1,1,336,404,0.4093498,"\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","Integrate[(f + g/x)^3*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","\frac{B g^3 n \left(\log (x) \left(a^2 d^2 x-b^2 c^2 x\right)+b^2 c^2 x \log (a+b x)+a \left(-a d^2 x \log (c+d x)+a c d-b c^2\right)\right)}{2 a^2 c^2 x}+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}-3 B f^2 g n \left(\log (x) \left(\log \left(\frac{b x}{a}+1\right)-\log \left(\frac{d x}{c}+1\right)\right)+\text{Li}_2\left(-\frac{b x}{a}\right)-\text{Li}_2\left(-\frac{d x}{c}\right)\right)+\frac{3 B f g^2 n (\log (x) (b c-a d)-b c \log (a+b x)+a d \log (c+d x))}{a c}+A f^3 x","-\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 \text{Li}_2\left(-\frac{b x}{a}\right)-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 \text{Li}_2\left(-\frac{d x}{c}\right)+3 B f^2 g n \log (x) \log \left(\frac{d x}{c}+1\right)",1,"A*f^3*x + (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*f*g^2*n*((b*c - a*d)*Log[x] - b*c*Log[a + b*x] + a*d*Log[c + d*x]))/(a*c) + (B*g^3*n*((-(b^2*c^2*x) + a^2*d^2*x)*Log[x] + b^2*c^2*x*Log[a + b*x] + a*(-(b*c^2) + a*c*d - a*d^2*x*Log[c + d*x])))/(2*a^2*c^2*x) - 3*B*f^2*g*n*(Log[x]*(Log[1 + (b*x)/a] - Log[1 + (d*x)/c]) + PolyLog[2, -((b*x)/a)] - PolyLog[2, -((d*x)/c)])","A",1
2,1,217,263,0.2138244,"\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","Integrate[(f + g/x)^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","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}-2 B f g n \left(\log (x) \left(\log \left(\frac{b x}{a}+1\right)-\log \left(\frac{d x}{c}+1\right)\right)+\text{Li}_2\left(-\frac{b x}{a}\right)-\text{Li}_2\left(-\frac{d x}{c}\right)\right)+\frac{B g^2 n (\log (x) (b c-a d)-b c \log (a+b x)+a d \log (c+d x))}{a c}+A f^2 x","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 \text{Li}_2\left(-\frac{b x}{a}\right)-2 B f g n \log (x) \log \left(\frac{b x}{a}+1\right)+A f^2 x+2 B f g n \text{Li}_2\left(-\frac{d x}{c}\right)+2 B f g n \log (x) \log \left(\frac{d x}{c}+1\right)",1,"A*f^2*x + (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*g^2*n*((b*c - a*d)*Log[x] - b*c*Log[a + b*x] + a*d*Log[c + d*x]))/(a*c) - 2*B*f*g*n*(Log[x]*(Log[1 + (b*x)/a] - Log[1 + (d*x)/c]) + PolyLog[2, -((b*x)/a)] - PolyLog[2, -((d*x)/c)])","A",1
3,1,135,143,0.096393,"\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","Integrate[(f + g/x)*(A + B*Log[e*((a + b*x)/(c + d*x))^n]),x]","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 \left(\log (x) \left(\log \left(\frac{b x}{a}+1\right)-\log \left(\frac{d x}{c}+1\right)\right)+\text{Li}_2\left(-\frac{b x}{a}\right)-\text{Li}_2\left(-\frac{d x}{c}\right)\right)+A f x","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 \text{Li}_2\left(-\frac{b x}{a}\right)-B g n \log (x) \log \left(\frac{b x}{a}+1\right)+A f x+B g n \text{Li}_2\left(-\frac{d x}{c}\right)+B g n \log (x) \log \left(\frac{d x}{c}+1\right)",1,"A*f*x + (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 + (b*x)/a] - Log[1 + (d*x)/c]) + PolyLog[2, -((b*x)/a)] - PolyLog[2, -((d*x)/c)])","A",1
4,1,185,217,0.1546388,"\int \frac{A+B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f+\frac{g}{x}} \, dx","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g/x),x]","\frac{-g \log (f x+g) \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}+B g n \left(\log (f x+g) \left(\log \left(\frac{f (a+b x)}{a f-b g}\right)-\log \left(\frac{f (c+d x)}{c f-d g}\right)\right)+\text{Li}_2\left(\frac{b (g+f x)}{b g-a f}\right)-\text{Li}_2\left(\frac{d (g+f x)}{d g-c f}\right)\right)-\frac{B f n (b c-a d) \log (c+d x)}{b d}+A f x}{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 \text{Li}_2\left(-\frac{b (g+f x)}{a f-b g}\right)}{f^2}+\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 \text{Li}_2\left(-\frac{d (g+f x)}{c f-d g}\right)}{f^2}-\frac{B g n \log (f x+g) \log \left(\frac{f (c+d x)}{c f-d g}\right)}{f^2}",1,"(A*f*x + (B*f*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/b - (B*(b*c - a*d)*f*n*Log[c + d*x])/(b*d) - g*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[g + f*x] + B*g*n*((Log[(f*(a + b*x))/(a*f - b*g)] - Log[(f*(c + d*x))/(c*f - d*g)])*Log[g + f*x] + PolyLog[2, (b*(g + f*x))/(-(a*f) + b*g)] - PolyLog[2, (d*(g + f*x))/(-(c*f) + d*g)]))/f^2","A",1
