1,1,385,0,0.4930552,"\int \left(f+\frac{g}{x}\right)^3 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Int[(f + g/x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","-3 B f^2 g n \text{PolyLog}\left(2,-\frac{b x}{a}\right)+3 B f^2 g n \text{PolyLog}\left(2,-\frac{d x}{c}\right)-\frac{1}{2} B g^3 n \log (x) \left(\frac{b^2}{a^2}-\frac{d^2}{c^2}\right)+\frac{b^2 B g^3 n \log (a+b x)}{2 a^2}+3 f^2 g \log (x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-\frac{3 f g^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{x}-\frac{g^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 x^2}+\frac{B f^3 (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b}-\frac{B f^3 n (b c-a d) \log (c+d x)}{b d}+\frac{3 B f g^2 n \log (x) (b c-a d)}{a c}-\frac{B g^3 n (b c-a d)}{2 a c x}-3 B f^2 g n \log (x) \log \left(\frac{b x}{a}+1\right)-\frac{3 b B f g^2 n \log (a+b x)}{a}+A f^3 x-\frac{B d^2 g^3 n \log (c+d x)}{2 c^2}+3 B f^2 g n \log (x) \log \left(\frac{d x}{c}+1\right)+\frac{3 B d f g^2 n \log (c+d x)}{c}","-3 B f^2 g n \text{PolyLog}\left(2,-\frac{b x}{a}\right)+3 B f^2 g n \text{PolyLog}\left(2,-\frac{d x}{c}\right)-\frac{1}{2} B g^3 n \log (x) \left(\frac{b^2}{a^2}-\frac{d^2}{c^2}\right)+\frac{b^2 B g^3 n \log (a+b x)}{2 a^2}+3 f^2 g \log (x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+\frac{3 f 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)}{a (c+d x) \left(a-\frac{c (a+b x)}{c+d x}\right)}-\frac{g^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 x^2}+\frac{B f^3 (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b}-\frac{B f^3 n (b c-a d) \log (c+d x)}{b d}+\frac{3 B f g^2 n (b c-a d) \log \left(a-\frac{c (a+b x)}{c+d x}\right)}{a c}-\frac{B g^3 n (b c-a d)}{2 a c x}-3 B f^2 g n \log (x) \log \left(\frac{b x}{a}+1\right)+A f^3 x-\frac{B d^2 g^3 n \log (c+d x)}{2 c^2}+3 B f^2 g n \log (x) \log \left(\frac{d x}{c}+1\right)",1,"-(B*(b*c - a*d)*g^3*n)/(2*a*c*x) + A*f^3*x + (3*B*(b*c - a*d)*f*g^2*n*Log[x])/(a*c) - (B*(b^2/a^2 - d^2/c^2)*g^3*n*Log[x])/2 - (3*b*B*f*g^2*n*Log[a + b*x])/a + (b^2*B*g^3*n*Log[a + b*x])/(2*a^2) - 3*B*f^2*g*n*Log[x]*Log[1 + (b*x)/a] + (B*f^3*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/b - (g^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*x^2) - (3*f*g^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/x + 3*f^2*g*Log[x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - (B*(b*c - a*d)*f^3*n*Log[c + d*x])/(b*d) + (3*B*d*f*g^2*n*Log[c + d*x])/c - (B*d^2*g^3*n*Log[c + d*x])/(2*c^2) + 3*B*f^2*g*n*Log[x]*Log[1 + (d*x)/c] - 3*B*f^2*g*n*PolyLog[2, -((b*x)/a)] + 3*B*f^2*g*n*PolyLog[2, -((d*x)/c)]","A",20,10,32,0.3125,1,"{2528, 2486, 31, 2525, 12, 72, 2524, 2357, 2317, 2391}"
2,1,242,0,0.3373624,"\int \left(f+\frac{g}{x}\right)^2 \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Int[(f + g/x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","-2 B f g n \text{PolyLog}\left(2,-\frac{b x}{a}\right)+2 B f g n \text{PolyLog}\left(2,-\frac{d x}{c}\right)+2 f g \log (x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)-\frac{g^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{x}+\frac{B f^2 (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b}-\frac{B f^2 n (b c-a d) \log (c+d x)}{b d}+\frac{B g^2 n \log (x) (b c-a d)}{a c}-2 B f g n \log (x) \log \left(\frac{b x}{a}+1\right)-\frac{b B g^2 n \log (a+b x)}{a}+A f^2 x+2 B f g n \log (x) \log \left(\frac{d x}{c}+1\right)+\frac{B d g^2 n \log (c+d x)}{c}","-2 B f g n \text{PolyLog}\left(2,-\frac{b x}{a}\right)+2 B f g n \text{PolyLog}\left(2,-\frac{d x}{c}\right)+2 f g \log (x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+\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)}{a (c+d x) \left(a-\frac{c (a+b x)}{c+d x}\right)}+\frac{B f^2 (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b}-\frac{B f^2 n (b c-a d) \log (c+d x)}{b d}+\frac{B g^2 n (b c-a d) \log \left(a-\frac{c (a+b x)}{c+d x}\right)}{a c}-2 B f g n \log (x) \log \left(\frac{b x}{a}+1\right)+A f^2 x+2 B f g n \log (x) \log \left(\frac{d x}{c}+1\right)",1,"A*f^2*x + (B*(b*c - a*d)*g^2*n*Log[x])/(a*c) - (b*B*g^2*n*Log[a + b*x])/a - 2*B*f*g*n*Log[x]*Log[1 + (b*x)/a] + (B*f^2*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/b - (g^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/x + 2*f*g*Log[x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - (B*(b*c - a*d)*f^2*n*Log[c + d*x])/(b*d) + (B*d*g^2*n*Log[c + d*x])/c + 2*B*f*g*n*Log[x]*Log[1 + (d*x)/c] - 2*B*f*g*n*PolyLog[2, -((b*x)/a)] + 2*B*f*g*n*PolyLog[2, -((d*x)/c)]","A",16,10,32,0.3125,1,"{2528, 2486, 31, 2525, 12, 72, 2524, 2357, 2317, 2391}"
3,1,143,0,0.2248878,"\int \left(f+\frac{g}{x}\right) \left(A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right) \, dx","Int[(f + g/x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","-B g n \text{PolyLog}\left(2,-\frac{b x}{a}\right)+B g n \text{PolyLog}\left(2,-\frac{d x}{c}\right)+g \log (x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+\frac{B f (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b}-\frac{B f n (b c-a d) \log (c+d x)}{b d}-B g n \log (x) \log \left(\frac{b x}{a}+1\right)+A f x+B g n \log (x) \log \left(\frac{d x}{c}+1\right)","-B g n \text{PolyLog}\left(2,-\frac{b x}{a}\right)+B g n \text{PolyLog}\left(2,-\frac{d x}{c}\right)+g \log (x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+\frac{B f (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b}-\frac{B f n (b c-a d) \log (c+d x)}{b d}-B g n \log (x) \log \left(\frac{b x}{a}+1\right)+A f x+B g n \log (x) \log \left(\frac{d x}{c}+1\right)",1,"A*f*x - B*g*n*Log[x]*Log[1 + (b*x)/a] + (B*f*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/b + g*Log[x]*(A + B*Log[e*((a + b*x)/(c + d*x))^n]) - (B*(b*c - a*d)*f*n*Log[c + d*x])/(b*d) + B*g*n*Log[x]*Log[1 + (d*x)/c] - B*g*n*PolyLog[2, -((b*x)/a)] + B*g*n*PolyLog[2, -((d*x)/c)]","A",12,7,30,0.2333,1,"{2528, 2486, 31, 2524, 2357, 2317, 2391}"
4,1,217,0,0.3322503,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f+\frac{g}{x}} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g/x),x]","\frac{B g n \text{PolyLog}\left(2,-\frac{b (f x+g)}{a f-b g}\right)}{f^2}-\frac{B g n \text{PolyLog}\left(2,-\frac{d (f x+g)}{c f-d g}\right)}{f^2}-\frac{g \log (f x+g) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{f^2}+\frac{B (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b f}-\frac{B n (b c-a d) \log (c+d x)}{b d f}+\frac{B g n \log (f x+g) \log \left(\frac{f (a+b x)}{a f-b g}\right)}{f^2}+\frac{A x}{f}-\frac{B g n \log (f x+g) \log \left(\frac{f (c+d x)}{c f-d g}\right)}{f^2}","\frac{B g n \text{PolyLog}\left(2,-\frac{b (f x+g)}{a f-b g}\right)}{f^2}-\frac{B g n \text{PolyLog}\left(2,-\frac{d (f x+g)}{c f-d g}\right)}{f^2}-\frac{g \log (f x+g) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{f^2}+\frac{B (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b f}-\frac{B n (b c-a d) \log (c+d x)}{b d f}+\frac{B g n \log (f x+g) \log \left(\frac{f (a+b x)}{a f-b g}\right)}{f^2}+\frac{A x}{f}-\frac{B g n \log (f x+g) \log \left(\frac{f (c+d x)}{c f-d g}\right)}{f^2}",1,"(A*x)/f + (B*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/(b*f) - (B*(b*c - a*d)*n*Log[c + d*x])/(b*d*f) + (B*g*n*Log[(f*(a + b*x))/(a*f - b*g)]*Log[g + f*x])/f^2 - (g*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[g + f*x])/f^2 - (B*g*n*Log[(f*(c + d*x))/(c*f - d*g)]*Log[g + f*x])/f^2 + (B*g*n*PolyLog[2, -((b*(g + f*x))/(a*f - b*g))])/f^2 - (B*g*n*PolyLog[2, -((d*(g + f*x))/(c*f - d*g))])/f^2","A",14,8,32,0.2500,1,"{2528, 2486, 31, 2524, 2418, 2394, 2393, 2391}"
5,1,352,0,0.4937585,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{\left(f+\frac{g}{x}\right)^2} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g/x)^2,x]","\frac{2 B g n \text{PolyLog}\left(2,-\frac{b (f x+g)}{a f-b g}\right)}{f^3}-\frac{2 B g n \text{PolyLog}\left(2,-\frac{d (f x+g)}{c f-d g}\right)}{f^3}-\frac{g^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{f^3 (f x+g)}-\frac{2 g \log (f x+g) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{f^3}+\frac{B (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b f^2}+\frac{B g^2 n (b c-a d) \log (f x+g)}{f^2 (a f-b g) (c f-d g)}-\frac{B n (b c-a d) \log (c+d x)}{b d f^2}-\frac{b B g^2 n \log (a+b x)}{f^3 (a f-b g)}+\frac{2 B g n \log (f x+g) \log \left(\frac{f (a+b x)}{a f-b g}\right)}{f^3}+\frac{A x}{f^2}+\frac{B d g^2 n \log (c+d x)}{f^3 (c f-d g)}-\frac{2 B g n \log (f x+g) \log \left(\frac{f (c+d x)}{c f-d g}\right)}{f^3}","\frac{2 B g n \text{PolyLog}\left(2,-\frac{b (f x+g)}{a f-b g}\right)}{f^3}-\frac{2 B g n \text{PolyLog}\left(2,-\frac{d (f x+g)}{c f-d g}\right)}{f^3}-\frac{g^2 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{f^2 (f x+g) (a f-b g)}-\frac{2 g \log (f x+g) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{f^3}+\frac{B (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b f^2}+\frac{B g^2 n (b c-a d) \log \left(\frac{f x+g}{c+d x}\right)}{f^2 (a f-b g) (c f-d g)}-\frac{B n (b c-a d) \log (c+d x)}{b d f^2}+\frac{2 B g n \log (f x+g) \log \left(\frac{f (a+b x)}{a f-b g}\right)}{f^3}+\frac{A x}{f^2}-\frac{2 B g n \log (f x+g) \log \left(\frac{f (c+d x)}{c f-d g}\right)}{f^3}",1,"(A*x)/f^2 - (b*B*g^2*n*Log[a + b*x])/(f^3*(a*f - b*g)) + (B*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/(b*f^2) - (g^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(f^3*(g + f*x)) - (B*(b*c - a*d)*n*Log[c + d*x])/(b*d*f^2) + (B*d*g^2*n*Log[c + d*x])/(f^3*(c*f - d*g)) + (B*(b*c - a*d)*g^2*n*Log[g + f*x])/(f^2*(a*f - b*g)*(c*f - d*g)) + (2*B*g*n*Log[(f*(a + b*x))/(a*f - b*g)]*Log[g + f*x])/f^3 - (2*g*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[g + f*x])/f^3 - (2*B*g*n*Log[(f*(c + d*x))/(c*f - d*g)]*Log[g + f*x])/f^3 + (2*B*g*n*PolyLog[2, -((b*(g + f*x))/(a*f - b*g))])/f^3 - (2*B*g*n*PolyLog[2, -((d*(g + f*x))/(c*f - d*g))])/f^3","A",18,11,32,0.3438,1,"{2528, 2486, 31, 2525, 12, 72, 2524, 2418, 2394, 2393, 2391}"
6,1,562,0,0.7969405,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{\left(f+\frac{g}{x}\right)^3} \, dx","Int[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g/x)^3,x]","\frac{3 B g n \text{PolyLog}\left(2,-\frac{b (f x+g)}{a f-b g}\right)}{f^4}-\frac{3 B g n \text{PolyLog}\left(2,-\frac{d (f x+g)}{c f-d g}\right)}{f^4}+\frac{g^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 f^4 (f x+g)^2}-\frac{3 g^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{f^4 (f x+g)}-\frac{3 g \log (f x+g) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{f^4}-\frac{b^2 B g^3 n \log (a+b x)}{2 f^4 (a f-b g)^2}+\frac{B (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b f^3}+\frac{B g^3 n (b c-a d)}{2 f^3 (f x+g) (a f-b g) (c f-d g)}+\frac{B g^3 n (b c-a d) \log (f x+g) (a d f+b c f-2 b d g)}{2 f^3 (a f-b g)^2 (c f-d g)^2}+\frac{3 B g^2 n (b c-a d) \log (f x+g)}{f^3 (a f-b g) (c f-d g)}-\frac{B n (b c-a d) \log (c+d x)}{b d f^3}-\frac{3 b B g^2 n \log (a+b x)}{f^4 (a f-b g)}+\frac{3 B g n \log (f x+g) \log \left(\frac{f (a+b x)}{a f-b g}\right)}{f^4}+\frac{A x}{f^3}+\frac{B d^2 g^3 n \log (c+d x)}{2 f^4 (c f-d g)^2}+\frac{3 B d g^2 n \log (c+d x)}{f^4 (c f-d g)}-\frac{3 B g n \log (f x+g) \log \left(\frac{f (c+d x)}{c f-d g}\right)}{f^4}","\frac{3 B g n \text{PolyLog}\left(2,-\frac{b (f x+g)}{a f-b g}\right)}{f^4}-\frac{3 B g n \text{PolyLog}\left(2,-\frac{d (f x+g)}{c f-d g}\right)}{f^4}+\frac{g^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{2 f^4 (f x+g)^2}-\frac{3 g^2 (a+b x) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{f^3 (f x+g) (a f-b g)}-\frac{3 g \log (f x+g) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{f^4}-\frac{b^2 B g^3 n \log (a+b x)}{2 f^4 (a f-b g)^2}+\frac{B (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b f^3}+\frac{B g^3 n (b c-a d)}{2 f^3 (f x+g) (a f-b g) (c f-d g)}+\frac{B g^3 n (b c-a d) \log (f x+g) (a d f+b c f-2 b d g)}{2 f^3 (a f-b g)^2 (c f-d g)^2}+\frac{3 B g^2 n (b c-a d) \log \left(\frac{f x+g}{c+d x}\right)}{f^3 (a f-b g) (c f-d g)}-\frac{B n (b c-a d) \log (c+d x)}{b d f^3}+\frac{3 B g n \log (f x+g) \log \left(\frac{f (a+b x)}{a f-b g}\right)}{f^4}+\frac{A x}{f^3}+\frac{B d^2 g^3 n \log (c+d x)}{2 f^4 (c f-d g)^2}-\frac{3 B g n \log (f x+g) \log \left(\frac{f (c+d x)}{c f-d g}\right)}{f^4}",1,"(A*x)/f^3 + (B*(b*c - a*d)*g^3*n)/(2*f^3*(a*f - b*g)*(c*f - d*g)*(g + f*x)) - (b^2*B*g^3*n*Log[a + b*x])/(2*f^4*(a*f - b*g)^2) - (3*b*B*g^2*n*Log[a + b*x])/(f^4*(a*f - b*g)) + (B*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/(b*f^3) + (g^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(2*f^4*(g + f*x)^2) - (3*g^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(f^4*(g + f*x)) - (B*(b*c - a*d)*n*Log[c + d*x])/(b*d*f^3) + (B*d^2*g^3*n*Log[c + d*x])/(2*f^4*(c*f - d*g)^2) + (3*B*d*g^2*n*Log[c + d*x])/(f^4*(c*f - d*g)) + (3*B*(b*c - a*d)*g^2*n*Log[g + f*x])/(f^3*(a*f - b*g)*(c*f - d*g)) + (B*(b*c - a*d)*g^3*(b*c*f + a*d*f - 2*b*d*g)*n*Log[g + f*x])/(2*f^3*(a*f - b*g)^2*(c*f - d*g)^2) + (3*B*g*n*Log[(f*(a + b*x))/(a*f - b*g)]*Log[g + f*x])/f^4 - (3*g*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[g + f*x])/f^4 - (3*B*g*n*Log[(f*(c + d*x))/(c*f - d*g)]*Log[g + f*x])/f^4 + (3*B*g*n*PolyLog[2, -((b*(g + f*x))/(a*f - b*g))])/f^4 - (3*B*g*n*PolyLog[2, -((d*(g + f*x))/(c*f - d*g))])/f^4","A",22,11,32,0.3438,1,"{2528, 2486, 31, 2525, 12, 72, 2524, 2418, 2394, 2393, 2391}"
7,1,201,0,0.0949281,"\int (a+b x)^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[(a + b*x)^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","-\frac{q r x (b c-a d)^4}{5 d^4}+\frac{q r (a+b x)^2 (b c-a d)^3}{10 b d^3}-\frac{q r (a+b x)^3 (b c-a d)^2}{15 b d^2}+\frac{q r (b c-a d)^5 \log (c+d x)}{5 b d^5}+\frac{(a+b x)^5 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{5 b}+\frac{q r (a+b x)^4 (b c-a d)}{20 b d}-\frac{p r (a+b x)^5}{25 b}-\frac{q r (a+b x)^5}{25 b}","-\frac{q r x (b c-a d)^4}{5 d^4}+\frac{q r (a+b x)^2 (b c-a d)^3}{10 b d^3}-\frac{q r (a+b x)^3 (b c-a d)^2}{15 b d^2}+\frac{q r (b c-a d)^5 \log (c+d x)}{5 b d^5}+\frac{(a+b x)^5 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{5 b}+\frac{q r (a+b x)^4 (b c-a d)}{20 b d}-\frac{p r (a+b x)^5}{25 b}-\frac{q r (a+b x)^5}{25 b}",1,"-((b*c - a*d)^4*q*r*x)/(5*d^4) + ((b*c - a*d)^3*q*r*(a + b*x)^2)/(10*b*d^3) - ((b*c - a*d)^2*q*r*(a + b*x)^3)/(15*b*d^2) + ((b*c - a*d)*q*r*(a + b*x)^4)/(20*b*d) - (p*r*(a + b*x)^5)/(25*b) - (q*r*(a + b*x)^5)/(25*b) + ((b*c - a*d)^5*q*r*Log[c + d*x])/(5*b*d^5) + ((a + b*x)^5*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(5*b)","A",4,3,29,0.1034,1,"{2495, 32, 43}"
8,1,172,0,0.0722046,"\int (a+b x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[(a + b*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","\frac{q r x (b c-a d)^3}{4 d^3}-\frac{q r (a+b x)^2 (b c-a d)^2}{8 b d^2}-\frac{q r (b c-a d)^4 \log (c+d x)}{4 b d^4}+\frac{(a+b x)^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 b}+\frac{q r (a+b x)^3 (b c-a d)}{12 b d}-\frac{p r (a+b x)^4}{16 b}-\frac{q r (a+b x)^4}{16 b}","\frac{q r x (b c-a d)^3}{4 d^3}-\frac{q r (a+b x)^2 (b c-a d)^2}{8 b d^2}-\frac{q r (b c-a d)^4 \log (c+d x)}{4 b d^4}+\frac{(a+b x)^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 b}+\frac{q r (a+b x)^3 (b c-a d)}{12 b d}-\frac{p r (a+b x)^4}{16 b}-\frac{q r (a+b x)^4}{16 b}",1,"((b*c - a*d)^3*q*r*x)/(4*d^3) - ((b*c - a*d)^2*q*r*(a + b*x)^2)/(8*b*d^2) + ((b*c - a*d)*q*r*(a + b*x)^3)/(12*b*d) - (p*r*(a + b*x)^4)/(16*b) - (q*r*(a + b*x)^4)/(16*b) - ((b*c - a*d)^4*q*r*Log[c + d*x])/(4*b*d^4) + ((a + b*x)^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(4*b)","A",4,3,29,0.1034,1,"{2495, 32, 43}"
9,1,143,0,0.0608917,"\int (a+b x)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[(a + b*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","-\frac{q r x (b c-a d)^2}{3 d^2}+\frac{q r (b c-a d)^3 \log (c+d x)}{3 b d^3}+\frac{(a+b x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b}+\frac{q r (a+b x)^2 (b c-a d)}{6 b d}-\frac{p r (a+b x)^3}{9 b}-\frac{q r (a+b x)^3}{9 b}","-\frac{q r x (b c-a d)^2}{3 d^2}+\frac{q r (b c-a d)^3 \log (c+d x)}{3 b d^3}+\frac{(a+b x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b}+\frac{q r (a+b x)^2 (b c-a d)}{6 b d}-\frac{p r (a+b x)^3}{9 b}-\frac{q r (a+b x)^3}{9 b}",1,"-((b*c - a*d)^2*q*r*x)/(3*d^2) + ((b*c - a*d)*q*r*(a + b*x)^2)/(6*b*d) - (p*r*(a + b*x)^3)/(9*b) - (q*r*(a + b*x)^3)/(9*b) + ((b*c - a*d)^3*q*r*Log[c + d*x])/(3*b*d^3) + ((a + b*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(3*b)","A",4,3,29,0.1034,1,"{2495, 32, 43}"
10,1,116,0,0.0432106,"\int (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[(a + b*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","-\frac{q r (b c-a d)^2 \log (c+d x)}{2 b d^2}+\frac{(a+b x)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 b}+\frac{q r x (b c-a d)}{2 d}-\frac{q r (a+b x)^2}{4 b}-\frac{1}{2} a p r x-\frac{1}{4} b p r x^2","-\frac{q r (b c-a d)^2 \log (c+d x)}{2 b d^2}+\frac{(a+b x)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 b}+\frac{q r x (b c-a d)}{2 d}-\frac{q r (a+b x)^2}{4 b}-\frac{1}{2} a p r x-\frac{1}{4} b p r x^2",1,"-(a*p*r*x)/2 + ((b*c - a*d)*q*r*x)/(2*d) - (b*p*r*x^2)/4 - (q*r*(a + b*x)^2)/(4*b) - ((b*c - a*d)^2*q*r*Log[c + d*x])/(2*b*d^2) + ((a + b*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(2*b)","A",4,2,27,0.07407,1,"{2495, 43}"
11,1,107,0,0.0829128,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{a+b x} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(a + b*x),x]","-\frac{q r \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b}+\frac{\log (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b}-\frac{q r \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b}-\frac{p r \log ^2(a+b x)}{2 b}","-\frac{q r \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b}+\frac{\log (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b}-\frac{q r \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b}-\frac{p r \log ^2(a+b x)}{2 b}",1,"-(p*r*Log[a + b*x]^2)/(2*b) - (q*r*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/b + (Log[a + b*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/b - (q*r*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/b","A",6,6,29,0.2069,1,"{2494, 2390, 2301, 2394, 2393, 2391}"
12,1,95,0,0.0374773,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^2} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(a + b*x)^2,x]","-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b (a+b x)}+\frac{d q r \log (a+b x)}{b (b c-a d)}-\frac{d q r \log (c+d x)}{b (b c-a d)}-\frac{p r}{b (a+b x)}","-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b (a+b x)}+\frac{d q r \log (a+b x)}{b (b c-a d)}-\frac{d q r \log (c+d x)}{b (b c-a d)}-\frac{p r}{b (a+b x)}",1,"-((p*r)/(b*(a + b*x))) + (d*q*r*Log[a + b*x])/(b*(b*c - a*d)) - (d*q*r*Log[c + d*x])/(b*(b*c - a*d)) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(b*(a + b*x))","A",5,4,29,0.1379,1,"{2495, 32, 36, 31}"
13,1,135,0,0.0561178,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^3} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(a + b*x)^3,x]","-\frac{d^2 q r \log (a+b x)}{2 b (b c-a d)^2}+\frac{d^2 q r \log (c+d x)}{2 b (b c-a d)^2}-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 b (a+b x)^2}-\frac{d q r}{2 b (a+b x) (b c-a d)}-\frac{p r}{4 b (a+b x)^2}","-\frac{d^2 q r \log (a+b x)}{2 b (b c-a d)^2}+\frac{d^2 q r \log (c+d x)}{2 b (b c-a d)^2}-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 b (a+b x)^2}-\frac{d q r}{2 b (a+b x) (b c-a d)}-\frac{p r}{4 b (a+b x)^2}",1,"-(p*r)/(4*b*(a + b*x)^2) - (d*q*r)/(2*b*(b*c - a*d)*(a + b*x)) - (d^2*q*r*Log[a + b*x])/(2*b*(b*c - a*d)^2) + (d^2*q*r*Log[c + d*x])/(2*b*(b*c - a*d)^2) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(2*b*(a + b*x)^2)","A",4,3,29,0.1034,1,"{2495, 32, 44}"
14,1,164,0,0.0693974,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^4} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(a + b*x)^4,x]","\frac{d^2 q r}{3 b (a+b x) (b c-a d)^2}+\frac{d^3 q r \log (a+b x)}{3 b (b c-a d)^3}-\frac{d^3 q r \log (c+d x)}{3 b (b c-a d)^3}-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b (a+b x)^3}-\frac{d q r}{6 b (a+b x)^2 (b c-a d)}-\frac{p r}{9 b (a+b x)^3}","\frac{d^2 q r}{3 b (a+b x) (b c-a d)^2}+\frac{d^3 q r \log (a+b x)}{3 b (b c-a d)^3}-\frac{d^3 q r \log (c+d x)}{3 b (b c-a d)^3}-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b (a+b x)^3}-\frac{d q r}{6 b (a+b x)^2 (b c-a d)}-\frac{p r}{9 b (a+b x)^3}",1,"-(p*r)/(9*b*(a + b*x)^3) - (d*q*r)/(6*b*(b*c - a*d)*(a + b*x)^2) + (d^2*q*r)/(3*b*(b*c - a*d)^2*(a + b*x)) + (d^3*q*r*Log[a + b*x])/(3*b*(b*c - a*d)^3) - (d^3*q*r*Log[c + d*x])/(3*b*(b*c - a*d)^3) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(3*b*(a + b*x)^3)","A",4,3,29,0.1034,1,"{2495, 32, 44}"
15,1,193,0,0.0854361,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^5} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(a + b*x)^5,x]","-\frac{d^3 q r}{4 b (a+b x) (b c-a d)^3}+\frac{d^2 q r}{8 b (a+b x)^2 (b c-a d)^2}-\frac{d^4 q r \log (a+b x)}{4 b (b c-a d)^4}+\frac{d^4 q r \log (c+d x)}{4 b (b c-a d)^4}-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 b (a+b x)^4}-\frac{d q r}{12 b (a+b x)^3 (b c-a d)}-\frac{p r}{16 b (a+b x)^4}","-\frac{d^3 q r}{4 b (a+b x) (b c-a d)^3}+\frac{d^2 q r}{8 b (a+b x)^2 (b c-a d)^2}-\frac{d^4 q r \log (a+b x)}{4 b (b c-a d)^4}+\frac{d^4 q r \log (c+d x)}{4 b (b c-a d)^4}-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 b (a+b x)^4}-\frac{d q r}{12 b (a+b x)^3 (b c-a d)}-\frac{p r}{16 b (a+b x)^4}",1,"-(p*r)/(16*b*(a + b*x)^4) - (d*q*r)/(12*b*(b*c - a*d)*(a + b*x)^3) + (d^2*q*r)/(8*b*(b*c - a*d)^2*(a + b*x)^2) - (d^3*q*r)/(4*b*(b*c - a*d)^3*(a + b*x)) - (d^4*q*r*Log[a + b*x])/(4*b*(b*c - a*d)^4) + (d^4*q*r*Log[c + d*x])/(4*b*(b*c - a*d)^4) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(4*b*(a + b*x)^4)","A",4,3,29,0.1034,1,"{2495, 32, 44}"
16,1,920,0,0.8448965,"\int (a+b x)^4 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[(a + b*x)^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2,x]","-\frac{q^2 r^2 \log ^2(c+d x) (b c-a d)^5}{5 b d^5}-\frac{137 q^2 r^2 \log (c+d x) (b c-a d)^5}{150 b d^5}-\frac{2 p q r^2 \log (c+d x) (b c-a d)^5}{25 b d^5}-\frac{2 p q r^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) (b c-a d)^5}{5 b d^5}+\frac{2 q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)^5}{5 b d^5}-\frac{2 p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) (b c-a d)^5}{5 b d^5}+\frac{77 q^2 r^2 x (b c-a d)^4}{150 d^4}+\frac{2 p q r^2 x (b c-a d)^4}{25 d^4}+\frac{2 q (p+q) r^2 x (b c-a d)^4}{5 d^4}-\frac{2 q r (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)^4}{5 b d^4}-\frac{b p q r^2 x^2 (b c-a d)^3}{10 d^3}-\frac{77 q^2 r^2 (a+b x)^2 (b c-a d)^3}{300 b d^3}-\frac{p q r^2 (a+b x)^2 (b c-a d)^3}{25 b d^3}-\frac{a p q r^2 x (b c-a d)^3}{5 d^3}+\frac{q r (a+b x)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)^3}{5 b d^3}+\frac{47 q^2 r^2 (a+b x)^3 (b c-a d)^2}{450 b d^2}+\frac{16 p q r^2 (a+b x)^3 (b c-a d)^2}{225 b d^2}-\frac{2 q r (a+b x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)^2}{15 b d^2}-\frac{9 q^2 r^2 (a+b x)^4 (b c-a d)}{200 b d}-\frac{9 p q r^2 (a+b x)^4 (b c-a d)}{200 b d}+\frac{q r (a+b x)^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)}{10 b d}+\frac{2 p^2 r^2 (a+b x)^5}{125 b}+\frac{2 q^2 r^2 (a+b x)^5}{125 b}+\frac{4 p q r^2 (a+b x)^5}{125 b}+\frac{(a+b x)^5 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{5 b}-\frac{2 p r (a+b x)^5 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{25 b}-\frac{2 q r (a+b x)^5 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{25 b}","-\frac{q^2 r^2 \log ^2(c+d x) (b c-a d)^5}{5 b d^5}-\frac{137 q^2 r^2 \log (c+d x) (b c-a d)^5}{150 b d^5}-\frac{2 p q r^2 \log (c+d x) (b c-a d)^5}{25 b d^5}-\frac{2 p q r^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) (b c-a d)^5}{5 b d^5}+\frac{2 q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)^5}{5 b d^5}-\frac{2 p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) (b c-a d)^5}{5 b d^5}+\frac{77 q^2 r^2 x (b c-a d)^4}{150 d^4}+\frac{2 p q r^2 x (b c-a d)^4}{25 d^4}+\frac{2 q (p+q) r^2 x (b c-a d)^4}{5 d^4}-\frac{2 q r (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)^4}{5 b d^4}-\frac{b p q r^2 x^2 (b c-a d)^3}{10 d^3}-\frac{77 q^2 r^2 (a+b x)^2 (b c-a d)^3}{300 b d^3}-\frac{p q r^2 (a+b x)^2 (b c-a d)^3}{25 b d^3}-\frac{a p q r^2 x (b c-a d)^3}{5 d^3}+\frac{q r (a+b x)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)^3}{5 b d^3}+\frac{47 q^2 r^2 (a+b x)^3 (b c-a d)^2}{450 b d^2}+\frac{16 p q r^2 (a+b x)^3 (b c-a d)^2}{225 b d^2}-\frac{2 q r (a+b x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)^2}{15 b d^2}-\frac{9 q^2 r^2 (a+b x)^4 (b c-a d)}{200 b d}-\frac{9 p q r^2 (a+b x)^4 (b c-a d)}{200 b d}+\frac{q r (a+b x)^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)}{10 b d}+\frac{2 p^2 r^2 (a+b x)^5}{125 b}+\frac{2 q^2 r^2 (a+b x)^5}{125 b}+\frac{4 p q r^2 (a+b x)^5}{125 b}+\frac{(a+b x)^5 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{5 b}-\frac{2 p r (a+b x)^5 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{25 b}-\frac{2 q r (a+b x)^5 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{25 b}",1,"-(a*(b*c - a*d)^3*p*q*r^2*x)/(5*d^3) + (2*(b*c - a*d)^4*p*q*r^2*x)/(25*d^4) + (77*(b*c - a*d)^4*q^2*r^2*x)/(150*d^4) + (2*(b*c - a*d)^4*q*(p + q)*r^2*x)/(5*d^4) - (b*(b*c - a*d)^3*p*q*r^2*x^2)/(10*d^3) - ((b*c - a*d)^3*p*q*r^2*(a + b*x)^2)/(25*b*d^3) - (77*(b*c - a*d)^3*q^2*r^2*(a + b*x)^2)/(300*b*d^3) + (16*(b*c - a*d)^2*p*q*r^2*(a + b*x)^3)/(225*b*d^2) + (47*(b*c - a*d)^2*q^2*r^2*(a + b*x)^3)/(450*b*d^2) - (9*(b*c - a*d)*p*q*r^2*(a + b*x)^4)/(200*b*d) - (9*(b*c - a*d)*q^2*r^2*(a + b*x)^4)/(200*b*d) + (2*p^2*r^2*(a + b*x)^5)/(125*b) + (4*p*q*r^2*(a + b*x)^5)/(125*b) + (2*q^2*r^2*(a + b*x)^5)/(125*b) - (2*(b*c - a*d)^5*p*q*r^2*Log[c + d*x])/(25*b*d^5) - (137*(b*c - a*d)^5*q^2*r^2*Log[c + d*x])/(150*b*d^5) - (2*(b*c - a*d)^5*p*q*r^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(5*b*d^5) - ((b*c - a*d)^5*q^2*r^2*Log[c + d*x]^2)/(5*b*d^5) - (2*(b*c - a*d)^4*q*r*(a + b*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(5*b*d^4) + ((b*c - a*d)^3*q*r*(a + b*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(5*b*d^3) - (2*(b*c - a*d)^2*q*r*(a + b*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(15*b*d^2) + ((b*c - a*d)*q*r*(a + b*x)^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(10*b*d) - (2*p*r*(a + b*x)^5*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(25*b) - (2*q*r*(a + b*x)^5*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(25*b) + (2*(b*c - a*d)^5*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(5*b*d^5) + ((a + b*x)^5*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2)/(5*b) - (2*(b*c - a*d)^5*p*q*r^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(5*b*d^5)","A",32,14,31,0.4516,1,"{2498, 2495, 32, 43, 2514, 2487, 31, 8, 2494, 2394, 2393, 2391, 2390, 2301}"
17,1,805,0,0.66471,"\int (a+b x)^3 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[(a + b*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2,x]","\frac{q^2 r^2 \log ^2(c+d x) (b c-a d)^4}{4 b d^4}+\frac{25 q^2 r^2 \log (c+d x) (b c-a d)^4}{24 b d^4}+\frac{p q r^2 \log (c+d x) (b c-a d)^4}{8 b d^4}+\frac{p q r^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) (b c-a d)^4}{2 b d^4}-\frac{q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)^4}{2 b d^4}+\frac{p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) (b c-a d)^4}{2 b d^4}-\frac{13 q^2 r^2 x (b c-a d)^3}{24 d^3}-\frac{p q r^2 x (b c-a d)^3}{8 d^3}-\frac{q (p+q) r^2 x (b c-a d)^3}{2 d^3}+\frac{q r (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)^3}{2 b d^3}+\frac{b p q r^2 x^2 (b c-a d)^2}{8 d^2}+\frac{13 q^2 r^2 (a+b x)^2 (b c-a d)^2}{48 b d^2}+\frac{p q r^2 (a+b x)^2 (b c-a d)^2}{16 b d^2}+\frac{a p q r^2 x (b c-a d)^2}{4 d^2}-\frac{q r (a+b x)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)^2}{4 b d^2}-\frac{7 q^2 r^2 (a+b x)^3 (b c-a d)}{72 b d}-\frac{7 p q r^2 (a+b x)^3 (b c-a d)}{72 b d}+\frac{q r (a+b x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)}{6 b d}+\frac{p^2 r^2 (a+b x)^4}{32 b}+\frac{q^2 r^2 (a+b x)^4}{32 b}+\frac{p q r^2 (a+b x)^4}{16 b}+\frac{(a+b x)^4 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 b}-\frac{p r (a+b x)^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{8 b}-\frac{q r (a+b x)^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{8 b}","\frac{q^2 r^2 \log ^2(c+d x) (b c-a d)^4}{4 b d^4}+\frac{25 q^2 r^2 \log (c+d x) (b c-a d)^4}{24 b d^4}+\frac{p q r^2 \log (c+d x) (b c-a d)^4}{8 b d^4}+\frac{p q r^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) (b c-a d)^4}{2 b d^4}-\frac{q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)^4}{2 b d^4}+\frac{p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) (b c-a d)^4}{2 b d^4}-\frac{13 q^2 r^2 x (b c-a d)^3}{24 d^3}-\frac{p q r^2 x (b c-a d)^3}{8 d^3}-\frac{q (p+q) r^2 x (b c-a d)^3}{2 d^3}+\frac{q r (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)^3}{2 b d^3}+\frac{b p q r^2 x^2 (b c-a d)^2}{8 d^2}+\frac{13 q^2 r^2 (a+b x)^2 (b c-a d)^2}{48 b d^2}+\frac{p q r^2 (a+b x)^2 (b c-a d)^2}{16 b d^2}+\frac{a p q r^2 x (b c-a d)^2}{4 d^2}-\frac{q r (a+b x)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)^2}{4 b d^2}-\frac{7 q^2 r^2 (a+b x)^3 (b c-a d)}{72 b d}-\frac{7 p q r^2 (a+b x)^3 (b c-a d)}{72 b d}+\frac{q r (a+b x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) (b c-a d)}{6 b d}+\frac{p^2 r^2 (a+b x)^4}{32 b}+\frac{q^2 r^2 (a+b x)^4}{32 b}+\frac{p q r^2 (a+b x)^4}{16 b}+\frac{(a+b x)^4 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 b}-\frac{p r (a+b x)^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{8 b}-\frac{q r (a+b x)^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{8 b}",1,"(a*(b*c - a*d)^2*p*q*r^2*x)/(4*d^2) - ((b*c - a*d)^3*p*q*r^2*x)/(8*d^3) - (13*(b*c - a*d)^3*q^2*r^2*x)/(24*d^3) - ((b*c - a*d)^3*q*(p + q)*r^2*x)/(2*d^3) + (b*(b*c - a*d)^2*p*q*r^2*x^2)/(8*d^2) + ((b*c - a*d)^2*p*q*r^2*(a + b*x)^2)/(16*b*d^2) + (13*(b*c - a*d)^2*q^2*r^2*(a + b*x)^2)/(48*b*d^2) - (7*(b*c - a*d)*p*q*r^2*(a + b*x)^3)/(72*b*d) - (7*(b*c - a*d)*q^2*r^2*(a + b*x)^3)/(72*b*d) + (p^2*r^2*(a + b*x)^4)/(32*b) + (p*q*r^2*(a + b*x)^4)/(16*b) + (q^2*r^2*(a + b*x)^4)/(32*b) + ((b*c - a*d)^4*p*q*r^2*Log[c + d*x])/(8*b*d^4) + (25*(b*c - a*d)^4*q^2*r^2*Log[c + d*x])/(24*b*d^4) + ((b*c - a*d)^4*p*q*r^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(2*b*d^4) + ((b*c - a*d)^4*q^2*r^2*Log[c + d*x]^2)/(4*b*d^4) + ((b*c - a*d)^3*q*r*(a + b*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(2*b*d^3) - ((b*c - a*d)^2*q*r*(a + b*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(4*b*d^2) + ((b*c - a*d)*q*r*(a + b*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(6*b*d) - (p*r*(a + b*x)^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(8*b) - (q*r*(a + b*x)^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(8*b) - ((b*c - a*d)^4*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(2*b*d^4) + ((a + b*x)^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2)/(4*b) + ((b*c - a*d)^4*p*q*r^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*b*d^4)","A",28,14,31,0.4516,1,"{2498, 2495, 32, 43, 2514, 2487, 31, 8, 2494, 2394, 2393, 2391, 2390, 2301}"
