)^4*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] + 60*b^2*(b*c - a*d)^3*(c + d*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 40*b^3*(b*c - a*d)^2*(c + d*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 30*b^4*(b*c - a*d)*(c + d*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 24*b^5*(c + d*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 120*(b*c - a*d)^5*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 120*B*(b*c - a*d)^5*Log[c + d*x] - 60*B*(b*c - a*d)^5*(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)))/(60*d^3)","A",1
76,1,901,730,0.7389882,"\int (a g+b g x) (c i+d i 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)*(c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{g i^3 \left(4 b \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (c+d x)^5-5 (b c-a d) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 (c+d x)^4+\frac{5 B (b c-a d)^2 \left(6 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^3-6 B \log (c+d x) (b c-a d)^3-3 B \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 c-a d)^3+6 A b d x (b c-a d)^2-3 B (b d x+(b c-a d) \log (a+b x)) (b c-a d)^2+6 B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right) (b c-a d)^2-B \left(2 \log (a+b x) (b c-a d)^2+2 b d x (b c-a d)+b^2 (c+d x)^2\right) (b c-a d)+3 b^2 (c+d x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)+2 b^3 (c+d x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)\right)}{3 b^4}-\frac{B (b c-a d) \left(24 \log (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^4-24 B \log (c+d x) (b c-a d)^4-12 B \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 c-a d)^4+24 A b d x (b c-a d)^3-12 B (b d x+(b c-a d) \log (a+b x)) (b c-a d)^3+24 B d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right) (b c-a d)^3-4 B \left(2 \log (a+b x) (b c-a d)^2+2 b d x (b c-a d)+b^2 (c+d x)^2\right) (b c-a d)^2+12 b^2 (c+d x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) (b c-a d)^2-B \left(6 \log (a+b x) (b c-a d)^3+6 b d x (b c-a d)^2+3 b^2 (c+d x)^2 (b c-a d)+2 b^3 (c+d x)^3\right) (b c-a d)+8 b^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^4 (c+d x)^4 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)\right)}{3 b^4}\right)}{20 d^2}","-\frac{B g i^3 (b c-a d)^5 \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)}{10 b^4 d^2}-\frac{B g i^3 (a+b x) (b c-a d)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{10 b^4 d}+\frac{g i^3 (a+b x)^2 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{20 b^4}-\frac{B g i^3 (a+b x)^2 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{10 b^4}+\frac{g i^3 (a+b x)^2 (c+d x) (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{10 b^3}+\frac{3 B g i^3 (c+d x)^2 (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{20 b^2 d^2}+\frac{3 g i^3 (a+b x)^2 (c+d x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{20 b^2}+\frac{B g i^3 (c+d x)^3 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{30 b d^2}-\frac{B g i^3 (c+d x)^4 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{10 d^2}+\frac{g i^3 (a+b x)^2 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{5 b}-\frac{B^2 g i^3 (b c-a d)^5 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{10 b^4 d^2}-\frac{B^2 g i^3 (b c-a d)^5 \log \left(\frac{a+b x}{c+d x}\right)}{12 b^4 d^2}-\frac{11 B^2 g i^3 (b c-a d)^5 \log (c+d x)}{60 b^4 d^2}+\frac{B^2 g i^3 x (b c-a d)^4}{60 b^3 d}+\frac{B^2 g i^3 (c+d x)^2 (b c-a d)^3}{30 b^2 d^2}+\frac{B^2 g i^3 (c+d x)^3 (b c-a d)^2}{30 b d^2}",1,"(g*i^3*(-5*(b*c - a*d)*(c + d*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 4*b*(c + d*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + (5*B*(b*c - a*d)^2*(6*A*b*d*(b*c - a*d)^2*x - 3*B*(b*c - a*d)^2*(b*d*x + (b*c - a*d)*Log[a + b*x]) - B*(b*c - a*d)*(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)] + 3*b^2*(b*c - a*d)*(c + d*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*b^3*(c + d*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6*(b*c - a*d)^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 6*B*(b*c - a*d)^3*Log[c + d*x] - 3*B*(b*c - a*d)^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)])))/(3*b^4) - (B*(b*c - a*d)*(24*A*b*d*(b*c - a*d)^3*x - 12*B*(b*c - a*d)^3*(b*d*x + (b*c - a*d)*Log[a + b*x]) - 4*B*(b*c - a*d)^2*(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)*(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)] + 12*b^2*(b*c - a*d)^2*(c + d*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 8*b^3*(b*c - a*d)*(c + d*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6*b^4*(c + d*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 24*(b*c - a*d)^4*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 24*B*(b*c - a*d)^4*Log[c + d*x] - 12*B*(b*c - a*d)^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)))/(20*d^2)","A",1
77,1,389,420,0.3090064,"\int (c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 \, dx","Integrate[(c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2,x]","\frac{i^3 \left((c+d 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 b^3 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+3 b^2 (c+d x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+6 (b c-a d)^3 \log (a+b 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 (a+b x)+b^2 (c+d 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(\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 (b c-a d)^3 \log (c+d x)-3 B (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 i^3 (b c-a d)^4 \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^4 d}-\frac{B i^3 (a+b x) (b c-a d)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b^4}-\frac{B i^3 (c+d x)^2 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{4 b^2 d}-\frac{B i^3 (c+d 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{i^3 (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{4 d}-\frac{B^2 i^3 (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 i^3 (b c-a d)^4 \log \left(\frac{a+b x}{c+d x}\right)}{12 b^4 d}+\frac{11 B^2 i^3 (b c-a d)^4 \log (c+d x)}{12 b^4 d}+\frac{5 B^2 i^3 x (b c-a d)^3}{12 b^3}+\frac{B^2 i^3 (c+d x)^2 (b c-a d)^2}{12 b^2 d}",1,"(i^3*((c + d*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 - 3*B*(b*c - a*d)^2*(b*d*x + (b*c - a*d)*Log[a + b*x]) - B*(b*c - a*d)*(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)] + 3*b^2*(b*c - a*d)*(c + d*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*b^3*(c + d*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6*(b*c - a*d)^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 6*B*(b*c - a*d)^3*Log[c + d*x] - 3*B*(b*c - a*d)^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)])))/(3*b^4)))/(4*d)","A",1
78,1,3984,712,4.1393154,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{a g+b g x} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x),x]","\text{Result too large to show}","\frac{2 B i^3 (b c-a d)^3 \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^4 g}+\frac{d i^3 (a+b x) (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{b^4 g}-\frac{5 B d i^3 (a+b x) (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 b^4 g}+\frac{2 B i^3 (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)}{c+d x}\right)+A\right)}{b^4 g}-\frac{i^3 (b c-a d)^3 \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^4 g}+\frac{5 B i^3 (b c-a d)^3 \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)}{3 b^4 g}+\frac{i^3 (c+d x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 b^2 g}-\frac{B i^3 (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^2 g}+\frac{i^3 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 b g}+\frac{2 B^2 i^3 (b c-a d)^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^4 g}-\frac{5 B^2 i^3 (b c-a d)^3 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{3 b^4 g}+\frac{2 B^2 i^3 (b c-a d)^3 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g}+\frac{B^2 i^3 (b c-a d)^3 \log \left(\frac{a+b x}{c+d x}\right)}{3 b^4 g}+\frac{2 B^2 i^3 (b c-a d)^3 \log (c+d x)}{b^4 g}+\frac{B^2 d i^3 x (b c-a d)^2}{3 b^3 g}",1,"(i^3*(108*A*b^3*B*c^3 - 216*a*A*b^2*B*c^2*d - 12*a*b^2*B^2*c^2*d + 144*a^2*A*b*B*c*d^2 - 18*a^2*b*B^2*c*d^2 - 36*a^3*A*B*d^3 - 36*a^3*B^2*d^3 + 54*A^2*b^3*c^2*d*x - 42*A*b^3*B*c^2*d*x + 6*b^3*B^2*c^2*d*x - 54*a*A^2*b^2*c*d^2*x + 72*a*A*b^2*B*c*d^2*x - 12*a*b^2*B^2*c*d^2*x + 18*a^2*A^2*b*d^3*x - 30*a^2*A*b*B*d^3*x + 6*a^2*b*B^2*d^3*x + 27*A^2*b^3*c*d^2*x^2 - 6*A*b^3*B*c*d^2*x^2 - 9*a*A^2*b^2*d^3*x^2 + 6*a*A*b^2*B*d^3*x^2 + 6*A^2*b^3*d^3*x^3 + 108*a*A*b^2*B*c^2*d*Log[a/b + x] + 12*a*b^2*B^2*c^2*d*Log[a/b + x] - 108*a^2*A*b*B*c*d^2*Log[a/b + x] - 18*a^2*b*B^2*c*d^2*Log[a/b + x] + 36*a^3*A*B*d^3*Log[a/b + x] - 13*a^3*B^2*d^3*Log[a/b + x] + 18*A*b^3*B*c^3*Log[a/b + x]^2 - 54*a*A*b^2*B*c^2*d*Log[a/b + x]^2 + 54*a^2*A*b*B*c*d^2*Log[a/b + x]^2 - 18*a^3*A*B*d^3*Log[a/b + x]^2 - 3*a^3*B^2*d^3*Log[a/b + x]^2 + 12*a^3*B^2*d^3*Log[a/b + x]^3 - 108*A*b^3*B*c^3*Log[c/d + x] - 22*b^3*B^2*c^3*Log[c/d + x] + 108*a*A*b^2*B*c^2*d*Log[c/d + x] - 27*a*b^2*B^2*c^2*d*Log[c/d + x] - 36*a^2*A*b*B*c*d^2*Log[c/d + x] - 36*a^3*B^2*d^3*Log[c/d + x] + 36*a^2*b*B^2*c*d^2*Log[a/b + x]*Log[c/d + x] - 30*a^3*B^2*d^3*Log[a/b + x]*Log[c/d + x] + 6*b^3*B^2*c^3*Log[c/d + x]^2 + 9*a*b^2*B^2*c^2*d*Log[c/d + x]^2 - 18*a^2*b*B^2*c*d^2*Log[c/d + x]^2 + 18*A^2*b^3*c^3*Log[a + b*x] - 54*a*A^2*b^2*c^2*d*Log[a + b*x] + 54*a^2*A^2*b*c*d^2*Log[a + b*x] - 54*a^2*A*b*B*c*d^2*Log[a + b*x] + 6*a^2*b*B^2*c*d^2*Log[a + b*x] - 18*a^3*A^2*d^3*Log[a + b*x] + 30*a^3*A*B*d^3*Log[a + b*x] + 13*a^3*B^2*d^3*Log[a + b*x] - 36*A*b^3*B*c^3*Log[a/b + x]*Log[a + b*x] + 108*a*A*b^2*B*c^2*d*Log[a/b + x]*Log[a + b*x] - 108*a^2*A*b*B*c*d^2*Log[a/b + x]*Log[a + b*x] + 36*a^3*A*B*d^3*Log[a/b + x]*Log[a + b*x] - 30*a^3*B^2*d^3*Log[a/b + x]*Log[a + b*x] - 18*a^3*B^2*d^3*Log[a/b + x]^2*Log[a + b*x] + 36*A*b^3*B*c^3*Log[c/d + x]*Log[a + b*x] - 108*a*A*b^2*B*c^2*d*Log[c/d + x]*Log[a + b*x] + 108*a^2*A*b*B*c*d^2*Log[c/d + x]*Log[a + b*x] - 36*a^3*A*B*d^3*Log[c/d + x]*Log[a + b*x] + 30*a^3*B^2*d^3*Log[c/d + x]*Log[a + b*x] + 36*a^3*B^2*d^3*Log[a/b + x]*Log[c/d + x]*Log[a + b*x] - 18*a^3*B^2*d^3*Log[c/d + x]^2*Log[a + b*x] - 36*A*b^3*B*c^3*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 108*a*A*b^2*B*c^2*d*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 108*a^2*A*b*B*c*d^2*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 36*a^3*A*B*d^3*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 36*a^3*B^2*d^3*Log[a/b + x]*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 18*a^3*B^2*d^3*Log[c/d + x]^2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 54*b^3*B^2*c^3*Log[((b*c - a*d)*e)/(c + d*x)] + 108*a*b^2*B^2*c^2*d*Log[((b*c - a*d)*e)/(c + d*x)] - 54*a^2*b*B^2*c*d^2*Log[((b*c - a*d)*e)/(c + d*x)] - 54*a*b^2*B^2*c^2*d*Log[(e*(a + b*x))/(c + d*x)] + 90*a^2*b*B^2*c*d^2*Log[(e*(a + b*x))/(c + d*x)] - 36*a^3*B^2*d^3*Log[(e*(a + b*x))/(c + d*x)] + 108*A*b^3*B*c^2*d*x*Log[(e*(a + b*x))/(c + d*x)] - 42*b^3*B^2*c^2*d*x*Log[(e*(a + b*x))/(c + d*x)] - 108*a*A*b^2*B*c*d^2*x*Log[(e*(a + b*x))/(c + d*x)] + 72*a*b^2*B^2*c*d^2*x*Log[(e*(a + b*x))/(c + d*x)] + 36*a^2*A*b*B*d^3*x*Log[(e*(a + b*x))/(c + d*x)] - 30*a^2*b*B^2*d^3*x*Log[(e*(a + b*x))/(c + d*x)] + 54*A*b^3*B*c*d^2*x^2*Log[(e*(a + b*x))/(c + d*x)] - 6*b^3*B^2*c*d^2*x^2*Log[(e*(a + b*x))/(c + d*x)] - 18*a*A*b^2*B*d^3*x^2*Log[(e*(a + b*x))/(c + d*x)] + 6*a*b^2*B^2*d^3*x^2*Log[(e*(a + b*x))/(c + d*x)] + 12*A*b^3*B*d^3*x^3*Log[(e*(a + b*x))/(c + d*x)] + 36*a^3*B^2*d^3*Log[a/b + x]*Log[(e*(a + b*x))/(c + d*x)] - 18*a^3*B^2*d^3*Log[a/b + x]^2*Log[(e*(a + b*x))/(c + d*x)] - 36*a^2*b*B^2*c*d^2*Log[c/d + x]*Log[(e*(a + b*x))/(c + d*x)] + 36*A*b^3*B*c^3*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] - 108*a*A*b^2*B*c^2*d*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + 108*a^2*A*b*B*c*d^2*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] - 36*a^3*A*B*d^3*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + 30*a^3*B^2*d^3*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + 36*a^3*B^2*d^3*Log[a/b + x]*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] - 36*a^3*B^2*d^3*Log[c/d + x]*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + 36*a^3*B^2*d^3*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[(e*(a + b*x))/(c + d*x)] + 54*a*b^2*B^2*c^2*d*Log[(e*(a + b*x))/(c + d*x)]^2 - 81*a^2*b*B^2*c*d^2*Log[(e*(a + b*x))/(c + d*x)]^2 + 54*b^3*B^2*c^2*d*x*Log[(e*(a + b*x))/(c + d*x)]^2 - 54*a*b^2*B^2*c*d^2*x*Log[(e*(a + b*x))/(c + d*x)]^2 + 18*a^2*b*B^2*d^3*x*Log[(e*(a + b*x))/(c + d*x)]^2 + 27*b^3*B^2*c*d^2*x^2*Log[(e*(a + b*x))/(c + d*x)]^2 - 9*a*b^2*B^2*d^3*x^2*Log[(e*(a + b*x))/(c + d*x)]^2 + 6*b^3*B^2*d^3*x^3*Log[(e*(a + b*x))/(c + d*x)]^2 - 18*b^3*B^2*c^3*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(e*(a + b*x))/(c + d*x)]^2 - 18*a^3*B^2*d^3*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)]^2 - 18*a*b^2*B^2*c^2*d*Log[(e*(a + b*x))/(c + d*x)]^3 + 18*a^2*b*B^2*c*d^2*Log[(e*(a + b*x))/(c + d*x)]^3 + 42*A*b^3*B*c^3*Log[c + d*x] + 4*b^3*B^2*c^3*Log[c + d*x] - 18*a*A*b^2*B*c^2*d*Log[c + d*x] + 15*a*b^2*B^2*c^2*d*Log[c + d*x] + 66*a^2*b*B^2*c*d^2*Log[c + d*x] + 12*b^3*B^2*c^3*Log[a/b + x]*Log[c + d*x] + 18*a*b^2*B^2*c^2*d*Log[a/b + x]*Log[c + d*x] - 12*b^3*B^2*c^3*Log[c/d + x]*Log[c + d*x] - 18*a*b^2*B^2*c^2*d*Log[c/d + x]*Log[c + d*x] - 12*b^3*B^2*c^3*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] - 18*a*b^2*B^2*c^2*d*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] - 12*b^3*B^2*c^3*Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] - 18*a*b^2*B^2*c^2*d*Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] - 36*a^2*b*B^2*c*d^2*Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + 66*a^3*B^2*d^3*Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] - 18*a^3*B^2*d^3*Log[a/b + x]^2*Log[(b*(c + d*x))/(b*c - a*d)] + 54*b^3*B^2*c^3*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 216*a*b^2*B^2*c^2*d*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 162*a^2*b*B^2*c*d^2*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 54*a*b^2*B^2*c^2*d*Log[(e*(a + b*x))/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - 54*a^2*b*B^2*c*d^2*Log[(e*(a + b*x))/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - 6*B^2*(2*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 11*a^3*d^3 + 6*a^3*d^3*Log[a/b + x])*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 54*b*B^2*c*(b*c - a*d)*(b*c - 3*a*d + 2*a*d*Log[(e*(a + b*x))/(c + d*x)])*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 36*A*b^3*B*c^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 108*a*A*b^2*B*c^2*d*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 108*a^2*A*b*B*c*d^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 36*a^3*A*B*d^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 36*a^3*B^2*d^3*Log[a/b + x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 36*a^3*B^2*d^3*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 36*b^3*B^2*c^3*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] + 36*a^3*B^2*d^3*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)] - 108*a*b^2*B^2*c^2*d*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] + 108*a^2*b*B^2*c*d^2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] + 36*a^3*B^2*d^3*PolyLog[3, (b*(c + d*x))/(b*c - a*d)] + 36*b^3*B^2*c^3*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))]))/(18*b^4*g)","B",1
79,1,5108,692,17.4707651,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^2} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x)^2,x]","\text{Result too large to show}","\frac{2 d^2 i^3 (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{b^4 g^2}-\frac{B d^2 i^3 (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^4 g^2}+\frac{6 B d i^3 (b c-a d)^2 \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^4 g^2}+\frac{4 B d i^3 (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\right)}{b^4 g^2}-\frac{3 d i^3 (b c-a d)^2 \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^4 g^2}+\frac{B d i^3 (b c-a d)^2 \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)}{b^4 g^2}-\frac{i^3 (c+d x) (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{b^3 g^2 (a+b x)}-\frac{2 B i^3 (c+d x) (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^3 g^2 (a+b x)}+\frac{d i^3 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 b^2 g^2}+\frac{4 B^2 d i^3 (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^4 g^2}-\frac{B^2 d i^3 (b c-a d)^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g^2}+\frac{6 B^2 d i^3 (b c-a d)^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g^2}+\frac{B^2 d i^3 (b c-a d)^2 \log (c+d x)}{b^4 g^2}-\frac{2 B^2 i^3 (c+d x) (b c-a d)^2}{b^3 g^2 (a+b x)}",1,"Result too large to show","B",1
80,1,6284,604,14.2487453,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^3} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x)^3,x]","\text{Result too large to show}","\frac{d^3 i^3 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{b^4 g^3}+\frac{6 B d^2 i^3 (b c-a d) \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^4 g^3}+\frac{2 B d^2 i^3 (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^4 g^3}-\frac{3 d^2 i^3 (b c-a d) \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^4 g^3}-\frac{2 d i^3 (c+d x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{b^3 g^3 (a+b x)}-\frac{4 B d i^3 (c+d x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{b^3 g^3 (a+b x)}-\frac{i^3 (c+d x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 b^2 g^3 (a+b x)^2}-\frac{B i^3 (c+d x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 b^2 g^3 (a+b x)^2}+\frac{2 B^2 d^2 i^3 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^4 g^3}+\frac{6 B^2 d^2 i^3 (b c-a d) \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g^3}-\frac{4 B^2 d i^3 (c+d x) (b c-a d)}{b^3 g^3 (a+b x)}-\frac{B^2 i^3 (c+d x)^2 (b c-a d)}{4 b^2 g^3 (a+b x)^2}",1,"Result too large to show","B",1
81,1,2470,147,1.4351081,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^5} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x)^5,x]","\text{Result too large to show}","-\frac{i^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)}-\frac{B i^3 (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)}-\frac{B^2 i^3 (c+d x)^4}{32 g^5 (a+b x)^4 (b c-a d)}",1,"-1/32*(i^3*(8*A^2*b^4*c^4 + 4*A*b^4*B*c^4 + b^4*B^2*c^4 - 8*a^4*A^2*d^4 - 4*a^4*A*B*d^4 - a^4*B^2*d^4 + 32*A^2*b^4*c^3*d*x + 16*A*b^4*B*c^3*d*x + 4*b^4*B^2*c^3*d*x - 32*a^3*A^2*b*d^4*x - 16*a^3*A*b*B*d^4*x - 4*a^3*b*B^2*d^4*x + 48*A^2*b^4*c^2*d^2*x^2 + 24*A*b^4*B*c^2*d^2*x^2 + 6*b^4*B^2*c^2*d^2*x^2 - 48*a^2*A^2*b^2*d^4*x^2 - 24*a^2*A*b^2*B*d^4*x^2 - 6*a^2*b^2*B^2*d^4*x^2 + 32*A^2*b^4*c*d^3*x^3 + 16*A*b^4*B*c*d^3*x^3 + 4*b^4*B^2*c*d^3*x^3 - 32*a*A^2*b^3*d^4*x^3 - 16*a*A*b^3*B*d^4*x^3 - 4*a*b^3*B^2*d^4*x^3 + 16*a^4*A*B*d^4*Log[a + b*x] + 4*a^4*B^2*d^4*Log[a + b*x] + 64*a^3*A*b*B*d^4*x*Log[a + b*x] + 16*a^3*b*B^2*d^4*x*Log[a + b*x] + 96*a^2*A*b^2*B*d^4*x^2*Log[a + b*x] + 24*a^2*b^2*B^2*d^4*x^2*Log[a + b*x] + 64*a*A*b^3*B*d^4*x^3*Log[a + b*x] + 16*a*b^3*B^2*d^4*x^3*Log[a + b*x] + 16*A*b^4*B*d^4*x^4*Log[a + b*x] + 4*b^4*B^2*d^4*x^4*Log[a + b*x] - 8*a^4*B^2*d^4*Log[a + b*x]^2 - 32*a^3*b*B^2*d^4*x*Log[a + b*x]^2 - 48*a^2*b^2*B^2*d^4*x^2*Log[a + b*x]^2 - 32*a*b^3*B^2*d^4*x^3*Log[a + b*x]^2 - 8*b^4*B^2*d^4*x^4*Log[a + b*x]^2 + 16*A*b^4*B*c^4*Log[(e*(a + b*x))/(c + d*x)] + 4*b^4*B^2*c^4*Log[(e*(a + b*x))/(c + d*x)] - 16*a^4*A*B*d^4*Log[(e*(a + b*x))/(c + d*x)] - 4*a^4*B^2*d^4*Log[(e*(a + b*x))/(c + d*x)] + 64*A*b^4*B*c^3*d*x*Log[(e*(a + b*x))/(c + d*x)] + 16*b^4*B^2*c^3*d*x*Log[(e*(a + b*x))/(c + d*x)] - 64*a^3*A*b*B*d^4*x*Log[(e*(a + b*x))/(c + d*x)] - 16*a^3*b*B^2*d^4*x*Log[(e*(a + b*x))/(c + d*x)] + 96*A*b^4*B*c^2*d^2*x^2*Log[(e*(a + b*x))/(c + d*x)] + 24*b^4*B^2*c^2*d^2*x^2*Log[(e*(a + b*x))/(c + d*x)] - 96*a^2*A*b^2*B*d^4*x^2*Log[(e*(a + b*x))/(c + d*x)] - 24*a^2*b^2*B^2*d^4*x^2*Log[(e*(a + b*x))/(c + d*x)] + 64*A*b^4*B*c*d^3*x^3*Log[(e*(a + b*x))/(c + d*x)] + 16*b^4*B^2*c*d^3*x^3*Log[(e*(a + b*x))/(c + d*x)] - 64*a*A*b^3*B*d^4*x^3*Log[(e*(a + b*x))/(c + d*x)] - 16*a*b^3*B^2*d^4*x^3*Log[(e*(a + b*x))/(c + d*x)] + 16*a^4*B^2*d^4*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + 64*a^3*b*B^2*d^4*x*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + 96*a^2*b^2*B^2*d^4*x^2*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + 64*a*b^3*B^2*d^4*x^3*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + 16*b^4*B^2*d^4*x^4*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + 8*b^4*B^2*c^4*Log[(e*(a + b*x))/(c + d*x)]^2 - 8*a^4*B^2*d^4*Log[(e*(a + b*x))/(c + d*x)]^2 + 32*b^4*B^2*c^3*d*x*Log[(e*(a + b*x))/(c + d*x)]^2 - 32*a^3*b*B^2*d^4*x*Log[(e*(a + b*x))/(c + d*x)]^2 + 48*b^4*B^2*c^2*d^2*x^2*Log[(e*(a + b*x))/(c + d*x)]^2 - 48*a^2*b^2*B^2*d^4*x^2*Log[(e*(a + b*x))/(c + d*x)]^2 + 32*b^4*B^2*c*d^3*x^3*Log[(e*(a + b*x))/(c + d*x)]^2 - 32*a*b^3*B^2*d^4*x^3*Log[(e*(a + b*x))/(c + d*x)]^2 - 16*a^4*A*B*d^4*Log[c + d*x] - 4*a^4*B^2*d^4*Log[c + d*x] - 64*a^3*A*b*B*d^4*x*Log[c + d*x] - 16*a^3*b*B^2*d^4*x*Log[c + d*x] - 96*a^2*A*b^2*B*d^4*x^2*Log[c + d*x] - 24*a^2*b^2*B^2*d^4*x^2*Log[c + d*x] - 64*a*A*b^3*B*d^4*x^3*Log[c + d*x] - 16*a*b^3*B^2*d^4*x^3*Log[c + d*x] - 16*A*b^4*B*d^4*x^4*Log[c + d*x] - 4*b^4*B^2*d^4*x^4*Log[c + d*x] + 16*a^4*B^2*d^4*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] + 64*a^3*b*B^2*d^4*x*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] + 96*a^2*b^2*B^2*d^4*x^2*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] + 64*a*b^3*B^2*d^4*x^3*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] + 16*b^4*B^2*d^4*x^4*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] - 16*a^4*B^2*d^4*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] - 64*a^3*b*B^2*d^4*x*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] - 96*a^2*b^2*B^2*d^4*x^2*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] - 64*a*b^3*B^2*d^4*x^3*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] - 16*b^4*B^2*d^4*x^4*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] - 8*a^4*B^2*d^4*Log[c + d*x]^2 - 32*a^3*b*B^2*d^4*x*Log[c + d*x]^2 - 48*a^2*b^2*B^2*d^4*x^2*Log[c + d*x]^2 - 32*a*b^3*B^2*d^4*x^3*Log[c + d*x]^2 - 8*b^4*B^2*d^4*x^4*Log[c + d*x]^2 + 16*a^4*B^2*d^4*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] + 64*a^3*b*B^2*d^4*x*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] + 96*a^2*b^2*B^2*d^4*x^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] + 64*a*b^3*B^2*d^4*x^3*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] + 16*b^4*B^2*d^4*x^4*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] + 16*B^2*d^4*(a + b*x)^4*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 16*B^2*d^4*(a + b*x)^4*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]))/(b^4*(b*c - a*d)*g^5*(a + b*x)^4)","C",1
82,1,2289,299,4.204294,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^6} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x)^6,x]","\text{Result too large to show}","-\frac{b i^3 (c+d x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{5 g^6 (a+b x)^5 (b c-a d)^2}-\frac{2 b B i^3 (c+d x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{25 g^6 (a+b x)^5 (b c-a d)^2}+\frac{d i^3 (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{4 g^6 (a+b x)^4 (b c-a d)^2}+\frac{B d i^3 (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{8 g^6 (a+b x)^4 (b c-a d)^2}-\frac{2 b B^2 i^3 (c+d x)^5}{125 g^6 (a+b x)^5 (b c-a d)^2}+\frac{B^2 d i^3 (c+d x)^4}{32 g^6 (a+b x)^4 (b c-a d)^2}",1,"(i^3*(2000*a^2*B^2*d^2*(b*c - a*d)^3 - 825*a*B^2*d*(b*c - a*d)^4 - 192*B^2*(b*c - a*d)^5 + 4000*a*b*B^2*d^2*(b*c - a*d)^3*x - 825*b*B^2*d*(b*c - a*d)^4*x + 2000*b^2*B^2*d^2*(b*c - a*d)^3*x^2 - 3000*a^2*B^2*d^3*(b*c - a*d)^2*(a + b*x) + 1100*a*B^2*d^2*(b*c - a*d)^3*(a + b*x) + 240*B^2*d*(b*c - a*d)^4*(a + b*x) - 6000*a*b*B^2*d^3*(b*c - a*d)^2*x*(a + b*x) + 1100*b*B^2*d^2*(b*c - a*d)^3*x*(a + b*x) - 3000*b^2*B^2*d^3*(b*c - a*d)^2*x^2*(a + b*x) + 6000*a^2*B^2*d^4*(b*c - a*d)*(a + b*x)^2 - 6150*a*B^2*d^3*(b*c - a*d)^2*(a + b*x)^2 + 3520*B^2*d^2*(-(b*c) + a*d)^3*(a + b*x)^2 + 12000*a*b*B^2*d^4*(b*c - a*d)*x*(a + b*x)^2 - 6150*b*B^2*d^3*(b*c - a*d)^2*x*(a + b*x)^2 + 6000*b^2*B^2*d^4*(b*c - a*d)*x^2*(a + b*x)^2 + 18000*a*b*B^2*c*d^4*(a + b*x)^3 - 18000*a^2*B^2*d^5*(a + b*x)^3 + 12300*a*B^2*d^4*(b*c - a*d)*(a + b*x)^3 + 9480*B^2*d^3*(b*c - a*d)^2*(a + b*x)^3 + 18000*b^2*B^2*c*d^4*x*(a + b*x)^3 - 18000*a*b*B^2*d^5*x*(a + b*x)^3 + 12300*b*B^2*d^4*(b*c - a*d)*x*(a + b*x)^3 - 16800*b*B^2*c*d^4*(a + b*x)^4 + 16800*a*B^2*d^5*(a + b*x)^4 + 18960*B^2*d^4*(-(b*c) + a*d)*(a + b*x)^4 + 6000*a^2*B^2*d^5*(a + b*x)^3*Log[a + b*x] + 12000*a*b*B^2*d^5*x*(a + b*x)^3*Log[a + b*x] + 6000*b^2*B^2*d^5*x^2*(a + b*x)^3*Log[a + b*x] + 30300*a*B^2*d^5*(a + b*x)^4*Log[a + b*x] + 30300*b*B^2*d^5*x*(a + b*x)^4*Log[a + b*x] - 35760*B^2*d^5*(a + b*x)^5*Log[a + b*x] - 4500*a*B*d*(b*c - a*d)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 960*B*(b*c - a*d)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 4500*b*B*d*(b*c - a*d)^4*x*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6000*a*B*d^2*(b*c - a*d)^3*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 1200*B*d*(b*c - a*d)^4*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6000*b*B*d^2*(b*c - a*d)^3*x*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 9000*a*B*d^3*(b*c - a*d)^2*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 9600*B*d^2*(-(b*c) + a*d)^3*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 9000*b*B*d^3*(b*c - a*d)^2*x*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 18000*a*B*d^4*(b*c - a*d)*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 8400*B*d^3*(b*c - a*d)^2*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 18000*b*B*d^4*(b*c - a*d)*x*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 16800*B*d^4*(-(b*c) + a*d)*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 18000*a*B*d^5*(a + b*x)^4*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 18000*b*B*d^5*x*(a + b*x)^4*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 16800*B*d^5*(a + b*x)^5*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 2400*(b*c - a*d)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - 9000*d*(b*c - a*d)^4*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 12000*d^2*(-(b*c) + a*d)^3*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - 6000*d^3*(b*c - a*d)^2*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - 6000*a^2*B^2*d^5*(a + b*x)^3*Log[c + d*x] - 12000*a*b*B^2*d^5*x*(a + b*x)^3*Log[c + d*x] - 6000*b^2*B^2*d^5*x^2*(a + b*x)^3*Log[c + d*x] - 30300*a*B^2*d^5*(a + b*x)^4*Log[c + d*x] - 30300*b*B^2*d^5*x*(a + b*x)^4*Log[c + d*x] + 35760*B^2*d^5*(a + b*x)^5*Log[c + d*x] - 18000*a*B*d^5*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 18000*b*B*d^5*x*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 16800*B*d^5*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 9000*a*B^2*d^5*(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)]) - 9000*b*B^2*d^5*x*(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)]) + 8400*B^2*d^5*(a + b*x)^5*(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)]) + 9000*a*B^2*d^5*(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)]) + 9000*b*B^2*d^5*x*(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)]) - 8400*B^2*d^5*(a + b*x)^5*((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)])))/(12000*b^4*(b*c - a*d)^2*g^6*(a + b*x)^5)","C",1
83,1,2583,463,6.2547358,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^7} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x)^7,x]","\text{Result too large to show}","-\frac{b^2 i^3 (c+d x)^6 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{6 g^7 (a+b x)^6 (b c-a d)^3}-\frac{b^2 B i^3 (c+d x)^6 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{18 g^7 (a+b x)^6 (b c-a d)^3}-\frac{d^2 i^3 (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{4 g^7 (a+b x)^4 (b c-a d)^3}-\frac{B d^2 i^3 (c+d x)^4 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{8 g^7 (a+b x)^4 (b c-a d)^3}+\frac{2 b d i^3 (c+d x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{5 g^7 (a+b x)^5 (b c-a d)^3}+\frac{4 b B d i^3 (c+d x)^5 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{25 g^7 (a+b x)^5 (b c-a d)^3}-\frac{b^2 B^2 i^3 (c+d x)^6}{108 g^7 (a+b x)^6 (b c-a d)^3}-\frac{B^2 d^2 i^3 (c+d x)^4}{32 g^7 (a+b x)^4 (b c-a d)^3}+\frac{4 b B^2 d i^3 (c+d x)^5}{125 g^7 (a+b x)^5 (b c-a d)^3}",1,"(i^3*(8100*a^2*B^2*d^2*(b*c - a*d)^4 - 1000*B^2*(b*c - a*d)^6 + 3744*a*B^2*d*(-(b*c) + a*d)^5 + 16200*a*b*B^2*d^2*(b*c - a*d)^4*x - 3744*b*B^2*d*(b*c - a*d)^5*x + 8100*b^2*B^2*d^2*(b*c - a*d)^4*x^2 + 4680*a*B^2*d^2*(b*c - a*d)^4*(a + b*x) + 1200*B^2*d*(b*c - a*d)^5*(a + b*x) + 10800*a^2*B^2*d^3*(-(b*c) + a*d)^3*(a + b*x) + 4680*b*B^2*d^2*(b*c - a*d)^4*x*(a + b*x) + 21600*a*b*B^2*d^3*(-(b*c) + a*d)^3*x*(a + b*x) - 10800*b^2*B^2*d^3*(b*c - a*d)^3*x^2*(a + b*x) + 16200*a^2*B^2*d^4*(b*c - a*d)^2*(a + b*x)^2 - 13875*B^2*d^2*(b*c - a*d)^4*(a + b*x)^2 + 20640*a*B^2*d^3*(-(b*c) + a*d)^3*(a + b*x)^2 + 32400*a*b*B^2*d^4*(b*c - a*d)^2*x*(a + b*x)^2 - 20640*b*B^2*d^3*(b*c - a*d)^3*x*(a + b*x)^2 + 16200*b^2*B^2*d^4*(b*c - a*d)^2*x^2*(a + b*x)^2 + 63360*a*B^2*d^4*(b*c - a*d)^2*(a + b*x)^3 + 32500*B^2*d^3*(b*c - a*d)^3*(a + b*x)^3 + 32400*a^2*B^2*d^5*(-(b*c) + a*d)*(a + b*x)^3 + 63360*b*B^2*d^4*(b*c - a*d)^2*x*(a + b*x)^3 + 64800*a*b*B^2*d^5*(-(b*c) + a*d)*x*(a + b*x)^3 - 32400*b^2*B^2*d^5*(b*c - a*d)*x^2*(a + b*x)^3 - 129600*a*b*B^2*c*d^5*(a + b*x)^4 + 129600*a^2*B^2*d^6*(a + b*x)^4 - 80250*B^2*d^4*(b*c - a*d)^2*(a + b*x)^4 + 126720*a*B^2*d^5*(-(b*c) + a*d)*(a + b*x)^4 - 129600*b^2*B^2*c*d^5*x*(a + b*x)^4 + 129600*a*b*B^2*d^6*x*(a + b*x)^4 - 126720*b*B^2*d^5*(b*c - a*d)*x*(a + b*x)^4 + 126000*b*B^2*c*d^5*(a + b*x)^5 - 126000*a*B^2*d^6*(a + b*x)^5 + 160500*B^2*d^5*(b*c - a*d)*(a + b*x)^5 - 32400*a^2*B^2*d^6*(a + b*x)^4*Log[a + b*x] - 64800*a*b*B^2*d^6*x*(a + b*x)^4*Log[a + b*x] - 32400*b^2*B^2*d^6*x^2*(a + b*x)^4*Log[a + b*x] - 256320*a*B^2*d^6*(a + b*x)^5*Log[a + b*x] - 256320*b*B^2*d^6*x*(a + b*x)^5*Log[a + b*x] + 286500*B^2*d^6*(a + b*x)^6*Log[a + b*x] - 6000*B*(b*c - a*d)^6*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 25920*a*B*d*(-(b*c) + a*d)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 25920*b*B*d*(b*c - a*d)^5*x*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 32400*a*B*d^2*(b*c - a*d)^4*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 7200*B*d*(b*c - a*d)^5*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 32400*b*B*d^2*(b*c - a*d)^4*x*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 49500*B*d^2*(b*c - a*d)^4*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 43200*a*B*d^3*(-(b*c) + a*d)^3*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 43200*b*B*d^3*(b*c - a*d)^3*x*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 64800*a*B*d^4*(b*c - a*d)^2*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 42000*B*d^3*(b*c - a*d)^3*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 64800*b*B*d^4*(b*c - a*d)^2*x*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 63000*B*d^4*(b*c - a*d)^2*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 129600*a*B*d^5*(-(b*c) + a*d)*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 129600*b*B*d^5*(b*c - a*d)*x*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 126000*B*d^5*(b*c - a*d)*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 129600*a*B*d^6*(a + b*x)^5*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 129600*b*B*d^6*x*(a + b*x)^5*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 126000*B*d^6*(a + b*x)^6*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 18000*(b*c - a*d)^6*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 64800*d*(-(b*c) + a*d)^5*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - 81000*d^2*(b*c - a*d)^4*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 36000*d^3*(-(b*c) + a*d)^3*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 32400*a^2*B^2*d^6*(a + b*x)^4*Log[c + d*x] + 64800*a*b*B^2*d^6*x*(a + b*x)^4*Log[c + d*x] + 32400*b^2*B^2*d^6*x^2*(a + b*x)^4*Log[c + d*x] + 256320*a*B^2*d^6*(a + b*x)^5*Log[c + d*x] + 256320*b*B^2*d^6*x*(a + b*x)^5*Log[c + d*x] - 286500*B^2*d^6*(a + b*x)^6*Log[c + d*x] + 129600*a*B*d^6*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 129600*b*B*d^6*x*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 126000*B*d^6*(a + b*x)^6*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 64800*a*B^2*d^6*(a + b*x)^5*(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)]) + 64800*b*B^2*d^6*x*(a + b*x)^5*(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)]) - 63000*B^2*d^6*(a + b*x)^6*(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)]) - 64800*a*B^2*d^6*(a + b*x)^5*((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)]) - 64800*b*B^2*d^6*x*(a + b*x)^5*((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)]) + 63000*B^2*d^6*(a + b*x)^6*((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)])))/(108000*b^4*(b*c - a*d)^3*g^7*(a + b*x)^6)","C",1
84,1,4802,718,1.9006594,"\int \frac{(a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{c i+d i x} \, dx","Integrate[((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(c*i + d*i*x),x]","\text{Result too large to show}","\frac{b^3 g^3 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 d^4 i}-\frac{3 b^2 g^3 (c+d x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 d^4 i}-\frac{b^2 B g^3 (c+d x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{3 d^4 i}+\frac{2 B g^3 (b c-a d)^3 \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)}{d^4 i}+\frac{g^3 (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)}{c+d x}\right)+A\right)^2}{d^4 i}+\frac{6 B g^3 (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)}{c+d x}\right)+A\right)}{d^4 i}-\frac{7 B g^3 (b c-a d)^3 \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)}{3 d^4 i}+\frac{3 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)^2}{d^3 i}+\frac{7 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)}{3 d^3 i}+\frac{6 B^2 g^3 (b c-a d)^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i}+\frac{7 B^2 g^3 (b c-a d)^3 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{3 d^4 i}-\frac{2 B^2 g^3 (b c-a d)^3 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i}+\frac{B^2 g^3 (b c-a d)^3 \log \left(\frac{a+b x}{c+d x}\right)}{3 d^4 i}-\frac{2 B^2 g^3 (b c-a d)^3 \log (c+d x)}{d^4 i}+\frac{b B^2 g^3 x (b c-a d)^2}{3 d^3 i}",1,"(g^3*(36*A*b^3*B*c^3 - 144*a*A*b^2*B*c^2*d - 66*a*b^2*B^2*c^2*d + 216*a^2*A*b*B*c*d^2 + 162*a^2*b*B^2*c*d^2 - 108*a^3*A*B*d^3 - 108*a^3*B^2*d^3 + 18*A^2*b^3*c^2*d*x + 30*A*b^3*B*c^2*d*x + 6*b^3*B^2*c^2*d*x - 54*a*A^2*b^2*c*d^2*x - 72*a*A*b^2*B*c*d^2*x - 12*a*b^2*B^2*c*d^2*x + 54*a^2*A^2*b*d^3*x + 42*a^2*A*b*B*d^3*x + 6*a^2*b*B^2*d^3*x - 9*A^2*b^3*c*d^2*x^2 - 6*A*b^3*B*c*d^2*x^2 + 27*a*A^2*b^2*d^3*x^2 + 6*a*A*b^2*B*d^3*x^2 + 6*A^2*b^3*d^3*x^3 - 36*b^3*B^2*c^3*Log[a/b + x] + 36*a*A*b^2*B*c^2*d*Log[a/b + x] + 174*a*b^2*B^2*c^2*d*Log[a/b + x] - 108*a^2*A*b*B*c*d^2*Log[a/b + x] - 297*a^2*b*B^2*c*d^2*Log[a/b + x] + 108*a^3*A*B*d^3*Log[a/b + x] + 167*a^3*B^2*d^3*Log[a/b + x] - 18*a*b^2*B^2*c^2*d*Log[a/b + x]^2 + 63*a^2*b*B^2*c*d^2*Log[a/b + x]^2 - 75*a^3*B^2*d^3*Log[a/b + x]^2 - 36*A*b^3*B*c^3*Log[c/d + x] - 49*b^3*B^2*c^3*Log[c/d + x] + 108*a*A*b^2*B*c^2*d*Log[c/d + x] + 45*a*b^2*B^2*c^2*d*Log[c/d + x] - 108*a^2*A*b*B*c*d^2*Log[c/d + x] + 108*a^2*b*B^2*c*d^2*Log[c/d + x] - 108*a^3*B^2*d^3*Log[c/d + x] + 36*b^3*B^2*c^3*Log[a/b + x]*Log[c/d + x] - 108*a*b^2*B^2*c^2*d*Log[a/b + x]*Log[c/d + x] + 90*a^2*b*B^2*c*d^2*Log[a/b + x]*Log[c/d + x] + 42*a^3*B^2*d^3*Log[a/b + x]*Log[c/d + x] + 18*A*b^3*B*c^3*Log[c/d + x]^2 - 3*b^3*B^2*c^3*Log[c/d + x]^2 - 54*a*A*b^2*B*c^2*d*Log[c/d + x]^2 + 27*a*b^2*B^2*c^2*d*Log[c/d + x]^2 + 54*a^2*A*b*B*c*d^2*Log[c/d + x]^2 - 54*a^2*b*B^2*c*d^2*Log[c/d + x]^2 - 18*a^3*A*B*d^3*Log[c/d + x]^2 + 12*b^3*B^2*c^3*Log[c/d + x]^3 - 36*a*b^2*B^2*c^2*d*Log[c/d + x]^3 + 36*a^2*b*B^2*c*d^2*Log[c/d + x]^3 + 18*a^2*A*b*B*c*d^2*Log[a + b*x] + 15*a^2*b*B^2*c*d^2*Log[a + b*x] - 42*a^3*A*B*d^3*Log[a + b*x] - 23*a^3*B^2*d^3*Log[a + b*x] - 18*a^2*b*B^2*c*d^2*Log[a/b + x]*Log[a + b*x] + 42*a^3*B^2*d^3*Log[a/b + x]*Log[a + b*x] + 18*a^2*b*B^2*c*d^2*Log[c/d + x]*Log[a + b*x] - 42*a^3*B^2*d^3*Log[c/d + x]*Log[a + b*x] - 18*b^3*B^2*c^3*Log[c/d + x]^2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 54*a*b^2*B^2*c^2*d*Log[c/d + x]^2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 54*a^2*b*B^2*c*d^2*Log[c/d + x]^2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 36*b^3*B^2*c^3*Log[(e*(a + b*x))/(c + d*x)] - 144*a*b^2*B^2*c^2*d*Log[(e*(a + b*x))/(c + d*x)] + 216*a^2*b*B^2*c*d^2*Log[(e*(a + b*x))/(c + d*x)] - 108*a^3*B^2*d^3*Log[(e*(a + b*x))/(c + d*x)] + 36*A*b^3*B*c^2*d*x*Log[(e*(a + b*x))/(c + d*x)] + 30*b^3*B^2*c^2*d*x*Log[(e*(a + b*x))/(c + d*x)] - 108*a*A*b^2*B*c*d^2*x*Log[(e*(a + b*x))/(c + d*x)] - 72*a*b^2*B^2*c*d^2*x*Log[(e*(a + b*x))/(c + d*x)] + 108*a^2*A*b*B*d^3*x*Log[(e*(a + b*x))/(c + d*x)] + 42*a^2*b*B^2*d^3*x*Log[(e*(a + b*x))/(c + d*x)] - 18*A*b^3*B*c*d^2*x^2*Log[(e*(a + b*x))/(c + d*x)] - 6*b^3*B^2*c*d^2*x^2*Log[(e*(a + b*x))/(c + d*x)] + 54*a*A*b^2*B*d^3*x^2*Log[(e*(a + b*x))/(c + d*x)] + 6*a*b^2*B^2*d^3*x^2*Log[(e*(a + b*x))/(c + d*x)] + 12*A*b^3*B*d^3*x^3*Log[(e*(a + b*x))/(c + d*x)] + 36*a*b^2*B^2*c^2*d*Log[a/b + x]*Log[(e*(a + b*x))/(c + d*x)] - 108*a^2*b*B^2*c*d^2*Log[a/b + x]*Log[(e*(a + b*x))/(c + d*x)] + 108*a^3*B^2*d^3*Log[a/b + x]*Log[(e*(a + b*x))/(c + d*x)] - 36*b^3*B^2*c^3*Log[c/d + x]*Log[(e*(a + b*x))/(c + d*x)] + 108*a*b^2*B^2*c^2*d*Log[c/d + x]*Log[(e*(a + b*x))/(c + d*x)] - 108*a^2*b*B^2*c*d^2*Log[c/d + x]*Log[(e*(a + b*x))/(c + d*x)] + 18*b^3*B^2*c^3*Log[c/d + x]^2*Log[(e*(a + b*x))/(c + d*x)] - 54*a*b^2*B^2*c^2*d*Log[c/d + x]^2*Log[(e*(a + b*x))/(c + d*x)] + 54*a^2*b*B^2*c*d^2*Log[c/d + x]^2*Log[(e*(a + b*x))/(c + d*x)] + 18*a^2*b*B^2*c*d^2*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] - 42*a^3*B^2*d^3*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + 18*b^3*B^2*c^2*d*x*Log[(e*(a + b*x))/(c + d*x)]^2 - 54*a*b^2*B^2*c*d^2*x*Log[(e*(a + b*x))/(c + d*x)]^2 + 54*a^2*b*B^2*d^3*x*Log[(e*(a + b*x))/(c + d*x)]^2 - 9*b^3*B^2*c*d^2*x^2*Log[(e*(a + b*x))/(c + d*x)]^2 + 27*a*b^2*B^2*d^3*x^2*Log[(e*(a + b*x))/(c + d*x)]^2 + 6*b^3*B^2*d^3*x^3*Log[(e*(a + b*x))/(c + d*x)]^2 - 18*A^2*b^3*c^3*Log[c + d*x] - 30*A*b^3*B*c^3*Log[c + d*x] + 49*b^3*B^2*c^3*Log[c + d*x] + 54*a*A^2*b^2*c^2*d*Log[c + d*x] + 54*a*A*b^2*B*c^2*d*Log[c + d*x] - 111*a*b^2*B^2*c^2*d*Log[c + d*x] - 54*a^2*A^2*b*c*d^2*Log[c + d*x] + 66*a^2*b*B^2*c*d^2*Log[c + d*x] + 18*a^3*A^2*d^3*Log[c + d*x] + 36*A*b^3*B*c^3*Log[a/b + x]*Log[c + d*x] + 30*b^3*B^2*c^3*Log[a/b + x]*Log[c + d*x] - 108*a*A*b^2*B*c^2*d*Log[a/b + x]*Log[c + d*x] - 54*a*b^2*B^2*c^2*d*Log[a/b + x]*Log[c + d*x] + 108*a^2*A*b*B*c*d^2*Log[a/b + x]*Log[c + d*x] - 36*a^3*A*B*d^3*Log[a/b + x]*Log[c + d*x] - 18*b^3*B^2*c^3*Log[a/b + x]^2*Log[c + d*x] + 54*a*b^2*B^2*c^2*d*Log[a/b + x]^2*Log[c + d*x] - 54*a^2*b*B^2*c*d^2*Log[a/b + x]^2*Log[c + d*x] - 36*A*b^3*B*c^3*Log[c/d + x]*Log[c + d*x] - 30*b^3*B^2*c^3*Log[c/d + x]*Log[c + d*x] + 108*a*A*b^2*B*c^2*d*Log[c/d + x]*Log[c + d*x] + 54*a*b^2*B^2*c^2*d*Log[c/d + x]*Log[c + d*x] - 108*a^2*A*b*B*c*d^2*Log[c/d + x]*Log[c + d*x] + 36*a^3*A*B*d^3*Log[c/d + x]*Log[c + d*x] + 36*b^3*B^2*c^3*Log[a/b + x]*Log[c/d + x]*Log[c + d*x] - 108*a*b^2*B^2*c^2*d*Log[a/b + x]*Log[c/d + x]*Log[c + d*x] + 108*a^2*b*B^2*c*d^2*Log[a/b + x]*Log[c/d + x]*Log[c + d*x] - 18*b^3*B^2*c^3*Log[c/d + x]^2*Log[c + d*x] + 54*a*b^2*B^2*c^2*d*Log[c/d + x]^2*Log[c + d*x] - 54*a^2*b*B^2*c*d^2*Log[c/d + x]^2*Log[c + d*x] - 36*A*b^3*B*c^3*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] - 30*b^3*B^2*c^3*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] + 108*a*A*b^2*B*c^2*d*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] + 54*a*b^2*B^2*c^2*d*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] - 108*a^2*A*b*B*c*d^2*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] + 36*a^3*A*B*d^3*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] + 36*b^3*B^2*c^3*Log[a/b + x]*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] - 108*a*b^2*B^2*c^2*d*Log[a/b + x]*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] + 108*a^2*b*B^2*c*d^2*Log[a/b + x]*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] - 36*b^3*B^2*c^3*Log[c/d + x]*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] + 108*a*b^2*B^2*c^2*d*Log[c/d + x]*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] - 108*a^2*b*B^2*c*d^2*Log[c/d + x]*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] - 18*b^3*B^2*c^3*Log[(e*(a + b*x))/(c + d*x)]^2*Log[c + d*x] + 54*a*b^2*B^2*c^2*d*Log[(e*(a + b*x))/(c + d*x)]^2*Log[c + d*x] - 54*a^2*b*B^2*c*d^2*Log[(e*(a + b*x))/(c + d*x)]^2*Log[c + d*x] - 36*A*b^3*B*c^3*Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] - 66*b^3*B^2*c^3*Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + 108*a*A*b^2*B*c^2*d*Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + 198*a*b^2*B^2*c^2*d*Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] - 108*a^2*A*b*B*c*d^2*Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] - 198*a^2*b*B^2*c*d^2*Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + 36*a^3*A*B*d^3*Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + 66*a^3*B^2*d^3*Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + 18*b^3*B^2*c^3*Log[a/b + x]^2*Log[(b*(c + d*x))/(b*c - a*d)] - 54*a*b^2*B^2*c^2*d*Log[a/b + x]^2*Log[(b*(c + d*x))/(b*c - a*d)] + 54*a^2*b*B^2*c*d^2*Log[a/b + x]^2*Log[(b*(c + d*x))/(b*c - a*d)] - 36*b^3*B^2*c^3*Log[a/b + x]*Log[c/d + x]*Log[(b*(c + d*x))/(b*c - a*d)] + 108*a*b^2*B^2*c^2*d*Log[a/b + x]*Log[c/d + x]*Log[(b*(c + d*x))/(b*c - a*d)] - 108*a^2*b*B^2*c*d^2*Log[a/b + x]*Log[c/d + x]*Log[(b*(c + d*x))/(b*c - a*d)] - 36*b^3*B^2*c^3*Log[a/b + x]*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*(c + d*x))/(b*c - a*d)] + 108*a*b^2*B^2*c^2*d*Log[a/b + x]*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*(c + d*x))/(b*c - a*d)] - 108*a^2*b*B^2*c*d^2*Log[a/b + x]*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*(c + d*x))/(b*c - a*d)] - 18*a^3*B^2*d^3*Log[(e*(a + b*x))/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - 6*B*((6*A + 11*B)*(b*c - a*d)^3 + 6*b*B*c*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2)*Log[c/d + x] + 6*b*B*c*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2)*Log[(e*(a + b*x))/(c + d*x)])*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] - 36*a^3*B^2*d^3*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 36*b^3*B^2*c^3*Log[c/d + x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 108*a*b^2*B^2*c^2*d*Log[c/d + x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 108*a^2*b*B^2*c*d^2*Log[c/d + x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 36*b^3*B^2*c^3*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)] - 108*a*b^2*B^2*c^2*d*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)] + 108*a^2*b*B^2*c*d^2*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)] + 36*a^3*B^2*d^3*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] + 36*b^3*B^2*c^3*PolyLog[3, (b*(c + d*x))/(b*c - a*d)] - 108*a*b^2*B^2*c^2*d*PolyLog[3, (b*(c + d*x))/(b*c - a*d)] + 108*a^2*b*B^2*c*d^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)]))/(18*d^4*i)","B",1
85,1,1514,536,1.7348129,"\int \frac{(a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{c i+d i x} \, dx","Integrate[((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(c*i + d*i*x),x]","\frac{g^2 \left(b^2 d^2 x^2 A^2-2 b d (b c-2 a d) x A^2+2 (b c-a d)^2 \log (c+d x) A^2+2 B \left(-2 c^2 b^2-c^2 \log ^2\left(\frac{c}{d}+x\right) b^2-c d x b^2+2 c^2 \log \left(\frac{c}{d}+x\right) b^2+d^2 x^2 \log \left(\frac{e (a+b x)}{c+d x}\right) b^2-2 c d x \log \left(\frac{e (a+b x)}{c+d x}\right) b^2+c^2 \log (c+d x) b^2+2 c^2 \log \left(\frac{c}{d}+x\right) \log (c+d x) b^2+2 c^2 \log \left(\frac{e (a+b x)}{c+d x}\right) \log (c+d x) b^2+2 c^2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right) b^2+2 a c d b+a d^2 x b-2 c \log \left(\frac{a}{b}+x\right) \left(a d+b c \log (c+d x)-b c \log \left(\frac{b (c+d x)}{b c-a d}\right)\right) b-a^2 d^2 \log (a+b x)\right) A-2 a^2 B d^2 \left(\log ^2\left(\frac{c}{d}+x\right)+2 \left(\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)-\log \left(\frac{e (a+b x)}{c+d x}\right)\right) \log (c+d x)-2 \left(\log \left(\frac{a}{b}+x\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)+\text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)\right) A-4 a B d \left(-b c \log ^2\left(\frac{c}{d}+x\right)-2 d (a+b x) \left(\log \left(\frac{a}{b}+x\right)-1\right)+2 b (c+d x) \left(\log \left(\frac{c}{d}+x\right)-1\right)+2 b \left(\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)-\log \left(\frac{e (a+b x)}{c+d x}\right)\right) (d x-c \log (c+d x))+2 b c \left(\log \left(\frac{a}{b}+x\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)+\text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)\right) A+4 a B^2 d \left(d (a+b x) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)+b c \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)-(b c-a d) \left(\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{e (a+b x)}{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)\right)+2 b c \left(\log \left(\frac{e (a+b x)}{c+d x}\right) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)-\text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right)\right)+B^2 \left(-2 b^2 \log ^2\left(\frac{e (a+b x)}{c+d x}\right) \log \left(\frac{b c-a d}{b c+b d x}\right) c^2-2 b^2 \log \left(\frac{e (a+b x)}{c+d x}\right) \log \left(\frac{b c-a d}{b c+b d x}\right) c^2+b^2 \left(\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)+\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)\right) c^2-4 b^2 \left(\log \left(\frac{e (a+b x)}{c+d x}\right) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)-\text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right) c^2-2 b d (a+b x) \log ^2\left(\frac{e (a+b x)}{c+d x}\right) c+2 b (b c-a d) \left(\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{e (a+b x)}{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)\right) c+b^2 d^2 x^2 \log ^2\left(\frac{e (a+b x)}{c+d x}\right)+2 d (a d-b c) (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 a^2 d^2 \log (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)+2 (b c-a d)^2 \log (c+d x)+a^2 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)\right)-2 a^2 B^2 d^2 \left(\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 \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)-2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right)\right)}{2 d^3 i}","\frac{b^2 g^2 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 d^3 i}-\frac{2 B g^2 (b c-a d)^2 \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)}{d^3 i}-\frac{g^2 (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\right)^2}{d^3 i}-\frac{4 B g^2 (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\right)}{d^3 i}+\frac{B g^2 (b c-a d)^2 \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)}{d^3 i}-\frac{2 g^2 (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{d^2 i}-\frac{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)}{d^2 i}-\frac{4 B^2 g^2 (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^3 i}-\frac{B^2 g^2 (b c-a d)^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{d^3 i}+\frac{2 B^2 g^2 (b c-a d)^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^3 i}+\frac{B^2 g^2 (b c-a d)^2 \log (c+d x)}{d^3 i}",1,"(g^2*(-2*A^2*b*d*(b*c - 2*a*d)*x + A^2*b^2*d^2*x^2 + 2*A^2*(b*c - a*d)^2*Log[c + d*x] + 2*A*B*(-2*b^2*c^2 + 2*a*b*c*d - b^2*c*d*x + a*b*d^2*x + 2*b^2*c^2*Log[c/d + x] - b^2*c^2*Log[c/d + x]^2 - a^2*d^2*Log[a + b*x] - 2*b^2*c*d*x*Log[(e*(a + b*x))/(c + d*x)] + b^2*d^2*x^2*Log[(e*(a + b*x))/(c + d*x)] + b^2*c^2*Log[c + d*x] + 2*b^2*c^2*Log[c/d + x]*Log[c + d*x] + 2*b^2*c^2*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] - 2*b*c*Log[a/b + x]*(a*d + b*c*Log[c + d*x] - b*c*Log[(b*(c + d*x))/(b*c - a*d)]) + 2*b^2*c^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - 2*a^2*A*B*d^2*(Log[c/d + x]^2 + 2*(Log[a/b + x] - Log[c/d + x] - Log[(e*(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)])) - 4*a*A*B*d*(-2*d*(a + b*x)*(-1 + Log[a/b + x]) + 2*b*(c + d*x)*(-1 + Log[c/d + x]) - b*c*Log[c/d + x]^2 + 2*b*(Log[a/b + x] - Log[c/d + x] - Log[(e*(a + b*x))/(c + d*x)])*(d*x - c*Log[c + d*x]) + 2*b*c*(Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])) + 4*a*B^2*d*(d*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)]^2 + b*c*Log[(e*(a + b*x))/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - (b*c - a*d)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*Log[(e*(a + b*x))/(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*b*c*(Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])) + B^2*(2*d*(-(b*c) + a*d)*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)] - 2*a^2*d^2*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + b^2*d^2*x^2*Log[(e*(a + b*x))/(c + d*x)]^2 - 2*b*c*d*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)]^2 + 2*(b*c - a*d)^2*Log[c + d*x] - 2*b^2*c^2*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 2*b^2*c^2*Log[(e*(a + b*x))/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + a^2*d^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*c^2*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 2*b*c*(b*c - a*d)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*Log[(e*(a + b*x))/(c + d*x)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) - 4*b^2*c^2*(Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])) - 2*a^2*B^2*d^2*(Log[(e*(a + b*x))/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])))/(2*d^3*i)","B",1
86,1,646,283,0.7213219,"\int \frac{(a g+b g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{c i+d i x} \, dx","Integrate[((a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(c*i + d*i*x),x]","-\frac{g \left(A^2 (b c-a d) \log (c+d x)+a A B d \left(2 \log (c+d x) \left(-\log \left(\frac{e (a+b x)}{c+d x}\right)+\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)\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)+\log ^2\left(\frac{c}{d}+x\right)\right)+A B \left(2 b (d x-c \log (c+d x)) \left(-\log \left(\frac{e (a+b x)}{c+d x}\right)+\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)\right)+2 b c \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 d (a+b x) \left(\log \left(\frac{a}{b}+x\right)-1\right)-b c \log ^2\left(\frac{c}{d}+x\right)+2 b (c+d x) \left(\log \left(\frac{c}{d}+x\right)-1\right)\right)-B^2 \left(-(b c-a d) \left(\log \left(\frac{b c-a d}{b c+b d x}\right) \left(-2 \log \left(\frac{e (a+b x)}{c+d x}\right)+2 \log \left(\frac{d (a+b x)}{a d-b c}\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)\right)+2 b c \left(\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)-\text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right)+d (a+b x) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)+b c \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)\right)+a B^2 d \left(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)+\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 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right)+A^2 (-b) d x\right)}{d^2 i}","\frac{2 B g (b c-a d) \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)}{d^2 i}+\frac{2 B g (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)}{d^2 i}+\frac{g (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)^2}{d^2 i}+\frac{g (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{d i}+\frac{2 B^2 g (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^2 i}-\frac{2 B^2 g (b c-a d) \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^2 i}",1,"-((g*(-(A^2*b*d*x) + A^2*(b*c - a*d)*Log[c + d*x] + a*A*B*d*(Log[c/d + x]^2 + 2*(Log[a/b + x] - Log[c/d + x] - Log[(e*(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)])) + A*B*(-2*d*(a + b*x)*(-1 + Log[a/b + x]) + 2*b*(c + d*x)*(-1 + Log[c/d + x]) - b*c*Log[c/d + x]^2 + 2*b*(Log[a/b + x] - Log[c/d + x] - Log[(e*(a + b*x))/(c + d*x)])*(d*x - c*Log[c + d*x]) + 2*b*c*(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*(d*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)]^2 + b*c*Log[(e*(a + b*x))/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - (b*c - a*d)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*Log[(e*(a + b*x))/(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*b*c*(Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])) + a*B^2*d*(Log[(e*(a + b*x))/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])))/(d^2*i))","B",1
87,1,251,127,0.2568824,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{c i+d i x} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(c*i + d*i*x),x]","\frac{2 A B \log (c+d x) \log \left(\frac{e (a+b x)}{c+d x}\right)+2 A B \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)-2 A B \log \left(\frac{a}{b}+x\right) \log (c+d x)+2 A B \log \left(\frac{a}{b}+x\right) \log \left(\frac{b (c+d x)}{b c-a d}\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 (a+b x)}{b (c+d x)}\right)+A^2 \log (c+d x)-A B \log ^2\left(\frac{c}{d}+x\right)+2 A B \log \left(\frac{c}{d}+x\right) \log (c+d x)}{d i}","-\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)}{d i}-\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}{d i}+\frac{2 B^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d i}",1,"(-(A*B*Log[c/d + x]^2) + A^2*Log[c + d*x] - 2*A*B*Log[a/b + x]*Log[c + d*x] + 2*A*B*Log[c/d + x]*Log[c + d*x] + 2*A*B*Log[(e*(a + b*x))/(c + d*x)]*Log[c + d*x] + 2*A*B*Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] - B^2*Log[(e*(a + b*x))/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*A*B*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] - 2*B^2*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] + 2*B^2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])/(d*i)","A",1
88,1,79,44,0.3699032,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x) (c i+d i x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/((a*g + b*g*x)*(c*i + d*i*x)),x]","\frac{3 A^2 \log \left(\frac{e (a+b x)}{c+d x}\right)+3 A B \log ^2\left(\frac{e (a+b x)}{c+d x}\right)+B^2 \log ^3\left(\frac{e (a+b x)}{c+d x}\right)}{3 b c g i-3 a d g i}","\frac{\left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^3}{3 B g i (b c-a d)}",1,"(3*A^2*Log[(e*(a + b*x))/(c + d*x)] + 3*A*B*Log[(e*(a + b*x))/(c + d*x)]^2 + B^2*Log[(e*(a + b*x))/(c + d*x)]^3)/(3*b*c*g*i - 3*a*d*g*i)","A",1