18,1,686,0,0.5328635,"\int (a+b x)^2 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[(a + b*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2,x]","-\frac{2 p q r^2 (b c-a d)^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 b d^3}+\frac{2 q r (b c-a d)^3 \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b d^3}-\frac{2 q r (a+b x) (b c-a d)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b d^2}+\frac{2 p q r^2 x (b c-a d)^2}{9 d^2}+\frac{2 q r^2 x (p+q) (b c-a d)^2}{3 d^2}-\frac{2 p q r^2 (b c-a d)^3 \log (c+d x)}{9 b d^3}-\frac{2 p q r^2 (b c-a d)^3 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 b d^3}+\frac{5 q^2 r^2 x (b c-a d)^2}{9 d^2}-\frac{q^2 r^2 (b c-a d)^3 \log ^2(c+d x)}{3 b d^3}-\frac{11 q^2 r^2 (b c-a d)^3 \log (c+d x)}{9 b d^3}+\frac{(a+b x)^3 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b}+\frac{q r (a+b x)^2 (b c-a d) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b d}-\frac{2 p r (a+b x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{9 b}-\frac{2 q r (a+b x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{9 b}-\frac{b p q r^2 x^2 (b c-a d)}{6 d}-\frac{p q r^2 (a+b x)^2 (b c-a d)}{9 b d}-\frac{a p q r^2 x (b c-a d)}{3 d}-\frac{5 q^2 r^2 (a+b x)^2 (b c-a d)}{18 b d}+\frac{2 p^2 r^2 (a+b x)^3}{27 b}+\frac{4 p q r^2 (a+b x)^3}{27 b}+\frac{2 q^2 r^2 (a+b x)^3}{27 b}","-\frac{2 p q r^2 (b c-a d)^3 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 b d^3}+\frac{2 q r (b c-a d)^3 \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b d^3}-\frac{2 q r (a+b x) (b c-a d)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b d^2}+\frac{2 p q r^2 x (b c-a d)^2}{9 d^2}+\frac{2 q r^2 x (p+q) (b c-a d)^2}{3 d^2}-\frac{2 p q r^2 (b c-a d)^3 \log (c+d x)}{9 b d^3}-\frac{2 p q r^2 (b c-a d)^3 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 b d^3}+\frac{5 q^2 r^2 x (b c-a d)^2}{9 d^2}-\frac{q^2 r^2 (b c-a d)^3 \log ^2(c+d x)}{3 b d^3}-\frac{11 q^2 r^2 (b c-a d)^3 \log (c+d x)}{9 b d^3}+\frac{(a+b x)^3 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b}+\frac{q r (a+b x)^2 (b c-a d) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b d}-\frac{2 p r (a+b x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{9 b}-\frac{2 q r (a+b x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{9 b}-\frac{b p q r^2 x^2 (b c-a d)}{6 d}-\frac{p q r^2 (a+b x)^2 (b c-a d)}{9 b d}-\frac{a p q r^2 x (b c-a d)}{3 d}-\frac{5 q^2 r^2 (a+b x)^2 (b c-a d)}{18 b d}+\frac{2 p^2 r^2 (a+b x)^3}{27 b}+\frac{4 p q r^2 (a+b x)^3}{27 b}+\frac{2 q^2 r^2 (a+b x)^3}{27 b}",1,"-(a*(b*c - a*d)*p*q*r^2*x)/(3*d) + (2*(b*c - a*d)^2*p*q*r^2*x)/(9*d^2) + (5*(b*c - a*d)^2*q^2*r^2*x)/(9*d^2) + (2*(b*c - a*d)^2*q*(p + q)*r^2*x)/(3*d^2) - (b*(b*c - a*d)*p*q*r^2*x^2)/(6*d) - ((b*c - a*d)*p*q*r^2*(a + b*x)^2)/(9*b*d) - (5*(b*c - a*d)*q^2*r^2*(a + b*x)^2)/(18*b*d) + (2*p^2*r^2*(a + b*x)^3)/(27*b) + (4*p*q*r^2*(a + b*x)^3)/(27*b) + (2*q^2*r^2*(a + b*x)^3)/(27*b) - (2*(b*c - a*d)^3*p*q*r^2*Log[c + d*x])/(9*b*d^3) - (11*(b*c - a*d)^3*q^2*r^2*Log[c + d*x])/(9*b*d^3) - (2*(b*c - a*d)^3*p*q*r^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*b*d^3) - ((b*c - a*d)^3*q^2*r^2*Log[c + d*x]^2)/(3*b*d^3) - (2*(b*c - a*d)^2*q*r*(a + b*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(3*b*d^2) + ((b*c - a*d)*q*r*(a + b*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(3*b*d) - (2*p*r*(a + b*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(9*b) - (2*q*r*(a + b*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(9*b) + (2*(b*c - a*d)^3*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(3*b*d^3) + ((a + b*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2)/(3*b) - (2*(b*c - a*d)^3*p*q*r^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*b*d^3)","A",24,14,31,0.4516,1,"{2498, 2495, 32, 43, 2514, 2487, 31, 8, 2494, 2394, 2393, 2391, 2390, 2301}"
19,1,540,0,0.390924,"\int (a+b x) \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[(a + b*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2,x]","\frac{p q r^2 (b c-a d)^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b d^2}-\frac{q r (b c-a d)^2 \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b d^2}+\frac{p q r^2 (b c-a d)^2 \log (c+d x)}{2 b d^2}+\frac{p q r^2 (b c-a d)^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b d^2}+\frac{q^2 r^2 (b c-a d)^2 \log ^2(c+d x)}{2 b d^2}+\frac{3 q^2 r^2 (b c-a d)^2 \log (c+d x)}{2 b d^2}+\frac{(a+b x)^2 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 b}+\frac{q r (a+b x) (b c-a d) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b d}-\frac{p r (a+b x)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 b}-\frac{q r (a+b x)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 b}-\frac{p q r^2 x (b c-a d)}{2 d}-\frac{q r^2 x (p+q) (b c-a d)}{d}-\frac{q^2 r^2 x (b c-a d)}{2 d}+\frac{p q r^2 (a+b x)^2}{4 b}+\frac{q^2 r^2 (a+b x)^2}{4 b}+\frac{1}{2} a p^2 r^2 x+\frac{1}{2} a p q r^2 x+\frac{1}{4} b p^2 r^2 x^2+\frac{1}{4} b p q r^2 x^2","\frac{p q r^2 (b c-a d)^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b d^2}-\frac{q r (b c-a d)^2 \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b d^2}+\frac{p q r^2 (b c-a d)^2 \log (c+d x)}{2 b d^2}+\frac{p q r^2 (b c-a d)^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b d^2}+\frac{q^2 r^2 (b c-a d)^2 \log ^2(c+d x)}{2 b d^2}+\frac{3 q^2 r^2 (b c-a d)^2 \log (c+d x)}{2 b d^2}+\frac{(a+b x)^2 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 b}+\frac{q r (a+b x) (b c-a d) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b d}-\frac{p r (a+b x)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 b}-\frac{q r (a+b x)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 b}-\frac{p q r^2 x (b c-a d)}{2 d}-\frac{q r^2 x (p+q) (b c-a d)}{d}-\frac{q^2 r^2 x (b c-a d)}{2 d}+\frac{p q r^2 (a+b x)^2}{4 b}+\frac{q^2 r^2 (a+b x)^2}{4 b}+\frac{1}{2} a p^2 r^2 x+\frac{1}{2} a p q r^2 x+\frac{1}{4} b p^2 r^2 x^2+\frac{1}{4} b p q r^2 x^2",1,"(a*p^2*r^2*x)/2 + (a*p*q*r^2*x)/2 - ((b*c - a*d)*p*q*r^2*x)/(2*d) - ((b*c - a*d)*q^2*r^2*x)/(2*d) - ((b*c - a*d)*q*(p + q)*r^2*x)/d + (b*p^2*r^2*x^2)/4 + (b*p*q*r^2*x^2)/4 + (p*q*r^2*(a + b*x)^2)/(4*b) + (q^2*r^2*(a + b*x)^2)/(4*b) + ((b*c - a*d)^2*p*q*r^2*Log[c + d*x])/(2*b*d^2) + (3*(b*c - a*d)^2*q^2*r^2*Log[c + d*x])/(2*b*d^2) + ((b*c - a*d)^2*p*q*r^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*d^2) + ((b*c - a*d)^2*q^2*r^2*Log[c + d*x]^2)/(2*b*d^2) + ((b*c - a*d)*q*r*(a + b*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(b*d) - (p*r*(a + b*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(2*b) - (q*r*(a + b*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(2*b) - ((b*c - a*d)^2*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(b*d^2) + ((a + b*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2)/(2*b) + ((b*c - a*d)^2*p*q*r^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*d^2)","A",20,13,29,0.4483,1,"{2498, 2495, 43, 2514, 2487, 31, 8, 2494, 2394, 2393, 2391, 2390, 2301}"
20,1,431,0,0.4915177,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{a+b x} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(a + b*x),x]","-\frac{1}{4} \left(-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+\log \left((a+b x)^{p r}\right)+\log \left((c+d x)^{q r}\right)\right) \left(8 \left(\frac{q r \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b}+\frac{\log \left(-\frac{d (a+b x)}{b c-a d}\right) \log \left((c+d x)^{q r}\right)}{b}\right)+\frac{\left(\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+\log \left((a+b x)^{p r}\right)-\log \left((c+d x)^{q r}\right)\right)^2}{b p r}\right)+\frac{2 p q r^2 \text{PolyLog}\left(3,-\frac{d (a+b x)}{b c-a d}\right)}{b}-\frac{2 q r \log \left((a+b x)^{p r}\right) \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b}-\frac{2 q^2 r^2 \text{PolyLog}\left(3,\frac{b (c+d x)}{b c-a d}\right)}{b}+\frac{2 q r \log \left((c+d x)^{q r}\right) \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b}-\frac{q \log \left(\frac{b (c+d x)}{b c-a d}\right) \log ^2\left((a+b x)^{p r}\right)}{b p}+\frac{\log ^2\left((a+b x)^{p r}\right) \log \left((c+d x)^{q r}\right)}{b p r}+\frac{\log \left(-\frac{d (a+b x)}{b c-a d}\right) \log ^2\left((c+d x)^{q r}\right)}{b}+\frac{\log ^3\left((a+b x)^{p r}\right)}{3 b p r}","-\frac{1}{4} \left(-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+\log \left((a+b x)^{p r}\right)+\log \left((c+d x)^{q r}\right)\right) \left(8 \left(\frac{q r \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b}+\frac{\log \left(-\frac{d (a+b x)}{b c-a d}\right) \log \left((c+d x)^{q r}\right)}{b}\right)+\frac{\left(\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+\log \left((a+b x)^{p r}\right)-\log \left((c+d x)^{q r}\right)\right)^2}{b p r}\right)+\frac{2 p q r^2 \text{PolyLog}\left(3,-\frac{d (a+b x)}{b c-a d}\right)}{b}-\frac{2 q r \log \left((a+b x)^{p r}\right) \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b}-\frac{2 q^2 r^2 \text{PolyLog}\left(3,\frac{b (c+d x)}{b c-a d}\right)}{b}+\frac{2 q r \log \left((c+d x)^{q r}\right) \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b}-\frac{q \log \left(\frac{b (c+d x)}{b c-a d}\right) \log ^2\left((a+b x)^{p r}\right)}{b p}+\frac{\log ^2\left((a+b x)^{p r}\right) \log \left((c+d x)^{q r}\right)}{b p r}+\frac{\log \left(-\frac{d (a+b x)}{b c-a d}\right) \log ^2\left((c+d x)^{q r}\right)}{b}+\frac{\log ^3\left((a+b x)^{p r}\right)}{3 b p r}",1,"Log[(a + b*x)^(p*r)]^3/(3*b*p*r) - (q*Log[(a + b*x)^(p*r)]^2*Log[(b*(c + d*x))/(b*c - a*d)])/(b*p) + (Log[(a + b*x)^(p*r)]^2*Log[(c + d*x)^(q*r)])/(b*p*r) + (Log[-((d*(a + b*x))/(b*c - a*d))]*Log[(c + d*x)^(q*r)]^2)/b - (2*q*r*Log[(a + b*x)^(p*r)]*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/b + (2*q*r*Log[(c + d*x)^(q*r)]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/b - ((Log[(a + b*x)^(p*r)] + Log[(c + d*x)^(q*r)] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])*((Log[(a + b*x)^(p*r)] - Log[(c + d*x)^(q*r)] + Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])^2/(b*p*r) + 8*((Log[-((d*(a + b*x))/(b*c - a*d))]*Log[(c + d*x)^(q*r)])/b + (q*r*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/b)))/4 + (2*p*q*r^2*PolyLog[3, -((d*(a + b*x))/(b*c - a*d))])/b - (2*q^2*r^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])/b","A",19,15,31,0.4839,1,"{2496, 6742, 2390, 2302, 30, 2433, 2375, 2317, 2374, 6589, 2396, 2394, 2393, 2391, 6686}"
21,1,465,0,0.3871237,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^2} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(a + b*x)^2,x]","\frac{2 d p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b (b c-a d)}-\frac{2 d q^2 r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b (b c-a d)}-\frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b (a+b x)}+\frac{2 d q r \log (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b (b c-a d)}-\frac{2 d q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b (b c-a d)}-\frac{2 p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b (a+b x)}-\frac{d p q r^2 \log ^2(a+b x)}{b (b c-a d)}+\frac{2 d p q r^2 \log (a+b x)}{b (b c-a d)}-\frac{2 d p q r^2 \log (c+d x)}{b (b c-a d)}+\frac{2 d p q r^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b (b c-a d)}+\frac{d q^2 r^2 \log ^2(c+d x)}{b (b c-a d)}-\frac{2 d q^2 r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b (b c-a d)}-\frac{2 p^2 r^2}{b (a+b x)}","\frac{2 d p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b (b c-a d)}-\frac{2 d q^2 r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b (b c-a d)}-\frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b (a+b x)}+\frac{2 d q r \log (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b (b c-a d)}-\frac{2 d q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b (b c-a d)}-\frac{2 p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b (a+b x)}-\frac{d p q r^2 \log ^2(a+b x)}{b (b c-a d)}+\frac{2 d p q r^2 \log (a+b x)}{b (b c-a d)}-\frac{2 d p q r^2 \log (c+d x)}{b (b c-a d)}+\frac{2 d p q r^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b (b c-a d)}+\frac{d q^2 r^2 \log ^2(c+d x)}{b (b c-a d)}-\frac{2 d q^2 r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b (b c-a d)}-\frac{2 p^2 r^2}{b (a+b x)}",1,"(-2*p^2*r^2)/(b*(a + b*x)) + (2*d*p*q*r^2*Log[a + b*x])/(b*(b*c - a*d)) - (d*p*q*r^2*Log[a + b*x]^2)/(b*(b*c - a*d)) - (2*d*p*q*r^2*Log[c + d*x])/(b*(b*c - a*d)) + (2*d*p*q*r^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*(b*c - a*d)) + (d*q^2*r^2*Log[c + d*x]^2)/(b*(b*c - a*d)) - (2*d*q^2*r^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)) - (2*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(b*(a + b*x)) + (2*d*q*r*Log[a + b*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(b*(b*c - a*d)) - (2*d*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(b*(b*c - a*d)) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(b*(a + b*x)) - (2*d*q^2*r^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*(b*c - a*d)) + (2*d*p*q*r^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d))","A",20,12,31,0.3871,1,"{2498, 2495, 32, 36, 31, 2514, 2494, 2390, 2301, 2394, 2393, 2391}"
22,1,632,0,0.4897099,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^3} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(a + b*x)^3,x]","-\frac{d^2 p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b (b c-a d)^2}+\frac{d^2 q^2 r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b (b c-a d)^2}-\frac{d^2 q r \log (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b (b c-a d)^2}+\frac{d^2 q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b (b c-a d)^2}+\frac{d^2 p q r^2 \log ^2(a+b x)}{2 b (b c-a d)^2}-\frac{d^2 p q r^2 \log (a+b x)}{2 b (b c-a d)^2}+\frac{d^2 p q r^2 \log (c+d x)}{2 b (b c-a d)^2}-\frac{d^2 p q r^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b (b c-a d)^2}-\frac{d^2 q^2 r^2 \log ^2(c+d x)}{2 b (b c-a d)^2}+\frac{d^2 q^2 r^2 \log (a+b x)}{b (b c-a d)^2}-\frac{d^2 q^2 r^2 \log (c+d x)}{b (b c-a d)^2}+\frac{d^2 q^2 r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b (b c-a d)^2}-\frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 b (a+b x)^2}-\frac{d q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b (a+b x) (b c-a d)}-\frac{p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 b (a+b x)^2}-\frac{3 d p q r^2}{2 b (a+b x) (b c-a d)}-\frac{p^2 r^2}{4 b (a+b x)^2}","-\frac{d^2 p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b (b c-a d)^2}+\frac{d^2 q^2 r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{b (b c-a d)^2}-\frac{d^2 q r \log (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b (b c-a d)^2}+\frac{d^2 q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b (b c-a d)^2}+\frac{d^2 p q r^2 \log ^2(a+b x)}{2 b (b c-a d)^2}-\frac{d^2 p q r^2 \log (a+b x)}{2 b (b c-a d)^2}+\frac{d^2 p q r^2 \log (c+d x)}{2 b (b c-a d)^2}-\frac{d^2 p q r^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b (b c-a d)^2}-\frac{d^2 q^2 r^2 \log ^2(c+d x)}{2 b (b c-a d)^2}+\frac{d^2 q^2 r^2 \log (a+b x)}{b (b c-a d)^2}-\frac{d^2 q^2 r^2 \log (c+d x)}{b (b c-a d)^2}+\frac{d^2 q^2 r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{b (b c-a d)^2}-\frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 b (a+b x)^2}-\frac{d q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b (a+b x) (b c-a d)}-\frac{p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 b (a+b x)^2}-\frac{3 d p q r^2}{2 b (a+b x) (b c-a d)}-\frac{p^2 r^2}{4 b (a+b x)^2}",1,"-(p^2*r^2)/(4*b*(a + b*x)^2) - (3*d*p*q*r^2)/(2*b*(b*c - a*d)*(a + b*x)) - (d^2*p*q*r^2*Log[a + b*x])/(2*b*(b*c - a*d)^2) + (d^2*q^2*r^2*Log[a + b*x])/(b*(b*c - a*d)^2) + (d^2*p*q*r^2*Log[a + b*x]^2)/(2*b*(b*c - a*d)^2) + (d^2*p*q*r^2*Log[c + d*x])/(2*b*(b*c - a*d)^2) - (d^2*q^2*r^2*Log[c + d*x])/(b*(b*c - a*d)^2) - (d^2*p*q*r^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*(b*c - a*d)^2) - (d^2*q^2*r^2*Log[c + d*x]^2)/(2*b*(b*c - a*d)^2) + (d^2*q^2*r^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)^2) - (p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(2*b*(a + b*x)^2) - (d*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(b*(b*c - a*d)*(a + b*x)) - (d^2*q*r*Log[a + b*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(b*(b*c - a*d)^2) + (d^2*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(b*(b*c - a*d)^2) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(2*b*(a + b*x)^2) + (d^2*q^2*r^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(b*(b*c - a*d)^2) - (d^2*p*q*r^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)^2)","A",24,13,31,0.4194,1,"{2498, 2495, 32, 44, 2514, 36, 31, 2494, 2390, 2301, 2394, 2393, 2391}"
23,1,764,0,0.6064621,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^4} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(a + b*x)^4,x]","\frac{2 d^3 p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 b (b c-a d)^3}-\frac{2 d^3 q^2 r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{3 b (b c-a d)^3}+\frac{2 d^3 q r \log (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b (b c-a d)^3}-\frac{2 d^3 q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b (b c-a d)^3}+\frac{2 d^2 q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b (a+b x) (b c-a d)^2}+\frac{8 d^2 p q r^2}{9 b (a+b x) (b c-a d)^2}-\frac{d^3 p q r^2 \log ^2(a+b x)}{3 b (b c-a d)^3}+\frac{2 d^3 p q r^2 \log (a+b x)}{9 b (b c-a d)^3}-\frac{2 d^3 p q r^2 \log (c+d x)}{9 b (b c-a d)^3}+\frac{2 d^3 p q r^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 b (b c-a d)^3}-\frac{d^2 q^2 r^2}{3 b (a+b x) (b c-a d)^2}+\frac{d^3 q^2 r^2 \log ^2(c+d x)}{3 b (b c-a d)^3}-\frac{d^3 q^2 r^2 \log (a+b x)}{b (b c-a d)^3}+\frac{d^3 q^2 r^2 \log (c+d x)}{b (b c-a d)^3}-\frac{2 d^3 q^2 r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{3 b (b c-a d)^3}-\frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b (a+b x)^3}-\frac{d q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b (a+b x)^2 (b c-a d)}-\frac{2 p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{9 b (a+b x)^3}-\frac{5 d p q r^2}{18 b (a+b x)^2 (b c-a d)}-\frac{2 p^2 r^2}{27 b (a+b x)^3}","\frac{2 d^3 p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{3 b (b c-a d)^3}-\frac{2 d^3 q^2 r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{3 b (b c-a d)^3}+\frac{2 d^3 q r \log (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b (b c-a d)^3}-\frac{2 d^3 q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b (b c-a d)^3}+\frac{2 d^2 q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b (a+b x) (b c-a d)^2}+\frac{8 d^2 p q r^2}{9 b (a+b x) (b c-a d)^2}-\frac{d^3 p q r^2 \log ^2(a+b x)}{3 b (b c-a d)^3}+\frac{2 d^3 p q r^2 \log (a+b x)}{9 b (b c-a d)^3}-\frac{2 d^3 p q r^2 \log (c+d x)}{9 b (b c-a d)^3}+\frac{2 d^3 p q r^2 \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{3 b (b c-a d)^3}-\frac{d^2 q^2 r^2}{3 b (a+b x) (b c-a d)^2}+\frac{d^3 q^2 r^2 \log ^2(c+d x)}{3 b (b c-a d)^3}-\frac{d^3 q^2 r^2 \log (a+b x)}{b (b c-a d)^3}+\frac{d^3 q^2 r^2 \log (c+d x)}{b (b c-a d)^3}-\frac{2 d^3 q^2 r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{3 b (b c-a d)^3}-\frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b (a+b x)^3}-\frac{d q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 b (a+b x)^2 (b c-a d)}-\frac{2 p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{9 b (a+b x)^3}-\frac{5 d p q r^2}{18 b (a+b x)^2 (b c-a d)}-\frac{2 p^2 r^2}{27 b (a+b x)^3}",1,"(-2*p^2*r^2)/(27*b*(a + b*x)^3) - (5*d*p*q*r^2)/(18*b*(b*c - a*d)*(a + b*x)^2) + (8*d^2*p*q*r^2)/(9*b*(b*c - a*d)^2*(a + b*x)) - (d^2*q^2*r^2)/(3*b*(b*c - a*d)^2*(a + b*x)) + (2*d^3*p*q*r^2*Log[a + b*x])/(9*b*(b*c - a*d)^3) - (d^3*q^2*r^2*Log[a + b*x])/(b*(b*c - a*d)^3) - (d^3*p*q*r^2*Log[a + b*x]^2)/(3*b*(b*c - a*d)^3) - (2*d^3*p*q*r^2*Log[c + d*x])/(9*b*(b*c - a*d)^3) + (d^3*q^2*r^2*Log[c + d*x])/(b*(b*c - a*d)^3) + (2*d^3*p*q*r^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*b*(b*c - a*d)^3) + (d^3*q^2*r^2*Log[c + d*x]^2)/(3*b*(b*c - a*d)^3) - (2*d^3*q^2*r^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3*b*(b*c - a*d)^3) - (2*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(9*b*(a + b*x)^3) - (d*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(3*b*(b*c - a*d)*(a + b*x)^2) + (2*d^2*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(3*b*(b*c - a*d)^2*(a + b*x)) + (2*d^3*q*r*Log[a + b*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(3*b*(b*c - a*d)^3) - (2*d^3*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(3*b*(b*c - a*d)^3) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(3*b*(a + b*x)^3) - (2*d^3*q^2*r^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(3*b*(b*c - a*d)^3) + (2*d^3*p*q*r^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*b*(b*c - a*d)^3)","A",28,13,31,0.4194,1,"{2498, 2495, 32, 44, 2514, 36, 31, 2494, 2390, 2301, 2394, 2393, 2391}"
24,1,884,0,0.7378911,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^5} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(a + b*x)^5,x]","\frac{p q r^2 \log ^2(a+b x) d^4}{4 b (b c-a d)^4}-\frac{q^2 r^2 \log ^2(c+d x) d^4}{4 b (b c-a d)^4}+\frac{11 q^2 r^2 \log (a+b x) d^4}{12 b (b c-a d)^4}-\frac{p q r^2 \log (a+b x) d^4}{8 b (b c-a d)^4}-\frac{11 q^2 r^2 \log (c+d x) d^4}{12 b (b c-a d)^4}+\frac{p q r^2 \log (c+d x) d^4}{8 b (b c-a d)^4}-\frac{p q r^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) d^4}{2 b (b c-a d)^4}+\frac{q^2 r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) d^4}{2 b (b c-a d)^4}-\frac{q r \log (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) d^4}{2 b (b c-a d)^4}+\frac{q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) d^4}{2 b (b c-a d)^4}+\frac{q^2 r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) d^4}{2 b (b c-a d)^4}-\frac{p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) d^4}{2 b (b c-a d)^4}-\frac{q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) d^3}{2 b (b c-a d)^3 (a+b x)}+\frac{5 q^2 r^2 d^3}{12 b (b c-a d)^3 (a+b x)}-\frac{5 p q r^2 d^3}{8 b (b c-a d)^3 (a+b x)}+\frac{q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) d^2}{4 b (b c-a d)^2 (a+b x)^2}-\frac{q^2 r^2 d^2}{12 b (b c-a d)^2 (a+b x)^2}+\frac{3 p q r^2 d^2}{16 b (b c-a d)^2 (a+b x)^2}-\frac{q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) d}{6 b (b c-a d) (a+b x)^3}-\frac{7 p q r^2 d}{72 b (b c-a d) (a+b x)^3}-\frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 b (a+b x)^4}-\frac{p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{8 b (a+b x)^4}-\frac{p^2 r^2}{32 b (a+b x)^4}","\frac{p q r^2 \log ^2(a+b x) d^4}{4 b (b c-a d)^4}-\frac{q^2 r^2 \log ^2(c+d x) d^4}{4 b (b c-a d)^4}+\frac{11 q^2 r^2 \log (a+b x) d^4}{12 b (b c-a d)^4}-\frac{p q r^2 \log (a+b x) d^4}{8 b (b c-a d)^4}-\frac{11 q^2 r^2 \log (c+d x) d^4}{12 b (b c-a d)^4}+\frac{p q r^2 \log (c+d x) d^4}{8 b (b c-a d)^4}-\frac{p q r^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) d^4}{2 b (b c-a d)^4}+\frac{q^2 r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) d^4}{2 b (b c-a d)^4}-\frac{q r \log (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) d^4}{2 b (b c-a d)^4}+\frac{q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) d^4}{2 b (b c-a d)^4}+\frac{q^2 r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) d^4}{2 b (b c-a d)^4}-\frac{p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) d^4}{2 b (b c-a d)^4}-\frac{q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) d^3}{2 b (b c-a d)^3 (a+b x)}+\frac{5 q^2 r^2 d^3}{12 b (b c-a d)^3 (a+b x)}-\frac{5 p q r^2 d^3}{8 b (b c-a d)^3 (a+b x)}+\frac{q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) d^2}{4 b (b c-a d)^2 (a+b x)^2}-\frac{q^2 r^2 d^2}{12 b (b c-a d)^2 (a+b x)^2}+\frac{3 p q r^2 d^2}{16 b (b c-a d)^2 (a+b x)^2}-\frac{q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) d}{6 b (b c-a d) (a+b x)^3}-\frac{7 p q r^2 d}{72 b (b c-a d) (a+b x)^3}-\frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 b (a+b x)^4}-\frac{p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{8 b (a+b x)^4}-\frac{p^2 r^2}{32 b (a+b x)^4}",1,"-(p^2*r^2)/(32*b*(a + b*x)^4) - (7*d*p*q*r^2)/(72*b*(b*c - a*d)*(a + b*x)^3) + (3*d^2*p*q*r^2)/(16*b*(b*c - a*d)^2*(a + b*x)^2) - (d^2*q^2*r^2)/(12*b*(b*c - a*d)^2*(a + b*x)^2) - (5*d^3*p*q*r^2)/(8*b*(b*c - a*d)^3*(a + b*x)) + (5*d^3*q^2*r^2)/(12*b*(b*c - a*d)^3*(a + b*x)) - (d^4*p*q*r^2*Log[a + b*x])/(8*b*(b*c - a*d)^4) + (11*d^4*q^2*r^2*Log[a + b*x])/(12*b*(b*c - a*d)^4) + (d^4*p*q*r^2*Log[a + b*x]^2)/(4*b*(b*c - a*d)^4) + (d^4*p*q*r^2*Log[c + d*x])/(8*b*(b*c - a*d)^4) - (11*d^4*q^2*r^2*Log[c + d*x])/(12*b*(b*c - a*d)^4) - (d^4*p*q*r^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(2*b*(b*c - a*d)^4) - (d^4*q^2*r^2*Log[c + d*x]^2)/(4*b*(b*c - a*d)^4) + (d^4*q^2*r^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(2*b*(b*c - a*d)^4) - (p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(8*b*(a + b*x)^4) - (d*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(6*b*(b*c - a*d)*(a + b*x)^3) + (d^2*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(4*b*(b*c - a*d)^2*(a + b*x)^2) - (d^3*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(2*b*(b*c - a*d)^3*(a + b*x)) - (d^4*q*r*Log[a + b*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(2*b*(b*c - a*d)^4) + (d^4*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(2*b*(b*c - a*d)^4) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(4*b*(a + b*x)^4) + (d^4*q^2*r^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(2*b*(b*c - a*d)^4) - (d^4*p*q*r^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*b*(b*c - a*d)^4)","A",32,13,31,0.4194,1,"{2498, 2495, 32, 44, 2514, 36, 31, 2494, 2390, 2301, 2394, 2393, 2391}"
25,1,334,0,0.1855634,"\int (g+h x)^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[(g + h*x)^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","-\frac{p r x (b g-a h)^4}{5 b^4}-\frac{p r (g+h x)^2 (b g-a h)^3}{10 b^3 h}-\frac{p r (g+h x)^3 (b g-a h)^2}{15 b^2 h}-\frac{p r (b g-a h)^5 \log (a+b x)}{5 b^5 h}+\frac{(g+h x)^5 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{5 h}-\frac{p r (g+h x)^4 (b g-a h)}{20 b h}-\frac{q r (g+h x)^3 (d g-c h)^2}{15 d^2 h}-\frac{q r (g+h x)^2 (d g-c h)^3}{10 d^3 h}-\frac{q r x (d g-c h)^4}{5 d^4}-\frac{q r (d g-c h)^5 \log (c+d x)}{5 d^5 h}-\frac{q r (g+h x)^4 (d g-c h)}{20 d h}-\frac{p r (g+h x)^5}{25 h}-\frac{q r (g+h x)^5}{25 h}","-\frac{p r x (b g-a h)^4}{5 b^4}-\frac{p r (g+h x)^2 (b g-a h)^3}{10 b^3 h}-\frac{p r (g+h x)^3 (b g-a h)^2}{15 b^2 h}-\frac{p r (b g-a h)^5 \log (a+b x)}{5 b^5 h}+\frac{(g+h x)^5 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{5 h}-\frac{p r (g+h x)^4 (b g-a h)}{20 b h}-\frac{q r (g+h x)^3 (d g-c h)^2}{15 d^2 h}-\frac{q r (g+h x)^2 (d g-c h)^3}{10 d^3 h}-\frac{q r x (d g-c h)^4}{5 d^4}-\frac{q r (d g-c h)^5 \log (c+d x)}{5 d^5 h}-\frac{q r (g+h x)^4 (d g-c h)}{20 d h}-\frac{p r (g+h x)^5}{25 h}-\frac{q r (g+h x)^5}{25 h}",1,"-((b*g - a*h)^4*p*r*x)/(5*b^4) - ((d*g - c*h)^4*q*r*x)/(5*d^4) - ((b*g - a*h)^3*p*r*(g + h*x)^2)/(10*b^3*h) - ((d*g - c*h)^3*q*r*(g + h*x)^2)/(10*d^3*h) - ((b*g - a*h)^2*p*r*(g + h*x)^3)/(15*b^2*h) - ((d*g - c*h)^2*q*r*(g + h*x)^3)/(15*d^2*h) - ((b*g - a*h)*p*r*(g + h*x)^4)/(20*b*h) - ((d*g - c*h)*q*r*(g + h*x)^4)/(20*d*h) - (p*r*(g + h*x)^5)/(25*h) - (q*r*(g + h*x)^5)/(25*h) - ((b*g - a*h)^5*p*r*Log[a + b*x])/(5*b^5*h) - ((d*g - c*h)^5*q*r*Log[c + d*x])/(5*d^5*h) + ((g + h*x)^5*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(5*h)","A",5,2,29,0.06897,1,"{2495, 43}"
26,1,276,0,0.1274185,"\int (g+h x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[(g + h*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","-\frac{p r x (b g-a h)^3}{4 b^3}-\frac{p r (g+h x)^2 (b g-a h)^2}{8 b^2 h}-\frac{p r (b g-a h)^4 \log (a+b x)}{4 b^4 h}+\frac{(g+h x)^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 h}-\frac{p r (g+h x)^3 (b g-a h)}{12 b h}-\frac{q r (g+h x)^2 (d g-c h)^2}{8 d^2 h}-\frac{q r x (d g-c h)^3}{4 d^3}-\frac{q r (d g-c h)^4 \log (c+d x)}{4 d^4 h}-\frac{q r (g+h x)^3 (d g-c h)}{12 d h}-\frac{p r (g+h x)^4}{16 h}-\frac{q r (g+h x)^4}{16 h}","-\frac{p r x (b g-a h)^3}{4 b^3}-\frac{p r (g+h x)^2 (b g-a h)^2}{8 b^2 h}-\frac{p r (b g-a h)^4 \log (a+b x)}{4 b^4 h}+\frac{(g+h x)^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 h}-\frac{p r (g+h x)^3 (b g-a h)}{12 b h}-\frac{q r (g+h x)^2 (d g-c h)^2}{8 d^2 h}-\frac{q r x (d g-c h)^3}{4 d^3}-\frac{q r (d g-c h)^4 \log (c+d x)}{4 d^4 h}-\frac{q r (g+h x)^3 (d g-c h)}{12 d h}-\frac{p r (g+h x)^4}{16 h}-\frac{q r (g+h x)^4}{16 h}",1,"-((b*g - a*h)^3*p*r*x)/(4*b^3) - ((d*g - c*h)^3*q*r*x)/(4*d^3) - ((b*g - a*h)^2*p*r*(g + h*x)^2)/(8*b^2*h) - ((d*g - c*h)^2*q*r*(g + h*x)^2)/(8*d^2*h) - ((b*g - a*h)*p*r*(g + h*x)^3)/(12*b*h) - ((d*g - c*h)*q*r*(g + h*x)^3)/(12*d*h) - (p*r*(g + h*x)^4)/(16*h) - (q*r*(g + h*x)^4)/(16*h) - ((b*g - a*h)^4*p*r*Log[a + b*x])/(4*b^4*h) - ((d*g - c*h)^4*q*r*Log[c + d*x])/(4*d^4*h) + ((g + h*x)^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(4*h)","A",5,2,29,0.06897,1,"{2495, 43}"
27,1,218,0,0.0987066,"\int (g+h x)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[(g + h*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","-\frac{p r x (b g-a h)^2}{3 b^2}-\frac{p r (b g-a h)^3 \log (a+b x)}{3 b^3 h}+\frac{(g+h x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 h}-\frac{p r (g+h x)^2 (b g-a h)}{6 b h}-\frac{q r x (d g-c h)^2}{3 d^2}-\frac{q r (d g-c h)^3 \log (c+d x)}{3 d^3 h}-\frac{q r (g+h x)^2 (d g-c h)}{6 d h}-\frac{p r (g+h x)^3}{9 h}-\frac{q r (g+h x)^3}{9 h}","-\frac{p r x (b g-a h)^2}{3 b^2}-\frac{p r (b g-a h)^3 \log (a+b x)}{3 b^3 h}+\frac{(g+h x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 h}-\frac{p r (g+h x)^2 (b g-a h)}{6 b h}-\frac{q r x (d g-c h)^2}{3 d^2}-\frac{q r (d g-c h)^3 \log (c+d x)}{3 d^3 h}-\frac{q r (g+h x)^2 (d g-c h)}{6 d h}-\frac{p r (g+h x)^3}{9 h}-\frac{q r (g+h x)^3}{9 h}",1,"-((b*g - a*h)^2*p*r*x)/(3*b^2) - ((d*g - c*h)^2*q*r*x)/(3*d^2) - ((b*g - a*h)*p*r*(g + h*x)^2)/(6*b*h) - ((d*g - c*h)*q*r*(g + h*x)^2)/(6*d*h) - (p*r*(g + h*x)^3)/(9*h) - (q*r*(g + h*x)^3)/(9*h) - ((b*g - a*h)^3*p*r*Log[a + b*x])/(3*b^3*h) - ((d*g - c*h)^3*q*r*Log[c + d*x])/(3*d^3*h) + ((g + h*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(3*h)","A",5,2,29,0.06897,1,"{2495, 43}"
28,1,160,0,0.0687969,"\int (g+h x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[(g + h*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","-\frac{p r (b g-a h)^2 \log (a+b x)}{2 b^2 h}+\frac{(g+h x)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 h}-\frac{p r x (b g-a h)}{2 b}-\frac{q r (d g-c h)^2 \log (c+d x)}{2 d^2 h}-\frac{q r x (d g-c h)}{2 d}-\frac{p r (g+h x)^2}{4 h}-\frac{q r (g+h x)^2}{4 h}","-\frac{p r (b g-a h)^2 \log (a+b x)}{2 b^2 h}+\frac{(g+h x)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 h}-\frac{p r x (b g-a h)}{2 b}-\frac{q r (d g-c h)^2 \log (c+d x)}{2 d^2 h}-\frac{q r x (d g-c h)}{2 d}-\frac{p r (g+h x)^2}{4 h}-\frac{q r (g+h x)^2}{4 h}",1,"-((b*g - a*h)*p*r*x)/(2*b) - ((d*g - c*h)*q*r*x)/(2*d) - (p*r*(g + h*x)^2)/(4*h) - (q*r*(g + h*x)^2)/(4*h) - ((b*g - a*h)^2*p*r*Log[a + b*x])/(2*b^2*h) - ((d*g - c*h)^2*q*r*Log[c + d*x])/(2*d^2*h) + ((g + h*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(2*h)","A",5,2,27,0.07407,1,"{2495, 43}"
29,1,61,0,0.0148794,"\int \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","\frac{(a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b}+\frac{q r (b c-a d) \log (c+d x)}{b d}+r x (-(p+q))","\frac{(a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b}+\frac{q r (b c-a d) \log (c+d x)}{b d}+r x (-(p+q))",1,"-((p + q)*r*x) + ((b*c - a*d)*q*r*Log[c + d*x])/(b*d) + ((a + b*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/b","A",3,3,21,0.1429,1,"{2487, 31, 8}"
30,1,148,0,0.1200074,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{g+h x} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(g + h*x),x]","-\frac{p r \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right)}{h}-\frac{q r \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right)}{h}+\frac{\log (g+h x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{h}-\frac{p r \log (g+h x) \log \left(-\frac{h (a+b x)}{b g-a h}\right)}{h}-\frac{q r \log (g+h x) \log \left(-\frac{h (c+d x)}{d g-c h}\right)}{h}","-\frac{p r \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right)}{h}-\frac{q r \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right)}{h}+\frac{\log (g+h x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{h}-\frac{p r \log (g+h x) \log \left(-\frac{h (a+b x)}{b g-a h}\right)}{h}-\frac{q r \log (g+h x) \log \left(-\frac{h (c+d x)}{d g-c h}\right)}{h}",1,"-((p*r*Log[-((h*(a + b*x))/(b*g - a*h))]*Log[g + h*x])/h) - (q*r*Log[-((h*(c + d*x))/(d*g - c*h))]*Log[g + h*x])/h + (Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[g + h*x])/h - (p*r*PolyLog[2, (b*(g + h*x))/(b*g - a*h)])/h - (q*r*PolyLog[2, (d*(g + h*x))/(d*g - c*h)])/h","A",7,4,29,0.1379,1,"{2494, 2394, 2393, 2391}"
31,1,128,0,0.0524397,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g+h x)^2} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(g + h*x)^2,x]","-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{h (g+h x)}+\frac{b p r \log (a+b x)}{h (b g-a h)}-\frac{b p r \log (g+h x)}{h (b g-a h)}+\frac{d q r \log (c+d x)}{h (d g-c h)}-\frac{d q r \log (g+h x)}{h (d g-c h)}","-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{h (g+h x)}+\frac{b p r \log (a+b x)}{h (b g-a h)}-\frac{b p r \log (g+h x)}{h (b g-a h)}+\frac{d q r \log (c+d x)}{h (d g-c h)}-\frac{d q r \log (g+h x)}{h (d g-c h)}",1,"(b*p*r*Log[a + b*x])/(h*(b*g - a*h)) + (d*q*r*Log[c + d*x])/(h*(d*g - c*h)) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(h*(g + h*x)) - (b*p*r*Log[g + h*x])/(h*(b*g - a*h)) - (d*q*r*Log[g + h*x])/(h*(d*g - c*h))","A",7,3,29,0.1034,1,"{2495, 36, 31}"
32,1,202,0,0.111538,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g+h x)^3} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(g + h*x)^3,x]","\frac{b^2 p r \log (a+b x)}{2 h (b g-a h)^2}-\frac{b^2 p r \log (g+h x)}{2 h (b g-a h)^2}-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 h (g+h x)^2}+\frac{b p r}{2 h (g+h x) (b g-a h)}+\frac{d^2 q r \log (c+d x)}{2 h (d g-c h)^2}-\frac{d^2 q r \log (g+h x)}{2 h (d g-c h)^2}+\frac{d q r}{2 h (g+h x) (d g-c h)}","\frac{b^2 p r \log (a+b x)}{2 h (b g-a h)^2}-\frac{b^2 p r \log (g+h x)}{2 h (b g-a h)^2}-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 h (g+h x)^2}+\frac{b p r}{2 h (g+h x) (b g-a h)}+\frac{d^2 q r \log (c+d x)}{2 h (d g-c h)^2}-\frac{d^2 q r \log (g+h x)}{2 h (d g-c h)^2}+\frac{d q r}{2 h (g+h x) (d g-c h)}",1,"(b*p*r)/(2*h*(b*g - a*h)*(g + h*x)) + (d*q*r)/(2*h*(d*g - c*h)*(g + h*x)) + (b^2*p*r*Log[a + b*x])/(2*h*(b*g - a*h)^2) + (d^2*q*r*Log[c + d*x])/(2*h*(d*g - c*h)^2) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(2*h*(g + h*x)^2) - (b^2*p*r*Log[g + h*x])/(2*h*(b*g - a*h)^2) - (d^2*q*r*Log[g + h*x])/(2*h*(d*g - c*h)^2)","A",5,2,29,0.06897,1,"{2495, 44}"
33,1,260,0,0.1519592,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g+h x)^4} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(g + h*x)^4,x]","\frac{b^2 p r}{3 h (g+h x) (b g-a h)^2}+\frac{b^3 p r \log (a+b x)}{3 h (b g-a h)^3}-\frac{b^3 p r \log (g+h x)}{3 h (b g-a h)^3}-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 h (g+h x)^3}+\frac{b p r}{6 h (g+h x)^2 (b g-a h)}+\frac{d^2 q r}{3 h (g+h x) (d g-c h)^2}+\frac{d^3 q r \log (c+d x)}{3 h (d g-c h)^3}-\frac{d^3 q r \log (g+h x)}{3 h (d g-c h)^3}+\frac{d q r}{6 h (g+h x)^2 (d g-c h)}","\frac{b^2 p r}{3 h (g+h x) (b g-a h)^2}+\frac{b^3 p r \log (a+b x)}{3 h (b g-a h)^3}-\frac{b^3 p r \log (g+h x)}{3 h (b g-a h)^3}-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 h (g+h x)^3}+\frac{b p r}{6 h (g+h x)^2 (b g-a h)}+\frac{d^2 q r}{3 h (g+h x) (d g-c h)^2}+\frac{d^3 q r \log (c+d x)}{3 h (d g-c h)^3}-\frac{d^3 q r \log (g+h x)}{3 h (d g-c h)^3}+\frac{d q r}{6 h (g+h x)^2 (d g-c h)}",1,"(b*p*r)/(6*h*(b*g - a*h)*(g + h*x)^2) + (d*q*r)/(6*h*(d*g - c*h)*(g + h*x)^2) + (b^2*p*r)/(3*h*(b*g - a*h)^2*(g + h*x)) + (d^2*q*r)/(3*h*(d*g - c*h)^2*(g + h*x)) + (b^3*p*r*Log[a + b*x])/(3*h*(b*g - a*h)^3) + (d^3*q*r*Log[c + d*x])/(3*h*(d*g - c*h)^3) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(3*h*(g + h*x)^3) - (b^3*p*r*Log[g + h*x])/(3*h*(b*g - a*h)^3) - (d^3*q*r*Log[g + h*x])/(3*h*(d*g - c*h)^3)","A",5,2,29,0.06897,1,"{2495, 44}"
34,1,318,0,0.1948349,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g+h x)^5} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(g + h*x)^5,x]","\frac{b^3 p r}{4 h (g+h x) (b g-a h)^3}+\frac{b^2 p r}{8 h (g+h x)^2 (b g-a h)^2}+\frac{b^4 p r \log (a+b x)}{4 h (b g-a h)^4}-\frac{b^4 p r \log (g+h x)}{4 h (b g-a h)^4}-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 h (g+h x)^4}+\frac{b p r}{12 h (g+h x)^3 (b g-a h)}+\frac{d^3 q r}{4 h (g+h x) (d g-c h)^3}+\frac{d^2 q r}{8 h (g+h x)^2 (d g-c h)^2}+\frac{d^4 q r \log (c+d x)}{4 h (d g-c h)^4}-\frac{d^4 q r \log (g+h x)}{4 h (d g-c h)^4}+\frac{d q r}{12 h (g+h x)^3 (d g-c h)}","\frac{b^3 p r}{4 h (g+h x) (b g-a h)^3}+\frac{b^2 p r}{8 h (g+h x)^2 (b g-a h)^2}+\frac{b^4 p r \log (a+b x)}{4 h (b g-a h)^4}-\frac{b^4 p r \log (g+h x)}{4 h (b g-a h)^4}-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 h (g+h x)^4}+\frac{b p r}{12 h (g+h x)^3 (b g-a h)}+\frac{d^3 q r}{4 h (g+h x) (d g-c h)^3}+\frac{d^2 q r}{8 h (g+h x)^2 (d g-c h)^2}+\frac{d^4 q r \log (c+d x)}{4 h (d g-c h)^4}-\frac{d^4 q r \log (g+h x)}{4 h (d g-c h)^4}+\frac{d q r}{12 h (g+h x)^3 (d g-c h)}",1,"(b*p*r)/(12*h*(b*g - a*h)*(g + h*x)^3) + (d*q*r)/(12*h*(d*g - c*h)*(g + h*x)^3) + (b^2*p*r)/(8*h*(b*g - a*h)^2*(g + h*x)^2) + (d^2*q*r)/(8*h*(d*g - c*h)^2*(g + h*x)^2) + (b^3*p*r)/(4*h*(b*g - a*h)^3*(g + h*x)) + (d^3*q*r)/(4*h*(d*g - c*h)^3*(g + h*x)) + (b^4*p*r*Log[a + b*x])/(4*h*(b*g - a*h)^4) + (d^4*q*r*Log[c + d*x])/(4*h*(d*g - c*h)^4) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(4*h*(g + h*x)^4) - (b^4*p*r*Log[g + h*x])/(4*h*(b*g - a*h)^4) - (d^4*q*r*Log[g + h*x])/(4*h*(d*g - c*h)^4)","A",5,2,29,0.06897,1,"{2495, 44}"
35,1,2220,0,2.4356913,"\int (g+h x)^3 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[(g + h*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2,x]","\frac{p^2 r^2 \log ^2(a+b x) (b g-a h)^4}{4 b^4 h}+\frac{p q r^2 \log (a+b x) (b g-a h)^4}{8 b^4 h}-\frac{p q r^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) (b g-a h)^4}{2 b^4 h}+\frac{p r \log (a+b x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)^4}{2 b^4 h}-\frac{p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) (b g-a h)^4}{2 b^4 h}+\frac{2 p^2 r^2 x (b g-a h)^3}{b^3}+\frac{5 p q r^2 x (b g-a h)^3}{8 b^3}+\frac{(d g-c h) p q r^2 \log (a+b x) (b g-a h)^3}{6 b^3 d h}-\frac{p q r^2 (c+d x) \log (c+d x) (b g-a h)^3}{2 b^3 d}+\frac{p r x \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)^3}{2 b^3}+\frac{3 h p^2 r^2 (a+b x)^2 (b g-a h)^2}{4 b^4}+\frac{3 p q r^2 (g+h x)^2 (b g-a h)^2}{16 b^2 h}+\frac{5 (d g-c h) p q r^2 x (b g-a h)^2}{12 b^2 d}+\frac{(d g-c h)^2 p q r^2 \log (a+b x) (b g-a h)^2}{4 b^2 d^2 h}+\frac{(d g-c h)^2 p q r^2 \log (c+d x) (b g-a h)^2}{4 b^2 d^2 h}-\frac{p q r^2 (g+h x)^2 \log (c+d x) (b g-a h)^2}{4 b^2 h}+\frac{p r (g+h x)^2 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)^2}{4 b^2 h}+\frac{2 h^2 p^2 r^2 (a+b x)^3 (b g-a h)}{9 b^4}+\frac{7 p q r^2 (g+h x)^3 (b g-a h)}{72 b h}+\frac{(d g-c h) p q r^2 (g+h x)^2 (b g-a h)}{6 b d h}+\frac{5 (d g-c h)^2 p q r^2 x (b g-a h)}{12 b d^2}-\frac{p q r^2 (g+h x)^3 \log (c+d x) (b g-a h)}{6 b h}+\frac{(d g-c h)^3 p q r^2 \log (c+d x) (b g-a h)}{6 b d^3 h}+\frac{p r (g+h x)^3 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)}{6 b h}+\frac{h^3 p^2 r^2 (a+b x)^4}{32 b^4}+\frac{h^3 q^2 r^2 (c+d x)^4}{32 d^4}+\frac{p q r^2 (g+h x)^4}{16 h}+\frac{2 h^2 (d g-c h) q^2 r^2 (c+d x)^3}{9 d^4}+\frac{7 (d g-c h) p q r^2 (g+h x)^3}{72 d h}+\frac{3 h (d g-c h)^2 q^2 r^2 (c+d x)^2}{4 d^4}+\frac{3 (d g-c h)^2 p q r^2 (g+h x)^2}{16 d^2 h}+\frac{(d g-c h)^4 q^2 r^2 \log ^2(c+d x)}{4 d^4 h}+\frac{(g+h x)^4 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 h}+\frac{2 (d g-c h)^3 q^2 r^2 x}{d^3}+\frac{5 (d g-c h)^3 p q r^2 x}{8 d^3}-\frac{p q r^2 (g+h x)^4 \log (a+b x)}{8 h}-\frac{(d g-c h) p q r^2 (g+h x)^3 \log (a+b x)}{6 d h}-\frac{(d g-c h)^2 p q r^2 (g+h x)^2 \log (a+b x)}{4 d^2 h}-\frac{(d g-c h)^3 p q r^2 (a+b x) \log (a+b x)}{2 b d^3}-\frac{p^2 r^2 \log (a+b x) \left(\frac{12 \log (a+b x) (b g-a h)^4}{b^4}+\frac{48 h (a+b x) (b g-a h)^3}{b^4}+\frac{36 h^2 (a+b x)^2 (b g-a h)^2}{b^4}+\frac{16 h^3 (a+b x)^3 (b g-a h)}{b^4}+\frac{3 h^4 (a+b x)^4}{b^4}\right)}{24 h}-\frac{p q r^2 (g+h x)^4 \log (c+d x)}{8 h}+\frac{(d g-c h)^4 p q r^2 \log (c+d x)}{8 d^4 h}-\frac{q^2 r^2 \log (c+d x) \left(\frac{12 \log (c+d x) (d g-c h)^4}{d^4}+\frac{48 h (c+d x) (d g-c h)^3}{d^4}+\frac{36 h^2 (c+d x)^2 (d g-c h)^2}{d^4}+\frac{16 h^3 (c+d x)^3 (d g-c h)}{d^4}+\frac{3 h^4 (c+d x)^4}{d^4}\right)}{24 h}-\frac{(d g-c h)^4 p q r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{2 d^4 h}+\frac{p r (g+h x)^4 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{8 h}+\frac{q r (g+h x)^4 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{8 h}+\frac{(d g-c h) q r (g+h x)^3 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{6 d h}+\frac{(d g-c h)^2 q r (g+h x)^2 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{4 d^2 h}+\frac{(d g-c h)^3 q r x \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{2 d^3}+\frac{(d g-c h)^4 q r \log (c+d x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{2 d^4 h}-\frac{(d g-c h)^4 p q r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{2 d^4 h}","-\frac{p^2 r^2 \log ^2(a+b x) (b g-a h)^4}{4 b^4 h}+\frac{p q r^2 \log (a+b x) (b g-a h)^4}{8 b^4 h}-\frac{p q r^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) (b g-a h)^4}{2 b^4 h}+\frac{p r \log (a+b x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)^4}{2 b^4 h}-\frac{p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) (b g-a h)^4}{2 b^4 h}+\frac{2 p^2 r^2 x (b g-a h)^3}{b^3}+\frac{5 p q r^2 x (b g-a h)^3}{8 b^3}+\frac{(d g-c h) p q r^2 \log (a+b x) (b g-a h)^3}{6 b^3 d h}-\frac{2 p^2 r^2 (a+b x) \log (a+b x) (b g-a h)^3}{b^4}-\frac{p q r^2 (c+d x) \log (c+d x) (b g-a h)^3}{2 b^3 d}+\frac{p r x \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)^3}{2 b^3}+\frac{3 h p^2 r^2 (a+b x)^2 (b g-a h)^2}{4 b^4}+\frac{3 p q r^2 (g+h x)^2 (b g-a h)^2}{16 b^2 h}+\frac{5 (d g-c h) p q r^2 x (b g-a h)^2}{12 b^2 d}+\frac{(d g-c h)^2 p q r^2 \log (a+b x) (b g-a h)^2}{4 b^2 d^2 h}-\frac{3 h p^2 r^2 (a+b x)^2 \log (a+b x) (b g-a h)^2}{2 b^4}+\frac{(d g-c h)^2 p q r^2 \log (c+d x) (b g-a h)^2}{4 b^2 d^2 h}-\frac{p q r^2 (g+h x)^2 \log (c+d x) (b g-a h)^2}{4 b^2 h}+\frac{p r (g+h x)^2 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)^2}{4 b^2 h}+\frac{2 h^2 p^2 r^2 (a+b x)^3 (b g-a h)}{9 b^4}+\frac{7 p q r^2 (g+h x)^3 (b g-a h)}{72 b h}+\frac{(d g-c h) p q r^2 (g+h x)^2 (b g-a h)}{6 b d h}+\frac{5 (d g-c h)^2 p q r^2 x (b g-a h)}{12 b d^2}-\frac{2 h^2 p^2 r^2 (a+b x)^3 \log (a+b x) (b g-a h)}{3 b^4}-\frac{p q r^2 (g+h x)^3 \log (c+d x) (b g-a h)}{6 b h}+\frac{(d g-c h)^3 p q r^2 \log (c+d x) (b g-a h)}{6 b d^3 h}+\frac{p r (g+h x)^3 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)}{6 b h}+\frac{h^3 p^2 r^2 (a+b x)^4}{32 b^4}+\frac{h^3 q^2 r^2 (c+d x)^4}{32 d^4}+\frac{p q r^2 (g+h x)^4}{16 h}+\frac{2 h^2 (d g-c h) q^2 r^2 (c+d x)^3}{9 d^4}+\frac{7 (d g-c h) p q r^2 (g+h x)^3}{72 d h}+\frac{3 h (d g-c h)^2 q^2 r^2 (c+d x)^2}{4 d^4}+\frac{3 (d g-c h)^2 p q r^2 (g+h x)^2}{16 d^2 h}-\frac{(d g-c h)^4 q^2 r^2 \log ^2(c+d x)}{4 d^4 h}+\frac{(g+h x)^4 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 h}+\frac{2 (d g-c h)^3 q^2 r^2 x}{d^3}+\frac{5 (d g-c h)^3 p q r^2 x}{8 d^3}-\frac{h^3 p^2 r^2 (a+b x)^4 \log (a+b x)}{8 b^4}-\frac{p q r^2 (g+h x)^4 \log (a+b x)}{8 h}-\frac{(d g-c h) p q r^2 (g+h x)^3 \log (a+b x)}{6 d h}-\frac{(d g-c h)^2 p q r^2 (g+h x)^2 \log (a+b x)}{4 d^2 h}-\frac{(d g-c h)^3 p q r^2 (a+b x) \log (a+b x)}{2 b d^3}-\frac{h^3 q^2 r^2 (c+d x)^4 \log (c+d x)}{8 d^4}-\frac{p q r^2 (g+h x)^4 \log (c+d x)}{8 h}-\frac{2 h^2 (d g-c h) q^2 r^2 (c+d x)^3 \log (c+d x)}{3 d^4}+\frac{(d g-c h)^4 p q r^2 \log (c+d x)}{8 d^4 h}-\frac{3 h (d g-c h)^2 q^2 r^2 (c+d x)^2 \log (c+d x)}{2 d^4}-\frac{2 (d g-c h)^3 q^2 r^2 (c+d x) \log (c+d x)}{d^4}-\frac{(d g-c h)^4 p q r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{2 d^4 h}+\frac{p r (g+h x)^4 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{8 h}+\frac{q r (g+h x)^4 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{8 h}+\frac{(d g-c h) q r (g+h x)^3 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{6 d h}+\frac{(d g-c h)^2 q r (g+h x)^2 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{4 d^2 h}+\frac{(d g-c h)^3 q r x \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{2 d^3}+\frac{(d g-c h)^4 q r \log (c+d x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{2 d^4 h}-\frac{(d g-c h)^4 p q r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{2 d^4 h}",1,"(2*(b*g - a*h)^3*p^2*r^2*x)/b^3 + (5*(b*g - a*h)^3*p*q*r^2*x)/(8*b^3) + (5*(b*g - a*h)^2*(d*g - c*h)*p*q*r^2*x)/(12*b^2*d) + (5*(b*g - a*h)*(d*g - c*h)^2*p*q*r^2*x)/(12*b*d^2) + (5*(d*g - c*h)^3*p*q*r^2*x)/(8*d^3) + (2*(d*g - c*h)^3*q^2*r^2*x)/d^3 + (3*h*(b*g - a*h)^2*p^2*r^2*(a + b*x)^2)/(4*b^4) + (2*h^2*(b*g - a*h)*p^2*r^2*(a + b*x)^3)/(9*b^4) + (h^3*p^2*r^2*(a + b*x)^4)/(32*b^4) + (3*h*(d*g - c*h)^2*q^2*r^2*(c + d*x)^2)/(4*d^4) + (2*h^2*(d*g - c*h)*q^2*r^2*(c + d*x)^3)/(9*d^4) + (h^3*q^2*r^2*(c + d*x)^4)/(32*d^4) + (3*(b*g - a*h)^2*p*q*r^2*(g + h*x)^2)/(16*b^2*h) + ((b*g - a*h)*(d*g - c*h)*p*q*r^2*(g + h*x)^2)/(6*b*d*h) + (3*(d*g - c*h)^2*p*q*r^2*(g + h*x)^2)/(16*d^2*h) + (7*(b*g - a*h)*p*q*r^2*(g + h*x)^3)/(72*b*h) + (7*(d*g - c*h)*p*q*r^2*(g + h*x)^3)/(72*d*h) + (p*q*r^2*(g + h*x)^4)/(16*h) + ((b*g - a*h)^4*p*q*r^2*Log[a + b*x])/(8*b^4*h) + ((b*g - a*h)^3*(d*g - c*h)*p*q*r^2*Log[a + b*x])/(6*b^3*d*h) + ((b*g - a*h)^2*(d*g - c*h)^2*p*q*r^2*Log[a + b*x])/(4*b^2*d^2*h) - ((d*g - c*h)^3*p*q*r^2*(a + b*x)*Log[a + b*x])/(2*b*d^3) - ((d*g - c*h)^2*p*q*r^2*(g + h*x)^2*Log[a + b*x])/(4*d^2*h) - ((d*g - c*h)*p*q*r^2*(g + h*x)^3*Log[a + b*x])/(6*d*h) - (p*q*r^2*(g + h*x)^4*Log[a + b*x])/(8*h) + ((b*g - a*h)^4*p^2*r^2*Log[a + b*x]^2)/(4*b^4*h) - (p^2*r^2*Log[a + b*x]*((48*h*(b*g - a*h)^3*(a + b*x))/b^4 + (36*h^2*(b*g - a*h)^2*(a + b*x)^2)/b^4 + (16*h^3*(b*g - a*h)*(a + b*x)^3)/b^4 + (3*h^4*(a + b*x)^4)/b^4 + (12*(b*g - a*h)^4*Log[a + b*x])/b^4))/(24*h) + ((b*g - a*h)^2*(d*g - c*h)^2*p*q*r^2*Log[c + d*x])/(4*b^2*d^2*h) + ((b*g - a*h)*(d*g - c*h)^3*p*q*r^2*Log[c + d*x])/(6*b*d^3*h) + ((d*g - c*h)^4*p*q*r^2*Log[c + d*x])/(8*d^4*h) - ((b*g - a*h)^3*p*q*r^2*(c + d*x)*Log[c + d*x])/(2*b^3*d) - ((b*g - a*h)^2*p*q*r^2*(g + h*x)^2*Log[c + d*x])/(4*b^2*h) - ((b*g - a*h)*p*q*r^2*(g + h*x)^3*Log[c + d*x])/(6*b*h) - (p*q*r^2*(g + h*x)^4*Log[c + d*x])/(8*h) - ((b*g - a*h)^4*p*q*r^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(2*b^4*h) + ((d*g - c*h)^4*q^2*r^2*Log[c + d*x]^2)/(4*d^4*h) - (q^2*r^2*Log[c + d*x]*((48*h*(d*g - c*h)^3*(c + d*x))/d^4 + (36*h^2*(d*g - c*h)^2*(c + d*x)^2)/d^4 + (16*h^3*(d*g - c*h)*(c + d*x)^3)/d^4 + (3*h^4*(c + d*x)^4)/d^4 + (12*(d*g - c*h)^4*Log[c + d*x])/d^4))/(24*h) - ((d*g - c*h)^4*p*q*r^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(2*d^4*h) + ((b*g - a*h)^3*p*r*x*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(2*b^3) + ((d*g - c*h)^3*q*r*x*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(2*d^3) + ((b*g - a*h)^2*p*r*(g + h*x)^2*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(4*b^2*h) + ((d*g - c*h)^2*q*r*(g + h*x)^2*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(4*d^2*h) + ((b*g - a*h)*p*r*(g + h*x)^3*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(6*b*h) + ((d*g - c*h)*q*r*(g + h*x)^3*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(6*d*h) + (p*r*(g + h*x)^4*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(8*h) + (q*r*(g + h*x)^4*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(8*h) + ((b*g - a*h)^4*p*r*Log[a + b*x]*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(2*b^4*h) + ((d*g - c*h)^4*q*r*Log[c + d*x]*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(2*d^4*h) + ((g + h*x)^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2)/(4*h) - ((d*g - c*h)^4*p*q*r^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(2*d^4*h) - ((b*g - a*h)^4*p*q*r^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(2*b^4*h)","A",49,14,31,0.4516,1,"{2498, 2513, 2411, 43, 2334, 12, 2301, 2418, 2389, 2295, 2394, 2393, 2391, 2395}"
36,1,1657,0,1.7584407,"\int (g+h x)^2 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[(g + h*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2,x]","\frac{p^2 r^2 \log ^2(a+b x) (b g-a h)^3}{3 b^3 h}+\frac{2 p q r^2 \log (a+b x) (b g-a h)^3}{9 b^3 h}-\frac{2 p q r^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) (b g-a h)^3}{3 b^3 h}+\frac{2 p r \log (a+b x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)^3}{3 b^3 h}-\frac{2 p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) (b g-a h)^3}{3 b^3 h}+\frac{2 p^2 r^2 x (b g-a h)^2}{b^2}+\frac{8 p q r^2 x (b g-a h)^2}{9 b^2}+\frac{(d g-c h) p q r^2 \log (a+b x) (b g-a h)^2}{3 b^2 d h}-\frac{2 p q r^2 (c+d x) \log (c+d x) (b g-a h)^2}{3 b^2 d}+\frac{2 p r x \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)^2}{3 b^2}+\frac{h p^2 r^2 (a+b x)^2 (b g-a h)}{2 b^3}+\frac{5 p q r^2 (g+h x)^2 (b g-a h)}{18 b h}+\frac{2 (d g-c h) p q r^2 x (b g-a h)}{3 b d}+\frac{(d g-c h)^2 p q r^2 \log (c+d x) (b g-a h)}{3 b d^2 h}-\frac{p q r^2 (g+h x)^2 \log (c+d x) (b g-a h)}{3 b h}+\frac{p r (g+h x)^2 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)}{3 b h}+\frac{2 h^2 p^2 r^2 (a+b x)^3}{27 b^3}+\frac{2 h^2 q^2 r^2 (c+d x)^3}{27 d^3}+\frac{4 p q r^2 (g+h x)^3}{27 h}+\frac{h (d g-c h) q^2 r^2 (c+d x)^2}{2 d^3}+\frac{5 (d g-c h) p q r^2 (g+h x)^2}{18 d h}+\frac{(d g-c h)^3 q^2 r^2 \log ^2(c+d x)}{3 d^3 h}+\frac{(g+h x)^3 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 h}+\frac{2 (d g-c h)^2 q^2 r^2 x}{d^2}+\frac{8 (d g-c h)^2 p q r^2 x}{9 d^2}-\frac{2 p q r^2 (g+h x)^3 \log (a+b x)}{9 h}-\frac{(d g-c h) p q r^2 (g+h x)^2 \log (a+b x)}{3 d h}-\frac{2 (d g-c h)^2 p q r^2 (a+b x) \log (a+b x)}{3 b d^2}-\frac{p^2 r^2 \log (a+b x) \left(\frac{6 \log (a+b x) (b g-a h)^3}{b^3}+\frac{18 h (a+b x) (b g-a h)^2}{b^3}+\frac{9 h^2 (a+b x)^2 (b g-a h)}{b^3}+\frac{2 h^3 (a+b x)^3}{b^3}\right)}{9 h}-\frac{2 p q r^2 (g+h x)^3 \log (c+d x)}{9 h}+\frac{2 (d g-c h)^3 p q r^2 \log (c+d x)}{9 d^3 h}-\frac{q^2 r^2 \log (c+d x) \left(\frac{6 \log (c+d x) (d g-c h)^3}{d^3}+\frac{18 h (c+d x) (d g-c h)^2}{d^3}+\frac{9 h^2 (c+d x)^2 (d g-c h)}{d^3}+\frac{2 h^3 (c+d x)^3}{d^3}\right)}{9 h}-\frac{2 (d g-c h)^3 p q r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{3 d^3 h}+\frac{2 p r (g+h x)^3 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{9 h}+\frac{2 q r (g+h x)^3 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{9 h}+\frac{(d g-c h) q r (g+h x)^2 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{3 d h}+\frac{2 (d g-c h)^2 q r x \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{3 d^2}+\frac{2 (d g-c h)^3 q r \log (c+d x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{3 d^3 h}-\frac{2 (d g-c h)^3 p q r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{3 d^3 h}","-\frac{p^2 r^2 \log ^2(a+b x) (b g-a h)^3}{3 b^3 h}+\frac{2 p q r^2 \log (a+b x) (b g-a h)^3}{9 b^3 h}-\frac{2 p q r^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) (b g-a h)^3}{3 b^3 h}+\frac{2 p r \log (a+b x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)^3}{3 b^3 h}-\frac{2 p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) (b g-a h)^3}{3 b^3 h}+\frac{2 p^2 r^2 x (b g-a h)^2}{b^2}+\frac{8 p q r^2 x (b g-a h)^2}{9 b^2}+\frac{(d g-c h) p q r^2 \log (a+b x) (b g-a h)^2}{3 b^2 d h}-\frac{2 p^2 r^2 (a+b x) \log (a+b x) (b g-a h)^2}{b^3}-\frac{2 p q r^2 (c+d x) \log (c+d x) (b g-a h)^2}{3 b^2 d}+\frac{2 p r x \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)^2}{3 b^2}+\frac{h p^2 r^2 (a+b x)^2 (b g-a h)}{2 b^3}+\frac{5 p q r^2 (g+h x)^2 (b g-a h)}{18 b h}+\frac{2 (d g-c h) p q r^2 x (b g-a h)}{3 b d}-\frac{h p^2 r^2 (a+b x)^2 \log (a+b x) (b g-a h)}{b^3}+\frac{(d g-c h)^2 p q r^2 \log (c+d x) (b g-a h)}{3 b d^2 h}-\frac{p q r^2 (g+h x)^2 \log (c+d x) (b g-a h)}{3 b h}+\frac{p r (g+h x)^2 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)}{3 b h}+\frac{2 h^2 p^2 r^2 (a+b x)^3}{27 b^3}+\frac{2 h^2 q^2 r^2 (c+d x)^3}{27 d^3}+\frac{4 p q r^2 (g+h x)^3}{27 h}+\frac{h (d g-c h) q^2 r^2 (c+d x)^2}{2 d^3}+\frac{5 (d g-c h) p q r^2 (g+h x)^2}{18 d h}-\frac{(d g-c h)^3 q^2 r^2 \log ^2(c+d x)}{3 d^3 h}+\frac{(g+h x)^3 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 h}+\frac{2 (d g-c h)^2 q^2 r^2 x}{d^2}+\frac{8 (d g-c h)^2 p q r^2 x}{9 d^2}-\frac{2 h^2 p^2 r^2 (a+b x)^3 \log (a+b x)}{9 b^3}-\frac{2 p q r^2 (g+h x)^3 \log (a+b x)}{9 h}-\frac{(d g-c h) p q r^2 (g+h x)^2 \log (a+b x)}{3 d h}-\frac{2 (d g-c h)^2 p q r^2 (a+b x) \log (a+b x)}{3 b d^2}-\frac{2 h^2 q^2 r^2 (c+d x)^3 \log (c+d x)}{9 d^3}-\frac{2 p q r^2 (g+h x)^3 \log (c+d x)}{9 h}+\frac{2 (d g-c h)^3 p q r^2 \log (c+d x)}{9 d^3 h}-\frac{h (d g-c h) q^2 r^2 (c+d x)^2 \log (c+d x)}{d^3}-\frac{2 (d g-c h)^2 q^2 r^2 (c+d x) \log (c+d x)}{d^3}-\frac{2 (d g-c h)^3 p q r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{3 d^3 h}+\frac{2 p r (g+h x)^3 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{9 h}+\frac{2 q r (g+h x)^3 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{9 h}+\frac{(d g-c h) q r (g+h x)^2 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{3 d h}+\frac{2 (d g-c h)^2 q r x \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{3 d^2}+\frac{2 (d g-c h)^3 q r \log (c+d x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{3 d^3 h}-\frac{2 (d g-c h)^3 p q r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{3 d^3 h}",1,"(2*(b*g - a*h)^2*p^2*r^2*x)/b^2 + (8*(b*g - a*h)^2*p*q*r^2*x)/(9*b^2) + (2*(b*g - a*h)*(d*g - c*h)*p*q*r^2*x)/(3*b*d) + (8*(d*g - c*h)^2*p*q*r^2*x)/(9*d^2) + (2*(d*g - c*h)^2*q^2*r^2*x)/d^2 + (h*(b*g - a*h)*p^2*r^2*(a + b*x)^2)/(2*b^3) + (2*h^2*p^2*r^2*(a + b*x)^3)/(27*b^3) + (h*(d*g - c*h)*q^2*r^2*(c + d*x)^2)/(2*d^3) + (2*h^2*q^2*r^2*(c + d*x)^3)/(27*d^3) + (5*(b*g - a*h)*p*q*r^2*(g + h*x)^2)/(18*b*h) + (5*(d*g - c*h)*p*q*r^2*(g + h*x)^2)/(18*d*h) + (4*p*q*r^2*(g + h*x)^3)/(27*h) + (2*(b*g - a*h)^3*p*q*r^2*Log[a + b*x])/(9*b^3*h) + ((b*g - a*h)^2*(d*g - c*h)*p*q*r^2*Log[a + b*x])/(3*b^2*d*h) - (2*(d*g - c*h)^2*p*q*r^2*(a + b*x)*Log[a + b*x])/(3*b*d^2) - ((d*g - c*h)*p*q*r^2*(g + h*x)^2*Log[a + b*x])/(3*d*h) - (2*p*q*r^2*(g + h*x)^3*Log[a + b*x])/(9*h) + ((b*g - a*h)^3*p^2*r^2*Log[a + b*x]^2)/(3*b^3*h) - (p^2*r^2*Log[a + b*x]*((18*h*(b*g - a*h)^2*(a + b*x))/b^3 + (9*h^2*(b*g - a*h)*(a + b*x)^2)/b^3 + (2*h^3*(a + b*x)^3)/b^3 + (6*(b*g - a*h)^3*Log[a + b*x])/b^3))/(9*h) + ((b*g - a*h)*(d*g - c*h)^2*p*q*r^2*Log[c + d*x])/(3*b*d^2*h) + (2*(d*g - c*h)^3*p*q*r^2*Log[c + d*x])/(9*d^3*h) - (2*(b*g - a*h)^2*p*q*r^2*(c + d*x)*Log[c + d*x])/(3*b^2*d) - ((b*g - a*h)*p*q*r^2*(g + h*x)^2*Log[c + d*x])/(3*b*h) - (2*p*q*r^2*(g + h*x)^3*Log[c + d*x])/(9*h) - (2*(b*g - a*h)^3*p*q*r^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*b^3*h) + ((d*g - c*h)^3*q^2*r^2*Log[c + d*x]^2)/(3*d^3*h) - (q^2*r^2*Log[c + d*x]*((18*h*(d*g - c*h)^2*(c + d*x))/d^3 + (9*h^2*(d*g - c*h)*(c + d*x)^2)/d^3 + (2*h^3*(c + d*x)^3)/d^3 + (6*(d*g - c*h)^3*Log[c + d*x])/d^3))/(9*h) - (2*(d*g - c*h)^3*p*q*r^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3*d^3*h) + (2*(b*g - a*h)^2*p*r*x*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(3*b^2) + (2*(d*g - c*h)^2*q*r*x*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(3*d^2) + ((b*g - a*h)*p*r*(g + h*x)^2*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(3*b*h) + ((d*g - c*h)*q*r*(g + h*x)^2*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(3*d*h) + (2*p*r*(g + h*x)^3*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(9*h) + (2*q*r*(g + h*x)^3*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(9*h) + (2*(b*g - a*h)^3*p*r*Log[a + b*x]*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(3*b^3*h) + (2*(d*g - c*h)^3*q*r*Log[c + d*x]*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(3*d^3*h) + ((g + h*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2)/(3*h) - (2*(d*g - c*h)^3*p*q*r^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(3*d^3*h) - (2*(b*g - a*h)^3*p*q*r^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*b^3*h)","A",47,15,31,0.4839,1,"{2498, 2513, 2411, 43, 2334, 12, 14, 2301, 2418, 2389, 2295, 2394, 2393, 2391, 2395}"