89,1,186,183,0.6709869,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^2 (c i+d i x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/((a*g + b*g*x)^2*(c*i + d*i*x)),x]","-\frac{3 \left(A^2+2 A B+2 B^2\right) (-d (a+b x) \log (c+d x)-a d+b c)+3 d \left(A^2+2 A B+2 B^2\right) (a+b x) \log (a+b x)+3 B (a A d+A b d x+b B (c+d x)) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)+6 B (A+B) (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)+B^2 d (a+b x) \log ^3\left(\frac{e (a+b x)}{c+d x}\right)}{3 g^2 i (a+b x) (b c-a d)^2}","-\frac{d \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^3}{3 B g^2 i (b c-a d)^2}-\frac{b (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^2 i (a+b x) (b c-a d)^2}-\frac{2 b B (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^2 i (a+b x) (b c-a d)^2}-\frac{2 b B^2 (c+d x)}{g^2 i (a+b x) (b c-a d)^2}",1,"-1/3*(3*(A^2 + 2*A*B + 2*B^2)*d*(a + b*x)*Log[a + b*x] + 6*B*(A + B)*(b*c - a*d)*Log[(e*(a + b*x))/(c + d*x)] + 3*B*(a*A*d + A*b*d*x + b*B*(c + d*x))*Log[(e*(a + b*x))/(c + d*x)]^2 + B^2*d*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)]^3 + 3*(A^2 + 2*A*B + 2*B^2)*(b*c - a*d - d*(a + b*x)*Log[c + d*x]))/((b*c - a*d)^2*g^2*i*(a + b*x))","A",1
90,1,318,343,1.1108681,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^3 (c i+d i x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/((a*g + b*g*x)^3*(c*i + d*i*x)),x]","\frac{-6 B \left(-2 a^2 A d^2-4 a b d (A d x+B (c+d x))+b^2 \left(B \left(c^2-2 c d x-3 d^2 x^2\right)-2 A d^2 x^2\right)\right) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)-6 d^2 \left(2 A^2+6 A B+7 B^2\right) (a+b x)^2 \log (c+d x)+6 d \left(2 A^2+6 A B+7 B^2\right) (a+b x) (b c-a d)-3 \left(2 A^2+2 A B+B^2\right) (b c-a d)^2+6 d^2 \left(2 A^2+6 A B+7 B^2\right) (a+b x)^2 \log (a+b x)-6 B (b c-a d) (-6 a A d-7 a B d+2 A b (c-2 d x)+b B (c-6 d x)) \log \left(\frac{e (a+b x)}{c+d x}\right)+4 B^2 d^2 (a+b x)^2 \log ^3\left(\frac{e (a+b x)}{c+d x}\right)}{12 g^3 i (a+b x)^2 (b c-a d)^3}","-\frac{b^2 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 g^3 i (a+b x)^2 (b c-a d)^3}-\frac{b^2 B (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^3 i (a+b x)^2 (b c-a d)^3}+\frac{d^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^3}{3 B g^3 i (b c-a d)^3}+\frac{2 b d (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^3 i (a+b x) (b c-a d)^3}+\frac{4 b B d (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^3 i (a+b x) (b c-a d)^3}-\frac{b^2 B^2 (c+d x)^2}{4 g^3 i (a+b x)^2 (b c-a d)^3}+\frac{4 b B^2 d (c+d x)}{g^3 i (a+b x) (b c-a d)^3}",1,"(-3*(2*A^2 + 2*A*B + B^2)*(b*c - a*d)^2 + 6*(2*A^2 + 6*A*B + 7*B^2)*d*(b*c - a*d)*(a + b*x) + 6*(2*A^2 + 6*A*B + 7*B^2)*d^2*(a + b*x)^2*Log[a + b*x] - 6*B*(b*c - a*d)*(-6*a*A*d - 7*a*B*d + b*B*(c - 6*d*x) + 2*A*b*(c - 2*d*x))*Log[(e*(a + b*x))/(c + d*x)] - 6*B*(-2*a^2*A*d^2 - 4*a*b*d*(A*d*x + B*(c + d*x)) + b^2*(-2*A*d^2*x^2 + B*(c^2 - 2*c*d*x - 3*d^2*x^2)))*Log[(e*(a + b*x))/(c + d*x)]^2 + 4*B^2*d^2*(a + b*x)^2*Log[(e*(a + b*x))/(c + d*x)]^3 - 6*(2*A^2 + 6*A*B + 7*B^2)*d^2*(a + b*x)^2*Log[c + d*x])/(12*(b*c - a*d)^3*g^3*i*(a + b*x)^2)","A",1
91,1,442,507,1.4576807,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^4 (c i+d i x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/((a*g + b*g*x)^4*(c*i + d*i*x)),x]","-\frac{18 B \left(6 a^3 A d^3+18 a^2 b d^2 (A d x+B (c+d x))+9 a b^2 d \left(2 A d^2 x^2+B \left(-c^2+2 c d x+3 d^2 x^2\right)\right)+b^3 \left(6 A d^3 x^3+B \left(2 c^3-3 c^2 d x+6 c d^2 x^2+11 d^3 x^3\right)\right)\right) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)-6 d^3 \left(18 A^2+66 A B+85 B^2\right) (a+b x)^3 \log (c+d x)-6 d^2 \left(18 A^2+66 A B+85 B^2\right) (a+b x)^2 (a d-b c)-3 d \left(18 A^2+30 A B+19 B^2\right) (a+b x) (b c-a d)^2+4 \left(9 A^2+6 A B+2 B^2\right) (b c-a d)^3+6 d^3 \left(18 A^2+66 A B+85 B^2\right) (a+b x)^3 \log (a+b x)+6 B (b c-a d) \left(3 d (6 A+5 B) (a+b x) (a d-b c)+4 (3 A+B) (b c-a d)^2+6 d^2 (6 A+11 B) (a+b x)^2\right) \log \left(\frac{e (a+b x)}{c+d x}\right)+36 B^2 d^3 (a+b x)^3 \log ^3\left(\frac{e (a+b x)}{c+d x}\right)}{108 g^4 i (a+b x)^3 (b c-a d)^4}","-\frac{b^3 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 g^4 i (a+b x)^3 (b c-a d)^4}-\frac{2 b^3 B (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{9 g^4 i (a+b x)^3 (b c-a d)^4}+\frac{3 b^2 d (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 g^4 i (a+b x)^2 (b c-a d)^4}+\frac{3 b^2 B d (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^4 i (a+b x)^2 (b c-a d)^4}-\frac{d^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^3}{3 B g^4 i (b c-a d)^4}-\frac{3 b d^2 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^4 i (a+b x) (b c-a d)^4}-\frac{6 b B d^2 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^4 i (a+b x) (b c-a d)^4}-\frac{2 b^3 B^2 (c+d x)^3}{27 g^4 i (a+b x)^3 (b c-a d)^4}+\frac{3 b^2 B^2 d (c+d x)^2}{4 g^4 i (a+b x)^2 (b c-a d)^4}-\frac{6 b B^2 d^2 (c+d x)}{g^4 i (a+b x) (b c-a d)^4}",1,"-1/108*(4*(9*A^2 + 6*A*B + 2*B^2)*(b*c - a*d)^3 - 3*(18*A^2 + 30*A*B + 19*B^2)*d*(b*c - a*d)^2*(a + b*x) - 6*(18*A^2 + 66*A*B + 85*B^2)*d^2*(-(b*c) + a*d)*(a + b*x)^2 + 6*(18*A^2 + 66*A*B + 85*B^2)*d^3*(a + b*x)^3*Log[a + b*x] + 6*B*(b*c - a*d)*(4*(3*A + B)*(b*c - a*d)^2 + 3*(6*A + 5*B)*d*(-(b*c) + a*d)*(a + b*x) + 6*(6*A + 11*B)*d^2*(a + b*x)^2)*Log[(e*(a + b*x))/(c + d*x)] + 18*B*(6*a^3*A*d^3 + 18*a^2*b*d^2*(A*d*x + B*(c + d*x)) + 9*a*b^2*d*(2*A*d^2*x^2 + B*(-c^2 + 2*c*d*x + 3*d^2*x^2)) + b^3*(6*A*d^3*x^3 + B*(2*c^3 - 3*c^2*d*x + 6*c*d^2*x^2 + 11*d^3*x^3)))*Log[(e*(a + b*x))/(c + d*x)]^2 + 36*B^2*d^3*(a + b*x)^3*Log[(e*(a + b*x))/(c + d*x)]^3 - 6*(18*A^2 + 66*A*B + 85*B^2)*d^3*(a + b*x)^3*Log[c + d*x])/((b*c - a*d)^4*g^4*i*(a + b*x)^3)","A",1
92,1,5193,722,7.4149123,"\int \frac{(a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(c i+d i x)^2} \, dx","Integrate[((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(c*i + d*i*x)^2,x]","\text{Result too large to show}","\frac{b^3 g^3 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 d^4 i^2}-\frac{6 b B g^3 (b c-a d)^2 \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)}{d^4 i^2}-\frac{3 b g^3 (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\right)^2}{d^4 i^2}-\frac{6 b B g^3 (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\right)}{d^4 i^2}+\frac{b B g^3 (b c-a d)^2 \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)}{d^4 i^2}-\frac{3 b g^3 (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{d^3 i^2}-\frac{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)^2}{d^3 i^2 (c+d x)}-\frac{b B g^3 (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{d^3 i^2}+\frac{2 A B g^3 (a+b x) (b c-a d)^2}{d^3 i^2 (c+d x)}-\frac{6 b B^2 g^3 (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i^2}-\frac{b B^2 g^3 (b c-a d)^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{d^4 i^2}+\frac{6 b B^2 g^3 (b c-a d)^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i^2}+\frac{b B^2 g^3 (b c-a d)^2 \log (c+d x)}{d^4 i^2}+\frac{2 B^2 g^3 (a+b x) (b c-a d)^2 \log \left(\frac{e (a+b x)}{c+d x}\right)}{d^3 i^2 (c+d x)}-\frac{2 B^2 g^3 (a+b x) (b c-a d)^2}{d^3 i^2 (c+d x)}",1,"Result too large to show","B",1
93,1,1969,469,4.2077849,"\int \frac{(a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(c i+d i x)^2} \, dx","Integrate[((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(c*i + d*i*x)^2,x]","\frac{g^2 \left(b^2 d x A^2+2 b (a d-b c) \log (c+d x) A^2-\frac{(b c-a d)^2 A^2}{c+d x}+\frac{2 a^2 B d^2 \left(b c-b \log \left(\frac{b (c+d x)}{b c-a d}\right) c-a d+b (c+d x) \log \left(\frac{a}{b}+x\right)+(a d-b c) \log \left(\frac{e (a+b x)}{c+d x}\right)-b d x \log \left(\frac{b (c+d x)}{b c-a d}\right)\right) A}{(b c-a d) (c+d x)}+2 a b B d \left(-\log ^2\left(\frac{c}{d}+x\right)+2 \log (c+d x) \log \left(\frac{c}{d}+x\right)+2 \left(\frac{b \log (a+b x) c}{a d-b c}+\frac{b \log (c+d x) c}{b c-a d}-\frac{c}{c+d x}-\log \left(\frac{a}{b}+x\right) \log (c+d x)+\log \left(\frac{e (a+b x)}{c+d x}\right) \left(\frac{c}{c+d x}+\log (c+d x)\right)+\log \left(\frac{a}{b}+x\right) \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) A+2 b^2 B \left(-\frac{\log \left(\frac{a}{b}+x\right) c^2}{c+d x}+\frac{\left(\log \left(\frac{c}{d}+x\right)+1\right) c^2}{c+d x}+\frac{b (\log (a+b x)-\log (c+d x)) c^2}{b c-a d}+\log ^2\left(\frac{c}{d}+x\right) c-2 \left(\log \left(\frac{a}{b}+x\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)+\text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right) c+d \left(\frac{a}{b}+x\right) \left(\log \left(\frac{a}{b}+x\right)-1\right)-(c+d x) \left(\log \left(\frac{c}{d}+x\right)-1\right)+\left(-\log \left(\frac{a}{b}+x\right)+\log \left(\frac{c}{d}+x\right)+\log \left(\frac{e (a+b x)}{c+d x}\right)\right) \left(-\frac{c^2}{c+d x}-2 \log (c+d x) c+d x\right)\right) A-\frac{a^2 B^2 d^2 \left((b c-a d) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)-2 (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 b (c+d x) \log (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 b (c+d x) \log \left(\frac{b c-a d}{b c+b d x}\right) \log \left(\frac{e (a+b x)}{c+d x}\right)+2 b c-2 a d+2 b (c+d x) \log (a+b x)-2 b (c+d x) \log (c+d x)+b (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 (c+d x) \left(\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)+\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)\right)\right)}{(b c-a d) (c+d x)}+b^2 B^2 \left(-\frac{\log ^2\left(\frac{e (a+b x)}{c+d x}\right) c^2}{c+d x}-\frac{\left(2 b c-2 a d+2 b (c+d x) \log (a+b x)-2 (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 b (c+d x) \log (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 b (c+d x) \log (c+d x)-2 b (c+d x) \log \left(\frac{e (a+b x)}{c+d x}\right) \log \left(\frac{b c-a d}{b c+b d x}\right)+b (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 (c+d x) \left(\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)+\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)\right)\right) c^2}{(b c-a d) (c+d x)}+2 \log ^2\left(\frac{e (a+b x)}{c+d x}\right) \log \left(\frac{b c-a d}{b c+b d x}\right) c+4 \left(\log \left(\frac{e (a+b x)}{c+d x}\right) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)-\text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right) c+\frac{d (a+b x) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)}{b}-\frac{(b c-a d) \left(\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{e (a+b x)}{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)\right)}{b}\right)+2 a b B^2 d \left(-\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)+\frac{c \log ^2\left(\frac{e (a+b x)}{c+d x}\right)}{c+d x}-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)+\frac{c \left(2 b c-2 a d+2 b (c+d x) \log (a+b x)-2 (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 b (c+d x) \log (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 b (c+d x) \log (c+d x)-2 b (c+d x) \log \left(\frac{e (a+b x)}{c+d x}\right) \log \left(\frac{b c-a d}{b c+b d x}\right)+b (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 (c+d x) \left(\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)+\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)\right)\right)}{(b c-a d) (c+d x)}+2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right)\right)}{d^3 i^2}","\frac{4 b B g^2 (b c-a d) \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)}{d^3 i^2}+\frac{2 b g^2 (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)^2}{d^3 i^2}+\frac{2 b B g^2 (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)}{d^3 i^2}+\frac{b g^2 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{d^2 i^2}+\frac{g^2 (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{d^2 i^2 (c+d x)}-\frac{2 A B g^2 (a+b x) (b c-a d)}{d^2 i^2 (c+d x)}+\frac{2 b B^2 g^2 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^3 i^2}-\frac{4 b B^2 g^2 (b c-a d) \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^3 i^2}-\frac{2 B^2 g^2 (a+b x) (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)}{d^2 i^2 (c+d x)}+\frac{2 B^2 g^2 (a+b x) (b c-a d)}{d^2 i^2 (c+d x)}",1,"(g^2*(A^2*b^2*d*x - (A^2*(b*c - a*d)^2)/(c + d*x) + 2*A^2*b*(-(b*c) + a*d)*Log[c + d*x] + (2*a^2*A*B*d^2*(b*c - a*d + b*(c + d*x)*Log[a/b + x] + (-(b*c) + a*d)*Log[(e*(a + b*x))/(c + d*x)] - b*c*Log[(b*(c + d*x))/(b*c - a*d)] - b*d*x*Log[(b*(c + d*x))/(b*c - a*d)]))/((b*c - a*d)*(c + d*x)) + 2*a*A*b*B*d*(-Log[c/d + x]^2 + 2*Log[c/d + x]*Log[c + d*x] + 2*(-(c/(c + d*x)) + (b*c*Log[a + b*x])/(-(b*c) + a*d) + (b*c*Log[c + d*x])/(b*c - a*d) - Log[a/b + x]*Log[c + d*x] + Log[(e*(a + b*x))/(c + d*x)]*(c/(c + d*x) + Log[c + d*x]) + 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*A*b^2*B*(d*(a/b + x)*(-1 + Log[a/b + x]) - (c^2*Log[a/b + x])/(c + d*x) - (c + d*x)*(-1 + Log[c/d + x]) + c*Log[c/d + x]^2 + (c^2*(1 + Log[c/d + x]))/(c + d*x) + (b*c^2*(Log[a + b*x] - Log[c + d*x]))/(b*c - a*d) + (-Log[a/b + x] + Log[c/d + x] + Log[(e*(a + b*x))/(c + d*x)])*(d*x - c^2/(c + d*x) - 2*c*Log[c + d*x]) - 2*c*(Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])) - (a^2*B^2*d^2*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(e*(a + b*x))/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + (b*c - a*d)*Log[(e*(a + b*x))/(c + d*x)]^2 - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(c + d*x)) + b^2*B^2*((d*(a + b*x)*Log[(e*(a + b*x))/(c + d*x)]^2)/b - (c^2*Log[(e*(a + b*x))/(c + d*x)]^2)/(c + d*x) + 2*c*Log[(e*(a + b*x))/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - (c^2*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(e*(a + b*x))/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(c + d*x)) - ((b*c - a*d)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*Log[(e*(a + b*x))/(c + d*x)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]))/b + 4*c*(Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])) + 2*a*b*B^2*d*((c*Log[(e*(a + b*x))/(c + d*x)]^2)/(c + d*x) - Log[(e*(a + b*x))/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - 2*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] + (c*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(e*(a + b*x))/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(c + d*x)) + 2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])))/(d^3*i^2)","B",1
94,1,1107,261,1.708194,"\int \frac{(a g+b g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(c i+d i x)^2} \, dx","Integrate[((a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(c*i + d*i*x)^2,x]","\frac{g \left(b \log (c+d x) A^2+\frac{(b c-a d) A^2}{c+d x}+\frac{2 a B d \left(b c-b \log \left(\frac{b (c+d x)}{b c-a d}\right) c-a d+b (c+d x) \log \left(\frac{a}{b}+x\right)+(a d-b c) \log \left(\frac{e (a+b x)}{c+d x}\right)-b d x \log \left(\frac{b (c+d x)}{b c-a d}\right)\right) A}{(b c-a d) (c+d x)}+b B \left(-\log ^2\left(\frac{c}{d}+x\right)+2 \log (c+d x) \log \left(\frac{c}{d}+x\right)+2 \left(\frac{b \log (a+b x) c}{a d-b c}+\frac{b \log (c+d x) c}{b c-a d}-\frac{c}{c+d x}-\log \left(\frac{a}{b}+x\right) \log (c+d x)+\log \left(\frac{e (a+b x)}{c+d x}\right) \left(\frac{c}{c+d x}+\log (c+d x)\right)+\log \left(\frac{a}{b}+x\right) \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) A-\frac{a B^2 d \left((b c-a d) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)-2 (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 b (c+d x) \log (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 b (c+d x) \log \left(\frac{b c-a d}{b c+b d x}\right) \log \left(\frac{e (a+b x)}{c+d x}\right)+2 b c-2 a d+2 b (c+d x) \log (a+b x)-2 b (c+d x) \log (c+d x)+b (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 (c+d x) \left(\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)+\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)\right)\right)}{(b c-a d) (c+d x)}+b B^2 \left(-\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)+\frac{c \log ^2\left(\frac{e (a+b x)}{c+d x}\right)}{c+d x}-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)+\frac{c \left(2 b c-2 a d+2 b (c+d x) \log (a+b x)-2 (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 b (c+d x) \log (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 b (c+d x) \log (c+d x)-2 b (c+d x) \log \left(\frac{e (a+b x)}{c+d x}\right) \log \left(\frac{b c-a d}{b c+b d x}\right)+b (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 (c+d x) \left(\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)+\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)\right)\right)}{(b c-a d) (c+d x)}+2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right)\right)}{d^2 i^2}","-\frac{2 b B g \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)}{d^2 i^2}-\frac{b g \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}{d^2 i^2}-\frac{g (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{d i^2 (c+d x)}+\frac{2 A B g (a+b x)}{d i^2 (c+d x)}+\frac{2 b B^2 g \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^2 i^2}+\frac{2 B^2 g (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{d i^2 (c+d x)}-\frac{2 B^2 g (a+b x)}{d i^2 (c+d x)}",1,"(g*((A^2*(b*c - a*d))/(c + d*x) + A^2*b*Log[c + d*x] + (2*a*A*B*d*(b*c - a*d + b*(c + d*x)*Log[a/b + x] + (-(b*c) + a*d)*Log[(e*(a + b*x))/(c + d*x)] - b*c*Log[(b*(c + d*x))/(b*c - a*d)] - b*d*x*Log[(b*(c + d*x))/(b*c - a*d)]))/((b*c - a*d)*(c + d*x)) + A*b*B*(-Log[c/d + x]^2 + 2*Log[c/d + x]*Log[c + d*x] + 2*(-(c/(c + d*x)) + (b*c*Log[a + b*x])/(-(b*c) + a*d) + (b*c*Log[c + d*x])/(b*c - a*d) - Log[a/b + x]*Log[c + d*x] + Log[(e*(a + b*x))/(c + d*x)]*(c/(c + d*x) + Log[c + d*x]) + Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)]) + 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - (a*B^2*d*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(e*(a + b*x))/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + (b*c - a*d)*Log[(e*(a + b*x))/(c + d*x)]^2 - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(c + d*x)) + b*B^2*((c*Log[(e*(a + b*x))/(c + d*x)]^2)/(c + d*x) - Log[(e*(a + b*x))/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - 2*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] + (c*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(e*(a + b*x))/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(c + d*x)) + 2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])))/(d^2*i^2)","B",1
95,1,315,152,0.4884509,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(c i+d i x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(c*i + d*i*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 b (c+d x) \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-2 b (c+d x) \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-b B (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 (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 (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(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{d i^2 (c+d x)}","\frac{(a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{i^2 (c+d x) (b c-a d)}-\frac{2 A B (a+b x)}{i^2 (c+d x) (b c-a d)}-\frac{2 B^2 (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{i^2 (c+d x) (b c-a d)}+\frac{2 B^2 (a+b x)}{i^2 (c+d 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*b*(c + d*x)*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 2*b*(c + d*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 2*B*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]) - b*B*(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*(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*i^2*(c + d*x))","C",1
96,1,187,214,0.7419355,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x) (c i+d i x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/((a*g + b*g*x)*(c*i + d*i*x)^2),x]","\frac{3 b \left(A^2-2 A B+2 B^2\right) (c+d x) \log (a+b x)-3 \left(A^2-2 A B+2 B^2\right) (a d+b (c+d x) \log (c+d x)-b c)+3 B (A b (c+d x)-B d (a+b x)) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)+6 B (A-B) (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)+b B^2 (c+d x) \log ^3\left(\frac{e (a+b x)}{c+d x}\right)}{3 g i^2 (c+d x) (b c-a d)^2}","\frac{b \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^3}{3 B g i^2 (b c-a d)^2}-\frac{d (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g i^2 (c+d x) (b c-a d)^2}+\frac{2 A B d (a+b x)}{g i^2 (c+d x) (b c-a d)^2}+\frac{2 B^2 d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{g i^2 (c+d x) (b c-a d)^2}-\frac{2 B^2 d (a+b x)}{g i^2 (c+d x) (b c-a d)^2}",1,"(3*b*(A^2 - 2*A*B + 2*B^2)*(c + d*x)*Log[a + b*x] + 6*(A - B)*B*(b*c - a*d)*Log[(e*(a + b*x))/(c + d*x)] + 3*B*(-(B*d*(a + b*x)) + A*b*(c + d*x))*Log[(e*(a + b*x))/(c + d*x)]^2 + b*B^2*(c + d*x)*Log[(e*(a + b*x))/(c + d*x)]^3 - 3*(A^2 - 2*A*B + 2*B^2)*(-(b*c) + a*d + b*(c + d*x)*Log[c + d*x]))/(3*(b*c - a*d)^2*g*i^2*(c + d*x))","A",1
97,1,307,365,1.1018001,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^2 (c i+d i x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/((a*g + b*g*x)^2*(c*i + d*i*x)^2),x]","-\frac{3 B \left(-a^2 B d^2+2 a b d (A (c+d x)-B d x)+b^2 (2 A d x (c+d x)+B c (c+2 d x))\right) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)-3 d \left(A^2-2 A B+2 B^2\right) (a+b x) (a d-b c)+3 b \left(A^2+2 A B+2 B^2\right) (c+d x) (b c-a d)+6 b d \left(A^2+2 B^2\right) (a+b x) (c+d x) \log (a+b x)-6 b d \left(A^2+2 B^2\right) (a+b x) (c+d x) \log (c+d x)+6 B (b c-a d) (a A d-a B d+A b c+2 A b d x+b B c) \log \left(\frac{e (a+b x)}{c+d x}\right)+2 b B^2 d (a+b x) (c+d x) \log ^3\left(\frac{e (a+b x)}{c+d x}\right)}{3 g^2 i^2 (a+b x) (c+d x) (b c-a d)^3}","-\frac{b^2 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^2 i^2 (a+b x) (b c-a d)^3}-\frac{2 b^2 B (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^2 i^2 (a+b x) (b c-a d)^3}+\frac{d^2 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^2 i^2 (c+d x) (b c-a d)^3}-\frac{2 A B d^2 (a+b x)}{g^2 i^2 (c+d x) (b c-a d)^3}-\frac{2 b d \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^3}{3 B g^2 i^2 (b c-a d)^3}-\frac{2 b^2 B^2 (c+d x)}{g^2 i^2 (a+b x) (b c-a d)^3}-\frac{2 B^2 d^2 (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{g^2 i^2 (c+d x) (b c-a d)^3}+\frac{2 B^2 d^2 (a+b x)}{g^2 i^2 (c+d x) (b c-a d)^3}",1,"-1/3*(-3*(A^2 - 2*A*B + 2*B^2)*d*(-(b*c) + a*d)*(a + b*x) + 3*b*(A^2 + 2*A*B + 2*B^2)*(b*c - a*d)*(c + d*x) + 6*b*(A^2 + 2*B^2)*d*(a + b*x)*(c + d*x)*Log[a + b*x] + 6*B*(b*c - a*d)*(A*b*c + b*B*c + a*A*d - a*B*d + 2*A*b*d*x)*Log[(e*(a + b*x))/(c + d*x)] + 3*B*(-(a^2*B*d^2) + 2*a*b*d*(-(B*d*x) + A*(c + d*x)) + b^2*(2*A*d*x*(c + d*x) + B*c*(c + 2*d*x)))*Log[(e*(a + b*x))/(c + d*x)]^2 + 2*b*B^2*d*(a + b*x)*(c + d*x)*Log[(e*(a + b*x))/(c + d*x)]^3 - 6*b*(A^2 + 2*B^2)*d*(a + b*x)*(c + d*x)*Log[c + d*x])/((b*c - a*d)^3*g^2*i^2*(a + b*x)*(c + d*x))","A",1
98,1,466,523,1.5253993,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^3 (c i+d i x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/((a*g + b*g*x)^3*(c*i + d*i*x)^2),x]","\frac{-2 B \left(2 a^3 B d^3-6 a^2 b d^2 (A (c+d x)-B d x)-6 a b^2 d (2 A d x (c+d x)+B c (c+2 d x))+b^3 \left(B \left(c^3-3 c^2 d x-9 c d^2 x^2-3 d^3 x^3\right)-6 A d^2 x^2 (c+d x)\right)\right) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)+4 d^2 \left(A^2-2 A B+2 B^2\right) (a+b x)^2 (b c-a d)+6 b d^2 \left(2 A^2+2 A B+5 B^2\right) (a+b x)^2 (c+d x) \log (a+b x)-6 b d^2 \left(2 A^2+2 A B+5 B^2\right) (a+b x)^2 (c+d x) \log (c+d x)-b \left(2 A^2+2 A B+B^2\right) (c+d x) (b c-a d)^2+2 b d \left(4 A^2+10 A B+11 B^2\right) (a+b x) (c+d x) (b c-a d)+2 B (b c-a d) \left(2 b d (4 A+5 B) (a+b x) (c+d x)-b (2 A+B) (c+d x) (b c-a d)+4 d^2 (A-B) (a+b x)^2\right) \log \left(\frac{e (a+b x)}{c+d x}\right)+4 b B^2 d^2 (a+b x)^2 (c+d x) \log ^3\left(\frac{e (a+b x)}{c+d x}\right)}{4 g^3 i^2 (a+b x)^2 (c+d x) (b c-a d)^4}","-\frac{b^3 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 g^3 i^2 (a+b x)^2 (b c-a d)^4}-\frac{b^3 B (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^3 i^2 (a+b x)^2 (b c-a d)^4}+\frac{3 b^2 d (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^3 i^2 (a+b x) (b c-a d)^4}+\frac{6 b^2 B d (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^3 i^2 (a+b x) (b c-a d)^4}-\frac{d^3 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^3 i^2 (c+d x) (b c-a d)^4}+\frac{2 A B d^3 (a+b x)}{g^3 i^2 (c+d x) (b c-a d)^4}+\frac{b d^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^3}{B g^3 i^2 (b c-a d)^4}-\frac{b^3 B^2 (c+d x)^2}{4 g^3 i^2 (a+b x)^2 (b c-a d)^4}+\frac{6 b^2 B^2 d (c+d x)}{g^3 i^2 (a+b x) (b c-a d)^4}+\frac{2 B^2 d^3 (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{g^3 i^2 (c+d x) (b c-a d)^4}-\frac{2 B^2 d^3 (a+b x)}{g^3 i^2 (c+d x) (b c-a d)^4}",1,"(4*(A^2 - 2*A*B + 2*B^2)*d^2*(b*c - a*d)*(a + b*x)^2 - b*(2*A^2 + 2*A*B + B^2)*(b*c - a*d)^2*(c + d*x) + 2*b*(4*A^2 + 10*A*B + 11*B^2)*d*(b*c - a*d)*(a + b*x)*(c + d*x) + 6*b*(2*A^2 + 2*A*B + 5*B^2)*d^2*(a + b*x)^2*(c + d*x)*Log[a + b*x] + 2*B*(b*c - a*d)*(4*(A - B)*d^2*(a + b*x)^2 - b*(2*A + B)*(b*c - a*d)*(c + d*x) + 2*b*(4*A + 5*B)*d*(a + b*x)*(c + d*x))*Log[(e*(a + b*x))/(c + d*x)] - 2*B*(2*a^3*B*d^3 - 6*a^2*b*d^2*(-(B*d*x) + A*(c + d*x)) - 6*a*b^2*d*(2*A*d*x*(c + d*x) + B*c*(c + 2*d*x)) + b^3*(-6*A*d^2*x^2*(c + d*x) + B*(c^3 - 3*c^2*d*x - 9*c*d^2*x^2 - 3*d^3*x^3)))*Log[(e*(a + b*x))/(c + d*x)]^2 + 4*b*B^2*d^2*(a + b*x)^2*(c + d*x)*Log[(e*(a + b*x))/(c + d*x)]^3 - 6*b*(2*A^2 + 2*A*B + 5*B^2)*d^2*(a + b*x)^2*(c + d*x)*Log[c + d*x])/(4*(b*c - a*d)^4*g^3*i^2*(a + b*x)^2*(c + d*x))","A",1
99,1,613,682,2.2452466,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^4 (c i+d i x)^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/((a*g + b*g*x)^4*(c*i + d*i*x)^2),x]","-\frac{9 B \left(-3 a^4 B d^4+12 a^3 b d^3 (A (c+d x)-B d x)+18 a^2 b^2 d^2 (2 A d x (c+d x)+B c (c+2 d x))+6 a b^3 d \left(6 A d^2 x^2 (c+d x)+B \left(-c^3+3 c^2 d x+9 c d^2 x^2+3 d^3 x^3\right)\right)+b^4 \left(12 A d^3 x^3 (c+d x)+B \left(c^4-2 c^3 d x+6 c^2 d^2 x^2+22 c d^3 x^3+10 d^4 x^4\right)\right)\right) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)-27 d^3 \left(A^2-2 A B+2 B^2\right) (a+b x)^3 (a d-b c)+6 b d^3 \left(18 A^2+30 A B+55 B^2\right) (a+b x)^3 (c+d x) \log (a+b x)-6 b d^3 \left(18 A^2+30 A B+55 B^2\right) (a+b x)^3 (c+d x) \log (c+d x)+3 b d^2 \left(27 A^2+78 A B+92 B^2\right) (a+b x)^2 (c+d x) (b c-a d)+b \left(9 A^2+6 A B+2 B^2\right) (c+d x) (b c-a d)^3-3 b d \left(9 A^2+12 A B+7 B^2\right) (a+b x) (c+d x) (b c-a d)^2+6 B (b c-a d) \left(3 b d^2 (9 A+13 B) (a+b x)^2 (c+d x)-3 b d (3 A+2 B) (a+b x) (c+d x) (b c-a d)+b (3 A+B) (c+d x) (b c-a d)^2+9 d^3 (A-B) (a+b x)^3\right) \log \left(\frac{e (a+b x)}{c+d x}\right)+36 b B^2 d^3 (a+b x)^3 (c+d x) \log ^3\left(\frac{e (a+b x)}{c+d x}\right)}{27 g^4 i^2 (a+b x)^3 (c+d x) (b c-a d)^5}","-\frac{b^4 (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{3 g^4 i^2 (a+b x)^3 (b c-a d)^5}-\frac{2 b^4 B (c+d x)^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{9 g^4 i^2 (a+b x)^3 (b c-a d)^5}+\frac{2 b^3 d (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^4 i^2 (a+b x)^2 (b c-a d)^5}+\frac{2 b^3 B d (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^4 i^2 (a+b x)^2 (b c-a d)^5}-\frac{6 b^2 d^2 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^4 i^2 (a+b x) (b c-a d)^5}-\frac{12 b^2 B d^2 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^4 i^2 (a+b x) (b c-a d)^5}+\frac{d^4 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^4 i^2 (c+d x) (b c-a d)^5}-\frac{2 A B d^4 (a+b x)}{g^4 i^2 (c+d x) (b c-a d)^5}-\frac{4 b d^3 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^3}{3 B g^4 i^2 (b c-a d)^5}-\frac{2 b^4 B^2 (c+d x)^3}{27 g^4 i^2 (a+b x)^3 (b c-a d)^5}+\frac{b^3 B^2 d (c+d x)^2}{g^4 i^2 (a+b x)^2 (b c-a d)^5}-\frac{12 b^2 B^2 d^2 (c+d x)}{g^4 i^2 (a+b x) (b c-a d)^5}-\frac{2 B^2 d^4 (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{g^4 i^2 (c+d x) (b c-a d)^5}+\frac{2 B^2 d^4 (a+b x)}{g^4 i^2 (c+d x) (b c-a d)^5}",1,"-1/27*(-27*(A^2 - 2*A*B + 2*B^2)*d^3*(-(b*c) + a*d)*(a + b*x)^3 + b*(9*A^2 + 6*A*B + 2*B^2)*(b*c - a*d)^3*(c + d*x) - 3*b*(9*A^2 + 12*A*B + 7*B^2)*d*(b*c - a*d)^2*(a + b*x)*(c + d*x) + 3*b*(27*A^2 + 78*A*B + 92*B^2)*d^2*(b*c - a*d)*(a + b*x)^2*(c + d*x) + 6*b*(18*A^2 + 30*A*B + 55*B^2)*d^3*(a + b*x)^3*(c + d*x)*Log[a + b*x] + 6*B*(b*c - a*d)*(9*(A - B)*d^3*(a + b*x)^3 + b*(3*A + B)*(b*c - a*d)^2*(c + d*x) - 3*b*(3*A + 2*B)*d*(b*c - a*d)*(a + b*x)*(c + d*x) + 3*b*(9*A + 13*B)*d^2*(a + b*x)^2*(c + d*x))*Log[(e*(a + b*x))/(c + d*x)] + 9*B*(-3*a^4*B*d^4 + 12*a^3*b*d^3*(-(B*d*x) + A*(c + d*x)) + 18*a^2*b^2*d^2*(2*A*d*x*(c + d*x) + B*c*(c + 2*d*x)) + 6*a*b^3*d*(6*A*d^2*x^2*(c + d*x) + B*(-c^3 + 3*c^2*d*x + 9*c*d^2*x^2 + 3*d^3*x^3)) + b^4*(12*A*d^3*x^3*(c + d*x) + B*(c^4 - 2*c^3*d*x + 6*c^2*d^2*x^2 + 22*c*d^3*x^3 + 10*d^4*x^4)))*Log[(e*(a + b*x))/(c + d*x)]^2 + 36*b*B^2*d^3*(a + b*x)^3*(c + d*x)*Log[(e*(a + b*x))/(c + d*x)]^3 - 6*b*(18*A^2 + 30*A*B + 55*B^2)*d^3*(a + b*x)^3*(c + d*x)*Log[c + d*x])/((b*c - a*d)^5*g^4*i^2*(a + b*x)^3*(c + d*x))","A",1
100,1,6052,635,7.8614861,"\int \frac{(a g+b g x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(c i+d i x)^3} \, dx","Integrate[((a*g + b*g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(c*i + d*i*x)^3,x]","\text{Result too large to show}","\frac{6 b^2 B g^3 (b c-a d) \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)}{d^4 i^3}+\frac{3 b^2 g^3 (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)^2}{d^4 i^3}+\frac{2 b^2 B g^3 (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)}{d^4 i^3}+\frac{b^2 g^3 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{d^3 i^3}+\frac{2 b g^3 (a+b x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{d^3 i^3 (c+d x)}-\frac{4 A b B g^3 (a+b x) (b c-a d)}{d^3 i^3 (c+d x)}+\frac{g^3 (a+b x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 d^2 i^3 (c+d x)^2}-\frac{B g^3 (a+b x)^2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 d^2 i^3 (c+d x)^2}+\frac{2 b^2 B^2 g^3 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i^3}-\frac{6 b^2 B^2 g^3 (b c-a d) \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i^3}-\frac{4 b B^2 g^3 (a+b x) (b c-a d) \log \left(\frac{e (a+b x)}{c+d x}\right)}{d^3 i^3 (c+d x)}+\frac{4 b B^2 g^3 (a+b x) (b c-a d)}{d^3 i^3 (c+d x)}+\frac{B^2 g^3 (a+b x)^2 (b c-a d)}{4 d^2 i^3 (c+d x)^2}",1,"Result too large to show","B",1
101,1,2950,410,5.1134595,"\int \frac{(a g+b g x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(c i+d i x)^3} \, dx","Integrate[((a*g + b*g*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(c*i + d*i*x)^3,x]","\text{Result too large to show}","-\frac{2 b^2 B g^2 \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)}{d^3 i^3}-\frac{b^2 g^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\right)^2}{d^3 i^3}-\frac{b g^2 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{d^2 i^3 (c+d x)}+\frac{2 A b B g^2 (a+b x)}{d^2 i^3 (c+d x)}-\frac{g^2 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 d i^3 (c+d x)^2}+\frac{B g^2 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 d i^3 (c+d x)^2}+\frac{2 b^2 B^2 g^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^3 i^3}+\frac{2 b B^2 g^2 (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{d^2 i^3 (c+d x)}-\frac{2 b B^2 g^2 (a+b x)}{d^2 i^3 (c+d x)}-\frac{B^2 g^2 (a+b x)^2}{4 d i^3 (c+d x)^2}",1,"(g^2*((-2*A^2*(b*c - a*d)^2)/(c + d*x)^2 + (8*A^2*b*(b*c - a*d))/(c + d*x) + 4*A^2*b^2*Log[c + d*x] - (4*a*A*b*B*d*(-(b^2*c^3) + 4*a*b*c^2*d - 3*a^2*c*d^2 - 2*b^2*c^2*d*x + 6*a*b*c*d^2*x - 4*a^2*d^3*x - 2*b*(b*c - 2*a*d)*(c + d*x)^2*Log[a + b*x] + 2*(b*c - a*d)^2*(c + 2*d*x)*Log[(e*(a + b*x))/(c + d*x)] + 2*b^2*c^3*Log[c + d*x] - 4*a*b*c^2*d*Log[c + d*x] + 4*b^2*c^2*d*x*Log[c + d*x] - 8*a*b*c*d^2*x*Log[c + d*x] + 2*b^2*c*d^2*x^2*Log[c + d*x] - 4*a*b*d^3*x^2*Log[c + d*x]))/((b*c - a*d)^2*(c + d*x)^2) - (2*a^2*A*B*d^2*(-(b^2*c^2) + 4*a*b*c*d - a^2*d^2 + 2*b^2*c*d*x + 2*a*b*d^2*x + 2*b^2*d^2*x^2 - 2*b^2*(c + d*x)^2*Log[a/b + x] + 2*(b*c - a*d)^2*Log[(e*(a + b*x))/(c + d*x)] + 2*b^2*c^2*Log[(b*(c + d*x))/(b*c - a*d)] + 4*b^2*c*d*x*Log[(b*(c + d*x))/(b*c - a*d)] + 2*b^2*d^2*x^2*Log[(b*(c + d*x))/(b*c - a*d)]))/((b*c - a*d)^2*(c + d*x)^2) + 2*A*b^2*B*(-2*Log[c/d + x]^2 - (8*c*(1 + Log[c/d + x]))/(c + d*x) + (c^2*(1 + 2*Log[c/d + x]))/(c + d*x)^2 + 8*c*(Log[a/b + x]/(c + d*x) + (b*(Log[a + b*x] - Log[c + d*x]))/(-(b*c) + a*d)) + 2*(-Log[a/b + x] + Log[c/d + x] + Log[(e*(a + b*x))/(c + d*x)])*((c*(3*c + 4*d*x))/(c + d*x)^2 + 2*Log[c + d*x]) + (2*c^2*(-Log[a/b + x] + (b*(c + d*x)*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]))/(b*c - a*d)^2))/(c + d*x)^2 + 4*(Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])) + (2*a*b*B^2*d*(2*c*Log[(e*(a + b*x))/(c + d*x)]^2 - 4*(c + d*x)*Log[(e*(a + b*x))/(c + d*x)]^2 - (4*(c + d*x)*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(e*(a + b*x))/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d) + (c*((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*c - a*d)^2*Log[(e*(a + b*x))/(c + d*x)] - 4*b*(b*c - a*d)*(c + d*x)*Log[(e*(a + b*x))/(c + d*x)] - 4*b^2*(c + d*x)^2*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] - 2*b^2*(c + d*x)^2*Log[c + d*x] + 4*b*(c + d*x)*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]) - 4*b^2*(c + d*x)^2*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*b^2*(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*(c + d*x)^2*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^2))/(c + d*x)^2 - (a^2*B^2*d^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*c - a*d)^2*Log[(e*(a + b*x))/(c + d*x)] - 4*b*(b*c - a*d)*(c + d*x)*Log[(e*(a + b*x))/(c + d*x)] - 4*b^2*(c + d*x)^2*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] + 2*(b*c - a*d)^2*Log[(e*(a + b*x))/(c + d*x)]^2 - 2*b^2*(c + d*x)^2*Log[c + d*x] + 4*b*(c + d*x)*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]) - 4*b^2*(c + d*x)^2*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*b^2*(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*(c + d*x)^2*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)^2*(c + d*x)^2) - 2*b^2*B^2*((c^2*Log[(e*(a + b*x))/(c + d*x)]^2)/(c + d*x)^2 - (4*c*Log[(e*(a + b*x))/(c + d*x)]^2)/(c + d*x) + 2*Log[(e*(a + b*x))/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 4*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - (4*c*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(e*(a + b*x))/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(c + d*x)) + (c^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*c - a*d)^2*Log[(e*(a + b*x))/(c + d*x)] - 4*b*(b*c - a*d)*(c + d*x)*Log[(e*(a + b*x))/(c + d*x)] - 4*b^2*(c + d*x)^2*Log[a + b*x]*Log[(e*(a + b*x))/(c + d*x)] - 2*b^2*(c + d*x)^2*Log[c + d*x] + 4*b*(c + d*x)*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]) - 4*b^2*(c + d*x)^2*Log[(e*(a + b*x))/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*b^2*(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*(c + d*x)^2*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(2*(b*c - a*d)^2*(c + d*x)^2) - 4*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])))/(4*d^3*i^3)","B",1
102,1,767,141,0.9099862,"\int \frac{(a g+b g x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(c i+d i x)^3} \, dx","Integrate[((a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(c*i + d*i*x)^3,x]","\frac{g \left(-B \left(4 b^2 (c+d x)^2 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-4 b^2 (c+d 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 b (c+d x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-2 b^2 B (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 (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 \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 (c+d x) (b (c+d x) \log (a+b x)-a d-b (c+d x) \log (c+d x)+b c)\right)+4 b B (c+d x) \left(2 (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)+2 b (c+d x) \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-2 b (c+d x) \log (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-b B (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 (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 (b (c+d x) \log (a+b x)-a d-b (c+d x) \log (c+d x)+b c)\right)+2 (b c-a d)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2-4 b (c+d x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2\right)}{4 d^2 i^3 (c+d x)^2 (b c-a d)}","\frac{g (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 i^3 (c+d x)^2 (b c-a d)}-\frac{B g (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 i^3 (c+d x)^2 (b c-a d)}+\frac{B^2 g (a+b x)^2}{4 i^3 (c+d x)^2 (b c-a d)}",1,"(g*(2*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - 4*b*(b*c - a*d)*(c + d*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 4*b*B*(c + d*x)*(2*(b*c - a*d)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 2*b*(c + d*x)*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 2*b*(c + d*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 2*B*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]) - b*B*(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*(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*(2*(b*c - a*d)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 4*b*(b*c - a*d)*(c + d*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 4*b^2*(c + d*x)^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 4*b^2*(c + d*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 4*b*B*(c + d*x)*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]) - B*((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*(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*(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)]))))/(4*d^2*(b*c - a*d)*i^3*(c + d*x)^2)","C",1
103,1,444,296,0.4325049,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(c i+d i x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/(c*i + d*i*x)^3,x]","\frac{\frac{B \left(4 b^2 (c+d x)^2 \log (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-4 b^2 (c+d 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 b (c+d x) (b c-a d) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)-2 b^2 B (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 (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 \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 (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(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{4 d i^3 (c+d x)^2}","\frac{B d (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 i^3 (c+d x)^2 (b c-a d)^2}+\frac{b (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{i^3 (c+d x) (b c-a d)^2}-\frac{d (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 i^3 (c+d x)^2 (b c-a d)^2}-\frac{2 A b B (a+b x)}{i^3 (c+d x) (b c-a d)^2}-\frac{2 b B^2 (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{i^3 (c+d x) (b c-a d)^2}+\frac{2 b B^2 (a+b x)}{i^3 (c+d x) (b c-a d)^2}-\frac{B^2 d (a+b x)^2}{4 i^3 (c+d x)^2 (b c-a d)^2}",1,"(-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*b*(b*c - a*d)*(c + d*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 4*b^2*(c + d*x)^2*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 4*b^2*(c + d*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 4*b*B*(c + d*x)*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]) - B*((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*(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*(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*i^3*(c + d*x)^2)","C",1
104,1,290,375,1.2610968,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x) (c i+d i x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/((a*g + b*g*x)*(c*i + d*i*x)^3),x]","\frac{6 b^2 \left(2 A^2-6 A B+7 B^2\right) \log (a+b x)+\frac{6 b \left(2 A^2-6 A B+7 B^2\right) (b c-a d)}{c+d x}+\frac{3 \left(2 A^2-2 A B+B^2\right) (b c-a d)^2}{(c+d x)^2}+\frac{6 B \left(B d (a+b x) (a d-4 b c-3 b d x)+2 A b^2 (c+d x)^2\right) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)}{(c+d x)^2}+\frac{6 B (b c-a d) (A (-2 a d+6 b c+4 b d x)+B (a d-7 b c-6 b d x)) \log \left(\frac{e (a+b x)}{c+d x}\right)}{(c+d x)^2}+4 b^2 B^2 \log ^3\left(\frac{e (a+b x)}{c+d x}\right)-6 b^2 \left(2 A^2-6 A B+7 B^2\right) \log (c+d x)}{12 g i^3 (b c-a d)^3}","\frac{b^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^3}{3 B g i^3 (b c-a d)^3}+\frac{d^2 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 g i^3 (c+d x)^2 (b c-a d)^3}-\frac{B d^2 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g i^3 (c+d x)^2 (b c-a d)^3}-\frac{2 b d (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g i^3 (c+d x) (b c-a d)^3}+\frac{4 A b B d (a+b x)}{g i^3 (c+d x) (b c-a d)^3}+\frac{B^2 d^2 (a+b x)^2}{4 g i^3 (c+d x)^2 (b c-a d)^3}+\frac{4 b B^2 d (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{g i^3 (c+d x) (b c-a d)^3}-\frac{4 b B^2 d (a+b x)}{g i^3 (c+d x) (b c-a d)^3}",1,"((3*(2*A^2 - 2*A*B + B^2)*(b*c - a*d)^2)/(c + d*x)^2 + (6*b*(2*A^2 - 6*A*B + 7*B^2)*(b*c - a*d))/(c + d*x) + 6*b^2*(2*A^2 - 6*A*B + 7*B^2)*Log[a + b*x] + (6*B*(b*c - a*d)*(B*(-7*b*c + a*d - 6*b*d*x) + A*(6*b*c - 2*a*d + 4*b*d*x))*Log[(e*(a + b*x))/(c + d*x)])/(c + d*x)^2 + (6*B*(2*A*b^2*(c + d*x)^2 + B*d*(a + b*x)*(-4*b*c + a*d - 3*b*d*x))*Log[(e*(a + b*x))/(c + d*x)]^2)/(c + d*x)^2 + 4*b^2*B^2*Log[(e*(a + b*x))/(c + d*x)]^3 - 6*b^2*(2*A^2 - 6*A*B + 7*B^2)*Log[c + d*x])/(12*(b*c - a*d)^3*g*i^3)","A",1
105,1,453,525,1.5512659,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^2 (c i+d i x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/((a*g + b*g*x)^2*(c*i + d*i*x)^3),x]","-\frac{2 B \left(a^3 B d^3-3 a^2 b B d^2 (2 c+d x)+3 a b^2 d \left(2 A (c+d x)^2-B d x (4 c+3 d x)\right)+b^3 \left(6 A d x (c+d x)^2+B \left(2 c^3+6 c^2 d x-3 d^3 x^3\right)\right)\right) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)+4 b^2 \left(A^2+2 A B+2 B^2\right) (c+d x)^2 (b c-a d)+6 b^2 d \left(2 A^2-2 A B+5 B^2\right) (a+b x) (c+d x)^2 \log (a+b x)-6 b^2 d \left(2 A^2-2 A B+5 B^2\right) (a+b x) (c+d x)^2 \log (c+d x)+d \left(2 A^2-2 A B+B^2\right) (a+b x) (b c-a d)^2+2 b d \left(4 A^2-10 A B+11 B^2\right) (a+b x) (c+d x) (b c-a d)+2 B (b c-a d) \left(2 b d (4 A-5 B) (a+b x) (c+d x)+d (2 A-B) (a+b x) (b c-a d)+4 b^2 (A+B) (c+d x)^2\right) \log \left(\frac{e (a+b x)}{c+d x}\right)+4 b^2 B^2 d (a+b x) (c+d x)^2 \log ^3\left(\frac{e (a+b x)}{c+d x}\right)}{4 g^2 i^3 (a+b x) (c+d x)^2 (b c-a d)^4}","-\frac{b^3 (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^2 i^3 (a+b x) (b c-a d)^4}-\frac{2 b^3 B (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^2 i^3 (a+b x) (b c-a d)^4}-\frac{b^2 d \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^3}{B g^2 i^3 (b c-a d)^4}-\frac{d^3 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 g^2 i^3 (c+d x)^2 (b c-a d)^4}+\frac{B d^3 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^2 i^3 (c+d x)^2 (b c-a d)^4}+\frac{3 b d^2 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^2 i^3 (c+d x) (b c-a d)^4}-\frac{6 A b B d^2 (a+b x)}{g^2 i^3 (c+d x) (b c-a d)^4}-\frac{2 b^3 B^2 (c+d x)}{g^2 i^3 (a+b x) (b c-a d)^4}-\frac{B^2 d^3 (a+b x)^2}{4 g^2 i^3 (c+d x)^2 (b c-a d)^4}-\frac{6 b B^2 d^2 (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{g^2 i^3 (c+d x) (b c-a d)^4}+\frac{6 b B^2 d^2 (a+b x)}{g^2 i^3 (c+d x) (b c-a d)^4}",1,"-1/4*((2*A^2 - 2*A*B + B^2)*d*(b*c - a*d)^2*(a + b*x) + 2*b*(4*A^2 - 10*A*B + 11*B^2)*d*(b*c - a*d)*(a + b*x)*(c + d*x) + 4*b^2*(A^2 + 2*A*B + 2*B^2)*(b*c - a*d)*(c + d*x)^2 + 6*b^2*(2*A^2 - 2*A*B + 5*B^2)*d*(a + b*x)*(c + d*x)^2*Log[a + b*x] + 2*B*(b*c - a*d)*((2*A - B)*d*(b*c - a*d)*(a + b*x) + 2*b*(4*A - 5*B)*d*(a + b*x)*(c + d*x) + 4*b^2*(A + B)*(c + d*x)^2)*Log[(e*(a + b*x))/(c + d*x)] + 2*B*(a^3*B*d^3 - 3*a^2*b*B*d^2*(2*c + d*x) + 3*a*b^2*d*(2*A*(c + d*x)^2 - B*d*x*(4*c + 3*d*x)) + b^3*(6*A*d*x*(c + d*x)^2 + B*(2*c^3 + 6*c^2*d*x - 3*d^3*x^3)))*Log[(e*(a + b*x))/(c + d*x)]^2 + 4*b^2*B^2*d*(a + b*x)*(c + d*x)^2*Log[(e*(a + b*x))/(c + d*x)]^3 - 6*b^2*(2*A^2 - 2*A*B + 5*B^2)*d*(a + b*x)*(c + d*x)^2*Log[c + d*x])/((b*c - a*d)^4*g^2*i^3*(a + b*x)*(c + d*x)^2)","A",1
106,1,611,685,2.1962181,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^3 (c i+d i x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/((a*g + b*g*x)^3*(c*i + d*i*x)^3),x]","\frac{-2 B \left(-a^4 B d^4+4 a^3 b B d^3 (2 c+d x)-6 a^2 b^2 d^2 \left(2 A (c+d x)^2-B d x (4 c+3 d x)\right)-4 a b^3 d \left(6 A d x (c+d x)^2+B \left(2 c^3+6 c^2 d x-3 d^3 x^3\right)\right)+b^4 \left(B c \left(c^3-4 c^2 d x-18 c d^2 x^2-12 d^3 x^3\right)-12 A d^2 x^2 (c+d x)^2\right)\right) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)+12 b^2 d^2 \left(2 A^2+5 B^2\right) (a+b x)^2 (c+d x)^2 \log (a+b x)-12 b^2 d^2 \left(2 A^2+5 B^2\right) (a+b x)^2 (c+d x)^2 \log (c+d x)-b^2 \left(2 A^2+2 A B+B^2\right) (c+d x)^2 (b c-a d)^2+2 b^2 d \left(6 A^2+14 A B+15 B^2\right) (a+b x) (c+d x)^2 (b c-a d)+d^2 \left(2 A^2-2 A B+B^2\right) (a+b x)^2 (b c-a d)^2+2 b d^2 \left(6 A^2-14 A B+15 B^2\right) (a+b x)^2 (c+d x) (b c-a d)+2 B (b c-a d) \left(2 b^2 d (6 A+7 B) (a+b x) (c+d x)^2-b^2 (2 A+B) (c+d x)^2 (b c-a d)+d^2 (2 A-B) (a+b x)^2 (b c-a d)+2 b d^2 (6 A-7 B) (a+b x)^2 (c+d x)\right) \log \left(\frac{e (a+b x)}{c+d x}\right)+8 b^2 B^2 d^2 (a+b x)^2 (c+d x)^2 \log ^3\left(\frac{e (a+b x)}{c+d x}\right)}{4 g^3 i^3 (a+b x)^2 (c+d x)^2 (b c-a d)^5}","-\frac{b^4 (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 g^3 i^3 (a+b x)^2 (b c-a d)^5}-\frac{b^4 B (c+d x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^3 i^3 (a+b x)^2 (b c-a d)^5}+\frac{4 b^3 d (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^3 i^3 (a+b x) (b c-a d)^5}+\frac{8 b^3 B d (c+d x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{g^3 i^3 (a+b x) (b c-a d)^5}+\frac{2 b^2 d^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^3}{B g^3 i^3 (b c-a d)^5}+\frac{d^4 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{2 g^3 i^3 (c+d x)^2 (b c-a d)^5}-\frac{B d^4 (a+b x)^2 \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)}{2 g^3 i^3 (c+d x)^2 (b c-a d)^5}-\frac{4 b d^3 (a+b x) \left(B \log \left(\frac{e (a+b x)}{c+d x}\right)+A\right)^2}{g^3 i^3 (c+d x) (b c-a d)^5}+\frac{8 A b B d^3 (a+b x)}{g^3 i^3 (c+d x) (b c-a d)^5}-\frac{b^4 B^2 (c+d x)^2}{4 g^3 i^3 (a+b x)^2 (b c-a d)^5}+\frac{8 b^3 B^2 d (c+d x)}{g^3 i^3 (a+b x) (b c-a d)^5}+\frac{B^2 d^4 (a+b x)^2}{4 g^3 i^3 (c+d x)^2 (b c-a d)^5}+\frac{8 b B^2 d^3 (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right)}{g^3 i^3 (c+d x) (b c-a d)^5}-\frac{8 b B^2 d^3 (a+b x)}{g^3 i^3 (c+d x) (b c-a d)^5}",1,"((2*A^2 - 2*A*B + B^2)*d^2*(b*c - a*d)^2*(a + b*x)^2 + 2*b*(6*A^2 - 14*A*B + 15*B^2)*d^2*(b*c - a*d)*(a + b*x)^2*(c + d*x) - b^2*(2*A^2 + 2*A*B + B^2)*(b*c - a*d)^2*(c + d*x)^2 + 2*b^2*(6*A^2 + 14*A*B + 15*B^2)*d*(b*c - a*d)*(a + b*x)*(c + d*x)^2 + 12*b^2*(2*A^2 + 5*B^2)*d^2*(a + b*x)^2*(c + d*x)^2*Log[a + b*x] + 2*B*(b*c - a*d)*((2*A - B)*d^2*(b*c - a*d)*(a + b*x)^2 + 2*b*(6*A - 7*B)*d^2*(a + b*x)^2*(c + d*x) - b^2*(2*A + B)*(b*c - a*d)*(c + d*x)^2 + 2*b^2*(6*A + 7*B)*d*(a + b*x)*(c + d*x)^2)*Log[(e*(a + b*x))/(c + d*x)] - 2*B*(-(a^4*B*d^4) + 4*a^3*b*B*d^3*(2*c + d*x) - 6*a^2*b^2*d^2*(2*A*(c + d*x)^2 - B*d*x*(4*c + 3*d*x)) + b^4*(-12*A*d^2*x^2*(c + d*x)^2 + B*c*(c^3 - 4*c^2*d*x - 18*c*d^2*x^2 - 12*d^3*x^3)) - 4*a*b^3*d*(6*A*d*x*(c + d*x)^2 + B*(2*c^3 + 6*c^2*d*x - 3*d^3*x^3)))*Log[(e*(a + b*x))/(c + d*x)]^2 + 8*b^2*B^2*d^2*(a + b*x)^2*(c + d*x)^2*Log[(e*(a + b*x))/(c + d*x)]^3 - 12*b^2*(2*A^2 + 5*B^2)*d^2*(a + b*x)^2*(c + d*x)^2*Log[c + d*x])/(4*(b*c - a*d)^5*g^3*i^3*(a + b*x)^2*(c + d*x)^2)","A",1
107,1,793,851,3.0538669,"\int \frac{\left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{(a g+b g x)^4 (c i+d i x)^3} \, dx","Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^2/((a*g + b*g*x)^4*(c*i + d*i*x)^3),x]","-\frac{18 B \left(3 a^5 B d^5-15 a^4 b B d^4 (2 c+d x)+30 a^3 b^2 d^3 \left(2 A (c+d x)^2-B d x (4 c+3 d x)\right)+30 a^2 b^3 d^2 \left(6 A d x (c+d x)^2+B \left(2 c^3+6 c^2 d x-3 d^3 x^3\right)\right)+15 a b^4 d \left(12 A d^2 x^2 (c+d x)^2+B c \left(-c^3+4 c^2 d x+18 c d^2 x^2+12 d^3 x^3\right)\right)+b^5 \left(60 A d^3 x^3 (c+d x)^2+B \left(2 c^5-5 c^4 d x+20 c^3 d^2 x^2+110 c^2 d^3 x^3+100 c d^4 x^4+20 d^5 x^5\right)\right)\right) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)+60 b^2 d^3 \left(18 A^2+12 A B+49 B^2\right) (a+b x)^3 (c+d x)^2 \log (a+b x)-60 b^2 d^3 \left(18 A^2+12 A B+49 B^2\right) (a+b x)^3 (c+d x)^2 \log (c+d x)+6 b^2 d^2 \left(108 A^2+282 A B+319 B^2\right) (a+b x)^2 (c+d x)^2 (b c-a d)+4 b^2 \left(9 A^2+6 A B+2 B^2\right) (c+d x)^2 (b c-a d)^3-3 b^2 d \left(54 A^2+66 A B+37 B^2\right) (a+b x) (c+d x)^2 (b c-a d)^2+27 d^3 \left(2 A^2-2 A B+B^2\right) (a+b x)^3 (b c-a d)^2+54 b d^3 \left(8 A^2-18 A B+19 B^2\right) (a+b x)^3 (c+d x) (b c-a d)+6 B (b c-a d) \left(6 b^2 d^2 (36 A+47 B) (a+b x)^2 (c+d x)^2-3 b^2 d (18 A+11 B) (a+b x) (c+d x)^2 (b c-a d)+4 b^2 (3 A+B) (c+d x)^2 (b c-a d)^2+9 d^3 (2 A-B) (a+b x)^3 (b c-a d)+18 b d^3 (8 A-9 B) (a+b x)^3 (c+d x)\right) \log \left(\frac{e (a+b x)}{c+d x}\right)+360 b^2 B^2 d^3 (a+b x)^3 (c+d x)^2 \log ^3\left(\frac{e (a+b x)}{c+d x}\right)}{108 g^4 i^3 (a+b x)^3 (c+d x)^2 (b c-a d)^6}","-\frac{2 B^2 (c+d x)^3 b^5}{27 (b c-a d)^6 g^4 i^3 (a+b x)^3}-\frac{(c+d x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 b^5}{3 (b c-a d)^6 g^4 i^3 (a+b x)^3}-\frac{2 B (c+d x)^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) b^5}{9 (b c-a d)^6 g^4 i^3 (a+b x)^3}+\frac{5 B^2 d (c+d x)^2 b^4}{4 (b c-a d)^6 g^4 i^3 (a+b x)^2}+\frac{5 d (c+d x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 b^4}{2 (b c-a d)^6 g^4 i^3 (a+b x)^2}+\frac{5 B d (c+d x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) b^4}{2 (b c-a d)^6 g^4 i^3 (a+b x)^2}-\frac{10 d^2 (c+d x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 b^3}{(b c-a d)^6 g^4 i^3 (a+b x)}-\frac{20 B^2 d^2 (c+d x) b^3}{(b c-a d)^6 g^4 i^3 (a+b x)}-\frac{20 B d^2 (c+d x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right) b^3}{(b c-a d)^6 g^4 i^3 (a+b x)}-\frac{10 d^3 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^3 b^2}{3 B (b c-a d)^6 g^4 i^3}+\frac{5 d^4 (a+b x) \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2 b}{(b c-a d)^6 g^4 i^3 (c+d x)}-\frac{10 B^2 d^4 (a+b x) \log \left(\frac{e (a+b x)}{c+d x}\right) b}{(b c-a d)^6 g^4 i^3 (c+d x)}+\frac{10 B^2 d^4 (a+b x) b}{(b c-a d)^6 g^4 i^3 (c+d x)}-\frac{10 A B d^4 (a+b x) b}{(b c-a d)^6 g^4 i^3 (c+d x)}-\frac{d^5 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)^2}{2 (b c-a d)^6 g^4 i^3 (c+d x)^2}+\frac{B d^5 (a+b x)^2 \left(A+B \log \left(\frac{e (a+b x)}{c+d x}\right)\right)}{2 (b c-a d)^6 g^4 i^3 (c+d x)^2}-\frac{B^2 d^5 (a+b x)^2}{4 (b c-a d)^6 g^4 i^3 (c+d x)^2}",1,"-1/108*(27*(2*A^2 - 2*A*B + B^2)*d^3*(b*c - a*d)^2*(a + b*x)^3 + 54*b*(8*A^2 - 18*A*B + 19*B^2)*d^3*(b*c - a*d)*(a + b*x)^3*(c + d*x) + 4*b^2*(9*A^2 + 6*A*B + 2*B^2)*(b*c - a*d)^3*(c + d*x)^2 - 3*b^2*(54*A^2 + 66*A*B + 37*B^2)*d*(b*c - a*d)^2*(a + b*x)*(c + d*x)^2 + 6*b^2*(108*A^2 + 282*A*B + 319*B^2)*d^2*(b*c - a*d)*(a + b*x)^2*(c + d*x)^2 + 60*b^2*(18*A^2 + 12*A*B + 49*B^2)*d^3*(a + b*x)^3*(c + d*x)^2*Log[a + b*x] + 6*B*(b*c - a*d)*(9*(2*A - B)*d^3*(b*c - a*d)*(a + b*x)^3 + 18*b*(8*A - 9*B)*d^3*(a + b*x)^3*(c + d*x) + 4*b^2*(3*A + B)*(b*c - a*d)^2*(c + d*x)^2 - 3*b^2*(18*A + 11*B)*d*(b*c - a*d)*(a + b*x)*(c + d*x)^2 + 6*b^2*(36*A + 47*B)*d^2*(a + b*x)^2*(c + d*x)^2)*Log[(e*(a + b*x))/(c + d*x)] + 18*B*(3*a^5*B*d^5 - 15*a^4*b*B*d^4*(2*c + d*x) + 30*a^3*b^2*d^3*(2*A*(c + d*x)^2 - B*d*x*(4*c + 3*d*x)) + 30*a^2*b^3*d^2*(6*A*d*x*(c + d*x)^2 + B*(2*c^3 + 6*c^2*d*x - 3*d^3*x^3)) + 15*a*b^4*d*(12*A*d^2*x^2*(c + d*x)^2 + B*c*(-c^3 + 4*c^2*d*x + 18*c*d^2*x^2 + 12*d^3*x^3)) + b^5*(60*A*d^3*x^3*(c + d*x)^2 + B*(2*c^5 - 5*c^4*d*x + 20*c^3*d^2*x^2 + 110*c^2*d^3*x^3 + 100*c*d^4*x^4 + 20*d^5*x^5)))*Log[(e*(a + b*x))/(c + d*x)]^2 + 360*b^2*B^2*d^3*(a + b*x)^3*(c + d*x)^2*Log[(e*(a + b*x))/(c + d*x)]^3 - 60*b^2*(18*A^2 + 12*A*B + 49*B^2)*d^3*(a + b*x)^3*(c + d*x)^2*Log[c + d*x])/((b*c - a*d)^6*g^4*i^3*(a + b*x)^3*(c + d*x)^2)","A",1
108,1,269,223,0.2602731,"\int (a g+b g x)^3 (c i+d i 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)^3*(c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^3 i \left(24 d (a+b x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+30 (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)-\frac{5 B n (b c-a d)^2 \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)}{d^4}+\frac{2 B n (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)}{d^4}\right)}{120 b^2}","\frac{g^3 i (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-B n\right)}{20 b^2}+\frac{g^3 i (a+b x)^4 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 b}+\frac{B g^3 i n (b c-a d)^5 \log (c+d x)}{20 b^2 d^4}+\frac{B g^3 i n (a+b x)^2 (b c-a d)^3}{40 b^2 d^2}-\frac{B g^3 i n (a+b x)^3 (b c-a d)^2}{60 b^2 d}-\frac{B g^3 i n x (b c-a d)^4}{20 b d^3}",1,"(g^3*i*(30*(b*c - a*d)*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 24*d*(a + b*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - (5*B*(b*c - a*d)^2*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]))/d^4 + (2*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]))/d^4))/(120*b^2)","A",1
109,1,225,190,0.1833933,"\int (a g+b g x)^2 (c i+d i 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)^2*(c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^2 i \left(6 d (a+b x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+8 (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)+\frac{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)}{d^3}-\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)}{d^3}\right)}{24 b^2}","\frac{g^2 i (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-B n\right)}{12 b^2}+\frac{g^2 i (a+b x)^3 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{4 b}-\frac{B g^2 i n (b c-a d)^4 \log (c+d x)}{12 b^2 d^3}-\frac{B g^2 i n (a+b x)^2 (b c-a d)^2}{24 b^2 d}+\frac{B g^2 i n x (b c-a d)^3}{12 b d^2}",1,"(g^2*i*(8*(b*c - a*d)*(a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 6*d*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + (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]))/d^3 - (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]))/d^3))/(24*b^2)","A",1