37,1,1097,0,1.1628455,"\int (g+h x) \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[(g + h*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2,x]","\frac{p^2 r^2 \log ^2(a+b x) (b g-a h)^2}{2 b^2 h}+\frac{p q r^2 \log (a+b x) (b g-a h)^2}{2 b^2 h}-\frac{p q r^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) (b g-a h)^2}{b^2 h}+\frac{p r \log (a+b x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)^2}{b^2 h}-\frac{p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) (b g-a h)^2}{b^2 h}+\frac{3 p q r^2 x (b g-a h)}{2 b}-\frac{p q r^2 (c+d x) \log (c+d x) (b g-a h)}{b d}+\frac{p r x \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)}{b}+\frac{p q r^2 (g+h x)^2}{2 h}+\frac{p^2 r^2 (4 b g-3 a h+b h x)^2}{4 b^2 h}+\frac{q^2 r^2 (4 d g-3 c h+d h x)^2}{4 d^2 h}+\frac{(d g-c h)^2 q^2 r^2 \log ^2(c+d x)}{2 d^2 h}+\frac{(g+h x)^2 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 h}+\frac{3 (d g-c h) p q r^2 x}{2 d}-\frac{p q r^2 (g+h x)^2 \log (a+b x)}{2 h}-\frac{(d g-c h) p q r^2 (a+b x) \log (a+b x)}{b d}-\frac{p^2 r^2 \log (a+b x) \left(\frac{2 \log (a+b x) (b g-a h)^2}{b^2}+\frac{4 h (a+b x) (b g-a h)}{b^2}+\frac{h^2 (a+b x)^2}{b^2}\right)}{2 h}+\frac{(d g-c h)^2 p q r^2 \log (c+d x)}{2 d^2 h}-\frac{p q r^2 (g+h x)^2 \log (c+d x)}{2 h}-\frac{q^2 r^2 \log (c+d x) \left(\frac{2 \log (c+d x) (d g-c h)^2}{d^2}+\frac{4 h (c+d x) (d g-c h)}{d^2}+\frac{h^2 (c+d x)^2}{d^2}\right)}{2 h}-\frac{(d g-c h)^2 p q r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{d^2 h}+\frac{p r (g+h x)^2 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{2 h}+\frac{q r (g+h x)^2 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{2 h}+\frac{(d g-c h) q r x \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{d}+\frac{(d g-c h)^2 q r \log (c+d x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{d^2 h}-\frac{(d g-c h)^2 p q r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{d^2 h}","-\frac{p^2 r^2 \log ^2(a+b x) (b g-a h)^2}{2 b^2 h}+\frac{p q r^2 \log (a+b x) (b g-a h)^2}{2 b^2 h}-\frac{p q r^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) (b g-a h)^2}{b^2 h}+\frac{p r \log (a+b x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)^2}{b^2 h}-\frac{p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) (b g-a h)^2}{b^2 h}+\frac{3 p q r^2 x (b g-a h)}{2 b}-\frac{2 p^2 r^2 (a+b x) \log (a+b x) (b g-a h)}{b^2}-\frac{p q r^2 (c+d x) \log (c+d x) (b g-a h)}{b d}+\frac{p r x \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) (b g-a h)}{b}+\frac{p q r^2 (g+h x)^2}{2 h}+\frac{p^2 r^2 (4 b g-3 a h+b h x)^2}{4 b^2 h}+\frac{q^2 r^2 (4 d g-3 c h+d h x)^2}{4 d^2 h}-\frac{(d g-c h)^2 q^2 r^2 \log ^2(c+d x)}{2 d^2 h}+\frac{(g+h x)^2 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 h}+\frac{3 (d g-c h) p q r^2 x}{2 d}-\frac{h p^2 r^2 (a+b x)^2 \log (a+b x)}{2 b^2}-\frac{p q r^2 (g+h x)^2 \log (a+b x)}{2 h}-\frac{(d g-c h) p q r^2 (a+b x) \log (a+b x)}{b d}+\frac{(d g-c h)^2 p q r^2 \log (c+d x)}{2 d^2 h}-\frac{h q^2 r^2 (c+d x)^2 \log (c+d x)}{2 d^2}-\frac{p q r^2 (g+h x)^2 \log (c+d x)}{2 h}-\frac{2 (d g-c h) q^2 r^2 (c+d x) \log (c+d x)}{d^2}-\frac{(d g-c h)^2 p q r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{d^2 h}+\frac{p r (g+h x)^2 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{2 h}+\frac{q r (g+h x)^2 \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{2 h}+\frac{(d g-c h) q r x \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{d}+\frac{(d g-c h)^2 q r \log (c+d x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{d^2 h}-\frac{(d g-c h)^2 p q r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{d^2 h}",1,"(3*(b*g - a*h)*p*q*r^2*x)/(2*b) + (3*(d*g - c*h)*p*q*r^2*x)/(2*d) + (p*q*r^2*(g + h*x)^2)/(2*h) + (p^2*r^2*(4*b*g - 3*a*h + b*h*x)^2)/(4*b^2*h) + (q^2*r^2*(4*d*g - 3*c*h + d*h*x)^2)/(4*d^2*h) + ((b*g - a*h)^2*p*q*r^2*Log[a + b*x])/(2*b^2*h) - ((d*g - c*h)*p*q*r^2*(a + b*x)*Log[a + b*x])/(b*d) - (p*q*r^2*(g + h*x)^2*Log[a + b*x])/(2*h) + ((b*g - a*h)^2*p^2*r^2*Log[a + b*x]^2)/(2*b^2*h) - (p^2*r^2*Log[a + b*x]*((4*h*(b*g - a*h)*(a + b*x))/b^2 + (h^2*(a + b*x)^2)/b^2 + (2*(b*g - a*h)^2*Log[a + b*x])/b^2))/(2*h) + ((d*g - c*h)^2*p*q*r^2*Log[c + d*x])/(2*d^2*h) - ((b*g - a*h)*p*q*r^2*(c + d*x)*Log[c + d*x])/(b*d) - (p*q*r^2*(g + h*x)^2*Log[c + d*x])/(2*h) - ((b*g - a*h)^2*p*q*r^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b^2*h) + ((d*g - c*h)^2*q^2*r^2*Log[c + d*x]^2)/(2*d^2*h) - (q^2*r^2*Log[c + d*x]*((4*h*(d*g - c*h)*(c + d*x))/d^2 + (h^2*(c + d*x)^2)/d^2 + (2*(d*g - c*h)^2*Log[c + d*x])/d^2))/(2*h) - ((d*g - c*h)^2*p*q*r^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(d^2*h) + ((b*g - a*h)*p*r*x*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/b + ((d*g - c*h)*q*r*x*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/d + (p*r*(g + h*x)^2*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(2*h) + (q*r*(g + h*x)^2*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(2*h) + ((b*g - a*h)^2*p*r*Log[a + b*x]*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(b^2*h) + ((d*g - c*h)^2*q*r*Log[c + d*x]*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(d^2*h) + ((g + h*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2)/(2*h) - ((d*g - c*h)^2*p*q*r^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(d^2*h) - ((b*g - a*h)^2*p*q*r^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b^2*h)","A",39,15,29,0.5172,1,"{2498, 2513, 2411, 43, 2334, 12, 14, 2301, 2418, 2389, 2295, 2394, 2393, 2391, 2395}"
38,1,269,0,0.1530092,"\int \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2,x]","-\frac{2 p q r^2 (b c-a d) \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b d}+\frac{(a+b x) \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b}-\frac{2 r (p+q) (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b}+\frac{2 q r (b c-a d) \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b d}-\frac{2 q r^2 (p+q) (b c-a d) \log (c+d x)}{b d}-\frac{2 p q r^2 (b c-a d) \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b d}-\frac{q^2 r^2 (b c-a d) \log ^2(c+d x)}{b d}+2 r^2 x (p+q)^2","-\frac{2 p q r^2 (b c-a d) \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{b d}+\frac{(a+b x) \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b}-\frac{2 r (p+q) (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b}+\frac{2 q r (b c-a d) \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{b d}-\frac{2 q r^2 (p+q) (b c-a d) \log (c+d x)}{b d}-\frac{2 p q r^2 (b c-a d) \log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{b d}-\frac{q^2 r^2 (b c-a d) \log ^2(c+d x)}{b d}+2 r^2 x (p+q)^2",1,"2*(p + q)^2*r^2*x - (2*(b*c - a*d)*q*(p + q)*r^2*Log[c + d*x])/(b*d) - (2*(b*c - a*d)*p*q*r^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(b*d) - ((b*c - a*d)*q^2*r^2*Log[c + d*x]^2)/(b*d) - (2*(p + q)*r*(a + b*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/b + (2*(b*c - a*d)*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(b*d) + ((a + b*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2)/b - (2*(b*c - a*d)*p*q*r^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(b*d)","A",10,9,23,0.3913,1,"{2487, 2494, 2394, 2393, 2391, 2390, 2301, 31, 8}"
39,1,2096,0,1.9314848,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{g+h x} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(g + h*x),x]","-\frac{p q \left(\log \left(\frac{b (c+d x)}{b c-a d}\right)+\log \left(\frac{b g-a h}{b (g+h x)}\right)-\log \left(\frac{(b g-a h) (c+d x)}{(b c-a d) (g+h x)}\right)\right) \log ^2\left(-\frac{(b c-a d) (g+h x)}{(d g-c h) (a+b x)}\right) r^2}{h}+\frac{p q \left(\log \left(\frac{b (c+d x)}{b c-a d}\right)-\log \left(-\frac{h (c+d x)}{d g-c h}\right)\right) \left(\log (a+b x)+\log \left(-\frac{(b c-a d) (g+h x)}{(d g-c h) (a+b x)}\right)\right)^2 r^2}{h}-\frac{p q \left(\log \left(-\frac{d (a+b x)}{b c-a d}\right)+\log \left(\frac{d g-c h}{d (g+h x)}\right)-\log \left(-\frac{(d g-c h) (a+b x)}{(b c-a d) (g+h x)}\right)\right) \log ^2\left(\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right) r^2}{h}+\frac{p q \left(\log \left(-\frac{d (a+b x)}{b c-a d}\right)-\log \left(-\frac{h (a+b x)}{b g-a h}\right)\right) \left(\log (c+d x)+\log \left(\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right)\right)^2 r^2}{h}-\frac{2 p q \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) \log (g+h x) r^2}{h}-\frac{2 p q \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) \log (g+h x) r^2}{h}-\frac{2 p q \left(\log (g+h x)-\log \left(-\frac{(b c-a d) (g+h x)}{(d g-c h) (a+b x)}\right)\right) \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) r^2}{h}-\frac{2 p q \left(\log (g+h x)-\log \left(\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right)\right) \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) r^2}{h}+\frac{2 p q \log \left(-\frac{(b c-a d) (g+h x)}{(d g-c h) (a+b x)}\right) \text{PolyLog}\left(2,\frac{h (a+b x)}{b (g+h x)}\right) r^2}{h}-\frac{2 p q \log \left(-\frac{(b c-a d) (g+h x)}{(d g-c h) (a+b x)}\right) \text{PolyLog}\left(2,-\frac{(d g-c h) (a+b x)}{(b c-a d) (g+h x)}\right) r^2}{h}+\frac{2 p q \log \left(\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right) \text{PolyLog}\left(2,\frac{h (c+d x)}{d (g+h x)}\right) r^2}{h}-\frac{2 p q \log \left(\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right) \text{PolyLog}\left(2,\frac{(b g-a h) (c+d x)}{(b c-a d) (g+h x)}\right) r^2}{h}-\frac{2 p q \left(\log (c+d x)+\log \left(\frac{(b c-a d) (g+h x)}{(b g-a h) (c+d x)}\right)\right) \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right) r^2}{h}-\frac{2 p q \left(\log (a+b x)+\log \left(-\frac{(b c-a d) (g+h x)}{(d g-c h) (a+b x)}\right)\right) \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right) r^2}{h}+\frac{2 p q \text{PolyLog}\left(3,-\frac{d (a+b x)}{b c-a d}\right) r^2}{h}-\frac{2 p^2 \text{PolyLog}\left(3,-\frac{h (a+b x)}{b g-a h}\right) r^2}{h}+\frac{2 p q \text{PolyLog}\left(3,\frac{b (c+d x)}{b c-a d}\right) r^2}{h}-\frac{2 q^2 \text{PolyLog}\left(3,-\frac{h (c+d x)}{d g-c h}\right) r^2}{h}+\frac{2 p q \text{PolyLog}\left(3,\frac{h (a+b x)}{b (g+h x)}\right) r^2}{h}-\frac{2 p q \text{PolyLog}\left(3,-\frac{(d g-c h) (a+b x)}{(b c-a d) (g+h x)}\right) r^2}{h}+\frac{2 p q \text{PolyLog}\left(3,\frac{h (c+d x)}{d (g+h x)}\right) r^2}{h}-\frac{2 p q \text{PolyLog}\left(3,\frac{(b g-a h) (c+d x)}{(b c-a d) (g+h x)}\right) r^2}{h}+\frac{2 p q \text{PolyLog}\left(3,\frac{b (g+h x)}{b g-a h}\right) r^2}{h}+\frac{2 p q \text{PolyLog}\left(3,\frac{d (g+h x)}{d g-c h}\right) r^2}{h}+\frac{2 q \left(p r \log (a+b x)-\log \left((a+b x)^{p r}\right)\right) \log \left(-\frac{h (c+d x)}{d g-c h}\right) \log (g+h x) r}{h}+\frac{2 p \log \left(-\frac{h (a+b x)}{b g-a h}\right) \left(q r \log (c+d x)-\log \left((c+d x)^{q r}\right)\right) \log (g+h x) r}{h}+\frac{2 p \log \left(-\frac{h (a+b x)}{b g-a h}\right) \left(\log \left((a+b x)^{p r}\right)+\log \left((c+d x)^{q r}\right)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \log (g+h x) r}{h}+\frac{2 q \log \left(-\frac{h (c+d x)}{d g-c h}\right) \left(\log \left((a+b x)^{p r}\right)+\log \left((c+d x)^{q r}\right)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \log (g+h x) r}{h}+\frac{2 p \log \left((a+b x)^{p r}\right) \text{PolyLog}\left(2,-\frac{h (a+b x)}{b g-a h}\right) r}{h}+\frac{2 q \log \left((c+d x)^{q r}\right) \text{PolyLog}\left(2,-\frac{h (c+d x)}{d g-c h}\right) r}{h}+\frac{2 p \left(q r \log (c+d x)-\log \left((c+d x)^{q r}\right)\right) \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right) r}{h}+\frac{2 p \left(\log \left((a+b x)^{p r}\right)+\log \left((c+d x)^{q r}\right)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right) r}{h}+\frac{2 q \left(p r \log (a+b x)-\log \left((a+b x)^{p r}\right)\right) \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right) r}{h}+\frac{2 q \left(\log \left((a+b x)^{p r}\right)+\log \left((c+d x)^{q r}\right)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right) r}{h}-\frac{\log ^2\left((a+b x)^{p r}\right) \log (g+h x)}{h}-\frac{\log ^2\left((c+d x)^{q r}\right) \log (g+h x)}{h}+\frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \log (g+h x)}{h}+\frac{\log ^2\left((a+b x)^{p r}\right) \log \left(\frac{b (g+h x)}{b g-a h}\right)}{h}+\frac{\log ^2\left((c+d x)^{q r}\right) \log \left(\frac{d (g+h x)}{d g-c h}\right)}{h}","\frac{p q \log \left(-\frac{b c-a d}{d (a+b x)}\right) \log ^2\left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right) r^2}{h}+\frac{p^2 \log ^2(a+b x) \log (g+h x) r^2}{h}+\frac{q^2 \log ^2(c+d x) \log (g+h x) r^2}{h}+\frac{2 p q \log (a+b x) \log (c+d x) \log (g+h x) r^2}{h}-\frac{p^2 \log ^2(a+b x) \log \left(\frac{b (g+h x)}{b g-a h}\right) r^2}{h}+\frac{p q \log ^2\left(-\frac{h (c+d x)}{d g-c h}\right) \log \left(\frac{b (g+h x)}{b g-a h}\right) r^2}{h}+\frac{p q \log ^2\left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right) \log \left(\frac{b (g+h x)}{b g-a h}\right) r^2}{h}-\frac{2 p q \log (a+b x) \log \left(-\frac{h (c+d x)}{d g-c h}\right) \log \left(\frac{b (g+h x)}{b g-a h}\right) r^2}{h}-\frac{2 p q \log \left(-\frac{h (c+d x)}{d g-c h}\right) \log \left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right) \log \left(\frac{b (g+h x)}{b g-a h}\right) r^2}{h}-\frac{q^2 \log ^2(c+d x) \log \left(\frac{d (g+h x)}{d g-c h}\right) r^2}{h}-\frac{p q \log ^2\left(-\frac{h (c+d x)}{d g-c h}\right) \log \left(\frac{d (g+h x)}{d g-c h}\right) r^2}{h}-\frac{2 p q \log (a+b x) \log (c+d x) \log \left(\frac{d (g+h x)}{d g-c h}\right) r^2}{h}+\frac{2 p q \log (a+b x) \log \left(-\frac{h (c+d x)}{d g-c h}\right) \log \left(\frac{d (g+h x)}{d g-c h}\right) r^2}{h}+\frac{2 p q \log \left(-\frac{h (c+d x)}{d g-c h}\right) \log \left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right) \log \left(\frac{d (g+h x)}{d g-c h}\right) r^2}{h}-\frac{p q \log ^2\left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right) \log \left(-\frac{(b c-a d) (g+h x)}{(d g-c h) (a+b x)}\right) r^2}{h}+\frac{2 p q \log \left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right) \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right) r^2}{h}-\frac{2 p q \log \left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right) \text{PolyLog}\left(2,\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right) r^2}{h}-\frac{2 p^2 \text{PolyLog}\left(3,-\frac{h (a+b x)}{b g-a h}\right) r^2}{h}-\frac{2 p q \text{PolyLog}\left(3,-\frac{h (a+b x)}{b g-a h}\right) r^2}{h}-\frac{2 q^2 \text{PolyLog}\left(3,-\frac{h (c+d x)}{d g-c h}\right) r^2}{h}-\frac{2 p q \text{PolyLog}\left(3,-\frac{h (c+d x)}{d g-c h}\right) r^2}{h}-\frac{2 p q \text{PolyLog}\left(3,\frac{b (c+d x)}{d (a+b x)}\right) r^2}{h}+\frac{2 p q \text{PolyLog}\left(3,\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right) r^2}{h}-\frac{2 p \log (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \log (g+h x) r}{h}-\frac{2 q \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \log (g+h x) r}{h}+\frac{2 p \log (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \log \left(\frac{b (g+h x)}{b g-a h}\right) r}{h}+\frac{2 q \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \log \left(\frac{d (g+h x)}{d g-c h}\right) r}{h}-\frac{2 p \left(q r \log \left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \text{PolyLog}\left(2,-\frac{h (a+b x)}{b g-a h}\right) r}{h}+\frac{2 q \left(p r \log \left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right)+\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \text{PolyLog}\left(2,-\frac{h (c+d x)}{d g-c h}\right) r}{h}+\frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \log (g+h x)}{h}",1,"-((Log[(a + b*x)^(p*r)]^2*Log[g + h*x])/h) - (2*p*q*r^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x]*Log[g + h*x])/h - (2*p*q*r^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)]*Log[g + h*x])/h + (2*q*r*(p*r*Log[a + b*x] - Log[(a + b*x)^(p*r)])*Log[-((h*(c + d*x))/(d*g - c*h))]*Log[g + h*x])/h + (2*p*r*Log[-((h*(a + b*x))/(b*g - a*h))]*(q*r*Log[c + d*x] - Log[(c + d*x)^(q*r)])*Log[g + h*x])/h - (Log[(c + d*x)^(q*r)]^2*Log[g + h*x])/h + (2*p*r*Log[-((h*(a + b*x))/(b*g - a*h))]*(Log[(a + b*x)^(p*r)] + Log[(c + d*x)^(q*r)] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])*Log[g + h*x])/h + (2*q*r*Log[-((h*(c + d*x))/(d*g - c*h))]*(Log[(a + b*x)^(p*r)] + Log[(c + d*x)^(q*r)] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])*Log[g + h*x])/h + (Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2*Log[g + h*x])/h + (Log[(a + b*x)^(p*r)]^2*Log[(b*(g + h*x))/(b*g - a*h)])/h + (Log[(c + d*x)^(q*r)]^2*Log[(d*(g + h*x))/(d*g - c*h)])/h - (p*q*r^2*(Log[(b*(c + d*x))/(b*c - a*d)] + Log[(b*g - a*h)/(b*(g + h*x))] - Log[((b*g - a*h)*(c + d*x))/((b*c - a*d)*(g + h*x))])*Log[-(((b*c - a*d)*(g + h*x))/((d*g - c*h)*(a + b*x)))]^2)/h + (p*q*r^2*(Log[(b*(c + d*x))/(b*c - a*d)] - Log[-((h*(c + d*x))/(d*g - c*h))])*(Log[a + b*x] + Log[-(((b*c - a*d)*(g + h*x))/((d*g - c*h)*(a + b*x)))])^2)/h - (p*q*r^2*(Log[-((d*(a + b*x))/(b*c - a*d))] + Log[(d*g - c*h)/(d*(g + h*x))] - Log[-(((d*g - c*h)*(a + b*x))/((b*c - a*d)*(g + h*x)))])*Log[((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))]^2)/h + (p*q*r^2*(Log[-((d*(a + b*x))/(b*c - a*d))] - Log[-((h*(a + b*x))/(b*g - a*h))])*(Log[c + d*x] + Log[((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])^2)/h - (2*p*q*r^2*(Log[g + h*x] - Log[-(((b*c - a*d)*(g + h*x))/((d*g - c*h)*(a + b*x)))])*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/h + (2*p*r*Log[(a + b*x)^(p*r)]*PolyLog[2, -((h*(a + b*x))/(b*g - a*h))])/h - (2*p*q*r^2*(Log[g + h*x] - Log[((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/h + (2*q*r*Log[(c + d*x)^(q*r)]*PolyLog[2, -((h*(c + d*x))/(d*g - c*h))])/h + (2*p*q*r^2*Log[-(((b*c - a*d)*(g + h*x))/((d*g - c*h)*(a + b*x)))]*PolyLog[2, (h*(a + b*x))/(b*(g + h*x))])/h - (2*p*q*r^2*Log[-(((b*c - a*d)*(g + h*x))/((d*g - c*h)*(a + b*x)))]*PolyLog[2, -(((d*g - c*h)*(a + b*x))/((b*c - a*d)*(g + h*x)))])/h + (2*p*q*r^2*Log[((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))]*PolyLog[2, (h*(c + d*x))/(d*(g + h*x))])/h - (2*p*q*r^2*Log[((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))]*PolyLog[2, ((b*g - a*h)*(c + d*x))/((b*c - a*d)*(g + h*x))])/h + (2*p*r*(q*r*Log[c + d*x] - Log[(c + d*x)^(q*r)])*PolyLog[2, (b*(g + h*x))/(b*g - a*h)])/h + (2*p*r*(Log[(a + b*x)^(p*r)] + Log[(c + d*x)^(q*r)] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])*PolyLog[2, (b*(g + h*x))/(b*g - a*h)])/h - (2*p*q*r^2*(Log[c + d*x] + Log[((b*c - a*d)*(g + h*x))/((b*g - a*h)*(c + d*x))])*PolyLog[2, (b*(g + h*x))/(b*g - a*h)])/h + (2*q*r*(p*r*Log[a + b*x] - Log[(a + b*x)^(p*r)])*PolyLog[2, (d*(g + h*x))/(d*g - c*h)])/h + (2*q*r*(Log[(a + b*x)^(p*r)] + Log[(c + d*x)^(q*r)] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])*PolyLog[2, (d*(g + h*x))/(d*g - c*h)])/h - (2*p*q*r^2*(Log[a + b*x] + Log[-(((b*c - a*d)*(g + h*x))/((d*g - c*h)*(a + b*x)))])*PolyLog[2, (d*(g + h*x))/(d*g - c*h)])/h + (2*p*q*r^2*PolyLog[3, -((d*(a + b*x))/(b*c - a*d))])/h - (2*p^2*r^2*PolyLog[3, -((h*(a + b*x))/(b*g - a*h))])/h + (2*p*q*r^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])/h - (2*q^2*r^2*PolyLog[3, -((h*(c + d*x))/(d*g - c*h))])/h + (2*p*q*r^2*PolyLog[3, (h*(a + b*x))/(b*(g + h*x))])/h - (2*p*q*r^2*PolyLog[3, -(((d*g - c*h)*(a + b*x))/((b*c - a*d)*(g + h*x)))])/h + (2*p*q*r^2*PolyLog[3, (h*(c + d*x))/(d*(g + h*x))])/h - (2*p*q*r^2*PolyLog[3, ((b*g - a*h)*(c + d*x))/((b*c - a*d)*(g + h*x))])/h + (2*p*q*r^2*PolyLog[3, (b*(g + h*x))/(b*g - a*h)])/h + (2*p*q*r^2*PolyLog[3, (d*(g + h*x))/(d*g - c*h)])/h","A",29,14,31,0.4516,1,"{2497, 2500, 2394, 2393, 2391, 2433, 2375, 2317, 2374, 6589, 2440, 2437, 2435, 2315}"
40,1,878,0,0.9317403,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g+h x)^2} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(g + h*x)^2,x]","\frac{b p^2 \log ^2(a+b x) r^2}{h (b g-a h)}+\frac{d q^2 \log ^2(c+d x) r^2}{h (d g-c h)}+\frac{2 b p q \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) r^2}{h (b g-a h)}+\frac{2 d p q \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) r^2}{h (d g-c h)}-\frac{2 b p^2 \log (a+b x) \log \left(\frac{b (g+h x)}{b g-a h}\right) r^2}{h (b g-a h)}-\frac{2 d p q \log (a+b x) \log \left(\frac{b (g+h x)}{b g-a h}\right) r^2}{h (d g-c h)}-\frac{2 d q^2 \log (c+d x) \log \left(\frac{d (g+h x)}{d g-c h}\right) r^2}{h (d g-c h)}-\frac{2 b p q \log (c+d x) \log \left(\frac{d (g+h x)}{d g-c h}\right) r^2}{h (b g-a h)}+\frac{2 d p q \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) r^2}{h (d g-c h)}-\frac{2 b p^2 \text{PolyLog}\left(2,-\frac{h (a+b x)}{b g-a h}\right) r^2}{h (b g-a h)}-\frac{2 d p q \text{PolyLog}\left(2,-\frac{h (a+b x)}{b g-a h}\right) r^2}{h (d g-c h)}+\frac{2 b p q \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) r^2}{h (b g-a h)}-\frac{2 d q^2 \text{PolyLog}\left(2,-\frac{h (c+d x)}{d g-c h}\right) r^2}{h (d g-c h)}-\frac{2 b p q \text{PolyLog}\left(2,-\frac{h (c+d x)}{d g-c h}\right) r^2}{h (b g-a h)}-\frac{2 b p \log (a+b x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) r}{h (b g-a h)}-\frac{2 d q \log (c+d x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) r}{h (d g-c h)}+\frac{2 b p \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \log (g+h x) r}{h (b g-a h)}+\frac{2 d q \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \log (g+h x) r}{h (d g-c h)}-\frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{h (g+h x)}","\frac{2 b p q \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) r^2}{h (b g-a h)}+\frac{2 d p q \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right) r^2}{h (d g-c h)}-\frac{2 d p q \log (a+b x) \log \left(\frac{b (g+h x)}{b g-a h}\right) r^2}{h (d g-c h)}-\frac{2 b p q \log (c+d x) \log \left(\frac{d (g+h x)}{d g-c h}\right) r^2}{h (b g-a h)}-\frac{2 b p^2 \log (a+b x) \log \left(\frac{b g-a h}{h (a+b x)}+1\right) r^2}{h (b g-a h)}-\frac{2 d q^2 \log (c+d x) \log \left(\frac{d g-c h}{h (c+d x)}+1\right) r^2}{h (d g-c h)}+\frac{2 b p^2 \text{PolyLog}\left(2,-\frac{b g-a h}{h (a+b x)}\right) r^2}{h (b g-a h)}+\frac{2 d p q \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right) r^2}{h (d g-c h)}-\frac{2 d p q \text{PolyLog}\left(2,-\frac{h (a+b x)}{b g-a h}\right) r^2}{h (d g-c h)}+\frac{2 d q^2 \text{PolyLog}\left(2,-\frac{d g-c h}{h (c+d x)}\right) r^2}{h (d g-c h)}+\frac{2 b p q \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) r^2}{h (b g-a h)}-\frac{2 b p q \text{PolyLog}\left(2,-\frac{h (c+d x)}{d g-c h}\right) r^2}{h (b g-a h)}-\frac{2 b p \log (a+b x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) r}{h (b g-a h)}-\frac{2 d q \log (c+d x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) r}{h (d g-c h)}+\frac{2 b p \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \log (g+h x) r}{h (b g-a h)}+\frac{2 d q \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \log (g+h x) r}{h (d g-c h)}-\frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{h (g+h x)}",1,"(b*p^2*r^2*Log[a + b*x]^2)/(h*(b*g - a*h)) + (2*b*p*q*r^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(h*(b*g - a*h)) + (d*q^2*r^2*Log[c + d*x]^2)/(h*(d*g - c*h)) + (2*d*p*q*r^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(h*(d*g - c*h)) - (2*b*p*r*Log[a + b*x]*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(h*(b*g - a*h)) - (2*d*q*r*Log[c + d*x]*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(h*(d*g - c*h)) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(h*(g + h*x)) + (2*b*p*r*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])*Log[g + h*x])/(h*(b*g - a*h)) + (2*d*q*r*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])*Log[g + h*x])/(h*(d*g - c*h)) - (2*b*p^2*r^2*Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)])/(h*(b*g - a*h)) - (2*d*p*q*r^2*Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)])/(h*(d*g - c*h)) - (2*b*p*q*r^2*Log[c + d*x]*Log[(d*(g + h*x))/(d*g - c*h)])/(h*(b*g - a*h)) - (2*d*q^2*r^2*Log[c + d*x]*Log[(d*(g + h*x))/(d*g - c*h)])/(h*(d*g - c*h)) + (2*d*p*q*r^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(h*(d*g - c*h)) - (2*b*p^2*r^2*PolyLog[2, -((h*(a + b*x))/(b*g - a*h))])/(h*(b*g - a*h)) - (2*d*p*q*r^2*PolyLog[2, -((h*(a + b*x))/(b*g - a*h))])/(h*(d*g - c*h)) + (2*b*p*q*r^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(h*(b*g - a*h)) - (2*b*p*q*r^2*PolyLog[2, -((h*(c + d*x))/(d*g - c*h))])/(h*(b*g - a*h)) - (2*d*q^2*r^2*PolyLog[2, -((h*(c + d*x))/(d*g - c*h))])/(h*(d*g - c*h))","A",35,12,31,0.3871,1,"{2498, 2513, 2411, 2344, 2301, 2317, 2391, 2418, 2394, 2393, 36, 31}"
41,1,1362,0,1.4075652,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g+h x)^3} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(g + h*x)^3,x]","\frac{p^2 r^2 \log ^2(a+b x) b^2}{2 h (b g-a h)^2}+\frac{p q r^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) b^2}{h (b g-a h)^2}-\frac{p r \log (a+b x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) b^2}{h (b g-a h)^2}+\frac{p^2 r^2 \log (g+h x) b^2}{h (b g-a h)^2}+\frac{p r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \log (g+h x) b^2}{h (b g-a h)^2}-\frac{p^2 r^2 \log (a+b x) \log \left(\frac{b (g+h x)}{b g-a h}\right) b^2}{h (b g-a h)^2}-\frac{p q r^2 \log (c+d x) \log \left(\frac{d (g+h x)}{d g-c h}\right) b^2}{h (b g-a h)^2}-\frac{p^2 r^2 \text{PolyLog}\left(2,-\frac{h (a+b x)}{b g-a h}\right) b^2}{h (b g-a h)^2}+\frac{p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) b^2}{h (b g-a h)^2}-\frac{p q r^2 \text{PolyLog}\left(2,-\frac{h (c+d x)}{d g-c h}\right) b^2}{h (b g-a h)^2}-\frac{d p q r^2 \log (a+b x) b}{h (b g-a h) (d g-c h)}-\frac{p^2 r^2 (a+b x) \log (a+b x) b}{(b g-a h)^2 (g+h x)}-\frac{d p q r^2 \log (c+d x) b}{h (b g-a h) (d g-c h)}+\frac{p q r^2 \log (c+d x) b}{h (b g-a h) (g+h x)}-\frac{p r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) b}{h (b g-a h) (g+h x)}+\frac{2 d p q r^2 \log (g+h x) b}{h (b g-a h) (d g-c h)}+\frac{d^2 q^2 r^2 \log ^2(c+d x)}{2 h (d g-c h)^2}-\frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 h (g+h x)^2}+\frac{d p q r^2 \log (a+b x)}{h (d g-c h) (g+h x)}-\frac{d q^2 r^2 (c+d x) \log (c+d x)}{(d g-c h)^2 (g+h x)}+\frac{d^2 p q r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{h (d g-c h)^2}-\frac{d^2 q r \log (c+d x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{h (d g-c h)^2}-\frac{d q r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{h (d g-c h) (g+h x)}+\frac{d^2 q^2 r^2 \log (g+h x)}{h (d g-c h)^2}+\frac{d^2 q r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \log (g+h x)}{h (d g-c h)^2}-\frac{d^2 p q r^2 \log (a+b x) \log \left(\frac{b (g+h x)}{b g-a h}\right)}{h (d g-c h)^2}-\frac{d^2 q^2 r^2 \log (c+d x) \log \left(\frac{d (g+h x)}{d g-c h}\right)}{h (d g-c h)^2}+\frac{d^2 p q r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{h (d g-c h)^2}-\frac{d^2 p q r^2 \text{PolyLog}\left(2,-\frac{h (a+b x)}{b g-a h}\right)}{h (d g-c h)^2}-\frac{d^2 q^2 r^2 \text{PolyLog}\left(2,-\frac{h (c+d x)}{d g-c h}\right)}{h (d g-c h)^2}","\frac{p q r^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) b^2}{h (b g-a h)^2}-\frac{p r \log (a+b x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) b^2}{h (b g-a h)^2}+\frac{p^2 r^2 \log (g+h x) b^2}{h (b g-a h)^2}+\frac{p r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \log (g+h x) b^2}{h (b g-a h)^2}-\frac{p q r^2 \log (c+d x) \log \left(\frac{d (g+h x)}{d g-c h}\right) b^2}{h (b g-a h)^2}-\frac{p^2 r^2 \log (a+b x) \log \left(\frac{b g-a h}{h (a+b x)}+1\right) b^2}{h (b g-a h)^2}+\frac{p^2 r^2 \text{PolyLog}\left(2,-\frac{b g-a h}{h (a+b x)}\right) b^2}{h (b g-a h)^2}+\frac{p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) b^2}{h (b g-a h)^2}-\frac{p q r^2 \text{PolyLog}\left(2,-\frac{h (c+d x)}{d g-c h}\right) b^2}{h (b g-a h)^2}-\frac{d p q r^2 \log (a+b x) b}{h (b g-a h) (d g-c h)}-\frac{p^2 r^2 (a+b x) \log (a+b x) b}{(b g-a h)^2 (g+h x)}-\frac{d p q r^2 \log (c+d x) b}{h (b g-a h) (d g-c h)}+\frac{p q r^2 \log (c+d x) b}{h (b g-a h) (g+h x)}-\frac{p r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) b}{h (b g-a h) (g+h x)}+\frac{2 d p q r^2 \log (g+h x) b}{h (b g-a h) (d g-c h)}-\frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 h (g+h x)^2}+\frac{d p q r^2 \log (a+b x)}{h (d g-c h) (g+h x)}-\frac{d q^2 r^2 (c+d x) \log (c+d x)}{(d g-c h)^2 (g+h x)}+\frac{d^2 p q r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{h (d g-c h)^2}-\frac{d^2 q r \log (c+d x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{h (d g-c h)^2}-\frac{d q r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{h (d g-c h) (g+h x)}+\frac{d^2 q^2 r^2 \log (g+h x)}{h (d g-c h)^2}+\frac{d^2 q r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \log (g+h x)}{h (d g-c h)^2}-\frac{d^2 p q r^2 \log (a+b x) \log \left(\frac{b (g+h x)}{b g-a h}\right)}{h (d g-c h)^2}-\frac{d^2 q^2 r^2 \log (c+d x) \log \left(\frac{d g-c h}{h (c+d x)}+1\right)}{h (d g-c h)^2}+\frac{d^2 p q r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{h (d g-c h)^2}-\frac{d^2 p q r^2 \text{PolyLog}\left(2,-\frac{h (a+b x)}{b g-a h}\right)}{h (d g-c h)^2}+\frac{d^2 q^2 r^2 \text{PolyLog}\left(2,-\frac{d g-c h}{h (c+d x)}\right)}{h (d g-c h)^2}",1,"-((b*d*p*q*r^2*Log[a + b*x])/(h*(b*g - a*h)*(d*g - c*h))) + (d*p*q*r^2*Log[a + b*x])/(h*(d*g - c*h)*(g + h*x)) - (b*p^2*r^2*(a + b*x)*Log[a + b*x])/((b*g - a*h)^2*(g + h*x)) + (b^2*p^2*r^2*Log[a + b*x]^2)/(2*h*(b*g - a*h)^2) - (b*d*p*q*r^2*Log[c + d*x])/(h*(b*g - a*h)*(d*g - c*h)) + (b*p*q*r^2*Log[c + d*x])/(h*(b*g - a*h)*(g + h*x)) - (d*q^2*r^2*(c + d*x)*Log[c + d*x])/((d*g - c*h)^2*(g + h*x)) + (b^2*p*q*r^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(h*(b*g - a*h)^2) + (d^2*q^2*r^2*Log[c + d*x]^2)/(2*h*(d*g - c*h)^2) + (d^2*p*q*r^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(h*(d*g - c*h)^2) - (b*p*r*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(h*(b*g - a*h)*(g + h*x)) - (d*q*r*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(h*(d*g - c*h)*(g + h*x)) - (b^2*p*r*Log[a + b*x]*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(h*(b*g - a*h)^2) - (d^2*q*r*Log[c + d*x]*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(h*(d*g - c*h)^2) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(2*h*(g + h*x)^2) + (b^2*p^2*r^2*Log[g + h*x])/(h*(b*g - a*h)^2) + (2*b*d*p*q*r^2*Log[g + h*x])/(h*(b*g - a*h)*(d*g - c*h)) + (d^2*q^2*r^2*Log[g + h*x])/(h*(d*g - c*h)^2) + (b^2*p*r*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])*Log[g + h*x])/(h*(b*g - a*h)^2) + (d^2*q*r*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])*Log[g + h*x])/(h*(d*g - c*h)^2) - (b^2*p^2*r^2*Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)])/(h*(b*g - a*h)^2) - (d^2*p*q*r^2*Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)])/(h*(d*g - c*h)^2) - (b^2*p*q*r^2*Log[c + d*x]*Log[(d*(g + h*x))/(d*g - c*h)])/(h*(b*g - a*h)^2) - (d^2*q^2*r^2*Log[c + d*x]*Log[(d*(g + h*x))/(d*g - c*h)])/(h*(d*g - c*h)^2) + (d^2*p*q*r^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(h*(d*g - c*h)^2) - (b^2*p^2*r^2*PolyLog[2, -((h*(a + b*x))/(b*g - a*h))])/(h*(b*g - a*h)^2) - (d^2*p*q*r^2*PolyLog[2, -((h*(a + b*x))/(b*g - a*h))])/(h*(d*g - c*h)^2) + (b^2*p*q*r^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(h*(b*g - a*h)^2) - (b^2*p*q*r^2*PolyLog[2, -((h*(c + d*x))/(d*g - c*h))])/(h*(b*g - a*h)^2) - (d^2*q^2*r^2*PolyLog[2, -((h*(c + d*x))/(d*g - c*h))])/(h*(d*g - c*h)^2)","A",47,16,31,0.5161,1,"{2498, 2513, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2418, 2394, 2393, 2395, 36, 44}"
42,1,2013,0,2.1019224,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g+h x)^4} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(g + h*x)^4,x]","\frac{p^2 r^2 \log ^2(a+b x) b^3}{3 h (b g-a h)^3}-\frac{p^2 r^2 \log (a+b x) b^3}{3 h (b g-a h)^3}+\frac{2 p q r^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) b^3}{3 h (b g-a h)^3}-\frac{2 p r \log (a+b x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) b^3}{3 h (b g-a h)^3}+\frac{p^2 r^2 \log (g+h x) b^3}{h (b g-a h)^3}+\frac{2 p r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \log (g+h x) b^3}{3 h (b g-a h)^3}-\frac{2 p^2 r^2 \log (a+b x) \log \left(\frac{b (g+h x)}{b g-a h}\right) b^3}{3 h (b g-a h)^3}-\frac{2 p q r^2 \log (c+d x) \log \left(\frac{d (g+h x)}{d g-c h}\right) b^3}{3 h (b g-a h)^3}-\frac{2 p^2 r^2 \text{PolyLog}\left(2,-\frac{h (a+b x)}{b g-a h}\right) b^3}{3 h (b g-a h)^3}+\frac{2 p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) b^3}{3 h (b g-a h)^3}-\frac{2 p q r^2 \text{PolyLog}\left(2,-\frac{h (c+d x)}{d g-c h}\right) b^3}{3 h (b g-a h)^3}-\frac{d p q r^2 \log (a+b x) b^2}{3 h (b g-a h)^2 (d g-c h)}-\frac{2 p^2 r^2 (a+b x) \log (a+b x) b^2}{3 (b g-a h)^3 (g+h x)}-\frac{2 d p q r^2 \log (c+d x) b^2}{3 h (b g-a h)^2 (d g-c h)}+\frac{2 p q r^2 \log (c+d x) b^2}{3 h (b g-a h)^2 (g+h x)}-\frac{2 p r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) b^2}{3 h (b g-a h)^2 (g+h x)}+\frac{d p q r^2 \log (g+h x) b^2}{h (b g-a h)^2 (d g-c h)}-\frac{p^2 r^2 b^2}{3 h (b g-a h)^2 (g+h x)}-\frac{2 d^2 p q r^2 \log (a+b x) b}{3 h (b g-a h) (d g-c h)^2}+\frac{p^2 r^2 \log (a+b x) b}{3 h (b g-a h) (g+h x)^2}-\frac{d^2 p q r^2 \log (c+d x) b}{3 h (b g-a h) (d g-c h)^2}+\frac{p q r^2 \log (c+d x) b}{3 h (b g-a h) (g+h x)^2}-\frac{p r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) b}{3 h (b g-a h) (g+h x)^2}+\frac{d^2 p q r^2 \log (g+h x) b}{h (b g-a h) (d g-c h)^2}-\frac{2 d p q r^2 b}{3 h (b g-a h) (d g-c h) (g+h x)}+\frac{d^3 q^2 r^2 \log ^2(c+d x)}{3 h (d g-c h)^3}-\frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 h (g+h x)^3}+\frac{2 d^2 p q r^2 \log (a+b x)}{3 h (d g-c h)^2 (g+h x)}+\frac{d p q r^2 \log (a+b x)}{3 h (d g-c h) (g+h x)^2}-\frac{d^3 q^2 r^2 \log (c+d x)}{3 h (d g-c h)^3}-\frac{2 d^2 q^2 r^2 (c+d x) \log (c+d x)}{3 (d g-c h)^3 (g+h x)}+\frac{d q^2 r^2 \log (c+d x)}{3 h (d g-c h) (g+h x)^2}+\frac{2 d^3 p q r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{3 h (d g-c h)^3}-\frac{2 d^3 q r \log (c+d x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{3 h (d g-c h)^3}-\frac{2 d^2 q r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{3 h (d g-c h)^2 (g+h x)}-\frac{d q r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{3 h (d g-c h) (g+h x)^2}+\frac{d^3 q^2 r^2 \log (g+h x)}{h (d g-c h)^3}+\frac{2 d^3 q r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \log (g+h x)}{3 h (d g-c h)^3}-\frac{2 d^3 p q r^2 \log (a+b x) \log \left(\frac{b (g+h x)}{b g-a h}\right)}{3 h (d g-c h)^3}-\frac{2 d^3 q^2 r^2 \log (c+d x) \log \left(\frac{d (g+h x)}{d g-c h}\right)}{3 h (d g-c h)^3}+\frac{2 d^3 p q r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{3 h (d g-c h)^3}-\frac{2 d^3 p q r^2 \text{PolyLog}\left(2,-\frac{h (a+b x)}{b g-a h}\right)}{3 h (d g-c h)^3}-\frac{2 d^3 q^2 r^2 \text{PolyLog}\left(2,-\frac{h (c+d x)}{d g-c h}\right)}{3 h (d g-c h)^3}-\frac{d^2 q^2 r^2}{3 h (d g-c h)^2 (g+h x)}","-\frac{p^2 r^2 \log (a+b x) b^3}{3 h (b g-a h)^3}+\frac{2 p q r^2 \log \left(-\frac{d (a+b x)}{b c-a d}\right) \log (c+d x) b^3}{3 h (b g-a h)^3}-\frac{2 p r \log (a+b x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) b^3}{3 h (b g-a h)^3}+\frac{p^2 r^2 \log (g+h x) b^3}{h (b g-a h)^3}+\frac{2 p r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \log (g+h x) b^3}{3 h (b g-a h)^3}-\frac{2 p q r^2 \log (c+d x) \log \left(\frac{d (g+h x)}{d g-c h}\right) b^3}{3 h (b g-a h)^3}-\frac{2 p^2 r^2 \log (a+b x) \log \left(\frac{b g-a h}{h (a+b x)}+1\right) b^3}{3 h (b g-a h)^3}+\frac{2 p^2 r^2 \text{PolyLog}\left(2,-\frac{b g-a h}{h (a+b x)}\right) b^3}{3 h (b g-a h)^3}+\frac{2 p q r^2 \text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right) b^3}{3 h (b g-a h)^3}-\frac{2 p q r^2 \text{PolyLog}\left(2,-\frac{h (c+d x)}{d g-c h}\right) b^3}{3 h (b g-a h)^3}-\frac{d p q r^2 \log (a+b x) b^2}{3 h (b g-a h)^2 (d g-c h)}-\frac{2 p^2 r^2 (a+b x) \log (a+b x) b^2}{3 (b g-a h)^3 (g+h x)}-\frac{2 d p q r^2 \log (c+d x) b^2}{3 h (b g-a h)^2 (d g-c h)}+\frac{2 p q r^2 \log (c+d x) b^2}{3 h (b g-a h)^2 (g+h x)}-\frac{2 p r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) b^2}{3 h (b g-a h)^2 (g+h x)}+\frac{d p q r^2 \log (g+h x) b^2}{h (b g-a h)^2 (d g-c h)}-\frac{p^2 r^2 b^2}{3 h (b g-a h)^2 (g+h x)}-\frac{2 d^2 p q r^2 \log (a+b x) b}{3 h (b g-a h) (d g-c h)^2}+\frac{p^2 r^2 \log (a+b x) b}{3 h (b g-a h) (g+h x)^2}-\frac{d^2 p q r^2 \log (c+d x) b}{3 h (b g-a h) (d g-c h)^2}+\frac{p q r^2 \log (c+d x) b}{3 h (b g-a h) (g+h x)^2}-\frac{p r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) b}{3 h (b g-a h) (g+h x)^2}+\frac{d^2 p q r^2 \log (g+h x) b}{h (b g-a h) (d g-c h)^2}-\frac{2 d p q r^2 b}{3 h (b g-a h) (d g-c h) (g+h x)}-\frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 h (g+h x)^3}+\frac{2 d^2 p q r^2 \log (a+b x)}{3 h (d g-c h)^2 (g+h x)}+\frac{d p q r^2 \log (a+b x)}{3 h (d g-c h) (g+h x)^2}-\frac{d^3 q^2 r^2 \log (c+d x)}{3 h (d g-c h)^3}-\frac{2 d^2 q^2 r^2 (c+d x) \log (c+d x)}{3 (d g-c h)^3 (g+h x)}+\frac{d q^2 r^2 \log (c+d x)}{3 h (d g-c h) (g+h x)^2}+\frac{2 d^3 p q r^2 \log (a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)}{3 h (d g-c h)^3}-\frac{2 d^3 q r \log (c+d x) \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{3 h (d g-c h)^3}-\frac{2 d^2 q r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{3 h (d g-c h)^2 (g+h x)}-\frac{d q r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)}{3 h (d g-c h) (g+h x)^2}+\frac{d^3 q^2 r^2 \log (g+h x)}{h (d g-c h)^3}+\frac{2 d^3 q r \left(p r \log (a+b x)+q r \log (c+d x)-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \log (g+h x)}{3 h (d g-c h)^3}-\frac{2 d^3 p q r^2 \log (a+b x) \log \left(\frac{b (g+h x)}{b g-a h}\right)}{3 h (d g-c h)^3}-\frac{2 d^3 q^2 r^2 \log (c+d x) \log \left(\frac{d g-c h}{h (c+d x)}+1\right)}{3 h (d g-c h)^3}+\frac{2 d^3 p q r^2 \text{PolyLog}\left(2,-\frac{d (a+b x)}{b c-a d}\right)}{3 h (d g-c h)^3}-\frac{2 d^3 p q r^2 \text{PolyLog}\left(2,-\frac{h (a+b x)}{b g-a h}\right)}{3 h (d g-c h)^3}+\frac{2 d^3 q^2 r^2 \text{PolyLog}\left(2,-\frac{d g-c h}{h (c+d x)}\right)}{3 h (d g-c h)^3}-\frac{d^2 q^2 r^2}{3 h (d g-c h)^2 (g+h x)}",1,"-(b^2*p^2*r^2)/(3*h*(b*g - a*h)^2*(g + h*x)) - (2*b*d*p*q*r^2)/(3*h*(b*g - a*h)*(d*g - c*h)*(g + h*x)) - (d^2*q^2*r^2)/(3*h*(d*g - c*h)^2*(g + h*x)) - (b^3*p^2*r^2*Log[a + b*x])/(3*h*(b*g - a*h)^3) - (2*b*d^2*p*q*r^2*Log[a + b*x])/(3*h*(b*g - a*h)*(d*g - c*h)^2) - (b^2*d*p*q*r^2*Log[a + b*x])/(3*h*(b*g - a*h)^2*(d*g - c*h)) + (b*p^2*r^2*Log[a + b*x])/(3*h*(b*g - a*h)*(g + h*x)^2) + (d*p*q*r^2*Log[a + b*x])/(3*h*(d*g - c*h)*(g + h*x)^2) + (2*d^2*p*q*r^2*Log[a + b*x])/(3*h*(d*g - c*h)^2*(g + h*x)) - (2*b^2*p^2*r^2*(a + b*x)*Log[a + b*x])/(3*(b*g - a*h)^3*(g + h*x)) + (b^3*p^2*r^2*Log[a + b*x]^2)/(3*h*(b*g - a*h)^3) - (b*d^2*p*q*r^2*Log[c + d*x])/(3*h*(b*g - a*h)*(d*g - c*h)^2) - (2*b^2*d*p*q*r^2*Log[c + d*x])/(3*h*(b*g - a*h)^2*(d*g - c*h)) - (d^3*q^2*r^2*Log[c + d*x])/(3*h*(d*g - c*h)^3) + (b*p*q*r^2*Log[c + d*x])/(3*h*(b*g - a*h)*(g + h*x)^2) + (d*q^2*r^2*Log[c + d*x])/(3*h*(d*g - c*h)*(g + h*x)^2) + (2*b^2*p*q*r^2*Log[c + d*x])/(3*h*(b*g - a*h)^2*(g + h*x)) - (2*d^2*q^2*r^2*(c + d*x)*Log[c + d*x])/(3*(d*g - c*h)^3*(g + h*x)) + (2*b^3*p*q*r^2*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(3*h*(b*g - a*h)^3) + (d^3*q^2*r^2*Log[c + d*x]^2)/(3*h*(d*g - c*h)^3) + (2*d^3*p*q*r^2*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3*h*(d*g - c*h)^3) - (b*p*r*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(3*h*(b*g - a*h)*(g + h*x)^2) - (d*q*r*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(3*h*(d*g - c*h)*(g + h*x)^2) - (2*b^2*p*r*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(3*h*(b*g - a*h)^2*(g + h*x)) - (2*d^2*q*r*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(3*h*(d*g - c*h)^2*(g + h*x)) - (2*b^3*p*r*Log[a + b*x]*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(3*h*(b*g - a*h)^3) - (2*d^3*q*r*Log[c + d*x]*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(3*h*(d*g - c*h)^3) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(3*h*(g + h*x)^3) + (b^3*p^2*r^2*Log[g + h*x])/(h*(b*g - a*h)^3) + (b*d^2*p*q*r^2*Log[g + h*x])/(h*(b*g - a*h)*(d*g - c*h)^2) + (b^2*d*p*q*r^2*Log[g + h*x])/(h*(b*g - a*h)^2*(d*g - c*h)) + (d^3*q^2*r^2*Log[g + h*x])/(h*(d*g - c*h)^3) + (2*b^3*p*r*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])*Log[g + h*x])/(3*h*(b*g - a*h)^3) + (2*d^3*q*r*(p*r*Log[a + b*x] + q*r*Log[c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])*Log[g + h*x])/(3*h*(d*g - c*h)^3) - (2*b^3*p^2*r^2*Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)])/(3*h*(b*g - a*h)^3) - (2*d^3*p*q*r^2*Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)])/(3*h*(d*g - c*h)^3) - (2*b^3*p*q*r^2*Log[c + d*x]*Log[(d*(g + h*x))/(d*g - c*h)])/(3*h*(b*g - a*h)^3) - (2*d^3*q^2*r^2*Log[c + d*x]*Log[(d*(g + h*x))/(d*g - c*h)])/(3*h*(d*g - c*h)^3) + (2*d^3*p*q*r^2*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(3*h*(d*g - c*h)^3) - (2*b^3*p^2*r^2*PolyLog[2, -((h*(a + b*x))/(b*g - a*h))])/(3*h*(b*g - a*h)^3) - (2*d^3*p*q*r^2*PolyLog[2, -((h*(a + b*x))/(b*g - a*h))])/(3*h*(d*g - c*h)^3) + (2*b^3*p*q*r^2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(3*h*(b*g - a*h)^3) - (2*b^3*p*q*r^2*PolyLog[2, -((h*(c + d*x))/(d*g - c*h))])/(3*h*(b*g - a*h)^3) - (2*d^3*q^2*r^2*PolyLog[2, -((h*(c + d*x))/(d*g - c*h))])/(3*h*(d*g - c*h)^3)","A",61,17,31,0.5484,1,"{2498, 2513, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44, 2418, 2394, 2393, 2395, 36}"
43,1,42,0,0.0802486,"\int \frac{\left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^n}{1-c^2 x^2} \, dx","Int[(a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2),x]","-\frac{\left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^{n+1}}{b c (n+1)}","-\frac{\left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^{n+1}}{b c (n+1)}",1,"-((a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^(1 + n)/(b*c*(1 + n)))","A",3,3,40,0.07500,1,"{2512, 2302, 30}"
44,1,37,0,0.0611698,"\int \frac{\left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^3}{1-c^2 x^2} \, dx","Int[(a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3/(1 - c^2*x^2),x]","-\frac{\left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^4}{4 b c}","-\frac{\left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^4}{4 b c}",1,"-(a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^4/(4*b*c)","A",3,3,40,0.07500,1,"{2512, 2302, 30}"
45,1,37,0,0.0628152,"\int \frac{\left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2}{1-c^2 x^2} \, dx","Int[(a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2/(1 - c^2*x^2),x]","-\frac{\left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{3 b c}","-\frac{\left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{3 b c}",1,"-(a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3/(3*b*c)","A",3,3,40,0.07500,1,"{2512, 2302, 30}"
46,1,37,0,0.0379821,"\int \frac{a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)}{1-c^2 x^2} \, dx","Int[(a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])/(1 - c^2*x^2),x]","-\frac{\left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 b c}","-\frac{\left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 b c}",1,"-(a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2/(2*b*c)","A",2,2,38,0.05263,1,"{2512, 2301}"
47,1,34,0,0.0677073,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)} \, dx","Int[1/((1 - c^2*x^2)*(a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])),x]","-\frac{\log \left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{b c}","-\frac{\log \left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{b c}",1,"-(Log[a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]]]/(b*c))","A",3,3,40,0.07500,1,"{2512, 2302, 29}"
48,1,34,0,0.0654521,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2} \, dx","Int[1/((1 - c^2*x^2)*(a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2),x]","\frac{1}{b c \left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}","\frac{1}{b c \left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}",1,"1/(b*c*(a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]]))","A",3,3,40,0.07500,1,"{2512, 2302, 30}"
49,1,37,0,0.0651834,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^3} \, dx","Int[1/((1 - c^2*x^2)*(a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3),x]","\frac{1}{2 b c \left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}","\frac{1}{2 b c \left(a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}",1,"1/(2*b*c*(a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2)","A",3,3,40,0.07500,1,"{2512, 2302, 30}"
50,1,30,0,0.0232066,"\int \frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Int[Log[Sqrt[1 - a*x]/Sqrt[1 + a*x]]/(1 - a^2*x^2),x]","-\frac{\log ^2\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}","-\frac{\log ^2\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}",1,"-Log[Sqrt[1 - a*x]/Sqrt[1 + a*x]]^2/(2*a)","A",1,1,34,0.02941,1,"{2505}"
51,1,410,0,0.4712315,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \left(s+t \log \left(i (g+h x)^n\right)\right)^2}{g k+h k x} \, dx","Int[(Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*(s + t*Log[i*(g + h*x)^n])^2)/(g*k + h*k*x),x]","-\frac{p r \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)^2}{h k}+\frac{2 n p r t \text{PolyLog}\left(3,\frac{b (g+h x)}{b g-a h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)}{h k}-\frac{2 n^2 p r t^2 \text{PolyLog}\left(4,\frac{b (g+h x)}{b g-a h}\right)}{h k}-\frac{q r \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)^2}{h k}+\frac{2 n q r t \text{PolyLog}\left(3,\frac{d (g+h x)}{d g-c h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)}{h k}-\frac{2 n^2 q r t^2 \text{PolyLog}\left(4,\frac{d (g+h x)}{d g-c h}\right)}{h k}+\frac{\left(t \log \left(i (g+h x)^n\right)+s\right)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 h k n t}-\frac{p r \log \left(-\frac{h (a+b x)}{b g-a h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)^3}{3 h k n t}-\frac{q r \log \left(-\frac{h (c+d x)}{d g-c h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)^3}{3 h k n t}","-\frac{p r \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)^2}{h k}+\frac{2 n p r t \text{PolyLog}\left(3,\frac{b (g+h x)}{b g-a h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)}{h k}-\frac{2 n^2 p r t^2 \text{PolyLog}\left(4,\frac{b (g+h x)}{b g-a h}\right)}{h k}-\frac{q r \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)^2}{h k}+\frac{2 n q r t \text{PolyLog}\left(3,\frac{d (g+h x)}{d g-c h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)}{h k}-\frac{2 n^2 q r t^2 \text{PolyLog}\left(4,\frac{d (g+h x)}{d g-c h}\right)}{h k}+\frac{\left(t \log \left(i (g+h x)^n\right)+s\right)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 h k n t}-\frac{p r \log \left(-\frac{h (a+b x)}{b g-a h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)^3}{3 h k n t}-\frac{q r \log \left(-\frac{h (c+d x)}{d g-c h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)^3}{3 h k n t}",1,"-(p*r*Log[-((h*(a + b*x))/(b*g - a*h))]*(s + t*Log[i*(g + h*x)^n])^3)/(3*h*k*n*t) - (q*r*Log[-((h*(c + d*x))/(d*g - c*h))]*(s + t*Log[i*(g + h*x)^n])^3)/(3*h*k*n*t) + (Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*(s + t*Log[i*(g + h*x)^n])^3)/(3*h*k*n*t) - (p*r*(s + t*Log[i*(g + h*x)^n])^2*PolyLog[2, (b*(g + h*x))/(b*g - a*h)])/(h*k) - (q*r*(s + t*Log[i*(g + h*x)^n])^2*PolyLog[2, (d*(g + h*x))/(d*g - c*h)])/(h*k) + (2*n*p*r*t*(s + t*Log[i*(g + h*x)^n])*PolyLog[3, (b*(g + h*x))/(b*g - a*h)])/(h*k) + (2*n*q*r*t*(s + t*Log[i*(g + h*x)^n])*PolyLog[3, (d*(g + h*x))/(d*g - c*h)])/(h*k) - (2*n^2*p*r*t^2*PolyLog[4, (b*(g + h*x))/(b*g - a*h)])/(h*k) - (2*n^2*q*r*t^2*PolyLog[4, (d*(g + h*x))/(d*g - c*h)])/(h*k)","A",11,6,48,0.1250,1,"{2499, 2396, 2433, 2374, 2383, 6589}"
52,1,306,0,0.2875419,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \left(s+t \log \left(i (g+h x)^n\right)\right)}{g k+h k x} \, dx","Int[(Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*(s + t*Log[i*(g + h*x)^n]))/(g*k + h*k*x),x]","-\frac{p r \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)}{h k}+\frac{n p r t \text{PolyLog}\left(3,\frac{b (g+h x)}{b g-a h}\right)}{h k}-\frac{q r \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)}{h k}+\frac{n q r t \text{PolyLog}\left(3,\frac{d (g+h x)}{d g-c h}\right)}{h k}+\frac{\left(t \log \left(i (g+h x)^n\right)+s\right)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 h k n t}-\frac{p r \log \left(-\frac{h (a+b x)}{b g-a h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)^2}{2 h k n t}-\frac{q r \log \left(-\frac{h (c+d x)}{d g-c h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)^2}{2 h k n t}","-\frac{p r \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)}{h k}+\frac{n p r t \text{PolyLog}\left(3,\frac{b (g+h x)}{b g-a h}\right)}{h k}-\frac{q r \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)}{h k}+\frac{n q r t \text{PolyLog}\left(3,\frac{d (g+h x)}{d g-c h}\right)}{h k}+\frac{\left(t \log \left(i (g+h x)^n\right)+s\right)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 h k n t}-\frac{p r \log \left(-\frac{h (a+b x)}{b g-a h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)^2}{2 h k n t}-\frac{q r \log \left(-\frac{h (c+d x)}{d g-c h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)^2}{2 h k n t}",1,"-(p*r*Log[-((h*(a + b*x))/(b*g - a*h))]*(s + t*Log[i*(g + h*x)^n])^2)/(2*h*k*n*t) - (q*r*Log[-((h*(c + d*x))/(d*g - c*h))]*(s + t*Log[i*(g + h*x)^n])^2)/(2*h*k*n*t) + (Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*(s + t*Log[i*(g + h*x)^n])^2)/(2*h*k*n*t) - (p*r*(s + t*Log[i*(g + h*x)^n])*PolyLog[2, (b*(g + h*x))/(b*g - a*h)])/(h*k) - (q*r*(s + t*Log[i*(g + h*x)^n])*PolyLog[2, (d*(g + h*x))/(d*g - c*h)])/(h*k) + (n*p*r*t*PolyLog[3, (b*(g + h*x))/(b*g - a*h)])/(h*k) + (n*q*r*t*PolyLog[3, (d*(g + h*x))/(d*g - c*h)])/(h*k)","A",9,5,46,0.1087,1,"{2499, 2396, 2433, 2374, 6589}"
53,1,172,0,0.1359411,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{g k+h k x} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(g*k + h*k*x),x]","-\frac{p r \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right)}{h k}-\frac{q r \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right)}{h k}+\frac{\log (g k+h k x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{h k}-\frac{p r \log (g k+h k x) \log \left(-\frac{h (a+b x)}{b g-a h}\right)}{h k}-\frac{q r \log (g k+h k x) \log \left(-\frac{h (c+d x)}{d g-c h}\right)}{h k}","-\frac{p r \text{PolyLog}\left(2,\frac{b (g+h x)}{b g-a h}\right)}{h k}-\frac{q r \text{PolyLog}\left(2,\frac{d (g+h x)}{d g-c h}\right)}{h k}+\frac{\log (g k+h k x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{h k}-\frac{p r \log (g k+h k x) \log \left(-\frac{h (a+b x)}{b g-a h}\right)}{h k}-\frac{q r \log (g k+h k x) \log \left(-\frac{h (c+d x)}{d g-c h}\right)}{h k}",1,"-((p*r*Log[-((h*(a + b*x))/(b*g - a*h))]*Log[g*k + h*k*x])/(h*k)) - (q*r*Log[-((h*(c + d*x))/(d*g - c*h))]*Log[g*k + h*k*x])/(h*k) + (Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[g*k + h*k*x])/(h*k) - (p*r*PolyLog[2, (b*(g + h*x))/(b*g - a*h)])/(h*k) - (q*r*PolyLog[2, (d*(g + h*x))/(d*g - c*h)])/(h*k)","A",7,4,32,0.1250,1,"{2494, 2394, 2393, 2391}"
54,0,0,0,0.0532358,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g k+h k x) \left(s+t \log \left(i (g+h x)^n\right)\right)} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/((g*k + h*k*x)*(s + t*Log[i*(g + h*x)^n])),x]","\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g k+h k x) \left(s+t \log \left(i (g+h x)^n\right)\right)} \, dx","\text{Int}\left(\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g k+h k x) \left(t \log \left(i (g+h x)^n\right)+s\right)},x\right)",0,"Defer[Int][Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/((g*k + h*k*x)*(s + t*Log[i*(g + h*x)^n])), x]","A",0,0,0,0,-1,"{}"
55,0,0,0,0.0525536,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g k+h k x) \left(s+t \log \left(i (g+h x)^n\right)\right)^2} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/((g*k + h*k*x)*(s + t*Log[i*(g + h*x)^n])^2),x]","\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g k+h k x) \left(s+t \log \left(i (g+h x)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g k+h k x) \left(t \log \left(i (g+h x)^n\right)+s\right)^2},x\right)",0,"Defer[Int][Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/((g*k + h*k*x)*(s + t*Log[i*(g + h*x)^n])^2), x]","A",0,0,0,0,-1,"{}"
56,1,328,0,1.2515735,"\int \frac{\log ^3\left(i \left(j (h x)^t\right)^u\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{x} \, dx","Int[(Log[i*(j*(h*x)^t)^u]^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/x,x]","-6 p r t^2 u^2 \text{PolyLog}\left(4,-\frac{b x}{a}\right) \log \left(i \left(j (h x)^t\right)^u\right)-p r \text{PolyLog}\left(2,-\frac{b x}{a}\right) \log ^3\left(i \left(j (h x)^t\right)^u\right)+3 p r t u \text{PolyLog}\left(3,-\frac{b x}{a}\right) \log ^2\left(i \left(j (h x)^t\right)^u\right)+6 p r t^3 u^3 \text{PolyLog}\left(5,-\frac{b x}{a}\right)-6 q r t^2 u^2 \text{PolyLog}\left(4,-\frac{d x}{c}\right) \log \left(i \left(j (h x)^t\right)^u\right)-q r \text{PolyLog}\left(2,-\frac{d x}{c}\right) \log ^3\left(i \left(j (h x)^t\right)^u\right)+3 q r t u \text{PolyLog}\left(3,-\frac{d x}{c}\right) \log ^2\left(i \left(j (h x)^t\right)^u\right)+6 q r t^3 u^3 \text{PolyLog}\left(5,-\frac{d x}{c}\right)+\frac{\log ^4\left(i \left(j (h x)^t\right)^u\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 t u}-\frac{p r \log \left(\frac{b x}{a}+1\right) \log ^4\left(i \left(j (h x)^t\right)^u\right)}{4 t u}-\frac{q r \log \left(\frac{d x}{c}+1\right) \log ^4\left(i \left(j (h x)^t\right)^u\right)}{4 t u}","-6 p r t^2 u^2 \text{PolyLog}\left(4,-\frac{b x}{a}\right) \log \left(i \left(j (h x)^t\right)^u\right)-p r \text{PolyLog}\left(2,-\frac{b x}{a}\right) \log ^3\left(i \left(j (h x)^t\right)^u\right)+3 p r t u \text{PolyLog}\left(3,-\frac{b x}{a}\right) \log ^2\left(i \left(j (h x)^t\right)^u\right)+6 p r t^3 u^3 \text{PolyLog}\left(5,-\frac{b x}{a}\right)-6 q r t^2 u^2 \text{PolyLog}\left(4,-\frac{d x}{c}\right) \log \left(i \left(j (h x)^t\right)^u\right)-q r \text{PolyLog}\left(2,-\frac{d x}{c}\right) \log ^3\left(i \left(j (h x)^t\right)^u\right)+3 q r t u \text{PolyLog}\left(3,-\frac{d x}{c}\right) \log ^2\left(i \left(j (h x)^t\right)^u\right)+6 q r t^3 u^3 \text{PolyLog}\left(5,-\frac{d x}{c}\right)+\frac{\log ^4\left(i \left(j (h x)^t\right)^u\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 t u}-\frac{p r \log \left(\frac{b x}{a}+1\right) \log ^4\left(i \left(j (h x)^t\right)^u\right)}{4 t u}-\frac{q r \log \left(\frac{d x}{c}+1\right) \log ^4\left(i \left(j (h x)^t\right)^u\right)}{4 t u}",1,"-(p*r*Log[i*(j*(h*x)^t)^u]^4*Log[1 + (b*x)/a])/(4*t*u) + (Log[i*(j*(h*x)^t)^u]^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(4*t*u) - (q*r*Log[i*(j*(h*x)^t)^u]^4*Log[1 + (d*x)/c])/(4*t*u) - p*r*Log[i*(j*(h*x)^t)^u]^3*PolyLog[2, -((b*x)/a)] - q*r*Log[i*(j*(h*x)^t)^u]^3*PolyLog[2, -((d*x)/c)] + 3*p*r*t*u*Log[i*(j*(h*x)^t)^u]^2*PolyLog[3, -((b*x)/a)] + 3*q*r*t*u*Log[i*(j*(h*x)^t)^u]^2*PolyLog[3, -((d*x)/c)] - 6*p*r*t^2*u^2*Log[i*(j*(h*x)^t)^u]*PolyLog[4, -((b*x)/a)] - 6*q*r*t^2*u^2*Log[i*(j*(h*x)^t)^u]*PolyLog[4, -((d*x)/c)] + 6*p*r*t^3*u^3*PolyLog[5, -((b*x)/a)] + 6*q*r*t^3*u^3*PolyLog[5, -((d*x)/c)]","A",13,6,39,0.1538,1,"{2499, 2317, 2374, 2383, 6589, 2445}"
57,1,262,0,0.9102141,"\int \frac{\log ^2\left(i \left(j (h x)^t\right)^u\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{x} \, dx","Int[(Log[i*(j*(h*x)^t)^u]^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/x,x]","-p r \text{PolyLog}\left(2,-\frac{b x}{a}\right) \log ^2\left(i \left(j (h x)^t\right)^u\right)+2 p r t u \text{PolyLog}\left(3,-\frac{b x}{a}\right) \log \left(i \left(j (h x)^t\right)^u\right)-2 p r t^2 u^2 \text{PolyLog}\left(4,-\frac{b x}{a}\right)-q r \text{PolyLog}\left(2,-\frac{d x}{c}\right) \log ^2\left(i \left(j (h x)^t\right)^u\right)+2 q r t u \text{PolyLog}\left(3,-\frac{d x}{c}\right) \log \left(i \left(j (h x)^t\right)^u\right)-2 q r t^2 u^2 \text{PolyLog}\left(4,-\frac{d x}{c}\right)+\frac{\log ^3\left(i \left(j (h x)^t\right)^u\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 t u}-\frac{p r \log \left(\frac{b x}{a}+1\right) \log ^3\left(i \left(j (h x)^t\right)^u\right)}{3 t u}-\frac{q r \log \left(\frac{d x}{c}+1\right) \log ^3\left(i \left(j (h x)^t\right)^u\right)}{3 t u}","-p r \text{PolyLog}\left(2,-\frac{b x}{a}\right) \log ^2\left(i \left(j (h x)^t\right)^u\right)+2 p r t u \text{PolyLog}\left(3,-\frac{b x}{a}\right) \log \left(i \left(j (h x)^t\right)^u\right)-2 p r t^2 u^2 \text{PolyLog}\left(4,-\frac{b x}{a}\right)-q r \text{PolyLog}\left(2,-\frac{d x}{c}\right) \log ^2\left(i \left(j (h x)^t\right)^u\right)+2 q r t u \text{PolyLog}\left(3,-\frac{d x}{c}\right) \log \left(i \left(j (h x)^t\right)^u\right)-2 q r t^2 u^2 \text{PolyLog}\left(4,-\frac{d x}{c}\right)+\frac{\log ^3\left(i \left(j (h x)^t\right)^u\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{3 t u}-\frac{p r \log \left(\frac{b x}{a}+1\right) \log ^3\left(i \left(j (h x)^t\right)^u\right)}{3 t u}-\frac{q r \log \left(\frac{d x}{c}+1\right) \log ^3\left(i \left(j (h x)^t\right)^u\right)}{3 t u}",1,"-(p*r*Log[i*(j*(h*x)^t)^u]^3*Log[1 + (b*x)/a])/(3*t*u) + (Log[i*(j*(h*x)^t)^u]^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(3*t*u) - (q*r*Log[i*(j*(h*x)^t)^u]^3*Log[1 + (d*x)/c])/(3*t*u) - p*r*Log[i*(j*(h*x)^t)^u]^2*PolyLog[2, -((b*x)/a)] - q*r*Log[i*(j*(h*x)^t)^u]^2*PolyLog[2, -((d*x)/c)] + 2*p*r*t*u*Log[i*(j*(h*x)^t)^u]*PolyLog[3, -((b*x)/a)] + 2*q*r*t*u*Log[i*(j*(h*x)^t)^u]*PolyLog[3, -((d*x)/c)] - 2*p*r*t^2*u^2*PolyLog[4, -((b*x)/a)] - 2*q*r*t^2*u^2*PolyLog[4, -((d*x)/c)]","A",11,6,39,0.1538,1,"{2499, 2317, 2374, 2383, 6589, 2445}"
58,1,194,0,0.6033606,"\int \frac{\log \left(i \left(j (h x)^t\right)^u\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{x} \, dx","Int[(Log[i*(j*(h*x)^t)^u]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/x,x]","-p r \text{PolyLog}\left(2,-\frac{b x}{a}\right) \log \left(i \left(j (h x)^t\right)^u\right)+p r t u \text{PolyLog}\left(3,-\frac{b x}{a}\right)-q r \text{PolyLog}\left(2,-\frac{d x}{c}\right) \log \left(i \left(j (h x)^t\right)^u\right)+q r t u \text{PolyLog}\left(3,-\frac{d x}{c}\right)+\frac{\log ^2\left(i \left(j (h x)^t\right)^u\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 t u}-\frac{p r \log \left(\frac{b x}{a}+1\right) \log ^2\left(i \left(j (h x)^t\right)^u\right)}{2 t u}-\frac{q r \log \left(\frac{d x}{c}+1\right) \log ^2\left(i \left(j (h x)^t\right)^u\right)}{2 t u}","-p r \text{PolyLog}\left(2,-\frac{b x}{a}\right) \log \left(i \left(j (h x)^t\right)^u\right)+p r t u \text{PolyLog}\left(3,-\frac{b x}{a}\right)-q r \text{PolyLog}\left(2,-\frac{d x}{c}\right) \log \left(i \left(j (h x)^t\right)^u\right)+q r t u \text{PolyLog}\left(3,-\frac{d x}{c}\right)+\frac{\log ^2\left(i \left(j (h x)^t\right)^u\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 t u}-\frac{p r \log \left(\frac{b x}{a}+1\right) \log ^2\left(i \left(j (h x)^t\right)^u\right)}{2 t u}-\frac{q r \log \left(\frac{d x}{c}+1\right) \log ^2\left(i \left(j (h x)^t\right)^u\right)}{2 t u}",1,"-(p*r*Log[i*(j*(h*x)^t)^u]^2*Log[1 + (b*x)/a])/(2*t*u) + (Log[i*(j*(h*x)^t)^u]^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(2*t*u) - (q*r*Log[i*(j*(h*x)^t)^u]^2*Log[1 + (d*x)/c])/(2*t*u) - p*r*Log[i*(j*(h*x)^t)^u]*PolyLog[2, -((b*x)/a)] - q*r*Log[i*(j*(h*x)^t)^u]*PolyLog[2, -((d*x)/c)] + p*r*t*u*PolyLog[3, -((b*x)/a)] + q*r*t*u*PolyLog[3, -((d*x)/c)]","A",9,5,37,0.1351,1,"{2499, 2317, 2374, 6589, 2445}"