110,1,189,149,0.2802716,"\int (a g+b g x) (c i+d i 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)*(c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g i \left(b \left(d x \left(a^2 B d^2 n+a b d (6 A c+3 A d x+B d n x)+A b^2 d x (3 c+2 d x)+b^2 (-B) c n (c+d x)\right)+B c n \left(6 a^2 d^2-3 a b c d+b^2 c^2\right) \log (c+d x)+B d^2 \left(6 a^2 c+3 a b x (2 c+d x)+b^2 x^2 (3 c+2 d x)\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-a^2 B d^2 n (a d+3 b c) \log (a+b x)\right)}{6 b^2 d^2}","\frac{g i (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-B n\right)}{6 b^2}+\frac{g i (a+b x)^2 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 b}+\frac{B g i n (b c-a d)^3 \log (c+d x)}{6 b^2 d^2}-\frac{B g i n x (b c-a d)^2}{6 b d}",1,"(g*i*(-(a^2*B*d^2*(3*b*c + a*d)*n*Log[a + b*x]) + b*(d*x*(a^2*B*d^2*n - b^2*B*c*n*(c + d*x) + A*b^2*d*x*(3*c + 2*d*x) + a*b*d*(6*A*c + 3*A*d*x + B*d*n*x)) + B*d^2*(6*a^2*c + 3*a*b*x*(2*c + d*x) + b^2*x^2*(3*c + 2*d*x))*Log[e*((a + b*x)/(c + d*x))^n] + B*c*(b^2*c^2 - 3*a*b*c*d + 6*a^2*d^2)*n*Log[c + d*x])))/(6*b^2*d^2)","A",1
111,1,74,86,0.0402098,"\int (c i+d i x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Integrate[(c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{i \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{i (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 i n (b c-a d)^2 \log (a+b x)}{2 b^2 d}-\frac{B i n x (b c-a d)}{2 b}",1,"(i*(-((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
112,1,172,141,0.133163,"\int \frac{(c i+d i x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{a g+b g x} \, dx","Integrate[((c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a*g + b*g*x),x]","\frac{i \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 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)+B n (a d-b c) \log ^2(a+b x)\right)}{2 b^2 g}","-\frac{i (b c-a d) \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-B n\right)}{b^2 g}+\frac{i (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b g}+\frac{B i n (b c-a d) \text{Li}_2\left(\frac{b c-a d}{d (a+b x)}+1\right)}{b^2 g}",1,"(i*(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)]))/(2*b^2*g)","A",1
113,1,189,150,0.1881334,"\int \frac{(c i+d i x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{(a g+b g x)^2} \, dx","Integrate[((c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a*g + b*g*x)^2,x]","\frac{i \left(\frac{d \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b^2}-\frac{(b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b^2 (a+b x)}-\frac{B d n \left(-2 \text{Li}_2\left(-\frac{d (a+b x)}{b c-a d}\right)-2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)+\log ^2(a+b x)\right)}{2 b^2}-\frac{B n \left(\frac{b c-a d}{a+b x}+d \log (a+b x)-d \log (c+d x)\right)}{b^2}\right)}{g^2}","-\frac{d i \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 g^2}-\frac{i (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b g^2 (a+b x)}+\frac{B d i n \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^2 g^2}-\frac{B i n (c+d x)}{b g^2 (a+b x)}",1,"(i*(-(((b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(b^2*(a + b*x))) + (d*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/b^2 - (B*n*((b*c - a*d)/(a + b*x) + d*Log[a + b*x] - d*Log[c + d*x]))/b^2 - (B*d*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^2)))/g^2","A",1
114,1,216,89,0.1705439,"\int \frac{(c i+d i x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{(a g+b g x)^3} \, dx","Integrate[((c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a*g + b*g*x)^3,x]","\frac{i \left(-\frac{d \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b^2 (a+b x)}-\frac{(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 (a+b x)^2}-\frac{B n \left(-\frac{2 d^2 \log (a+b x)}{b c-a d}+\frac{2 d^2 \log (c+d x)}{b c-a d}+\frac{b c-a d}{(a+b x)^2}-\frac{2 d}{a+b x}\right)}{4 b^2}-\frac{B d n \left(\frac{d \log (a+b x)}{b c-a d}-\frac{d \log (c+d x)}{b c-a d}+\frac{1}{a+b x}\right)}{b^2}\right)}{g^3}","-\frac{i (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)}-\frac{B i n (c+d x)^2}{4 g^3 (a+b x)^2 (b c-a d)}",1,"(i*(-1/2*((b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(b^2*(a + b*x)^2) - (d*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(b^2*(a + b*x)) - (B*d*n*((a + b*x)^(-1) + (d*Log[a + b*x])/(b*c - a*d) - (d*Log[c + d*x])/(b*c - a*d)))/b^2 - (B*n*((b*c - a*d)/(a + b*x)^2 - (2*d)/(a + b*x) - (2*d^2*Log[a + b*x])/(b*c - a*d) + (2*d^2*Log[c + d*x])/(b*c - a*d)))/(4*b^2)))/g^3","B",1
115,1,196,181,0.4523998,"\int \frac{(c i+d i x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{(a g+b g x)^4} \, dx","Integrate[((c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a*g + b*g*x)^4,x]","-\frac{i \left(\frac{12 A b c}{(a+b x)^3}+\frac{18 A d}{(a+b x)^2}-\frac{12 a A d}{(a+b x)^3}-\frac{6 B d^3 n \log (a+b x)}{(b c-a d)^2}+\frac{6 B d^3 n \log (c+d x)}{(b c-a d)^2}-\frac{6 B d^2 n}{(a+b x) (b c-a d)}+\frac{6 B (a d+2 b c+3 b d x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a+b x)^3}+\frac{4 b B c n}{(a+b x)^3}+\frac{3 B d n}{(a+b x)^2}-\frac{4 a B d n}{(a+b x)^3}\right)}{36 b^2 g^4}","-\frac{b i (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 g^4 (a+b x)^3 (b c-a d)^2}+\frac{d i (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)^2}-\frac{b B i n (c+d x)^3}{9 g^4 (a+b x)^3 (b c-a d)^2}+\frac{B d i n (c+d x)^2}{4 g^4 (a+b x)^2 (b c-a d)^2}",1,"-1/36*(i*((12*A*b*c)/(a + b*x)^3 - (12*a*A*d)/(a + b*x)^3 + (4*b*B*c*n)/(a + b*x)^3 - (4*a*B*d*n)/(a + b*x)^3 + (18*A*d)/(a + b*x)^2 + (3*B*d*n)/(a + b*x)^2 - (6*B*d^2*n)/((b*c - a*d)*(a + b*x)) - (6*B*d^3*n*Log[a + b*x])/(b*c - a*d)^2 + (6*B*(2*b*c + a*d + 3*b*d*x)*Log[e*((a + b*x)/(c + d*x))^n])/(a + b*x)^3 + (6*B*d^3*n*Log[c + d*x])/(b*c - a*d)^2))/(b^2*g^4)","A",1
116,1,220,281,0.4995428,"\int \frac{(c i+d i x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{(a g+b g x)^5} \, dx","Integrate[((c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a*g + b*g*x)^5,x]","-\frac{i \left(\frac{36 A b c}{(a+b x)^4}+\frac{48 A d}{(a+b x)^3}-\frac{36 a A d}{(a+b x)^4}+\frac{12 B d^4 n \log (a+b x)}{(b c-a d)^3}-\frac{12 B d^4 n \log (c+d x)}{(b c-a d)^3}+\frac{12 B d^3 n}{(a+b x) (b c-a d)^2}-\frac{6 B d^2 n}{(a+b x)^2 (b c-a d)}+\frac{12 B (a d+3 b c+4 b d x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a+b x)^4}+\frac{9 b B c n}{(a+b x)^4}+\frac{4 B d n}{(a+b x)^3}-\frac{9 a B d n}{(a+b x)^4}\right)}{144 b^2 g^5}","-\frac{b^2 i (c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{4 g^5 (a+b x)^4 (b c-a d)^3}-\frac{d^2 i (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)^3}+\frac{2 b d i (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)^3}-\frac{b^2 B i n (c+d x)^4}{16 g^5 (a+b x)^4 (b c-a d)^3}-\frac{B d^2 i n (c+d x)^2}{4 g^5 (a+b x)^2 (b c-a d)^3}+\frac{2 b B d i n (c+d x)^3}{9 g^5 (a+b x)^3 (b c-a d)^3}",1,"-1/144*(i*((36*A*b*c)/(a + b*x)^4 - (36*a*A*d)/(a + b*x)^4 + (9*b*B*c*n)/(a + b*x)^4 - (9*a*B*d*n)/(a + b*x)^4 + (48*A*d)/(a + b*x)^3 + (4*B*d*n)/(a + b*x)^3 - (6*B*d^2*n)/((b*c - a*d)*(a + b*x)^2) + (12*B*d^3*n)/((b*c - a*d)^2*(a + b*x)) + (12*B*d^4*n*Log[a + b*x])/(b*c - a*d)^3 + (12*B*(3*b*c + a*d + 4*b*d*x)*Log[e*((a + b*x)/(c + d*x))^n])/(a + b*x)^4 - (12*B*d^4*n*Log[c + d*x])/(b*c - a*d)^3))/(b^2*g^5)","A",1
117,1,441,442,0.4043774,"\int (a g+b g x)^3 (c i+d i 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)^3*(c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^3 i^2 \left(60 d^6 (a+b x)^6 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+144 d^5 (a+b x)^5 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+90 d^4 (a+b x)^4 (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 n (b c-a d)^3 \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 n (b c-a d)^2 \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)-B n (b c-a d) \left(15 d^4 (a+b x)^4 (a d-b c)+20 d^3 (a+b x)^3 (b c-a d)^2+30 d^2 (a+b x)^2 (a d-b c)^3+60 b d x (b c-a d)^4-60 (b c-a d)^5 \log (c+d x)+12 d^5 (a+b x)^5\right)\right)}{360 b^3 d^4}","\frac{b^3 g^3 i^2 (c+d x)^6 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{6 d^4}-\frac{3 b^2 g^3 i^2 (c+d x)^5 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 d^4}-\frac{g^3 i^2 (c+d x)^3 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 d^4}+\frac{3 b g^3 i^2 (c+d x)^4 (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^4}+\frac{B g^3 i^2 n (b c-a d)^6 \log \left(\frac{a+b x}{c+d x}\right)}{60 b^3 d^4}+\frac{B g^3 i^2 n (b c-a d)^6 \log (c+d x)}{60 b^3 d^4}-\frac{b^2 B g^3 i^2 n (c+d x)^5 (b c-a d)}{30 d^4}+\frac{B g^3 i^2 n x (b c-a d)^5}{60 b^2 d^3}+\frac{B g^3 i^2 n (c+d x)^2 (b c-a d)^4}{120 b d^4}-\frac{19 B g^3 i^2 n (c+d x)^3 (b c-a d)^3}{180 d^4}+\frac{13 b B g^3 i^2 n (c+d x)^4 (b c-a d)^2}{120 d^4}",1,"(g^3*i^2*(90*d^4*(b*c - a*d)^2*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 144*d^5*(b*c - a*d)*(a + b*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 60*d^6*(a + b*x)^6*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 15*B*(b*c - a*d)^3*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)^2*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]) - B*(b*c - a*d)*n*(60*b*d*(b*c - a*d)^4*x + 30*d^2*(-(b*c) + a*d)^3*(a + b*x)^2 + 20*d^3*(b*c - a*d)^2*(a + b*x)^3 + 15*d^4*(-(b*c) + a*d)*(a + b*x)^4 + 12*d^5*(a + b*x)^5 - 60*(b*c - a*d)^5*Log[c + d*x])))/(360*b^3*d^4)","A",1
118,1,374,352,0.2820531,"\int (a g+b g x)^2 (c i+d i 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*(c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^2 i^2 \left(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)+30 d^4 (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)+20 d^3 (a+b x)^3 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+10 B n (b c-a d)^3 \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)-5 B n (b c-a d)^2 \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)+B n (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)\right)}{60 b^3 d^3}","\frac{b^2 g^2 i^2 (c+d x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 d^3}+\frac{g^2 i^2 (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)}{3 d^3}-\frac{b g^2 i^2 (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)}{2 d^3}-\frac{B g^2 i^2 n (b c-a d)^5 \log \left(\frac{a+b x}{c+d x}\right)}{30 b^3 d^3}-\frac{B g^2 i^2 n (b c-a d)^5 \log (c+d x)}{30 b^3 d^3}-\frac{B g^2 i^2 n x (b c-a d)^4}{30 b^2 d^2}-\frac{B g^2 i^2 n (c+d x)^2 (b c-a d)^3}{60 b d^3}+\frac{B g^2 i^2 n (c+d x)^3 (b c-a d)^2}{10 d^3}-\frac{b B g^2 i^2 n (c+d x)^4 (b c-a d)}{20 d^3}",1,"(g^2*i^2*(20*d^3*(b*c - a*d)^2*(a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 30*d^4*(b*c - a*d)*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 12*d^5*(a + b*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 10*B*(b*c - a*d)^3*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]) - 5*B*(b*c - a*d)^2*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]) + 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])))/(60*b^3*d^3)","A",1
119,1,224,250,0.2040022,"\int (a g+b g x) (c i+d i 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)*(c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g i^2 \left(6 b (c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-8 (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)+\frac{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^3}-\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)}{b^3}\right)}{24 d^2}","-\frac{g i^2 (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)}{3 d^2}+\frac{b g i^2 (c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{4 d^2}+\frac{B g i^2 n (b c-a d)^4 \log \left(\frac{a+b x}{c+d x}\right)}{12 b^3 d^2}+\frac{B g i^2 n (b c-a d)^4 \log (c+d x)}{12 b^3 d^2}+\frac{B g i^2 n x (b c-a d)^3}{12 b^2 d}+\frac{B g i^2 n (c+d x)^2 (b c-a d)^2}{24 b d^2}-\frac{B g i^2 n (c+d x)^3 (b c-a d)}{12 d^2}",1,"(g*i^2*((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^3 - (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^3 - 8*(b*c - a*d)*(c + d*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 6*b*(c + d*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])))/(24*d^2)","A",1
120,1,101,124,0.0458425,"\int (c i+d i x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Integrate[(c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{i^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{i^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 i^2 n (b c-a d)^3 \log (a+b x)}{3 b^3 d}-\frac{B i^2 n x (b c-a d)^2}{3 b^2}-\frac{B i^2 n (c+d x)^2 (b c-a d)}{6 b d}",1,"(i^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
121,1,264,289,0.1971897,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{a g+b g x} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a*g + b*g*x),x]","\frac{i^2 \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 (g (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(2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)-\log (g (a+b x)) \left(\log (g (a+b x))-2 \log \left(\frac{b (c+d x)}{b c-a d}\right)\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)}{2 b^3 g}","\frac{d i^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)}{b^3 g}-\frac{i^2 (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^3 g}+\frac{i^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 g}+\frac{B i^2 n (b c-a d)^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^3 g}-\frac{B i^2 n (b c-a d)^2 \log \left(\frac{a+b x}{c+d x}\right)}{2 b^3 g}-\frac{3 B i^2 n (b c-a d)^2 \log (c+d x)}{2 b^3 g}-\frac{B d i^2 n x (b c-a d)}{2 b^2 g}",1,"(i^2*(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[g*(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[g*(a + b*x)]*(Log[g*(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*g)","A",1
122,1,233,259,0.2538734,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{(a g+b g x)^2} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a*g + b*g*x)^2,x]","\frac{i^2 \left(2 d (b c-a d) \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-\frac{(b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{a+b x}+B d^2 (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B d n (a d-b c) \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)-\frac{B n (b c-a d)^2}{a+b x}+B d n (a d-b c) \log (a+b x)+A b d^2 x\right)}{b^3 g^2}","\frac{d^2 i^2 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b^3 g^2}-\frac{2 d i^2 (b c-a d) \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^3 g^2}-\frac{i^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)}{b^2 g^2 (a+b x)}+\frac{2 B d i^2 n (b c-a d) \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^3 g^2}-\frac{B d i^2 n (b c-a d) \log (c+d x)}{b^3 g^2}-\frac{B i^2 n (c+d x) (b c-a d)}{b^2 g^2 (a+b x)}",1,"(i^2*(A*b*d^2*x - (B*(b*c - a*d)^2*n)/(a + b*x) + B*d*(-(b*c) + a*d)*n*Log[a + b*x] + B*d^2*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] - ((b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x) + 2*d*(b*c - a*d)*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + B*d*(-(b*c) + a*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^3*g^2)","A",1
123,1,258,242,0.3473402,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{(a g+b g x)^3} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a*g + b*g*x)^3,x]","\frac{i^2 \left(4 d^2 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+\frac{8 d (a d-b c) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{a+b x}-\frac{2 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(a+b x)^2}-2 B d^2 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)+\frac{6 B d n (a d-b c)}{a+b x}-\frac{B n (b c-a d)^2}{(a+b x)^2}-6 B d^2 n \log (a+b x)+6 B d^2 n \log (c+d x)\right)}{4 b^3 g^3}","-\frac{d^2 i^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^3 g^3}-\frac{d i^2 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b^2 g^3 (a+b x)}-\frac{i^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 g^3 (a+b x)^2}+\frac{B d^2 i^2 n \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^3 g^3}-\frac{B d i^2 n (c+d x)}{b^2 g^3 (a+b x)}-\frac{B i^2 n (c+d x)^2}{4 b g^3 (a+b x)^2}",1,"(i^2*(-((B*(b*c - a*d)^2*n)/(a + b*x)^2) + (6*B*d*(-(b*c) + a*d)*n)/(a + b*x) - 6*B*d^2*n*Log[a + b*x] - (2*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x)^2 + (8*d*(-(b*c) + a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x) + 4*d^2*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 6*B*d^2*n*Log[c + d*x] - 2*B*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)])))/(4*b^3*g^3)","A",1
124,1,329,93,0.3231144,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{(a g+b g x)^4} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a*g + b*g*x)^4,x]","-\frac{i^2 \left(-3 a^3 A d^3-3 a^3 B d^3 n \log (c+d x)-a^3 B d^3 n-9 a^2 A b d^3 x+3 B (b c-a d) \left(a^2 d^2+a b d (c+3 d x)+b^2 \left(c^2+3 c d x+3 d^2 x^2\right)\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-9 a^2 b B d^3 n x \log (c+d x)-3 a^2 b B d^3 n x-9 a A b^2 d^3 x^2-9 a b^2 B d^3 n x^2 \log (c+d x)-3 a b^2 B d^3 n x^2+3 B d^3 n (a+b x)^3 \log (a+b x)+3 A b^3 c^3+9 A b^3 c^2 d x+9 A b^3 c d^2 x^2+b^3 B c^3 n+3 b^3 B c^2 d n x-3 b^3 B d^3 n x^3 \log (c+d x)+3 b^3 B c d^2 n x^2\right)}{9 b^3 g^4 (a+b x)^3 (b c-a d)}","-\frac{i^2 (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 g^4 (a+b x)^3 (b c-a d)}-\frac{B i^2 n (c+d x)^3}{9 g^4 (a+b x)^3 (b c-a d)}",1,"-1/9*(i^2*(3*A*b^3*c^3 - 3*a^3*A*d^3 + b^3*B*c^3*n - a^3*B*d^3*n + 9*A*b^3*c^2*d*x - 9*a^2*A*b*d^3*x + 3*b^3*B*c^2*d*n*x - 3*a^2*b*B*d^3*n*x + 9*A*b^3*c*d^2*x^2 - 9*a*A*b^2*d^3*x^2 + 3*b^3*B*c*d^2*n*x^2 - 3*a*b^2*B*d^3*n*x^2 + 3*B*d^3*n*(a + b*x)^3*Log[a + b*x] + 3*B*(b*c - a*d)*(a^2*d^2 + a*b*d*(c + 3*d*x) + b^2*(c^2 + 3*c*d*x + 3*d^2*x^2))*Log[e*((a + b*x)/(c + d*x))^n] - 3*a^3*B*d^3*n*Log[c + d*x] - 9*a^2*b*B*d^3*n*x*Log[c + d*x] - 9*a*b^2*B*d^3*n*x^2*Log[c + d*x] - 3*b^3*B*d^3*n*x^3*Log[c + d*x]))/(b^3*(b*c - a*d)*g^4*(a + b*x)^3)","B",1
125,1,474,189,0.4232674,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{(a g+b g x)^5} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a*g + b*g*x)^5,x]","-\frac{d^2 i^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 b^3 g^5 (a+b x)^2}-\frac{2 d i^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^3 g^5 (a+b x)^3}-\frac{i^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^3 g^5 (a+b x)^4}-\frac{B d^2 i^2 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{2 d}{(a+b x) (b c-a d)}+\frac{1}{(a+b x)^2}\right)}{4 b^3 g^5}-\frac{B d i^2 n \left(\frac{6 d^3 \log (a+b x)}{(b c-a d)^2}-\frac{6 d^3 \log (c+d x)}{(b c-a d)^2}+\frac{6 d^2}{(a+b x) (b c-a d)}+\frac{2 (b c-a d)}{(a+b x)^3}-\frac{3 d}{(a+b x)^2}\right)}{9 b^3 g^5}-\frac{B i^2 n \left(-\frac{12 d^4 \log (a+b x)}{(b c-a d)^2}+\frac{12 d^4 \log (c+d x)}{(b c-a d)^2}-\frac{12 d^3}{(a+b x) (b c-a d)}-\frac{4 d (b c-a d)}{(a+b x)^3}+\frac{3 (b c-a d)^2}{(a+b x)^4}+\frac{6 d^2}{(a+b x)^2}\right)}{48 b^3 g^5}","-\frac{b i^2 (c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{4 g^5 (a+b x)^4 (b c-a d)^2}+\frac{d i^2 (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)^2}-\frac{b B i^2 n (c+d x)^4}{16 g^5 (a+b x)^4 (b c-a d)^2}+\frac{B d i^2 n (c+d x)^3}{9 g^5 (a+b x)^3 (b c-a d)^2}",1,"-1/4*((b*c - a*d)^2*i^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(b^3*g^5*(a + b*x)^4) - (2*d*(b*c - a*d)*i^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(3*b^3*g^5*(a + b*x)^3) - (d^2*i^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*b^3*g^5*(a + b*x)^2) - (B*d^2*i^2*n*((a + b*x)^(-2) - (2*d)/((b*c - a*d)*(a + b*x)) - (2*d^2*Log[a + b*x])/(b*c - a*d)^2 + (2*d^2*Log[c + d*x])/(b*c - a*d)^2))/(4*b^3*g^5) - (B*d*i^2*n*((2*(b*c - a*d))/(a + b*x)^3 - (3*d)/(a + b*x)^2 + (6*d^2)/((b*c - a*d)*(a + b*x)) + (6*d^3*Log[a + b*x])/(b*c - a*d)^2 - (6*d^3*Log[c + d*x])/(b*c - a*d)^2))/(9*b^3*g^5) - (B*i^2*n*((3*(b*c - a*d)^2)/(a + b*x)^4 - (4*d*(b*c - a*d))/(a + b*x)^3 + (6*d^2)/(a + b*x)^2 - (12*d^3)/((b*c - a*d)*(a + b*x)) - (12*d^4*Log[a + b*x])/(b*c - a*d)^2 + (12*d^4*Log[c + d*x])/(b*c - a*d)^2))/(48*b^3*g^5)","B",1
126,1,357,293,1.0518991,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{(a g+b g x)^6} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a*g + b*g*x)^6,x]","\frac{i^2 \left(-\frac{360 a^2 A d^2}{(a+b x)^5}-\frac{60 B \left(a^2 d^2+a b d (3 c+5 d x)+b^2 \left(6 c^2+15 c d x+10 d^2 x^2\right)\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a+b x)^5}-\frac{72 a^2 B d^2 n}{(a+b x)^5}-\frac{360 A b^2 c^2}{(a+b x)^5}-\frac{900 A b c d}{(a+b x)^4}+\frac{720 a A b c d}{(a+b x)^5}-\frac{600 A d^2}{(a+b x)^3}+\frac{900 a A d^2}{(a+b x)^4}-\frac{72 b^2 B c^2 n}{(a+b x)^5}-\frac{60 B d^5 n \log (a+b x)}{(b c-a d)^3}+\frac{60 B d^5 n \log (c+d x)}{(b c-a d)^3}-\frac{60 B d^4 n}{(a+b x) (b c-a d)^2}+\frac{30 B d^3 n}{(a+b x)^2 (b c-a d)}-\frac{135 b B c d n}{(a+b x)^4}+\frac{144 a b B c d n}{(a+b x)^5}-\frac{20 B d^2 n}{(a+b x)^3}+\frac{135 a B d^2 n}{(a+b x)^4}\right)}{1800 b^3 g^6}","-\frac{b^2 i^2 (c+d x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 g^6 (a+b x)^5 (b c-a d)^3}-\frac{d^2 i^2 (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 g^6 (a+b x)^3 (b c-a d)^3}+\frac{b d i^2 (c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 g^6 (a+b x)^4 (b c-a d)^3}-\frac{b^2 B i^2 n (c+d x)^5}{25 g^6 (a+b x)^5 (b c-a d)^3}-\frac{B d^2 i^2 n (c+d x)^3}{9 g^6 (a+b x)^3 (b c-a d)^3}+\frac{b B d i^2 n (c+d x)^4}{8 g^6 (a+b x)^4 (b c-a d)^3}",1,"(i^2*((-360*A*b^2*c^2)/(a + b*x)^5 + (720*a*A*b*c*d)/(a + b*x)^5 - (360*a^2*A*d^2)/(a + b*x)^5 - (72*b^2*B*c^2*n)/(a + b*x)^5 + (144*a*b*B*c*d*n)/(a + b*x)^5 - (72*a^2*B*d^2*n)/(a + b*x)^5 - (900*A*b*c*d)/(a + b*x)^4 + (900*a*A*d^2)/(a + b*x)^4 - (135*b*B*c*d*n)/(a + b*x)^4 + (135*a*B*d^2*n)/(a + b*x)^4 - (600*A*d^2)/(a + b*x)^3 - (20*B*d^2*n)/(a + b*x)^3 + (30*B*d^3*n)/((b*c - a*d)*(a + b*x)^2) - (60*B*d^4*n)/((b*c - a*d)^2*(a + b*x)) - (60*B*d^5*n*Log[a + b*x])/(b*c - a*d)^3 - (60*B*(a^2*d^2 + a*b*d*(3*c + 5*d*x) + b^2*(6*c^2 + 15*c*d*x + 10*d^2*x^2))*Log[e*((a + b*x)/(c + d*x))^n])/(a + b*x)^5 + (60*B*d^5*n*Log[c + d*x])/(b*c - a*d)^3))/(1800*b^3*g^6)","A",1
127,1,631,477,0.6715979,"\int (a g+b g x)^3 (c i+d i 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*(c*i + d*i*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^3 i^3 \left(120 d^7 (a+b x)^7 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+420 d^6 (a+b x)^6 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+504 d^5 (a+b x)^5 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+210 d^4 (a+b x)^4 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-35 B n (b c-a d)^4 \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)+42 B n (b c-a d)^3 \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)-7 B n (b c-a d)^2 \left(15 d^4 (a+b x)^4 (a d-b c)+20 d^3 (a+b x)^3 (b c-a d)^2+30 d^2 (a+b x)^2 (a d-b c)^3+60 b d x (b c-a d)^4-60 (b c-a d)^5 \log (c+d x)+12 d^5 (a+b x)^5\right)+2 B n (b c-a d) \left(12 d^5 (a+b x)^5 (b c-a d)-15 d^4 (a+b x)^4 (b c-a d)^2+20 d^3 (a+b x)^3 (b c-a d)^3-30 d^2 (a+b x)^2 (b c-a d)^4+60 b d x (b c-a d)^5-60 (b c-a d)^6 \log (c+d x)-10 d^6 (a+b x)^6\right)\right)}{840 b^4 d^4}","\frac{b^3 g^3 i^3 (c+d x)^7 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{7 d^4}-\frac{b^2 g^3 i^3 (c+d x)^6 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 d^4}-\frac{g^3 i^3 (c+d x)^4 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{4 d^4}+\frac{3 b g^3 i^3 (c+d x)^5 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 d^4}+\frac{B g^3 i^3 n (b c-a d)^7 \log \left(\frac{a+b x}{c+d x}\right)}{140 b^4 d^4}+\frac{B g^3 i^3 n (b c-a d)^7 \log (c+d x)}{140 b^4 d^4}+\frac{B g^3 i^3 n x (b c-a d)^6}{140 b^3 d^3}+\frac{B g^3 i^3 n (c+d x)^2 (b c-a d)^5}{280 b^2 d^4}-\frac{b^2 B g^3 i^3 n (c+d x)^6 (b c-a d)}{42 d^4}+\frac{B g^3 i^3 n (c+d x)^3 (b c-a d)^4}{420 b d^4}-\frac{17 B g^3 i^3 n (c+d x)^4 (b c-a d)^3}{280 d^4}+\frac{b B g^3 i^3 n (c+d x)^5 (b c-a d)^2}{14 d^4}",1,"(g^3*i^3*(210*d^4*(b*c - a*d)^3*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 504*d^5*(b*c - a*d)^2*(a + b*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 420*d^6*(b*c - a*d)*(a + b*x)^6*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 120*d^7*(a + b*x)^7*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 35*B*(b*c - a*d)^4*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]) + 42*B*(b*c - a*d)^3*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]) - 7*B*(b*c - a*d)^2*n*(60*b*d*(b*c - a*d)^4*x + 30*d^2*(-(b*c) + a*d)^3*(a + b*x)^2 + 20*d^3*(b*c - a*d)^2*(a + b*x)^3 + 15*d^4*(-(b*c) + a*d)*(a + b*x)^4 + 12*d^5*(a + b*x)^5 - 60*(b*c - a*d)^5*Log[c + d*x]) + 2*B*(b*c - a*d)*n*(60*b*d*(b*c - a*d)^5*x - 30*d^2*(b*c - a*d)^4*(a + b*x)^2 + 20*d^3*(b*c - a*d)^3*(a + b*x)^3 - 15*d^4*(b*c - a*d)^2*(a + b*x)^4 + 12*d^5*(b*c - a*d)*(a + b*x)^5 - 10*d^6*(a + b*x)^6 - 60*(b*c - a*d)^6*Log[c + d*x])))/(840*b^4*d^4)","A",1
128,1,441,387,0.3434277,"\int (a g+b g x)^2 (c i+d i 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)^2*(c*i + d*i*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g^2 i^3 \left(60 b^6 (c+d x)^6 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-144 b^5 (c+d x)^5 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+90 b^4 (c+d x)^4 (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 n (b c-a d)^3 \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)+12 B n (b c-a d)^2 \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)-B n (b c-a d) \left(15 b^4 (c+d x)^4 (b c-a d)+20 b^3 (c+d x)^3 (b c-a d)^2+30 b^2 (c+d x)^2 (b c-a d)^3+60 b d x (b c-a d)^4+60 (b c-a d)^5 \log (a+b x)+12 b^5 (c+d x)^5\right)\right)}{360 b^4 d^3}","\frac{b^2 g^2 i^3 (c+d x)^6 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{6 d^3}+\frac{g^2 i^3 (c+d x)^4 (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^3}-\frac{2 b g^2 i^3 (c+d x)^5 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 d^3}-\frac{B g^2 i^3 n (b c-a d)^6 \log \left(\frac{a+b x}{c+d x}\right)}{60 b^4 d^3}-\frac{B g^2 i^3 n (b c-a d)^6 \log (c+d x)}{60 b^4 d^3}-\frac{B g^2 i^3 n x (b c-a d)^5}{60 b^3 d^2}-\frac{B g^2 i^3 n (c+d x)^2 (b c-a d)^4}{120 b^2 d^3}-\frac{B g^2 i^3 n (c+d x)^3 (b c-a d)^3}{180 b d^3}+\frac{7 B g^2 i^3 n (c+d x)^4 (b c-a d)^2}{120 d^3}-\frac{b B g^2 i^3 n (c+d x)^5 (b c-a d)}{30 d^3}",1,"(g^2*i^3*(-15*B*(b*c - a*d)^3*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]) + 12*B*(b*c - a*d)^2*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*(b*c - a*d)*n*(60*b*d*(b*c - a*d)^4*x + 30*b^2*(b*c - a*d)^3*(c + d*x)^2 + 20*b^3*(b*c - a*d)^2*(c + d*x)^3 + 15*b^4*(b*c - a*d)*(c + d*x)^4 + 12*b^5*(c + d*x)^5 + 60*(b*c - a*d)^5*Log[a + b*x]) + 90*b^4*(b*c - a*d)^2*(c + d*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 144*b^5*(b*c - a*d)*(c + d*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 60*b^6*(c + d*x)^6*(A + B*Log[e*((a + b*x)/(c + d*x))^n])))/(360*b^4*d^3)","A",1
129,1,269,283,0.2280422,"\int (a g+b g x) (c i+d i 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)*(c*i + d*i*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{g i^3 \left(24 b (c+d x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-30 (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)+\frac{5 B n (b c-a d)^2 \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)}{b^4}-\frac{2 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)}{b^4}\right)}{120 d^2}","-\frac{g i^3 (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)}{4 d^2}+\frac{b g i^3 (c+d x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{5 d^2}+\frac{B g i^3 n (b c-a d)^5 \log \left(\frac{a+b x}{c+d x}\right)}{20 b^4 d^2}+\frac{B g i^3 n (b c-a d)^5 \log (c+d x)}{20 b^4 d^2}+\frac{B g i^3 n x (b c-a d)^4}{20 b^3 d}+\frac{B g i^3 n (c+d x)^2 (b c-a d)^3}{40 b^2 d^2}+\frac{B g i^3 n (c+d x)^3 (b c-a d)^2}{60 b d^2}-\frac{B g i^3 n (c+d x)^4 (b c-a d)}{20 d^2}",1,"(g*i^3*((5*B*(b*c - a*d)^2*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 - (2*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^4 - 30*(b*c - a*d)*(c + d*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 24*b*(c + d*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n])))/(120*d^2)","A",1
130,1,124,156,0.0746067,"\int (c i+d i x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Integrate[(c*i + d*i*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{i^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{i^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 i^3 n (b c-a d)^4 \log (a+b x)}{4 b^4 d}-\frac{B i^3 n x (b c-a d)^3}{4 b^3}-\frac{B i^3 n (c+d x)^2 (b c-a d)^2}{8 b^2 d}-\frac{B i^3 n (c+d x)^3 (b c-a d)}{12 b d}",1,"(i^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
131,1,368,373,0.2845763,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{a g+b g x} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a*g + b*g*x),x]","\frac{i^3 \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 (g (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 (g (a+b x)) \left(\log (g (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)}{6 b^4 g}","\frac{d i^3 (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)}{b^4 g}-\frac{i^3 (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)}{b^4 g}+\frac{i^3 (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)}{2 b^2 g}+\frac{i^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 g}+\frac{B i^3 n (b c-a d)^3 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g}-\frac{5 B i^3 n (b c-a d)^3 \log \left(\frac{a+b x}{c+d x}\right)}{6 b^4 g}-\frac{11 B i^3 n (b c-a d)^3 \log (c+d x)}{6 b^4 g}-\frac{5 B d i^3 n x (b c-a d)^2}{6 b^3 g}-\frac{B i^3 n (c+d x)^2 (b c-a d)}{6 b^2 g}",1,"(i^3*(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[g*(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[g*(a + b*x)]*(Log[g*(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*g)","A",1
132,1,394,390,0.4040612,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{(a g+b g x)^2} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a*g + b*g*x)^2,x]","\frac{i^3 \left(-a^2 B d^3 n \log (a+b x)+b^2 d^3 x^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+6 d (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)-\frac{2 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{a+b x}+2 A b d^2 x (3 b c-2 a d)+2 B d^2 (a+b x) (3 b c-2 a d) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-b B d^2 n x (b c-a d)-3 B d 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)-\frac{2 B n (b c-a d)^3}{a+b x}-2 B d n (b c-a d)^2 \log (a+b x)+2 B d n (b c-a d)^2 \log (c+d x)-2 B d n (a d-b c) (2 a d-3 b c) \log (c+d x)+b^2 B c^2 d n \log (c+d x)\right)}{2 b^4 g^2}","\frac{2 d^2 i^3 (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^4 g^2}-\frac{3 d i^3 (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^4 g^2}-\frac{i^3 (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)}{b^3 g^2 (a+b x)}+\frac{d i^3 (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 b^2 g^2}+\frac{3 B d i^3 n (b c-a d)^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g^2}-\frac{B d i^3 n (b c-a d)^2 \log \left(\frac{a+b x}{c+d x}\right)}{2 b^4 g^2}-\frac{5 B d i^3 n (b c-a d)^2 \log (c+d x)}{2 b^4 g^2}-\frac{B d^2 i^3 n x (b c-a d)}{2 b^3 g^2}-\frac{B i^3 n (c+d x) (b c-a d)^2}{b^3 g^2 (a+b x)}",1,"(i^3*(2*A*b*d^2*(3*b*c - 2*a*d)*x - b*B*d^2*(b*c - a*d)*n*x - (2*B*(b*c - a*d)^3*n)/(a + b*x) - a^2*B*d^3*n*Log[a + b*x] - 2*B*d*(b*c - a*d)^2*n*Log[a + b*x] + 2*B*d^2*(3*b*c - 2*a*d)*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] + b^2*d^3*x^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - (2*(b*c - a*d)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x) + 6*d*(b*c - a*d)^2*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + b^2*B*c^2*d*n*Log[c + d*x] + 2*B*d*(b*c - a*d)^2*n*Log[c + d*x] - 2*B*d*(-(b*c) + a*d)*(-3*b*c + 2*a*d)*n*Log[c + d*x] - 3*B*d*(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)])))/(2*b^4*g^2)","A",1
133,1,331,361,0.4873019,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{(a g+b g x)^3} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a*g + b*g*x)^3,x]","\frac{i^3 \left(12 d^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)+A\right)-\frac{12 d (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{a+b x}-\frac{2 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(a+b x)^2}+4 B d^3 (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+6 B d^2 n (a d-b c) \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)+10 B d^2 n (a d-b c) \log (a+b x)+6 B d^2 n (b c-a d) \log (c+d x)-\frac{10 B d n (b c-a d)^2}{a+b x}-\frac{B n (b c-a d)^3}{(a+b x)^2}+4 A b d^3 x\right)}{4 b^4 g^3}","\frac{d^3 i^3 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b^4 g^3}-\frac{3 d^2 i^3 (b c-a d) \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^4 g^3}-\frac{2 d i^3 (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)}{b^3 g^3 (a+b x)}-\frac{i^3 (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)}{2 b^2 g^3 (a+b x)^2}+\frac{3 B d^2 i^3 n (b c-a d) \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g^3}-\frac{B d^2 i^3 n (b c-a d) \log (c+d x)}{b^4 g^3}-\frac{2 B d i^3 n (c+d x) (b c-a d)}{b^3 g^3 (a+b x)}-\frac{B i^3 n (c+d x)^2 (b c-a d)}{4 b^2 g^3 (a+b x)^2}",1,"(i^3*(4*A*b*d^3*x - (B*(b*c - a*d)^3*n)/(a + b*x)^2 - (10*B*d*(b*c - a*d)^2*n)/(a + b*x) + 10*B*d^2*(-(b*c) + a*d)*n*Log[a + b*x] + 4*B*d^3*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] - (2*(b*c - a*d)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x)^2 - (12*d*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x) + 12*d^2*(b*c - a*d)*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 6*B*d^2*(b*c - a*d)*n*Log[c + d*x] + 6*B*d^2*(-(b*c) + a*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)])))/(4*b^4*g^3)","A",1
134,1,326,326,0.4649947,"\int \frac{(c i+d i x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{(a g+b g x)^4} \, dx","Integrate[((c*i + d*i*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a*g + b*g*x)^4,x]","\frac{i^3 \left(36 d^3 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+\frac{108 d^2 (a d-b c) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{a+b x}-\frac{54 d (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(a+b x)^2}-\frac{12 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(a+b x)^3}-18 B d^3 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)+\frac{66 B d^2 n (a d-b c)}{a+b x}-\frac{21 B d n (b c-a d)^2}{(a+b x)^2}-\frac{4 B n (b c-a d)^3}{(a+b x)^3}-66 B d^3 n \log (a+b x)+66 B d^3 n \log (c+d x)\right)}{36 b^4 g^4}","-\frac{d^3 i^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)}{b^4 g^4}-\frac{d^2 i^3 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b^3 g^4 (a+b x)}-\frac{d i^3 (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 b^2 g^4 (a+b x)^2}-\frac{i^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 g^4 (a+b x)^3}+\frac{B d^3 i^3 n \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g^4}-\frac{B d^2 i^3 n (c+d x)}{b^3 g^4 (a+b x)}-\frac{B d i^3 n (c+d x)^2}{4 b^2 g^4 (a+b x)^2}-\frac{B i^3 n (c+d x)^3}{9 b g^4 (a+b x)^3}",1,"(i^3*((-4*B*(b*c - a*d)^3*n)/(a + b*x)^3 - (21*B*d*(b*c - a*d)^2*n)/(a + b*x)^2 + (66*B*d^2*(-(b*c) + a*d)*n)/(a + b*x) - 66*B*d^3*n*Log[a + b*x] - (12*(b*c - a*d)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x)^3 - (54*d*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x)^2 + (108*d^2*(-(b*c) + a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x) + 36*d^3*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 66*B*d^3*n*Log[c + d*x] - 18*B*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)])))/(36*b^4*g^4)","A",1
135,1,370,269,0.2988942,"\int \frac{(a g+b g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{c i+d i x} \, dx","Integrate[((a*g + b*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c*i + d*i*x),x]","\frac{g^3 \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 (i (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(\log (i (c+d x)) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (i (c+d x))\right)+2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\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)}{6 d^4 i}","\frac{g^3 (b c-a d)^3 \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)}{6 d^4 i}+\frac{g^3 (a+b x) (b c-a d)^2 \left(6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+6 A+5 B n\right)}{6 d^3 i}-\frac{g^3 (a+b x)^2 (b c-a d) \left(3 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+3 A+B n\right)}{6 d^2 i}+\frac{g^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 i}+\frac{B g^3 n (b c-a d)^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i}",1,"(g^3*(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] + 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]) - 6*(b*c - a*d)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[i*(c + d*x)] + 3*B*(b*c - a*d)^3*n*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[i*(c + d*x)])*Log[i*(c + d*x)] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(6*d^4*i)","A",1
136,1,266,211,0.1878055,"\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)}{c i+d i x} \, dx","Integrate[((a*g + b*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c*i + d*i*x),x]","\frac{g^2 \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 (i (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) (a d-b c) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-B n (b c-a d)^2 \left(\log (i (c+d x)) \left(2 \log \left(\frac{d (a+b x)}{a d-b c}\right)-\log (i (c+d x))\right)+2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\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)}{2 d^3 i}","-\frac{g^2 (b c-a d)^2 \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)}{2 d^3 i}-\frac{g^2 (a+b x) (b c-a d) \left(2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 A+B n\right)}{2 d^2 i}+\frac{g^2 (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 d i}-\frac{B g^2 n (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^3 i}",1,"(g^2*(-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] - B*(b*c - a*d)*n*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 2*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[i*(c + d*x)] - B*(b*c - a*d)^2*n*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[i*(c + d*x)])*Log[i*(c + d*x)] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(2*d^3*i)","A",1
137,1,170,134,0.1188302,"\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)}{c i+d i x} \, dx","Integrate[((a*g + b*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c*i + d*i*x),x]","\frac{g \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)}{2 d^2 i}","\frac{g (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+B n\right)}{d^2 i}+\frac{g (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{d i}+\frac{B g n (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^2 i}",1,"(g*(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)])))/(2*d^2*i)","A",1
138,1,101,80,0.0315048,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{c i+d i x} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(c*i + d*i*x),x]","\frac{\log (i (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 (i (c+d x))\right)-2 B n \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)}{2 d i}","-\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 i}-\frac{B n \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d i}",1,"(Log[i*(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[i*(c + d*x)]) - 2*B*n*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*d*i)","A",1
139,1,219,50,0.1114809,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a g+b g x) (c i+d i x)} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/((a*g + b*g*x)*(c*i + d*i*x)),x]","\frac{2 A \log (a+b x)+2 B \log (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-2 B \log (c+d x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B n \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)+2 B n \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+2 B n \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)+2 B n \log (c+d x) \log \left(\frac{d (a+b x)}{a d-b c}\right)-B n \log ^2(a+b x)-2 A \log (c+d x)-B n \log ^2(c+d x)}{2 g i (b c-a d)}","\frac{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 B g i n (b c-a d)}",1,"(2*A*Log[a + b*x] - B*n*Log[a + b*x]^2 + 2*B*Log[a + b*x]*Log[e*((a + b*x)/(c + d*x))^n] - 2*A*Log[c + d*x] + 2*B*n*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] - 2*B*Log[e*((a + b*x)/(c + d*x))^n]*Log[c + d*x] - B*n*Log[c + d*x]^2 + 2*B*n*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] + 2*B*n*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 2*B*n*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*(b*c - a*d)*g*i)","C",1
140,1,304,181,0.2889848,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a g+b g x)^2 (c i+d i x)} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/((a*g + b*g*x)^2*(c*i + d*i*x)),x]","-\frac{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)}{2 g^2 i (a+b x) (b c-a d)^2}","-\frac{d \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)}{g^2 i (b c-a d)^2}-\frac{b (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^2 i (a+b x) (b c-a d)^2}-\frac{b B n (c+d x)}{g^2 i (a+b x) (b c-a d)^2}+\frac{B d n \log ^2\left(\frac{a+b x}{c+d x}\right)}{2 g^2 i (b c-a d)^2}",1,"-1/2*(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)^2*g^2*i*(a + b*x))","C",1
141,1,434,266,0.4131962,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a g+b g x)^3 (c i+d i x)} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/((a*g + b*g*x)^3*(c*i + d*i*x)),x]","\frac{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) (b c-a d) \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)}{4 g^3 i (a+b x)^2 (b c-a d)^3}","-\frac{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 g^3 i (a+b x)^2 (b c-a d)^3}+\frac{d^2 \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)}{g^3 i (b c-a d)^3}+\frac{2 b d (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^3 i (a+b x) (b c-a d)^3}-\frac{B d^2 n \log ^2\left(\frac{a+b x}{c+d x}\right)}{2 g^3 i (b c-a d)^3}-\frac{B n (c+d x)^2 \left(b-\frac{4 d (a+b x)}{c+d x}\right)^2}{4 g^3 i (a+b x)^2 (b c-a d)^3}",1,"(-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)]))/(4*(b*c - a*d)^3*g^3*i*(a + b*x)^2)","C",1
142,1,518,389,0.716709,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a g+b g x)^4 (c i+d i x)} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/((a*g + b*g*x)^4*(c*i + d*i*x)),x]","\frac{\frac{36 A d^2 (a d-b c)}{a+b x}+\frac{18 A d (b c-a d)^2}{(a+b x)^2}-\frac{12 A (b c-a d)^3}{(a+b x)^3}-36 A d^3 \log (a+b x)-36 B d^3 \log (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+36 B d^3 \log (c+d x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-36 B d^3 n \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)-36 B d^3 n \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-36 B d^3 n \log (c+d x) \log \left(\frac{d (a+b x)}{a d-b c}\right)-36 B d^3 n \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)+\frac{36 B d^2 (a d-b c) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{a+b x}+\frac{66 B d^2 n (a d-b c)}{a+b x}+\frac{18 B d (b c-a d)^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a+b x)^2}-\frac{12 B (b c-a d)^3 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a+b x)^3}+\frac{15 B d n (b c-a d)^2}{(a+b x)^2}-\frac{4 B n (b c-a d)^3}{(a+b x)^3}+18 B d^3 n \log ^2(a+b x)-66 B d^3 n \log (a+b x)+36 A d^3 \log (c+d x)+18 B d^3 n \log ^2(c+d x)+66 B d^3 n \log (c+d x)}{36 g^4 i (b c-a d)^4}","-\frac{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 g^4 i (a+b x)^3 (b c-a d)^4}+\frac{3 b^2 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 i (a+b x)^2 (b c-a d)^4}-\frac{d^3 \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)}{g^4 i (b c-a d)^4}-\frac{3 b d^2 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^4 i (a+b x) (b c-a d)^4}-\frac{b^3 B n (c+d x)^3}{9 g^4 i (a+b x)^3 (b c-a d)^4}+\frac{3 b^2 B d n (c+d x)^2}{4 g^4 i (a+b x)^2 (b c-a d)^4}+\frac{B d^3 n \log ^2\left(\frac{a+b x}{c+d x}\right)}{2 g^4 i (b c-a d)^4}-\frac{3 b B d^2 n (c+d x)}{g^4 i (a+b x) (b c-a d)^4}",1,"((-12*A*(b*c - a*d)^3)/(a + b*x)^3 - (4*B*(b*c - a*d)^3*n)/(a + b*x)^3 + (18*A*d*(b*c - a*d)^2)/(a + b*x)^2 + (15*B*d*(b*c - a*d)^2*n)/(a + b*x)^2 + (36*A*d^2*(-(b*c) + a*d))/(a + b*x) + (66*B*d^2*(-(b*c) + a*d)*n)/(a + b*x) - 36*A*d^3*Log[a + b*x] - 66*B*d^3*n*Log[a + b*x] + 18*B*d^3*n*Log[a + b*x]^2 - (12*B*(b*c - a*d)^3*Log[e*((a + b*x)/(c + d*x))^n])/(a + b*x)^3 + (18*B*d*(b*c - a*d)^2*Log[e*((a + b*x)/(c + d*x))^n])/(a + b*x)^2 + (36*B*d^2*(-(b*c) + a*d)*Log[e*((a + b*x)/(c + d*x))^n])/(a + b*x) - 36*B*d^3*Log[a + b*x]*Log[e*((a + b*x)/(c + d*x))^n] + 36*A*d^3*Log[c + d*x] + 66*B*d^3*n*Log[c + d*x] - 36*B*d^3*n*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] + 36*B*d^3*Log[e*((a + b*x)/(c + d*x))^n]*Log[c + d*x] + 18*B*d^3*n*Log[c + d*x]^2 - 36*B*d^3*n*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] - 36*B*d^3*n*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] - 36*B*d^3*n*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(36*(b*c - a*d)^4*g^4*i)","C",1
143,1,375,359,0.4512938,"\int \frac{(a g+b g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{(c i+d i x)^2} \, dx","Integrate[((a*g + b*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c*i + d*i*x)^2,x]","\frac{g^3 \left(b B n \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)+b^3 d^2 x^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-2 A b^2 d x (2 b c-3 a d)+6 b (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)+\frac{2 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{c+d x}-2 b B d (a+b x) (2 b c-3 a d) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-3 b 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 B n (2 b c-3 a d) (b c-a d) \log (c+d x)-2 B n (b c-a d)^2 \left(\frac{b c-a d}{c+d x}+b \log (a+b x)-b \log (c+d x)\right)\right)}{2 d^4 i^2}","-\frac{b g^3 (b c-a d)^2 \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+5 B n\right)}{2 d^4 i^2}-\frac{g^3 (a+b x) (6 A+5 B n) (b c-a d)^2}{2 d^3 i^2 (c+d x)}-\frac{g^3 (a+b x)^2 (b c-a d) \left(3 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+3 A+B n\right)}{2 d^2 i^2 (c+d x)}+\frac{g^3 (a+b x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 d i^2 (c+d x)}-\frac{3 b B g^3 n (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i^2}-\frac{3 B g^3 (a+b x) (b c-a d)^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{d^3 i^2 (c+d x)}+\frac{3 B g^3 n (a+b x) (b c-a d)^2}{d^3 i^2 (c+d x)}",1,"(g^3*(-2*A*b^2*d*(2*b*c - 3*a*d)*x - 2*b*B*d*(2*b*c - 3*a*d)*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] + b^3*d^2*x^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + (2*(b*c - a*d)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c + d*x) + 2*b*B*(2*b*c - 3*a*d)*(b*c - a*d)*n*Log[c + d*x] + 6*b*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - 2*B*(b*c - a*d)^2*n*((b*c - a*d)/(c + d*x) + b*Log[a + b*x] - b*Log[c + d*x]) + b*B*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*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)])))/(2*d^4*i^2)","A",1
144,1,252,275,0.2543096,"\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)}{(c i+d i x)^2} \, dx","Integrate[((a*g + b*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c*i + d*i*x)^2,x]","\frac{g^2 \left(-2 b (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)-\frac{(b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{c+d x}+b B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+b 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)+\frac{B n (b c-a d)^2}{c+d x}+b B n (b c-a d) \log (a+b x)-2 b B n (b c-a d) \log (c+d x)+A b^2 d x\right)}{d^3 i^2}","\frac{b g^2 (b c-a d) \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+B n\right)}{d^3 i^2}+\frac{g^2 (a+b x) (2 A+B n) (b c-a d)}{d^2 i^2 (c+d x)}+\frac{g^2 (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{d i^2 (c+d x)}+\frac{2 b B g^2 n (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^3 i^2}+\frac{2 B g^2 (a+b x) (b c-a d) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{d^2 i^2 (c+d x)}-\frac{2 B g^2 n (a+b x) (b c-a d)}{d^2 i^2 (c+d x)}",1,"(g^2*(A*b^2*d*x + (B*(b*c - a*d)^2*n)/(c + d*x) + b*B*(b*c - a*d)*n*Log[a + b*x] + b*B*d*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] - ((b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c + d*x) - 2*b*B*(b*c - a*d)*n*Log[c + d*x] - 2*b*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + b*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^3*i^2)","A",1
145,1,183,168,0.1834231,"\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)}{(c i+d i x)^2} \, dx","Integrate[((a*g + b*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c*i + d*i*x)^2,x]","\frac{g \left(2 b \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+\frac{2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{c+d x}-b B 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)-2 B n \left(\frac{b c-a d}{c+d x}+b \log (a+b x)-b \log (c+d x)\right)\right)}{2 d^2 i^2}","-\frac{b g \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^2 i^2}-\frac{A g (a+b x)}{d i^2 (c+d x)}-\frac{b B g n \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^2 i^2}-\frac{B g (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{d i^2 (c+d x)}+\frac{B g n (a+b x)}{d i^2 (c+d x)}",1,"(g*((2*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c + d*x) + 2*b*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - 2*B*n*((b*c - a*d)/(c + d*x) + b*Log[a + b*x] - b*Log[c + d*x]) - b*B*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*d^2*i^2)","A",1
146,1,114,102,0.0588486,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(c i+d i x)^2} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(c*i + d*i*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 i^2}-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{d i (c i+d i x)}","\frac{A (a+b x)}{i^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)}{i^2 (c+d x) (b c-a d)}-\frac{B n (a+b x)}{i^2 (c+d x) (b c-a d)}",1,"-((A + B*Log[e*((a + b*x)/(c + d*x))^n])/(d*i*(c*i + d*i*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*i^2)","A",1
147,1,304,166,0.3538484,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a g+b g x) (c i+d i x)^2} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/((a*g + b*g*x)*(c*i + d*i*x)^2),x]","\frac{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)}{2 g i^2 (c+d x) (b c-a d)^2}","\frac{b \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 B g i^2 n (b c-a d)^2}-\frac{A d (a+b x)}{g i^2 (c+d x) (b c-a d)^2}-\frac{B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{g i^2 (c+d x) (b c-a d)^2}+\frac{B d n (a+b x)}{g i^2 (c+d x) (b c-a d)^2}",1,"(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)]))/(2*(b*c - a*d)^2*g*i^2*(c + d*x))","C",1
148,1,342,273,0.4531479,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a g+b g x)^2 (c i+d i x)^2} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/((a*g + b*g*x)^2*(c*i + d*i*x)^2),x]","\frac{-2 b d \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-\frac{b (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{a+b x}+2 b d \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+\frac{d (a d-b c) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{c+d x}-\frac{b^2 B c n}{a+b x}+b 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 d 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)+\frac{a b B d n}{a+b x}-\frac{a B d^2 n}{c+d x}+\frac{b B c d n}{c+d x}}{g^2 i^2 (b c-a d)^3}","-\frac{b^2 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^2 i^2 (a+b x) (b c-a d)^3}+\frac{d^2 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^2 i^2 (c+d x) (b c-a d)^3}-\frac{2 b d \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)}{g^2 i^2 (b c-a d)^3}-\frac{b^2 B n (c+d x)}{g^2 i^2 (a+b x) (b c-a d)^3}-\frac{B d^2 n (a+b x)}{g^2 i^2 (c+d x) (b c-a d)^3}+\frac{b B d n \log ^2\left(\frac{a+b x}{c+d x}\right)}{g^2 i^2 (b c-a d)^3}",1,"(-((b^2*B*c*n)/(a + b*x)) + (a*b*B*d*n)/(a + b*x) + (b*B*c*d*n)/(c + d*x) - (a*B*d^2*n)/(c + d*x) - (b*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x) + (d*(-(b*c) + a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c + d*x) - 2*b*d*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 2*b*d*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + b*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*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)]))/((b*c - a*d)^3*g^2*i^2)","C",1
149,1,478,380,0.761991,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a g+b g x)^3 (c i+d i x)^2} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/((a*g + b*g*x)^3*(c*i + d*i*x)^2),x]","\frac{12 b d^2 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+\frac{4 d^2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{c+d x}-12 b d^2 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+\frac{8 b d (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{a+b x}-\frac{2 b (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(a+b x)^2}+\frac{8 b^2 B c d n}{a+b x}-6 b B d^2 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)+6 b B d^2 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)+\frac{2 b B d n (b c-a d)}{a+b x}-\frac{b B n (b c-a d)^2}{(a+b x)^2}-\frac{8 a b B d^2 n}{a+b x}+6 b B d^2 n \log (a+b x)+\frac{4 a B d^3 n}{c+d x}-\frac{4 b B c d^2 n}{c+d x}-6 b B d^2 n \log (c+d x)}{4 g^3 i^2 (b c-a d)^4}","-\frac{b^3 (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 i^2 (a+b x)^2 (b c-a d)^4}+\frac{3 b^2 d (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^3 i^2 (a+b x) (b c-a d)^4}-\frac{d^3 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^3 i^2 (c+d x) (b c-a d)^4}+\frac{3 b d^2 \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)}{g^3 i^2 (b c-a d)^4}-\frac{b^3 B n (c+d x)^2}{4 g^3 i^2 (a+b x)^2 (b c-a d)^4}+\frac{3 b^2 B d n (c+d x)}{g^3 i^2 (a+b x) (b c-a d)^4}+\frac{B d^3 n (a+b x)}{g^3 i^2 (c+d x) (b c-a d)^4}-\frac{3 b B d^2 n \log ^2\left(\frac{a+b x}{c+d x}\right)}{2 g^3 i^2 (b c-a d)^4}",1,"(-((b*B*(b*c - a*d)^2*n)/(a + b*x)^2) + (8*b^2*B*c*d*n)/(a + b*x) - (8*a*b*B*d^2*n)/(a + b*x) + (2*b*B*d*(b*c - a*d)*n)/(a + b*x) - (4*b*B*c*d^2*n)/(c + d*x) + (4*a*B*d^3*n)/(c + d*x) + 6*b*B*d^2*n*Log[a + b*x] - (2*b*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x)^2 + (8*b*d*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x) + (4*d^2*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c + d*x) + 12*b*d^2*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 6*b*B*d^2*n*Log[c + d*x] - 12*b*d^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - 6*b*B*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)]) + 6*b*B*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)]))/(4*(b*c - a*d)^4*g^3*i^2)","C",1
150,1,549,477,1.5382031,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a g+b g x)^4 (c i+d i x)^2} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/((a*g + b*g*x)^4*(c*i + d*i*x)^2),x]","-\frac{36 b d^3 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-\frac{9 d^3 (a d-b c) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{c+d x}-36 b d^3 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+\frac{27 b d^2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{a+b x}-\frac{9 b d (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(a+b x)^2}+\frac{3 b (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(a+b x)^3}+\frac{27 b^2 B c d^2 n}{a+b x}-18 b B d^3 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)+18 b B d^3 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)+\frac{12 b B d^2 n (b c-a d)}{a+b x}-\frac{6 b B d n (b c-a d)^2}{(a+b x)^2}+\frac{b B n (b c-a d)^3}{(a+b x)^3}-\frac{27 a b B d^3 n}{a+b x}+30 b B d^3 n \log (a+b x)+\frac{9 a B d^4 n}{c+d x}-\frac{9 b B c d^3 n}{c+d x}-30 b B d^3 n \log (c+d x)}{9 g^4 i^2 (b c-a d)^5}","-\frac{b^4 (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 g^4 i^2 (a+b x)^3 (b c-a d)^5}+\frac{2 b^3 d (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^4 i^2 (a+b x)^2 (b c-a d)^5}-\frac{6 b^2 d^2 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^4 i^2 (a+b x) (b c-a d)^5}+\frac{d^4 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^4 i^2 (c+d x) (b c-a d)^5}-\frac{4 b d^3 \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)}{g^4 i^2 (b c-a d)^5}-\frac{b^4 B n (c+d x)^3}{9 g^4 i^2 (a+b x)^3 (b c-a d)^5}+\frac{b^3 B d n (c+d x)^2}{g^4 i^2 (a+b x)^2 (b c-a d)^5}-\frac{6 b^2 B d^2 n (c+d x)}{g^4 i^2 (a+b x) (b c-a d)^5}-\frac{B d^4 n (a+b x)}{g^4 i^2 (c+d x) (b c-a d)^5}+\frac{2 b B d^3 n \log ^2\left(\frac{a+b x}{c+d x}\right)}{g^4 i^2 (b c-a d)^5}",1,"-1/9*((b*B*(b*c - a*d)^3*n)/(a + b*x)^3 - (6*b*B*d*(b*c - a*d)^2*n)/(a + b*x)^2 + (27*b^2*B*c*d^2*n)/(a + b*x) - (27*a*b*B*d^3*n)/(a + b*x) + (12*b*B*d^2*(b*c - a*d)*n)/(a + b*x) - (9*b*B*c*d^3*n)/(c + d*x) + (9*a*B*d^4*n)/(c + d*x) + 30*b*B*d^3*n*Log[a + b*x] + (3*b*(b*c - a*d)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x)^3 - (9*b*d*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x)^2 + (27*b*d^2*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x) - (9*d^3*(-(b*c) + a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c + d*x) + 36*b*d^3*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 30*b*B*d^3*n*Log[c + d*x] - 36*b*d^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - 18*b*B*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)]) + 18*b*B*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)]))/((b*c - a*d)^5*g^4*i^2)","C",1
151,1,334,382,0.448107,"\int \frac{(a g+b g x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{(c i+d i x)^3} \, dx","Integrate[((a*g + b*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c*i + d*i*x)^3,x]","\frac{g^3 \left(-12 b^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)-\frac{12 b (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{c+d x}+\frac{2 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(c+d x)^2}+4 b^2 B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+6 b^2 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)+10 b^2 B n (b c-a d) \log (a+b x)-14 b^2 B n (b c-a d) \log (c+d x)+\frac{10 b B n (b c-a d)^2}{c+d x}-\frac{B n (b c-a d)^3}{(c+d x)^2}+4 A b^3 d x\right)}{4 d^4 i^3}","\frac{b^2 g^3 (b c-a d) \log \left(\frac{b c-a d}{b (c+d x)}\right) \left(3 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+3 A+B n\right)}{d^4 i^3}+\frac{b g^3 (a+b x) (3 A+B n) (b c-a d)}{d^3 i^3 (c+d x)}+\frac{g^3 (a+b x)^2 (b c-a d) \left(3 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+3 A+B n\right)}{2 d^2 i^3 (c+d x)^2}+\frac{g^3 (a+b x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{d i^3 (c+d x)^2}+\frac{3 b^2 B g^3 n (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i^3}+\frac{3 b B g^3 (a+b x) (b c-a d) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{d^3 i^3 (c+d x)}-\frac{3 b B g^3 n (a+b x) (b c-a d)}{d^3 i^3 (c+d x)}-\frac{3 B g^3 n (a+b x)^2 (b c-a d)}{4 d^2 i^3 (c+d x)^2}",1,"(g^3*(4*A*b^3*d*x - (B*(b*c - a*d)^3*n)/(c + d*x)^2 + (10*b*B*(b*c - a*d)^2*n)/(c + d*x) + 10*b^2*B*(b*c - a*d)*n*Log[a + b*x] + 4*b^2*B*d*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] + (2*(b*c - a*d)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c + d*x)^2 - (12*b*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c + d*x) - 14*b^2*B*(b*c - a*d)*n*Log[c + d*x] - 12*b^2*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + 6*b^2*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)])))/(4*d^4*i^3)","A",1
152,1,259,263,0.3435308,"\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)}{(c i+d i x)^3} \, dx","Integrate[((a*g + b*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c*i + d*i*x)^3,x]","\frac{g^2 \left(4 b^2 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+\frac{8 b (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{c+d x}-\frac{2 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(c+d x)^2}-2 b^2 B 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)-6 b^2 B n \log (a+b x)-\frac{6 b B n (b c-a d)}{c+d x}+\frac{B n (b c-a d)^2}{(c+d x)^2}+6 b^2 B n \log (c+d x)\right)}{4 d^3 i^3}","-\frac{b^2 g^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\right)}{d^3 i^3}-\frac{g^2 (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 d i^3 (c+d x)^2}-\frac{A b g^2 (a+b x)}{d^2 i^3 (c+d x)}-\frac{b^2 B g^2 n \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^3 i^3}-\frac{b B g^2 (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{d^2 i^3 (c+d x)}+\frac{b B g^2 n (a+b x)}{d^2 i^3 (c+d x)}+\frac{B g^2 n (a+b x)^2}{4 d i^3 (c+d x)^2}",1,"(g^2*((B*(b*c - a*d)^2*n)/(c + d*x)^2 - (6*b*B*(b*c - a*d)*n)/(c + d*x) - 6*b^2*B*n*Log[a + b*x] - (2*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c + d*x)^2 + (8*b*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c + d*x) + 6*b^2*B*n*Log[c + d*x] + 4*b^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - 2*b^2*B*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)])))/(4*d^3*i^3)","A",1
153,1,215,89,0.1628178,"\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)}{(c i+d i x)^3} \, dx","Integrate[((a*g + b*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c*i + d*i*x)^3,x]","\frac{g \left(-\frac{b \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{d^2 (c+d x)}+\frac{(b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 d^2 (c+d x)^2}-\frac{B n \left(\frac{2 b^2 \log (a+b x)}{b c-a d}-\frac{2 b^2 \log (c+d x)}{b c-a d}+\frac{b c-a d}{(c+d x)^2}+\frac{2 b}{c+d x}\right)}{4 d^2}+\frac{b B n \left(\frac{b \log (a+b x)}{b c-a d}-\frac{b \log (c+d x)}{b c-a d}+\frac{1}{c+d x}\right)}{d^2}\right)}{i^3}","\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 i^3 (c+d x)^2 (b c-a d)}-\frac{B g n (a+b x)^2}{4 i^3 (c+d x)^2 (b c-a d)}",1,"(g*(((b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*d^2*(c + d*x)^2) - (b*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(d^2*(c + d*x)) + (b*B*n*((c + d*x)^(-1) + (b*Log[a + b*x])/(b*c - a*d) - (b*Log[c + d*x])/(b*c - a*d)))/d^2 - (B*n*((b*c - a*d)/(c + d*x)^2 + (2*b)/(c + d*x) + (2*b^2*Log[a + b*x])/(b*c - a*d) - (2*b^2*Log[c + d*x])/(b*c - a*d)))/(4*d^2)))/i^3","B",1
154,1,115,151,0.1398852,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(c i+d i x)^3} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(c*i + d*i*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 i^3 (c+d x)^2}","-\frac{B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A}{2 d i^3 (c+d x)^2}+\frac{b^2 B n \log (a+b x)}{2 d i^3 (b c-a d)^2}-\frac{b^2 B n \log (c+d x)}{2 d i^3 (b c-a d)^2}+\frac{b B n}{2 d i^3 (c+d x) (b c-a d)}+\frac{B n}{4 d i^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*i^3*(c + d*x)^2)","A",1
155,1,434,254,0.4221617,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a g+b g x) (c i+d i x)^3} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/((a*g + b*g*x)*(c*i + d*i*x)^3),x]","\frac{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)}{4 g i^3 (c+d x)^2 (b c-a d)^3}","\frac{b^2 \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)}{g i^3 (b c-a d)^3}+\frac{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 g i^3 (c+d x)^2 (b c-a d)^3}-\frac{2 b d (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g i^3 (c+d x) (b c-a d)^3}-\frac{b^2 B n \log ^2\left(\frac{a+b x}{c+d x}\right)}{2 g i^3 (b c-a d)^3}-\frac{B n \left(4 b-\frac{d (a+b x)}{c+d x}\right)^2}{4 g i^3 (b c-a d)^3}",1,"(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)]))/(4*(b*c - a*d)^3*g*i^3*(c + d*x)^2)","C",1
156,1,477,381,0.7871291,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a g+b g x)^2 (c i+d i x)^3} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/((a*g + b*g*x)^2*(c*i + d*i*x)^3),x]","\frac{-12 b^2 d \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-\frac{4 b^2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{a+b x}+12 b^2 d \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-\frac{8 b d (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{c+d x}-\frac{2 d (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(c+d x)^2}-\frac{4 b^3 B c n}{a+b x}+6 b^2 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)-6 b^2 B d 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)+\frac{4 a b^2 B d n}{a+b x}+6 b^2 B d n \log (a+b x)-\frac{8 a b B d^2 n}{c+d x}+\frac{2 b B d n (b c-a d)}{c+d x}+\frac{B d n (b c-a d)^2}{(c+d x)^2}+\frac{8 b^2 B c d n}{c+d x}-6 b^2 B d n \log (c+d x)}{4 g^2 i^3 (b c-a d)^4}","-\frac{b^3 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^2 i^3 (a+b x) (b c-a d)^4}-\frac{3 b^2 d \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)}{g^2 i^3 (b c-a d)^4}-\frac{d^3 (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 g^2 i^3 (c+d x)^2 (b c-a d)^4}+\frac{3 b d^2 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^2 i^3 (c+d x) (b c-a d)^4}-\frac{b^3 B n (c+d x)}{g^2 i^3 (a+b x) (b c-a d)^4}+\frac{3 b^2 B d n \log ^2\left(\frac{a+b x}{c+d x}\right)}{2 g^2 i^3 (b c-a d)^4}+\frac{B d^3 n (a+b x)^2}{4 g^2 i^3 (c+d x)^2 (b c-a d)^4}-\frac{3 b B d^2 n (a+b x)}{g^2 i^3 (c+d x) (b c-a d)^4}",1,"((-4*b^3*B*c*n)/(a + b*x) + (4*a*b^2*B*d*n)/(a + b*x) + (B*d*(b*c - a*d)^2*n)/(c + d*x)^2 + (8*b^2*B*c*d*n)/(c + d*x) - (8*a*b*B*d^2*n)/(c + d*x) + (2*b*B*d*(b*c - a*d)*n)/(c + d*x) + 6*b^2*B*d*n*Log[a + b*x] - (4*b^2*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x) - (2*d*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c + d*x)^2 - (8*b*d*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c + d*x) - 12*b^2*d*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 6*b^2*B*d*n*Log[c + d*x] + 12*b^2*d*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + 6*b^2*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)]) - 6*b^2*B*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)]))/(4*(b*c - a*d)^4*g^2*i^3)","C",1
157,1,561,483,1.2796625,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a g+b g x)^3 (c i+d i x)^3} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/((a*g + b*g*x)^3*(c*i + d*i*x)^3),x]","-\frac{-24 b^2 d^2 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+24 b^2 d^2 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-\frac{12 b^2 d (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{a+b x}+\frac{2 b^2 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(a+b x)^2}-\frac{12 b d^2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{c+d x}-\frac{2 d^2 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(c+d x)^2}-\frac{12 b^3 B c d n}{a+b x}+12 b^2 B d^2 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)-12 b^2 B d^2 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)-\frac{2 b^2 B d n (b c-a d)}{a+b x}+\frac{b^2 B n (b c-a d)^2}{(a+b x)^2}+\frac{12 a b^2 B d^2 n}{a+b x}-\frac{12 a b B d^3 n}{c+d x}+\frac{2 b B d^2 n (b c-a d)}{c+d x}+\frac{B d^2 n (b c-a d)^2}{(c+d x)^2}+\frac{12 b^2 B c d^2 n}{c+d x}}{4 g^3 i^3 (b c-a d)^5}","-\frac{b^4 (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 i^3 (a+b x)^2 (b c-a d)^5}+\frac{4 b^3 d (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^3 i^3 (a+b x) (b c-a d)^5}+\frac{6 b^2 d^2 \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)}{g^3 i^3 (b c-a d)^5}+\frac{d^4 (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 i^3 (c+d x)^2 (b c-a d)^5}-\frac{4 b d^3 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^3 i^3 (c+d x) (b c-a d)^5}-\frac{b^4 B n (c+d x)^2}{4 g^3 i^3 (a+b x)^2 (b c-a d)^5}+\frac{4 b^3 B d n (c+d x)}{g^3 i^3 (a+b x) (b c-a d)^5}-\frac{3 b^2 B d^2 n \log ^2\left(\frac{a+b x}{c+d x}\right)}{g^3 i^3 (b c-a d)^5}-\frac{B d^4 n (a+b x)^2}{4 g^3 i^3 (c+d x)^2 (b c-a d)^5}+\frac{4 b B d^3 n (a+b x)}{g^3 i^3 (c+d x) (b c-a d)^5}",1,"-1/4*((b^2*B*(b*c - a*d)^2*n)/(a + b*x)^2 - (12*b^3*B*c*d*n)/(a + b*x) + (12*a*b^2*B*d^2*n)/(a + b*x) - (2*b^2*B*d*(b*c - a*d)*n)/(a + b*x) + (B*d^2*(b*c - a*d)^2*n)/(c + d*x)^2 + (12*b^2*B*c*d^2*n)/(c + d*x) - (12*a*b*B*d^3*n)/(c + d*x) + (2*b*B*d^2*(b*c - a*d)*n)/(c + d*x) + (2*b^2*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x)^2 - (12*b^2*d*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x) - (2*d^2*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c + d*x)^2 - (12*b*d^2*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c + d*x) - 24*b^2*d^2*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 24*b^2*d^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + 12*b^2*B*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)]) - 12*b^2*B*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)]))/((b*c - a*d)^5*g^3*i^3)","C",1
158,1,671,587,2.0325179,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a g+b g x)^4 (c i+d i x)^3} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/((a*g + b*g*x)^4*(c*i + d*i*x)^3),x]","-\frac{360 b^2 d^3 \log (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-360 b^2 d^3 \log (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+\frac{216 b^2 d^2 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{a+b x}-\frac{54 b^2 d (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(a+b x)^2}+\frac{12 b^2 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(a+b x)^3}+\frac{144 b d^3 (b c-a d) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{c+d x}+\frac{18 d^3 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(c+d x)^2}+\frac{216 b^3 B c d^2 n}{a+b x}-180 b^2 B d^3 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)+180 b^2 B d^3 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)+\frac{66 b^2 B d^2 n (b c-a d)}{a+b x}-\frac{33 b^2 B d n (b c-a d)^2}{(a+b x)^2}+\frac{4 b^2 B n (b c-a d)^3}{(a+b x)^3}-\frac{216 a b^2 B d^3 n}{a+b x}+120 b^2 B d^3 n \log (a+b x)+\frac{144 a b B d^4 n}{c+d x}-\frac{18 b B d^3 n (b c-a d)}{c+d x}-\frac{9 B d^3 n (b c-a d)^2}{(c+d x)^2}-\frac{144 b^2 B c d^3 n}{c+d x}-120 b^2 B d^3 n \log (c+d x)}{36 g^4 i^3 (b c-a d)^6}","-\frac{b^5 (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{3 g^4 i^3 (a+b x)^3 (b c-a d)^6}+\frac{5 b^4 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 i^3 (a+b x)^2 (b c-a d)^6}-\frac{10 b^3 d^2 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^4 i^3 (a+b x) (b c-a d)^6}-\frac{10 b^2 d^3 \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)}{g^4 i^3 (b c-a d)^6}-\frac{d^5 (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 g^4 i^3 (c+d x)^2 (b c-a d)^6}+\frac{5 b d^4 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{g^4 i^3 (c+d x) (b c-a d)^6}-\frac{b^5 B n (c+d x)^3}{9 g^4 i^3 (a+b x)^3 (b c-a d)^6}+\frac{5 b^4 B d n (c+d x)^2}{4 g^4 i^3 (a+b x)^2 (b c-a d)^6}-\frac{10 b^3 B d^2 n (c+d x)}{g^4 i^3 (a+b x) (b c-a d)^6}+\frac{5 b^2 B d^3 n \log ^2\left(\frac{a+b x}{c+d x}\right)}{g^4 i^3 (b c-a d)^6}+\frac{B d^5 n (a+b x)^2}{4 g^4 i^3 (c+d x)^2 (b c-a d)^6}-\frac{5 b B d^4 n (a+b x)}{g^4 i^3 (c+d x) (b c-a d)^6}",1,"-1/36*((4*b^2*B*(b*c - a*d)^3*n)/(a + b*x)^3 - (33*b^2*B*d*(b*c - a*d)^2*n)/(a + b*x)^2 + (216*b^3*B*c*d^2*n)/(a + b*x) - (216*a*b^2*B*d^3*n)/(a + b*x) + (66*b^2*B*d^2*(b*c - a*d)*n)/(a + b*x) - (9*B*d^3*(b*c - a*d)^2*n)/(c + d*x)^2 - (144*b^2*B*c*d^3*n)/(c + d*x) + (144*a*b*B*d^4*n)/(c + d*x) - (18*b*B*d^3*(b*c - a*d)*n)/(c + d*x) + 120*b^2*B*d^3*n*Log[a + b*x] + (12*b^2*(b*c - a*d)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x)^3 - (54*b^2*d*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x)^2 + (216*b^2*d^2*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(a + b*x) + (18*d^3*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c + d*x)^2 + (144*b*d^3*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(c + d*x) + 360*b^2*d^3*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 120*b^2*B*d^3*n*Log[c + d*x] - 360*b^2*d^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - 180*b^2*B*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)]) + 180*b^2*B*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)]))/((b*c - a*d)^6*g^4*i^3)","C",1
159,1,949,584,0.9079227,"\int (a g+b g x)^3 (c i+d i 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)^3*(c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{g^3 i \left(4 d \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (a+b x)^5+5 (b c-a d) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (a+b x)^4-\frac{5 B (b c-a d)^2 n \left(-6 B n \log (c+d x) (b c-a d)^3-6 \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)^3+3 B n \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 c-a d)^3+6 A b d x (b c-a d)^2+6 B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) (b c-a d)^2+3 B n (b d x+(a d-b c) \log (c+d x)) (b c-a d)^2+B n \left(-2 \log (c+d x) (b c-a d)^2+2 b d x (b c-a d)-d^2 (a+b x)^2\right) (b c-a d)+2 d^3 (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+3 d^2 (a d-b c) (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)\right)}{3 d^4}+\frac{B (b c-a d) n \left(-24 B n \log (c+d x) (b c-a d)^4-24 \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)^4+12 B n \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 c-a d)^4+24 A b d x (b c-a d)^3+24 B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) (b c-a d)^3+12 B n (b d x+(a d-b c) \log (c+d x)) (b c-a d)^3-12 d^2 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^2+4 B n \left(-2 \log (c+d x) (b c-a d)^2+2 b d x (b c-a d)-d^2 (a+b x)^2\right) (b c-a d)^2+8 d^3 (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)+B n \left(-6 \log (c+d x) (b c-a d)^3+6 b d x (b c-a d)^2+2 d^3 (a+b x)^3+3 d^2 (a d-b c) (a+b x)^2\right) (b c-a d)-6 d^4 (a+b x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)\right)}{3 d^4}\right)}{20 b^2}","-\frac{B g^3 i n (b c-a d)^5 \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)}{60 b^2 d^4}-\frac{B g^3 i n (a+b x) (b c-a d)^4 \left(6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+6 A+5 B n\right)}{60 b^2 d^3}+\frac{B g^3 i n (a+b x)^2 (b c-a d)^3 \left(3 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+3 A+B n\right)}{60 b^2 d^2}-\frac{B g^3 i n (a+b x)^3 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{30 b^2 d}+\frac{g^3 i (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)^2}{20 b^2}-\frac{B g^3 i 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^2}+\frac{g^3 i (a+b x)^4 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{5 b}-\frac{B^2 g^3 i n^2 (b c-a d)^5 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{10 b^2 d^4}-\frac{B^2 g^3 i n^2 (b c-a d)^5 \log (c+d x)}{10 b^2 d^4}-\frac{3 B^2 g^3 i n^2 (c+d x)^2 (b c-a d)^3}{20 d^4}+\frac{b B^2 g^3 i n^2 (c+d x)^3 (b c-a d)^2}{30 d^4}+\frac{3 B^2 g^3 i n^2 x (b c-a d)^4}{10 b d^3}",1,"(g^3*i*(5*(b*c - a*d)*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 4*d*(a + b*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - (5*B*(b*c - a*d)^2*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) + (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)])))/(3*d^4)))/(20*b^2)","A",1
160,1,716,487,0.5730906,"\int (a g+b g x)^2 (c i+d i 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)^2*(c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{g^2 i \left(\frac{4 B n (b c-a d)^2 \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}-\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)}{d^3}+3 d (a+b x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2+4 (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)^2\right)}{12 b^2}","\frac{B g^2 i n (b c-a d)^4 \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)}{12 b^2 d^3}+\frac{B g^2 i n (a+b x) (b c-a d)^3 \left(2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 A+B n\right)}{12 b^2 d^2}-\frac{B g^2 i 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)}{12 b^2 d}+\frac{g^2 i (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)^2}{12 b^2}-\frac{B g^2 i 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^2}+\frac{g^2 i (a+b x)^3 (c+d x) \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^2 i n^2 (b c-a d)^4 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{6 b^2 d^3}+\frac{B^2 g^2 i n^2 (b c-a d)^4 \log (c+d x)}{6 b^2 d^3}+\frac{B^2 g^2 i n^2 (c+d x)^2 (b c-a d)^2}{12 d^3}-\frac{B^2 g^2 i n^2 x (b c-a d)^3}{3 b d^2}",1,"(g^2*i*(4*(b*c - a*d)*(a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 3*d*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (4*B*(b*c - a*d)^2*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 - (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)])))/d^3))/(12*b^2)","A",1
161,1,937,372,0.7437598,"\int (a g+b g x) (c i+d i 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)*(c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{g i \left(2 b^3 B n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \log (c+d x) c^3-b^3 B^2 n^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) c^3-6 a b^2 B d n \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \log (c+d x) c^2+3 a b^2 B^2 d n^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) c^2+6 a b^2 d^2 x \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 c-6 A b^2 B d (b c-a d) n x c-6 b B^2 d (b c-a d) n (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) c+6 a^2 b B d^2 n \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) c+6 b B^2 (b c-a d)^2 n^2 \log (c+d x) c-3 a^2 b B^2 d^2 n^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) c+2 b^3 d^3 x^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2+3 b^2 d^2 (b c+a d) x^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2+6 a A b B d^2 (a d-b c) n x+4 A b B d (b c-a d) (b c+a d) n x+6 a B^2 d^2 (a d-b c) n (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+4 B^2 d (b c-a d) (b c+a d) n (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-2 b^2 B d^2 (b c-a d) n x^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-2 a^3 B d^3 n \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+6 a B^2 d (b c-a d)^2 n^2 \log (c+d x)-4 B^2 (b c-a d)^2 (b c+a d) n^2 \log (c+d x)+2 B^2 (b c-a d) n^2 \left(a^2 d^2 \log (a+b x)-b \left(b \log (c+d x) c^2+d (a d-b c) x\right)\right)+a^3 B^2 d^3 n^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)\right)}{6 b^2 d^2}","-\frac{B g i n (b c-a d)^3 \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)}{3 b^2 d^2}-\frac{B g i 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^2 d}+\frac{g i (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)^2}{6 b^2}-\frac{B g i 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^2}+\frac{g i (a+b x)^2 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{3 b}-\frac{B^2 g i n^2 (b c-a d)^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{3 b^2 d^2}-\frac{B^2 g i n^2 (b c-a d)^3 \log (c+d x)}{3 b^2 d^2}+\frac{B^2 g i n^2 x (b c-a d)^2}{3 b d}",1,"(g*i*(-6*A*b^2*B*c*d*(b*c - a*d)*n*x + 6*a*A*b*B*d^2*(-(b*c) + a*d)*n*x + 4*A*b*B*d*(b*c - a*d)*(b*c + a*d)*n*x - 6*b*B^2*c*d*(b*c - a*d)*n*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] + 6*a*B^2*d^2*(-(b*c) + a*d)*n*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] + 4*B^2*d*(b*c - a*d)*(b*c + a*d)*n*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] - 2*b^2*B*d^2*(b*c - a*d)*n*x^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 6*a^2*b*B*c*d^2*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 2*a^3*B*d^3*n*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 6*a*b^2*c*d^2*x*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 3*b^2*d^2*(b*c + a*d)*x^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 2*b^3*d^3*x^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 6*b*B^2*c*(b*c - a*d)^2*n^2*Log[c + d*x] + 6*a*B^2*d*(b*c - a*d)^2*n^2*Log[c + d*x] - 4*B^2*(b*c - a*d)^2*(b*c + a*d)*n^2*Log[c + d*x] + 2*b^3*B*c^3*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - 6*a*b^2*B*c^2*d*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + 2*B^2*(b*c - a*d)*n^2*(a^2*d^2*Log[a + b*x] - b*(d*(-(b*c) + a*d)*x + b*c^2*Log[c + d*x])) - 3*a^2*b*B^2*c*d^2*n^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)]) + a^3*B^2*d^3*n^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^3*B^2*c^3*n^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)]) + 3*a*b^2*B^2*c^2*d*n^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)])))/(6*b^2*d^2)","B",1
162,1,216,220,0.1868234,"\int (c i+d i x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Integrate[(c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{i \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 i 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 i 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{i (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 i 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 i n^2 (b c-a d)^2 \log (c+d x)}{b^2 d}",1,"(i*((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
163,1,742,306,1.9603869,"\int \frac{(c i+d i x) \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[((c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(a*g + b*g*x),x]","\frac{i \left(-3 B n \left(-2 a d \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+2 \left(\log \left(\frac{c}{d}+x\right) \left(-a d \log \left(\frac{d (a+b x)}{a d-b c}\right)+a d \log (a+b x)+b c\right)+(a d \log (a+b x)-b d x) \log \left(\frac{a+b x}{c+d x}\right)+a d-b c\right)+a d \log ^2\left(\frac{a}{b}+x\right)-2 a d (\log (a+b x)+1) \log \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 b B c 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 b 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+3 (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{a+b x}{c+d x}\right)+A\right)^2+B^2 n^2 \left(-6 a d \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)+6 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right) \left(a d \log \left(\frac{a+b x}{c+d x}\right)-a d+b c\right)+\log \left(\frac{a+b x}{c+d x}\right) \left(-a d \log ^2\left(\frac{a+b x}{c+d x}\right)+3 d \left(a \log \left(\frac{b c-a d}{b c+b d x}\right)+a+b x\right) \log \left(\frac{a+b x}{c+d x}\right)+6 (b c-a d) \log \left(\frac{b c-a d}{b c+b d x}\right)\right)\right)-3 b B^2 c n^2 \left(-2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)-2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right) \log \left(\frac{a+b x}{c+d x}\right)+\log \left(\frac{a d-b c}{d (a+b x)}\right) \log ^2\left(\frac{a+b x}{c+d x}\right)\right)\right)}{3 b^2 g}","\frac{2 B i n (b c-a d) \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^2 g}+\frac{2 B i 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^2 g}+\frac{d i (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{b^2 g}-\frac{i (b c-a d) \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^2 g}+\frac{2 B^2 i n^2 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^2 g}+\frac{2 B^2 i n^2 (b c-a d) \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^2 g}",1,"(i*(3*b*d*x*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2 + 3*(b*c - a*d)*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)])*(a*d*Log[a/b + x]^2 - 2*a*d*Log[a/b + x]*(1 + Log[a + b*x]) + 2*(-(b*c) + a*d + Log[c/d + x]*(b*c + a*d*Log[a + b*x] - a*d*Log[(d*(a + b*x))/(-(b*c) + a*d)]) + (-(b*d*x) + a*d*Log[a + b*x])*Log[(a + b*x)/(c + d*x)]) - 2*a*d*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 3*b*B*c*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)/(c + d*x)]*(-(a*d*Log[(a + b*x)/(c + d*x)]^2) + 6*(b*c - a*d)*Log[(b*c - a*d)/(b*c + b*d*x)] + 3*d*Log[(a + b*x)/(c + d*x)]*(a + b*x + a*Log[(b*c - a*d)/(b*c + b*d*x)])) + 6*(b*c - a*d + a*d*Log[(a + b*x)/(c + d*x)])*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 6*a*d*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))]) - 3*b*B^2*c*n^2*(Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(a + b*x)/(c + d*x)]^2 - 2*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))])))/(3*b^2*g)","B",1
164,1,1556,261,3.2071151,"\int \frac{(c i+d i x) \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[((c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(a*g + b*g*x)^2,x]","\frac{i \left(\frac{3 b B^2 c \left(-\left((b c-a d) \log ^2\left(\frac{a+b x}{c+d x}\right)\right)-2 (b c-a d) \log \left(\frac{a+b x}{c+d x}\right)-2 d (a+b x) \log (a+b x) \log \left(\frac{a+b x}{c+d x}\right)-2 d (a+b x) \log \left(\frac{b c-a d}{b c+b d x}\right) \log \left(\frac{a+b x}{c+d x}\right)-2 b c+2 a d-2 d (a+b x) \log (a+b x)+2 d (a+b x) \log (c+d x)+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)+d (a+b x) \left(\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)+\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)\right)\right) n^2}{(b c-a d) (a+b x)}+\frac{B^2 d \left(-a d \log ^3\left(\frac{a+b x}{c+d x}\right)+3 a d \log ^2\left(\frac{a+b x}{c+d x}\right)+3 b d x \log ^2\left(\frac{a+b x}{c+d x}\right)-\frac{3 b^2 x (c+d x) \log ^2\left(\frac{a+b x}{c+d x}\right)}{a+b x}-3 b c \log \left(\frac{a d-b c}{d (a+b x)}\right) \log ^2\left(\frac{a+b x}{c+d x}\right)+3 a d \log \left(\frac{b c-a d}{b c+b d x}\right) \log ^2\left(\frac{a+b x}{c+d x}\right)+6 b c \log (a+b x) \log \left(\frac{a+b x}{c+d x}\right)-6 a d \log (a+b x) \log \left(\frac{a+b x}{c+d x}\right)+6 b c \log \left(\frac{b c-a d}{b c+b d x}\right) \log \left(\frac{a+b x}{c+d x}\right)-6 a d \log \left(\frac{b c-a d}{b c+b d x}\right) \log \left(\frac{a+b x}{c+d x}\right)+6 b c \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right) \log \left(\frac{a+b x}{c+d x}\right)-\frac{6 b (b c-a d) x \log \left(\frac{a+b x}{c+d x}\right)}{a+b x}+3 b c \log ^2\left(\frac{a}{b}+x\right)-3 a d \log ^2\left(\frac{a}{b}+x\right)+6 b c-6 a d+6 a d \log \left(\frac{a}{b}+x\right)-6 b c \log \left(\frac{c}{d}+x\right)+6 b c \log (a+b x)-6 a d \log (a+b x)-6 b c \log \left(\frac{a}{b}+x\right) \log (a+b x)+6 a d \log \left(\frac{a}{b}+x\right) \log (a+b x)+6 b c \log \left(\frac{c}{d}+x\right) \log (a+b x)-6 a d \log \left(\frac{c}{d}+x\right) \log (a+b x)-6 b c \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)+6 a d \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)+6 \left(b c-a d+a d \log \left(\frac{a+b x}{c+d x}\right)\right) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)-6 (b c-a d) \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-6 a d \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)+6 b c \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)-\frac{6 b^2 c x}{a+b x}+\frac{6 a b d x}{a+b x}\right) n^2}{b c-a d}+\frac{6 b B c \left(-A-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)\right) \left(-d (a+b x) \log \left(\frac{c}{d}+x\right)+d (a+b x) \log \left(\frac{d (a+b x)}{a d-b c}\right)+(b c-a d) \left(\log \left(\frac{a+b x}{c+d x}\right)+1\right)\right) n}{(b c-a d) (a+b x)}+3 B d \left(A+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)\right) \left(\log ^2\left(\frac{a}{b}+x\right)-2 \log (a+b x) \log \left(\frac{a}{b}+x\right)-2 \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)+2 \log (a+b x) \left(\frac{a d}{b c-a d}+\log \left(\frac{c}{d}+x\right)+\log \left(\frac{a+b x}{c+d x}\right)\right)+2 a \left(\frac{\log \left(\frac{a+b x}{c+d x}\right)}{a+b x}+\frac{d \log (c+d x)}{a d-b c}+\frac{1}{a+b x}\right)-2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right) n+3 d \log (a+b x) \left(A+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)\right)^2-\frac{3 (b c-a d) \left(A+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)\right)^2}{a+b x}\right)}{3 b^2 g^2}","\frac{2 B d i 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^2 g^2}-\frac{d i \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^2 g^2}-\frac{2 B i n (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b g^2 (a+b x)}-\frac{i (c+d x) \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^2 d i n^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^2 g^2}-\frac{2 B^2 i n^2 (c+d x)}{b g^2 (a+b x)}",1,"(i*((-3*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2)/(a + b*x) + 3*d*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 + (6*b*B*c*n*(-A - B*Log[e*((a + b*x)/(c + d*x))^n] + B*n*Log[(a + b*x)/(c + d*x)])*(-(d*(a + b*x)*Log[c/d + x]) + d*(a + b*x)*Log[(d*(a + b*x))/(-(b*c) + a*d)] + (b*c - a*d)*(1 + Log[(a + b*x)/(c + d*x)])))/((b*c - a*d)*(a + b*x)) + (3*b*B^2*c*n^2*(-2*b*c + 2*a*d - 2*d*(a + b*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(a + b*x)/(c + d*x)] - 2*d*(a + b*x)*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - (b*c - a*d)*Log[(a + b*x)/(c + d*x)]^2 + 2*d*(a + b*x)*Log[c + d*x] - 2*d*(a + b*x)*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 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)]) + d*(a + b*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(a + b*x)) + 3*B*d*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] - 2*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*Log[a + b*x]*((a*d)/(b*c - a*d) + Log[c/d + x] + Log[(a + b*x)/(c + d*x)]) + 2*a*((a + b*x)^(-1) + Log[(a + b*x)/(c + d*x)]/(a + b*x) + (d*Log[c + d*x])/(-(b*c) + a*d)) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + (B^2*d*n^2*(6*b*c - 6*a*d - (6*b^2*c*x)/(a + b*x) + (6*a*b*d*x)/(a + b*x) + 6*a*d*Log[a/b + x] + 3*b*c*Log[a/b + x]^2 - 3*a*d*Log[a/b + x]^2 - 6*b*c*Log[c/d + x] + 6*b*c*Log[a + b*x] - 6*a*d*Log[a + b*x] - 6*b*c*Log[a/b + x]*Log[a + b*x] + 6*a*d*Log[a/b + x]*Log[a + b*x] + 6*b*c*Log[c/d + x]*Log[a + b*x] - 6*a*d*Log[c/d + x]*Log[a + b*x] - 6*b*c*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 6*a*d*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] - (6*b*(b*c - a*d)*x*Log[(a + b*x)/(c + d*x)])/(a + b*x) + 6*b*c*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 6*a*d*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] + 3*a*d*Log[(a + b*x)/(c + d*x)]^2 + 3*b*d*x*Log[(a + b*x)/(c + d*x)]^2 - (3*b^2*x*(c + d*x)*Log[(a + b*x)/(c + d*x)]^2)/(a + b*x) - 3*b*c*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(a + b*x)/(c + d*x)]^2 - a*d*Log[(a + b*x)/(c + d*x)]^3 + 6*b*c*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 6*a*d*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 3*a*d*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*(b*c - a*d + a*d*Log[(a + b*x)/(c + d*x)])*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 6*(b*c - a*d)*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 6*b*c*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 6*a*d*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] + 6*b*c*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))]))/(b*c - a*d)))/(3*b^2*g^2)","B",1
165,1,801,151,0.9087292,"\int \frac{(c i+d i x) \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[((c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(a*g + b*g*x)^3,x]","-\frac{i \left(2 (b c-a d)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2-4 d (a d-b c) (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2+4 B d n (a+b x) \left(2 (b c-a d) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+2 d (a+b x) \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-2 d (a+b x) \log (c+d x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+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) \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(\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)\right)+B n \left(2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^2+4 d (a d-b c) (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-4 d^2 (a+b x)^2 \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+4 d^2 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \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 \left((b c-a d)^2+2 d (a d-b c) (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)\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(\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)\right)\right)}{4 b^2 (b c-a d) g^3 (a+b x)^2}","-\frac{i (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)}-\frac{B i 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)}-\frac{B^2 i n^2 (c+d x)^2}{4 g^3 (a+b x)^2 (b c-a d)}",1,"-1/4*(i*(2*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - 4*d*(-(b*c) + a*d)*(a + b*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 4*B*d*n*(a + b*x)*(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*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^2*(b*c - a*d)*g^3*(a + b*x)^2)","C",1
166,1,1079,307,1.2170124,"\int \frac{(c i+d i x) \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[((c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(a*g + b*g*x)^4,x]","-\frac{i \left(36 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (b c-a d)^3+54 d (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)^2+27 B d n (a+b x) \left(2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^2+4 d (a d-b c) (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-4 d^2 (a+b x)^2 \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+4 d^2 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \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 \left((b c-a d)^2+2 d (a d-b c) (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)\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(\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)\right)+2 B n \left(12 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^3-18 d (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+36 d^2 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)+36 d^3 (a+b x)^3 \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-36 d^3 (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \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) \left((b c-a d)^2+2 d (a d-b c) (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)\right)+2 B n \left(2 (b c-a d)^3-3 d (a+b x) (b c-a d)^2+6 d^2 (a+b x)^2 (b c-a d)+6 d^3 (a+b x)^3 \log (a+b x)-6 d^3 (a+b x)^3 \log (c+d x)\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(\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)\right)\right)}{108 b^2 (b c-a d)^2 g^4 (a+b x)^3}","-\frac{b i (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)^2}-\frac{2 b B i 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)^2}+\frac{d i (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^4 (a+b x)^2 (b c-a d)^2}+\frac{B d i 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^4 (a+b x)^2 (b c-a d)^2}-\frac{2 b B^2 i n^2 (c+d x)^3}{27 g^4 (a+b x)^3 (b c-a d)^2}+\frac{B^2 d i n^2 (c+d x)^2}{4 g^4 (a+b x)^2 (b c-a d)^2}",1,"-1/108*(i*(36*(b*c - a*d)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 54*d*(b*c - a*d)^2*(a + b*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 27*B*d*n*(a + b*x)*(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)])) + 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^2*(b*c - a*d)^2*g^4*(a + b*x)^3)","C",1
167,1,1392,475,1.3585681,"\int \frac{(c i+d i x) \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[((c*i + d*i*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(a*g + b*g*x)^5,x]","-\frac{i \left(216 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (b c-a d)^4-288 d (a d-b c)^3 (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2+16 B d n (a+b x) \left(12 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^3-18 d (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+36 d^2 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)+36 d^3 (a+b x)^3 \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-36 d^3 (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \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) \left((b c-a d)^2+2 d (a d-b c) (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)\right)+2 B n \left(2 (b c-a d)^3-3 d (a+b x) (b c-a d)^2+6 d^2 (a+b x)^2 (b c-a d)+6 d^3 (a+b x)^3 \log (a+b x)-6 d^3 (a+b x)^3 \log (c+d x)\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(\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)\right)+3 B n \left(36 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^4+72 d^2 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^2+144 d^3 (a d-b c) (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+48 d (a d-b c)^3 (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-144 d^4 (a+b x)^4 \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+144 d^4 (a+b x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \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 \left((b c-a d)^2+2 d (a d-b c) (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)\right)-8 B d n (a+b x) \left(2 (b c-a d)^3-3 d (a+b x) (b c-a d)^2+6 d^2 (a+b x)^2 (b c-a d)+6 d^3 (a+b x)^3 \log (a+b x)-6 d^3 (a+b x)^3 \log (c+d x)\right)+3 B n \left(3 (b c-a d)^4+6 d^2 (a+b x)^2 (b c-a d)^2+12 d^3 (a d-b c) (a+b x)^3+4 d (a d-b c)^3 (a+b x)-12 d^4 (a+b x)^4 \log (a+b x)+12 d^4 (a+b x)^4 \log (c+d x)\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(\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)\right)\right)}{864 b^2 (b c-a d)^3 g^5 (a+b x)^4}","-\frac{b^2 i (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)^3}-\frac{b^2 B i 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)^3}-\frac{d^2 i (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)^3}-\frac{B d^2 i 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)^3}+\frac{2 b d i (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^5 (a+b x)^3 (b c-a d)^3}+\frac{4 b B d i 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^5 (a+b x)^3 (b c-a d)^3}-\frac{b^2 B^2 i n^2 (c+d x)^4}{32 g^5 (a+b x)^4 (b c-a d)^3}-\frac{B^2 d^2 i n^2 (c+d x)^2}{4 g^5 (a+b x)^2 (b c-a d)^3}+\frac{4 b B^2 d i n^2 (c+d x)^3}{27 g^5 (a+b x)^3 (b c-a d)^3}",1,"-1/864*(i*(216*(b*c - a*d)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - 288*d*(-(b*c) + a*d)^3*(a + b*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 16*B*d*n*(a + b*x)*(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)])) + 3*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^2*(b*c - a*d)^3*g^5*(a + b*x)^4)","C",1
168,1,1634,766,1.5418452,"\int (a g+b g x)^3 (c i+d i 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)^3*(c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{g^3 i^2 \left(10 d^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (a+b x)^6+24 d (b c-a d) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (a+b x)^5+15 (b c-a d)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (a+b x)^4-\frac{5 B (b c-a d)^3 n \left(-6 B n \log (c+d x) (b c-a d)^3-6 \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)^3+3 B n \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 c-a d)^3+6 A b d x (b c-a d)^2+6 B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) (b c-a d)^2+3 B n (b d x+(a d-b c) \log (c+d x)) (b c-a d)^2+B n \left(-2 \log (c+d x) (b c-a d)^2+2 b d x (b c-a d)-d^2 (a+b x)^2\right) (b c-a d)+2 d^3 (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+3 d^2 (a d-b c) (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)\right)}{d^4}+\frac{2 B (b c-a d)^2 n \left(-24 B n \log (c+d x) (b c-a d)^4-24 \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)^4+12 B n \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 c-a d)^4+24 A b d x (b c-a d)^3+24 B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) (b c-a d)^3+12 B n (b d x+(a d-b c) \log (c+d x)) (b c-a d)^3-12 d^2 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^2+4 B n \left(-2 \log (c+d x) (b c-a d)^2+2 b d x (b c-a d)-d^2 (a+b x)^2\right) (b c-a d)^2+8 d^3 (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)+B n \left(-6 \log (c+d x) (b c-a d)^3+6 b d x (b c-a d)^2+2 d^3 (a+b x)^3+3 d^2 (a d-b c) (a+b x)^2\right) (b c-a d)-6 d^4 (a+b x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)\right)}{d^4}-\frac{B (b c-a d) n \left(-120 B n \log (c+d x) (b c-a d)^5-120 \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)^5+60 B n \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 c-a d)^5+120 A b d x (b c-a d)^4+120 B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) (b c-a d)^4+60 B n (b d x+(a d-b c) \log (c+d x)) (b c-a d)^4+20 B n \left(-2 \log (c+d x) (b c-a d)^2+2 b d x (b c-a d)-d^2 (a+b x)^2\right) (b c-a d)^3+40 d^3 (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^2+5 B n \left(-6 \log (c+d x) (b c-a d)^3+6 b d x (b c-a d)^2+2 d^3 (a+b x)^3+3 d^2 (a d-b c) (a+b x)^2\right) (b c-a d)^2+2 B n \left(-12 \log (c+d x) (b c-a d)^4+12 b d x (b c-a d)^3-6 d^2 (a+b x)^2 (b c-a d)^2+4 d^3 (a+b x)^3 (b c-a d)-3 d^4 (a+b x)^4\right) (b c-a d)+24 d^5 (a+b x)^5 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+30 d^4 (a d-b c) (a+b x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+60 d^2 (a d-b c)^3 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)\right)}{6 d^4}\right)}{60 b^3}","-\frac{B g^3 i^2 n (b c-a d)^6 \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)}{180 b^3 d^4}-\frac{B g^3 i^2 n (a+b x) (b c-a d)^5 \left(6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+6 A+5 B n\right)}{180 b^3 d^3}+\frac{B g^3 i^2 n (a+b x)^2 (b c-a d)^4 \left(3 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+3 A+B n\right)}{180 b^3 d^2}-\frac{B g^3 i^2 n (a+b x)^3 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{90 b^3 d}+\frac{g^3 i^2 (a+b x)^4 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{60 b^3}-\frac{B g^3 i^2 n (a+b x)^4 (b c-a d)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{20 b^3}+\frac{g^3 i^2 (a+b x)^4 (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}{15 b^2}-\frac{B g^3 i^2 n (a+b x)^4 (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)}{15 b^2}+\frac{g^3 i^2 (a+b x)^4 (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{6 b}-\frac{B^2 g^3 i^2 n^2 (b c-a d)^6 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{30 b^3 d^4}-\frac{B^2 g^3 i^2 n^2 (b c-a d)^6 \log (c+d x)}{20 b^3 d^4}+\frac{B^2 g^3 i^2 n^2 (a+b x)^4 (b c-a d)^2}{60 b^3}+\frac{3 B^2 g^3 i^2 n^2 x (b c-a d)^5}{20 b^2 d^3}-\frac{3 B^2 g^3 i^2 n^2 (c+d x)^2 (b c-a d)^4}{40 b d^4}+\frac{B^2 g^3 i^2 n^2 (c+d x)^3 (b c-a d)^3}{60 d^4}",1,"(g^3*i^2*(15*(b*c - a*d)^2*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 24*d*(b*c - a*d)*(a + b*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 10*d^2*(a + b*x)^6*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - (5*B*(b*c - a*d)^3*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)])))/d^4 + (2*B*(b*c - a*d)^2*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)])))/d^4 - (B*(b*c - a*d)*n*(120*A*b*d*(b*c - a*d)^4*x + 120*B*d*(b*c - a*d)^4*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] + 60*d^2*(-(b*c) + a*d)^3*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 40*d^3*(b*c - a*d)^2*(a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 30*d^4*(-(b*c) + a*d)*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 24*d^5*(a + b*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 120*B*(b*c - a*d)^5*n*Log[c + d*x] - 120*(b*c - a*d)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + 20*B*(b*c - a*d)^3*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]) + 5*B*(b*c - a*d)^2*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]) + 2*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]) + 60*B*(b*c - a*d)^4*n*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 60*B*(b*c - a*d)^5*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)])))/(6*d^4)))/(60*b^3)","B",1
169,1,1254,819,1.0193729,"\int (a g+b g x)^2 (c i+d i 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*(c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{g^2 i^2 \left(12 d^5 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (a+b x)^5+30 d^4 (b c-a d) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (a+b x)^4+20 d^3 (b c-a d)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (a+b x)^3+20 B (b c-a d)^3 n \left(-2 B n \log (c+d x) (b c-a d)^2-2 \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)^2+B n \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 c-a d)^2+2 A b d x (b c-a d)+2 B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) (b c-a d)+B n (b d x+(a d-b c) \log (c+d x)) (b c-a d)-d^2 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)\right)-10 B (b c-a d)^2 n \left(-6 B n \log (c+d x) (b c-a d)^3-6 \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)^3+3 B n \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 c-a d)^3+6 A b d x (b c-a d)^2+6 B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) (b c-a d)^2+3 B n (b d x+(a d-b c) \log (c+d x)) (b c-a d)^2+B n \left(-2 \log (c+d x) (b c-a d)^2+2 b d x (b c-a d)-d^2 (a+b x)^2\right) (b c-a d)+2 d^3 (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+3 d^2 (a d-b c) (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)\right)+B (b c-a d) n \left(-24 B n \log (c+d x) (b c-a d)^4-24 \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)^4+12 B n \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 c-a d)^4+24 A b d x (b c-a d)^3+24 B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) (b c-a d)^3+12 B n (b d x+(a d-b c) \log (c+d x)) (b c-a d)^3-12 d^2 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^2+4 B n \left(-2 \log (c+d x) (b c-a d)^2+2 b d x (b c-a d)-d^2 (a+b x)^2\right) (b c-a d)^2+8 d^3 (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)+B n \left(-6 \log (c+d x) (b c-a d)^3+6 b d x (b c-a d)^2+2 d^3 (a+b x)^3+3 d^2 (a d-b c) (a+b x)^2\right) (b c-a d)-6 d^4 (a+b x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)\right)\right)}{60 b^3 d^3}","\frac{B g^2 i^2 n \left(2 A+3 B n+2 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)^5}{30 b^3 d^3}+\frac{B^2 g^2 i^2 n^2 \log \left(\frac{a+b x}{c+d x}\right) (b c-a d)^5}{30 b^3 d^3}+\frac{B^2 g^2 i^2 n^2 \log (c+d x) (b c-a d)^5}{10 b^3 d^3}+\frac{B^2 g^2 i^2 n^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right) (b c-a d)^5}{15 b^3 d^3}-\frac{B^2 g^2 i^2 n^2 x (b c-a d)^4}{10 b^2 d^2}+\frac{B g^2 i^2 n (a+b x) \left(2 A+B n+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^4}{30 b^3 d^2}-\frac{B^2 g^2 i^2 n^2 (c+d x)^2 (b c-a d)^3}{20 b d^3}-\frac{B g^2 i^2 n (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^3}{30 b^3 d}-\frac{B g^2 i^2 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)^3}{5 b d^3}+\frac{B^2 g^2 i^2 n^2 (c+d x)^3 (b c-a d)^2}{30 d^3}+\frac{g^2 i^2 (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (b c-a d)^2}{30 b^3}-\frac{B g^2 i^2 n (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^2}{15 b^3}+\frac{4 B g^2 i^2 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)^2}{15 d^3}+\frac{g^2 i^2 (a+b x)^3 (c+d x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (b c-a d)}{10 b^2}-\frac{b B g^2 i^2 n (c+d x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)}{10 d^3}+\frac{g^2 i^2 (a+b x)^3 (c+d x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{5 b}",1,"(g^2*i^2*(20*d^3*(b*c - a*d)^2*(a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 30*d^4*(b*c - a*d)*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 12*d^5*(a + b*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 20*B*(b*c - a*d)^3*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)])) - 10*B*(b*c - a*d)^2*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)])) + 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)]))))/(60*b^3*d^3)","A",1
170,1,713,635,0.6421882,"\int (a g+b g x) (c i+d i 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)*(c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{g i^2 \left(\frac{4 B n (b c-a d)^2 \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}-\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)}{b^3}+3 b (c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2-4 (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)^2\right)}{12 d^2}","-\frac{B g i^2 n (b c-a d)^4 \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)}{6 b^3 d^2}-\frac{B g i^2 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)}{6 b^3 d}+\frac{g i^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)^2}{12 b^3}-\frac{B g i^2 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)}{6 b^3}+\frac{g i^2 (a+b x)^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)^2}{6 b^2}+\frac{B g i^2 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 d^2}-\frac{B g i^2 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 d^2}+\frac{g i^2 (a+b x)^2 (c+d x)^2 \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 i^2 n^2 (b c-a d)^4 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{6 b^3 d^2}-\frac{B^2 g i^2 n^2 (b c-a d)^4 \log \left(\frac{a+b x}{c+d x}\right)}{12 b^3 d^2}-\frac{B^2 g i^2 n^2 (b c-a d)^4 \log (c+d x)}{4 b^3 d^2}+\frac{B^2 g i^2 n^2 x (b c-a d)^3}{12 b^2 d}+\frac{B^2 g i^2 n^2 (c+d x)^2 (b c-a d)^2}{12 b d^2}",1,"(g*i^2*(-4*(b*c - a*d)*(c + d*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 3*b*(c + d*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (4*B*(b*c - a*d)^2*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 - (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)])))/b^3))/(12*d^2)","A",1