59,1,81,0,0.0657538,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{x} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/x,x]","-p r \text{PolyLog}\left(2,-\frac{b x}{a}\right)-q r \text{PolyLog}\left(2,-\frac{d x}{c}\right)+\log (x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-p r \log (x) \log \left(\frac{b x}{a}+1\right)-q r \log (x) \log \left(\frac{d x}{c}+1\right)","-p r \text{PolyLog}\left(2,-\frac{b x}{a}\right)-q r \text{PolyLog}\left(2,-\frac{d x}{c}\right)+\log (x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-p r \log (x) \log \left(\frac{b x}{a}+1\right)-q r \log (x) \log \left(\frac{d x}{c}+1\right)",1,"-(p*r*Log[x]*Log[1 + (b*x)/a]) + Log[x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - q*r*Log[x]*Log[1 + (d*x)/c] - p*r*PolyLog[2, -((b*x)/a)] - q*r*PolyLog[2, -((d*x)/c)]","A",5,3,25,0.1200,1,"{2494, 2317, 2391}"
60,0,0,0,0.5446519,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{x \log \left(i \left(j (h x)^t\right)^u\right)} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(x*Log[i*(j*(h*x)^t)^u]),x]","\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{x \log \left(i \left(j (h x)^t\right)^u\right)} \, dx","\text{Int}\left(\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{x \log \left(i \left(j (h x)^t\right)^u\right)},x\right)",0,"Defer[Int][Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(x*Log[i*(j*(h*x)^t)^u]), x]","A",0,0,0,0,-1,"{}"
61,0,0,0,0.4253098,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{x \log ^2\left(i \left(j (h x)^t\right)^u\right)} \, dx","Int[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(x*Log[i*(j*(h*x)^t)^u]^2),x]","\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{x \log ^2\left(i \left(j (h x)^t\right)^u\right)} \, dx","\text{Int}\left(\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{x \log ^2\left(i \left(j (h x)^t\right)^u\right)},x\right)",0,"Defer[Int][Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(x*Log[i*(j*(h*x)^t)^u]^2), x]","A",0,0,0,0,-1,"{}"
62,0,0,0,0.021354,"\int \frac{\log (x) \log ^3\left(\frac{a+b x}{(b c-a d) x}\right)}{x} \, dx","Int[(Log[x]*Log[(a + b*x)/((b*c - a*d)*x)]^3)/x,x]","\int \frac{\log (x) \log ^3\left(\frac{a+b x}{(b c-a d) x}\right)}{x} \, dx","\text{Int}\left(\frac{\log (x) \log ^3\left(\frac{a+b x}{x (b c-a d)}\right)}{x},x\right)",0,"Defer[Int][(Log[x]*Log[(a + b*x)/((b*c - a*d)*x)]^3)/x, x]","A",0,0,0,0,-1,"{}"
63,0,0,0,0.0213293,"\int \frac{\log (x) \log ^2\left(\frac{a+b x}{(b c-a d) x}\right)}{x} \, dx","Int[(Log[x]*Log[(a + b*x)/((b*c - a*d)*x)]^2)/x,x]","\int \frac{\log (x) \log ^2\left(\frac{a+b x}{(b c-a d) x}\right)}{x} \, dx","\text{Int}\left(\frac{\log (x) \log ^2\left(\frac{a+b x}{x (b c-a d)}\right)}{x},x\right)",0,"Defer[Int][(Log[x]*Log[(a + b*x)/((b*c - a*d)*x)]^2)/x, x]","A",0,0,0,0,-1,"{}"
64,1,82,0,0.176511,"\int \frac{\log (x) \log \left(\frac{a+b x}{(b c-a d) x}\right)}{x} \, dx","Int[(Log[x]*Log[(a + b*x)/((b*c - a*d)*x)])/x,x]","\text{PolyLog}\left(3,-\frac{a}{b x}\right)+\log (x) \text{PolyLog}\left(2,-\frac{a}{b x}\right)+\frac{1}{2} \log ^2(x) \log \left(\frac{a}{x (b c-a d)}+\frac{b}{b c-a d}\right)-\frac{1}{2} \log ^2(x) \log \left(\frac{a}{b x}+1\right)","\text{PolyLog}\left(3,-\frac{a}{b x}\right)+\log (x) \text{PolyLog}\left(2,-\frac{a}{b x}\right)+\frac{1}{2} \log ^2(x) \log \left(\frac{a}{x (b c-a d)}+\frac{b}{b c-a d}\right)-\frac{1}{2} \log ^2(x) \log \left(\frac{a}{b x}+1\right)",1,"-(Log[1 + a/(b*x)]*Log[x]^2)/2 + (Log[b/(b*c - a*d) + a/((b*c - a*d)*x)]*Log[x]^2)/2 + Log[x]*PolyLog[2, -(a/(b*x))] + PolyLog[3, -(a/(b*x))]","A",5,5,26,0.1923,1,"{2380, 2375, 2337, 2374, 6589}"
65,0,0,0,0.0216231,"\int \frac{\log (x)}{x \log \left(\frac{a+b x}{(b c-a d) x}\right)} \, dx","Int[Log[x]/(x*Log[(a + b*x)/((b*c - a*d)*x)]),x]","\int \frac{\log (x)}{x \log \left(\frac{a+b x}{(b c-a d) x}\right)} \, dx","\text{Int}\left(\frac{\log (x)}{x \log \left(\frac{a+b x}{x (b c-a d)}\right)},x\right)",0,"Defer[Int][Log[x]/(x*Log[(a + b*x)/((b*c - a*d)*x)]), x]","A",0,0,0,0,-1,"{}"
66,0,0,0,0.0219153,"\int \frac{\log (x)}{x \log ^2\left(\frac{a+b x}{(b c-a d) x}\right)} \, dx","Int[Log[x]/(x*Log[(a + b*x)/((b*c - a*d)*x)]^2),x]","\int \frac{\log (x)}{x \log ^2\left(\frac{a+b x}{(b c-a d) x}\right)} \, dx","\text{Int}\left(\frac{\log (x)}{x \log ^2\left(\frac{a+b x}{x (b c-a d)}\right)},x\right)",0,"Defer[Int][Log[x]/(x*Log[(a + b*x)/((b*c - a*d)*x)]^2), x]","A",0,0,0,0,-1,"{}"
67,1,649,0,1.1326293,"\int \frac{\log ^3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(h (f+g x)^m\right)}{(a+b x) (c+d x)} \, dx","Int[(Log[e*((a + b*x)/(c + d*x))^n]^3*Log[h*(f + g*x)^m])/((a + b*x)*(c + d*x)),x]","-\frac{6 m n^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{PolyLog}\left(4,1-\frac{(f+g x) (b c-a d)}{(c+d x) (b f-a g)}\right)}{b c-a d}-\frac{m \log ^3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{PolyLog}\left(2,1-\frac{(f+g x) (b c-a d)}{(c+d x) (b f-a g)}\right)}{b c-a d}+\frac{3 m n \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{PolyLog}\left(3,1-\frac{(f+g x) (b c-a d)}{(c+d x) (b f-a g)}\right)}{b c-a d}+\frac{6 m n^2 \text{PolyLog}\left(4,1-\frac{b c-a d}{b (c+d x)}\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b c-a d}+\frac{m \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) \log ^3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b c-a d}-\frac{3 m n \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b c-a d}+\frac{6 m n^3 \text{PolyLog}\left(5,1-\frac{(f+g x) (b c-a d)}{(c+d x) (b f-a g)}\right)}{b c-a d}-\frac{6 m n^3 \text{PolyLog}\left(5,1-\frac{b c-a d}{b (c+d x)}\right)}{b c-a d}+\frac{\log \left(h (f+g x)^m\right) \log ^4\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{4 n (b c-a d)}-\frac{m \log ^4\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(\frac{(f+g x) (b c-a d)}{(c+d x) (b f-a g)}\right)}{4 n (b c-a d)}+\frac{m \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^4\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{4 n (b c-a d)}","-\frac{6 m n^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{PolyLog}\left(4,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{b c-a d}-\frac{m \log ^3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{PolyLog}\left(2,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{b c-a d}+\frac{3 m n \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{PolyLog}\left(3,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{b c-a d}+\frac{6 m n^2 \text{PolyLog}\left(4,\frac{d (a+b x)}{b (c+d x)}\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b c-a d}+\frac{m \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) \log ^3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b c-a d}-\frac{3 m n \text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right) \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b c-a d}+\frac{6 m n^3 \text{PolyLog}\left(5,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{b c-a d}-\frac{6 m n^3 \text{PolyLog}\left(5,\frac{d (a+b x)}{b (c+d x)}\right)}{b c-a d}+\frac{\log \left(h (f+g x)^m\right) \log ^4\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{4 n (b c-a d)}-\frac{m \log ^4\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(1-\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{4 n (b c-a d)}+\frac{m \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^4\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{4 n (b c-a d)}",1,"(m*Log[e*((a + b*x)/(c + d*x))^n]^4*Log[(b*c - a*d)/(b*(c + d*x))])/(4*(b*c - a*d)*n) - (m*Log[e*((a + b*x)/(c + d*x))^n]^4*Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])/(4*(b*c - a*d)*n) + (Log[e*((a + b*x)/(c + d*x))^n]^4*Log[h*(f + g*x)^m])/(4*(b*c - a*d)*n) + (m*Log[e*((a + b*x)/(c + d*x))^n]^3*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*c - a*d) - (m*Log[e*((a + b*x)/(c + d*x))^n]^3*PolyLog[2, 1 - ((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])/(b*c - a*d) - (3*m*n*Log[e*((a + b*x)/(c + d*x))^n]^2*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*c - a*d) + (3*m*n*Log[e*((a + b*x)/(c + d*x))^n]^2*PolyLog[3, 1 - ((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])/(b*c - a*d) + (6*m*n^2*Log[e*((a + b*x)/(c + d*x))^n]*PolyLog[4, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*c - a*d) - (6*m*n^2*Log[e*((a + b*x)/(c + d*x))^n]*PolyLog[4, 1 - ((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])/(b*c - a*d) - (6*m*n^3*PolyLog[5, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*c - a*d) + (6*m*n^3*PolyLog[5, 1 - ((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])/(b*c - a*d)","A",12,7,45,0.1556,1,"{2507, 2489, 2488, 2506, 2508, 6610, 2503}"
68,1,517,0,0.8188832,"\int \frac{\log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(h (f+g x)^m\right)}{(a+b x) (c+d x)} \, dx","Int[(Log[e*((a + b*x)/(c + d*x))^n]^2*Log[h*(f + g*x)^m])/((a + b*x)*(c + d*x)),x]","-\frac{m \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{PolyLog}\left(2,1-\frac{(f+g x) (b c-a d)}{(c+d x) (b f-a g)}\right)}{b c-a d}+\frac{2 m n \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{PolyLog}\left(3,1-\frac{(f+g x) (b c-a d)}{(c+d x) (b f-a g)}\right)}{b c-a d}+\frac{m \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b c-a d}-\frac{2 m n \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b c-a d}-\frac{2 m n^2 \text{PolyLog}\left(4,1-\frac{(f+g x) (b c-a d)}{(c+d x) (b f-a g)}\right)}{b c-a d}+\frac{2 m n^2 \text{PolyLog}\left(4,1-\frac{b c-a d}{b (c+d x)}\right)}{b c-a d}+\frac{\log \left(h (f+g x)^m\right) \log ^3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{3 n (b c-a d)}-\frac{m \log ^3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(\frac{(f+g x) (b c-a d)}{(c+d x) (b f-a g)}\right)}{3 n (b c-a d)}+\frac{m \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{3 n (b c-a d)}","-\frac{m \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{PolyLog}\left(2,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{b c-a d}+\frac{2 m n \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{PolyLog}\left(3,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{b c-a d}+\frac{m \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b c-a d}-\frac{2 m n \text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b c-a d}-\frac{2 m n^2 \text{PolyLog}\left(4,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{b c-a d}+\frac{2 m n^2 \text{PolyLog}\left(4,\frac{d (a+b x)}{b (c+d x)}\right)}{b c-a d}+\frac{\log \left(h (f+g x)^m\right) \log ^3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{3 n (b c-a d)}-\frac{m \log ^3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(1-\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{3 n (b c-a d)}+\frac{m \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{3 n (b c-a d)}",1,"(m*Log[e*((a + b*x)/(c + d*x))^n]^3*Log[(b*c - a*d)/(b*(c + d*x))])/(3*(b*c - a*d)*n) - (m*Log[e*((a + b*x)/(c + d*x))^n]^3*Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])/(3*(b*c - a*d)*n) + (Log[e*((a + b*x)/(c + d*x))^n]^3*Log[h*(f + g*x)^m])/(3*(b*c - a*d)*n) + (m*Log[e*((a + b*x)/(c + d*x))^n]^2*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*c - a*d) - (m*Log[e*((a + b*x)/(c + d*x))^n]^2*PolyLog[2, 1 - ((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])/(b*c - a*d) - (2*m*n*Log[e*((a + b*x)/(c + d*x))^n]*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*c - a*d) + (2*m*n*Log[e*((a + b*x)/(c + d*x))^n]*PolyLog[3, 1 - ((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])/(b*c - a*d) + (2*m*n^2*PolyLog[4, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*c - a*d) - (2*m*n^2*PolyLog[4, 1 - ((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])/(b*c - a*d)","A",10,7,45,0.1556,1,"{2507, 2489, 2488, 2506, 2508, 6610, 2503}"
69,1,384,0,0.5576582,"\int \frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(h (f+g x)^m\right)}{(a+b x) (c+d x)} \, dx","Int[(Log[e*((a + b*x)/(c + d*x))^n]*Log[h*(f + g*x)^m])/((a + b*x)*(c + d*x)),x]","-\frac{m \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{PolyLog}\left(2,1-\frac{(f+g x) (b c-a d)}{(c+d x) (b f-a g)}\right)}{b c-a d}+\frac{m \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b c-a d}+\frac{m n \text{PolyLog}\left(3,1-\frac{(f+g x) (b c-a d)}{(c+d x) (b f-a g)}\right)}{b c-a d}-\frac{m n \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right)}{b c-a d}+\frac{\log \left(h (f+g x)^m\right) \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{2 n (b c-a d)}-\frac{m \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(\frac{(f+g x) (b c-a d)}{(c+d x) (b f-a g)}\right)}{2 n (b c-a d)}+\frac{m \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{2 n (b c-a d)}","-\frac{m \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{PolyLog}\left(2,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{b c-a d}+\frac{m \text{PolyLog}\left(2,\frac{d (a+b x)}{b (c+d x)}\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b c-a d}+\frac{m n \text{PolyLog}\left(3,\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{b c-a d}-\frac{m n \text{PolyLog}\left(3,\frac{d (a+b x)}{b (c+d x)}\right)}{b c-a d}+\frac{\log \left(h (f+g x)^m\right) \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{2 n (b c-a d)}-\frac{m \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(1-\frac{(a+b x) (d f-c g)}{(c+d x) (b f-a g)}\right)}{2 n (b c-a d)}+\frac{m \log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{2 n (b c-a d)}",1,"(m*Log[e*((a + b*x)/(c + d*x))^n]^2*Log[(b*c - a*d)/(b*(c + d*x))])/(2*(b*c - a*d)*n) - (m*Log[e*((a + b*x)/(c + d*x))^n]^2*Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])/(2*(b*c - a*d)*n) + (Log[e*((a + b*x)/(c + d*x))^n]^2*Log[h*(f + g*x)^m])/(2*(b*c - a*d)*n) + (m*Log[e*((a + b*x)/(c + d*x))^n]*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*c - a*d) - (m*Log[e*((a + b*x)/(c + d*x))^n]*PolyLog[2, 1 - ((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])/(b*c - a*d) - (m*n*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*c - a*d) + (m*n*PolyLog[3, 1 - ((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))])/(b*c - a*d)","A",8,6,43,0.1395,1,"{2507, 2489, 2488, 2506, 6610, 2503}"
70,0,0,0,0.500247,"\int \frac{\log \left(h (f+g x)^m\right)}{(a+b x) (c+d x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Int[Log[h*(f + g*x)^m]/((a + b*x)*(c + d*x)*Log[e*((a + b*x)/(c + d*x))^n]),x]","\int \frac{\log \left(h (f+g x)^m\right)}{(a+b x) (c+d x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","\frac{b \text{Int}\left(\frac{\log \left(h (f+g x)^m\right)}{(a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)},x\right)}{b c-a d}-\frac{d \text{Int}\left(\frac{\log \left(h (f+g x)^m\right)}{(c+d x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)},x\right)}{b c-a d}",0,"(b*Defer[Int][Log[h*(f + g*x)^m]/((a + b*x)*Log[e*((a + b*x)/(c + d*x))^n]), x])/(b*c - a*d) - (d*Defer[Int][Log[h*(f + g*x)^m]/((c + d*x)*Log[e*((a + b*x)/(c + d*x))^n]), x])/(b*c - a*d)","A",0,0,0,0,-1,"{}"
71,0,0,0,0.1281861,"\int \frac{\log \left(h (f+g x)^m\right)}{(a+b x) (c+d x) \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Int[Log[h*(f + g*x)^m]/((a + b*x)*(c + d*x)*Log[e*((a + b*x)/(c + d*x))^n]^2),x]","\int \frac{\log \left(h (f+g x)^m\right)}{(a+b x) (c+d x) \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","\frac{g m \text{Int}\left(\frac{1}{(f+g x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)},x\right)}{n (b c-a d)}-\frac{\log \left(h (f+g x)^m\right)}{n (b c-a d) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}",0,"-(Log[h*(f + g*x)^m]/((b*c - a*d)*n*Log[e*((a + b*x)/(c + d*x))^n])) + (g*m*Defer[Int][1/((f + g*x)*Log[e*((a + b*x)/(c + d*x))^n]), x])/((b*c - a*d)*n)","A",0,0,0,0,-1,"{}"
72,0,0,0,0.5192867,"\int \frac{\log \left(1-\frac{a+b x}{c+d x}\right)}{(a+b x) (c+d x) \log ^2\left(\frac{a+b x}{c+d x}\right)} \, dx","Int[Log[1 - (a + b*x)/(c + d*x)]/((a + b*x)*(c + d*x)*Log[(a + b*x)/(c + d*x)]^2),x]","\int \frac{\log \left(1-\frac{a+b x}{c+d x}\right)}{(a+b x) (c+d x) \log ^2\left(\frac{a+b x}{c+d x}\right)} \, dx","\frac{b \text{Int}\left(\frac{\log \left(1-\frac{a+b x}{c+d x}\right)}{(a+b x) \log ^2\left(\frac{a+b x}{c+d x}\right)},x\right)}{b c-a d}-\frac{d \text{Int}\left(\frac{\log \left(1-\frac{a+b x}{c+d x}\right)}{(c+d x) \log ^2\left(\frac{a+b x}{c+d x}\right)},x\right)}{b c-a d}",0,"(b*Defer[Int][Log[1 - (a + b*x)/(c + d*x)]/((a + b*x)*Log[(a + b*x)/(c + d*x)]^2), x])/(b*c - a*d) - (d*Defer[Int][Log[1 - (a + b*x)/(c + d*x)]/((c + d*x)*Log[(a + b*x)/(c + d*x)]^2), x])/(b*c - a*d)","A",0,0,0,0,-1,"{}"
73,0,0,0,0.483652,"\int \frac{\log \left(1-\frac{c+d x}{a+b x}\right)}{(a+b x) (c+d x) \log ^2\left(\frac{a+b x}{c+d x}\right)} \, dx","Int[Log[1 - (c + d*x)/(a + b*x)]/((a + b*x)*(c + d*x)*Log[(a + b*x)/(c + d*x)]^2),x]","\int \frac{\log \left(1-\frac{c+d x}{a+b x}\right)}{(a+b x) (c+d x) \log ^2\left(\frac{a+b x}{c+d x}\right)} \, dx","\frac{b \text{Int}\left(\frac{\log \left(1-\frac{c+d x}{a+b x}\right)}{(a+b x) \log ^2\left(\frac{a+b x}{c+d x}\right)},x\right)}{b c-a d}-\frac{d \text{Int}\left(\frac{\log \left(1-\frac{c+d x}{a+b x}\right)}{(c+d x) \log ^2\left(\frac{a+b x}{c+d x}\right)},x\right)}{b c-a d}",0,"(b*Defer[Int][Log[1 - (c + d*x)/(a + b*x)]/((a + b*x)*Log[(a + b*x)/(c + d*x)]^2), x])/(b*c - a*d) - (d*Defer[Int][Log[1 - (c + d*x)/(a + b*x)]/((c + d*x)*Log[(a + b*x)/(c + d*x)]^2), x])/(b*c - a*d)","A",0,0,0,0,-1,"{}"
74,0,0,0,0.5156425,"\int \left(\frac{1}{(c+d x) (-a+c+(-b+d) x) \log \left(\frac{a+b x}{c+d x}\right)}+\frac{\log \left(1-\frac{a+b x}{c+d x}\right)}{(a+b x) (c+d x) \log ^2\left(\frac{a+b x}{c+d x}\right)}\right) \, dx","Int[1/((c + d*x)*(-a + c + (-b + d)*x)*Log[(a + b*x)/(c + d*x)]) + Log[1 - (a + b*x)/(c + d*x)]/((a + b*x)*(c + d*x)*Log[(a + b*x)/(c + d*x)]^2),x]","\int \left(\frac{1}{(c+d x) (-a+c+(-b+d) x) \log \left(\frac{a+b x}{c+d x}\right)}+\frac{\log \left(1-\frac{a+b x}{c+d x}\right)}{(a+b x) (c+d x) \log ^2\left(\frac{a+b x}{c+d x}\right)}\right) \, dx","-\frac{\log \left(1-\frac{a+b x}{c+d x}\right)}{(b c-a d) \log \left(\frac{a+b x}{c+d x}\right)}",1,"Defer[Int][1/((c + d*x)*(-a + c + (-b + d)*x)*Log[(a + b*x)/(c + d*x)]), x] + (b*Defer[Int][Log[1 - (a + b*x)/(c + d*x)]/((a + b*x)*Log[(a + b*x)/(c + d*x)]^2), x])/(b*c - a*d) - (d*Defer[Int][Log[1 - (a + b*x)/(c + d*x)]/((c + d*x)*Log[(a + b*x)/(c + d*x)]^2), x])/(b*c - a*d)","F",0,0,0,0,-1,"{}"
75,0,0,0,0.5121039,"\int \left(-\frac{1}{(a+b x) (a-c+(b-d) x) \log \left(\frac{a+b x}{c+d x}\right)}+\frac{\log \left(1-\frac{c+d x}{a+b x}\right)}{(a+b x) (c+d x) \log ^2\left(\frac{a+b x}{c+d x}\right)}\right) \, dx","Int[-(1/((a + b*x)*(a - c + (b - d)*x)*Log[(a + b*x)/(c + d*x)])) + Log[1 - (c + d*x)/(a + b*x)]/((a + b*x)*(c + d*x)*Log[(a + b*x)/(c + d*x)]^2),x]","\int \left(-\frac{1}{(a+b x) (a-c+(b-d) x) \log \left(\frac{a+b x}{c+d x}\right)}+\frac{\log \left(1-\frac{c+d x}{a+b x}\right)}{(a+b x) (c+d x) \log ^2\left(\frac{a+b x}{c+d x}\right)}\right) \, dx","-\frac{\log \left(1-\frac{c+d x}{a+b x}\right)}{(b c-a d) \log \left(\frac{a+b x}{c+d x}\right)}",1,"-Defer[Int][1/((a + b*x)*(a - c + (b - d)*x)*Log[(a + b*x)/(c + d*x)]), x] + (b*Defer[Int][Log[1 - (c + d*x)/(a + b*x)]/((a + b*x)*Log[(a + b*x)/(c + d*x)]^2), x])/(b*c - a*d) - (d*Defer[Int][Log[1 - (c + d*x)/(a + b*x)]/((c + d*x)*Log[(a + b*x)/(c + d*x)]^2), x])/(b*c - a*d)","F",0,0,0,0,-1,"{}"
76,1,560,0,0.7347645,"\int \frac{x^3 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f-g x^2} \, dx","Int[(x^3*Log[e*((a + b*x)/(c + d*x))^n])/(f - g*x^2),x]","-\frac{f n \text{PolyLog}\left(2,-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 g^2}-\frac{f n \text{PolyLog}\left(2,\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 g^2}+\frac{f n \text{PolyLog}\left(2,-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 g^2}+\frac{f n \text{PolyLog}\left(2,\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 g^2}+\frac{a^2 n \log (a+b x)}{2 b^2 g}+\frac{f \log \left(f-g x^2\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{2 g^2}+\frac{x^2 \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{2 g}-\frac{f n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 g^2}-\frac{f n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}+\sqrt{g} x\right)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 g^2}-\frac{n x^2 \log (a+b x)}{2 g}-\frac{a n x}{2 b g}-\frac{c^2 n \log (c+d x)}{2 d^2 g}+\frac{f n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 g^2}+\frac{f n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}+\sqrt{g} x\right)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 g^2}+\frac{n x^2 \log (c+d x)}{2 g}+\frac{c n x}{2 d g}","-\frac{f n \text{PolyLog}\left(2,-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 g^2}-\frac{f n \text{PolyLog}\left(2,\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 g^2}+\frac{f n \text{PolyLog}\left(2,-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 g^2}+\frac{f n \text{PolyLog}\left(2,\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 g^2}+\frac{a^2 n \log (a+b x)}{2 b^2 g}+\frac{f \log \left(f-g x^2\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{2 g^2}+\frac{x^2 \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{2 g}-\frac{f n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 g^2}-\frac{f n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}+\sqrt{g} x\right)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 g^2}-\frac{n x^2 \log (a+b x)}{2 g}-\frac{a n x}{2 b g}-\frac{c^2 n \log (c+d x)}{2 d^2 g}+\frac{f n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 g^2}+\frac{f n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}+\sqrt{g} x\right)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 g^2}+\frac{n x^2 \log (c+d x)}{2 g}+\frac{c n x}{2 d g}",1,"-(a*n*x)/(2*b*g) + (c*n*x)/(2*d*g) + (a^2*n*Log[a + b*x])/(2*b^2*g) - (n*x^2*Log[a + b*x])/(2*g) - (c^2*n*Log[c + d*x])/(2*d^2*g) + (n*x^2*Log[c + d*x])/(2*g) + (x^2*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/(2*g) - (f*n*Log[a + b*x]*Log[(b*(Sqrt[f] - Sqrt[g]*x))/(b*Sqrt[f] + a*Sqrt[g])])/(2*g^2) + (f*n*Log[c + d*x]*Log[(d*(Sqrt[f] - Sqrt[g]*x))/(d*Sqrt[f] + c*Sqrt[g])])/(2*g^2) - (f*n*Log[a + b*x]*Log[(b*(Sqrt[f] + Sqrt[g]*x))/(b*Sqrt[f] - a*Sqrt[g])])/(2*g^2) + (f*n*Log[c + d*x]*Log[(d*(Sqrt[f] + Sqrt[g]*x))/(d*Sqrt[f] - c*Sqrt[g])])/(2*g^2) + (f*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x])*Log[f - g*x^2])/(2*g^2) - (f*n*PolyLog[2, -((Sqrt[g]*(a + b*x))/(b*Sqrt[f] - a*Sqrt[g]))])/(2*g^2) - (f*n*PolyLog[2, (Sqrt[g]*(a + b*x))/(b*Sqrt[f] + a*Sqrt[g])])/(2*g^2) + (f*n*PolyLog[2, -((Sqrt[g]*(c + d*x))/(d*Sqrt[f] - c*Sqrt[g]))])/(2*g^2) + (f*n*PolyLog[2, (Sqrt[g]*(c + d*x))/(d*Sqrt[f] + c*Sqrt[g])])/(2*g^2)","A",30,9,32,0.2812,1,"{2513, 266, 43, 2416, 2395, 260, 2394, 2393, 2391}"
77,1,550,0,0.5654284,"\int \frac{x^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f-g x^2} \, dx","Int[(x^2*Log[e*((a + b*x)/(c + d*x))^n])/(f - g*x^2),x]","\frac{\sqrt{f} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 g^{3/2}}-\frac{\sqrt{f} n \text{PolyLog}\left(2,\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 g^{3/2}}-\frac{\sqrt{f} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 g^{3/2}}+\frac{\sqrt{f} n \text{PolyLog}\left(2,\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 g^{3/2}}-\frac{\sqrt{f} \tanh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{g^{3/2}}+\frac{x \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{g}-\frac{\sqrt{f} n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 g^{3/2}}+\frac{\sqrt{f} n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}+\sqrt{g} x\right)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 g^{3/2}}-\frac{n (a+b x) \log (a+b x)}{b g}+\frac{\sqrt{f} n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 g^{3/2}}-\frac{\sqrt{f} n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}+\sqrt{g} x\right)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 g^{3/2}}+\frac{n (c+d x) \log (c+d x)}{d g}","\frac{\sqrt{f} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 g^{3/2}}-\frac{\sqrt{f} n \text{PolyLog}\left(2,\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 g^{3/2}}-\frac{\sqrt{f} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 g^{3/2}}+\frac{\sqrt{f} n \text{PolyLog}\left(2,\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 g^{3/2}}-\frac{\sqrt{f} \tanh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{g^{3/2}}+\frac{x \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{g}-\frac{\sqrt{f} n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 g^{3/2}}+\frac{\sqrt{f} n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}+\sqrt{g} x\right)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 g^{3/2}}-\frac{n (a+b x) \log (a+b x)}{b g}+\frac{\sqrt{f} n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 g^{3/2}}-\frac{\sqrt{f} n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}+\sqrt{g} x\right)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 g^{3/2}}+\frac{n (c+d x) \log (c+d x)}{d g}",1,"-((n*(a + b*x)*Log[a + b*x])/(b*g)) + (n*(c + d*x)*Log[c + d*x])/(d*g) + (x*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/g - (Sqrt[f]*ArcTanh[(Sqrt[g]*x)/Sqrt[f]]*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/g^(3/2) - (Sqrt[f]*n*Log[a + b*x]*Log[(b*(Sqrt[f] - Sqrt[g]*x))/(b*Sqrt[f] + a*Sqrt[g])])/(2*g^(3/2)) + (Sqrt[f]*n*Log[c + d*x]*Log[(d*(Sqrt[f] - Sqrt[g]*x))/(d*Sqrt[f] + c*Sqrt[g])])/(2*g^(3/2)) + (Sqrt[f]*n*Log[a + b*x]*Log[(b*(Sqrt[f] + Sqrt[g]*x))/(b*Sqrt[f] - a*Sqrt[g])])/(2*g^(3/2)) - (Sqrt[f]*n*Log[c + d*x]*Log[(d*(Sqrt[f] + Sqrt[g]*x))/(d*Sqrt[f] - c*Sqrt[g])])/(2*g^(3/2)) + (Sqrt[f]*n*PolyLog[2, -((Sqrt[g]*(a + b*x))/(b*Sqrt[f] - a*Sqrt[g]))])/(2*g^(3/2)) - (Sqrt[f]*n*PolyLog[2, (Sqrt[g]*(a + b*x))/(b*Sqrt[f] + a*Sqrt[g])])/(2*g^(3/2)) - (Sqrt[f]*n*PolyLog[2, -((Sqrt[g]*(c + d*x))/(d*Sqrt[f] - c*Sqrt[g]))])/(2*g^(3/2)) + (Sqrt[f]*n*PolyLog[2, (Sqrt[g]*(c + d*x))/(d*Sqrt[f] + c*Sqrt[g])])/(2*g^(3/2))","A",27,10,32,0.3125,1,"{2513, 321, 208, 2416, 2389, 2295, 2409, 2394, 2393, 2391}"
78,1,403,0,0.3523415,"\int \frac{x \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f-g x^2} \, dx","Int[(x*Log[e*((a + b*x)/(c + d*x))^n])/(f - g*x^2),x]","-\frac{n \text{PolyLog}\left(2,-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 g}-\frac{n \text{PolyLog}\left(2,\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 g}+\frac{n \text{PolyLog}\left(2,-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 g}+\frac{n \text{PolyLog}\left(2,\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 g}+\frac{\log \left(f-g x^2\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{2 g}-\frac{n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 g}-\frac{n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}+\sqrt{g} x\right)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 g}+\frac{n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 g}+\frac{n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}+\sqrt{g} x\right)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 g}","-\frac{n \text{PolyLog}\left(2,-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 g}-\frac{n \text{PolyLog}\left(2,\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 g}+\frac{n \text{PolyLog}\left(2,-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 g}+\frac{n \text{PolyLog}\left(2,\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 g}+\frac{\log \left(f-g x^2\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{2 g}-\frac{n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 g}-\frac{n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}+\sqrt{g} x\right)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 g}+\frac{n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 g}+\frac{n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}+\sqrt{g} x\right)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 g}",1,"-(n*Log[a + b*x]*Log[(b*(Sqrt[f] - Sqrt[g]*x))/(b*Sqrt[f] + a*Sqrt[g])])/(2*g) + (n*Log[c + d*x]*Log[(d*(Sqrt[f] - Sqrt[g]*x))/(d*Sqrt[f] + c*Sqrt[g])])/(2*g) - (n*Log[a + b*x]*Log[(b*(Sqrt[f] + Sqrt[g]*x))/(b*Sqrt[f] - a*Sqrt[g])])/(2*g) + (n*Log[c + d*x]*Log[(d*(Sqrt[f] + Sqrt[g]*x))/(d*Sqrt[f] - c*Sqrt[g])])/(2*g) + ((n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x])*Log[f - g*x^2])/(2*g) - (n*PolyLog[2, -((Sqrt[g]*(a + b*x))/(b*Sqrt[f] - a*Sqrt[g]))])/(2*g) - (n*PolyLog[2, (Sqrt[g]*(a + b*x))/(b*Sqrt[f] + a*Sqrt[g])])/(2*g) + (n*PolyLog[2, -((Sqrt[g]*(c + d*x))/(d*Sqrt[f] - c*Sqrt[g]))])/(2*g) + (n*PolyLog[2, (Sqrt[g]*(c + d*x))/(d*Sqrt[f] + c*Sqrt[g])])/(2*g)","A",18,6,30,0.2000,1,"{2513, 260, 2416, 2394, 2393, 2391}"