171,1,303,361,0.26773,"\int (c i+d i x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Integrate[(c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{i^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 i^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 i^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 i^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{i^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 i^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 i^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 i^2 n^2 (b c-a d)^3 \log (c+d x)}{b^3 d}+\frac{B^2 i^2 n^2 x (b c-a d)^2}{3 b^2}",1,"(i^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
172,1,1654,572,3.2523378,"\int \frac{(c i+d i x)^2 \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[((c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(a*g + b*g*x),x]","\frac{i^2 \left(6 b^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{a+b x}{c+d x}\right)\right) \left(\log ^2\left(\frac{a}{b}+x\right)-2 \log (a+b x) \left(\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)-\log \left(\frac{a+b x}{c+d x}\right)\right)-2 \left(\log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)+\text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right)\right) c^2-6 b^2 B^2 n^2 \left(\log \left(\frac{a d-b c}{d (a+b x)}\right) \log ^2\left(\frac{a+b x}{c+d x}\right)-2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right) \log \left(\frac{a+b x}{c+d x}\right)-2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)\right) c^2-12 b B n \left(A+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)\right) \left(a d \log ^2\left(\frac{a}{b}+x\right)-2 a d (\log (a+b x)+1) \log \left(\frac{a}{b}+x\right)+2 \left(-b c+a d+\log \left(\frac{c}{d}+x\right) \left(b c+a d \log (a+b x)-a d \log \left(\frac{d (a+b x)}{a d-b c}\right)\right)+(a d \log (a+b x)-b d x) \log \left(\frac{a+b x}{c+d x}\right)\right)-2 a d \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right) c+4 b B^2 n^2 \left(\log \left(\frac{a+b x}{c+d x}\right) \left(-a d \log ^2\left(\frac{a+b x}{c+d x}\right)+3 d \left(\log \left(\frac{b c-a d}{b c+b d x}\right) a+a+b x\right) \log \left(\frac{a+b x}{c+d x}\right)+6 (b c-a d) \log \left(\frac{b c-a d}{b c+b d x}\right)\right)+6 \left(b c-a d+a d \log \left(\frac{a+b x}{c+d x}\right)\right) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)-6 a d \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right) c+3 b^2 d^2 x^2 \left(A+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)\right)^2+6 b d (2 b c-a d) x \left(A+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)\right)^2+6 (b c-a d)^2 \log (a+b x) \left(A+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)\right)^2+3 B n \left(A+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)\right) \left(\left(2 \log (c+d x) c^2+d x (d x-2 c)-2 d^2 x^2 \log \left(\frac{c}{d}+x\right)\right) b^2+4 a d (c+d x) \left(\log \left(\frac{c}{d}+x\right)-1\right) b+2 a^2 d^2 \log ^2\left(\frac{a}{b}+x\right)-4 a d^2 (a+b x) \left(\log \left(\frac{a}{b}+x\right)-1\right)+d^2 \left(-2 \log (a+b x) a^2+b x (2 a-b x)+2 b^2 x^2 \log \left(\frac{a}{b}+x\right)\right)-2 d^2 \left(2 \log (a+b x) a^2+b x (b x-2 a)\right) \left(\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)-\log \left(\frac{a+b x}{c+d x}\right)\right)-4 a^2 d^2 \left(\log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)+\text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)\right)\right)-B^2 n^2 \left(-2 a^2 d^2 \log ^3\left(\frac{a+b x}{c+d x}\right)+9 a^2 d^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-3 b^2 d^2 x^2 \log ^2\left(\frac{a+b x}{c+d x}\right)+6 a b d^2 x \log ^2\left(\frac{a+b x}{c+d x}\right)+6 a^2 d^2 \log \left(\frac{b c-a d}{b c+b d x}\right) \log ^2\left(\frac{a+b x}{c+d x}\right)-6 a^2 d^2 \log \left(\frac{a+b x}{c+d x}\right)+6 a b c d \log \left(\frac{a+b x}{c+d x}\right)-6 a b d^2 x \log \left(\frac{a+b x}{c+d x}\right)+6 b^2 c d x \log \left(\frac{a+b x}{c+d x}\right)+6 b^2 c^2 \log \left(\frac{b c-a d}{b c+b d x}\right) \log \left(\frac{a+b x}{c+d x}\right)-18 a^2 d^2 \log \left(\frac{b c-a d}{b c+b d x}\right) \log \left(\frac{a+b x}{c+d x}\right)+12 a b c d \log \left(\frac{b c-a d}{b c+b d x}\right) \log \left(\frac{a+b x}{c+d x}\right)+6 b^2 c^2 \log \left(\frac{b c-a d}{c+d x}\right)+6 a^2 d^2 \log \left(\frac{b c-a d}{c+d x}\right)-12 a b c d \log \left(\frac{b c-a d}{c+d x}\right)+6 \left(b^2 c^2+2 a b d c-3 a^2 d^2+2 a^2 d^2 \log \left(\frac{a+b x}{c+d x}\right)\right) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)-12 a^2 d^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right)\right)}{6 b^3 g}","\frac{2 B i^2 n (b c-a d)^2 \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^3 g}+\frac{d i^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)^2}{b^3 g}-\frac{B d i^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)}{b^3 g}+\frac{2 B i^2 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\right)}{b^3 g}-\frac{i^2 (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)^2}{b^3 g}+\frac{B i^2 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^3 g}+\frac{i^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 b g}+\frac{2 B^2 i^2 n^2 (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^3 g}-\frac{B^2 i^2 n^2 (b c-a d)^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^3 g}+\frac{2 B^2 i^2 n^2 (b c-a d)^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^3 g}+\frac{B^2 i^2 n^2 (b c-a d)^2 \log (c+d x)}{b^3 g}",1,"(i^2*(6*b*d*(2*b*c - a*d)*x*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2 + 3*b^2*d^2*x^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2 + 6*(b*c - a*d)^2*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 - 12*b*B*c*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])*(a*d*Log[a/b + x]^2 - 2*a*d*Log[a/b + x]*(1 + Log[a + b*x]) + 2*(-(b*c) + a*d + Log[c/d + x]*(b*c + a*d*Log[a + b*x] - a*d*Log[(d*(a + b*x))/(-(b*c) + a*d)]) + (-(b*d*x) + a*d*Log[a + b*x])*Log[(a + b*x)/(c + d*x)]) - 2*a*d*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 6*b^2*B*c^2*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)])) + 3*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])*(-4*a*d^2*(a + b*x)*(-1 + Log[a/b + x]) + 2*a^2*d^2*Log[a/b + x]^2 + 4*a*b*d*(c + d*x)*(-1 + Log[c/d + x]) + d^2*(b*x*(2*a - b*x) + 2*b^2*x^2*Log[a/b + x] - 2*a^2*Log[a + b*x]) - 2*d^2*(b*x*(-2*a + b*x) + 2*a^2*Log[a + b*x])*(Log[a/b + x] - Log[c/d + x] - Log[(a + b*x)/(c + d*x)]) + b^2*(d*x*(-2*c + d*x) - 2*d^2*x^2*Log[c/d + x] + 2*c^2*Log[c + d*x]) - 4*a^2*d^2*(Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + PolyLog[2, (b*(c + d*x))/(b*c - a*d)])) + 4*b*B^2*c*n^2*(Log[(a + b*x)/(c + d*x)]*(-(a*d*Log[(a + b*x)/(c + d*x)]^2) + 6*(b*c - a*d)*Log[(b*c - a*d)/(b*c + b*d*x)] + 3*d*Log[(a + b*x)/(c + d*x)]*(a + b*x + a*Log[(b*c - a*d)/(b*c + b*d*x)])) + 6*(b*c - a*d + a*d*Log[(a + b*x)/(c + d*x)])*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 6*a*d*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))]) - B^2*n^2*(6*b^2*c^2*Log[(b*c - a*d)/(c + d*x)] - 12*a*b*c*d*Log[(b*c - a*d)/(c + d*x)] + 6*a^2*d^2*Log[(b*c - a*d)/(c + d*x)] + 6*a*b*c*d*Log[(a + b*x)/(c + d*x)] - 6*a^2*d^2*Log[(a + b*x)/(c + d*x)] + 6*b^2*c*d*x*Log[(a + b*x)/(c + d*x)] - 6*a*b*d^2*x*Log[(a + b*x)/(c + d*x)] + 9*a^2*d^2*Log[(a + b*x)/(c + d*x)]^2 + 6*a*b*d^2*x*Log[(a + b*x)/(c + d*x)]^2 - 3*b^2*d^2*x^2*Log[(a + b*x)/(c + d*x)]^2 - 2*a^2*d^2*Log[(a + b*x)/(c + d*x)]^3 + 6*b^2*c^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 12*a*b*c*d*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 18*a^2*d^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*a^2*d^2*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*(b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2 + 2*a^2*d^2*Log[(a + b*x)/(c + d*x)])*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 12*a^2*d^2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))]) - 6*b^2*B^2*c^2*n^2*(Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(a + b*x)/(c + d*x)]^2 - 2*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))])))/(6*b^3*g)","B",1
173,1,2834,472,12.3964729,"\int \frac{(c i+d i x)^2 \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[((c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(a*g + b*g*x)^2,x]","\text{Result too large to show}","\frac{d^2 i^2 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{b^3 g^2}+\frac{4 B d i^2 n (b c-a d) \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^3 g^2}+\frac{2 B d i^2 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^3 g^2}-\frac{2 d i^2 (b c-a d) \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^3 g^2}-\frac{i^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)^2}{b^2 g^2 (a+b x)}-\frac{2 B i^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)}{b^2 g^2 (a+b x)}+\frac{2 B^2 d i^2 n^2 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^3 g^2}+\frac{4 B^2 d i^2 n^2 (b c-a d) \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^3 g^2}-\frac{2 B^2 i^2 n^2 (c+d x) (b c-a d)}{b^2 g^2 (a+b x)}",1,"(i^2*(3*b*d^2*x*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2 - (3*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2)/(a + b*x) + 6*d*(b*c - a*d)*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 + (6*b^2*B*c^2*n*(-A - B*Log[e*((a + b*x)/(c + d*x))^n] + B*n*Log[(a + b*x)/(c + d*x)])*(-(d*(a + b*x)*Log[c/d + x]) + d*(a + b*x)*Log[(d*(a + b*x))/(-(b*c) + a*d)] + (b*c - a*d)*(1 + Log[(a + b*x)/(c + d*x)])))/((b*c - a*d)*(a + b*x)) + (3*b^2*B^2*c^2*n^2*(-2*b*c + 2*a*d - 2*d*(a + b*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(a + b*x)/(c + d*x)] - 2*d*(a + b*x)*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - (b*c - a*d)*Log[(a + b*x)/(c + d*x)]^2 + 2*d*(a + b*x)*Log[c + d*x] - 2*d*(a + b*x)*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 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)]) + d*(a + b*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(a + b*x)) + 6*b*B*c*d*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] - 2*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*Log[a + b*x]*((a*d)/(b*c - a*d) + Log[c/d + x] + Log[(a + b*x)/(c + d*x)]) + 2*a*((a + b*x)^(-1) + Log[(a + b*x)/(c + d*x)]/(a + b*x) + (d*Log[c + d*x])/(-(b*c) + a*d)) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 6*B*d^2*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])*((a + b*x)*(-1 + Log[a/b + x]) - a*Log[a/b + x]^2 - (a^2*(1 + Log[a/b + x]))/(a + b*x) - b*(c/d + x)*(-1 + Log[c/d + x]) + (a^2*Log[c/d + x])/(a + b*x) + (b*x - a^2/(a + b*x) - 2*a*Log[a + b*x])*(-Log[a/b + x] + Log[c/d + x] + Log[(a + b*x)/(c + d*x)]) + (a^2*d*(Log[a + b*x] - Log[c + d*x]))/(-(b*c) + a*d) + 2*a*(Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + PolyLog[2, (b*(c + d*x))/(b*c - a*d)])) + (2*b*B^2*c*d*n^2*(6*b*c - 6*a*d - (6*b^2*c*x)/(a + b*x) + (6*a*b*d*x)/(a + b*x) + 6*a*d*Log[a/b + x] + 3*b*c*Log[a/b + x]^2 - 3*a*d*Log[a/b + x]^2 - 6*b*c*Log[c/d + x] + 6*b*c*Log[a + b*x] - 6*a*d*Log[a + b*x] - 6*b*c*Log[a/b + x]*Log[a + b*x] + 6*a*d*Log[a/b + x]*Log[a + b*x] + 6*b*c*Log[c/d + x]*Log[a + b*x] - 6*a*d*Log[c/d + x]*Log[a + b*x] - 6*b*c*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 6*a*d*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] - (6*b*(b*c - a*d)*x*Log[(a + b*x)/(c + d*x)])/(a + b*x) + 6*b*c*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 6*a*d*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] + 3*a*d*Log[(a + b*x)/(c + d*x)]^2 + 3*b*d*x*Log[(a + b*x)/(c + d*x)]^2 - (3*b^2*x*(c + d*x)*Log[(a + b*x)/(c + d*x)]^2)/(a + b*x) - 3*b*c*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(a + b*x)/(c + d*x)]^2 - a*d*Log[(a + b*x)/(c + d*x)]^3 + 6*b*c*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 6*a*d*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 3*a*d*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*(b*c - a*d + a*d*Log[(a + b*x)/(c + d*x)])*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 6*(b*c - a*d)*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 6*b*c*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 6*a*d*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] + 6*b*c*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))]))/(b*c - a*d) - (B^2*d*n^2*(6*a^2*b*c*d + 6*a^2*b*d^2*x + 6*a^2*b*c*d*Log[(a + b*x)/(c + d*x)] + 6*a^2*b*d^2*x*Log[(a + b*x)/(c + d*x)] + 12*a^2*b*c*d*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(a + b*x)/(c + d*x)] + 12*a*b^2*c*d*x*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(a + b*x)/(c + d*x)] + 6*a^2*b*c*d*Log[(a + b*x)/(c + d*x)]^2 + 3*a^3*d^2*Log[(a + b*x)/(c + d*x)]^2 + 9*a^2*b*d^2*x*Log[(a + b*x)/(c + d*x)]^2 - 3*b^3*c*d*x^2*Log[(a + b*x)/(c + d*x)]^2 + 3*a*b^2*d^2*x^2*Log[(a + b*x)/(c + d*x)]^2 - 6*a^2*b*c*d*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(a + b*x)/(c + d*x)]^2 - 6*a*b^2*c*d*x*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(a + b*x)/(c + d*x)]^2 - 2*a^3*d^2*Log[(a + b*x)/(c + d*x)]^3 - 2*a^2*b*d^2*x*Log[(a + b*x)/(c + d*x)]^3 - 6*a*b^2*c^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 6*a^3*d^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 6*b^3*c^2*x*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 6*a^2*b*d^2*x*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*a^3*d^2*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*a^2*b*d^2*x*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*(a + b*x)*(-(b^2*c^2) - a^2*d^2 + 2*a^2*d^2*Log[(a + b*x)/(c + d*x)])*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] + 12*a*b*c*d*(a + b*x)*(-1 + Log[(a + b*x)/(c + d*x)])*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 12*a^3*d^2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] - 12*a^2*b*d^2*x*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] + 12*a^2*b*c*d*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))] + 12*a*b^2*c*d*x*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))]))/((b*c - a*d)*(a + b*x))))/(3*b^3*g^2)","B",1
174,1,4761,417,13.7006239,"\int \frac{(c i+d i x)^2 \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[((c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(a*g + b*g*x)^3,x]","\text{Result too large to show}","\frac{2 B d^2 i^2 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^3 g^3}-\frac{d^2 i^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)^2}{b^3 g^3}-\frac{d i^2 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{b^2 g^3 (a+b x)}-\frac{2 B d i^2 n (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b^2 g^3 (a+b x)}-\frac{i^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 b g^3 (a+b x)^2}-\frac{B i^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 b g^3 (a+b x)^2}+\frac{2 B^2 d^2 i^2 n^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^3 g^3}-\frac{2 B^2 d i^2 n^2 (c+d x)}{b^2 g^3 (a+b x)}-\frac{B^2 i^2 n^2 (c+d x)^2}{4 b g^3 (a+b x)^2}",1,"(d^2*i^2*Log[a + b*x]*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))^2)/(b^3*g^3) + (2*(-(A^2*b*c*d*i^2) + a*A^2*d^2*i^2 - 2*A*b*B*c*d*i^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + 2*a*A*B*d^2*i^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) - b*B^2*c*d*i^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2 + a*B^2*d^2*i^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2))/(b^3*g^3*(a + b*x)) + (-(A^2*b^2*c^2*i^2) + 2*a*A^2*b*c*d*i^2 - a^2*A^2*d^2*i^2 - 2*A*b^2*B*c^2*i^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + 4*a*A*b*B*c*d*i^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) - 2*a^2*A*B*d^2*i^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) - b^2*B^2*c^2*i^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2 + 2*a*b*B^2*c*d*i^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2 - a^2*B^2*d^2*i^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2)/(2*b^3*g^3*(a + b*x)^2) + (2*B*c^2*i^2*n*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))*(-1/8*((a/b + x)*(2*Log[a/b + x] + 4*Log[a/b + x]^2))/((a + b*x)^3*Log[a/b + x]) - ((b*(c/d + x))/((-a + (b*c)/d)^3*(1 - (b*(c/d + x))/(-a + (b*c)/d))) - ((b^2*(c/d + x)^2)/((-a + (b*c)/d)^4*(1 - (b*(c/d + x))/(-a + (b*c)/d))^2) + (2*b*(c/d + x))/((-a + (b*c)/d)^3*(1 - (b*(c/d + x))/(-a + (b*c)/d))))*Log[c/d + x] - Log[1 - (b*(c/d + x))/(-a + (b*c)/d)]/(-a + (b*c)/d)^2)/(2*b) - (-Log[a/b + x] + Log[c/d + x] + Log[a/(c + d*x) + (b*x)/(c + d*x)])/(2*b*(a + b*x)^2)))/g^3 + (4*B*c*d*i^2*n*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))*(-((1 + Log[a/b + x])/(b^2*(a + b*x))) + (a*(1 + 2*Log[a/b + x]))/(4*b^2*(a + b*x)^2) - (-(Log[c/d + x]/(b*(a + b*x))) + (d*(Log[a + b*x]/(b*c - a*d) - Log[c + d*x]/(b*c - a*d)))/b)/b - (a*(Log[c/d + x] + (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*c - a*d)^2))/(2*b^2*(a + b*x)^2) - ((a + 2*b*x)*(-Log[a/b + x] + Log[c/d + x] + Log[a/(c + d*x) + (b*x)/(c + d*x)]))/(2*b^2*(a + b*x)^2)))/g^3 + (2*B*d^2*i^2*n*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))*(Log[a/b + x]^2/(2*b^3) + (2*a*(1 + Log[a/b + x]))/(b^3*(a + b*x)) - (a^2*(1 + 2*Log[a/b + x]))/(4*b^3*(a + b*x)^2) + (2*a*(-(Log[c/d + x]/(b*(a + b*x))) + (d*(Log[a + b*x]/(b*c - a*d) - Log[c + d*x]/(b*c - a*d)))/b))/b^2 + (a^2*(Log[c/d + x] + (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*c - a*d)^2))/(2*b^3*(a + b*x)^2) + (((a*(3*a + 4*b*x))/(a + b*x)^2 + 2*Log[a + b*x])*(-Log[a/b + x] + Log[c/d + x] + Log[a/(c + d*x) + (b*x)/(c + d*x)]))/(2*b^3) - ((Log[c/d + x]*Log[(a + b*x)/(a - (b*c)/d)])/b + PolyLog[2, (b*d*(c/d + x))/(b*c - a*d)]/b)/b^2))/g^3 + (B^2*c*d*i^2*n^2*(2*a*Log[(a + b*x)/(c + d*x)]^2 - 4*(a + b*x)*Log[(a + b*x)/(c + d*x)]^2 - (4*(a + b*x)*(2*b*c - 2*a*d + 2*d*(a + b*x)*Log[a + b*x] + 2*(b*c - a*d)*Log[(a + b*x)/(c + d*x)] + 2*d*(a + b*x)*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 2*d*(a + b*x)*Log[c + d*x] + 2*d*(a + b*x)*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 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)]) - d*(a + b*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d) + (a*((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*(b*c - a*d)^2*Log[(a + b*x)/(c + d*x)] + 4*d*(-(b*c) + a*d)*(a + b*x)*Log[(a + b*x)/(c + d*x)] - 4*d^2*(a + b*x)^2*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] + 2*d^2*(a + b*x)^2*Log[c + d*x] - 4*d*(a + b*x)*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - 4*d^2*(a + b*x)^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*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*d^2*(a + b*x)^2*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^2))/(2*b^2*g^3*(a + b*x)^2) - (B^2*c^2*i^2*n^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*(b*c - a*d)^2*Log[(a + b*x)/(c + d*x)] + 4*d*(-(b*c) + a*d)*(a + b*x)*Log[(a + b*x)/(c + d*x)] - 4*d^2*(a + b*x)^2*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] + 2*(b*c - a*d)^2*Log[(a + b*x)/(c + d*x)]^2 + 2*d^2*(a + b*x)^2*Log[c + d*x] - 4*d*(a + b*x)*(b*c - a*d + d*(a + b*x)*Log[a + b*x] - d*(a + b*x)*Log[c + d*x]) - 4*d^2*(a + b*x)^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*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*d^2*(a + b*x)^2*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(4*b*(b*c - a*d)^2*g^3*(a + b*x)^2) - (B^2*d^2*i^2*n^2*((2*x*(7*b^2*c^2 - 14*a*b*c*d + 7*a^2*d^2 - 6*d*(a + b*x)*(a*d - b*(2*c + d*x))*Log[a + b*x] + 6*(b*c - a*d)^2*Log[(a + b*x)/(c + d*x)] + 2*b^2*(c + d*x)^2*Log[(a + b*x)/(c + d*x)]^2 - 12*a*b*c*d*Log[c + d*x] + 6*a^2*d^2*Log[c + d*x] - 12*b^2*c*d*x*Log[c + d*x] - 6*b^2*d^2*x^2*Log[c + d*x]))/(a + b*x) + (b*x^2*(b^2*c^2 - 8*a*b*c*d + 7*a^2*d^2 - 6*b^2*c*d*x + 6*a*b*d^2*x - 6*d^2*(a + b*x)^2*Log[a + b*x] + 2*(b*c - a*d)*(b*c - 3*a*d - 2*b*d*x)*Log[(a + b*x)/(c + d*x)] + 2*b*(c + d*x)*(b*c - 2*a*d - b*d*x)*Log[(a + b*x)/(c + d*x)]^2 + 6*a^2*d^2*Log[c + d*x] + 12*a*b*d^2*x*Log[c + d*x] + 6*b^2*d^2*x^2*Log[c + d*x]))/(a + b*x)^2 - 2*(12*b*c^2 - 18*a*c*d + (6*a^2*d^2)/b - 3*b*c*d*x + 3*a*d^2*x + 12*a*c*d*Log[a/b + x] - (6*a^2*d^2*Log[a/b + x])/b + 3*b*c^2*Log[a/b + x]^2 - 6*a*c*d*Log[a/b + x]^2 + (3*a^2*d^2*Log[a/b + x]^2)/b - 12*b*c^2*Log[c/d + x] + 6*a*c*d*Log[c/d + x] + 7*b*c^2*Log[a + b*x] - 14*a*c*d*Log[a + b*x] + (4*a^2*d^2*Log[a + b*x])/b + 12*b*c*d*x*Log[a + b*x] - 6*a*d^2*x*Log[a + b*x] + 3*b*d^2*x^2*Log[a + b*x] - 6*b*c^2*Log[a/b + x]*Log[a + b*x] + 12*a*c*d*Log[a/b + x]*Log[a + b*x] - (6*a^2*d^2*Log[a/b + x]*Log[a + b*x])/b + 6*b*c^2*Log[c/d + x]*Log[a + b*x] - 12*a*c*d*Log[c/d + x]*Log[a + b*x] + (6*a^2*d^2*Log[c/d + x]*Log[a + b*x])/b - 6*b*c^2*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 12*a*c*d*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] - (6*a^2*d^2*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)])/b - 2*b*c^2*Log[(b*c - a*d)/(c + d*x)] + 4*a*c*d*Log[(b*c - a*d)/(c + d*x)] - (2*a^2*d^2*Log[(b*c - a*d)/(c + d*x)])/b - 2*a*c*d*Log[(a + b*x)/(c + d*x)] + (2*a^2*d^2*Log[(a + b*x)/(c + d*x)])/b - 2*b*c*d*x*Log[(a + b*x)/(c + d*x)] + 2*a*d^2*x*Log[(a + b*x)/(c + d*x)] + 6*b*c^2*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 12*a*c*d*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] + (6*a^2*d^2*Log[a + b*x]*Log[(a + b*x)/(c + d*x)])/b + 4*a*c*d*Log[(a + b*x)/(c + d*x)]^2 - (3*a^2*d^2*Log[(a + b*x)/(c + d*x)]^2)/b + 4*b*c*d*x*Log[(a + b*x)/(c + d*x)]^2 - 2*a*d^2*x*Log[(a + b*x)/(c + d*x)]^2 + b*d^2*x^2*Log[(a + b*x)/(c + d*x)]^2 - 2*b*c^2*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(a + b*x)/(c + d*x)]^2 - (4*a*c*d*Log[(a + b*x)/(c + d*x)]^3)/3 + (2*a^2*d^2*Log[(a + b*x)/(c + d*x)]^3)/(3*b) + 3*b*c^2*Log[c + d*x] - 12*b*c*d*x*Log[c + d*x] + 6*a*d^2*x*Log[c + d*x] - 3*b*d^2*x^2*Log[c + d*x] + 6*b*c^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 12*a*c*d*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + (6*a^2*d^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)])/b + 4*a*c*d*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - (2*a^2*d^2*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)])/b + (2*(3*(b*c - a*d)^2 - 2*a*d*(-2*b*c + a*d)*Log[(a + b*x)/(c + d*x)])*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/b - (6*(b*c - a*d)^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/b + 4*b*c^2*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 8*a*c*d*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] + (4*a^2*d^2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])/b + 4*b*c^2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))])))/(4*b^2*(b*c - a*d)^2*g^3)","B",1
175,1,1415,157,2.2408407,"\int \frac{(c i+d i x)^2 \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[((c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(a*g + b*g*x)^4,x]","-\frac{i^2 \left(18 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (b c-a d)^3+54 d (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)^2-54 d^2 (a d-b c) (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2+54 B d^2 n (a+b x)^2 \left(2 (b c-a d) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+2 d (a+b x) \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-2 d (a+b x) \log (c+d x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+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) \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(\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)\right)+27 B d n (a+b x) \left(2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^2+4 d (a d-b c) (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-4 d^2 (a+b x)^2 \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+4 d^2 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \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 \left((b c-a d)^2+2 d (a d-b c) (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)\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(\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)\right)+B n \left(12 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^3-18 d (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+36 d^2 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)+36 d^3 (a+b x)^3 \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-36 d^3 (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \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) \left((b c-a d)^2+2 d (a d-b c) (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)\right)+2 B n \left(2 (b c-a d)^3-3 d (a+b x) (b c-a d)^2+6 d^2 (a+b x)^2 (b c-a d)+6 d^3 (a+b x)^3 \log (a+b x)-6 d^3 (a+b x)^3 \log (c+d x)\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(\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)\right)\right)}{54 b^3 (b c-a d) g^4 (a+b x)^3}","-\frac{i^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)}-\frac{2 B i^2 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)}-\frac{2 B^2 i^2 n^2 (c+d x)^3}{27 g^4 (a+b x)^3 (b c-a d)}",1,"-1/54*(i^2*(18*(b*c - a*d)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 54*d*(b*c - a*d)^2*(a + b*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - 54*d^2*(-(b*c) + a*d)*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 54*B*d^2*n*(a + b*x)^2*(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)])) + 27*B*d*n*(a + b*x)*(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*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^3*(b*c - a*d)*g^4*(a + b*x)^3)","C",1
176,1,1860,319,3.2798551,"\int \frac{(c i+d i x)^2 \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[((c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(a*g + b*g*x)^5,x]","-\frac{i^2 \left(216 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (b c-a d)^4+432 d^2 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (b c-a d)^2-576 d (a d-b c)^3 (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2+216 B d^2 n (a+b x)^2 \left(2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^2+4 d (a d-b c) (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-4 d^2 (a+b x)^2 \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+4 d^2 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \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 \left((b c-a d)^2+2 d (a d-b c) (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)\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(\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)\right)+32 B d n (a+b x) \left(12 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^3-18 d (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+36 d^2 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)+36 d^3 (a+b x)^3 \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-36 d^3 (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \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) \left((b c-a d)^2+2 d (a d-b c) (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)\right)+2 B n \left(2 (b c-a d)^3-3 d (a+b x) (b c-a d)^2+6 d^2 (a+b x)^2 (b c-a d)+6 d^3 (a+b x)^3 \log (a+b x)-6 d^3 (a+b x)^3 \log (c+d x)\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(\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)\right)+3 B n \left(36 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^4+72 d^2 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^2+144 d^3 (a d-b c) (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+48 d (a d-b c)^3 (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-144 d^4 (a+b x)^4 \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+144 d^4 (a+b x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \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 \left((b c-a d)^2+2 d (a d-b c) (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)\right)-8 B d n (a+b x) \left(2 (b c-a d)^3-3 d (a+b x) (b c-a d)^2+6 d^2 (a+b x)^2 (b c-a d)+6 d^3 (a+b x)^3 \log (a+b x)-6 d^3 (a+b x)^3 \log (c+d x)\right)+3 B n \left(3 (b c-a d)^4+6 d^2 (a+b x)^2 (b c-a d)^2+12 d^3 (a d-b c) (a+b x)^3+4 d (a d-b c)^3 (a+b x)-12 d^4 (a+b x)^4 \log (a+b x)+12 d^4 (a+b x)^4 \log (c+d x)\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(\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)\right)\right)}{864 b^3 (b c-a d)^2 g^5 (a+b x)^4}","-\frac{b i^2 (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)^2}-\frac{b B i^2 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)^2}+\frac{d i^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^5 (a+b x)^3 (b c-a d)^2}+\frac{2 B d i^2 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^5 (a+b x)^3 (b c-a d)^2}-\frac{b B^2 i^2 n^2 (c+d x)^4}{32 g^5 (a+b x)^4 (b c-a d)^2}+\frac{2 B^2 d i^2 n^2 (c+d x)^3}{27 g^5 (a+b x)^3 (b c-a d)^2}",1,"-1/864*(i^2*(216*(b*c - a*d)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - 576*d*(-(b*c) + a*d)^3*(a + b*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 432*d^2*(b*c - a*d)^2*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 216*B*d^2*n*(a + b*x)^2*(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)])) + 32*B*d*n*(a + b*x)*(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)])) + 3*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^3*(b*c - a*d)^2*g^5*(a + b*x)^4)","C",1
177,1,2320,493,3.9244794,"\int \frac{(c i+d i x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{(a g+b g x)^6} \, dx","Integrate[((c*i + d*i*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(a*g + b*g*x)^6,x]","\text{Result too large to show}","-\frac{b^2 i^2 (c+d x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{5 g^6 (a+b x)^5 (b c-a d)^3}-\frac{2 b^2 B i^2 n (c+d x)^5 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{25 g^6 (a+b x)^5 (b c-a d)^3}-\frac{d^2 i^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^6 (a+b x)^3 (b c-a d)^3}-\frac{2 B d^2 i^2 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^6 (a+b x)^3 (b c-a d)^3}+\frac{b d i^2 (c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 g^6 (a+b x)^4 (b c-a d)^3}+\frac{b B d i^2 n (c+d x)^4 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{4 g^6 (a+b x)^4 (b c-a d)^3}-\frac{2 b^2 B^2 i^2 n^2 (c+d x)^5}{125 g^6 (a+b x)^5 (b c-a d)^3}-\frac{2 B^2 d^2 i^2 n^2 (c+d x)^3}{27 g^6 (a+b x)^3 (b c-a d)^3}+\frac{b B^2 d i^2 n^2 (c+d x)^4}{16 g^6 (a+b x)^4 (b c-a d)^3}",1,"-1/54000*(i^2*(10800*(b*c - a*d)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 27000*d*(b*c - a*d)^4*(a + b*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - 18000*d^2*(-(b*c) + a*d)^3*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 1000*B*d^2*n*(a + b*x)^2*(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)])) + 375*B*d*n*(a + b*x)*(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)])) + 6*B*n*(-225*a*B*d*(b*c - a*d)^4*n + 144*B*(b*c - a*d)^5*n - 225*b*B*d*(b*c - a*d)^4*n*x + 300*a*B*d^2*(b*c - a*d)^3*n*(a + b*x) - 180*B*d*(b*c - a*d)^4*n*(a + b*x) + 300*b*B*d^2*(b*c - a*d)^3*n*x*(a + b*x) - 450*a*B*d^3*(b*c - a*d)^2*n*(a + b*x)^2 + 640*B*d^2*(b*c - a*d)^3*n*(a + b*x)^2 - 450*b*B*d^3*(b*c - a*d)^2*n*x*(a + b*x)^2 + 900*a*B*d^4*(b*c - a*d)*n*(a + b*x)^3 - 1860*B*d^3*(b*c - a*d)^2*n*(a + b*x)^3 + 900*b*B*d^4*(b*c - a*d)*n*x*(a + b*x)^3 + 3600*b*B*c*d^4*n*(a + b*x)^4 - 3600*a*B*d^5*n*(a + b*x)^4 + 3720*B*d^4*(b*c - a*d)*n*(a + b*x)^4 + 900*a*B*d^5*n*(a + b*x)^4*Log[a + b*x] + 900*b*B*d^5*n*x*(a + b*x)^4*Log[a + b*x] + 7320*B*d^5*n*(a + b*x)^5*Log[a + b*x] + 720*(b*c - a*d)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 900*d*(b*c - a*d)^4*(a + b*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 1200*d^2*(b*c - a*d)^3*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 1800*d^3*(b*c - a*d)^2*(a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 3600*d^4*(b*c - a*d)*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 3600*d^5*(a + b*x)^5*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 900*a*B*d^5*n*(a + b*x)^4*Log[c + d*x] - 900*b*B*d^5*n*x*(a + b*x)^4*Log[c + d*x] - 7320*B*d^5*n*(a + b*x)^5*Log[c + d*x] - 3600*d^5*(a + b*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] - 1800*B*d^5*n*(a + b*x)^5*(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)]) + 1800*B*d^5*n*(a + b*x)^5*((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*(b*c - a*d)^3*g^6*(a + b*x)^5)","C",1
178,1,2448,1172,3.5722934,"\int (a g+b g x)^3 (c i+d i 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*(c*i + d*i*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\text{Result too large to show}","-\frac{B g^3 i^3 n \left(6 A+11 B n+6 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)^7}{420 b^4 d^4}-\frac{B^2 g^3 i^3 n^2 \log \left(\frac{a+b x}{c+d x}\right) (b c-a d)^7}{210 b^4 d^4}-\frac{11 B^2 g^3 i^3 n^2 \log (c+d x) (b c-a d)^7}{420 b^4 d^4}-\frac{B^2 g^3 i^3 n^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right) (b c-a d)^7}{70 b^4 d^4}+\frac{5 B^2 g^3 i^3 n^2 x (b c-a d)^6}{84 b^3 d^3}-\frac{B g^3 i^3 n (a+b x) \left(6 A+5 B n+6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^6}{420 b^4 d^3}-\frac{29 B^2 g^3 i^3 n^2 (c+d x)^2 (b c-a d)^5}{840 b^2 d^4}+\frac{B g^3 i^3 n (a+b x)^2 \left(3 A+B n+3 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^5}{420 b^4 d^2}+\frac{47 B^2 g^3 i^3 n^2 (c+d x)^3 (b c-a d)^4}{1260 b d^4}-\frac{B g^3 i^3 n (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^4}{210 b^4 d}+\frac{2 B g^3 i^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)^4}{21 b d^4}+\frac{B^2 g^3 i^3 n^2 (a+b x)^4 (b c-a d)^3}{140 b^4}-\frac{13 B^2 g^3 i^3 n^2 (c+d x)^4 (b c-a d)^3}{420 d^4}+\frac{g^3 i^3 (a+b x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (b c-a d)^3}{140 b^4}-\frac{3 B g^3 i^3 n (a+b x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^3}{140 b^4}-\frac{3 B g^3 i^3 n (c+d x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^3}{14 d^4}+\frac{b B^2 g^3 i^3 n^2 (c+d x)^5 (b c-a d)^2}{105 d^4}+\frac{g^3 i^3 (a+b x)^4 (c+d x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (b c-a d)^2}{35 b^3}+\frac{6 b B g^3 i^3 n (c+d x)^5 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^2}{35 d^4}-\frac{B g^3 i^3 n (a+b x)^4 (c+d x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^2}{35 b^3}+\frac{g^3 i^3 (a+b x)^4 (c+d x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (b c-a d)}{14 b^2}-\frac{b^2 B g^3 i^3 n (c+d x)^6 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)}{21 d^4}+\frac{g^3 i^3 (a+b x)^4 (c+d x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{7 b}",1,"(g^3*i^3*(35*(b*c - a*d)^3*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 84*d*(b*c - a*d)^2*(a + b*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 70*d^2*(b*c - a*d)*(a + b*x)^6*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 20*d^3*(a + b*x)^7*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - (35*B*(b*c - a*d)^4*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) + (7*B*(b*c - a*d)^3*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)])))/d^4 - (7*B*(b*c - a*d)^2*n*(120*A*b*d*(b*c - a*d)^4*x + 120*B*d*(b*c - a*d)^4*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] + 60*d^2*(-(b*c) + a*d)^3*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 40*d^3*(b*c - a*d)^2*(a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 30*d^4*(-(b*c) + a*d)*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 24*d^5*(a + b*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 120*B*(b*c - a*d)^5*n*Log[c + d*x] - 120*(b*c - a*d)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + 20*B*(b*c - a*d)^3*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]) + 5*B*(b*c - a*d)^2*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]) + 2*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]) + 60*B*(b*c - a*d)^4*n*(b*d*x + (-(b*c) + a*d)*Log[c + d*x]) + 60*B*(b*c - a*d)^5*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)])))/(6*d^4) + (B*(b*c - a*d)*n*(360*A*b*d*(b*c - a*d)^5*x + 60*b^2*B*c*d*(b*c - a*d)^4*n*x - 60*a*b*B*d^2*(b*c - a*d)^4*n*x + 462*b*B*d*(b*c - a*d)^5*n*x - 30*b*B*c*d^2*(b*c - a*d)^3*n*(a + b*x)^2 + 30*a*B*d^3*(b*c - a*d)^3*n*(a + b*x)^2 - 141*B*d^2*(b*c - a*d)^4*n*(a + b*x)^2 + 20*b*B*c*d^3*(b*c - a*d)^2*n*(a + b*x)^3 - 20*a*B*d^4*(b*c - a*d)^2*n*(a + b*x)^3 + 54*B*d^3*(b*c - a*d)^3*n*(a + b*x)^3 - 15*b*B*c*d^4*(b*c - a*d)*n*(a + b*x)^4 + 15*a*B*d^5*(b*c - a*d)*n*(a + b*x)^4 - 18*B*d^4*(b*c - a*d)^2*n*(a + b*x)^4 + 12*b*B*c*d^5*n*(a + b*x)^5 - 12*a*B*d^6*n*(a + b*x)^5 + 360*B*d*(b*c - a*d)^5*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] - 180*d^2*(b*c - a*d)^4*(a + b*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 120*d^3*(b*c - a*d)^3*(a + b*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 90*d^4*(b*c - a*d)^2*(a + b*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 72*d^5*(b*c - a*d)*(a + b*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 60*d^6*(a + b*x)^6*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 60*b*B*c*(b*c - a*d)^5*n*Log[c + d*x] + 60*a*B*d*(b*c - a*d)^5*n*Log[c + d*x] - 822*B*(b*c - a*d)^6*n*Log[c + d*x] - 360*(b*c - a*d)^6*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[c + d*x] + 180*B*(b*c - a*d)^6*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)])))/(9*d^4)))/(140*b^4)","B",1
179,1,1627,976,1.5621431,"\int (a g+b g x)^2 (c i+d i 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)^2*(c*i + d*i*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{g^2 i^3 \left(10 b^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (c+d x)^6-24 b (b c-a d) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (c+d x)^5+15 (b c-a d)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (c+d x)^4-\frac{5 B (b c-a d)^3 n \left(6 \log (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)^3-6 B n \log (c+d x) (b c-a d)^3-3 B 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 c-a d)^3+6 A b d x (b c-a d)^2-3 B n (b d x+(b c-a d) \log (a+b x)) (b c-a d)^2+6 B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) (b c-a d)^2-B n \left(2 \log (a+b x) (b c-a d)^2+2 b d x (b c-a d)+b^2 (c+d x)^2\right) (b c-a d)+3 b^2 (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)+2 b^3 (c+d x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)\right)}{b^4}+\frac{2 B (b c-a d)^2 n \left(24 \log (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)^4-24 B n \log (c+d x) (b c-a d)^4-12 B 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 c-a d)^4+24 A b d x (b c-a d)^3-12 B n (b d x+(b c-a d) \log (a+b x)) (b c-a d)^3+24 B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) (b c-a d)^3-4 B n \left(2 \log (a+b x) (b c-a d)^2+2 b d x (b c-a d)+b^2 (c+d x)^2\right) (b c-a d)^2+12 b^2 (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)^2-B n \left(6 \log (a+b x) (b c-a d)^3+6 b d x (b c-a d)^2+3 b^2 (c+d x)^2 (b c-a d)+2 b^3 (c+d x)^3\right) (b c-a d)+8 b^3 (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^4 (c+d x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)\right)}{b^4}-\frac{B (b c-a d) n \left(120 \log (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)^5-120 B n \log (c+d x) (b c-a d)^5-60 B 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 c-a d)^5+120 A b d x (b c-a d)^4-60 B n (b d x+(b c-a d) \log (a+b x)) (b c-a d)^4+120 B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) (b c-a d)^4-20 B n \left(2 \log (a+b x) (b c-a d)^2+2 b d x (b c-a d)+b^2 (c+d x)^2\right) (b c-a d)^3+60 b^2 (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)^3-5 B n \left(6 \log (a+b x) (b c-a d)^3+6 b d x (b c-a d)^2+3 b^2 (c+d x)^2 (b c-a d)+2 b^3 (c+d x)^3\right) (b c-a d)^2+40 b^3 (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)^2-2 B n \left(12 \log (a+b x) (b c-a d)^4+12 b d x (b c-a d)^3+6 b^2 (c+d x)^2 (b c-a d)^2+4 b^3 (c+d x)^3 (b c-a d)+3 b^4 (c+d x)^4\right) (b c-a d)+30 b^4 (c+d x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)+24 b^5 (c+d x)^5 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)\right)}{6 b^4}\right)}{60 d^3}","\frac{B g^2 i^3 n \left(2 A+3 B n+2 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)^6}{60 b^4 d^3}+\frac{B^2 g^2 i^3 n^2 \log \left(\frac{a+b x}{c+d x}\right) (b c-a d)^6}{36 b^4 d^3}+\frac{11 B^2 g^2 i^3 n^2 \log (c+d x) (b c-a d)^6}{180 b^4 d^3}+\frac{B^2 g^2 i^3 n^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right) (b c-a d)^6}{30 b^4 d^3}-\frac{7 B^2 g^2 i^3 n^2 x (b c-a d)^5}{180 b^3 d^2}+\frac{B g^2 i^3 n (a+b x) \left(2 A+B n+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^5}{60 b^4 d^2}-\frac{7 B^2 g^2 i^3 n^2 (c+d x)^2 (b c-a d)^4}{360 b^2 d^3}-\frac{B g^2 i^3 n (a+b 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}{60 b^4 d}-\frac{B g^2 i^3 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}{10 b^2 d^3}-\frac{B^2 g^2 i^3 n^2 (c+d x)^3 (b c-a d)^3}{60 b d^3}+\frac{g^2 i^3 (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (b c-a d)^3}{60 b^4}-\frac{B g^2 i^3 n (a+b x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^3}{30 b^4}+\frac{B g^2 i^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)^3}{45 b d^3}+\frac{B^2 g^2 i^3 n^2 (c+d x)^4 (b c-a d)^2}{60 d^3}+\frac{g^2 i^3 (a+b x)^3 (c+d x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (b c-a d)^2}{20 b^3}+\frac{7 B g^2 i^3 n (c+d x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^2}{60 d^3}+\frac{g^2 i^3 (a+b x)^3 (c+d x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (b c-a d)}{10 b^2}-\frac{b B g^2 i^3 n (c+d x)^5 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)}{15 d^3}+\frac{g^2 i^3 (a+b x)^3 (c+d x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{6 b}",1,"(g^2*i^3*(15*(b*c - a*d)^2*(c + d*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - 24*b*(b*c - a*d)*(c + d*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 10*b^2*(c + d*x)^6*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - (5*B*(b*c - a*d)^3*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)])))/b^4 + (2*B*(b*c - a*d)^2*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)])))/b^4 - (B*(b*c - a*d)*n*(120*A*b*d*(b*c - a*d)^4*x - 60*B*(b*c - a*d)^4*n*(b*d*x + (b*c - a*d)*Log[a + b*x]) - 20*B*(b*c - a*d)^3*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]) - 5*B*(b*c - a*d)^2*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]) - 2*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]) + 120*B*d*(b*c - a*d)^4*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] + 60*b^2*(b*c - a*d)^3*(c + d*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 40*b^3*(b*c - a*d)^2*(c + d*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 30*b^4*(b*c - a*d)*(c + d*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 24*b^5*(c + d*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) + 120*(b*c - a*d)^5*Log[a + b*x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - 120*B*(b*c - a*d)^5*n*Log[c + d*x] - 60*B*(b*c - a*d)^5*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)])))/(6*b^4)))/(60*d^3)","A",1
180,1,945,786,0.7640194,"\int (a g+b g x) (c i+d i 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)*(c*i + d*i*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{g i^3 \left(4 b \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (c+d x)^5-5 (b c-a d) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 (c+d x)^4+\frac{5 B (b c-a d)^2 n \left(6 \log (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)^3-6 B n \log (c+d x) (b c-a d)^3-3 B 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 c-a d)^3+6 A b d x (b c-a d)^2-3 B n (b d x+(b c-a d) \log (a+b x)) (b c-a d)^2+6 B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) (b c-a d)^2-B n \left(2 \log (a+b x) (b c-a d)^2+2 b d x (b c-a d)+b^2 (c+d x)^2\right) (b c-a d)+3 b^2 (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)+2 b^3 (c+d x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)\right)}{3 b^4}-\frac{B (b c-a d) n \left(24 \log (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)^4-24 B n \log (c+d x) (b c-a d)^4-12 B 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 c-a d)^4+24 A b d x (b c-a d)^3-12 B n (b d x+(b c-a d) \log (a+b x)) (b c-a d)^3+24 B d (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) (b c-a d)^3-4 B n \left(2 \log (a+b x) (b c-a d)^2+2 b d x (b c-a d)+b^2 (c+d x)^2\right) (b c-a d)^2+12 b^2 (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)^2-B n \left(6 \log (a+b x) (b c-a d)^3+6 b d x (b c-a d)^2+3 b^2 (c+d x)^2 (b c-a d)+2 b^3 (c+d x)^3\right) (b c-a d)+8 b^3 (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^4 (c+d x)^4 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)\right)}{3 b^4}\right)}{20 d^2}","-\frac{B g i^3 n (b c-a d)^5 \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)}{10 b^4 d^2}-\frac{B g i^3 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)}{10 b^4 d}+\frac{g i^3 (a+b x)^2 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{20 b^4}-\frac{B g i^3 n (a+b x)^2 (b c-a d)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{10 b^4}+\frac{g i^3 (a+b x)^2 (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)^2}{10 b^3}+\frac{3 B g i^3 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)}{20 b^2 d^2}+\frac{3 g i^3 (a+b x)^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)^2}{20 b^2}+\frac{B g i^3 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)}{30 b d^2}-\frac{B g i^3 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 d^2}+\frac{g i^3 (a+b x)^2 (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{5 b}-\frac{B^2 g i^3 n^2 (b c-a d)^5 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{10 b^4 d^2}-\frac{B^2 g i^3 n^2 (b c-a d)^5 \log \left(\frac{a+b x}{c+d x}\right)}{12 b^4 d^2}-\frac{11 B^2 g i^3 n^2 (b c-a d)^5 \log (c+d x)}{60 b^4 d^2}+\frac{B^2 g i^3 n^2 x (b c-a d)^4}{60 b^3 d}+\frac{B^2 g i^3 n^2 (c+d x)^2 (b c-a d)^3}{30 b^2 d^2}+\frac{B^2 g i^3 n^2 (c+d x)^3 (b c-a d)^2}{30 b d^2}",1,"(g*i^3*(-5*(b*c - a*d)*(c + d*x)^4*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 4*b*(c + d*x)^5*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + (5*B*(b*c - a*d)^2*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) - (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)])))/(3*b^4)))/(20*d^2)","A",1
181,1,409,454,0.3207474,"\int (c i+d i x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 \, dx","Integrate[(c*i + d*i*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{i^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 i^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 i^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 i^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 i^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{i^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 i^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 i^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 i^3 n^2 (b c-a d)^4 \log (c+d x)}{12 b^4 d}+\frac{5 B^2 i^3 n^2 x (b c-a d)^3}{12 b^3}+\frac{B^2 i^3 n^2 (c+d x)^2 (b c-a d)^2}{12 b^2 d}",1,"(i^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
182,1,2941,762,5.2025336,"\int \frac{(c i+d i x)^3 \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[((c*i + d*i*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(a*g + b*g*x),x]","\text{Result too large to show}","\frac{2 B i^3 n (b c-a d)^3 \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^4 g}+\frac{d i^3 (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)^2}{b^4 g}-\frac{5 B d i^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)}{3 b^4 g}+\frac{2 B i^3 n (b c-a d)^3 \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^4 g}-\frac{i^3 (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)^2}{b^4 g}+\frac{5 B i^3 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^4 g}+\frac{i^3 (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)^2}{2 b^2 g}-\frac{B i^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)}{3 b^2 g}+\frac{i^3 (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{3 b g}+\frac{2 B^2 i^3 n^2 (b c-a d)^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^4 g}-\frac{5 B^2 i^3 n^2 (b c-a d)^3 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{3 b^4 g}+\frac{2 B^2 i^3 n^2 (b c-a d)^3 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g}+\frac{B^2 i^3 n^2 (b c-a d)^3 \log \left(\frac{a+b x}{c+d x}\right)}{3 b^4 g}+\frac{2 B^2 i^3 n^2 (b c-a d)^3 \log (c+d x)}{b^4 g}+\frac{B^2 d i^3 n^2 x (b c-a d)^2}{3 b^3 g}",1,"(i^3*(6*b*d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2 + 3*b^2*d^2*(3*b*c - a*d)*x^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2 + 2*b^3*d^3*x^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2 + 6*(b*c - a*d)^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 - 18*b^2*B*c^2*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])*(a*d*Log[a/b + x]^2 - 2*a*d*Log[a/b + x]*(1 + Log[a + b*x]) + 2*(-(b*c) + a*d + Log[c/d + x]*(b*c + a*d*Log[a + b*x] - a*d*Log[(d*(a + b*x))/(-(b*c) + a*d)]) + (-(b*d*x) + a*d*Log[a + b*x])*Log[(a + b*x)/(c + d*x)]) - 2*a*d*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) - 2*B*n*(-A - B*Log[e*((a + b*x)/(c + d*x))^n] + B*n*Log[(a + b*x)/(c + d*x)])*(6*a^2*b*c*d^2 - 6*a^3*d^3 + 2*b^3*c^2*d*x + 3*a*b^2*c*d^2*x - 5*a^2*b*d^3*x - b^3*c*d^2*x^2 + a*b^2*d^3*x^2 - 3*a^3*d^3*Log[a/b + x]^2 - 6*a^2*b*c*d^2*Log[c/d + x] + 5*a^3*d^3*Log[a + b*x] - 6*a^3*d^3*Log[c/d + x]*Log[a + b*x] + 6*a^3*d^3*Log[a/b + x]*(1 + Log[a + b*x]) + 6*a^3*d^3*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 6*a^2*b*d^3*x*Log[(a + b*x)/(c + d*x)] - 3*a*b^2*d^3*x^2*Log[(a + b*x)/(c + d*x)] + 2*b^3*d^3*x^3*Log[(a + b*x)/(c + d*x)] - 6*a^3*d^3*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 2*b^3*c^3*Log[c + d*x] - 3*a*b^2*c^2*d*Log[c + d*x] + 6*a^3*d^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 6*b^3*B*c^3*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)])) + 9*b*B*c*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])*(-4*a*d^2*(a + b*x)*(-1 + Log[a/b + x]) + 2*a^2*d^2*Log[a/b + x]^2 + 4*a*b*d*(c + d*x)*(-1 + Log[c/d + x]) + d^2*(b*x*(2*a - b*x) + 2*b^2*x^2*Log[a/b + x] - 2*a^2*Log[a + b*x]) - 2*d^2*(b*x*(-2*a + b*x) + 2*a^2*Log[a + b*x])*(Log[a/b + x] - Log[c/d + x] - Log[(a + b*x)/(c + d*x)]) + b^2*(d*x*(-2*c + d*x) - 2*d^2*x^2*Log[c/d + x] + 2*c^2*Log[c + d*x]) - 4*a^2*d^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*b^2*B^2*c^2*n^2*(Log[(a + b*x)/(c + d*x)]*(-(a*d*Log[(a + b*x)/(c + d*x)]^2) + 6*(b*c - a*d)*Log[(b*c - a*d)/(b*c + b*d*x)] + 3*d*Log[(a + b*x)/(c + d*x)]*(a + b*x + a*Log[(b*c - a*d)/(b*c + b*d*x)])) + 6*(b*c - a*d + a*d*Log[(a + b*x)/(c + d*x)])*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 6*a*d*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))]) - 3*b*B^2*c*n^2*(6*b^2*c^2*Log[(b*c - a*d)/(c + d*x)] - 12*a*b*c*d*Log[(b*c - a*d)/(c + d*x)] + 6*a^2*d^2*Log[(b*c - a*d)/(c + d*x)] + 6*a*b*c*d*Log[(a + b*x)/(c + d*x)] - 6*a^2*d^2*Log[(a + b*x)/(c + d*x)] + 6*b^2*c*d*x*Log[(a + b*x)/(c + d*x)] - 6*a*b*d^2*x*Log[(a + b*x)/(c + d*x)] + 9*a^2*d^2*Log[(a + b*x)/(c + d*x)]^2 + 6*a*b*d^2*x*Log[(a + b*x)/(c + d*x)]^2 - 3*b^2*d^2*x^2*Log[(a + b*x)/(c + d*x)]^2 - 2*a^2*d^2*Log[(a + b*x)/(c + d*x)]^3 + 6*b^2*c^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 12*a*b*c*d*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 18*a^2*d^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*a^2*d^2*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*(b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2 + 2*a^2*d^2*Log[(a + b*x)/(c + d*x)])*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 12*a^2*d^2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))]) + B^2*n^2*(2*b^3*c^3 - 4*a*b^2*c^2*d + 2*a^2*b*c*d^2 + 2*b^3*c^2*d*x - 4*a*b^2*c*d^2*x + 2*a^2*b*d^3*x + 6*b^3*c^3*Log[(b*c - a*d)/(c + d*x)] - 18*a^2*b*c*d^2*Log[(b*c - a*d)/(c + d*x)] + 12*a^3*d^3*Log[(b*c - a*d)/(c + d*x)] + 4*a*b^2*c^2*d*Log[(a + b*x)/(c + d*x)] + 8*a^2*b*c*d^2*Log[(a + b*x)/(c + d*x)] - 12*a^3*d^3*Log[(a + b*x)/(c + d*x)] + 4*b^3*c^2*d*x*Log[(a + b*x)/(c + d*x)] + 6*a*b^2*c*d^2*x*Log[(a + b*x)/(c + d*x)] - 10*a^2*b*d^3*x*Log[(a + b*x)/(c + d*x)] - 2*b^3*c*d^2*x^2*Log[(a + b*x)/(c + d*x)] + 2*a*b^2*d^3*x^2*Log[(a + b*x)/(c + d*x)] + 11*a^3*d^3*Log[(a + b*x)/(c + d*x)]^2 + 6*a^2*b*d^3*x*Log[(a + b*x)/(c + d*x)]^2 - 3*a*b^2*d^3*x^2*Log[(a + b*x)/(c + d*x)]^2 + 2*b^3*d^3*x^3*Log[(a + b*x)/(c + d*x)]^2 - 2*a^3*d^3*Log[(a + b*x)/(c + d*x)]^3 + 4*b^3*c^3*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*a*b^2*c^2*d*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 12*a^2*b*c*d^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 22*a^3*d^3*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*a^3*d^3*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*(2*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 11*a^3*d^3 + 6*a^3*d^3*Log[(a + b*x)/(c + d*x)])*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 12*a^3*d^3*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))]) - 6*b^3*B^2*c^3*n^2*(Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(a + b*x)/(c + d*x)]^2 - 2*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))])))/(6*b^4*g)","B",1
183,1,4942,739,14.8277688,"\int \frac{(c i+d i x)^3 \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[((c*i + d*i*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(a*g + b*g*x)^2,x]","\text{Result too large to show}","\frac{2 d^2 i^3 (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)^2}{b^4 g^2}-\frac{B d^2 i^3 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^4 g^2}+\frac{6 B d i^3 n (b c-a d)^2 \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^4 g^2}+\frac{4 B d i^3 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\right)}{b^4 g^2}-\frac{3 d i^3 (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)^2}{b^4 g^2}+\frac{B d i^3 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^4 g^2}-\frac{i^3 (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)^2}{b^3 g^2 (a+b x)}-\frac{2 B i^3 n (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)}{b^3 g^2 (a+b x)}+\frac{d i^3 (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 b^2 g^2}+\frac{4 B^2 d i^3 n^2 (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^4 g^2}-\frac{B^2 d i^3 n^2 (b c-a d)^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g^2}+\frac{6 B^2 d i^3 n^2 (b c-a d)^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g^2}+\frac{B^2 d i^3 n^2 (b c-a d)^2 \log (c+d x)}{b^4 g^2}-\frac{2 B^2 i^3 n^2 (c+d x) (b c-a d)^2}{b^3 g^2 (a+b x)}",1,"(d^2*(3*b*c - 2*a*d)*i^3*x*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))^2)/(b^3*g^2) + (d^3*i^3*x^2*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))^2)/(2*b^2*g^2) + (3*d*(b*c - a*d)^2*i^3*Log[a + b*x]*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))^2)/(b^4*g^2) + (-(A^2*b^3*c^3*i^3) + 3*a*A^2*b^2*c^2*d*i^3 - 3*a^2*A^2*b*c*d^2*i^3 + a^3*A^2*d^3*i^3 - 2*A*b^3*B*c^3*i^3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + 6*a*A*b^2*B*c^2*d*i^3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) - 6*a^2*A*b*B*c*d^2*i^3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + 2*a^3*A*B*d^3*i^3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) - b^3*B^2*c^3*i^3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2 + 3*a*b^2*B^2*c^2*d*i^3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2 - 3*a^2*b*B^2*c*d^2*i^3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2 + a^3*B^2*d^3*i^3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2)/(b^4*g^2*(a + b*x)) + (2*B*c^3*i^3*n*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))*(-(((a/b + x)*(Log[a/b + x] + Log[a/b + x]^2))/((a + b*x)^2*Log[a/b + x])) - ((b*(c/d + x)*Log[c/d + x])/((-a + (b*c)/d)^2*(1 - (b*(c/d + x))/(-a + (b*c)/d))) + Log[1 - (b*(c/d + x))/(-a + (b*c)/d)]/(-a + (b*c)/d))/b - (-Log[a/b + x] + Log[c/d + x] + Log[a/(c + d*x) + (b*x)/(c + d*x)])/(b*(a + b*x))))/g^2 + (2*B*d^3*i^3*n*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))*((-2*a*(a/b + x)*(-1 + Log[a/b + x]))/b^3 + (3*a^2*Log[a/b + x]^2)/(2*b^4) + (a^3*(1 + Log[a/b + x]))/(b^4*(a + b*x)) + (2*a*(c/d + x)*(-1 + Log[c/d + x]))/b^3 + ((a*x)/(2*b) - x^2/4 + (x^2*Log[a/b + x])/2 - (a^2*Log[a + b*x])/(2*b^2))/b^2 - ((c*x)/(2*d) - x^2/4 + (x^2*Log[c/d + x])/2 - (c^2*Log[c + d*x])/(2*d^2))/b^2 + (a^3*(-(Log[c/d + x]/(b*(a + b*x))) + (d*(Log[a + b*x]/(b*c - a*d) - Log[c + d*x]/(b*c - a*d)))/b))/b^3 + ((-4*a*b*x + b^2*x^2 + (2*a^3)/(a + b*x) + 6*a^2*Log[a + b*x])*(-Log[a/b + x] + Log[c/d + x] + Log[a/(c + d*x) + (b*x)/(c + d*x)]))/(2*b^4) - (3*a^2*((Log[c/d + x]*Log[(a + b*x)/(a - (b*c)/d)])/b + PolyLog[2, (b*d*(c/d + x))/(b*c - a*d)]/b))/b^3))/g^2 + (6*B*c*d^2*i^3*n*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))*(((a/b + x)*(-1 + Log[a/b + x]))/b^2 - (a*Log[a/b + x]^2)/b^3 - (a^2*(1 + Log[a/b + x]))/(b^3*(a + b*x)) - ((c/d + x)*(-1 + Log[c/d + x]))/b^2 - (a^2*(-(Log[c/d + x]/(b*(a + b*x))) + (d*(Log[a + b*x]/(b*c - a*d) - Log[c + d*x]/(b*c - a*d)))/b))/b^2 + ((b*x - a^2/(a + b*x) - 2*a*Log[a + b*x])*(-Log[a/b + x] + Log[c/d + x] + Log[a/(c + d*x) + (b*x)/(c + d*x)]))/b^3 + (2*a*((Log[c/d + x]*Log[(a + b*x)/(a - (b*c)/d)])/b + PolyLog[2, (b*d*(c/d + x))/(b*c - a*d)]/b))/b^2))/g^2 + (6*B*c^2*d*i^3*n*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))*(Log[a/b + x]^2/(2*b^2) + (a*(1 + Log[a/b + x]))/(b^2*(a + b*x)) + (a*(-(Log[c/d + x]/(b*(a + b*x))) + (d*(Log[a + b*x]/(b*c - a*d) - Log[c + d*x]/(b*c - a*d)))/b))/b + ((a/(a + b*x) + Log[a + b*x])*(-Log[a/b + x] + Log[c/d + x] + Log[a/(c + d*x) + (b*x)/(c + d*x)]))/b^2 - ((Log[c/d + x]*Log[(a + b*x)/(a - (b*c)/d)])/b + PolyLog[2, (b*d*(c/d + x))/(b*c - a*d)]/b)/b))/g^2 + (B^2*c^3*i^3*n^2*(-2*b*c + 2*a*d - 2*d*(a + b*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(a + b*x)/(c + d*x)] - 2*d*(a + b*x)*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - (b*c - a*d)*Log[(a + b*x)/(c + d*x)]^2 + 2*d*(a + b*x)*Log[c + d*x] - 2*d*(a + b*x)*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 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)]) + d*(a + b*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*(b*c - a*d)*g^2*(a + b*x)) + (B^2*d^3*i^3*n^2*((-2*b^2*c^2*(b*c - a*d)*Log[(b*c - a*d)/(c + d*x)])/d^2 + 2*a^2*(-(b*c) + a*d)*Log[(b*c - a*d)/(c + d*x)] - (4*a*b*c*(-(b*c) + a*d)*Log[(b*c - a*d)/(c + d*x)])/d + (b^3*c^3*Log[(a + b*x)/(c + d*x)]^2)/d^2 - (a*b^2*c^2*Log[(a + b*x)/(c + d*x)]^2)/d - ((b*c - a*d)^2*(b*c + 5*a*d)*Log[(a + b*x)/(c + d*x)]^2)/d^2 + (b*c - a*d)*(a + b*x)^2*Log[(a + b*x)/(c + d*x)]^2 + 2*a^2*b*c*Log[(a + b*x)/(c + d*x)]^3 - 2*a^3*d*Log[(a + b*x)/(c + d*x)]^3 + (2*(-(b*c) + a*d)*(a + b*x)*Log[(a + b*x)/(c + d*x)]*(b*c - a*d + 3*a*d*Log[(a + b*x)/(c + d*x)]))/d + (2*a^3*b*(c + d*x)*(2 + 2*Log[(a + b*x)/(c + d*x)] + Log[(a + b*x)/(c + d*x)]^2))/(a + b*x) - 9*a^2*b*c*(Log[(a + b*x)/(c + d*x)]*(Log[(a + b*x)/(c + d*x)] - 2*Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))]) + (4*a*b^2*c^2*(Log[(a + b*x)/(c + d*x)]*(Log[(a + b*x)/(c + d*x)] - 2*Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))]))/d + 5*a^3*d*(Log[(a + b*x)/(c + d*x)]*(Log[(a + b*x)/(c + d*x)] - 2*Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))]) - (b^2*c^2*(b*c - a*d)*(Log[(a + b*x)/(c + d*x)]*(2*Log[(-(b*c) + a*d)/(d*(a + b*x))] + Log[(a + b*x)/(c + d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))]))/d^2 + 2*a^2*(-(b*c) + a*d)*(Log[(a + b*x)/(c + d*x)]^2*(3*Log[(-(b*c) + a*d)/(d*(a + b*x))] + Log[(a + b*x)/(c + d*x)]) - 6*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 6*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))])))/(2*b^4*(b*c - a*d)*g^2) + (B^2*c^2*d*i^3*n^2*(6*b*c - 6*a*d - (6*b^2*c*x)/(a + b*x) + (6*a*b*d*x)/(a + b*x) + 6*a*d*Log[a/b + x] + 3*b*c*Log[a/b + x]^2 - 3*a*d*Log[a/b + x]^2 - 6*b*c*Log[c/d + x] + 6*b*c*Log[a + b*x] - 6*a*d*Log[a + b*x] - 6*b*c*Log[a/b + x]*Log[a + b*x] + 6*a*d*Log[a/b + x]*Log[a + b*x] + 6*b*c*Log[c/d + x]*Log[a + b*x] - 6*a*d*Log[c/d + x]*Log[a + b*x] - 6*b*c*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 6*a*d*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] - (6*b*(b*c - a*d)*x*Log[(a + b*x)/(c + d*x)])/(a + b*x) + 6*b*c*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 6*a*d*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] + 3*a*d*Log[(a + b*x)/(c + d*x)]^2 + 3*b*d*x*Log[(a + b*x)/(c + d*x)]^2 - (3*b^2*x*(c + d*x)*Log[(a + b*x)/(c + d*x)]^2)/(a + b*x) - 3*b*c*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(a + b*x)/(c + d*x)]^2 - a*d*Log[(a + b*x)/(c + d*x)]^3 + 6*b*c*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 6*a*d*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 3*a*d*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*(b*c - a*d + a*d*Log[(a + b*x)/(c + d*x)])*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 6*(b*c - a*d)*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 6*b*c*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 6*a*d*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] + 6*b*c*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))]))/(b^2*(b*c - a*d)*g^2) - (B^2*c*d*i^3*n^2*(6*a^2*b*c*d + 6*a^2*b*d^2*x + 6*a^2*b*c*d*Log[(a + b*x)/(c + d*x)] + 6*a^2*b*d^2*x*Log[(a + b*x)/(c + d*x)] + 12*a^2*b*c*d*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(a + b*x)/(c + d*x)] + 12*a*b^2*c*d*x*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(a + b*x)/(c + d*x)] + 6*a^2*b*c*d*Log[(a + b*x)/(c + d*x)]^2 + 3*a^3*d^2*Log[(a + b*x)/(c + d*x)]^2 + 9*a^2*b*d^2*x*Log[(a + b*x)/(c + d*x)]^2 - 3*b^3*c*d*x^2*Log[(a + b*x)/(c + d*x)]^2 + 3*a*b^2*d^2*x^2*Log[(a + b*x)/(c + d*x)]^2 - 6*a^2*b*c*d*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(a + b*x)/(c + d*x)]^2 - 6*a*b^2*c*d*x*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(a + b*x)/(c + d*x)]^2 - 2*a^3*d^2*Log[(a + b*x)/(c + d*x)]^3 - 2*a^2*b*d^2*x*Log[(a + b*x)/(c + d*x)]^3 - 6*a*b^2*c^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 6*a^3*d^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 6*b^3*c^2*x*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 6*a^2*b*d^2*x*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*a^3*d^2*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*a^2*b*d^2*x*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*(a + b*x)*(-(b^2*c^2) - a^2*d^2 + 2*a^2*d^2*Log[(a + b*x)/(c + d*x)])*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] + 12*a*b*c*d*(a + b*x)*(-1 + Log[(a + b*x)/(c + d*x)])*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 12*a^3*d^2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] - 12*a^2*b*d^2*x*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] + 12*a^2*b*c*d*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))] + 12*a*b^2*c*d*x*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))]))/(b^3*(b*c - a*d)*g^2*(a + b*x))","B",1
184,1,6221,644,25.2373172,"\int \frac{(c i+d i x)^3 \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[((c*i + d*i*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(a*g + b*g*x)^3,x]","\text{Result too large to show}","\frac{d^3 i^3 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{b^4 g^3}+\frac{6 B d^2 i^3 n (b c-a d) \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^4 g^3}+\frac{2 B d^2 i^3 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^4 g^3}-\frac{3 d^2 i^3 (b c-a d) \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 g^3}-\frac{2 d i^3 (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^3 g^3 (a+b x)}-\frac{4 B d i^3 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)}{b^3 g^3 (a+b x)}-\frac{i^3 (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)^2}{2 b^2 g^3 (a+b x)^2}-\frac{B i^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)}{2 b^2 g^3 (a+b x)^2}+\frac{2 B^2 d^2 i^3 n^2 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b^4 g^3}+\frac{6 B^2 d^2 i^3 n^2 (b c-a d) \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g^3}-\frac{4 B^2 d i^3 n^2 (c+d x) (b c-a d)}{b^3 g^3 (a+b x)}-\frac{B^2 i^3 n^2 (c+d x)^2 (b c-a d)}{4 b^2 g^3 (a+b x)^2}",1,"Result too large to show","B",1
185,1,8775,561,8.1656402,"\int \frac{(c i+d i x)^3 \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[((c*i + d*i*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(a*g + b*g*x)^4,x]","\text{Result too large to show}","\frac{2 B d^3 i^3 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^4 g^4}-\frac{d^3 i^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)^2}{b^4 g^4}-\frac{d^2 i^3 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{b^3 g^4 (a+b x)}-\frac{2 B d^2 i^3 n (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{b^3 g^4 (a+b x)}-\frac{d i^3 (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 b^2 g^4 (a+b x)^2}-\frac{B d i^3 n (c+d x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 b^2 g^4 (a+b x)^2}-\frac{i^3 (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{3 b g^4 (a+b x)^3}-\frac{2 B i^3 n (c+d x)^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{9 b g^4 (a+b x)^3}+\frac{2 B^2 d^3 i^3 n^2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b^4 g^4}-\frac{2 B^2 d^2 i^3 n^2 (c+d x)}{b^3 g^4 (a+b x)}-\frac{B^2 d i^3 n^2 (c+d x)^2}{4 b^2 g^4 (a+b x)^2}-\frac{2 B^2 i^3 n^2 (c+d x)^3}{27 b g^4 (a+b x)^3}",1,"Result too large to show","B",1
186,1,3265,768,4.3349414,"\int \frac{(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}{c i+d i x} \, dx","Integrate[((a*g + b*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(c*i + d*i*x),x]","\text{Result too large to show}","\frac{b^3 g^3 (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^4 i}-\frac{3 b^2 g^3 (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)^2}{2 d^4 i}-\frac{b^2 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)}{3 d^4 i}+\frac{2 B g^3 n (b c-a d)^3 \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^4 i}+\frac{g^3 (b c-a d)^3 \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^4 i}+\frac{6 B g^3 n (b c-a d)^3 \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^4 i}-\frac{7 B g^3 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 d^4 i}+\frac{3 g^3 (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)^2}{d^3 i}+\frac{7 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)}{3 d^3 i}+\frac{6 B^2 g^3 n^2 (b c-a d)^3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i}+\frac{7 B^2 g^3 n^2 (b c-a d)^3 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{3 d^4 i}-\frac{2 B^2 g^3 n^2 (b c-a d)^3 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i}+\frac{B^2 g^3 n^2 (b c-a d)^3 \log \left(\frac{a+b x}{c+d x}\right)}{3 d^4 i}-\frac{2 B^2 g^3 n^2 (b c-a d)^3 \log (c+d x)}{d^4 i}+\frac{b B^2 g^3 n^2 x (b c-a d)^2}{3 d^3 i}",1,"(g^3*(6*b*d*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2)*x*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2 - 3*b^2*d^2*(b*c - 3*a*d)*x^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2 + 2*b^3*d^3*x^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2 - 6*(b*c - a*d)^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] + 18*a*B*d*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])*(-2*b^2*c^2 + 2*a*b*c*d - b^2*c*d*x + a*b*d^2*x + 2*b^2*c^2*Log[c/d + x] - b^2*c^2*Log[c/d + x]^2 - a^2*d^2*Log[a + b*x] - 2*b^2*c*d*x*Log[(a + b*x)/(c + d*x)] + b^2*d^2*x^2*Log[(a + b*x)/(c + d*x)] + b^2*c^2*Log[c + d*x] + 2*b^2*c^2*Log[c/d + x]*Log[c + d*x] + 2*b^2*c^2*Log[(a + b*x)/(c + d*x)]*Log[c + d*x] - 2*b*c*Log[a/b + x]*(a*d + b*c*Log[c + d*x] - b*c*Log[(b*(c + d*x))/(b*c - a*d)]) + 2*b^2*c^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - 2*B*n*(-A - B*Log[e*((a + b*x)/(c + d*x))^n] + B*n*Log[(a + b*x)/(c + d*x)])*(6*b^3*c^3 - 6*a*b^2*c^2*d + 5*b^3*c^2*d*x - 3*a*b^2*c*d^2*x - 2*a^2*b*d^3*x - b^3*c*d^2*x^2 + a*b^2*d^3*x^2 - 6*b^3*c^3*Log[c/d + x] + 3*b^3*c^3*Log[c/d + x]^2 + 3*a^2*b*c*d^2*Log[a + b*x] + 2*a^3*d^3*Log[a + b*x] + 6*b^3*c^2*d*x*Log[(a + b*x)/(c + d*x)] - 3*b^3*c*d^2*x^2*Log[(a + b*x)/(c + d*x)] + 2*b^3*d^3*x^3*Log[(a + b*x)/(c + d*x)] - 5*b^3*c^3*Log[c + d*x] - 6*b^3*c^3*Log[c/d + x]*Log[c + d*x] - 6*b^3*c^3*Log[(a + b*x)/(c + d*x)]*Log[c + d*x] + 6*b^2*c^2*Log[a/b + x]*(a*d + b*c*Log[c + d*x] - b*c*Log[(b*(c + d*x))/(b*c - a*d)]) - 6*b^3*c^3*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - 6*a^3*B*d^3*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)])) - 18*a^2*B*d^2*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])*(-2*d*(a + b*x)*(-1 + Log[a/b + x]) + 2*b*(c + d*x)*(-1 + Log[c/d + x]) - b*c*Log[c/d + x]^2 + 2*b*(Log[a/b + x] - Log[c/d + x] - Log[(a + b*x)/(c + d*x)])*(d*x - c*Log[c + d*x]) + 2*b*c*(Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])) + 18*a^2*B^2*d^2*n^2*(d*(a + b*x)*Log[(a + b*x)/(c + d*x)]^2 + b*c*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - (b*c - a*d)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*Log[(a + b*x)/(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*b*c*(Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])) + 9*a*B^2*d*n^2*(2*d*(-(b*c) + a*d)*(a + b*x)*Log[(a + b*x)/(c + d*x)] - 2*a^2*d^2*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] + b^2*d^2*x^2*Log[(a + b*x)/(c + d*x)]^2 - 2*b*c*d*(a + b*x)*Log[(a + b*x)/(c + d*x)]^2 + 2*(b*c - a*d)^2*Log[c + d*x] - 2*b^2*c^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 2*b^2*c^2*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + a^2*d^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*c^2*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 2*b*c*(b*c - a*d)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*Log[(a + b*x)/(c + d*x)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) - 4*b^2*c^2*(Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])) - 6*a^3*B^2*d^3*n^2*(Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))]) + B^2*n^2*(2*b^3*c^2*d*x - 4*a*b^2*c*d^2*x + 2*a^2*b*d^3*x + 2*a^2*b*c*d^2*Log[a + b*x] - 2*a^3*d^3*Log[a + b*x] - 3*a^2*b*c*d^2*Log[a + b*x]^2 - 2*a^3*d^3*Log[a + b*x]^2 + 10*a*b^2*c^2*d*Log[(a + b*x)/(c + d*x)] - 6*a^2*b*c*d^2*Log[(a + b*x)/(c + d*x)] - 4*a^3*d^3*Log[(a + b*x)/(c + d*x)] + 10*b^3*c^2*d*x*Log[(a + b*x)/(c + d*x)] - 6*a*b^2*c*d^2*x*Log[(a + b*x)/(c + d*x)] - 4*a^2*b*d^3*x*Log[(a + b*x)/(c + d*x)] - 2*b^3*c*d^2*x^2*Log[(a + b*x)/(c + d*x)] + 2*a*b^2*d^3*x^2*Log[(a + b*x)/(c + d*x)] + 6*a^2*b*c*d^2*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] + 4*a^3*d^3*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] + 6*a*b^2*c^2*d*Log[(a + b*x)/(c + d*x)]^2 + 6*b^3*c^2*d*x*Log[(a + b*x)/(c + d*x)]^2 - 3*b^3*c*d^2*x^2*Log[(a + b*x)/(c + d*x)]^2 + 2*b^3*d^3*x^3*Log[(a + b*x)/(c + d*x)]^2 - 12*b^3*c^3*Log[c + d*x] + 18*a*b^2*c^2*d*Log[c + d*x] - 2*a^2*b*c*d^2*Log[c + d*x] - 4*a^3*d^3*Log[c + d*x] + 6*a^2*b*c*d^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] + 4*a^3*d^3*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)] - 22*b^3*c^3*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 12*a*b^2*c^2*d*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 22*b^3*c^3*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 12*a*b^2*c^2*d*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 6*b^3*c^3*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - 11*b^3*c^3*Log[(b*c - a*d)/(b*c + b*d*x)]^2 + 6*a*b^2*c^2*d*Log[(b*c - a*d)/(b*c + b*d*x)]^2 + 2*a^2*d^2*(3*b*c + 2*a*d)*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 12*b^3*c^3*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] + 22*b^3*c^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 12*a*b^2*c^2*d*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 12*b^3*c^3*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])))/(6*d^4*i)","B",1
187,1,1741,573,1.653309,"\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}{c i+d i x} \, dx","Integrate[((a*g + b*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(c*i + d*i*x),x]","\frac{g^2 \left(b^2 x^2 \left(A+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)\right)^2 d^2-2 a^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{a+b x}{c+d x}\right)\right) \left(\log ^2\left(\frac{c}{d}+x\right)+2 \left(\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)-\log \left(\frac{a+b x}{c+d x}\right)\right) \log (c+d x)-2 \left(\log \left(\frac{a}{b}+x\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)+\text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)\right) d^2-2 a^2 B^2 n^2 \left(\log \left(\frac{b c-a d}{b c+b d x}\right) \log ^2\left(\frac{a+b x}{c+d x}\right)+2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right) \log \left(\frac{a+b x}{c+d x}\right)-2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right) d^2-2 b (b c-2 a d) x \left(A+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)\right)^2 d-4 a B n \left(A+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)\right) \left(-b c \log ^2\left(\frac{c}{d}+x\right)-2 d (a+b x) \left(\log \left(\frac{a}{b}+x\right)-1\right)+2 b (c+d x) \left(\log \left(\frac{c}{d}+x\right)-1\right)+2 b \left(\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)-\log \left(\frac{a+b x}{c+d x}\right)\right) (d x-c \log (c+d x))+2 b c \left(\log \left(\frac{a}{b}+x\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)+\text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)\right) d+4 a B^2 n^2 \left(d (a+b x) \log ^2\left(\frac{a+b x}{c+d x}\right)+b c \log \left(\frac{b c-a d}{b c+b d x}\right) \log ^2\left(\frac{a+b x}{c+d x}\right)-(b c-a d) \left(\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{a+b x}{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)\right)+2 b c \left(\log \left(\frac{a+b x}{c+d x}\right) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)-\text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right)\right) d+2 (b c-a d)^2 \left(A+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)\right)^2 \log (c+d x)+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{a+b x}{c+d x}\right)\right) \left(-2 c^2 b^2-c^2 \log ^2\left(\frac{c}{d}+x\right) b^2-c d x b^2+2 c^2 \log \left(\frac{c}{d}+x\right) b^2+d^2 x^2 \log \left(\frac{a+b x}{c+d x}\right) b^2-2 c d x \log \left(\frac{a+b x}{c+d x}\right) b^2+c^2 \log (c+d x) b^2+2 c^2 \log \left(\frac{c}{d}+x\right) \log (c+d x) b^2+2 c^2 \log \left(\frac{a+b x}{c+d x}\right) \log (c+d x) b^2+2 c^2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right) b^2+2 a c d b+a d^2 x b-2 c \log \left(\frac{a}{b}+x\right) \left(a d+b c \log (c+d x)-b c \log \left(\frac{b (c+d x)}{b c-a d}\right)\right) b-a^2 d^2 \log (a+b x)\right)+B^2 n^2 \left(-2 b^2 \log ^2\left(\frac{a+b x}{c+d x}\right) \log \left(\frac{b c-a d}{b c+b d x}\right) c^2-2 b^2 \log \left(\frac{a+b x}{c+d x}\right) \log \left(\frac{b c-a d}{b c+b d x}\right) c^2+b^2 \left(\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)+\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)\right) c^2-4 b^2 \left(\log \left(\frac{a+b x}{c+d x}\right) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)-\text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right) c^2-2 b d (a+b x) \log ^2\left(\frac{a+b x}{c+d x}\right) c+2 b (b c-a d) \left(\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{a+b x}{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)\right) c+b^2 d^2 x^2 \log ^2\left(\frac{a+b x}{c+d x}\right)+2 d (a d-b c) (a+b x) \log \left(\frac{a+b x}{c+d x}\right)-2 a^2 d^2 \log (a+b x) \log \left(\frac{a+b x}{c+d x}\right)+2 (b c-a d)^2 \log (c+d x)+a^2 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)\right)\right)}{2 d^3 i}","\frac{b^2 g^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 d^3 i}-\frac{2 B g^2 n (b c-a d)^2 \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^3 i}-\frac{g^2 (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\right)^2}{d^3 i}-\frac{4 B g^2 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\right)}{d^3 i}+\frac{B g^2 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)}{d^3 i}-\frac{2 g^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)^2}{d^2 i}-\frac{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)}{d^2 i}-\frac{4 B^2 g^2 n^2 (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^3 i}-\frac{B^2 g^2 n^2 (b c-a d)^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{d^3 i}+\frac{2 B^2 g^2 n^2 (b c-a d)^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^3 i}+\frac{B^2 g^2 n^2 (b c-a d)^2 \log (c+d x)}{d^3 i}",1,"(g^2*(-2*b*d*(b*c - 2*a*d)*x*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2 + b^2*d^2*x^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2 + 2*(b*c - a*d)^2*(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] + 2*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])*(-2*b^2*c^2 + 2*a*b*c*d - b^2*c*d*x + a*b*d^2*x + 2*b^2*c^2*Log[c/d + x] - b^2*c^2*Log[c/d + x]^2 - a^2*d^2*Log[a + b*x] - 2*b^2*c*d*x*Log[(a + b*x)/(c + d*x)] + b^2*d^2*x^2*Log[(a + b*x)/(c + d*x)] + b^2*c^2*Log[c + d*x] + 2*b^2*c^2*Log[c/d + x]*Log[c + d*x] + 2*b^2*c^2*Log[(a + b*x)/(c + d*x)]*Log[c + d*x] - 2*b*c*Log[a/b + x]*(a*d + b*c*Log[c + d*x] - b*c*Log[(b*(c + d*x))/(b*c - a*d)]) + 2*b^2*c^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - 2*a^2*B*d^2*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)])) - 4*a*B*d*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])*(-2*d*(a + b*x)*(-1 + Log[a/b + x]) + 2*b*(c + d*x)*(-1 + Log[c/d + x]) - b*c*Log[c/d + x]^2 + 2*b*(Log[a/b + x] - Log[c/d + x] - Log[(a + b*x)/(c + d*x)])*(d*x - c*Log[c + d*x]) + 2*b*c*(Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])) + 4*a*B^2*d*n^2*(d*(a + b*x)*Log[(a + b*x)/(c + d*x)]^2 + b*c*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - (b*c - a*d)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*Log[(a + b*x)/(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*b*c*(Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])) + B^2*n^2*(2*d*(-(b*c) + a*d)*(a + b*x)*Log[(a + b*x)/(c + d*x)] - 2*a^2*d^2*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] + b^2*d^2*x^2*Log[(a + b*x)/(c + d*x)]^2 - 2*b*c*d*(a + b*x)*Log[(a + b*x)/(c + d*x)]^2 + 2*(b*c - a*d)^2*Log[c + d*x] - 2*b^2*c^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - 2*b^2*c^2*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + a^2*d^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*c^2*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 2*b*c*(b*c - a*d)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*Log[(a + b*x)/(c + d*x)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) - 4*b^2*c^2*(Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])) - 2*a^2*B^2*d^2*n^2*(Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])))/(2*d^3*i)","B",1
188,1,802,303,0.697936,"\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}{c i+d i x} \, dx","Integrate[((a*g + b*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(c*i + d*i*x),x]","-\frac{g \left(-B^2 \left(d (a+b x) \log ^2\left(\frac{a+b x}{c+d x}\right)+b c \log \left(\frac{b c-a d}{b c+b d x}\right) \log ^2\left(\frac{a+b x}{c+d x}\right)-(b c-a d) \left(\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{a+b x}{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)\right)+2 b c \left(\log \left(\frac{a+b x}{c+d x}\right) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)-\text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right)\right) n^2+a B^2 d \left(\log \left(\frac{b c-a d}{b c+b d x}\right) \log ^2\left(\frac{a+b x}{c+d x}\right)+2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right) \log \left(\frac{a+b x}{c+d x}\right)-2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right) n^2+a B d \left(A+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)\right) \left(\log ^2\left(\frac{c}{d}+x\right)+2 \left(\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)-\log \left(\frac{a+b x}{c+d x}\right)\right) \log (c+d x)-2 \left(\log \left(\frac{a}{b}+x\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)+\text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)\right) n+B \left(A+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)\right) \left(-b c \log ^2\left(\frac{c}{d}+x\right)-2 d (a+b x) \left(\log \left(\frac{a}{b}+x\right)-1\right)+2 b (c+d x) \left(\log \left(\frac{c}{d}+x\right)-1\right)+2 b \left(\log \left(\frac{a}{b}+x\right)-\log \left(\frac{c}{d}+x\right)-\log \left(\frac{a+b x}{c+d x}\right)\right) (d x-c \log (c+d x))+2 b c \left(\log \left(\frac{a}{b}+x\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)+\text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)\right)\right) n-b d x \left(A+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)\right)^2+(b c-a d) \left(A+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)\right)^2 \log (c+d x)\right)}{d^2 i}","\frac{2 B g n (b c-a d) \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^2 i}+\frac{2 B g 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)}{d^2 i}+\frac{g (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)^2}{d^2 i}+\frac{g (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{d i}+\frac{2 B^2 g n^2 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^2 i}-\frac{2 B^2 g n^2 (b c-a d) \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^2 i}",1,"-((g*(-(b*d*x*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2) + (b*c - a*d)*(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] + a*B*d*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*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])*(-2*d*(a + b*x)*(-1 + Log[a/b + x]) + 2*b*(c + d*x)*(-1 + Log[c/d + x]) - b*c*Log[c/d + x]^2 + 2*b*(Log[a/b + x] - Log[c/d + x] - Log[(a + b*x)/(c + d*x)])*(d*x - c*Log[c + d*x]) + 2*b*c*(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*(d*(a + b*x)*Log[(a + b*x)/(c + d*x)]^2 + b*c*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - (b*c - a*d)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*Log[(a + b*x)/(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*b*c*(Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])) + a*B^2*d*n^2*(Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])))/(d^2*i))","B",1
189,1,306,137,0.2793121,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{c i+d i x} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(c*i + d*i*x),x]","\frac{-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)+\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(-2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)+2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right) \log \left(\frac{a+b x}{c+d x}\right)+\log \left(\frac{b c-a d}{b c+b d x}\right) \log ^2\left(\frac{a+b x}{c+d x}\right)\right)}{d i}","-\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 i}-\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 i}+\frac{2 B^2 n^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d i}",1,"((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] - 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[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))]))/(d*i)","B",1
190,1,90,50,0.3911183,"\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) (c i+d i x)} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/((a*g + b*g*x)*(c*i + d*i*x)),x]","\frac{3 A^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+3 A B \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B^2 \log ^3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{3 b c g i n-3 a d g i n}","\frac{\left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^3}{3 B g i n (b c-a d)}",1,"(3*A^2*Log[e*((a + b*x)/(c + d*x))^n] + 3*A*B*Log[e*((a + b*x)/(c + d*x))^n]^2 + B^2*Log[e*((a + b*x)/(c + d*x))^n]^3)/(3*b*c*g*i*n - 3*a*d*g*i*n)","A",1
191,1,793,199,0.8285468,"\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 (c i+d i x)} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/((a*g + b*g*x)^2*(c*i + d*i*x)),x]","\frac{-2 A B \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)-B^2 \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)^2-2 B^2 n \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)-A^2-2 A B n-2 B^2 n^2}{g^2 i (a+b x) (b c-a d)}-\frac{d \log (a+b x) \left(2 A B \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)+B^2 \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)^2+2 B^2 n \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)+A^2+2 A B n+2 B^2 n^2\right)}{g^2 i (b c-a d)^2}+\frac{d \log (c+d x) \left(2 A B \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)+B^2 \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)^2+2 B^2 n \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)+A^2+2 A B n+2 B^2 n^2\right)}{g^2 i (b c-a d)^2}+\frac{\log ^2\left(\frac{a+b x}{c+d x}\right) \left(-a A B d n-a B^2 d n \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)-b B^2 d n x \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)-A b B d n x-b B^2 c n^2-b B^2 d n^2 x\right)}{g^2 i (a+b x) (a d-b c)^2}+\frac{2 B n \log \left(\frac{a+b x}{c+d x}\right) \left(B \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)+A+B n\right)}{g^2 i (a+b x) (a d-b c)}-\frac{B^2 d n^2 \log ^3\left(\frac{a+b x}{c+d x}\right)}{3 g^2 i (b c-a d)^2}","-\frac{d \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^3}{3 B g^2 i n (b c-a d)^2}-\frac{b (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g^2 i (a+b x) (b c-a d)^2}-\frac{2 b 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 i (a+b x) (b c-a d)^2}-\frac{2 b B^2 n^2 (c+d x)}{g^2 i (a+b x) (b c-a d)^2}",1,"-1/3*(B^2*d*n^2*Log[(a + b*x)/(c + d*x)]^3)/((b*c - a*d)^2*g^2*i) + (2*B*n*Log[(a + b*x)/(c + d*x)]*(A + B*n + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])))/((-(b*c) + a*d)*g^2*i*(a + b*x)) + (Log[(a + b*x)/(c + d*x)]^2*(-(a*A*B*d*n) - b*B^2*c*n^2 - A*b*B*d*n*x - b*B^2*d*n^2*x - a*B^2*d*n*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) - b*B^2*d*n*x*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])))/((-(b*c) + a*d)^2*g^2*i*(a + b*x)) + (-A^2 - 2*A*B*n - 2*B^2*n^2 - 2*A*B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) - 2*B^2*n*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) - B^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2)/((b*c - a*d)*g^2*i*(a + b*x)) - (d*Log[a + b*x]*(A^2 + 2*A*B*n + 2*B^2*n^2 + 2*A*B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + 2*B^2*n*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + B^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2))/((b*c - a*d)^2*g^2*i) + (d*(A^2 + 2*A*B*n + 2*B^2*n^2 + 2*A*B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + 2*B^2*n*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + B^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2)*Log[c + d*x])/((b*c - a*d)^2*g^2*i)","B",1
192,1,975,369,1.3992892,"\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 (c i+d i x)} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/((a*g + b*g*x)^3*(c*i + d*i*x)),x]","\frac{4 B^2 d^2 n^2 (a+b x)^2 \log ^3\left(\frac{a+b x}{c+d x}\right)+6 B n \left(2 A d^2 x^2 b^2+3 B d^2 n x^2 b^2-B c^2 n b^2+2 B c d n x b^2+4 a B c d n b+4 a A d^2 x b+4 a B d^2 n x b+2 a^2 A d^2+2 B d^2 (a+b x)^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-2 B d^2 n (a+b x)^2 \log \left(\frac{a+b x}{c+d x}\right)\right) \log ^2\left(\frac{a+b x}{c+d x}\right)-6 B (b c-a d) n \left(2 A b c+b B n c-6 a A d-7 a B d n-4 A b d x-6 b B d n x+2 B (b (c-2 d x)-3 a d) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B n (-b c+3 a d+2 b d x) \log \left(\frac{a+b x}{c+d x}\right)\right) \log \left(\frac{a+b x}{c+d x}\right)-3 (b c-a d)^2 \left(2 A^2+2 B n A+B^2 n^2+2 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-2 B n (2 A+B n) \log \left(\frac{a+b x}{c+d x}\right)+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(2 A+B n-2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)+6 d (b c-a d) (a+b x) \left(2 A^2+6 B n A+7 B^2 n^2+2 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-2 B n (2 A+3 B n) \log \left(\frac{a+b x}{c+d x}\right)+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(2 A+3 B n-2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)+6 d^2 (a+b x)^2 \log (a+b x) \left(2 A^2+6 B n A+7 B^2 n^2+2 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-2 B n (2 A+3 B n) \log \left(\frac{a+b x}{c+d x}\right)+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(2 A+3 B n-2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)-6 d^2 (a+b x)^2 \left(2 A^2+6 B n A+7 B^2 n^2+2 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-2 B n (2 A+3 B n) \log \left(\frac{a+b x}{c+d x}\right)+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(2 A+3 B n-2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) \log (c+d x)}{12 (b c-a d)^3 g^3 i (a+b x)^2}","-\frac{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}{2 g^3 i (a+b x)^2 (b c-a d)^3}-\frac{b^2 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 i (a+b x)^2 (b c-a d)^3}+\frac{d^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^3}{3 B g^3 i n (b c-a d)^3}+\frac{2 b 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 i (a+b x) (b c-a d)^3}+\frac{4 b 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 i (a+b x) (b c-a d)^3}-\frac{b^2 B^2 n^2 (c+d x)^2}{4 g^3 i (a+b x)^2 (b c-a d)^3}+\frac{4 b B^2 d n^2 (c+d x)}{g^3 i (a+b x) (b c-a d)^3}",1,"(4*B^2*d^2*n^2*(a + b*x)^2*Log[(a + b*x)/(c + d*x)]^3 + 6*B*n*Log[(a + b*x)/(c + d*x)]^2*(2*a^2*A*d^2 - b^2*B*c^2*n + 4*a*b*B*c*d*n + 4*a*A*b*d^2*x + 2*b^2*B*c*d*n*x + 4*a*b*B*d^2*n*x + 2*A*b^2*d^2*x^2 + 3*b^2*B*d^2*n*x^2 + 2*B*d^2*(a + b*x)^2*Log[e*((a + b*x)/(c + d*x))^n] - 2*B*d^2*n*(a + b*x)^2*Log[(a + b*x)/(c + d*x)]) - 6*B*(b*c - a*d)*n*Log[(a + b*x)/(c + d*x)]*(2*A*b*c - 6*a*A*d + b*B*c*n - 7*a*B*d*n - 4*A*b*d*x - 6*b*B*d*n*x + 2*B*(-3*a*d + b*(c - 2*d*x))*Log[e*((a + b*x)/(c + d*x))^n] + 2*B*n*(-(b*c) + 3*a*d + 2*b*d*x)*Log[(a + b*x)/(c + d*x)]) - 3*(b*c - a*d)^2*(2*A^2 + 2*A*B*n + B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 2*B*n*(2*A + B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(2*A + B*n - 2*B*n*Log[(a + b*x)/(c + d*x)])) + 6*d*(b*c - a*d)*(a + b*x)*(2*A^2 + 6*A*B*n + 7*B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 2*B*n*(2*A + 3*B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(2*A + 3*B*n - 2*B*n*Log[(a + b*x)/(c + d*x)])) + 6*d^2*(a + b*x)^2*Log[a + b*x]*(2*A^2 + 6*A*B*n + 7*B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 2*B*n*(2*A + 3*B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(2*A + 3*B*n - 2*B*n*Log[(a + b*x)/(c + d*x)])) - 6*d^2*(a + b*x)^2*(2*A^2 + 6*A*B*n + 7*B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 2*B*n*(2*A + 3*B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(2*A + 3*B*n - 2*B*n*Log[(a + b*x)/(c + d*x)]))*Log[c + d*x])/(12*(b*c - a*d)^3*g^3*i*(a + b*x)^2)","B",1
193,1,1295,543,1.9177901,"\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 (c i+d i x)} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/((a*g + b*g*x)^4*(c*i + d*i*x)),x]","-\frac{4 \left(9 A^2+6 B n A+2 B^2 n^2+9 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+9 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-6 B n (3 A+B n) \log \left(\frac{a+b x}{c+d x}\right)+6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(3 A+B n-3 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) (b c-a d)^3-3 d (a+b x) \left(18 A^2+30 B n A+19 B^2 n^2+18 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+18 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-6 B n (6 A+5 B n) \log \left(\frac{a+b x}{c+d x}\right)+6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(6 A+5 B n-6 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) (b c-a d)^2+6 d^2 (a+b x)^2 \left(18 A^2+66 B n A+85 B^2 n^2+18 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+18 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-6 B n (6 A+11 B n) \log \left(\frac{a+b x}{c+d x}\right)+6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(6 A+11 B n-6 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) (b c-a d)+6 B n \log \left(\frac{a+b x}{c+d x}\right) \left(4 \left(3 A+B n+3 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-3 B n \log \left(\frac{a+b x}{c+d x}\right)\right) (b c-a d)^2+3 d (a d-b c) (a+b x) \left(6 A+5 B n+6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-6 B n \log \left(\frac{a+b x}{c+d x}\right)\right)+6 d^2 (a+b x)^2 \left(6 A+11 B n+6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-6 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) (b c-a d)+36 B^2 d^3 n^2 (a+b x)^3 \log ^3\left(\frac{a+b x}{c+d x}\right)+18 B n \log ^2\left(\frac{a+b x}{c+d x}\right) \left(6 A d^3 x^3 b^3+11 B d^3 n x^3 b^3+6 B c d^2 n x^2 b^3+2 B c^3 n b^3-3 B c^2 d n x b^3+18 a A d^3 x^2 b^2+27 a B d^3 n x^2 b^2-9 a B c^2 d n b^2+18 a B c d^2 n x b^2+18 a^2 B c d^2 n b+18 a^2 A d^3 x b+18 a^2 B d^3 n x b+6 a^3 A d^3+6 B d^3 (a+b x)^3 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-6 B d^3 n (a+b x)^3 \log \left(\frac{a+b x}{c+d x}\right)\right)+6 d^3 (a+b x)^3 \log (a+b x) \left(18 A^2+66 B n A+85 B^2 n^2+18 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+18 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-6 B n (6 A+11 B n) \log \left(\frac{a+b x}{c+d x}\right)+6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(6 A+11 B n-6 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)-6 d^3 (a+b x)^3 \left(18 A^2+66 B n A+85 B^2 n^2+18 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+18 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-6 B n (6 A+11 B n) \log \left(\frac{a+b x}{c+d x}\right)+6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(6 A+11 B n-6 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) \log (c+d x)}{108 (b c-a d)^4 g^4 i (a+b x)^3}","-\frac{b^3 (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 i (a+b x)^3 (b c-a d)^4}-\frac{2 b^3 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 i (a+b x)^3 (b c-a d)^4}+\frac{3 b^2 d (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^4 i (a+b x)^2 (b c-a d)^4}+\frac{3 b^2 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)}{2 g^4 i (a+b x)^2 (b c-a d)^4}-\frac{d^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^3}{3 B g^4 i n (b c-a d)^4}-\frac{3 b 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 i (a+b x) (b c-a d)^4}-\frac{6 b 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 i (a+b x) (b c-a d)^4}-\frac{2 b^3 B^2 n^2 (c+d x)^3}{27 g^4 i (a+b x)^3 (b c-a d)^4}+\frac{3 b^2 B^2 d n^2 (c+d x)^2}{4 g^4 i (a+b x)^2 (b c-a d)^4}-\frac{6 b B^2 d^2 n^2 (c+d x)}{g^4 i (a+b x) (b c-a d)^4}",1,"-1/108*(36*B^2*d^3*n^2*(a + b*x)^3*Log[(a + b*x)/(c + d*x)]^3 + 18*B*n*Log[(a + b*x)/(c + d*x)]^2*(6*a^3*A*d^3 + 2*b^3*B*c^3*n - 9*a*b^2*B*c^2*d*n + 18*a^2*b*B*c*d^2*n + 18*a^2*A*b*d^3*x - 3*b^3*B*c^2*d*n*x + 18*a*b^2*B*c*d^2*n*x + 18*a^2*b*B*d^3*n*x + 18*a*A*b^2*d^3*x^2 + 6*b^3*B*c*d^2*n*x^2 + 27*a*b^2*B*d^3*n*x^2 + 6*A*b^3*d^3*x^3 + 11*b^3*B*d^3*n*x^3 + 6*B*d^3*(a + b*x)^3*Log[e*((a + b*x)/(c + d*x))^n] - 6*B*d^3*n*(a + b*x)^3*Log[(a + b*x)/(c + d*x)]) - 3*d*(b*c - a*d)^2*(a + b*x)*(18*A^2 + 30*A*B*n + 19*B^2*n^2 + 18*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 6*B*n*(6*A + 5*B*n)*Log[(a + b*x)/(c + d*x)] + 18*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 6*B*Log[e*((a + b*x)/(c + d*x))^n]*(6*A + 5*B*n - 6*B*n*Log[(a + b*x)/(c + d*x)])) + 6*d^2*(b*c - a*d)*(a + b*x)^2*(18*A^2 + 66*A*B*n + 85*B^2*n^2 + 18*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 6*B*n*(6*A + 11*B*n)*Log[(a + b*x)/(c + d*x)] + 18*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 6*B*Log[e*((a + b*x)/(c + d*x))^n]*(6*A + 11*B*n - 6*B*n*Log[(a + b*x)/(c + d*x)])) + 6*d^3*(a + b*x)^3*Log[a + b*x]*(18*A^2 + 66*A*B*n + 85*B^2*n^2 + 18*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 6*B*n*(6*A + 11*B*n)*Log[(a + b*x)/(c + d*x)] + 18*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 6*B*Log[e*((a + b*x)/(c + d*x))^n]*(6*A + 11*B*n - 6*B*n*Log[(a + b*x)/(c + d*x)])) + 4*(b*c - a*d)^3*(9*A^2 + 6*A*B*n + 2*B^2*n^2 + 9*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 6*B*n*(3*A + B*n)*Log[(a + b*x)/(c + d*x)] + 9*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 6*B*Log[e*((a + b*x)/(c + d*x))^n]*(3*A + B*n - 3*B*n*Log[(a + b*x)/(c + d*x)])) + 6*B*(b*c - a*d)*n*Log[(a + b*x)/(c + d*x)]*(3*d*(-(b*c) + a*d)*(a + b*x)*(6*A + 5*B*n + 6*B*Log[e*((a + b*x)/(c + d*x))^n] - 6*B*n*Log[(a + b*x)/(c + d*x)]) + 6*d^2*(a + b*x)^2*(6*A + 11*B*n + 6*B*Log[e*((a + b*x)/(c + d*x))^n] - 6*B*n*Log[(a + b*x)/(c + d*x)]) + 4*(b*c - a*d)^2*(3*A + B*n + 3*B*Log[e*((a + b*x)/(c + d*x))^n] - 3*B*n*Log[(a + b*x)/(c + d*x)])) - 6*d^3*(a + b*x)^3*(18*A^2 + 66*A*B*n + 85*B^2*n^2 + 18*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 6*B*n*(6*A + 11*B*n)*Log[(a + b*x)/(c + d*x)] + 18*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 6*B*Log[e*((a + b*x)/(c + d*x))^n]*(6*A + 11*B*n - 6*B*n*Log[(a + b*x)/(c + d*x)]))*Log[c + d*x])/((b*c - a*d)^4*g^4*i*(a + b*x)^3)","B",1
194,1,4312,770,8.9132617,"\int \frac{(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}{(c i+d i x)^2} \, dx","Integrate[((a*g + b*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(c*i + d*i*x)^2,x]","\text{Result too large to show}","\frac{b^3 g^3 (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^4 i^2}-\frac{6 b B g^3 n (b c-a d)^2 \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^4 i^2}-\frac{3 b g^3 (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\right)^2}{d^4 i^2}-\frac{6 b B g^3 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\right)}{d^4 i^2}+\frac{b B g^3 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)}{d^4 i^2}-\frac{3 b g^3 (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)^2}{d^3 i^2}-\frac{g^3 (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)^2}{d^3 i^2 (c+d x)}-\frac{b B g^3 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)}{d^3 i^2}+\frac{2 A B g^3 n (a+b x) (b c-a d)^2}{d^3 i^2 (c+d x)}-\frac{6 b B^2 g^3 n^2 (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i^2}-\frac{b B^2 g^3 n^2 (b c-a d)^2 \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)}{d^4 i^2}+\frac{6 b B^2 g^3 n^2 (b c-a d)^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i^2}+\frac{b B^2 g^3 n^2 (b c-a d)^2 \log (c+d x)}{d^4 i^2}+\frac{2 B^2 g^3 n (a+b x) (b c-a d)^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{d^3 i^2 (c+d x)}-\frac{2 B^2 g^3 n^2 (a+b x) (b c-a d)^2}{d^3 i^2 (c+d x)}",1,"-((b^2*(2*b*c - 3*a*d)*g^3*x*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))^2)/(d^3*i^2)) + (b^3*g^3*x^2*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))^2)/(2*d^2*i^2) + (A^2*b^3*c^3*g^3 - 3*a*A^2*b^2*c^2*d*g^3 + 3*a^2*A^2*b*c*d^2*g^3 - a^3*A^2*d^3*g^3 + 2*A*b^3*B*c^3*g^3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) - 6*a*A*b^2*B*c^2*d*g^3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + 6*a^2*A*b*B*c*d^2*g^3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) - 2*a^3*A*B*d^3*g^3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + b^3*B^2*c^3*g^3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2 - 3*a*b^2*B^2*c^2*d*g^3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2 + 3*a^2*b*B^2*c*d^2*g^3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2 - a^3*B^2*d^3*g^3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2)/(d^4*i^2*(c + d*x)) + (3*b*(b*c - a*d)^2*g^3*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))^2*Log[c + d*x])/(d^4*i^2) + (2*a^3*B*g^3*n*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))*(((c/d + x)*(Log[c/d + x] + Log[c/d + x]^2))/((c + d*x)^2*Log[c/d + x]) + ((d*(a/b + x)*Log[a/b + x])/((-c + (a*d)/b)^2*(1 - (d*(a/b + x))/(-c + (a*d)/b))) + Log[1 - (d*(a/b + x))/(-c + (a*d)/b)]/(-c + (a*d)/b))/d - (-Log[a/b + x] + Log[c/d + x] + Log[a/(c + d*x) + (b*x)/(c + d*x)])/(d*(c + d*x))))/i^2 + (2*b^3*B*g^3*n*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))*((-2*c*(a/b + x)*(-1 + Log[a/b + x]))/d^3 + (2*c*(c/d + x)*(-1 + Log[c/d + x]))/d^3 - (3*c^2*Log[c/d + x]^2)/(2*d^4) - (c^3*(1 + Log[c/d + x]))/(d^4*(c + d*x)) + ((a*x)/(2*b) - x^2/4 + (x^2*Log[a/b + x])/2 - (a^2*Log[a + b*x])/(2*b^2))/d^2 - ((c*x)/(2*d) - x^2/4 + (x^2*Log[c/d + x])/2 - (c^2*Log[c + d*x])/(2*d^2))/d^2 - (c^3*(-(Log[a/b + x]/(d*(c + d*x))) + (b*(Log[a + b*x]/(b*c - a*d) - Log[c + d*x]/(b*c - a*d)))/d))/d^3 + ((-4*c*d*x + d^2*x^2 + (2*c^3)/(c + d*x) + 6*c^2*Log[c + d*x])*(-Log[a/b + x] + Log[c/d + x] + Log[a/(c + d*x) + (b*x)/(c + d*x)]))/(2*d^4) + (3*c^2*((Log[a/b + x]*Log[(c + d*x)/(c - (a*d)/b)])/d + PolyLog[2, (b*d*(a/b + x))/(-(b*c) + a*d)]/d))/d^3))/i^2 + (6*a*b^2*B*g^3*n*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))*(((a/b + x)*(-1 + Log[a/b + x]))/d^2 - ((c/d + x)*(-1 + Log[c/d + x]))/d^2 + (c*Log[c/d + x]^2)/d^3 + (c^2*(1 + Log[c/d + x]))/(d^3*(c + d*x)) + (c^2*(-(Log[a/b + x]/(d*(c + d*x))) + (b*(Log[a + b*x]/(b*c - a*d) - Log[c + d*x]/(b*c - a*d)))/d))/d^2 + ((d*x - c^2/(c + d*x) - 2*c*Log[c + d*x])*(-Log[a/b + x] + Log[c/d + x] + Log[a/(c + d*x) + (b*x)/(c + d*x)]))/d^3 - (2*c*((Log[a/b + x]*Log[(c + d*x)/(c - (a*d)/b)])/d + PolyLog[2, (b*d*(a/b + x))/(-(b*c) + a*d)]/d))/d^2))/i^2 + (6*a^2*b*B*g^3*n*(A + B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))*(-1/2*Log[c/d + x]^2/d^2 - (c*(1 + Log[c/d + x]))/(d^2*(c + d*x)) - (c*(-(Log[a/b + x]/(d*(c + d*x))) + (b*(Log[a + b*x]/(b*c - a*d) - Log[c + d*x]/(b*c - a*d)))/d))/d + ((c/(c + d*x) + Log[c + d*x])*(-Log[a/b + x] + Log[c/d + x] + Log[a/(c + d*x) + (b*x)/(c + d*x)]))/d^2 + ((Log[a/b + x]*Log[(c + d*x)/(c - (a*d)/b)])/d + PolyLog[2, (b*d*(a/b + x))/(-(b*c) + a*d)]/d)/d))/i^2 - (a^3*B^2*g^3*n^2*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] + (b*c - a*d)*Log[(a + b*x)/(c + d*x)]^2 - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(d*(b*c - a*d)*i^2*(c + d*x)) + (3*a*b^2*B^2*g^3*n^2*((d*(a + b*x)*Log[(a + b*x)/(c + d*x)]^2)/b - (c^2*Log[(a + b*x)/(c + d*x)]^2)/(c + d*x) + 2*c*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - (c^2*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(c + d*x)) - ((b*c - a*d)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*Log[(a + b*x)/(c + d*x)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]))/b + 4*c*(Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])))/(d^3*i^2) + (b^3*B^2*g^3*n^2*(d^2*x^2*Log[(a + b*x)/(c + d*x)]^2 - (4*c*d*(a + b*x)*Log[(a + b*x)/(c + d*x)]^2)/b + (2*c^3*Log[(a + b*x)/(c + d*x)]^2)/(c + d*x) - 6*c^2*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - (2*d*(b*c - a*d)*(a + b*x)*Log[(a + b*x)/(c + d*x)] + 2*a^2*d^2*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 2*(b*c - a*d)^2*Log[c + d*x] + 2*b^2*c^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] - a^2*d^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*c^2*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]))/b^2 + (2*c^3*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(c + d*x)) + (4*c*(b*c - a*d)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*Log[(a + b*x)/(c + d*x)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]))/b - 12*c^2*(Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])))/(2*d^4*i^2) + (3*a^2*b*B^2*g^3*n^2*((c*Log[(a + b*x)/(c + d*x)]^2)/(c + d*x) - Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - 2*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] + (c*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(c + d*x)) + 2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))]))/(d^2*i^2)","B",1
195,1,2196,500,5.0263816,"\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}{(c i+d i x)^2} \, dx","Integrate[((a*g + b*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(c*i + d*i*x)^2,x]","\text{Result too large to show}","\frac{4 b B g^2 n (b c-a d) \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^3 i^2}+\frac{2 b g^2 (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)^2}{d^3 i^2}+\frac{2 b B g^2 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)}{d^3 i^2}+\frac{b g^2 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{d^2 i^2}+\frac{g^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)^2}{d^2 i^2 (c+d x)}-\frac{2 A B g^2 n (a+b x) (b c-a d)}{d^2 i^2 (c+d x)}+\frac{2 b B^2 g^2 n^2 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^3 i^2}-\frac{4 b B^2 g^2 n^2 (b c-a d) \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^3 i^2}-\frac{2 B^2 g^2 n (a+b x) (b c-a d) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{d^2 i^2 (c+d x)}+\frac{2 B^2 g^2 n^2 (a+b x) (b c-a d)}{d^2 i^2 (c+d x)}",1,"(g^2*(b^2*d*x*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2 - ((b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2)/(c + d*x) - 2*b*(b*c - a*d)*(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] + (2*a^2*B*d^2*n*(-A - B*Log[e*((a + b*x)/(c + d*x))^n] + B*n*Log[(a + b*x)/(c + d*x)])*(b*c - a*d + b*(c + d*x)*Log[a/b + x] + (-(b*c) + a*d)*Log[(a + b*x)/(c + d*x)] - b*c*Log[(b*(c + d*x))/(b*c - a*d)] - b*d*x*Log[(b*(c + d*x))/(b*c - a*d)]))/((-(b*c) + a*d)*(c + d*x)) + 2*a*b*B*d*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[c/d + x]*Log[c + d*x] + 2*(-(c/(c + d*x)) + (b*c*Log[a + b*x])/(-(b*c) + a*d) + (b*c*Log[c + d*x])/(b*c - a*d) - Log[a/b + x]*Log[c + d*x] + Log[(a + b*x)/(c + d*x)]*(c/(c + d*x) + Log[c + d*x]) + 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^2*B*n*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])*(d*(a/b + x)*(-1 + Log[a/b + x]) - (c^2*Log[a/b + x])/(c + d*x) - (c + d*x)*(-1 + Log[c/d + x]) + c*Log[c/d + x]^2 + (c^2*(1 + Log[c/d + x]))/(c + d*x) + (b*c^2*(Log[a + b*x] - Log[c + d*x]))/(b*c - a*d) + (-Log[a/b + x] + Log[c/d + x] + Log[(a + b*x)/(c + d*x)])*(d*x - c^2/(c + d*x) - 2*c*Log[c + d*x]) - 2*c*(Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])) - (a^2*B^2*d^2*n^2*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] + (b*c - a*d)*Log[(a + b*x)/(c + d*x)]^2 - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(c + d*x)) + b^2*B^2*n^2*((d*(a + b*x)*Log[(a + b*x)/(c + d*x)]^2)/b - (c^2*Log[(a + b*x)/(c + d*x)]^2)/(c + d*x) + 2*c*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - (c^2*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(c + d*x)) - ((b*c - a*d)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 2*Log[(a + b*x)/(c + d*x)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]))/b + 4*c*(Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])) + 2*a*b*B^2*d*n^2*((c*Log[(a + b*x)/(c + d*x)]^2)/(c + d*x) - Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - 2*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] + (c*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(c + d*x)) + 2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])))/(d^3*i^2)","B",1
196,1,1261,282,1.9851713,"\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}{(c i+d i x)^2} \, dx","Integrate[((a*g + b*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(c*i + d*i*x)^2,x]","\frac{g \left(-\frac{a B^2 d \left((b c-a d) \log ^2\left(\frac{a+b x}{c+d x}\right)-2 (b c-a d) \log \left(\frac{a+b x}{c+d x}\right)-2 b (c+d x) \log (a+b x) \log \left(\frac{a+b x}{c+d x}\right)-2 b (c+d x) \log \left(\frac{b c-a d}{b c+b d x}\right) \log \left(\frac{a+b x}{c+d x}\right)+2 b c-2 a d+2 b (c+d x) \log (a+b x)-2 b (c+d x) \log (c+d x)+b (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 (c+d x) \left(\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)+\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)\right)\right) n^2}{(b c-a d) (c+d x)}+b B^2 \left(-\log \left(\frac{b c-a d}{b c+b d x}\right) \log ^2\left(\frac{a+b x}{c+d x}\right)+\frac{c \log ^2\left(\frac{a+b x}{c+d x}\right)}{c+d x}-2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right) \log \left(\frac{a+b x}{c+d x}\right)+\frac{c \left(2 b c-2 a d+2 b (c+d x) \log (a+b x)-2 (b c-a d) \log \left(\frac{a+b x}{c+d x}\right)-2 b (c+d x) \log (a+b x) \log \left(\frac{a+b x}{c+d x}\right)-2 b (c+d x) \log (c+d x)-2 b (c+d x) \log \left(\frac{a+b x}{c+d x}\right) \log \left(\frac{b c-a d}{b c+b d x}\right)+b (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 (c+d x) \left(\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)+\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)\right)\right)}{(b c-a d) (c+d x)}+2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)\right) n^2+\frac{2 a B d \left(-A-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)\right) \left(b c-b \log \left(\frac{b (c+d x)}{b c-a d}\right) c-a d+b (c+d x) \log \left(\frac{a}{b}+x\right)+(a d-b c) \log \left(\frac{a+b x}{c+d x}\right)-b d x \log \left(\frac{b (c+d x)}{b c-a d}\right)\right) n}{(a d-b c) (c+d x)}+b B \left(A+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)\right) \left(-\log ^2\left(\frac{c}{d}+x\right)+2 \log (c+d x) \log \left(\frac{c}{d}+x\right)+2 \left(\frac{b \log (a+b x) c}{a d-b c}+\frac{b \log (c+d x) c}{b c-a d}-\frac{c}{c+d x}-\log \left(\frac{a}{b}+x\right) \log (c+d x)+\log \left(\frac{a+b x}{c+d x}\right) \left(\frac{c}{c+d x}+\log (c+d x)\right)+\log \left(\frac{a}{b}+x\right) \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) n+\frac{(b c-a d) \left(A+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)\right)^2}{c+d x}+b \left(A+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)\right)^2 \log (c+d x)\right)}{d^2 i^2}","-\frac{2 b B g 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^2 i^2}-\frac{b g \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^2 i^2}-\frac{g (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{d i^2 (c+d x)}+\frac{2 A B g n (a+b x)}{d i^2 (c+d x)}+\frac{2 b B^2 g n^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^2 i^2}+\frac{2 B^2 g n (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{d i^2 (c+d x)}-\frac{2 B^2 g n^2 (a+b x)}{d i^2 (c+d x)}",1,"(g*(((b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2)/(c + d*x) + b*(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] + (2*a*B*d*n*(-A - B*Log[e*((a + b*x)/(c + d*x))^n] + B*n*Log[(a + b*x)/(c + d*x)])*(b*c - a*d + b*(c + d*x)*Log[a/b + x] + (-(b*c) + a*d)*Log[(a + b*x)/(c + d*x)] - b*c*Log[(b*(c + d*x))/(b*c - a*d)] - b*d*x*Log[(b*(c + d*x))/(b*c - a*d)]))/((-(b*c) + a*d)*(c + d*x)) + b*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[c/d + x]*Log[c + d*x] + 2*(-(c/(c + d*x)) + (b*c*Log[a + b*x])/(-(b*c) + a*d) + (b*c*Log[c + d*x])/(b*c - a*d) - Log[a/b + x]*Log[c + d*x] + Log[(a + b*x)/(c + d*x)]*(c/(c + d*x) + Log[c + d*x]) + Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)]) + 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - (a*B^2*d*n^2*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] + (b*c - a*d)*Log[(a + b*x)/(c + d*x)]^2 - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(c + d*x)) + b*B^2*n^2*((c*Log[(a + b*x)/(c + d*x)]^2)/(c + d*x) - Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - 2*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] + (c*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(c + d*x)) + 2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])))/(d^2*i^2)","B",1