79,1,468,0,0.3174347,"\int \frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f-g x^2} \, dx","Int[Log[e*((a + b*x)/(c + d*x))^n]/(f - g*x^2),x]","\frac{n \text{PolyLog}\left(2,-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{n \text{PolyLog}\left(2,\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{n \text{PolyLog}\left(2,-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 \sqrt{f} \sqrt{g}}+\frac{n \text{PolyLog}\left(2,\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{\sqrt{f} \sqrt{g}}-\frac{n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 \sqrt{f} \sqrt{g}}+\frac{n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}+\sqrt{g} x\right)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 \sqrt{f} \sqrt{g}}+\frac{n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}+\sqrt{g} x\right)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 \sqrt{f} \sqrt{g}}","\frac{n \text{PolyLog}\left(2,\frac{(a+b x) \left(d \sqrt{f}-c \sqrt{g}\right)}{(c+d x) \left(b \sqrt{f}-a \sqrt{g}\right)}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{n \text{PolyLog}\left(2,\frac{(a+b x) \left(c \sqrt{g}+d \sqrt{f}\right)}{(c+d x) \left(a \sqrt{g}+b \sqrt{f}\right)}\right)}{2 \sqrt{f} \sqrt{g}}+\frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(1-\frac{(a+b x) \left(d \sqrt{f}-c \sqrt{g}\right)}{(c+d x) \left(b \sqrt{f}-a \sqrt{g}\right)}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(1-\frac{(a+b x) \left(c \sqrt{g}+d \sqrt{f}\right)}{(c+d x) \left(a \sqrt{g}+b \sqrt{f}\right)}\right)}{2 \sqrt{f} \sqrt{g}}",1,"-((ArcTanh[(Sqrt[g]*x)/Sqrt[f]]*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/(Sqrt[f]*Sqrt[g])) - (n*Log[a + b*x]*Log[(b*(Sqrt[f] - Sqrt[g]*x))/(b*Sqrt[f] + a*Sqrt[g])])/(2*Sqrt[f]*Sqrt[g]) + (n*Log[c + d*x]*Log[(d*(Sqrt[f] - Sqrt[g]*x))/(d*Sqrt[f] + c*Sqrt[g])])/(2*Sqrt[f]*Sqrt[g]) + (n*Log[a + b*x]*Log[(b*(Sqrt[f] + Sqrt[g]*x))/(b*Sqrt[f] - a*Sqrt[g])])/(2*Sqrt[f]*Sqrt[g]) - (n*Log[c + d*x]*Log[(d*(Sqrt[f] + Sqrt[g]*x))/(d*Sqrt[f] - c*Sqrt[g])])/(2*Sqrt[f]*Sqrt[g]) + (n*PolyLog[2, -((Sqrt[g]*(a + b*x))/(b*Sqrt[f] - a*Sqrt[g]))])/(2*Sqrt[f]*Sqrt[g]) - (n*PolyLog[2, (Sqrt[g]*(a + b*x))/(b*Sqrt[f] + a*Sqrt[g])])/(2*Sqrt[f]*Sqrt[g]) - (n*PolyLog[2, -((Sqrt[g]*(c + d*x))/(d*Sqrt[f] - c*Sqrt[g]))])/(2*Sqrt[f]*Sqrt[g]) + (n*PolyLog[2, (Sqrt[g]*(c + d*x))/(d*Sqrt[f] + c*Sqrt[g])])/(2*Sqrt[f]*Sqrt[g])","A",18,6,29,0.2069,1,"{2513, 2409, 2394, 2393, 2391, 208}"
80,1,518,0,0.6022648,"\int \frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{x \left(f-g x^2\right)} \, dx","Int[Log[e*((a + b*x)/(c + d*x))^n]/(x*(f - g*x^2)),x]","-\frac{n \text{PolyLog}\left(2,-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 f}-\frac{n \text{PolyLog}\left(2,\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 f}+\frac{n \text{PolyLog}\left(2,\frac{b x}{a}+1\right)}{f}+\frac{n \text{PolyLog}\left(2,-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 f}+\frac{n \text{PolyLog}\left(2,\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 f}-\frac{n \text{PolyLog}\left(2,\frac{d x}{c}+1\right)}{f}+\frac{\log \left(f-g x^2\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{2 f}-\frac{\log (x) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{f}-\frac{n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 f}-\frac{n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}+\sqrt{g} x\right)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 f}+\frac{n \log \left(-\frac{b x}{a}\right) \log (a+b x)}{f}+\frac{n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 f}+\frac{n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}+\sqrt{g} x\right)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 f}-\frac{n \log \left(-\frac{d x}{c}\right) \log (c+d x)}{f}","-\frac{n \text{PolyLog}\left(2,-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 f}-\frac{n \text{PolyLog}\left(2,\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 f}+\frac{n \text{PolyLog}\left(2,\frac{b x}{a}+1\right)}{f}+\frac{n \text{PolyLog}\left(2,-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 f}+\frac{n \text{PolyLog}\left(2,\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 f}-\frac{n \text{PolyLog}\left(2,\frac{d x}{c}+1\right)}{f}+\frac{\log \left(f-g x^2\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{2 f}-\frac{\log (x) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{f}-\frac{n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 f}-\frac{n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}+\sqrt{g} x\right)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 f}+\frac{n \log \left(-\frac{b x}{a}\right) \log (a+b x)}{f}+\frac{n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 f}+\frac{n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}+\sqrt{g} x\right)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 f}-\frac{n \log \left(-\frac{d x}{c}\right) \log (c+d x)}{f}",1,"(n*Log[-((b*x)/a)]*Log[a + b*x])/f - (n*Log[-((d*x)/c)]*Log[c + d*x])/f - (Log[x]*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/f - (n*Log[a + b*x]*Log[(b*(Sqrt[f] - Sqrt[g]*x))/(b*Sqrt[f] + a*Sqrt[g])])/(2*f) + (n*Log[c + d*x]*Log[(d*(Sqrt[f] - Sqrt[g]*x))/(d*Sqrt[f] + c*Sqrt[g])])/(2*f) - (n*Log[a + b*x]*Log[(b*(Sqrt[f] + Sqrt[g]*x))/(b*Sqrt[f] - a*Sqrt[g])])/(2*f) + (n*Log[c + d*x]*Log[(d*(Sqrt[f] + Sqrt[g]*x))/(d*Sqrt[f] - c*Sqrt[g])])/(2*f) + ((n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x])*Log[f - g*x^2])/(2*f) - (n*PolyLog[2, -((Sqrt[g]*(a + b*x))/(b*Sqrt[f] - a*Sqrt[g]))])/(2*f) - (n*PolyLog[2, (Sqrt[g]*(a + b*x))/(b*Sqrt[f] + a*Sqrt[g])])/(2*f) + (n*PolyLog[2, 1 + (b*x)/a])/f + (n*PolyLog[2, -((Sqrt[g]*(c + d*x))/(d*Sqrt[f] - c*Sqrt[g]))])/(2*f) + (n*PolyLog[2, (Sqrt[g]*(c + d*x))/(d*Sqrt[f] + c*Sqrt[g])])/(2*f) - (n*PolyLog[2, 1 + (d*x)/c])/f","A",29,11,32,0.3438,1,"{2513, 266, 36, 29, 31, 2416, 2394, 2315, 260, 2393, 2391}"
81,1,596,0,0.583434,"\int \frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{x^2 \left(f-g x^2\right)} \, dx","Int[Log[e*((a + b*x)/(c + d*x))^n]/(x^2*(f - g*x^2)),x]","\frac{\sqrt{g} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 f^{3/2}}-\frac{\sqrt{g} n \text{PolyLog}\left(2,\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 f^{3/2}}-\frac{\sqrt{g} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 f^{3/2}}+\frac{\sqrt{g} n \text{PolyLog}\left(2,\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 f^{3/2}}-\frac{\sqrt{g} \tanh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{f^{3/2}}+\frac{-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)}{f x}-\frac{\sqrt{g} n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 f^{3/2}}+\frac{\sqrt{g} n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}+\sqrt{g} x\right)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 f^{3/2}}+\frac{b n \log (x)}{a f}-\frac{b n \log (a+b x)}{a f}-\frac{n \log (a+b x)}{f x}+\frac{\sqrt{g} n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 f^{3/2}}-\frac{\sqrt{g} n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}+\sqrt{g} x\right)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 f^{3/2}}-\frac{d n \log (x)}{c f}+\frac{d n \log (c+d x)}{c f}+\frac{n \log (c+d x)}{f x}","\frac{\sqrt{g} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 f^{3/2}}-\frac{\sqrt{g} n \text{PolyLog}\left(2,\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 f^{3/2}}-\frac{\sqrt{g} n \text{PolyLog}\left(2,-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 f^{3/2}}+\frac{\sqrt{g} n \text{PolyLog}\left(2,\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 f^{3/2}}-\frac{\sqrt{g} \tanh ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{f^{3/2}}+\frac{-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)}{f x}-\frac{\sqrt{g} n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{a \sqrt{g}+b \sqrt{f}}\right)}{2 f^{3/2}}+\frac{\sqrt{g} n \log (a+b x) \log \left(\frac{b \left(\sqrt{f}+\sqrt{g} x\right)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 f^{3/2}}+\frac{b n \log (x)}{a f}-\frac{b n \log (a+b x)}{a f}-\frac{n \log (a+b x)}{f x}+\frac{\sqrt{g} n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{c \sqrt{g}+d \sqrt{f}}\right)}{2 f^{3/2}}-\frac{\sqrt{g} n \log (c+d x) \log \left(\frac{d \left(\sqrt{f}+\sqrt{g} x\right)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 f^{3/2}}-\frac{d n \log (x)}{c f}+\frac{d n \log (c+d x)}{c f}+\frac{n \log (c+d x)}{f x}",1,"(b*n*Log[x])/(a*f) - (d*n*Log[x])/(c*f) - (b*n*Log[a + b*x])/(a*f) - (n*Log[a + b*x])/(f*x) + (d*n*Log[c + d*x])/(c*f) + (n*Log[c + d*x])/(f*x) + (n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x])/(f*x) - (Sqrt[g]*ArcTanh[(Sqrt[g]*x)/Sqrt[f]]*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/f^(3/2) - (Sqrt[g]*n*Log[a + b*x]*Log[(b*(Sqrt[f] - Sqrt[g]*x))/(b*Sqrt[f] + a*Sqrt[g])])/(2*f^(3/2)) + (Sqrt[g]*n*Log[c + d*x]*Log[(d*(Sqrt[f] - Sqrt[g]*x))/(d*Sqrt[f] + c*Sqrt[g])])/(2*f^(3/2)) + (Sqrt[g]*n*Log[a + b*x]*Log[(b*(Sqrt[f] + Sqrt[g]*x))/(b*Sqrt[f] - a*Sqrt[g])])/(2*f^(3/2)) - (Sqrt[g]*n*Log[c + d*x]*Log[(d*(Sqrt[f] + Sqrt[g]*x))/(d*Sqrt[f] - c*Sqrt[g])])/(2*f^(3/2)) + (Sqrt[g]*n*PolyLog[2, -((Sqrt[g]*(a + b*x))/(b*Sqrt[f] - a*Sqrt[g]))])/(2*f^(3/2)) - (Sqrt[g]*n*PolyLog[2, (Sqrt[g]*(a + b*x))/(b*Sqrt[f] + a*Sqrt[g])])/(2*f^(3/2)) - (Sqrt[g]*n*PolyLog[2, -((Sqrt[g]*(c + d*x))/(d*Sqrt[f] - c*Sqrt[g]))])/(2*f^(3/2)) + (Sqrt[g]*n*PolyLog[2, (Sqrt[g]*(c + d*x))/(d*Sqrt[f] + c*Sqrt[g])])/(2*f^(3/2))","A",31,12,32,0.3750,1,"{2513, 325, 208, 2416, 2395, 36, 29, 31, 2409, 2394, 2393, 2391}"
82,1,1046,0,1.7170101,"\int \frac{x^3 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f+g x+h x^2} \, dx","Int[(x^3*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x + h*x^2),x]","-\frac{n \log (a+b x) a^2}{2 b^2 h}+\frac{n x a}{2 b h}-\frac{c n x}{2 d h}+\frac{n x^2 \log (a+b x)}{2 h}-\frac{g n (a+b x) \log (a+b x)}{b h^2}-\frac{n x^2 \log (c+d x)}{2 h}+\frac{c^2 n \log (c+d x)}{2 d^2 h}+\frac{g n (c+d x) \log (c+d x)}{d h^2}-\frac{x^2 \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right)}{2 h}+\frac{g x \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right)}{h^2}-\frac{g \left(g^2-3 f h\right) \tanh ^{-1}\left(\frac{g+2 h x}{\sqrt{g^2-4 f h}}\right) \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right)}{h^3 \sqrt{g^2-4 f h}}+\frac{\left(g^2-\frac{\left(g^2-3 f h\right) g}{\sqrt{g^2-4 f h}}-f h\right) n \log (a+b x) \log \left(-\frac{b \left(g+2 h x-\sqrt{g^2-4 f h}\right)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}-\frac{\left(g^2-\frac{\left(g^2-3 f h\right) g}{\sqrt{g^2-4 f h}}-f h\right) n \log (c+d x) \log \left(-\frac{d \left(g+2 h x-\sqrt{g^2-4 f h}\right)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}+\frac{\left(g^2+\frac{\left(g^2-3 f h\right) g}{\sqrt{g^2-4 f h}}-f h\right) n \log (a+b x) \log \left(-\frac{b \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}-\frac{\left(g^2+\frac{\left(g^2-3 f h\right) g}{\sqrt{g^2-4 f h}}-f h\right) n \log (c+d x) \log \left(-\frac{d \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}-\frac{\left(g^2-f h\right) \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right) \log \left(h x^2+g x+f\right)}{2 h^3}+\frac{\left(g^2-\frac{\left(g^2-3 f h\right) g}{\sqrt{g^2-4 f h}}-f h\right) n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}+\frac{\left(g^2+\frac{\left(g^2-3 f h\right) g}{\sqrt{g^2-4 f h}}-f h\right) n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}-\frac{\left(g^2-\frac{\left(g^2-3 f h\right) g}{\sqrt{g^2-4 f h}}-f h\right) n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}-\frac{\left(g^2+\frac{\left(g^2-3 f h\right) g}{\sqrt{g^2-4 f h}}-f h\right) n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}","-\frac{n \log (a+b x) a^2}{2 b^2 h}+\frac{n x a}{2 b h}-\frac{c n x}{2 d h}+\frac{n x^2 \log (a+b x)}{2 h}-\frac{g n (a+b x) \log (a+b x)}{b h^2}-\frac{n x^2 \log (c+d x)}{2 h}+\frac{c^2 n \log (c+d x)}{2 d^2 h}+\frac{g n (c+d x) \log (c+d x)}{d h^2}-\frac{x^2 \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right)}{2 h}+\frac{g x \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right)}{h^2}-\frac{g \left(g^2-3 f h\right) \tanh ^{-1}\left(\frac{g+2 h x}{\sqrt{g^2-4 f h}}\right) \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right)}{h^3 \sqrt{g^2-4 f h}}+\frac{\left(g^2-\frac{\left(g^2-3 f h\right) g}{\sqrt{g^2-4 f h}}-f h\right) n \log (a+b x) \log \left(-\frac{b \left(g+2 h x-\sqrt{g^2-4 f h}\right)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}-\frac{\left(g^2-\frac{\left(g^2-3 f h\right) g}{\sqrt{g^2-4 f h}}-f h\right) n \log (c+d x) \log \left(-\frac{d \left(g+2 h x-\sqrt{g^2-4 f h}\right)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}+\frac{\left(g^2+\frac{\left(g^2-3 f h\right) g}{\sqrt{g^2-4 f h}}-f h\right) n \log (a+b x) \log \left(-\frac{b \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}-\frac{\left(g^2+\frac{\left(g^2-3 f h\right) g}{\sqrt{g^2-4 f h}}-f h\right) n \log (c+d x) \log \left(-\frac{d \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}-\frac{\left(g^2-f h\right) \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right) \log \left(h x^2+g x+f\right)}{2 h^3}+\frac{\left(g^2-\frac{\left(g^2-3 f h\right) g}{\sqrt{g^2-4 f h}}-f h\right) n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}+\frac{\left(g^2+\frac{\left(g^2-3 f h\right) g}{\sqrt{g^2-4 f h}}-f h\right) n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}-\frac{\left(g^2-\frac{\left(g^2-3 f h\right) g}{\sqrt{g^2-4 f h}}-f h\right) n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}-\frac{\left(g^2+\frac{\left(g^2-3 f h\right) g}{\sqrt{g^2-4 f h}}-f h\right) n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}",1,"(a*n*x)/(2*b*h) - (c*n*x)/(2*d*h) - (a^2*n*Log[a + b*x])/(2*b^2*h) + (n*x^2*Log[a + b*x])/(2*h) - (g*n*(a + b*x)*Log[a + b*x])/(b*h^2) + (c^2*n*Log[c + d*x])/(2*d^2*h) - (n*x^2*Log[c + d*x])/(2*h) + (g*n*(c + d*x)*Log[c + d*x])/(d*h^2) + (g*x*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/h^2 - (x^2*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/(2*h) - (g*(g^2 - 3*f*h)*ArcTanh[(g + 2*h*x)/Sqrt[g^2 - 4*f*h]]*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/(h^3*Sqrt[g^2 - 4*f*h]) + ((g^2 - f*h - (g*(g^2 - 3*f*h))/Sqrt[g^2 - 4*f*h])*n*Log[a + b*x]*Log[-((b*(g - Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*a*h - b*(g - Sqrt[g^2 - 4*f*h])))])/(2*h^3) - ((g^2 - f*h - (g*(g^2 - 3*f*h))/Sqrt[g^2 - 4*f*h])*n*Log[c + d*x]*Log[-((d*(g - Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*c*h - d*(g - Sqrt[g^2 - 4*f*h])))])/(2*h^3) + ((g^2 - f*h + (g*(g^2 - 3*f*h))/Sqrt[g^2 - 4*f*h])*n*Log[a + b*x]*Log[-((b*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h])))])/(2*h^3) - ((g^2 - f*h + (g*(g^2 - 3*f*h))/Sqrt[g^2 - 4*f*h])*n*Log[c + d*x]*Log[-((d*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h])))])/(2*h^3) - ((g^2 - f*h)*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x])*Log[f + g*x + h*x^2])/(2*h^3) + ((g^2 - f*h - (g*(g^2 - 3*f*h))/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(a + b*x))/(2*a*h - b*(g - Sqrt[g^2 - 4*f*h]))])/(2*h^3) + ((g^2 - f*h + (g*(g^2 - 3*f*h))/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(a + b*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h]))])/(2*h^3) - ((g^2 - f*h - (g*(g^2 - 3*f*h))/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(c + d*x))/(2*c*h - d*(g - Sqrt[g^2 - 4*f*h]))])/(2*h^3) - ((g^2 - f*h + (g*(g^2 - 3*f*h))/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(c + d*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h]))])/(2*h^3)","A",37,14,34,0.4118,1,"{2513, 2418, 2389, 2295, 2395, 43, 2394, 2393, 2391, 701, 634, 618, 206, 628}"
83,1,831,0,1.0681714,"\int \frac{x^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f+g x+h x^2} \, dx","Int[(x^2*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x + h*x^2),x]","\frac{n (a+b x) \log (a+b x)}{b h}-\frac{\left(g-\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \log \left(-\frac{b \left(g+2 h x-\sqrt{g^2-4 f h}\right)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right) \log (a+b x)}{2 h^2}-\frac{\left(g+\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \log \left(-\frac{b \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right) \log (a+b x)}{2 h^2}-\frac{n (c+d x) \log (c+d x)}{d h}-\frac{x \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right)}{h}+\frac{\left(g^2-2 f h\right) \tanh ^{-1}\left(\frac{g+2 h x}{\sqrt{g^2-4 f h}}\right) \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right)}{h^2 \sqrt{g^2-4 f h}}+\frac{\left(g-\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \log (c+d x) \log \left(-\frac{d \left(g+2 h x-\sqrt{g^2-4 f h}\right)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h^2}+\frac{\left(g+\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \log (c+d x) \log \left(-\frac{d \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 h^2}+\frac{g \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right) \log \left(h x^2+g x+f\right)}{2 h^2}-\frac{\left(g-\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h^2}-\frac{\left(g+\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 h^2}+\frac{\left(g-\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h^2}+\frac{\left(g+\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 h^2}","\frac{n (a+b x) \log (a+b x)}{b h}-\frac{\left(g-\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \log \left(-\frac{b \left(g+2 h x-\sqrt{g^2-4 f h}\right)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right) \log (a+b x)}{2 h^2}-\frac{\left(g+\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \log \left(-\frac{b \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right) \log (a+b x)}{2 h^2}-\frac{n (c+d x) \log (c+d x)}{d h}-\frac{x \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right)}{h}+\frac{\left(g^2-2 f h\right) \tanh ^{-1}\left(\frac{g+2 h x}{\sqrt{g^2-4 f h}}\right) \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right)}{h^2 \sqrt{g^2-4 f h}}+\frac{\left(g-\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \log (c+d x) \log \left(-\frac{d \left(g+2 h x-\sqrt{g^2-4 f h}\right)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h^2}+\frac{\left(g+\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \log (c+d x) \log \left(-\frac{d \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 h^2}+\frac{g \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right) \log \left(h x^2+g x+f\right)}{2 h^2}-\frac{\left(g-\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h^2}-\frac{\left(g+\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 h^2}+\frac{\left(g-\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h^2}+\frac{\left(g+\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 h^2}",1,"(n*(a + b*x)*Log[a + b*x])/(b*h) - (n*(c + d*x)*Log[c + d*x])/(d*h) - (x*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/h + ((g^2 - 2*f*h)*ArcTanh[(g + 2*h*x)/Sqrt[g^2 - 4*f*h]]*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/(h^2*Sqrt[g^2 - 4*f*h]) - ((g - (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*n*Log[a + b*x]*Log[-((b*(g - Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*a*h - b*(g - Sqrt[g^2 - 4*f*h])))])/(2*h^2) + ((g - (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*n*Log[c + d*x]*Log[-((d*(g - Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*c*h - d*(g - Sqrt[g^2 - 4*f*h])))])/(2*h^2) - ((g + (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*n*Log[a + b*x]*Log[-((b*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h])))])/(2*h^2) + ((g + (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*n*Log[c + d*x]*Log[-((d*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h])))])/(2*h^2) + (g*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x])*Log[f + g*x + h*x^2])/(2*h^2) - ((g - (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(a + b*x))/(2*a*h - b*(g - Sqrt[g^2 - 4*f*h]))])/(2*h^2) - ((g + (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(a + b*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h]))])/(2*h^2) + ((g - (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(c + d*x))/(2*c*h - d*(g - Sqrt[g^2 - 4*f*h]))])/(2*h^2) + ((g + (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(c + d*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h]))])/(2*h^2)","A",30,12,34,0.3529,1,"{2513, 2418, 2389, 2295, 2394, 2393, 2391, 703, 634, 618, 206, 628}"
84,1,685,0,0.6355303,"\int \frac{x \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f+g x+h x^2} \, dx","Int[(x*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x + h*x^2),x]","\frac{n \left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h}+\frac{n \left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(\sqrt{g^2-4 f h}+g\right)}\right)}{2 h}-\frac{n \left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h}-\frac{n \left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(\sqrt{g^2-4 f h}+g\right)}\right)}{2 h}-\frac{g \tanh ^{-1}\left(\frac{g+2 h x}{\sqrt{g^2-4 f h}}\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{h \sqrt{g^2-4 f h}}-\frac{\log \left(f+g x+h x^2\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{2 h}+\frac{n \left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) \log (a+b x) \log \left(-\frac{b \left(-\sqrt{g^2-4 f h}+g+2 h x\right)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h}+\frac{n \left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) \log (a+b x) \log \left(-\frac{b \left(\sqrt{g^2-4 f h}+g+2 h x\right)}{2 a h-b \left(\sqrt{g^2-4 f h}+g\right)}\right)}{2 h}-\frac{n \left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) \log (c+d x) \log \left(-\frac{d \left(-\sqrt{g^2-4 f h}+g+2 h x\right)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h}-\frac{n \left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) \log (c+d x) \log \left(-\frac{d \left(\sqrt{g^2-4 f h}+g+2 h x\right)}{2 c h-d \left(\sqrt{g^2-4 f h}+g\right)}\right)}{2 h}","\frac{n \left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h}+\frac{n \left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(\sqrt{g^2-4 f h}+g\right)}\right)}{2 h}-\frac{n \left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h}-\frac{n \left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(\sqrt{g^2-4 f h}+g\right)}\right)}{2 h}-\frac{g \tanh ^{-1}\left(\frac{g+2 h x}{\sqrt{g^2-4 f h}}\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{h \sqrt{g^2-4 f h}}-\frac{\log \left(f+g x+h x^2\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{2 h}+\frac{n \left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) \log (a+b x) \log \left(-\frac{b \left(-\sqrt{g^2-4 f h}+g+2 h x\right)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h}+\frac{n \left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) \log (a+b x) \log \left(-\frac{b \left(\sqrt{g^2-4 f h}+g+2 h x\right)}{2 a h-b \left(\sqrt{g^2-4 f h}+g\right)}\right)}{2 h}-\frac{n \left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) \log (c+d x) \log \left(-\frac{d \left(-\sqrt{g^2-4 f h}+g+2 h x\right)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 h}-\frac{n \left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) \log (c+d x) \log \left(-\frac{d \left(\sqrt{g^2-4 f h}+g+2 h x\right)}{2 c h-d \left(\sqrt{g^2-4 f h}+g\right)}\right)}{2 h}",1,"-((g*ArcTanh[(g + 2*h*x)/Sqrt[g^2 - 4*f*h]]*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/(h*Sqrt[g^2 - 4*f*h])) + ((1 - g/Sqrt[g^2 - 4*f*h])*n*Log[a + b*x]*Log[-((b*(g - Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*a*h - b*(g - Sqrt[g^2 - 4*f*h])))])/(2*h) - ((1 - g/Sqrt[g^2 - 4*f*h])*n*Log[c + d*x]*Log[-((d*(g - Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*c*h - d*(g - Sqrt[g^2 - 4*f*h])))])/(2*h) + ((1 + g/Sqrt[g^2 - 4*f*h])*n*Log[a + b*x]*Log[-((b*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h])))])/(2*h) - ((1 + g/Sqrt[g^2 - 4*f*h])*n*Log[c + d*x]*Log[-((d*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h])))])/(2*h) - ((n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x])*Log[f + g*x + h*x^2])/(2*h) + ((1 - g/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(a + b*x))/(2*a*h - b*(g - Sqrt[g^2 - 4*f*h]))])/(2*h) + ((1 + g/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(a + b*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h]))])/(2*h) - ((1 - g/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(c + d*x))/(2*c*h - d*(g - Sqrt[g^2 - 4*f*h]))])/(2*h) - ((1 + g/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(c + d*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h]))])/(2*h)","A",21,9,32,0.2812,1,"{2513, 2418, 2394, 2393, 2391, 634, 618, 206, 628}"
85,1,545,0,0.5178698,"\int \frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f+g x+h x^2} \, dx","Int[Log[e*((a + b*x)/(c + d*x))^n]/(f + g*x + h*x^2),x]","\frac{n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{\sqrt{g^2-4 f h}}-\frac{n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(\sqrt{g^2-4 f h}+g\right)}\right)}{\sqrt{g^2-4 f h}}-\frac{n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{\sqrt{g^2-4 f h}}+\frac{n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(\sqrt{g^2-4 f h}+g\right)}\right)}{\sqrt{g^2-4 f h}}+\frac{2 \tanh ^{-1}\left(\frac{g+2 h x}{\sqrt{g^2-4 f h}}\right) \left(-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \log (a+b x)-n \log (c+d x)\right)}{\sqrt{g^2-4 f h}}+\frac{n \log (a+b x) \log \left(-\frac{b \left(-\sqrt{g^2-4 f h}+g+2 h x\right)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{\sqrt{g^2-4 f h}}-\frac{n \log (a+b x) \log \left(-\frac{b \left(\sqrt{g^2-4 f h}+g+2 h x\right)}{2 a h-b \left(\sqrt{g^2-4 f h}+g\right)}\right)}{\sqrt{g^2-4 f h}}-\frac{n \log (c+d x) \log \left(-\frac{d \left(-\sqrt{g^2-4 f h}+g+2 h x\right)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{\sqrt{g^2-4 f h}}+\frac{n \log (c+d x) \log \left(-\frac{d \left(\sqrt{g^2-4 f h}+g+2 h x\right)}{2 c h-d \left(\sqrt{g^2-4 f h}+g\right)}\right)}{\sqrt{g^2-4 f h}}","-\frac{n \text{PolyLog}\left(2,\frac{2 (a+b x) \left(c^2 h-c d g+d^2 f\right)}{(c+d x) \left(-\sqrt{g^2-4 f h} (b c-a d)+2 a c h-a d g-b c g+2 b d f\right)}\right)}{\sqrt{g^2-4 f h}}+\frac{n \text{PolyLog}\left(2,\frac{2 (a+b x) \left(c^2 h-c d g+d^2 f\right)}{(c+d x) \left(\sqrt{g^2-4 f h} (b c-a d)+2 a c h-a d g-b c g+2 b d f\right)}\right)}{\sqrt{g^2-4 f h}}-\frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(1-\frac{2 (a+b x) \left(c^2 h-c d g+d^2 f\right)}{(c+d x) \left(-\sqrt{g^2-4 f h} (b c-a d)+2 a c h-a d g-b c g+2 b d f\right)}\right)}{\sqrt{g^2-4 f h}}+\frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(1-\frac{2 (a+b x) \left(c^2 h-c d g+d^2 f\right)}{(c+d x) \left(\sqrt{g^2-4 f h} (b c-a d)+2 a c h-a d g-b c g+2 b d f\right)}\right)}{\sqrt{g^2-4 f h}}",1,"(2*ArcTanh[(g + 2*h*x)/Sqrt[g^2 - 4*f*h]]*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/Sqrt[g^2 - 4*f*h] + (n*Log[a + b*x]*Log[-((b*(g - Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*a*h - b*(g - Sqrt[g^2 - 4*f*h])))])/Sqrt[g^2 - 4*f*h] - (n*Log[c + d*x]*Log[-((d*(g - Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*c*h - d*(g - Sqrt[g^2 - 4*f*h])))])/Sqrt[g^2 - 4*f*h] - (n*Log[a + b*x]*Log[-((b*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h])))])/Sqrt[g^2 - 4*f*h] + (n*Log[c + d*x]*Log[-((d*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h])))])/Sqrt[g^2 - 4*f*h] + (n*PolyLog[2, (2*h*(a + b*x))/(2*a*h - b*(g - Sqrt[g^2 - 4*f*h]))])/Sqrt[g^2 - 4*f*h] - (n*PolyLog[2, (2*h*(a + b*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h]))])/Sqrt[g^2 - 4*f*h] - (n*PolyLog[2, (2*h*(c + d*x))/(2*c*h - d*(g - Sqrt[g^2 - 4*f*h]))])/Sqrt[g^2 - 4*f*h] + (n*PolyLog[2, (2*h*(c + d*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h]))])/Sqrt[g^2 - 4*f*h]","A",19,7,31,0.2258,1,"{2513, 2418, 2394, 2393, 2391, 618, 206}"