197,1,331,163,0.4483984,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{(c i+d i x)^2} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(c*i + d*i*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 i^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}{i^2 (c+d x) (b c-a d)}-\frac{2 A B n (a+b x)}{i^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)}{i^2 (c+d x) (b c-a d)}+\frac{2 B^2 n^2 (a+b x)}{i^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*i^2*(c + d*x))","C",1
198,1,789,231,0.9959935,"\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) (c i+d i x)^2} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/((a*g + b*g*x)*(c*i + d*i*x)^2),x]","\frac{b \log (a+b x) \left(2 A B \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)+B^2 \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)^2-2 B^2 n \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)+A^2-2 A B n+2 B^2 n^2\right)}{g i^2 (b c-a d)^2}+\frac{2 A B \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)+B^2 \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)^2-2 B^2 n \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)+A^2-2 A B n+2 B^2 n^2}{g i^2 (c+d x) (b c-a d)}-\frac{b \log (c+d x) \left(2 A B \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)+B^2 \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)^2-2 B^2 n \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)+A^2-2 A B n+2 B^2 n^2\right)}{g i^2 (b c-a d)^2}+\frac{\log ^2\left(\frac{a+b x}{c+d x}\right) \left(b B^2 c n \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)+b B^2 d n x \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)-a B^2 d n^2+A b B c n+A b B d n x-b B^2 d n^2 x\right)}{g i^2 (c+d x) (b c-a d)^2}-\frac{2 B n \log \left(\frac{a+b x}{c+d x}\right) \left(-B \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)-A+B n\right)}{g i^2 (c+d x) (b c-a d)}+\frac{b B^2 n^2 \log ^3\left(\frac{a+b x}{c+d x}\right)}{3 g i^2 (b c-a d)^2}","\frac{b \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^3}{3 B g i^2 n (b c-a d)^2}-\frac{d (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g i^2 (c+d x) (b c-a d)^2}+\frac{2 A B d n (a+b x)}{g i^2 (c+d x) (b c-a d)^2}+\frac{2 B^2 d n (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{g i^2 (c+d x) (b c-a d)^2}-\frac{2 B^2 d n^2 (a+b x)}{g i^2 (c+d x) (b c-a d)^2}",1,"(b*B^2*n^2*Log[(a + b*x)/(c + d*x)]^3)/(3*(b*c - a*d)^2*g*i^2) - (2*B*n*Log[(a + b*x)/(c + d*x)]*(-A + B*n - B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])))/((b*c - a*d)*g*i^2*(c + d*x)) + (Log[(a + b*x)/(c + d*x)]^2*(A*b*B*c*n - a*B^2*d*n^2 + A*b*B*d*n*x - b*B^2*d*n^2*x + b*B^2*c*n*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + b*B^2*d*n*x*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])))/((b*c - a*d)^2*g*i^2*(c + d*x)) + (A^2 - 2*A*B*n + 2*B^2*n^2 + 2*A*B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) - 2*B^2*n*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + B^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2)/((b*c - a*d)*g*i^2*(c + d*x)) + (b*Log[a + b*x]*(A^2 - 2*A*B*n + 2*B^2*n^2 + 2*A*B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) - 2*B^2*n*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + B^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2))/((b*c - a*d)^2*g*i^2) - (b*(A^2 - 2*A*B*n + 2*B^2*n^2 + 2*A*B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) - 2*B^2*n*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + B^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2)*Log[c + d*x])/((b*c - a*d)^2*g*i^2)","B",1
199,1,870,392,1.39038,"\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 (c i+d i x)^2} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/((a*g + b*g*x)^2*(c*i + d*i*x)^2),x]","-\frac{2 b B^2 d n^2 (a+b x) (c+d x) \log ^3\left(\frac{a+b x}{c+d x}\right)+3 B n \left(2 A d^2 x^2 b^2+B c^2 n b^2+2 A c d x b^2+2 B c d n x b^2+2 a A c d b+2 a A d^2 x b-2 a B d^2 n x b+2 B d (a+b x) (c+d x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) b-2 B d n (a+b x) (c+d x) \log \left(\frac{a+b x}{c+d x}\right) b-a^2 B d^2 n\right) \log ^2\left(\frac{a+b x}{c+d x}\right)+6 B (b c-a d) n \left(A b c+b B n c+a A d-a B d n+2 A b d x+B (a d+b (c+2 d x)) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-B n (b c+a d+2 b d x) \log \left(\frac{a+b x}{c+d x}\right)\right) \log \left(\frac{a+b x}{c+d x}\right)+6 b d (a+b x) (c+d x) \log (a+b x) \left(A^2+2 B \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right) A+2 B^2 n^2+B^2 \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)^2\right)+3 b (b c-a d) (c+d x) \left(A^2+2 B n A+2 B^2 n^2+B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-2 B n (A+B n) \log \left(\frac{a+b x}{c+d x}\right)+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(A+B n-B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)+3 d (b c-a d) (a+b x) \left(A^2-2 B n A+2 B^2 n^2+B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)+2 B n (B n-A) \log \left(\frac{a+b x}{c+d x}\right)-2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(-A+B n+B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)-6 b d (a+b x) (c+d x) \left(A^2+2 B \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right) A+2 B^2 n^2+B^2 \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)^2\right) \log (c+d x)}{3 (b c-a d)^3 g^2 i^2 (a+b x) (c+d x)}","-\frac{b^2 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g^2 i^2 (a+b x) (b c-a d)^3}-\frac{2 b^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 i^2 (a+b x) (b c-a d)^3}+\frac{d^2 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g^2 i^2 (c+d x) (b c-a d)^3}-\frac{2 A B d^2 n (a+b x)}{g^2 i^2 (c+d x) (b c-a d)^3}-\frac{2 b d \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^3}{3 B g^2 i^2 n (b c-a d)^3}-\frac{2 b^2 B^2 n^2 (c+d x)}{g^2 i^2 (a+b x) (b c-a d)^3}-\frac{2 B^2 d^2 n (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{g^2 i^2 (c+d x) (b c-a d)^3}+\frac{2 B^2 d^2 n^2 (a+b x)}{g^2 i^2 (c+d x) (b c-a d)^3}",1,"-1/3*(2*b*B^2*d*n^2*(a + b*x)*(c + d*x)*Log[(a + b*x)/(c + d*x)]^3 + 3*B*n*Log[(a + b*x)/(c + d*x)]^2*(2*a*A*b*c*d + b^2*B*c^2*n - a^2*B*d^2*n + 2*A*b^2*c*d*x + 2*a*A*b*d^2*x + 2*b^2*B*c*d*n*x - 2*a*b*B*d^2*n*x + 2*A*b^2*d^2*x^2 + 2*b*B*d*(a + b*x)*(c + d*x)*Log[e*((a + b*x)/(c + d*x))^n] - 2*b*B*d*n*(a + b*x)*(c + d*x)*Log[(a + b*x)/(c + d*x)]) + 6*B*(b*c - a*d)*n*Log[(a + b*x)/(c + d*x)]*(A*b*c + a*A*d + b*B*c*n - a*B*d*n + 2*A*b*d*x + B*(a*d + b*(c + 2*d*x))*Log[e*((a + b*x)/(c + d*x))^n] - B*n*(b*c + a*d + 2*b*d*x)*Log[(a + b*x)/(c + d*x)]) + 6*b*d*(a + b*x)*(c + d*x)*Log[a + b*x]*(A^2 + 2*B^2*n^2 + 2*A*B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + B^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2) + 3*b*(b*c - a*d)*(c + d*x)*(A^2 + 2*A*B*n + 2*B^2*n^2 + B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 2*B*n*(A + B*n)*Log[(a + b*x)/(c + d*x)] + B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(A + B*n - B*n*Log[(a + b*x)/(c + d*x)])) + 3*d*(b*c - a*d)*(a + b*x)*(A^2 - 2*A*B*n + 2*B^2*n^2 + B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 + 2*B*n*(-A + B*n)*Log[(a + b*x)/(c + d*x)] + B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 - 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(-A + B*n + B*n*Log[(a + b*x)/(c + d*x)])) - 6*b*d*(a + b*x)*(c + d*x)*(A^2 + 2*B^2*n^2 + 2*A*B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + B^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2)*Log[c + d*x])/((b*c - a*d)^3*g^2*i^2*(a + b*x)*(c + d*x))","B",1
200,1,1340,560,1.9866601,"\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 (c i+d i x)^2} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/((a*g + b*g*x)^3*(c*i + d*i*x)^2),x]","\frac{4 b B^2 d^2 n^2 (a+b x)^2 (c+d x) \log ^3\left(\frac{a+b x}{c+d x}\right)+2 B n \left(6 A d^3 x^3 b^3+3 B d^3 n x^3 b^3+6 A c d^2 x^2 b^3+9 B c d^2 n x^2 b^3-B c^3 n b^3+3 B c^2 d n x b^3+12 a A d^3 x^2 b^2+6 a B c^2 d n b^2+12 a A c d^2 x b^2+12 a B c d^2 n x b^2+6 a^2 A c d^2 b+6 a^2 A d^3 x b-6 a^2 B d^3 n x b+6 B d^2 (a+b x)^2 (c+d x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) b-6 B d^2 n (a+b x)^2 (c+d x) \log \left(\frac{a+b x}{c+d x}\right) b-2 a^3 B d^3 n\right) \log ^2\left(\frac{a+b x}{c+d x}\right)+2 B (b c-a d) n \left(4 d^2 \left(A-B n+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)\right) (a+b x)^2+2 b d (c+d x) \left(4 A+5 B n+4 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-4 B n \log \left(\frac{a+b x}{c+d x}\right)\right) (a+b x)-b (b c-a d) (c+d x) \left(2 A+B n+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) \log \left(\frac{a+b x}{c+d x}\right)+2 b d (b c-a d) (a+b x) (c+d x) \left(4 A^2+10 B n A+11 B^2 n^2+4 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+4 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-2 B n (4 A+5 B n) \log \left(\frac{a+b x}{c+d x}\right)+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(4 A+5 B n-4 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)-b (b c-a d)^2 (c+d x) \left(2 A^2+2 B n A+B^2 n^2+2 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-2 B n (2 A+B n) \log \left(\frac{a+b x}{c+d x}\right)+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(2 A+B n-2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)+6 b d^2 (a+b x)^2 (c+d x) \log (a+b x) \left(2 A^2+2 B n A+5 B^2 n^2+2 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-2 B n (2 A+B n) \log \left(\frac{a+b x}{c+d x}\right)+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(2 A+B n-2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)+4 d^2 (b c-a d) (a+b x)^2 \left(A^2-2 B n A+2 B^2 n^2+B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)+2 B n (B n-A) \log \left(\frac{a+b x}{c+d x}\right)-2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(-A+B n+B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)-6 b d^2 (a+b x)^2 (c+d x) \left(2 A^2+2 B n A+5 B^2 n^2+2 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-2 B n (2 A+B n) \log \left(\frac{a+b x}{c+d x}\right)+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(2 A+B n-2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) \log (c+d x)}{4 (b c-a d)^4 g^3 i^2 (a+b x)^2 (c+d x)}","-\frac{b^3 (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 i^2 (a+b x)^2 (b c-a d)^4}-\frac{b^3 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 i^2 (a+b x)^2 (b c-a d)^4}+\frac{3 b^2 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 i^2 (a+b x) (b c-a d)^4}+\frac{6 b^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 i^2 (a+b x) (b c-a d)^4}-\frac{d^3 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g^3 i^2 (c+d x) (b c-a d)^4}+\frac{2 A B d^3 n (a+b x)}{g^3 i^2 (c+d x) (b c-a d)^4}+\frac{b d^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^3}{B g^3 i^2 n (b c-a d)^4}-\frac{b^3 B^2 n^2 (c+d x)^2}{4 g^3 i^2 (a+b x)^2 (b c-a d)^4}+\frac{6 b^2 B^2 d n^2 (c+d x)}{g^3 i^2 (a+b x) (b c-a d)^4}+\frac{2 B^2 d^3 n (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{g^3 i^2 (c+d x) (b c-a d)^4}-\frac{2 B^2 d^3 n^2 (a+b x)}{g^3 i^2 (c+d x) (b c-a d)^4}",1,"(4*b*B^2*d^2*n^2*(a + b*x)^2*(c + d*x)*Log[(a + b*x)/(c + d*x)]^3 + 2*B*n*Log[(a + b*x)/(c + d*x)]^2*(6*a^2*A*b*c*d^2 - b^3*B*c^3*n + 6*a*b^2*B*c^2*d*n - 2*a^3*B*d^3*n + 12*a*A*b^2*c*d^2*x + 6*a^2*A*b*d^3*x + 3*b^3*B*c^2*d*n*x + 12*a*b^2*B*c*d^2*n*x - 6*a^2*b*B*d^3*n*x + 6*A*b^3*c*d^2*x^2 + 12*a*A*b^2*d^3*x^2 + 9*b^3*B*c*d^2*n*x^2 + 6*A*b^3*d^3*x^3 + 3*b^3*B*d^3*n*x^3 + 6*b*B*d^2*(a + b*x)^2*(c + d*x)*Log[e*((a + b*x)/(c + d*x))^n] - 6*b*B*d^2*n*(a + b*x)^2*(c + d*x)*Log[(a + b*x)/(c + d*x)]) + 2*b*d*(b*c - a*d)*(a + b*x)*(c + d*x)*(4*A^2 + 10*A*B*n + 11*B^2*n^2 + 4*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 2*B*n*(4*A + 5*B*n)*Log[(a + b*x)/(c + d*x)] + 4*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(4*A + 5*B*n - 4*B*n*Log[(a + b*x)/(c + d*x)])) - b*(b*c - a*d)^2*(c + d*x)*(2*A^2 + 2*A*B*n + B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 2*B*n*(2*A + B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(2*A + B*n - 2*B*n*Log[(a + b*x)/(c + d*x)])) + 6*b*d^2*(a + b*x)^2*(c + d*x)*Log[a + b*x]*(2*A^2 + 2*A*B*n + 5*B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 2*B*n*(2*A + B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(2*A + B*n - 2*B*n*Log[(a + b*x)/(c + d*x)])) + 2*B*(b*c - a*d)*n*Log[(a + b*x)/(c + d*x)]*(2*b*d*(a + b*x)*(c + d*x)*(4*A + 5*B*n + 4*B*Log[e*((a + b*x)/(c + d*x))^n] - 4*B*n*Log[(a + b*x)/(c + d*x)]) - b*(b*c - a*d)*(c + d*x)*(2*A + B*n + 2*B*Log[e*((a + b*x)/(c + d*x))^n] - 2*B*n*Log[(a + b*x)/(c + d*x)]) + 4*d^2*(a + b*x)^2*(A - B*n + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])) + 4*d^2*(b*c - a*d)*(a + b*x)^2*(A^2 - 2*A*B*n + 2*B^2*n^2 + B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 + 2*B*n*(-A + B*n)*Log[(a + b*x)/(c + d*x)] + B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 - 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(-A + B*n + B*n*Log[(a + b*x)/(c + d*x)])) - 6*b*d^2*(a + b*x)^2*(c + d*x)*(2*A^2 + 2*A*B*n + 5*B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 2*B*n*(2*A + B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(2*A + B*n - 2*B*n*Log[(a + b*x)/(c + d*x)]))*Log[c + d*x])/(4*(b*c - a*d)^4*g^3*i^2*(a + b*x)^2*(c + d*x))","B",1
201,1,1695,729,3.0388553,"\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 (c i+d i x)^2} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/((a*g + b*g*x)^4*(c*i + d*i*x)^2),x]","-\frac{b (c+d x) \left(9 A^2+6 B n A+2 B^2 n^2+9 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+9 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-6 B n (3 A+B n) \log \left(\frac{a+b x}{c+d x}\right)+6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(3 A+B n-3 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) (b c-a d)^3-3 b d (a+b x) (c+d x) \left(9 A^2+12 B n A+7 B^2 n^2+9 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+9 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-6 B n (3 A+2 B n) \log \left(\frac{a+b x}{c+d x}\right)+6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(3 A+2 B n-3 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) (b c-a d)^2+3 b d^2 (a+b x)^2 (c+d x) \left(27 A^2+78 B n A+92 B^2 n^2+27 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+27 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-6 B n (9 A+13 B n) \log \left(\frac{a+b x}{c+d x}\right)+6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(9 A+13 B n-9 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) (b c-a d)+6 B n \log \left(\frac{a+b x}{c+d x}\right) \left(9 d^3 \left(A-B n+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)\right) (a+b x)^3+3 b d^2 (c+d x) \left(9 A+13 B n+9 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-9 B n \log \left(\frac{a+b x}{c+d x}\right)\right) (a+b x)^2-3 b d (b c-a d) (c+d x) \left(3 A+2 B n+3 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-3 B n \log \left(\frac{a+b x}{c+d x}\right)\right) (a+b x)+b (b c-a d)^2 (c+d x) \left(3 A+B n+3 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-3 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) (b c-a d)+27 d^3 (a+b x)^3 \left(A^2-2 B n A+2 B^2 n^2+B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)+2 B n (B n-A) \log \left(\frac{a+b x}{c+d x}\right)-2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(-A+B n+B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) (b c-a d)+36 b B^2 d^3 n^2 (a+b x)^3 (c+d x) \log ^3\left(\frac{a+b x}{c+d x}\right)+9 B n \log ^2\left(\frac{a+b x}{c+d x}\right) \left(12 A d^4 x^4 b^4+10 B d^4 n x^4 b^4+12 A c d^3 x^3 b^4+22 B c d^3 n x^3 b^4+6 B c^2 d^2 n x^2 b^4+B c^4 n b^4-2 B c^3 d n x b^4+36 a A d^4 x^3 b^3+18 a B d^4 n x^3 b^3+36 a A c d^3 x^2 b^3+54 a B c d^3 n x^2 b^3-6 a B c^3 d n b^3+18 a B c^2 d^2 n x b^3+36 a^2 A d^4 x^2 b^2+18 a^2 B c^2 d^2 n b^2+36 a^2 A c d^3 x b^2+36 a^2 B c d^3 n x b^2+12 a^3 A c d^3 b+12 a^3 A d^4 x b-12 a^3 B d^4 n x b+12 B d^3 (a+b x)^3 (c+d x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) b-12 B d^3 n (a+b x)^3 (c+d x) \log \left(\frac{a+b x}{c+d x}\right) b-3 a^4 B d^4 n\right)+6 b d^3 (a+b x)^3 (c+d x) \log (a+b x) \left(18 A^2+30 B n A+55 B^2 n^2+18 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+18 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-6 B n (6 A+5 B n) \log \left(\frac{a+b x}{c+d x}\right)+6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(6 A+5 B n-6 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)-6 b d^3 (a+b x)^3 (c+d x) \left(18 A^2+30 B n A+55 B^2 n^2+18 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+18 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-6 B n (6 A+5 B n) \log \left(\frac{a+b x}{c+d x}\right)+6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(6 A+5 B n-6 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) \log (c+d x)}{27 (b c-a d)^5 g^4 i^2 (a+b x)^3 (c+d x)}","-\frac{b^4 (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 i^2 (a+b x)^3 (b c-a d)^5}-\frac{2 b^4 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 i^2 (a+b x)^3 (b c-a d)^5}+\frac{2 b^3 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 i^2 (a+b x)^2 (b c-a d)^5}+\frac{2 b^3 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 i^2 (a+b x)^2 (b c-a d)^5}-\frac{6 b^2 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 i^2 (a+b x) (b c-a d)^5}-\frac{12 b^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 i^2 (a+b x) (b c-a d)^5}+\frac{d^4 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g^4 i^2 (c+d x) (b c-a d)^5}-\frac{2 A B d^4 n (a+b x)}{g^4 i^2 (c+d x) (b c-a d)^5}-\frac{4 b d^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^3}{3 B g^4 i^2 n (b c-a d)^5}-\frac{2 b^4 B^2 n^2 (c+d x)^3}{27 g^4 i^2 (a+b x)^3 (b c-a d)^5}+\frac{b^3 B^2 d n^2 (c+d x)^2}{g^4 i^2 (a+b x)^2 (b c-a d)^5}-\frac{12 b^2 B^2 d^2 n^2 (c+d x)}{g^4 i^2 (a+b x) (b c-a d)^5}-\frac{2 B^2 d^4 n (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{g^4 i^2 (c+d x) (b c-a d)^5}+\frac{2 B^2 d^4 n^2 (a+b x)}{g^4 i^2 (c+d x) (b c-a d)^5}",1,"-1/27*(36*b*B^2*d^3*n^2*(a + b*x)^3*(c + d*x)*Log[(a + b*x)/(c + d*x)]^3 + 9*B*n*Log[(a + b*x)/(c + d*x)]^2*(12*a^3*A*b*c*d^3 + b^4*B*c^4*n - 6*a*b^3*B*c^3*d*n + 18*a^2*b^2*B*c^2*d^2*n - 3*a^4*B*d^4*n + 36*a^2*A*b^2*c*d^3*x + 12*a^3*A*b*d^4*x - 2*b^4*B*c^3*d*n*x + 18*a*b^3*B*c^2*d^2*n*x + 36*a^2*b^2*B*c*d^3*n*x - 12*a^3*b*B*d^4*n*x + 36*a*A*b^3*c*d^3*x^2 + 36*a^2*A*b^2*d^4*x^2 + 6*b^4*B*c^2*d^2*n*x^2 + 54*a*b^3*B*c*d^3*n*x^2 + 12*A*b^4*c*d^3*x^3 + 36*a*A*b^3*d^4*x^3 + 22*b^4*B*c*d^3*n*x^3 + 18*a*b^3*B*d^4*n*x^3 + 12*A*b^4*d^4*x^4 + 10*b^4*B*d^4*n*x^4 + 12*b*B*d^3*(a + b*x)^3*(c + d*x)*Log[e*((a + b*x)/(c + d*x))^n] - 12*b*B*d^3*n*(a + b*x)^3*(c + d*x)*Log[(a + b*x)/(c + d*x)]) + 3*b*d^2*(b*c - a*d)*(a + b*x)^2*(c + d*x)*(27*A^2 + 78*A*B*n + 92*B^2*n^2 + 27*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 6*B*n*(9*A + 13*B*n)*Log[(a + b*x)/(c + d*x)] + 27*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 6*B*Log[e*((a + b*x)/(c + d*x))^n]*(9*A + 13*B*n - 9*B*n*Log[(a + b*x)/(c + d*x)])) + 6*b*d^3*(a + b*x)^3*(c + d*x)*Log[a + b*x]*(18*A^2 + 30*A*B*n + 55*B^2*n^2 + 18*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 6*B*n*(6*A + 5*B*n)*Log[(a + b*x)/(c + d*x)] + 18*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 6*B*Log[e*((a + b*x)/(c + d*x))^n]*(6*A + 5*B*n - 6*B*n*Log[(a + b*x)/(c + d*x)])) + b*(b*c - a*d)^3*(c + d*x)*(9*A^2 + 6*A*B*n + 2*B^2*n^2 + 9*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 6*B*n*(3*A + B*n)*Log[(a + b*x)/(c + d*x)] + 9*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 6*B*Log[e*((a + b*x)/(c + d*x))^n]*(3*A + B*n - 3*B*n*Log[(a + b*x)/(c + d*x)])) - 3*b*d*(b*c - a*d)^2*(a + b*x)*(c + d*x)*(9*A^2 + 12*A*B*n + 7*B^2*n^2 + 9*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 6*B*n*(3*A + 2*B*n)*Log[(a + b*x)/(c + d*x)] + 9*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 6*B*Log[e*((a + b*x)/(c + d*x))^n]*(3*A + 2*B*n - 3*B*n*Log[(a + b*x)/(c + d*x)])) + 6*B*(b*c - a*d)*n*Log[(a + b*x)/(c + d*x)]*(3*b*d^2*(a + b*x)^2*(c + d*x)*(9*A + 13*B*n + 9*B*Log[e*((a + b*x)/(c + d*x))^n] - 9*B*n*Log[(a + b*x)/(c + d*x)]) + b*(b*c - a*d)^2*(c + d*x)*(3*A + B*n + 3*B*Log[e*((a + b*x)/(c + d*x))^n] - 3*B*n*Log[(a + b*x)/(c + d*x)]) - 3*b*d*(b*c - a*d)*(a + b*x)*(c + d*x)*(3*A + 2*B*n + 3*B*Log[e*((a + b*x)/(c + d*x))^n] - 3*B*n*Log[(a + b*x)/(c + d*x)]) + 9*d^3*(a + b*x)^3*(A - B*n + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])) + 27*d^3*(b*c - a*d)*(a + b*x)^3*(A^2 - 2*A*B*n + 2*B^2*n^2 + B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 + 2*B*n*(-A + B*n)*Log[(a + b*x)/(c + d*x)] + B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 - 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(-A + B*n + B*n*Log[(a + b*x)/(c + d*x)])) - 6*b*d^3*(a + b*x)^3*(c + d*x)*(18*A^2 + 30*A*B*n + 55*B^2*n^2 + 18*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 6*B*n*(6*A + 5*B*n)*Log[(a + b*x)/(c + d*x)] + 18*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 6*B*Log[e*((a + b*x)/(c + d*x))^n]*(6*A + 5*B*n - 6*B*n*Log[(a + b*x)/(c + d*x)]))*Log[c + d*x])/((b*c - a*d)^5*g^4*i^2*(a + b*x)^3*(c + d*x))","B",1
202,1,5730,676,9.7996841,"\int \frac{(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}{(c i+d i x)^3} \, dx","Integrate[((a*g + b*g*x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(c*i + d*i*x)^3,x]","\text{Result too large to show}","\frac{6 b^2 B g^3 n (b c-a d) \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^4 i^3}+\frac{3 b^2 g^3 (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)^2}{d^4 i^3}+\frac{2 b^2 B g^3 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)}{d^4 i^3}+\frac{b^2 g^3 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{d^3 i^3}+\frac{2 b g^3 (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)^2}{d^3 i^3 (c+d x)}-\frac{4 A b B g^3 n (a+b x) (b c-a d)}{d^3 i^3 (c+d x)}+\frac{g^3 (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)^2}{2 d^2 i^3 (c+d x)^2}-\frac{B g^3 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)}{2 d^2 i^3 (c+d x)^2}+\frac{2 b^2 B^2 g^3 n^2 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i^3}-\frac{6 b^2 B^2 g^3 n^2 (b c-a d) \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^4 i^3}-\frac{4 b B^2 g^3 n (a+b x) (b c-a d) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{d^3 i^3 (c+d x)}+\frac{4 b B^2 g^3 n^2 (a+b x) (b c-a d)}{d^3 i^3 (c+d x)}+\frac{B^2 g^3 n^2 (a+b x)^2 (b c-a d)}{4 d^2 i^3 (c+d x)^2}",1,"Result too large to show","B",1
203,1,3172,441,6.5922344,"\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}{(c i+d i x)^3} \, dx","Integrate[((a*g + b*g*x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(c*i + d*i*x)^3,x]","\text{Result too large to show}","-\frac{2 b^2 B g^2 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^3 i^3}-\frac{b^2 g^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\right)^2}{d^3 i^3}-\frac{b g^2 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{d^2 i^3 (c+d x)}+\frac{2 A b B g^2 n (a+b x)}{d^2 i^3 (c+d x)}-\frac{g^2 (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 d i^3 (c+d x)^2}+\frac{B g^2 n (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 d i^3 (c+d x)^2}+\frac{2 b^2 B^2 g^2 n^2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{d^3 i^3}+\frac{2 b B^2 g^2 n (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{d^2 i^3 (c+d x)}-\frac{2 b B^2 g^2 n^2 (a+b x)}{d^2 i^3 (c+d x)}-\frac{B^2 g^2 n^2 (a+b x)^2}{4 d i^3 (c+d x)^2}",1,"(g^2*((-2*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2)/(c + d*x)^2 + (8*b*(b*c - a*d)*(A + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])^2)/(c + d*x) + 4*b^2*(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] + (4*a*b*B*d*n*(-A - B*Log[e*((a + b*x)/(c + d*x))^n] + B*n*Log[(a + b*x)/(c + d*x)])*(-(b^2*c^3) + 4*a*b*c^2*d - 3*a^2*c*d^2 - 2*b^2*c^2*d*x + 6*a*b*c*d^2*x - 4*a^2*d^3*x - 2*b*(b*c - 2*a*d)*(c + d*x)^2*Log[a + b*x] + 2*(b*c - a*d)^2*(c + 2*d*x)*Log[(a + b*x)/(c + d*x)] + 2*b^2*c^3*Log[c + d*x] - 4*a*b*c^2*d*Log[c + d*x] + 4*b^2*c^2*d*x*Log[c + d*x] - 8*a*b*c*d^2*x*Log[c + d*x] + 2*b^2*c*d^2*x^2*Log[c + d*x] - 4*a*b*d^3*x^2*Log[c + d*x]))/((b*c - a*d)^2*(c + d*x)^2) + (2*a^2*B*d^2*n*(-A - B*Log[e*((a + b*x)/(c + d*x))^n] + B*n*Log[(a + b*x)/(c + d*x)])*(-(b^2*c^2) + 4*a*b*c*d - a^2*d^2 + 2*b^2*c*d*x + 2*a*b*d^2*x + 2*b^2*d^2*x^2 - 2*b^2*(c + d*x)^2*Log[a/b + x] + 2*(b*c - a*d)^2*Log[(a + b*x)/(c + d*x)] + 2*b^2*c^2*Log[(b*(c + d*x))/(b*c - a*d)] + 4*b^2*c*d*x*Log[(b*(c + d*x))/(b*c - a*d)] + 2*b^2*d^2*x^2*Log[(b*(c + d*x))/(b*c - a*d)]))/((b*c - a*d)^2*(c + d*x)^2) + 2*b^2*B*n*(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]^2 - (8*c*(1 + Log[c/d + x]))/(c + d*x) + (c^2*(1 + 2*Log[c/d + x]))/(c + d*x)^2 + 8*c*(Log[a/b + x]/(c + d*x) + (b*(Log[a + b*x] - Log[c + d*x]))/(-(b*c) + a*d)) + 2*(-Log[a/b + x] + Log[c/d + x] + Log[(a + b*x)/(c + d*x)])*((c*(3*c + 4*d*x))/(c + d*x)^2 + 2*Log[c + d*x]) + (2*c^2*(-Log[a/b + x] + (b*(c + d*x)*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]))/(b*c - a*d)^2))/(c + d*x)^2 + 4*(Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])) + (2*a*b*B^2*d*n^2*(2*c*Log[(a + b*x)/(c + d*x)]^2 - 4*(c + d*x)*Log[(a + b*x)/(c + d*x)]^2 - (4*(c + d*x)*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d) + (c*((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*c - a*d)^2*Log[(a + b*x)/(c + d*x)] - 4*b*(b*c - a*d)*(c + d*x)*Log[(a + b*x)/(c + d*x)] - 4*b^2*(c + d*x)^2*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 2*b^2*(c + d*x)^2*Log[c + d*x] + 4*b*(c + d*x)*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]) - 4*b^2*(c + d*x)^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*b^2*(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*(c + d*x)^2*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(b*c - a*d)^2))/(c + d*x)^2 - (a^2*B^2*d^2*n^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*c - a*d)^2*Log[(a + b*x)/(c + d*x)] - 4*b*(b*c - a*d)*(c + d*x)*Log[(a + b*x)/(c + d*x)] - 4*b^2*(c + d*x)^2*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] + 2*(b*c - a*d)^2*Log[(a + b*x)/(c + d*x)]^2 - 2*b^2*(c + d*x)^2*Log[c + d*x] + 4*b*(c + d*x)*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]) - 4*b^2*(c + d*x)^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*b^2*(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*(c + d*x)^2*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)^2*(c + d*x)^2) - 2*b^2*B^2*n^2*((c^2*Log[(a + b*x)/(c + d*x)]^2)/(c + d*x)^2 - (4*c*Log[(a + b*x)/(c + d*x)]^2)/(c + d*x) + 2*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 4*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - (4*c*(2*b*c - 2*a*d + 2*b*(c + d*x)*Log[a + b*x] - 2*(b*c - a*d)*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 2*b*(c + d*x)*Log[c + d*x] - 2*b*(c + d*x)*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + b*(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*(c + d*x)*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/((b*c - a*d)*(c + d*x)) + (c^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*c - a*d)^2*Log[(a + b*x)/(c + d*x)] - 4*b*(b*c - a*d)*(c + d*x)*Log[(a + b*x)/(c + d*x)] - 4*b^2*(c + d*x)^2*Log[a + b*x]*Log[(a + b*x)/(c + d*x)] - 2*b^2*(c + d*x)^2*Log[c + d*x] + 4*b*(c + d*x)*(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x]) - 4*b^2*(c + d*x)^2*Log[(a + b*x)/(c + d*x)]*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*b^2*(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*(c + d*x)^2*(Log[(b*c - a*d)/(b*c + b*d*x)]*(2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + Log[(b*c - a*d)/(b*c + b*d*x)]) - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(2*(b*c - a*d)^2*(c + d*x)^2) - 4*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))])))/(4*d^3*i^3)","B",1
204,1,803,151,0.9866249,"\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}{(c i+d i x)^3} \, dx","Integrate[((a*g + b*g*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2)/(c*i + d*i*x)^3,x]","\frac{g \left(2 (b c-a d)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2-4 b (b c-a d) (c+d x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2+4 b B n (c+d x) \left(2 (b c-a d) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+2 b (c+d x) \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+d x) \log (c+d x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-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) \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(\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)\right)-B n \left(2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) (b c-a d)^2+4 b (c+d x) \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 (c+d x)^2 \log (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)-4 b^2 (c+d x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \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 \left((b c-a d)^2+2 b (c+d x) (b c-a d)+2 b^2 (c+d x)^2 \log (a+b x)-2 b^2 (c+d x)^2 \log (c+d x)\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(\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)\right)\right)}{4 d^2 (b c-a d) i^3 (c+d x)^2}","\frac{g (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{2 i^3 (c+d x)^2 (b c-a d)}-\frac{B g n (a+b x)^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 i^3 (c+d x)^2 (b c-a d)}+\frac{B^2 g n^2 (a+b x)^2}{4 i^3 (c+d x)^2 (b c-a d)}",1,"(g*(2*(b*c - a*d)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 - 4*b*(b*c - a*d)*(c + d*x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2 + 4*b*B*n*(c + d*x)*(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*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)]))))/(4*d^2*(b*c - a*d)*i^3*(c + d*x)^2)","C",1
205,1,464,317,0.4356265,"\int \frac{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{(c i+d i x)^3} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/(c*i + d*i*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 i^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 i^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}{i^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 i^3 (c+d x)^2 (b c-a d)^2}-\frac{2 A b B n (a+b x)}{i^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)}{i^3 (c+d x) (b c-a d)^2}+\frac{2 b B^2 n^2 (a+b x)}{i^3 (c+d x) (b c-a d)^2}-\frac{B^2 d n^2 (a+b x)^2}{4 i^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*i^3*(c + d*x)^2)","C",1
206,1,971,402,1.3740641,"\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) (c i+d i x)^3} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/((a*g + b*g*x)*(c*i + d*i*x)^3),x]","\frac{4 b^2 B^2 n^2 \log ^3\left(\frac{a+b x}{c+d x}\right)-\frac{6 B n \left(-2 A c^2 b^2-2 A d^2 x^2 b^2+3 B d^2 n x^2 b^2-4 A c d x b^2+4 B c d n x b^2-2 B (c+d x)^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) b^2+2 B n (c+d x)^2 \log \left(\frac{a+b x}{c+d x}\right) b^2+4 a B c d n b+2 a B d^2 n x b-a^2 B d^2 n\right) \log ^2\left(\frac{a+b x}{c+d x}\right)}{(c+d x)^2}-\frac{6 B (b c-a d) n \left(-6 A b c+7 b B n c+2 a A d-a B d n-4 A b d x+6 b B d n x+2 B (-3 b c+a d-2 b d x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B n (3 b c-a d+2 b d x) \log \left(\frac{a+b x}{c+d x}\right)\right) \log \left(\frac{a+b x}{c+d x}\right)}{(c+d x)^2}+\frac{3 (b c-a d)^2 \left(2 A^2-2 B n A+B^2 n^2+2 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)+2 B n (B n-2 A) \log \left(\frac{a+b x}{c+d x}\right)-2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(-2 A+B n+2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)}{(c+d x)^2}+6 b^2 \log (a+b x) \left(2 A^2-6 B n A+7 B^2 n^2+2 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)+2 B n (3 B n-2 A) \log \left(\frac{a+b x}{c+d x}\right)-2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(-2 A+3 B n+2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)+\frac{6 b (b c-a d) \left(2 A^2-6 B n A+7 B^2 n^2+2 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)+2 B n (3 B n-2 A) \log \left(\frac{a+b x}{c+d x}\right)-2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(-2 A+3 B n+2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)}{c+d x}-6 b^2 \left(2 A^2-6 B n A+7 B^2 n^2+2 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)+2 B n (3 B n-2 A) \log \left(\frac{a+b x}{c+d x}\right)-2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(-2 A+3 B n+2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) \log (c+d x)}{12 (b c-a d)^3 g i^3}","\frac{b^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^3}{3 B g i^3 n (b c-a d)^3}+\frac{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}{2 g i^3 (c+d x)^2 (b c-a d)^3}-\frac{B d^2 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 i^3 (c+d x)^2 (b c-a d)^3}-\frac{2 b d (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g i^3 (c+d x) (b c-a d)^3}+\frac{4 A b B d n (a+b x)}{g i^3 (c+d x) (b c-a d)^3}+\frac{B^2 d^2 n^2 (a+b x)^2}{4 g i^3 (c+d x)^2 (b c-a d)^3}+\frac{4 b B^2 d n (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{g i^3 (c+d x) (b c-a d)^3}-\frac{4 b B^2 d n^2 (a+b x)}{g i^3 (c+d x) (b c-a d)^3}",1,"(4*b^2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^3 - (6*B*n*Log[(a + b*x)/(c + d*x)]^2*(-2*A*b^2*c^2 + 4*a*b*B*c*d*n - a^2*B*d^2*n - 4*A*b^2*c*d*x + 4*b^2*B*c*d*n*x + 2*a*b*B*d^2*n*x - 2*A*b^2*d^2*x^2 + 3*b^2*B*d^2*n*x^2 - 2*b^2*B*(c + d*x)^2*Log[e*((a + b*x)/(c + d*x))^n] + 2*b^2*B*n*(c + d*x)^2*Log[(a + b*x)/(c + d*x)]))/(c + d*x)^2 - (6*B*(b*c - a*d)*n*Log[(a + b*x)/(c + d*x)]*(-6*A*b*c + 2*a*A*d + 7*b*B*c*n - a*B*d*n - 4*A*b*d*x + 6*b*B*d*n*x + 2*B*(-3*b*c + a*d - 2*b*d*x)*Log[e*((a + b*x)/(c + d*x))^n] + 2*B*n*(3*b*c - a*d + 2*b*d*x)*Log[(a + b*x)/(c + d*x)]))/(c + d*x)^2 + (3*(b*c - a*d)^2*(2*A^2 - 2*A*B*n + B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 + 2*B*n*(-2*A + B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 - 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(-2*A + B*n + 2*B*n*Log[(a + b*x)/(c + d*x)])))/(c + d*x)^2 + (6*b*(b*c - a*d)*(2*A^2 - 6*A*B*n + 7*B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 + 2*B*n*(-2*A + 3*B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 - 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(-2*A + 3*B*n + 2*B*n*Log[(a + b*x)/(c + d*x)])))/(c + d*x) + 6*b^2*Log[a + b*x]*(2*A^2 - 6*A*B*n + 7*B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 + 2*B*n*(-2*A + 3*B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 - 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(-2*A + 3*B*n + 2*B*n*Log[(a + b*x)/(c + d*x)])) - 6*b^2*(2*A^2 - 6*A*B*n + 7*B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 + 2*B*n*(-2*A + 3*B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 - 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(-2*A + 3*B*n + 2*B*n*Log[(a + b*x)/(c + d*x)]))*Log[c + d*x])/(12*(b*c - a*d)^3*g*i^3)","B",1
207,1,1334,562,2.1519849,"\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 (c i+d i x)^3} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/((a*g + b*g*x)^2*(c*i + d*i*x)^3),x]","-\frac{4 b^2 B^2 d n^2 (a+b x) (c+d x)^2 \log ^3\left(\frac{a+b x}{c+d x}\right)+2 B n \left(6 A d^3 x^3 b^3-3 B d^3 n x^3 b^3+12 A c d^2 x^2 b^3+2 B c^3 n b^3+6 A c^2 d x b^3+6 B c^2 d n x b^3+6 a A d^3 x^2 b^2-9 a B d^3 n x^2 b^2+6 a A c^2 d b^2+12 a A c d^2 x b^2-12 a B c d^2 n x b^2+6 B d (a+b x) (c+d x)^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) b^2-6 B d n (a+b x) (c+d x)^2 \log \left(\frac{a+b x}{c+d x}\right) b^2-6 a^2 B c d^2 n b-3 a^2 B d^3 n x b+a^3 B d^3 n\right) \log ^2\left(\frac{a+b x}{c+d x}\right)+2 B (b c-a d) n \left(4 b^2 \left(A+B n+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)\right) (c+d x)^2+2 b d (a+b x) \left(4 A-5 B n+4 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-4 B n \log \left(\frac{a+b x}{c+d x}\right)\right) (c+d x)+d (b c-a d) (a+b x) \left(2 A-B n+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) \log \left(\frac{a+b x}{c+d x}\right)+4 b^2 (b c-a d) (c+d x)^2 \left(A^2+2 B n A+2 B^2 n^2+B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-2 B n (A+B n) \log \left(\frac{a+b x}{c+d x}\right)+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(A+B n-B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)+d (b c-a d)^2 (a+b x) \left(2 A^2-2 B n A+B^2 n^2+2 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)+2 B n (B n-2 A) \log \left(\frac{a+b x}{c+d x}\right)-2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(-2 A+B n+2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)+6 b^2 d (a+b x) (c+d x)^2 \log (a+b x) \left(2 A^2-2 B n A+5 B^2 n^2+2 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)+2 B n (B n-2 A) \log \left(\frac{a+b x}{c+d x}\right)-2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(-2 A+B n+2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)+2 b d (b c-a d) (a+b x) (c+d x) \left(4 A^2-10 B n A+11 B^2 n^2+4 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+4 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)+2 B n (5 B n-4 A) \log \left(\frac{a+b x}{c+d x}\right)-2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(-4 A+5 B n+4 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)-6 b^2 d (a+b x) (c+d x)^2 \left(2 A^2-2 B n A+5 B^2 n^2+2 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)+2 B n (B n-2 A) \log \left(\frac{a+b x}{c+d x}\right)-2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(-2 A+B n+2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) \log (c+d x)}{4 (b c-a d)^4 g^2 i^3 (a+b x) (c+d x)^2}","-\frac{b^3 (c+d x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g^2 i^3 (a+b x) (b c-a d)^4}-\frac{2 b^3 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 i^3 (a+b x) (b c-a d)^4}-\frac{b^2 d \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^3}{B g^2 i^3 n (b c-a d)^4}-\frac{d^3 (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^2 i^3 (c+d x)^2 (b c-a d)^4}+\frac{B d^3 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^2 i^3 (c+d x)^2 (b c-a d)^4}+\frac{3 b d^2 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g^2 i^3 (c+d x) (b c-a d)^4}-\frac{6 A b B d^2 n (a+b x)}{g^2 i^3 (c+d x) (b c-a d)^4}-\frac{2 b^3 B^2 n^2 (c+d x)}{g^2 i^3 (a+b x) (b c-a d)^4}-\frac{B^2 d^3 n^2 (a+b x)^2}{4 g^2 i^3 (c+d x)^2 (b c-a d)^4}-\frac{6 b B^2 d^2 n (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{g^2 i^3 (c+d x) (b c-a d)^4}+\frac{6 b B^2 d^2 n^2 (a+b x)}{g^2 i^3 (c+d x) (b c-a d)^4}",1,"-1/4*(4*b^2*B^2*d*n^2*(a + b*x)*(c + d*x)^2*Log[(a + b*x)/(c + d*x)]^3 + 2*B*n*Log[(a + b*x)/(c + d*x)]^2*(6*a*A*b^2*c^2*d + 2*b^3*B*c^3*n - 6*a^2*b*B*c*d^2*n + a^3*B*d^3*n + 6*A*b^3*c^2*d*x + 12*a*A*b^2*c*d^2*x + 6*b^3*B*c^2*d*n*x - 12*a*b^2*B*c*d^2*n*x - 3*a^2*b*B*d^3*n*x + 12*A*b^3*c*d^2*x^2 + 6*a*A*b^2*d^3*x^2 - 9*a*b^2*B*d^3*n*x^2 + 6*A*b^3*d^3*x^3 - 3*b^3*B*d^3*n*x^3 + 6*b^2*B*d*(a + b*x)*(c + d*x)^2*Log[e*((a + b*x)/(c + d*x))^n] - 6*b^2*B*d*n*(a + b*x)*(c + d*x)^2*Log[(a + b*x)/(c + d*x)]) + 4*b^2*(b*c - a*d)*(c + d*x)^2*(A^2 + 2*A*B*n + 2*B^2*n^2 + B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 2*B*n*(A + B*n)*Log[(a + b*x)/(c + d*x)] + B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(A + B*n - B*n*Log[(a + b*x)/(c + d*x)])) + 2*B*(b*c - a*d)*n*Log[(a + b*x)/(c + d*x)]*(2*b*d*(a + b*x)*(c + d*x)*(4*A - 5*B*n + 4*B*Log[e*((a + b*x)/(c + d*x))^n] - 4*B*n*Log[(a + b*x)/(c + d*x)]) + d*(b*c - a*d)*(a + b*x)*(2*A - B*n + 2*B*Log[e*((a + b*x)/(c + d*x))^n] - 2*B*n*Log[(a + b*x)/(c + d*x)]) + 4*b^2*(c + d*x)^2*(A + B*n + B*Log[e*((a + b*x)/(c + d*x))^n] - B*n*Log[(a + b*x)/(c + d*x)])) + d*(b*c - a*d)^2*(a + b*x)*(2*A^2 - 2*A*B*n + B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 + 2*B*n*(-2*A + B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 - 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(-2*A + B*n + 2*B*n*Log[(a + b*x)/(c + d*x)])) + 6*b^2*d*(a + b*x)*(c + d*x)^2*Log[a + b*x]*(2*A^2 - 2*A*B*n + 5*B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 + 2*B*n*(-2*A + B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 - 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(-2*A + B*n + 2*B*n*Log[(a + b*x)/(c + d*x)])) + 2*b*d*(b*c - a*d)*(a + b*x)*(c + d*x)*(4*A^2 - 10*A*B*n + 11*B^2*n^2 + 4*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 + 2*B*n*(-4*A + 5*B*n)*Log[(a + b*x)/(c + d*x)] + 4*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 - 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(-4*A + 5*B*n + 4*B*n*Log[(a + b*x)/(c + d*x)])) - 6*b^2*d*(a + b*x)*(c + d*x)^2*(2*A^2 - 2*A*B*n + 5*B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 + 2*B*n*(-2*A + B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 - 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(-2*A + B*n + 2*B*n*Log[(a + b*x)/(c + d*x)]))*Log[c + d*x])/((b*c - a*d)^4*g^2*i^3*(a + b*x)*(c + d*x)^2)","B",1
208,1,1653,732,2.6739042,"\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 (c i+d i x)^3} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/((a*g + b*g*x)^3*(c*i + d*i*x)^3),x]","\frac{8 b^2 B^2 d^2 n^2 (a+b x)^2 (c+d x)^2 \log ^3\left(\frac{a+b x}{c+d x}\right)+2 B n \left(12 A d^4 x^4 b^4+24 A c d^3 x^3 b^4+12 B c d^3 n x^3 b^4+12 A c^2 d^2 x^2 b^4+18 B c^2 d^2 n x^2 b^4-B c^4 n b^4+4 B c^3 d n x b^4+24 a A d^4 x^3 b^3-12 a B d^4 n x^3 b^3+48 a A c d^3 x^2 b^3+8 a B c^3 d n b^3+24 a A c^2 d^2 x b^3+24 a B c^2 d^2 n x b^3+12 a^2 A c^2 d^2 b^2+12 a^2 A d^4 x^2 b^2-18 a^2 B d^4 n x^2 b^2+24 a^2 A c d^3 x b^2-24 a^2 B c d^3 n x b^2+12 B d^2 (a+b x)^2 (c+d x)^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) b^2-12 B d^2 n (a+b x)^2 (c+d x)^2 \log \left(\frac{a+b x}{c+d x}\right) b^2-8 a^3 B c d^3 n b-4 a^3 B d^4 n x b+a^4 B d^4 n\right) \log ^2\left(\frac{a+b x}{c+d x}\right)+2 B (b c-a d) n \left(2 b d^2 (c+d x) \left(6 A-7 B n+6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-6 B n \log \left(\frac{a+b x}{c+d x}\right)\right) (a+b x)^2+d^2 (b c-a d) \left(2 A-B n+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-2 B n \log \left(\frac{a+b x}{c+d x}\right)\right) (a+b x)^2+2 b^2 d (c+d x)^2 \left(6 A+7 B n+6 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-6 B n \log \left(\frac{a+b x}{c+d x}\right)\right) (a+b x)-b^2 (b c-a d) (c+d x)^2 \left(2 A+B n+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right) \log \left(\frac{a+b x}{c+d x}\right)+12 b^2 d^2 (a+b x)^2 (c+d x)^2 \log (a+b x) \left(2 A^2+4 B \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right) A+5 B^2 n^2+2 B^2 \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)^2\right)+2 b^2 d (b c-a d) (a+b x) (c+d x)^2 \left(6 A^2+14 B n A+15 B^2 n^2+6 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+6 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-2 B n (6 A+7 B n) \log \left(\frac{a+b x}{c+d x}\right)+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(6 A+7 B n-6 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)-b^2 (b c-a d)^2 (c+d x)^2 \left(2 A^2+2 B n A+B^2 n^2+2 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)-2 B n (2 A+B n) \log \left(\frac{a+b x}{c+d x}\right)+2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(2 A+B n-2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)+d^2 (b c-a d)^2 (a+b x)^2 \left(2 A^2-2 B n A+B^2 n^2+2 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)+2 B n (B n-2 A) \log \left(\frac{a+b x}{c+d x}\right)-2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(-2 A+B n+2 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)+2 b d^2 (b c-a d) (a+b x)^2 (c+d x) \left(6 A^2-14 B n A+15 B^2 n^2+6 B^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+6 B^2 n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)+2 B n (7 B n-6 A) \log \left(\frac{a+b x}{c+d x}\right)-2 B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \left(-6 A+7 B n+6 B n \log \left(\frac{a+b x}{c+d x}\right)\right)\right)-12 b^2 d^2 (a+b x)^2 (c+d x)^2 \left(2 A^2+4 B \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right) A+5 B^2 n^2+2 B^2 \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)^2\right) \log (c+d x)}{4 (b c-a d)^5 g^3 i^3 (a+b x)^2 (c+d x)^2}","-\frac{b^4 (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 i^3 (a+b x)^2 (b c-a d)^5}-\frac{b^4 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 i^3 (a+b x)^2 (b c-a d)^5}+\frac{4 b^3 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 i^3 (a+b x) (b c-a d)^5}+\frac{8 b^3 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 i^3 (a+b x) (b c-a d)^5}+\frac{2 b^2 d^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^3}{B g^3 i^3 n (b c-a d)^5}+\frac{d^4 (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 i^3 (c+d x)^2 (b c-a d)^5}-\frac{B d^4 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 i^3 (c+d x)^2 (b c-a d)^5}-\frac{4 b d^3 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{g^3 i^3 (c+d x) (b c-a d)^5}+\frac{8 A b B d^3 n (a+b x)}{g^3 i^3 (c+d x) (b c-a d)^5}-\frac{b^4 B^2 n^2 (c+d x)^2}{4 g^3 i^3 (a+b x)^2 (b c-a d)^5}+\frac{8 b^3 B^2 d n^2 (c+d x)}{g^3 i^3 (a+b x) (b c-a d)^5}+\frac{B^2 d^4 n^2 (a+b x)^2}{4 g^3 i^3 (c+d x)^2 (b c-a d)^5}+\frac{8 b B^2 d^3 n (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{g^3 i^3 (c+d x) (b c-a d)^5}-\frac{8 b B^2 d^3 n^2 (a+b x)}{g^3 i^3 (c+d x) (b c-a d)^5}",1,"(8*b^2*B^2*d^2*n^2*(a + b*x)^2*(c + d*x)^2*Log[(a + b*x)/(c + d*x)]^3 + 2*B*n*Log[(a + b*x)/(c + d*x)]^2*(12*a^2*A*b^2*c^2*d^2 - b^4*B*c^4*n + 8*a*b^3*B*c^3*d*n - 8*a^3*b*B*c*d^3*n + a^4*B*d^4*n + 24*a*A*b^3*c^2*d^2*x + 24*a^2*A*b^2*c*d^3*x + 4*b^4*B*c^3*d*n*x + 24*a*b^3*B*c^2*d^2*n*x - 24*a^2*b^2*B*c*d^3*n*x - 4*a^3*b*B*d^4*n*x + 12*A*b^4*c^2*d^2*x^2 + 48*a*A*b^3*c*d^3*x^2 + 12*a^2*A*b^2*d^4*x^2 + 18*b^4*B*c^2*d^2*n*x^2 - 18*a^2*b^2*B*d^4*n*x^2 + 24*A*b^4*c*d^3*x^3 + 24*a*A*b^3*d^4*x^3 + 12*b^4*B*c*d^3*n*x^3 - 12*a*b^3*B*d^4*n*x^3 + 12*A*b^4*d^4*x^4 + 12*b^2*B*d^2*(a + b*x)^2*(c + d*x)^2*Log[e*((a + b*x)/(c + d*x))^n] - 12*b^2*B*d^2*n*(a + b*x)^2*(c + d*x)^2*Log[(a + b*x)/(c + d*x)]) + 12*b^2*d^2*(a + b*x)^2*(c + d*x)^2*Log[a + b*x]*(2*A^2 + 5*B^2*n^2 + 4*A*B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + 2*B^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2) + 2*b^2*d*(b*c - a*d)*(a + b*x)*(c + d*x)^2*(6*A^2 + 14*A*B*n + 15*B^2*n^2 + 6*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 2*B*n*(6*A + 7*B*n)*Log[(a + b*x)/(c + d*x)] + 6*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(6*A + 7*B*n - 6*B*n*Log[(a + b*x)/(c + d*x)])) - b^2*(b*c - a*d)^2*(c + d*x)^2*(2*A^2 + 2*A*B*n + B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 2*B*n*(2*A + B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(2*A + B*n - 2*B*n*Log[(a + b*x)/(c + d*x)])) + 2*B*(b*c - a*d)*n*Log[(a + b*x)/(c + d*x)]*(2*b*d^2*(a + b*x)^2*(c + d*x)*(6*A - 7*B*n + 6*B*Log[e*((a + b*x)/(c + d*x))^n] - 6*B*n*Log[(a + b*x)/(c + d*x)]) + 2*b^2*d*(a + b*x)*(c + d*x)^2*(6*A + 7*B*n + 6*B*Log[e*((a + b*x)/(c + d*x))^n] - 6*B*n*Log[(a + b*x)/(c + d*x)]) + d^2*(b*c - a*d)*(a + b*x)^2*(2*A - B*n + 2*B*Log[e*((a + b*x)/(c + d*x))^n] - 2*B*n*Log[(a + b*x)/(c + d*x)]) - b^2*(b*c - a*d)*(c + d*x)^2*(2*A + B*n + 2*B*Log[e*((a + b*x)/(c + d*x))^n] - 2*B*n*Log[(a + b*x)/(c + d*x)])) + d^2*(b*c - a*d)^2*(a + b*x)^2*(2*A^2 - 2*A*B*n + B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 + 2*B*n*(-2*A + B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 - 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(-2*A + B*n + 2*B*n*Log[(a + b*x)/(c + d*x)])) + 2*b*d^2*(b*c - a*d)*(a + b*x)^2*(c + d*x)*(6*A^2 - 14*A*B*n + 15*B^2*n^2 + 6*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 + 2*B*n*(-6*A + 7*B*n)*Log[(a + b*x)/(c + d*x)] + 6*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 - 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(-6*A + 7*B*n + 6*B*n*Log[(a + b*x)/(c + d*x)])) - 12*b^2*d^2*(a + b*x)^2*(c + d*x)^2*(2*A^2 + 5*B^2*n^2 + 4*A*B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]) + 2*B^2*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2)*Log[c + d*x])/(4*(b*c - a*d)^5*g^3*i^3*(a + b*x)^2*(c + d*x)^2)","B",1
209,1,2138,908,4.2452847,"\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 (c i+d i x)^3} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2/((a*g + b*g*x)^4*(c*i + d*i*x)^3),x]","\text{Result too large to show}","-\frac{2 B^2 n^2 (c+d x)^3 b^5}{27 (b c-a d)^6 g^4 i^3 (a+b x)^3}-\frac{(c+d x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 b^5}{3 (b c-a d)^6 g^4 i^3 (a+b x)^3}-\frac{2 B n (c+d x)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) b^5}{9 (b c-a d)^6 g^4 i^3 (a+b x)^3}+\frac{5 B^2 d n^2 (c+d x)^2 b^4}{4 (b c-a d)^6 g^4 i^3 (a+b x)^2}+\frac{5 d (c+d x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 b^4}{2 (b c-a d)^6 g^4 i^3 (a+b x)^2}+\frac{5 B d n (c+d x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) b^4}{2 (b c-a d)^6 g^4 i^3 (a+b x)^2}-\frac{10 d^2 (c+d x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 b^3}{(b c-a d)^6 g^4 i^3 (a+b x)}-\frac{20 B^2 d^2 n^2 (c+d x) b^3}{(b c-a d)^6 g^4 i^3 (a+b x)}-\frac{20 B d^2 n (c+d x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) b^3}{(b c-a d)^6 g^4 i^3 (a+b x)}-\frac{10 d^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^3 b^2}{3 B (b c-a d)^6 g^4 i^3 n}+\frac{5 d^4 (a+b x) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2 b}{(b c-a d)^6 g^4 i^3 (c+d x)}-\frac{10 B^2 d^4 n (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) b}{(b c-a d)^6 g^4 i^3 (c+d x)}+\frac{10 B^2 d^4 n^2 (a+b x) b}{(b c-a d)^6 g^4 i^3 (c+d x)}-\frac{10 A B d^4 n (a+b x) b}{(b c-a d)^6 g^4 i^3 (c+d x)}-\frac{d^5 (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2}{2 (b c-a d)^6 g^4 i^3 (c+d x)^2}+\frac{B d^5 n (a+b x)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{2 (b c-a d)^6 g^4 i^3 (c+d x)^2}-\frac{B^2 d^5 n^2 (a+b x)^2}{4 (b c-a d)^6 g^4 i^3 (c+d x)^2}",1,"-1/108*(360*b^2*B^2*d^3*n^2*(a + b*x)^3*(c + d*x)^2*Log[(a + b*x)/(c + d*x)]^3 + 18*B*n*Log[(a + b*x)/(c + d*x)]^2*(60*a^3*A*b^2*c^2*d^3 + 2*b^5*B*c^5*n - 15*a*b^4*B*c^4*d*n + 60*a^2*b^3*B*c^3*d^2*n - 30*a^4*b*B*c*d^4*n + 3*a^5*B*d^5*n + 180*a^2*A*b^3*c^2*d^3*x + 120*a^3*A*b^2*c*d^4*x - 5*b^5*B*c^4*d*n*x + 60*a*b^4*B*c^3*d^2*n*x + 180*a^2*b^3*B*c^2*d^3*n*x - 120*a^3*b^2*B*c*d^4*n*x - 15*a^4*b*B*d^5*n*x + 180*a*A*b^4*c^2*d^3*x^2 + 360*a^2*A*b^3*c*d^4*x^2 + 60*a^3*A*b^2*d^5*x^2 + 20*b^5*B*c^3*d^2*n*x^2 + 270*a*b^4*B*c^2*d^3*n*x^2 - 90*a^3*b^2*B*d^5*n*x^2 + 60*A*b^5*c^2*d^3*x^3 + 360*a*A*b^4*c*d^4*x^3 + 180*a^2*A*b^3*d^5*x^3 + 110*b^5*B*c^2*d^3*n*x^3 + 180*a*b^4*B*c*d^4*n*x^3 - 90*a^2*b^3*B*d^5*n*x^3 + 120*A*b^5*c*d^4*x^4 + 180*a*A*b^4*d^5*x^4 + 100*b^5*B*c*d^4*n*x^4 + 60*A*b^5*d^5*x^5 + 20*b^5*B*d^5*n*x^5 + 60*b^2*B*d^3*(a + b*x)^3*(c + d*x)^2*Log[e*((a + b*x)/(c + d*x))^n] - 60*b^2*B*d^3*n*(a + b*x)^3*(c + d*x)^2*Log[(a + b*x)/(c + d*x)]) + 6*b^2*d^2*(b*c - a*d)*(a + b*x)^2*(c + d*x)^2*(108*A^2 + 282*A*B*n + 319*B^2*n^2 + 108*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 6*B*n*(36*A + 47*B*n)*Log[(a + b*x)/(c + d*x)] + 108*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 6*B*Log[e*((a + b*x)/(c + d*x))^n]*(36*A + 47*B*n - 36*B*n*Log[(a + b*x)/(c + d*x)])) - 3*b^2*d*(b*c - a*d)^2*(a + b*x)*(c + d*x)^2*(54*A^2 + 66*A*B*n + 37*B^2*n^2 + 54*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 6*B*n*(18*A + 11*B*n)*Log[(a + b*x)/(c + d*x)] + 54*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 6*B*Log[e*((a + b*x)/(c + d*x))^n]*(18*A + 11*B*n - 18*B*n*Log[(a + b*x)/(c + d*x)])) + 4*b^2*(b*c - a*d)^3*(c + d*x)^2*(9*A^2 + 6*A*B*n + 2*B^2*n^2 + 9*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 6*B*n*(3*A + B*n)*Log[(a + b*x)/(c + d*x)] + 9*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 6*B*Log[e*((a + b*x)/(c + d*x))^n]*(3*A + B*n - 3*B*n*Log[(a + b*x)/(c + d*x)])) + 60*b^2*d^3*(a + b*x)^3*(c + d*x)^2*Log[a + b*x]*(18*A^2 + 12*A*B*n + 49*B^2*n^2 + 18*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 12*B*n*(3*A + B*n)*Log[(a + b*x)/(c + d*x)] + 18*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 12*B*Log[e*((a + b*x)/(c + d*x))^n]*(3*A + B*n - 3*B*n*Log[(a + b*x)/(c + d*x)])) + 27*d^3*(b*c - a*d)^2*(a + b*x)^3*(2*A^2 - 2*A*B*n + B^2*n^2 + 2*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 + 2*B*n*(-2*A + B*n)*Log[(a + b*x)/(c + d*x)] + 2*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 - 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(-2*A + B*n + 2*B*n*Log[(a + b*x)/(c + d*x)])) + 54*b*d^3*(b*c - a*d)*(a + b*x)^3*(c + d*x)*(8*A^2 - 18*A*B*n + 19*B^2*n^2 + 8*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 + 2*B*n*(-8*A + 9*B*n)*Log[(a + b*x)/(c + d*x)] + 8*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 - 2*B*Log[e*((a + b*x)/(c + d*x))^n]*(-8*A + 9*B*n + 8*B*n*Log[(a + b*x)/(c + d*x)])) + 6*B*(b*c - a*d)*n*Log[(a + b*x)/(c + d*x)]*(18*b*d^3*(a + b*x)^3*(c + d*x)*(8*A - 9*B*n + 8*B*Log[e*((a + b*x)/(c + d*x))^n] - 8*B*n*Log[(a + b*x)/(c + d*x)]) + 4*b^2*(b*c - a*d)^2*(c + d*x)^2*(3*A + B*n + 3*B*Log[e*((a + b*x)/(c + d*x))^n] - 3*B*n*Log[(a + b*x)/(c + d*x)]) + 9*d^3*(b*c - a*d)*(a + b*x)^3*(2*A - B*n + 2*B*Log[e*((a + b*x)/(c + d*x))^n] - 2*B*n*Log[(a + b*x)/(c + d*x)]) - 3*b^2*d*(b*c - a*d)*(a + b*x)*(c + d*x)^2*(18*A + 11*B*n + 18*B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])) + 6*b^2*d^2*(a + b*x)^2*(c + d*x)^2*(36*A + 47*B*n + 36*B*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)]))) - 60*b^2*d^3*(a + b*x)^3*(c + d*x)^2*(18*A^2 + 12*A*B*n + 49*B^2*n^2 + 18*B^2*Log[e*((a + b*x)/(c + d*x))^n]^2 - 12*B*n*(3*A + B*n)*Log[(a + b*x)/(c + d*x)] + 18*B^2*n^2*Log[(a + b*x)/(c + d*x)]^2 + 12*B*Log[e*((a + b*x)/(c + d*x))^n]*(3*A + B*n - 3*B*n*Log[(a + b*x)/(c + d*x)]))*Log[c + d*x])/((b*c - a*d)^6*g^4*i^3*(a + b*x)^3*(c + d*x)^2)","B",1
210,0,0,189,0.5532437,"\int (a g+b g x)^m (c i+d i x)^{-2-m} \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^p \, dx","Integrate[(a*g + b*g*x)^m*(c*i + d*i*x)^(-2 - m)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^p,x]","\int (a g+b g x)^m (c i+d i x)^{-2-m} \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^p \, dx","\frac{(a+b x) e^{-\frac{A (m+1)}{B n}} (g (a+b x))^m (i (c+d x))^{-m} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-\frac{m+1}{n}} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^p \left(-\frac{(m+1) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{B n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+1) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{B n}\right)}{i^2 (m+1) (c+d x) (b c-a d)}",1,"Integrate[(a*g + b*g*x)^m*(c*i + d*i*x)^(-2 - m)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^p, x]","F",-1
211,0,0,190,0.573951,"\int (a g+b g x)^{-2-m} (c i+d i x)^m \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^p \, dx","Integrate[(a*g + b*g*x)^(-2 - m)*(c*i + d*i*x)^m*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^p,x]","\int (a g+b g x)^{-2-m} (c i+d i x)^m \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^p \, dx","-\frac{(a+b x) e^{\frac{A (m+1)}{B n}} (g (a+b x))^{-m-2} (i (c+d x))^{m+2} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{\frac{m+1}{n}} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^p \left(\frac{(m+1) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{B n}\right)^{-p} \Gamma \left(p+1,\frac{(m+1) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{B n}\right)}{i^2 (m+1) (c+d x) (b c-a d)}",1,"Integrate[(a*g + b*g*x)^(-2 - m)*(c*i + d*i*x)^m*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^p, x]","F",-1
212,1,206,292,6.9550443,"\int (a g+b g x)^m (c i+d i x)^{-2-m} \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^3 \, dx","Integrate[(a*g + b*g*x)^m*(c*i + d*i*x)^(-2 - m)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^3,x]","\frac{(a+b x) (g (a+b x))^m (i (c+d x))^{-m-1} \left(3 B (m+1) \left(A^2 (m+1)^2-2 A B (m+1) n+2 B^2 n^2\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+3 B^2 (m+1)^2 (A m+A-B n) \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B^3 (m+1)^3 \log ^3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A^3 (m+1)^3-3 A^2 B (m+1)^2 n+6 A B^2 (m+1) n^2-6 B^3 n^3\right)}{i (m+1)^4 (b c-a d)}","\frac{6 B^2 n^2 (a+b x) (g (a+b x))^m (i (c+d x))^{-m} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{i^2 (m+1)^3 (c+d x) (b c-a d)}+\frac{(a+b x) (g (a+b x))^m (i (c+d x))^{-m} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^3}{i^2 (m+1) (c+d x) (b c-a d)}-\frac{3 B n (a+b x) (g (a+b x))^m (i (c+d x))^{-m} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{i^2 (m+1)^2 (c+d x) (b c-a d)}-\frac{6 B^3 n^3 (a+b x) (g (a+b x))^m (i (c+d x))^{-m}}{i^2 (m+1)^4 (c+d x) (b c-a d)}",1,"((a + b*x)*(g*(a + b*x))^m*(i*(c + d*x))^(-1 - m)*(A^3*(1 + m)^3 - 3*A^2*B*(1 + m)^2*n + 6*A*B^2*(1 + m)*n^2 - 6*B^3*n^3 + 3*B*(1 + m)*(A^2*(1 + m)^2 - 2*A*B*(1 + m)*n + 2*B^2*n^2)*Log[e*((a + b*x)/(c + d*x))^n] + 3*B^2*(1 + m)^2*(A + A*m - B*n)*Log[e*((a + b*x)/(c + d*x))^n]^2 + B^3*(1 + m)^3*Log[e*((a + b*x)/(c + d*x))^n]^3))/((b*c - a*d)*i*(1 + m)^4)","A",1
213,1,134,210,2.0159578,"\int (a g+b g x)^m (c i+d i x)^{-2-m} \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)^m*(c*i + d*i*x)^(-2 - m)*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\frac{(a+b x) (g (a+b x))^m (i (c+d x))^{-m-1} \left(2 B (m+1) (A m+A-B n) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B^2 (m+1)^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A^2 (m+1)^2-2 A B (m+1) n+2 B^2 n^2\right)}{i (m+1)^3 (b c-a d)}","\frac{(a+b x) (g (a+b x))^m (i (c+d x))^{-m} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{i^2 (m+1) (c+d x) (b c-a d)}-\frac{2 B n (a+b x) (g (a+b x))^m (i (c+d x))^{-m} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{i^2 (m+1)^2 (c+d x) (b c-a d)}+\frac{2 B^2 n^2 (a+b x) (g (a+b x))^m (i (c+d x))^{-m}}{i^2 (m+1)^3 (c+d x) (b c-a d)}",1,"((a + b*x)*(g*(a + b*x))^m*(i*(c + d*x))^(-1 - m)*(A^2*(1 + m)^2 - 2*A*B*(1 + m)*n + 2*B^2*n^2 + 2*B*(1 + m)*(A + A*m - B*n)*Log[e*((a + b*x)/(c + d*x))^n] + B^2*(1 + m)^2*Log[e*((a + b*x)/(c + d*x))^n]^2))/((b*c - a*d)*i*(1 + m)^3)","A",1
214,1,78,128,0.5185044,"\int (a g+b g x)^m (c i+d i x)^{-2-m} \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)^m*(c*i + d*i*x)^(-2 - m)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{(a+b x) (g (a+b x))^m (i (c+d x))^{-m-1} \left(B (m+1) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A m+A-B n\right)}{i (m+1)^2 (b c-a d)}","\frac{(a+b x) (g (a+b x))^m (i (c+d x))^{-m} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{i^2 (m+1) (c+d x) (b c-a d)}-\frac{B n (a+b x) (g (a+b x))^m (i (c+d x))^{-m}}{i^2 (m+1)^2 (c+d x) (b c-a d)}",1,"((a + b*x)*(g*(a + b*x))^m*(i*(c + d*x))^(-1 - m)*(A + A*m - B*n + B*(1 + m)*Log[e*((a + b*x)/(c + d*x))^n]))/((b*c - a*d)*i*(1 + m)^2)","A",1
215,0,0,125,0.2470917,"\int \frac{(a g+b g x)^m (c i+d i x)^{-2-m}}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Integrate[((a*g + b*g*x)^m*(c*i + d*i*x)^(-2 - m))/(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\int \frac{(a g+b g x)^m (c i+d i x)^{-2-m}}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","\frac{(a+b x) e^{-\frac{A (m+1)}{B n}} (g (a+b x))^m (i (c+d x))^{-m} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-\frac{m+1}{n}} \text{Ei}\left(\frac{(m+1) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{B n}\right)}{B i^2 n (c+d x) (b c-a d)}",1,"Integrate[((a*g + b*g*x)^m*(c*i + d*i*x)^(-2 - m))/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x]","F",-1
216,0,0,206,0.276252,"\int \frac{(a g+b g x)^m (c i+d i x)^{-2-m}}{\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)^m*(c*i + d*i*x)^(-2 - m))/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\int \frac{(a g+b g x)^m (c i+d i x)^{-2-m}}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","\frac{(m+1) (a+b x) e^{-\frac{A (m+1)}{B n}} (g (a+b x))^m (i (c+d x))^{-m} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-\frac{m+1}{n}} \text{Ei}\left(\frac{(m+1) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{B n}\right)}{B^2 i^2 n^2 (c+d x) (b c-a d)}-\frac{(a+b x) (g (a+b x))^m (i (c+d x))^{-m}}{B i^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,"Integrate[((a*g + b*g*x)^m*(c*i + d*i*x)^(-2 - m))/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x]","F",-1
217,0,0,295,0.335015,"\int \frac{(a g+b g x)^m (c i+d i x)^{-2-m}}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^3} \, dx","Integrate[((a*g + b*g*x)^m*(c*i + d*i*x)^(-2 - m))/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^3,x]","\int \frac{(a g+b g x)^m (c i+d i x)^{-2-m}}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^3} \, dx","\frac{(m+1)^2 (a+b x) e^{-\frac{A (m+1)}{B n}} (g (a+b x))^m (i (c+d x))^{-m} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-\frac{m+1}{n}} \text{Ei}\left(\frac{(m+1) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{B n}\right)}{2 B^3 i^2 n^3 (c+d x) (b c-a d)}-\frac{(m+1) (a+b x) (g (a+b x))^m (i (c+d x))^{-m}}{2 B^2 i^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) (g (a+b x))^m (i (c+d x))^{-m}}{2 B i^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)^2}",1,"Integrate[((a*g + b*g*x)^m*(c*i + d*i*x)^(-2 - m))/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^3, x]","F",-1
218,1,206,309,7.1808615,"\int (a g+b g x)^{-2-m} (c i+d i x)^m \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^3 \, dx","Integrate[(a*g + b*g*x)^(-2 - m)*(c*i + d*i*x)^m*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^3,x]","-\frac{(c+d x) (g (a+b x))^{-m-1} (i (c+d x))^m \left(3 B (m+1) \left(A^2 (m+1)^2+2 A B (m+1) n+2 B^2 n^2\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+3 B^2 (m+1)^2 (A m+A+B n) \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B^3 (m+1)^3 \log ^3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A^3 (m+1)^3+3 A^2 B (m+1)^2 n+6 A B^2 (m+1) n^2+6 B^3 n^3\right)}{g (m+1)^4 (b c-a d)}","-\frac{6 B^2 n^2 (a+b x) (g (a+b x))^{-m-2} (i (c+d x))^{m+2} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{i^2 (m+1)^3 (c+d x) (b c-a d)}-\frac{(a+b x) (g (a+b x))^{-m-2} (i (c+d x))^{m+2} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^3}{i^2 (m+1) (c+d x) (b c-a d)}-\frac{3 B n (a+b x) (g (a+b x))^{-m-2} (i (c+d x))^{m+2} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{i^2 (m+1)^2 (c+d x) (b c-a d)}-\frac{6 B^3 n^3 (a+b x) (g (a+b x))^{-m-2} (i (c+d x))^{m+2}}{i^2 (m+1)^4 (c+d x) (b c-a d)}",1,"-(((g*(a + b*x))^(-1 - m)*(c + d*x)*(i*(c + d*x))^m*(A^3*(1 + m)^3 + 3*A^2*B*(1 + m)^2*n + 6*A*B^2*(1 + m)*n^2 + 6*B^3*n^3 + 3*B*(1 + m)*(A^2*(1 + m)^2 + 2*A*B*(1 + m)*n + 2*B^2*n^2)*Log[e*((a + b*x)/(c + d*x))^n] + 3*B^2*(1 + m)^2*(A + A*m + B*n)*Log[e*((a + b*x)/(c + d*x))^n]^2 + B^3*(1 + m)^3*Log[e*((a + b*x)/(c + d*x))^n]^3))/((b*c - a*d)*g*(1 + m)^4))","A",1
219,1,134,223,2.0910767,"\int (a g+b g x)^{-2-m} (c i+d i x)^m \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 - m)*(c*i + d*i*x)^m*(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","-\frac{(c+d x) (g (a+b x))^{-m-1} (i (c+d x))^m \left(2 B (m+1) (A m+A+B n) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+B^2 (m+1)^2 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A^2 (m+1)^2+2 A B (m+1) n+2 B^2 n^2\right)}{g (m+1)^3 (b c-a d)}","-\frac{(a+b x) (g (a+b x))^{-m-2} (i (c+d x))^{m+2} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2}{i^2 (m+1) (c+d x) (b c-a d)}-\frac{2 B n (a+b x) (g (a+b x))^{-m-2} (i (c+d x))^{m+2} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{i^2 (m+1)^2 (c+d x) (b c-a d)}-\frac{2 B^2 n^2 (a+b x) (g (a+b x))^{-m-2} (i (c+d x))^{m+2}}{i^2 (m+1)^3 (c+d x) (b c-a d)}",1,"-(((g*(a + b*x))^(-1 - m)*(c + d*x)*(i*(c + d*x))^m*(A^2*(1 + m)^2 + 2*A*B*(1 + m)*n + 2*B^2*n^2 + 2*B*(1 + m)*(A + A*m + B*n)*Log[e*((a + b*x)/(c + d*x))^n] + B^2*(1 + m)^2*Log[e*((a + b*x)/(c + d*x))^n]^2))/((b*c - a*d)*g*(1 + m)^3))","A",1
220,1,78,137,0.5272099,"\int (a g+b g x)^{-2-m} (c i+d i x)^m \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 - m)*(c*i + d*i*x)^m*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","-\frac{(c+d x) (g (a+b x))^{-m-1} (i (c+d x))^m \left(B (m+1) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A m+A+B n\right)}{g (m+1)^2 (b c-a d)}","-\frac{(a+b x) (g (a+b x))^{-m-2} (i (c+d x))^{m+2} \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{i^2 (m+1) (c+d x) (b c-a d)}-\frac{B n (a+b x) (g (a+b x))^{-m-2} (i (c+d x))^{m+2}}{i^2 (m+1)^2 (c+d x) (b c-a d)}",1,"-(((g*(a + b*x))^(-1 - m)*(c + d*x)*(i*(c + d*x))^m*(A + A*m + B*n + B*(1 + m)*Log[e*((a + b*x)/(c + d*x))^n]))/((b*c - a*d)*g*(1 + m)^2))","A",1
221,0,0,128,0.249215,"\int \frac{(a g+b g x)^{-2-m} (c i+d i x)^m}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Integrate[((a*g + b*g*x)^(-2 - m)*(c*i + d*i*x)^m)/(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\int \frac{(a g+b g x)^{-2-m} (c i+d i x)^m}{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","\frac{(a+b x) e^{\frac{A (m+1)}{B n}} (g (a+b x))^{-m-2} (i (c+d x))^{m+2} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{\frac{m+1}{n}} \text{Ei}\left(-\frac{(m+1) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{B n}\right)}{B i^2 n (c+d x) (b c-a d)}",1,"Integrate[((a*g + b*g*x)^(-2 - m)*(c*i + d*i*x)^m)/(A + B*Log[e*((a + b*x)/(c + d*x))^n]), x]","F",-1
222,0,0,214,0.2738778,"\int \frac{(a g+b g x)^{-2-m} (c i+d i x)^m}{\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 - m)*(c*i + d*i*x)^m)/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2,x]","\int \frac{(a g+b g x)^{-2-m} (c i+d i x)^m}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^2} \, dx","-\frac{(m+1) (a+b x) e^{\frac{A (m+1)}{B n}} (g (a+b x))^{-m-2} (i (c+d x))^{m+2} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{\frac{m+1}{n}} \text{Ei}\left(-\frac{(m+1) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{B n}\right)}{B^2 i^2 n^2 (c+d x) (b c-a d)}-\frac{(a+b x) (g (a+b x))^{-m-2} (i (c+d x))^{m+2}}{B i^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,"Integrate[((a*g + b*g*x)^(-2 - m)*(c*i + d*i*x)^m)/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^2, x]","F",-1
223,0,0,306,0.3348852,"\int \frac{(a g+b g x)^{-2-m} (c i+d i x)^m}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^3} \, dx","Integrate[((a*g + b*g*x)^(-2 - m)*(c*i + d*i*x)^m)/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^3,x]","\int \frac{(a g+b g x)^{-2-m} (c i+d i x)^m}{\left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)^3} \, dx","\frac{(m+1)^2 (a+b x) e^{\frac{A (m+1)}{B n}} (g (a+b x))^{-m-2} (i (c+d x))^{m+2} \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{\frac{m+1}{n}} \text{Ei}\left(-\frac{(m+1) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{B n}\right)}{2 B^3 i^2 n^3 (c+d x) (b c-a d)}+\frac{(m+1) (a+b x) (g (a+b x))^{-m-2} (i (c+d x))^{m+2}}{2 B^2 i^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) (g (a+b x))^{-m-2} (i (c+d x))^{m+2}}{2 B i^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)^2}",1,"Integrate[((a*g + b*g*x)^(-2 - m)*(c*i + d*i*x)^m)/(A + B*Log[e*((a + b*x)/(c + d*x))^n])^3, x]","F",-1
224,1,40,41,0.0280161,"\int \frac{\log ^p\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a+b x) (c+d x)} \, dx","Integrate[Log[e*((a + b*x)/(c + d*x))^n]^p/((a + b*x)*(c + d*x)),x]","\frac{\log ^{p+1}\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(p+1) (b c n-a d n)}","\frac{\log ^{p+1}\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n (p+1) (b c-a d)}",1,"Log[e*((a + b*x)/(c + d*x))^n]^(1 + p)/((b*c*n - a*d*n)*(1 + p))","A",1
225,1,40,41,0.01227,"\int \frac{\log ^p\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{a c+(b c+a d) x+b d x^2} \, dx","Integrate[Log[e*((a + b*x)/(c + d*x))^n]^p/(a*c + (b*c + a*d)*x + b*d*x^2),x]","\frac{\log ^{p+1}\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(p+1) (b c n-a d n)}","\frac{\log ^{p+1}\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n (p+1) (b c-a d)}",1,"Log[e*((a + b*x)/(c + d*x))^n]^(1 + p)/((b*c*n - a*d*n)*(1 + p))","A",1
226,0,0,193,0.4452432,"\int (a g+b g x)^m (c i+d i x)^{-2-m} \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^p \, dx","Integrate[(a*g + b*g*x)^m*(c*i + d*i*x)^(-2 - m)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^p,x]","\int (a g+b g x)^m (c i+d i x)^{-2-m} \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^p \, dx","\frac{(a+b x) e^{-\frac{A (m+1)}{B n}} (g (a+b x))^m (i (c+d x))^{-m} \left(e (a+b x)^n (c+d x)^{-n}\right)^{-\frac{m+1}{n}} \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^p \left(-\frac{(m+1) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{B n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+1) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)}{B n}\right)}{i^2 (m+1) (c+d x) (b c-a d)}",1,"Integrate[(a*g + b*g*x)^m*(c*i + d*i*x)^(-2 - m)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^p, x]","F",-1
227,0,0,194,0.406398,"\int (a g+b g x)^{-2-m} (c i+d i x)^m \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^p \, dx","Integrate[(a*g + b*g*x)^(-2 - m)*(c*i + d*i*x)^m*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^p,x]","\int (a g+b g x)^{-2-m} (c i+d i x)^m \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^p \, dx","-\frac{(a+b x) e^{\frac{A (m+1)}{B n}} (g (a+b x))^{-m-2} (i (c+d x))^{m+2} \left(e (a+b x)^n (c+d x)^{-n}\right)^{\frac{m+1}{n}} \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^p \left(\frac{(m+1) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{B n}\right)^{-p} \Gamma \left(p+1,\frac{(m+1) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)}{B n}\right)}{i^2 (m+1) (c+d x) (b c-a d)}",1,"Integrate[(a*g + b*g*x)^(-2 - m)*(c*i + d*i*x)^m*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^p, x]","F",-1
228,1,43,45,0.0207022,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(a+b x) (c+d x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/((a + b*x)*(c + d*x)),x]","\frac{\left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^4}{4 (b B c n-a B d n)}","\frac{\left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^4}{4 B n (b c-a d)}",1,"(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^4/(4*(b*B*c*n - a*B*d*n))","A",1
229,1,43,45,0.0166505,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{(a+b x) (c+d x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/((a + b*x)*(c + d*x)),x]","\frac{\left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{3 (b B c n-a B d n)}","\frac{\left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{3 B n (b c-a d)}",1,"(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(3*(b*B*c*n - a*B*d*n))","A",1
230,1,43,45,0.0131159,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(a+b x) (c+d x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((a + b*x)*(c + d*x)),x]","\frac{\left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 (b B c n-a B d n)}","\frac{\left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{2 B n (b c-a d)}",1,"(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(2*(b*B*c*n - a*B*d*n))","A",1
231,1,39,41,0.0926236,"\int \frac{1}{(a+b x) (c+d x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)} \, dx","Integrate[1/((a + b*x)*(c + d*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])),x]","\frac{\log \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b B c n-a B d n}","\frac{\log \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{B n (b c-a d)}",1,"Log[A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]]/(b*B*c*n - a*B*d*n)","A",1
232,1,41,43,0.0220186,"\int \frac{1}{(a+b x) (c+d x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2} \, dx","Integrate[1/((a + b*x)*(c + d*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2),x]","-\frac{1}{(b B c n-a B d n) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}","-\frac{1}{B n (b c-a d) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}",1,"-(1/((b*B*c*n - a*B*d*n)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])))","A",1
233,1,43,45,0.0205714,"\int \frac{1}{(a+b x) (c+d x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3} \, dx","Integrate[1/((a + b*x)*(c + d*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3),x]","-\frac{1}{2 (b B c n-a B d n) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}","-\frac{1}{2 B n (b c-a d) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}",1,"-1/2*1/((b*B*c*n - a*B*d*n)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2)","A",1
234,1,47,49,0.0294953,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^p}{(a+b x) (c+d x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^p/((a + b*x)*(c + d*x)),x]","\frac{\left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^{p+1}}{(p+1) (b B c n-a B d n)}","\frac{\left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^{p+1}}{B n (p+1) (b c-a d)}",1,"(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^(1 + p)/((b*B*c*n - a*B*d*n)*(1 + p))","A",1
235,1,51,55,0.0563822,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^p}{(a f+b f x) (c g+d g x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^p/((a*f + b*f*x)*(c*g + d*g*x)),x]","\frac{\left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^{p+1}}{(p+1) (b B c f g n-a B d f g n)}","\frac{\left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^{p+1}}{B f g n (p+1) (b c-a d)}",1,"(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^(1 + p)/((b*B*c*f*g*n - a*B*d*f*g*n)*(1 + p))","A",1
236,1,50,52,0.0128184,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^p}{a c f+(b c+a d) f x+b d f x^2} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^p/(a*c*f + (b*c + a*d)*f*x + b*d*f*x^2),x]","\frac{\left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^{p+1}}{f (p+1) (b B c n-a B d n)}","\frac{\left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^{p+1}}{B f n (p+1) (b c-a d)}",1,"(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^(1 + p)/(f*(b*B*c*n - a*B*d*n)*(1 + p))","A",1
237,1,39,41,0.0684585,"\int \frac{1}{(a+b x) (c+d x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)} \, dx","Integrate[1/((a + b*x)*(c + d*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])),x]","\frac{\log \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b B c n-a B d n}","\frac{\log \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{B n (b c-a d)}",1,"Log[A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]]/(b*B*c*n - a*B*d*n)","A",1
238,1,43,47,0.1496729,"\int \frac{1}{(a f+b f x) (c g+d g x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)} \, dx","Integrate[1/((a*f + b*f*x)*(c*g + d*g*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])),x]","\frac{\log \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{b B c f g n-a B d f g n}","\frac{\log \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{B f g n (b c-a d)}",1,"Log[A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]]/(b*B*c*f*g*n - a*B*d*f*g*n)","A",1
239,1,42,44,0.0688126,"\int \frac{1}{\left(a c f+(b c+a d) f x+b d f x^2\right) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)} \, dx","Integrate[1/((a*c*f + (b*c + a*d)*f*x + b*d*f*x^2)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])),x]","\frac{\log \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{f (b B c n-a B d n)}","\frac{\log \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{B f n (b c-a d)}",1,"Log[A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n]]/(f*(b*B*c*n - a*B*d*n))","A",1
240,0,0,88,0.3996328,"\int \frac{(a+b x)^m (c+d x)^{-2-m}}{\log \left(e (a+b x)^n (c+d x)^{-n}\right)} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(-2 - m))/Log[(e*(a + b*x)^n)/(c + d*x)^n],x]","\int \frac{(a+b x)^m (c+d x)^{-2-m}}{\log \left(e (a+b x)^n (c+d x)^{-n}\right)} \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \left(e (a+b x)^n (c+d x)^{-n}\right)^{-\frac{m+1}{n}} \text{Ei}\left(\frac{(m+1) \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{n}\right)}{n (b c-a d)}",1,"Integrate[((a + b*x)^m*(c + d*x)^(-2 - m))/Log[(e*(a + b*x)^n)/(c + d*x)^n], x]","F",-1
241,1,75,75,0.0284151,"\int \frac{(a+b x)^3}{(c+d x)^5 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Integrate[(a + b*x)^3/((c + d*x)^5*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{(a+b x)^4 \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-4/n} \text{Ei}\left(\frac{4 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n}\right)}{n (c+d x)^4 (b c-a d)}","\frac{(a+b x)^4 \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-4/n} \text{Ei}\left(\frac{4 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n}\right)}{n (c+d x)^4 (b c-a d)}",1,"((a + b*x)^4*ExpIntegralEi[(4*Log[e*((a + b*x)/(c + d*x))^n])/n])/((b*c - a*d)*n*(e*((a + b*x)/(c + d*x))^n)^(4/n)*(c + d*x)^4)","A",1
242,1,75,75,0.0266989,"\int \frac{(a+b x)^2}{(c+d x)^4 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Integrate[(a + b*x)^2/((c + d*x)^4*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{(a+b x)^3 \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-3/n} \text{Ei}\left(\frac{3 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n}\right)}{n (c+d x)^3 (b c-a d)}","\frac{(a+b x)^3 \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-3/n} \text{Ei}\left(\frac{3 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n}\right)}{n (c+d x)^3 (b c-a d)}",1,"((a + b*x)^3*ExpIntegralEi[(3*Log[e*((a + b*x)/(c + d*x))^n])/n])/((b*c - a*d)*n*(e*((a + b*x)/(c + d*x))^n)^(3/n)*(c + d*x)^3)","A",1
243,1,75,75,0.0210922,"\int \frac{a+b x}{(c+d x)^3 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Integrate[(a + b*x)/((c + d*x)^3*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{(a+b x)^2 \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n}\right)}{n (c+d x)^2 (b c-a d)}","\frac{(a+b x)^2 \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-2/n} \text{Ei}\left(\frac{2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n}\right)}{n (c+d x)^2 (b c-a d)}",1,"((a + b*x)^2*ExpIntegralEi[(2*Log[e*((a + b*x)/(c + d*x))^n])/n])/((b*c - a*d)*n*(e*((a + b*x)/(c + d*x))^n)^(2/n)*(c + d*x)^2)","A",1
244,1,72,72,0.0743414,"\int \frac{1}{(c+d x)^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Integrate[1/((c + d*x)^2*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{(a+b x) \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-1/n} \text{Ei}\left(\frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n}\right)}{n (c+d x) (b c-a d)}","\frac{(a+b x) \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{-1/n} \text{Ei}\left(\frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n}\right)}{n (c+d x) (b c-a d)}",1,"((a + b*x)*ExpIntegralEi[Log[e*((a + b*x)/(c + d*x))^n]/n])/((b*c - a*d)*n*(e*((a + b*x)/(c + d*x))^n)^n^(-1)*(c + d*x))","A",1
245,1,34,33,0.0754011,"\int \frac{1}{(a+b x) (c+d x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Integrate[1/((a + b*x)*(c + d*x)*Log[e*((a + b*x)/(c + d*x))^n]),x]","-\frac{\log \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{n (a d-b c)}","\frac{\log \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)}{n (b c-a d)}",1,"-(Log[Log[e*((a + b*x)/(c + d*x))^n]]/((-(b*c) + a*d)*n))","A",1
246,1,71,71,0.0716722,"\int \frac{1}{(a+b x)^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Integrate[1/((a + b*x)^2*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{(c+d x) \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{\frac{1}{n}} \text{Ei}\left(-\frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n}\right)}{n (a+b x) (b c-a d)}","\frac{(c+d x) \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{\frac{1}{n}} \text{Ei}\left(-\frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n}\right)}{n (a+b x) (b c-a d)}",1,"((e*((a + b*x)/(c + d*x))^n)^n^(-1)*(c + d*x)*ExpIntegralEi[-(Log[e*((a + b*x)/(c + d*x))^n]/n)])/((b*c - a*d)*n*(a + b*x))","A",1
247,1,75,75,0.0156932,"\int \frac{c+d x}{(a+b x)^3 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Integrate[(c + d*x)/((a + b*x)^3*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{(c+d x)^2 \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{2/n} \text{Ei}\left(-\frac{2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n}\right)}{n (a+b x)^2 (b c-a d)}","\frac{(c+d x)^2 \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{2/n} \text{Ei}\left(-\frac{2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n}\right)}{n (a+b x)^2 (b c-a d)}",1,"((e*((a + b*x)/(c + d*x))^n)^(2/n)*(c + d*x)^2*ExpIntegralEi[(-2*Log[e*((a + b*x)/(c + d*x))^n])/n])/((b*c - a*d)*n*(a + b*x)^2)","A",1
248,1,75,75,0.0184267,"\int \frac{(c+d x)^2}{(a+b x)^4 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Integrate[(c + d*x)^2/((a + b*x)^4*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{(c+d x)^3 \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{3/n} \text{Ei}\left(-\frac{3 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n}\right)}{n (a+b x)^3 (b c-a d)}","\frac{(c+d x)^3 \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)^{3/n} \text{Ei}\left(-\frac{3 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n}\right)}{n (a+b x)^3 (b c-a d)}",1,"((e*((a + b*x)/(c + d*x))^n)^(3/n)*(c + d*x)^3*ExpIntegralEi[(-3*Log[e*((a + b*x)/(c + d*x))^n])/n])/((b*c - a*d)*n*(a + b*x)^3)","A",1
249,0,0,361,4.4058815,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^4}{(f+g x) (a h+b h x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^4/((f + g*x)*(a*h + b*h*x)),x]","\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^4}{(f+g x) (a h+b h x)} \, dx","\frac{24 B^3 n^3 \text{Li}_4\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{h (b f-a g)}+\frac{12 B^2 n^2 \text{Li}_3\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{h (b f-a g)}+\frac{4 B n \text{Li}_2\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{h (b f-a g)}-\frac{\log \left(1-\frac{(c+d x) (b f-a g)}{(a+b x) (d f-c g)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^4}{h (b f-a g)}+\frac{24 B^4 n^4 \text{Li}_5\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right)}{h (b f-a g)}",1,"Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^4/((f + g*x)*(a*h + b*h*x)), x]","F",-1
250,0,0,282,3.2346379,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(f+g x) (a h+b h x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/((f + g*x)*(a*h + b*h*x)),x]","\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{(f+g x) (a h+b h x)} \, dx","\frac{6 B^2 n^2 \text{Li}_3\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{h (b f-a g)}+\frac{3 B n \text{Li}_2\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{h (b f-a g)}-\frac{\log \left(1-\frac{(c+d x) (b f-a g)}{(a+b x) (d f-c g)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{h (b f-a g)}+\frac{6 B^3 n^3 \text{Li}_4\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right)}{h (b f-a g)}",1,"Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/((f + g*x)*(a*h + b*h*x)), x]","F",-1
251,1,1415,203,1.0500692,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{(f+g x) (a h+b h x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/((f + g*x)*(a*h + b*h*x)),x]","\frac{6 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) \left(\log \left(\frac{d (a+b x)}{a d-b c}\right)-\log \left(\frac{d (f+g x)}{d f-c g}\right)\right)+\text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-\text{Li}_2\left(\frac{g (c+d x)}{c g-d f}\right)\right) B^2+n^2 \left(\left(\log (a+b x)-3 \log \left(\frac{b (f+g x)}{b f-a g}\right)\right) \log ^2(a+b x)-6 \text{Li}_2\left(\frac{g (a+b x)}{a g-b f}\right) \log (a+b x)+6 \text{Li}_3\left(\frac{g (a+b x)}{a g-b f}\right)\right) B^2+3 n^2 \left(\log \left(\frac{d (a+b x)}{a d-b c}\right) \log ^2(c+d x)-\log \left(\frac{d (f+g x)}{d f-c g}\right) \log ^2(c+d x)+2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right) \log (c+d x)-2 \text{Li}_2\left(\frac{g (c+d x)}{c g-d f}\right) \log (c+d x)-2 \text{Li}_3\left(\frac{b (c+d x)}{b c-a d}\right)+2 \text{Li}_3\left(\frac{g (c+d x)}{c g-d f}\right)\right) B^2-6 n^2 \left(\frac{1}{2} \left(\log (c+d x)-\log \left(\frac{b (c+d x)}{b c-a d}\right)\right) \log ^2(a+b x)-\log (c+d x) \log \left(\frac{b (f+g x)}{b f-a g}\right) \log (a+b x)-\text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right) \log (a+b x)-\frac{1}{2} \log \left(\frac{g (c+d x)}{c g-d f}\right) \left(\log \left(\frac{g (c+d x)}{c g-d f}\right)-2 \log (a+b x)\right) \left(\log \left(\frac{b (f+g x)}{b f-a g}\right)-\log \left(\frac{d (f+g x)}{d f-c g}\right)\right)+\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) \left(\log \left(\frac{b (f+g x)}{b f-a g}\right)-\log \left(\frac{d (f+g x)}{d f-c g}\right)\right)-\frac{1}{2} \log ^2\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \left(\log \left(\frac{a d-b c}{d (a+b x)}\right)+\log \left(\frac{b (f+g x)}{b f-a g}\right)-\log \left(\frac{(a d-b c) (f+g x)}{(d f-c g) (a+b x)}\right)\right)-\left(\log (c+d x)-\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)-\left(\log (a+b x)+\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)-\log \left(\frac{(b f-a g) (c+d x)}{(d f-c g) (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 f-a g) (c+d x)}{(d f-c g) (a+b x)}\right)\right)+\text{Li}_3\left(\frac{d (a+b x)}{a d-b c}\right)+\text{Li}_3\left(\frac{g (a+b x)}{a g-b f}\right)+\text{Li}_3\left(\frac{g (c+d x)}{c g-d f}\right)+\text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)-\text{Li}_3\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right)\right) B^2+3 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 ^2(a+b x)-2 \left(\log (a+b x) \log \left(\frac{b (f+g x)}{b f-a g}\right)+\text{Li}_2\left(\frac{g (a+b x)}{a g-b f}\right)\right)\right) B-6 A n \left(\log (c+d x) \left(\log \left(\frac{d (a+b x)}{a d-b c}\right)-\log \left(\frac{d (f+g x)}{d f-c g}\right)\right)+\text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-\text{Li}_2\left(\frac{g (c+d x)}{c g-d f}\right)\right) B+3 \log (a+b x) \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)^2-3 \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 (f+g x)}{3 (b f-a g) h}","\frac{2 B n \text{Li}_2\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{h (b f-a g)}-\frac{\log \left(1-\frac{(c+d x) (b f-a g)}{(a+b x) (d f-c g)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{h (b f-a g)}+\frac{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)}{h (b f-a g)}",1,"(3*Log[a + b*x]*(A + B*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n]))^2 - 3*(A + B*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n]))^2*Log[f + g*x] + 3*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]^2 - 2*(Log[a + b*x]*Log[(b*(f + g*x))/(b*f - a*g)] + PolyLog[2, (g*(a + b*x))/(-(b*f) + a*g)])) - 6*A*B*n*(Log[c + d*x]*(Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[(d*(f + g*x))/(d*f - c*g)]) + PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - PolyLog[2, (g*(c + d*x))/(-(d*f) + c*g)]) + 6*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*(a + b*x))/(-(b*c) + a*d)] - Log[(d*(f + g*x))/(d*f - c*g)]) + PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - PolyLog[2, (g*(c + d*x))/(-(d*f) + c*g)]) + B^2*n^2*(Log[a + b*x]^2*(Log[a + b*x] - 3*Log[(b*(f + g*x))/(b*f - a*g)]) - 6*Log[a + b*x]*PolyLog[2, (g*(a + b*x))/(-(b*f) + a*g)] + 6*PolyLog[3, (g*(a + b*x))/(-(b*f) + a*g)]) + 3*B^2*n^2*(Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x]^2 - Log[c + d*x]^2*Log[(d*(f + g*x))/(d*f - c*g)] + 2*Log[c + d*x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 2*Log[c + d*x]*PolyLog[2, (g*(c + d*x))/(-(d*f) + c*g)] - 2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)] + 2*PolyLog[3, (g*(c + d*x))/(-(d*f) + c*g)]) - 6*B^2*n^2*((Log[a + b*x]^2*(Log[c + d*x] - Log[(b*(c + d*x))/(b*c - a*d)]))/2 - Log[a + b*x]*Log[c + d*x]*Log[(b*(f + g*x))/(b*f - a*g)] - (Log[(g*(c + d*x))/(-(d*f) + c*g)]*(-2*Log[a + b*x] + Log[(g*(c + d*x))/(-(d*f) + c*g)])*(Log[(b*(f + g*x))/(b*f - a*g)] - Log[(d*(f + g*x))/(d*f - c*g)]))/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)] - Log[(d*(f + g*x))/(d*f - c*g)]) - (Log[((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))]^2*(Log[(-(b*c) + a*d)/(d*(a + b*x))] + Log[(b*(f + g*x))/(b*f - a*g)] - Log[((-(b*c) + a*d)*(f + g*x))/((d*f - c*g)*(a + b*x))]))/2 - Log[a + b*x]*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] - (Log[c + d*x] - 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)] - (Log[a + b*x] + 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)] - 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))] - PolyLog[2, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))]) + PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)] + PolyLog[3, (g*(a + b*x))/(-(b*f) + a*g)] + PolyLog[3, (g*(c + d*x))/(-(d*f) + c*g)] + PolyLog[3, (b*(c + d*x))/(d*(a + b*x))] - PolyLog[3, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))]))/(3*(b*f - a*g)*h)","B",1
252,1,304,123,0.3108119,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{(f+g x) (a h+b h x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/((f + g*x)*(a*h + b*h*x)),x]","-\frac{-2 A \log (a+b x)+2 B \log (f+g x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)-2 B \log (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 B n \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-2 B n \log (a+b x) \log (c+d x)+2 B n \log (c+d x) \log \left(\frac{d (a+b x)}{a d-b c}\right)+2 B n \text{Li}_2\left(\frac{g (a+b x)}{a g-b f}\right)-2 B n \log (a+b x) \log (f+g x)+2 B n \log (a+b x) \log \left(\frac{b (f+g x)}{b f-a g}\right)+B n \log ^2(a+b x)+2 A \log (f+g x)-2 B n \text{Li}_2\left(\frac{g (c+d x)}{c g-d f}\right)+2 B n \log (c+d x) \log (f+g x)-2 B n \log (c+d x) \log \left(\frac{d (f+g x)}{d f-c g}\right)}{2 h (b f-a g)}","\frac{B n \text{Li}_2\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right)}{h (b f-a g)}-\frac{\log \left(1-\frac{(c+d x) (b f-a g)}{(a+b x) (d f-c g)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{h (b f-a g)}",1,"-1/2*(-2*A*Log[a + b*x] + B*n*Log[a + b*x]^2 - 2*B*n*Log[a + b*x]*Log[c + d*x] + 2*B*n*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] - 2*B*Log[a + b*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*A*Log[f + g*x] - 2*B*n*Log[a + b*x]*Log[f + g*x] + 2*B*n*Log[c + d*x]*Log[f + g*x] + 2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[f + g*x] + 2*B*n*Log[a + b*x]*Log[(b*(f + g*x))/(b*f - a*g)] - 2*B*n*Log[c + d*x]*Log[(d*(f + g*x))/(d*f - c*g)] + 2*B*n*PolyLog[2, (g*(a + b*x))/(-(b*f) + a*g)] + 2*B*n*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 2*B*n*PolyLog[2, (g*(c + d*x))/(-(d*f) + c*g)])/((b*f - a*g)*h)","B",1
253,0,0,82,0.1643234,"\int \frac{1}{(f+g x) (a h+b h x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)} \, dx","Integrate[1/((f + g*x)*(a*h + b*h*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])),x]","\int \frac{1}{(f+g x) (a h+b h x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)} \, dx","\text{Subst}\left(\text{Int}\left(\frac{1}{(f+g x) (a h+b h x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)},x\right),e \left(\frac{a+b x}{c+d x}\right)^n,e (a+b x)^n (c+d x)^{-n}\right)",0,"Integrate[1/((f + g*x)*(a*h + b*h*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])), x]","A",-1
254,0,0,82,0.3489521,"\int \frac{1}{(f+g x) (a h+b h x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2} \, dx","Integrate[1/((f + g*x)*(a*h + b*h*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2),x]","\int \frac{1}{(f+g x) (a h+b h x) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2} \, dx","\text{Subst}\left(\text{Int}\left(\frac{1}{(f+g x) (a h+b h x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2},x\right),e \left(\frac{a+b x}{c+d x}\right)^n,e (a+b x)^n (c+d x)^{-n}\right)",0,"Integrate[1/((f + g*x)*(a*h + b*h*x)*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2), x]","A",-1
255,1,298,33,0.1898844,"\int \frac{\log \left(\frac{c+d x}{a+b x}\right)}{(a+b x) ((a-c) h+(b-d) h x)} \, dx","Integrate[Log[(c + d*x)/(a + b*x)]/((a + b*x)*((a - c)*h + (b - d)*h*x)),x]","\frac{2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)+2 \text{Li}_2\left(-\frac{b (a-c+b x-d x)}{b c-a d}\right)-2 \text{Li}_2\left(-\frac{d (-a+c-b x+d x)}{a d-b c}\right)-\log ^2\left(\frac{a d-b c}{d (a+b x)}\right)-2 \log \left(\frac{b (c+d x)}{b c-a d}\right) \log \left(\frac{a d-b c}{d (a+b x)}\right)+2 \log \left(\frac{c+d x}{a+b x}\right) \log \left(\frac{a d-b c}{d (a+b x)}\right)+2 \log \left(\frac{(b-d) (a+b x)}{b c-a d}\right) \log (a+b x-c-d x)-2 \log (a+b x-c-d x) \log \left(\frac{(b-d) (c+d x)}{b c-a d}\right)+2 \log (a+b x-c-d x) \log \left(\frac{c+d x}{a+b x}\right)}{h (2 b c-2 a d)}","-\frac{\text{Li}_2\left(1-\frac{c+d x}{a+b x}\right)}{h (b c-a d)}",1,"(-Log[(-(b*c) + a*d)/(d*(a + b*x))]^2 + 2*Log[((b - d)*(a + b*x))/(b*c - a*d)]*Log[a - c + b*x - d*x] - 2*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(b*(c + d*x))/(b*c - a*d)] - 2*Log[a - c + b*x - d*x]*Log[((b - d)*(c + d*x))/(b*c - a*d)] + 2*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(c + d*x)/(a + b*x)] + 2*Log[a - c + b*x - d*x]*Log[(c + d*x)/(a + b*x)] + 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 2*PolyLog[2, -((b*(a - c + b*x - d*x))/(b*c - a*d))] - 2*PolyLog[2, -((d*(-a + c - b*x + d*x))/(-(b*c) + a*d))])/((2*b*c - 2*a*d)*h)","B",1
256,1,320,27,0.2558696,"\int \frac{\log \left(\frac{a-c g+(b-d g) x}{a+b x}\right)}{(a+b x) (c+d x)} \, dx","Integrate[Log[(a - c*g + (b - d*g)*x)/(a + b*x)]/((a + b*x)*(c + d*x)),x]","\frac{-2 \text{Li}_2\left(\frac{(b-d g) (a+b x)}{(b c-a d) g}\right)+2 \text{Li}_2\left(\frac{(b-d g) (c+d x)}{b c-a d}\right)+\log ^2\left(\frac{g (b c-a d)}{(a+b x) (b-d g)}\right)+2 \log \left(-\frac{b (a+b x-c g-d g x)}{g (b c-a d)}\right) \log \left(\frac{g (b c-a d)}{(a+b x) (b-d g)}\right)-2 \log \left(\frac{a+b x-c g-d g x}{a+b x}\right) \log \left(\frac{g (b c-a d)}{(a+b x) (b-d g)}\right)+2 \log (c+d x) \log \left(-\frac{d (a+b x-c g-d g x)}{b c-a d}\right)-2 \log (c+d x) \log \left(\frac{a+b x-c g-d g x}{a+b x}\right)-2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-2 \log (c+d x) \log \left(\frac{d (a+b x)}{a d-b c}\right)}{2 b c-2 a d}","\frac{\text{Li}_2\left(\frac{g (c+d x)}{a+b x}\right)}{b c-a d}",1,"(Log[((b*c - a*d)*g)/((b - d*g)*(a + b*x))]^2 - 2*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] + 2*Log[c + d*x]*Log[-((d*(a - c*g + b*x - d*g*x))/(b*c - a*d))] + 2*Log[((b*c - a*d)*g)/((b - d*g)*(a + b*x))]*Log[-((b*(a - c*g + b*x - d*g*x))/((b*c - a*d)*g))] - 2*Log[((b*c - a*d)*g)/((b - d*g)*(a + b*x))]*Log[(a - c*g + b*x - d*g*x)/(a + b*x)] - 2*Log[c + d*x]*Log[(a - c*g + b*x - d*g*x)/(a + b*x)] - 2*PolyLog[2, ((b - d*g)*(a + b*x))/((b*c - a*d)*g)] - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 2*PolyLog[2, ((b - d*g)*(c + d*x))/(b*c - a*d)])/(2*b*c - 2*a*d)","B",1
257,1,320,27,0.1866893,"\int \frac{\log \left(1-\frac{g (c+d x)}{a+b x}\right)}{(a+b x) (c+d x)} \, dx","Integrate[Log[1 - (g*(c + d*x))/(a + b*x)]/((a + b*x)*(c + d*x)),x]","\frac{-2 \text{Li}_2\left(\frac{(b-d g) (a+b x)}{(b c-a d) g}\right)+2 \text{Li}_2\left(\frac{(b-d g) (c+d x)}{b c-a d}\right)+\log ^2\left(\frac{g (b c-a d)}{(a+b x) (b-d g)}\right)+2 \log \left(-\frac{b (a+b x-c g-d g x)}{g (b c-a d)}\right) \log \left(\frac{g (b c-a d)}{(a+b x) (b-d g)}\right)-2 \log \left(\frac{a+b x-c g-d g x}{a+b x}\right) \log \left(\frac{g (b c-a d)}{(a+b x) (b-d g)}\right)+2 \log (c+d x) \log \left(-\frac{d (a+b x-c g-d g x)}{b c-a d}\right)-2 \log (c+d x) \log \left(\frac{a+b x-c g-d g x}{a+b x}\right)-2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-2 \log (c+d x) \log \left(\frac{d (a+b x)}{a d-b c}\right)}{2 b c-2 a d}","\frac{\text{Li}_2\left(\frac{g (c+d x)}{a+b x}\right)}{b c-a d}",1,"(Log[((b*c - a*d)*g)/((b - d*g)*(a + b*x))]^2 - 2*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] + 2*Log[c + d*x]*Log[-((d*(a - c*g + b*x - d*g*x))/(b*c - a*d))] + 2*Log[((b*c - a*d)*g)/((b - d*g)*(a + b*x))]*Log[-((b*(a - c*g + b*x - d*g*x))/((b*c - a*d)*g))] - 2*Log[((b*c - a*d)*g)/((b - d*g)*(a + b*x))]*Log[(a - c*g + b*x - d*g*x)/(a + b*x)] - 2*Log[c + d*x]*Log[(a - c*g + b*x - d*g*x)/(a + b*x)] - 2*PolyLog[2, ((b - d*g)*(a + b*x))/((b*c - a*d)*g)] - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 2*PolyLog[2, ((b - d*g)*(c + d*x))/(b*c - a*d)])/(2*b*c - 2*a*d)","B",1
258,1,320,27,0.1763641,"\int \frac{\log \left(\frac{a-c g+b x-d g x}{a+b x}\right)}{(a+b x) (c+d x)} \, dx","Integrate[Log[(a - c*g + b*x - d*g*x)/(a + b*x)]/((a + b*x)*(c + d*x)),x]","\frac{-2 \text{Li}_2\left(\frac{(b-d g) (a+b x)}{(b c-a d) g}\right)+2 \text{Li}_2\left(\frac{(b-d g) (c+d x)}{b c-a d}\right)+\log ^2\left(\frac{g (b c-a d)}{(a+b x) (b-d g)}\right)+2 \log \left(-\frac{b (a+b x-c g-d g x)}{g (b c-a d)}\right) \log \left(\frac{g (b c-a d)}{(a+b x) (b-d g)}\right)-2 \log \left(\frac{a+b x-c g-d g x}{a+b x}\right) \log \left(\frac{g (b c-a d)}{(a+b x) (b-d g)}\right)+2 \log (c+d x) \log \left(-\frac{d (a+b x-c g-d g x)}{b c-a d}\right)-2 \log (c+d x) \log \left(\frac{a+b x-c g-d g x}{a+b x}\right)-2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-2 \log (c+d x) \log \left(\frac{d (a+b x)}{a d-b c}\right)}{2 b c-2 a d}","\frac{\text{Li}_2\left(\frac{g (c+d x)}{a+b x}\right)}{b c-a d}",1,"(Log[((b*c - a*d)*g)/((b - d*g)*(a + b*x))]^2 - 2*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] + 2*Log[c + d*x]*Log[-((d*(a - c*g + b*x - d*g*x))/(b*c - a*d))] + 2*Log[((b*c - a*d)*g)/((b - d*g)*(a + b*x))]*Log[-((b*(a - c*g + b*x - d*g*x))/((b*c - a*d)*g))] - 2*Log[((b*c - a*d)*g)/((b - d*g)*(a + b*x))]*Log[(a - c*g + b*x - d*g*x)/(a + b*x)] - 2*Log[c + d*x]*Log[(a - c*g + b*x - d*g*x)/(a + b*x)] - 2*PolyLog[2, ((b - d*g)*(a + b*x))/((b*c - a*d)*g)] - 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 2*PolyLog[2, ((b - d*g)*(c + d*x))/(b*c - a*d)])/(2*b*c - 2*a*d)","B",1
259,0,0,282,2.8641635,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{a f h+b g h x^2+h (b f x+a g x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(a*f*h + b*g*h*x^2 + h*(b*f*x + a*g*x)),x]","\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^3}{a f h+b g h x^2+h (b f x+a g x)} \, dx","\frac{6 B^2 n^2 \text{Li}_3\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{h (b f-a g)}+\frac{3 B n \text{Li}_2\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{h (b f-a g)}-\frac{\log \left(1-\frac{(c+d x) (b f-a g)}{(a+b x) (d f-c g)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^3}{h (b f-a g)}+\frac{6 B^3 n^3 \text{Li}_4\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right)}{h (b f-a g)}",1,"Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^3/(a*f*h + b*g*h*x^2 + h*(b*f*x + a*g*x)), x]","F",-1
260,1,1415,203,0.8978849,"\int \frac{\left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2}{a f h+b g h x^2+h (b f x+a g x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2/(a*f*h + b*g*h*x^2 + h*(b*f*x + a*g*x)),x]","\frac{6 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) \left(\log \left(\frac{d (a+b x)}{a d-b c}\right)-\log \left(\frac{d (f+g x)}{d f-c g}\right)\right)+\text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-\text{Li}_2\left(\frac{g (c+d x)}{c g-d f}\right)\right) B^2+n^2 \left(\left(\log (a+b x)-3 \log \left(\frac{b (f+g x)}{b f-a g}\right)\right) \log ^2(a+b x)-6 \text{Li}_2\left(\frac{g (a+b x)}{a g-b f}\right) \log (a+b x)+6 \text{Li}_3\left(\frac{g (a+b x)}{a g-b f}\right)\right) B^2+3 n^2 \left(\log \left(\frac{d (a+b x)}{a d-b c}\right) \log ^2(c+d x)-\log \left(\frac{d (f+g x)}{d f-c g}\right) \log ^2(c+d x)+2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right) \log (c+d x)-2 \text{Li}_2\left(\frac{g (c+d x)}{c g-d f}\right) \log (c+d x)-2 \text{Li}_3\left(\frac{b (c+d x)}{b c-a d}\right)+2 \text{Li}_3\left(\frac{g (c+d x)}{c g-d f}\right)\right) B^2-6 n^2 \left(\frac{1}{2} \left(\log (c+d x)-\log \left(\frac{b (c+d x)}{b c-a d}\right)\right) \log ^2(a+b x)-\log (c+d x) \log \left(\frac{b (f+g x)}{b f-a g}\right) \log (a+b x)-\text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right) \log (a+b x)-\frac{1}{2} \log \left(\frac{g (c+d x)}{c g-d f}\right) \left(\log \left(\frac{g (c+d x)}{c g-d f}\right)-2 \log (a+b x)\right) \left(\log \left(\frac{b (f+g x)}{b f-a g}\right)-\log \left(\frac{d (f+g x)}{d f-c g}\right)\right)+\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) \left(\log \left(\frac{b (f+g x)}{b f-a g}\right)-\log \left(\frac{d (f+g x)}{d f-c g}\right)\right)-\frac{1}{2} \log ^2\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \left(\log \left(\frac{a d-b c}{d (a+b x)}\right)+\log \left(\frac{b (f+g x)}{b f-a g}\right)-\log \left(\frac{(a d-b c) (f+g x)}{(d f-c g) (a+b x)}\right)\right)-\left(\log (c+d x)-\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)-\left(\log (a+b x)+\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)-\log \left(\frac{(b f-a g) (c+d x)}{(d f-c g) (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 f-a g) (c+d x)}{(d f-c g) (a+b x)}\right)\right)+\text{Li}_3\left(\frac{d (a+b x)}{a d-b c}\right)+\text{Li}_3\left(\frac{g (a+b x)}{a g-b f}\right)+\text{Li}_3\left(\frac{g (c+d x)}{c g-d f}\right)+\text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)-\text{Li}_3\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right)\right) B^2+3 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 ^2(a+b x)-2 \left(\log (a+b x) \log \left(\frac{b (f+g x)}{b f-a g}\right)+\text{Li}_2\left(\frac{g (a+b x)}{a g-b f}\right)\right)\right) B-6 A n \left(\log (c+d x) \left(\log \left(\frac{d (a+b x)}{a d-b c}\right)-\log \left(\frac{d (f+g x)}{d f-c g}\right)\right)+\text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-\text{Li}_2\left(\frac{g (c+d x)}{c g-d f}\right)\right) B+3 \log (a+b x) \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)^2-3 \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 (f+g x)}{3 (b f-a g) h}","\frac{2 B n \text{Li}_2\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{h (b f-a g)}-\frac{\log \left(1-\frac{(c+d x) (b f-a g)}{(a+b x) (d f-c g)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)^2}{h (b f-a g)}+\frac{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)}{h (b f-a g)}",1,"(3*Log[a + b*x]*(A + B*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n]))^2 - 3*(A + B*(-(n*Log[a + b*x]) + n*Log[c + d*x] + Log[(e*(a + b*x)^n)/(c + d*x)^n]))^2*Log[f + g*x] + 3*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]^2 - 2*(Log[a + b*x]*Log[(b*(f + g*x))/(b*f - a*g)] + PolyLog[2, (g*(a + b*x))/(-(b*f) + a*g)])) - 6*A*B*n*(Log[c + d*x]*(Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[(d*(f + g*x))/(d*f - c*g)]) + PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - PolyLog[2, (g*(c + d*x))/(-(d*f) + c*g)]) + 6*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*(a + b*x))/(-(b*c) + a*d)] - Log[(d*(f + g*x))/(d*f - c*g)]) + PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - PolyLog[2, (g*(c + d*x))/(-(d*f) + c*g)]) + B^2*n^2*(Log[a + b*x]^2*(Log[a + b*x] - 3*Log[(b*(f + g*x))/(b*f - a*g)]) - 6*Log[a + b*x]*PolyLog[2, (g*(a + b*x))/(-(b*f) + a*g)] + 6*PolyLog[3, (g*(a + b*x))/(-(b*f) + a*g)]) + 3*B^2*n^2*(Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x]^2 - Log[c + d*x]^2*Log[(d*(f + g*x))/(d*f - c*g)] + 2*Log[c + d*x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 2*Log[c + d*x]*PolyLog[2, (g*(c + d*x))/(-(d*f) + c*g)] - 2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)] + 2*PolyLog[3, (g*(c + d*x))/(-(d*f) + c*g)]) - 6*B^2*n^2*((Log[a + b*x]^2*(Log[c + d*x] - Log[(b*(c + d*x))/(b*c - a*d)]))/2 - Log[a + b*x]*Log[c + d*x]*Log[(b*(f + g*x))/(b*f - a*g)] - (Log[(g*(c + d*x))/(-(d*f) + c*g)]*(-2*Log[a + b*x] + Log[(g*(c + d*x))/(-(d*f) + c*g)])*(Log[(b*(f + g*x))/(b*f - a*g)] - Log[(d*(f + g*x))/(d*f - c*g)]))/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)] - Log[(d*(f + g*x))/(d*f - c*g)]) - (Log[((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))]^2*(Log[(-(b*c) + a*d)/(d*(a + b*x))] + Log[(b*(f + g*x))/(b*f - a*g)] - Log[((-(b*c) + a*d)*(f + g*x))/((d*f - c*g)*(a + b*x))]))/2 - Log[a + b*x]*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] - (Log[c + d*x] - 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)] - (Log[a + b*x] + 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)] - 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))] - PolyLog[2, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))]) + PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)] + PolyLog[3, (g*(a + b*x))/(-(b*f) + a*g)] + PolyLog[3, (g*(c + d*x))/(-(d*f) + c*g)] + PolyLog[3, (b*(c + d*x))/(d*(a + b*x))] - PolyLog[3, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))]))/(3*(b*f - a*g)*h)","B",1
261,1,303,123,0.2675458,"\int \frac{A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)}{a f h+b g h x^2+h (b f x+a g x)} \, dx","Integrate[(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])/(a*f*h + b*g*h*x^2 + h*(b*f*x + a*g*x)),x]","-\frac{-2 A \log (a+b x)+2 B \log (f+g x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)-2 B \log (a+b x) \log \left(e (a+b x)^n (c+d x)^{-n}\right)+2 B n \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-2 B n \log (a+b x) \log (c+d x)+2 B n \log (c+d x) \log \left(\frac{d (a+b x)}{a d-b c}\right)+2 B n \text{Li}_2\left(\frac{g (a+b x)}{a g-b f}\right)-2 B n \log (a+b x) \log (f+g x)+2 B n \log (a+b x) \log \left(\frac{b (f+g x)}{b f-a g}\right)+B n \log ^2(a+b x)+2 A \log (f+g x)-2 B n \text{Li}_2\left(\frac{g (c+d x)}{c g-d f}\right)+2 B n \log (c+d x) \log (f+g x)-2 B n \log (c+d x) \log \left(\frac{d (f+g x)}{d f-c g}\right)}{h (2 b f-2 a g)}","\frac{B n \text{Li}_2\left(\frac{(b f-a g) (c+d x)}{(d f-c g) (a+b x)}\right)}{h (b f-a g)}-\frac{\log \left(1-\frac{(c+d x) (b f-a g)}{(a+b x) (d f-c g)}\right) \left(B \log \left(e (a+b x)^n (c+d x)^{-n}\right)+A\right)}{h (b f-a g)}",1,"-((-2*A*Log[a + b*x] + B*n*Log[a + b*x]^2 - 2*B*n*Log[a + b*x]*Log[c + d*x] + 2*B*n*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] - 2*B*Log[a + b*x]*Log[(e*(a + b*x)^n)/(c + d*x)^n] + 2*A*Log[f + g*x] - 2*B*n*Log[a + b*x]*Log[f + g*x] + 2*B*n*Log[c + d*x]*Log[f + g*x] + 2*B*Log[(e*(a + b*x)^n)/(c + d*x)^n]*Log[f + g*x] + 2*B*n*Log[a + b*x]*Log[(b*(f + g*x))/(b*f - a*g)] - 2*B*n*Log[c + d*x]*Log[(d*(f + g*x))/(d*f - c*g)] + 2*B*n*PolyLog[2, (g*(a + b*x))/(-(b*f) + a*g)] + 2*B*n*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 2*B*n*PolyLog[2, (g*(c + d*x))/(-(d*f) + c*g)])/((2*b*f - 2*a*g)*h))","B",1
262,0,0,83,0.1334646,"\int \frac{1}{\left(a f h+b g h x^2+h (b f x+a g x)\right) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)} \, dx","Integrate[1/((a*f*h + b*g*h*x^2 + h*(b*f*x + a*g*x))*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])),x]","\int \frac{1}{\left(a f h+b g h x^2+h (b f x+a g x)\right) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)} \, dx","\frac{\text{Subst}\left(\text{Int}\left(\frac{1}{(a+b x) (f+g x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)},x\right),e \left(\frac{a+b x}{c+d x}\right)^n,e (a+b x)^n (c+d x)^{-n}\right)}{h}",0,"Integrate[1/((a*f*h + b*g*h*x^2 + h*(b*f*x + a*g*x))*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])), x]","A",-1
263,0,0,83,0.2713445,"\int \frac{1}{\left(a f h+b g h x^2+h (b f x+a g x)\right) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2} \, dx","Integrate[1/((a*f*h + b*g*h*x^2 + h*(b*f*x + a*g*x))*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2),x]","\int \frac{1}{\left(a f h+b g h x^2+h (b f x+a g x)\right) \left(A+B \log \left(e (a+b x)^n (c+d x)^{-n}\right)\right)^2} \, dx","\frac{\text{Subst}\left(\text{Int}\left(\frac{1}{(a+b x) (f+g x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)^2},x\right),e \left(\frac{a+b x}{c+d x}\right)^n,e (a+b x)^n (c+d x)^{-n}\right)}{h}",0,"Integrate[1/((a*f*h + b*g*h*x^2 + h*(b*f*x + a*g*x))*(A + B*Log[(e*(a + b*x)^n)/(c + d*x)^n])^2), x]","A",-1