86,1,800,0,0.9800365,"\int \frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{x \left(f+g x+h x^2\right)} \, dx","Int[Log[e*((a + b*x)/(c + d*x))^n]/(x*(f + g*x + h*x^2)),x]","\frac{n \log \left(-\frac{b x}{a}\right) \log (a+b x)}{f}-\frac{\left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) n \log \left(-\frac{b \left(g+2 h x-\sqrt{g^2-4 f h}\right)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right) \log (a+b x)}{2 f}-\frac{\left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) n \log \left(-\frac{b \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right) \log (a+b x)}{2 f}-\frac{n \log \left(-\frac{d x}{c}\right) \log (c+d x)}{f}-\frac{g \tanh ^{-1}\left(\frac{g+2 h x}{\sqrt{g^2-4 f h}}\right) \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right)}{f \sqrt{g^2-4 f h}}-\frac{\log (x) \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right)}{f}+\frac{\left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) n \log (c+d x) \log \left(-\frac{d \left(g+2 h x-\sqrt{g^2-4 f h}\right)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 f}+\frac{\left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) n \log (c+d x) \log \left(-\frac{d \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 f}+\frac{\left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right) \log \left(h x^2+g x+f\right)}{2 f}-\frac{\left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 f}-\frac{\left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 f}+\frac{n \text{PolyLog}\left(2,\frac{b x}{a}+1\right)}{f}+\frac{\left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 f}+\frac{\left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 f}-\frac{n \text{PolyLog}\left(2,\frac{d x}{c}+1\right)}{f}","\frac{n \log \left(-\frac{b x}{a}\right) \log (a+b x)}{f}-\frac{\left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) n \log \left(-\frac{b \left(g+2 h x-\sqrt{g^2-4 f h}\right)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right) \log (a+b x)}{2 f}-\frac{\left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) n \log \left(-\frac{b \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right) \log (a+b x)}{2 f}-\frac{n \log \left(-\frac{d x}{c}\right) \log (c+d x)}{f}-\frac{g \tanh ^{-1}\left(\frac{g+2 h x}{\sqrt{g^2-4 f h}}\right) \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right)}{f \sqrt{g^2-4 f h}}-\frac{\log (x) \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right)}{f}+\frac{\left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) n \log (c+d x) \log \left(-\frac{d \left(g+2 h x-\sqrt{g^2-4 f h}\right)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 f}+\frac{\left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) n \log (c+d x) \log \left(-\frac{d \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 f}+\frac{\left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right) \log \left(h x^2+g x+f\right)}{2 f}-\frac{\left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 f}-\frac{\left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 f}+\frac{n \text{PolyLog}\left(2,\frac{b x}{a}+1\right)}{f}+\frac{\left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 f}+\frac{\left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 f}-\frac{n \text{PolyLog}\left(2,\frac{d x}{c}+1\right)}{f}",1,"(n*Log[-((b*x)/a)]*Log[a + b*x])/f - (n*Log[-((d*x)/c)]*Log[c + d*x])/f - (g*ArcTanh[(g + 2*h*x)/Sqrt[g^2 - 4*f*h]]*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/(f*Sqrt[g^2 - 4*f*h]) - (Log[x]*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/f - ((1 + g/Sqrt[g^2 - 4*f*h])*n*Log[a + b*x]*Log[-((b*(g - Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*a*h - b*(g - Sqrt[g^2 - 4*f*h])))])/(2*f) + ((1 + g/Sqrt[g^2 - 4*f*h])*n*Log[c + d*x]*Log[-((d*(g - Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*c*h - d*(g - Sqrt[g^2 - 4*f*h])))])/(2*f) - ((1 - g/Sqrt[g^2 - 4*f*h])*n*Log[a + b*x]*Log[-((b*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h])))])/(2*f) + ((1 - g/Sqrt[g^2 - 4*f*h])*n*Log[c + d*x]*Log[-((d*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h])))])/(2*f) + ((n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x])*Log[f + g*x + h*x^2])/(2*f) - ((1 + g/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(a + b*x))/(2*a*h - b*(g - Sqrt[g^2 - 4*f*h]))])/(2*f) - ((1 - g/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(a + b*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h]))])/(2*f) + (n*PolyLog[2, 1 + (b*x)/a])/f + ((1 + g/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(c + d*x))/(2*c*h - d*(g - Sqrt[g^2 - 4*f*h]))])/(2*f) + ((1 - g/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(c + d*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h]))])/(2*f) - (n*PolyLog[2, 1 + (d*x)/c])/f","A",31,12,34,0.3529,1,"{2513, 2418, 2394, 2315, 2393, 2391, 705, 29, 634, 618, 206, 628}"
87,1,995,0,1.2913133,"\int \frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{x^2 \left(f+g x+h x^2\right)} \, dx","Int[Log[e*((a + b*x)/(c + d*x))^n]/(x^2*(f + g*x + h*x^2)),x]","\frac{b n \log (x)}{a f}-\frac{d n \log (x)}{c f}+\frac{g \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right) \log (x)}{f^2}-\frac{b n \log (a+b x)}{a f}-\frac{g n \log \left(-\frac{b x}{a}\right) \log (a+b x)}{f^2}-\frac{n \log (a+b x)}{f x}+\frac{d n \log (c+d x)}{c f}+\frac{g n \log \left(-\frac{d x}{c}\right) \log (c+d x)}{f^2}+\frac{n \log (c+d x)}{f x}+\frac{\left(g^2-2 f h\right) \tanh ^{-1}\left(\frac{g+2 h x}{\sqrt{g^2-4 f h}}\right) \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right)}{f^2 \sqrt{g^2-4 f h}}+\frac{n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)}{f x}+\frac{\left(g+\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \log (a+b x) \log \left(-\frac{b \left(g+2 h x-\sqrt{g^2-4 f h}\right)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 f^2}-\frac{\left(g+\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \log (c+d x) \log \left(-\frac{d \left(g+2 h x-\sqrt{g^2-4 f h}\right)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 f^2}+\frac{\left(g-\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \log (a+b x) \log \left(-\frac{b \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 f^2}-\frac{\left(g-\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \log (c+d x) \log \left(-\frac{d \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 f^2}-\frac{g \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right) \log \left(h x^2+g x+f\right)}{2 f^2}+\frac{\left(g+\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 f^2}+\frac{\left(g-\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 f^2}-\frac{g n \text{PolyLog}\left(2,\frac{b x}{a}+1\right)}{f^2}-\frac{\left(g+\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 f^2}-\frac{\left(g-\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 f^2}+\frac{g n \text{PolyLog}\left(2,\frac{d x}{c}+1\right)}{f^2}","\frac{b n \log (x)}{a f}-\frac{d n \log (x)}{c f}+\frac{g \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right) \log (x)}{f^2}-\frac{b n \log (a+b x)}{a f}-\frac{g n \log \left(-\frac{b x}{a}\right) \log (a+b x)}{f^2}-\frac{n \log (a+b x)}{f x}+\frac{d n \log (c+d x)}{c f}+\frac{g n \log \left(-\frac{d x}{c}\right) \log (c+d x)}{f^2}+\frac{n \log (c+d x)}{f x}+\frac{\left(g^2-2 f h\right) \tanh ^{-1}\left(\frac{g+2 h x}{\sqrt{g^2-4 f h}}\right) \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right)}{f^2 \sqrt{g^2-4 f h}}+\frac{n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)}{f x}+\frac{\left(g+\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \log (a+b x) \log \left(-\frac{b \left(g+2 h x-\sqrt{g^2-4 f h}\right)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 f^2}-\frac{\left(g+\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \log (c+d x) \log \left(-\frac{d \left(g+2 h x-\sqrt{g^2-4 f h}\right)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 f^2}+\frac{\left(g-\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \log (a+b x) \log \left(-\frac{b \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 f^2}-\frac{\left(g-\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \log (c+d x) \log \left(-\frac{d \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 f^2}-\frac{g \left(n \log (a+b x)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log (c+d x)\right) \log \left(h x^2+g x+f\right)}{2 f^2}+\frac{\left(g+\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 f^2}+\frac{\left(g-\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (a+b x)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 f^2}-\frac{g n \text{PolyLog}\left(2,\frac{b x}{a}+1\right)}{f^2}-\frac{\left(g+\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g-\sqrt{g^2-4 f h}\right)}\right)}{2 f^2}-\frac{\left(g-\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}\right) n \text{PolyLog}\left(2,\frac{2 h (c+d x)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 f^2}+\frac{g n \text{PolyLog}\left(2,\frac{d x}{c}+1\right)}{f^2}",1,"(b*n*Log[x])/(a*f) - (d*n*Log[x])/(c*f) - (b*n*Log[a + b*x])/(a*f) - (n*Log[a + b*x])/(f*x) - (g*n*Log[-((b*x)/a)]*Log[a + b*x])/f^2 + (d*n*Log[c + d*x])/(c*f) + (n*Log[c + d*x])/(f*x) + (g*n*Log[-((d*x)/c)]*Log[c + d*x])/f^2 + (n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x])/(f*x) + ((g^2 - 2*f*h)*ArcTanh[(g + 2*h*x)/Sqrt[g^2 - 4*f*h]]*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/(f^2*Sqrt[g^2 - 4*f*h]) + (g*Log[x]*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x]))/f^2 + ((g + (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*n*Log[a + b*x]*Log[-((b*(g - Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*a*h - b*(g - Sqrt[g^2 - 4*f*h])))])/(2*f^2) - ((g + (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*n*Log[c + d*x]*Log[-((d*(g - Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*c*h - d*(g - Sqrt[g^2 - 4*f*h])))])/(2*f^2) + ((g - (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*n*Log[a + b*x]*Log[-((b*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h])))])/(2*f^2) - ((g - (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*n*Log[c + d*x]*Log[-((d*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h])))])/(2*f^2) - (g*(n*Log[a + b*x] - Log[e*((a + b*x)/(c + d*x))^n] - n*Log[c + d*x])*Log[f + g*x + h*x^2])/(2*f^2) + ((g + (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(a + b*x))/(2*a*h - b*(g - Sqrt[g^2 - 4*f*h]))])/(2*f^2) + ((g - (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(a + b*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h]))])/(2*f^2) - (g*n*PolyLog[2, 1 + (b*x)/a])/f^2 - ((g + (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(c + d*x))/(2*c*h - d*(g - Sqrt[g^2 - 4*f*h]))])/(2*f^2) - ((g - (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*n*PolyLog[2, (2*h*(c + d*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h]))])/(2*f^2) + (g*n*PolyLog[2, 1 + (d*x)/c])/f^2","A",40,16,34,0.4706,1,"{2513, 2418, 2395, 36, 29, 31, 2394, 2315, 2393, 2391, 709, 800, 634, 618, 206, 628}"
88,1,46,0,0.1586008,"\int \frac{\log \left(\frac{c x}{a+b x}\right)}{a+b x} \, dx","Int[Log[(c*x)/(a + b*x)]/(a + b*x),x]","-\frac{\text{PolyLog}\left(2,1-\frac{a}{a+b x}\right)}{b}-\frac{\log \left(\frac{a}{a+b x}\right) \log \left(\frac{c x}{a+b x}\right)}{b}","-\frac{\text{PolyLog}\left(2,1-\frac{a}{a+b x}\right)}{b}-\frac{\log \left(\frac{a}{a+b x}\right) \log \left(\frac{c x}{a+b x}\right)}{b}",1,"-((Log[a/(a + b*x)]*Log[(c*x)/(a + b*x)])/b) - PolyLog[2, 1 - a/(a + b*x)]/b","A",5,5,19,0.2632,1,"{2488, 2411, 2343, 2333, 2315}"
89,1,20,0,0.0579114,"\int \frac{\log ^2\left(\frac{c x}{a+b x}\right)}{x (a+b x)} \, dx","Int[Log[(c*x)/(a + b*x)]^2/(x*(a + b*x)),x]","\frac{\log ^3\left(\frac{c x}{a+b x}\right)}{3 a}","\frac{\log ^3\left(\frac{c x}{a+b x}\right)}{3 a}",1,"Log[(c*x)/(a + b*x)]^3/(3*a)","A",1,1,24,0.04167,1,"{2505}"
90,1,82,0,0.1682578,"\int \frac{\log \left(\frac{a}{a+b x}\right) \log ^2\left(\frac{c x}{a+b x}\right)}{x (a+b x)} \, dx","Int[(Log[a/(a + b*x)]*Log[(c*x)/(a + b*x)]^2)/(x*(a + b*x)),x]","-\frac{\text{PolyLog}\left(2,1-\frac{a}{a+b x}\right) \log ^2\left(\frac{c x}{a+b x}\right)}{a}+\frac{2 \text{PolyLog}\left(3,1-\frac{a}{a+b x}\right) \log \left(\frac{c x}{a+b x}\right)}{a}-\frac{2 \text{PolyLog}\left(4,1-\frac{a}{a+b x}\right)}{a}","-\frac{\text{PolyLog}\left(2,1-\frac{a}{a+b x}\right) \log ^2\left(\frac{c x}{a+b x}\right)}{a}+\frac{2 \text{PolyLog}\left(3,1-\frac{a}{a+b x}\right) \log \left(\frac{c x}{a+b x}\right)}{a}-\frac{2 \text{PolyLog}\left(4,1-\frac{a}{a+b x}\right)}{a}",1,"-((Log[(c*x)/(a + b*x)]^2*PolyLog[2, 1 - a/(a + b*x)])/a) + (2*Log[(c*x)/(a + b*x)]*PolyLog[3, 1 - a/(a + b*x)])/a - (2*PolyLog[4, 1 - a/(a + b*x)])/a","A",3,3,34,0.08824,1,"{2506, 2508, 6610}"
91,1,150,0,0.2476385,"\int \frac{\log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)}{(c+d x) (a g+b g x)} \, dx","Int[(Log[(b*c - a*d)/(b*(c + d*x))]*Log[(e*(a + b*x))/(c + d*x)]^2)/((c + d*x)*(a*g + b*g*x)),x]","-\frac{\text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)}{g (b c-a d)}+\frac{2 \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right) \log \left(\frac{e (a+b x)}{c+d x}\right)}{g (b c-a d)}-\frac{2 \text{PolyLog}\left(4,1-\frac{b c-a d}{b (c+d x)}\right)}{g (b c-a d)}","-\frac{\text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)}{g (b c-a d)}+\frac{2 \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right) \log \left(\frac{e (a+b x)}{c+d x}\right)}{g (b c-a d)}-\frac{2 \text{PolyLog}\left(4,1-\frac{b c-a d}{b (c+d x)}\right)}{g (b c-a d)}",1,"-((Log[(e*(a + b*x))/(c + d*x)]^2*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/((b*c - a*d)*g)) + (2*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/((b*c - a*d)*g) - (2*PolyLog[4, 1 - (b*c - a*d)/(b*(c + d*x))])/((b*c - a*d)*g)","A",3,3,55,0.05455,1,"{2506, 2508, 6610}"
92,1,160,0,0.2501512,"\int \frac{\log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(\frac{b c-a d}{b (c+d x)}\right)}{(c+d x) (a g+b g x)} \, dx","Int[(Log[e*((a + b*x)/(c + d*x))^n]^2*Log[(b*c - a*d)/(b*(c + d*x))])/((c + d*x)*(a*g + b*g*x)),x]","-\frac{\text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{g (b c-a d)}+\frac{2 n \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{g (b c-a d)}-\frac{2 n^2 \text{PolyLog}\left(4,1-\frac{b c-a d}{b (c+d x)}\right)}{g (b c-a d)}","-\frac{\text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{g (b c-a d)}+\frac{2 n \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{g (b c-a d)}-\frac{2 n^2 \text{PolyLog}\left(4,1-\frac{b c-a d}{b (c+d x)}\right)}{g (b c-a d)}",1,"-((Log[e*((a + b*x)/(c + d*x))^n]^2*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/((b*c - a*d)*g)) + (2*n*Log[e*((a + b*x)/(c + d*x))^n]*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/((b*c - a*d)*g) - (2*n^2*PolyLog[4, 1 - (b*c - a*d)/(b*(c + d*x))])/((b*c - a*d)*g)","A",3,3,58,0.05172,1,"{2506, 2508, 6610}"
93,1,25,0,0.0115837,"\int \log \left(\frac{c (b+a x)}{x}\right) \, dx","Int[Log[(c*(b + a*x))/x],x]","x \log \left(a c+\frac{b c}{x}\right)+\frac{b \log (a x+b)}{a}","x \log \left(a c+\frac{b c}{x}\right)+\frac{b \log (a x+b)}{a}",1,"x*Log[a*c + (b*c)/x] + (b*Log[b + a*x])/a","A",4,4,11,0.3636,1,"{2453, 2448, 263, 31}"
94,1,67,0,0.0737622,"\int \log ^2\left(\frac{c (b+a x)}{x}\right) \, dx","Int[Log[(c*(b + a*x))/x]^2,x]","-\frac{2 b \text{PolyLog}\left(2,\frac{b}{a x}+1\right)}{a}+\frac{(a x+b) \log ^2\left(a c+\frac{b c}{x}\right)}{a}-\frac{2 b \log \left(-\frac{b}{a x}\right) \log \left(c \left(a+\frac{b}{x}\right)\right)}{a}","-\frac{2 b \text{PolyLog}\left(2,\frac{b}{a x}+1\right)}{a}+\frac{(a x+b) \log ^2\left(a c+\frac{b c}{x}\right)}{a}-\frac{2 b \log \left(-\frac{b}{a x}\right) \log \left(c \left(a+\frac{b}{x}\right)\right)}{a}",1,"((b + a*x)*Log[a*c + (b*c)/x]^2)/a - (2*b*Log[c*(a + b/x)]*Log[-(b/(a*x))])/a - (2*b*PolyLog[2, 1 + b/(a*x)])/a","A",5,5,13,0.3846,1,"{2453, 2449, 2454, 2394, 2315}"
95,1,97,0,0.1103278,"\int \log ^3\left(\frac{c (b+a x)}{x}\right) \, dx","Int[Log[(c*(b + a*x))/x]^3,x]","-\frac{6 b \text{PolyLog}\left(2,\frac{b}{a x}+1\right) \log \left(c \left(a+\frac{b}{x}\right)\right)}{a}+\frac{6 b \text{PolyLog}\left(3,\frac{b}{a x}+1\right)}{a}+\frac{(a x+b) \log ^3\left(a c+\frac{b c}{x}\right)}{a}-\frac{3 b \log \left(-\frac{b}{a x}\right) \log ^2\left(c \left(a+\frac{b}{x}\right)\right)}{a}","-\frac{6 b \text{PolyLog}\left(2,\frac{b}{a x}+1\right) \log \left(c \left(a+\frac{b}{x}\right)\right)}{a}+\frac{6 b \text{PolyLog}\left(3,\frac{b}{a x}+1\right)}{a}+\frac{(a x+b) \log ^3\left(a c+\frac{b c}{x}\right)}{a}-\frac{3 b \log \left(-\frac{b}{a x}\right) \log ^2\left(c \left(a+\frac{b}{x}\right)\right)}{a}",1,"((b + a*x)*Log[a*c + (b*c)/x]^3)/a - (3*b*Log[c*(a + b/x)]^2*Log[-(b/(a*x))])/a - (6*b*Log[c*(a + b/x)]*PolyLog[2, 1 + b/(a*x)])/a + (6*b*PolyLog[3, 1 + b/(a*x)])/a","A",7,7,13,0.5385,1,"{2453, 2449, 2454, 2396, 2433, 2374, 6589}"
96,1,28,0,0.0068001,"\int \log \left(\frac{c (b+a x)^2}{x^2}\right) \, dx","Int[Log[(c*(b + a*x)^2)/x^2],x]","x \log \left(\frac{c (a x+b)^2}{x^2}\right)+\frac{2 b \log (a x+b)}{a}","x \log \left(\frac{c (a x+b)^2}{x^2}\right)+\frac{2 b \log (a x+b)}{a}",1,"(2*b*Log[b + a*x])/a + x*Log[(c*(b + a*x)^2)/x^2]","A",2,2,13,0.1538,1,"{2486, 31}"
97,1,67,0,0.1568014,"\int \log ^2\left(\frac{c (b+a x)^2}{x^2}\right) \, dx","Int[Log[(c*(b + a*x)^2)/x^2]^2,x]","\frac{8 b \text{PolyLog}\left(2,1-\frac{b}{a x+b}\right)}{a}+x \log ^2\left(\frac{c (a x+b)^2}{x^2}\right)-\frac{4 b \log \left(\frac{b}{a x+b}\right) \log \left(\frac{c (a x+b)^2}{x^2}\right)}{a}","\frac{8 b \text{PolyLog}\left(2,1-\frac{b}{a x+b}\right)}{a}+x \log ^2\left(\frac{c (a x+b)^2}{x^2}\right)-\frac{4 b \log \left(\frac{b}{a x+b}\right) \log \left(\frac{c (a x+b)^2}{x^2}\right)}{a}",1,"(-4*b*Log[b/(b + a*x)]*Log[(c*(b + a*x)^2)/x^2])/a + x*Log[(c*(b + a*x)^2)/x^2]^2 + (8*b*PolyLog[2, 1 - b/(b + a*x)])/a","A",6,6,15,0.4000,1,"{2486, 2488, 2411, 2343, 2333, 2315}"
98,1,102,0,0.1318484,"\int \log ^3\left(\frac{c (b+a x)^2}{x^2}\right) \, dx","Int[Log[(c*(b + a*x)^2)/x^2]^3,x]","\frac{24 b \text{PolyLog}\left(2,1-\frac{b}{a x+b}\right) \log \left(\frac{c (a x+b)^2}{x^2}\right)}{a}+\frac{48 b \text{PolyLog}\left(3,1-\frac{b}{a x+b}\right)}{a}+x \log ^3\left(\frac{c (a x+b)^2}{x^2}\right)-\frac{6 b \log \left(\frac{b}{a x+b}\right) \log ^2\left(\frac{c (a x+b)^2}{x^2}\right)}{a}","\frac{24 b \text{PolyLog}\left(2,\frac{a x}{a x+b}\right) \log \left(\frac{c (a x+b)^2}{x^2}\right)}{a}+\frac{48 b \text{PolyLog}\left(3,\frac{a x}{a x+b}\right)}{a}+x \log ^3\left(\frac{c (a x+b)^2}{x^2}\right)-\frac{6 b \log \left(1-\frac{a x}{a x+b}\right) \log ^2\left(\frac{c (a x+b)^2}{x^2}\right)}{a}",1,"(-6*b*Log[b/(b + a*x)]*Log[(c*(b + a*x)^2)/x^2]^2)/a + x*Log[(c*(b + a*x)^2)/x^2]^3 + (24*b*Log[(c*(b + a*x)^2)/x^2]*PolyLog[2, 1 - b/(b + a*x)])/a + (48*b*PolyLog[3, 1 - b/(b + a*x)])/a","A",4,4,15,0.2667,1,"{2486, 2488, 2506, 6610}"
99,1,28,0,0.0066862,"\int \log \left(\frac{c x^2}{(b+a x)^2}\right) \, dx","Int[Log[(c*x^2)/(b + a*x)^2],x]","x \log \left(\frac{c x^2}{(a x+b)^2}\right)-\frac{2 b \log (a x+b)}{a}","x \log \left(\frac{c x^2}{(a x+b)^2}\right)-\frac{2 b \log (a x+b)}{a}",1,"x*Log[(c*x^2)/(b + a*x)^2] - (2*b*Log[b + a*x])/a","A",2,2,13,0.1538,1,"{2486, 31}"
100,1,67,0,0.1548647,"\int \log ^2\left(\frac{c x^2}{(b+a x)^2}\right) \, dx","Int[Log[(c*x^2)/(b + a*x)^2]^2,x]","\frac{8 b \text{PolyLog}\left(2,1-\frac{b}{a x+b}\right)}{a}+x \log ^2\left(\frac{c x^2}{(a x+b)^2}\right)+\frac{4 b \log \left(\frac{b}{a x+b}\right) \log \left(\frac{c x^2}{(a x+b)^2}\right)}{a}","\frac{8 b \text{PolyLog}\left(2,1-\frac{b}{a x+b}\right)}{a}+x \log ^2\left(\frac{c x^2}{(a x+b)^2}\right)+\frac{4 b \log \left(\frac{b}{a x+b}\right) \log \left(\frac{c x^2}{(a x+b)^2}\right)}{a}",1,"x*Log[(c*x^2)/(b + a*x)^2]^2 + (4*b*Log[(c*x^2)/(b + a*x)^2]*Log[b/(b + a*x)])/a + (8*b*PolyLog[2, 1 - b/(b + a*x)])/a","A",6,6,15,0.4000,1,"{2486, 2488, 2411, 2343, 2333, 2315}"
101,1,102,0,0.1270852,"\int \log ^3\left(\frac{c x^2}{(b+a x)^2}\right) \, dx","Int[Log[(c*x^2)/(b + a*x)^2]^3,x]","\frac{24 b \text{PolyLog}\left(2,1-\frac{b}{a x+b}\right) \log \left(\frac{c x^2}{(a x+b)^2}\right)}{a}-\frac{48 b \text{PolyLog}\left(3,1-\frac{b}{a x+b}\right)}{a}+x \log ^3\left(\frac{c x^2}{(a x+b)^2}\right)+\frac{6 b \log \left(\frac{b}{a x+b}\right) \log ^2\left(\frac{c x^2}{(a x+b)^2}\right)}{a}","\frac{24 b \text{PolyLog}\left(2,\frac{a x}{a x+b}\right) \log \left(\frac{c x^2}{(a x+b)^2}\right)}{a}-\frac{48 b \text{PolyLog}\left(3,\frac{a x}{a x+b}\right)}{a}+x \log ^3\left(\frac{c x^2}{(a x+b)^2}\right)+\frac{6 b \log \left(\frac{b}{a x+b}\right) \log ^2\left(\frac{c x^2}{(a x+b)^2}\right)}{a}",1,"x*Log[(c*x^2)/(b + a*x)^2]^3 + (6*b*Log[(c*x^2)/(b + a*x)^2]^2*Log[b/(b + a*x)])/a + (24*b*Log[(c*x^2)/(b + a*x)^2]*PolyLog[2, 1 - b/(b + a*x)])/a - (48*b*PolyLog[3, 1 - b/(b + a*x)])/a","A",4,4,15,0.2667,1,"{2486, 2488, 2506, 6610}"
102,1,35,0,0.0638609,"\int \frac{\text{PolyLog}\left(2,1+\frac{b c-a d}{d (a+b x)}\right)}{(a+b x) (c+d x)} \, dx","Int[PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))]/((a + b*x)*(c + d*x)),x]","-\frac{\text{PolyLog}\left(3,\frac{b c-a d}{d (a+b x)}+1\right)}{b c-a d}","-\frac{\text{PolyLog}\left(3,\frac{b c-a d}{d (a+b x)}+1\right)}{b c-a d}",1,"-(PolyLog[3, 1 + (b*c - a*d)/(d*(a + b*x))]/(b*c - a*d))","A",1,1,38,0.02632,1,"{6610}"
103,1,85,0,0.1343568,"\int \frac{\log \left(\frac{-b c+a d}{d (a+b x)}\right) \log \left(\frac{e (c+d x)}{a+b x}\right)}{(a+b x) (c+d x)} \, dx","Int[(Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[(e*(c + d*x))/(a + b*x)])/((a + b*x)*(c + d*x)),x]","\frac{\text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right) \log \left(\frac{e (c+d x)}{a+b x}\right)}{b c-a d}-\frac{\text{PolyLog}\left(3,\frac{b c-a d}{d (a+b x)}+1\right)}{b c-a d}","\frac{\text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right) \log \left(\frac{e (c+d x)}{a+b x}\right)}{b c-a d}-\frac{\text{PolyLog}\left(3,\frac{b c-a d}{d (a+b x)}+1\right)}{b c-a d}",1,"(Log[(e*(c + d*x))/(a + b*x)]*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/(b*c - a*d) - PolyLog[3, 1 + (b*c - a*d)/(d*(a + b*x))]/(b*c - a*d)","A",2,2,50,0.04000,1,"{2506, 6610}"
104,1,149,0,0.1802684,"\int \frac{\log ^2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{a+b x} \, dx","Int[Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]^2/(a + b*x),x]","-\frac{2 \text{PolyLog}\left(2,\frac{b c-a d}{d (a+b x)}+1\right) \log \left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{b}+\frac{2 \text{PolyLog}\left(3,\frac{b c-a d}{d (a+b x)}+1\right)}{b}-\frac{\log \left(-\frac{b c-a d}{d (a+b x)}\right) \log ^2\left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{b}","-\frac{2 \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right) \log \left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{b}+\frac{2 \text{PolyLog}\left(3,\frac{b (c+d x)}{d (a+b x)}\right)}{b}-\frac{\log \left(\frac{a d-b c}{d (a+b x)}\right) \log ^2\left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{b}",1,"-((Log[-((b*c - a*d)/(d*(a + b*x)))]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]^2)/b) - (2*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))])/b + (2*PolyLog[3, 1 + (b*c - a*d)/(d*(a + b*x))])/b","A",3,3,42,0.07143,1,"{2488, 2506, 6610}"
105,1,109,0,0.1638205,"\int \frac{\log \left(\frac{e (c+d x)}{a+b x}\right) \log \left(\frac{(-b c+a d) (e+f x)}{(d e-c f) (a+b x)}\right)}{(a+b x) (c+d x)} \, dx","Int[(Log[(e*(c + d*x))/(a + b*x)]*Log[((-(b*c) + a*d)*(e + f*x))/((d*e - c*f)*(a + b*x))])/((a + b*x)*(c + d*x)),x]","\frac{\log \left(\frac{e (c+d x)}{a+b x}\right) \text{PolyLog}\left(2,\frac{(e+f x) (b c-a d)}{(a+b x) (d e-c f)}+1\right)}{b c-a d}-\frac{\text{PolyLog}\left(3,\frac{(e+f x) (b c-a d)}{(a+b x) (d e-c f)}+1\right)}{b c-a d}","\frac{\log \left(\frac{e (c+d x)}{a+b x}\right) \text{PolyLog}\left(2,\frac{(e+f x) (b c-a d)}{(a+b x) (d e-c f)}+1\right)}{b c-a d}-\frac{\text{PolyLog}\left(3,\frac{(e+f x) (b c-a d)}{(a+b x) (d e-c f)}+1\right)}{b c-a d}",1,"(Log[(e*(c + d*x))/(a + b*x)]*PolyLog[2, 1 + ((b*c - a*d)*(e + f*x))/((d*e - c*f)*(a + b*x))])/(b*c - a*d) - PolyLog[3, 1 + ((b*c - a*d)*(e + f*x))/((d*e - c*f)*(a + b*x))]/(b*c - a*d)","A",2,2,62,0.03226,1,"{2506, 6610}"
106,1,206,0,0.253539,"\int \frac{\log ^2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{(a+b x) (e+f x)} \, dx","Int[Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]^2/((a + b*x)*(e + f*x)),x]","\frac{2 \text{PolyLog}\left(3,\frac{(e+f x) (b c-a d)}{(a+b x) (d e-c f)}+1\right)}{b e-a f}-\frac{2 \log \left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right) \text{PolyLog}\left(2,\frac{(e+f x) (b c-a d)}{(a+b x) (d e-c f)}+1\right)}{b e-a f}-\frac{\log \left(-\frac{(e+f x) (b c-a d)}{(a+b x) (d e-c f)}\right) \log ^2\left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{b e-a f}","\frac{2 \text{PolyLog}\left(3,\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{b e-a f}-\frac{2 \log \left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right) \text{PolyLog}\left(2,\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{b e-a f}-\frac{\log \left(1-\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right) \log ^2\left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{b e-a f}",1,"-((Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]^2*Log[-(((b*c - a*d)*(e + f*x))/((d*e - c*f)*(a + b*x)))])/(b*e - a*f)) - (2*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*PolyLog[2, 1 + ((b*c - a*d)*(e + f*x))/((d*e - c*f)*(a + b*x))])/(b*e - a*f) + (2*PolyLog[3, 1 + ((b*c - a*d)*(e + f*x))/((d*e - c*f)*(a + b*x))])/(b*e - a*f)","A",3,3,49,0.06122,1,"{2503, 2506, 6610}"
107,1,334,0,0.507152,"\int \frac{\log ^2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{e+f x} \, dx","Int[Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]^2/(e + f*x),x]","-\frac{2 \text{PolyLog}\left(3,1-\frac{(e+f x) (b c-a d)}{(c+d x) (b e-a f)}\right)}{f}+\frac{2 \text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) \log \left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{f}-\frac{2 \log \left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right) \text{PolyLog}\left(2,1-\frac{(e+f x) (b c-a d)}{(c+d x) (b e-a f)}\right)}{f}+\frac{2 \text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right)}{f}-\frac{\log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{f}+\frac{\log \left(\frac{(e+f x) (b c-a d)}{(c+d x) (b e-a f)}\right) \log ^2\left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{f}","-\frac{2 \text{PolyLog}\left(3,\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{f}-\frac{2 \text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right) \log \left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{f}+\frac{2 \log \left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right) \text{PolyLog}\left(2,\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{f}+\frac{2 \text{PolyLog}\left(3,\frac{b (c+d x)}{d (a+b x)}\right)}{f}-\frac{\log \left(-\frac{b c-a d}{d (a+b x)}\right) \log ^2\left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{f}+\frac{\log \left(1-\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right) \log ^2\left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{f}",1,"-((Log[(b*c - a*d)/(b*(c + d*x))]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]^2)/f) + (Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]^2*Log[((b*c - a*d)*(e + f*x))/((b*e - a*f)*(c + d*x))])/f + (2*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/f - (2*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*PolyLog[2, 1 - ((b*c - a*d)*(e + f*x))/((b*e - a*f)*(c + d*x))])/f + (2*PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))])/f - (2*PolyLog[3, 1 - ((b*c - a*d)*(e + f*x))/((b*e - a*f)*(c + d*x))])/f","A",7,5,42,0.1190,1,"{2489, 2488, 2506, 6610, 2503}"
108,1,445,0,0.5944955,"\int \frac{\log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log \left(\frac{b (e+f x)}{b e-a f}\right)}{(a+b x) (c+d x)} \, dx","Int[(Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[(b*(e + f*x))/(b*e - a*f)])/((a + b*x)*(c + d*x)),x]","-\frac{\text{PolyLog}\left(3,1-\frac{(e+f x) (b c-a d)}{(c+d x) (b e-a f)}\right)}{b c-a d}+\frac{\text{PolyLog}\left(2,1-\frac{b c-a d}{b (c+d x)}\right) \log \left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{b c-a d}-\frac{\log \left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right) \text{PolyLog}\left(2,1-\frac{(e+f x) (b c-a d)}{(c+d x) (b e-a f)}\right)}{b c-a d}+\frac{\text{PolyLog}\left(3,1-\frac{b c-a d}{b (c+d x)}\right)}{b c-a d}-\frac{\log \left(\frac{b c-a d}{b (c+d x)}\right) \log ^2\left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{2 (b c-a d)}-\frac{\log \left(\frac{b (e+f x)}{b e-a f}\right) \log ^2\left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{2 (b c-a d)}+\frac{\log \left(\frac{(e+f x) (b c-a d)}{(c+d x) (b e-a f)}\right) \log ^2\left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{2 (b c-a d)}","-\frac{\text{PolyLog}\left(3,\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{b c-a d}-\frac{\text{PolyLog}\left(2,\frac{b (c+d x)}{d (a+b x)}\right) \log \left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{b c-a d}+\frac{\log \left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right) \text{PolyLog}\left(2,\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{b c-a d}+\frac{\text{PolyLog}\left(3,\frac{b (c+d x)}{d (a+b x)}\right)}{b c-a d}-\frac{\log \left(-\frac{b c-a d}{d (a+b x)}\right) \log ^2\left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{2 (b c-a d)}-\frac{\log \left(\frac{b (e+f x)}{b e-a f}\right) \log ^2\left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{2 (b c-a d)}+\frac{\log \left(1-\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right) \log ^2\left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\right)}{2 (b c-a d)}",1,"-(Log[(b*c - a*d)/(b*(c + d*x))]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]^2)/(2*(b*c - a*d)) - (Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]^2*Log[(b*(e + f*x))/(b*e - a*f)])/(2*(b*c - a*d)) + (Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]^2*Log[((b*c - a*d)*(e + f*x))/((b*e - a*f)*(c + d*x))])/(2*(b*c - a*d)) + (Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*PolyLog[2, 1 - (b*c - a*d)/(b*(c + d*x))])/(b*c - a*d) - (Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*PolyLog[2, 1 - ((b*c - a*d)*(e + f*x))/((b*e - a*f)*(c + d*x))])/(b*c - a*d) + PolyLog[3, 1 - (b*c - a*d)/(b*(c + d*x))]/(b*c - a*d) - PolyLog[3, 1 - ((b*c - a*d)*(e + f*x))/((b*e - a*f)*(c + d*x))]/(b*c - a*d)","A",8,6,65,0.09231,1,"{2507, 2489, 2488, 2506, 6610, 2503}"