5,1,295,322,0.4778049,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g/x)^2,x]","\frac{-\frac{g^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{f x+g}-2 g \log (f x+g) \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 g^2 n (b \log (a+b x) (d g-c f)+d (a f-b g) \log (c+d x)+f (b c-a d) \log (f x+g))}{(a f-b g) (c f-d g)}+2 B g n \left(\log (f x+g) \left(\log \left(\frac{f (a+b x)}{a f-b g}\right)-\log \left(\frac{f (c+d x)}{c f-d g}\right)\right)+\text{Li}_2\left(\frac{b (g+f x)}{b g-a f}\right)-\text{Li}_2\left(\frac{d (g+f x)}{d g-c f}\right)\right)-\frac{B f n (b c-a d) \log (c+d x)}{b d}+A f x}{f^3}","-\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{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{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 \text{Li}_2\left(-\frac{b (g+f x)}{a f-b g}\right)}{f^3}+\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 \text{Li}_2\left(-\frac{d (g+f x)}{c f-d g}\right)}{f^3}-\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*f*x + (B*f*(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]))/(g + f*x) - (B*(b*c - a*d)*f*n*Log[c + d*x])/(b*d) - 2*g*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[g + f*x] + (B*g^2*n*(b*(-(c*f) + d*g)*Log[a + b*x] + d*(a*f - b*g)*Log[c + d*x] + (b*c - a*d)*f*Log[g + f*x]))/((a*f - b*g)*(c*f - d*g)) + 2*B*g*n*((Log[(f*(a + b*x))/(a*f - b*g)] - Log[(f*(c + d*x))/(c*f - d*g)])*Log[g + f*x] + PolyLog[2, (b*(g + f*x))/(-(a*f) + b*g)] - PolyLog[2, (d*(g + f*x))/(-(c*f) + d*g)]))/f^3","A",1
6,1,470,531,1.2246015,"\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","Integrate[(A + B*Log[e*((a + b*x)/(c + d*x))^n])/(f + g/x)^3,x]","\frac{\frac{g^3 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{(f x+g)^2}-\frac{6 g^2 \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)}{f x+g}-6 g \log (f x+g) \left(B \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+A\right)+B g^3 n (b c-a d) \left(\frac{\frac{d^2 \log (c+d x)}{b c-a d}+\frac{f \left(\frac{(a f-b g) (c f-d g)}{f x+g}+\log (f x+g) (a d f+b c f-2 b d g)\right)}{(a f-b g)^2}}{(c f-d g)^2}-\frac{b^2 \log (a+b x)}{(b c-a d) (a f-b g)^2}\right)+\frac{2 B f (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b}+\frac{6 B g^2 n (b \log (a+b x) (d g-c f)+d (a f-b g) \log (c+d x)+f (b c-a d) \log (f x+g))}{(a f-b g) (c f-d g)}+6 B g n \left(\log (f x+g) \left(\log \left(\frac{f (a+b x)}{a f-b g}\right)-\log \left(\frac{f (c+d x)}{c f-d g}\right)\right)+\text{Li}_2\left(\frac{b (g+f x)}{b g-a f}\right)-\text{Li}_2\left(\frac{d (g+f x)}{d g-c f}\right)\right)-\frac{2 B f n (b c-a d) \log (c+d x)}{b d}+2 A f x}{2 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 \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{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{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 \text{Li}_2\left(-\frac{b (g+f x)}{a f-b g}\right)}{f^4}+\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 \text{Li}_2\left(-\frac{d (g+f x)}{c f-d g}\right)}{f^4}-\frac{3 B g n \log (f x+g) \log \left(\frac{f (c+d x)}{c f-d g}\right)}{f^4}",1,"(2*A*f*x + (2*B*f*(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]))/(g + f*x)^2 - (6*g^2*(A + B*Log[e*((a + b*x)/(c + d*x))^n]))/(g + f*x) - (2*B*(b*c - a*d)*f*n*Log[c + d*x])/(b*d) - 6*g*(A + B*Log[e*((a + b*x)/(c + d*x))^n])*Log[g + f*x] + (6*B*g^2*n*(b*(-(c*f) + d*g)*Log[a + b*x] + d*(a*f - b*g)*Log[c + d*x] + (b*c - a*d)*f*Log[g + f*x]))/((a*f - b*g)*(c*f - d*g)) + B*(b*c - a*d)*g^3*n*(-((b^2*Log[a + b*x])/((b*c - a*d)*(a*f - b*g)^2)) + ((d^2*Log[c + d*x])/(b*c - a*d) + (f*(((a*f - b*g)*(c*f - d*g))/(g + f*x) + (b*c*f + a*d*f - 2*b*d*g)*Log[g + f*x]))/(a*f - b*g)^2)/(c*f - d*g)^2) + 6*B*g*n*((Log[(f*(a + b*x))/(a*f - b*g)] - Log[(f*(c + d*x))/(c*f - d*g)])*Log[g + f*x] + PolyLog[2, (b*(g + f*x))/(-(a*f) + b*g)] - PolyLog[2, (d*(g + f*x))/(-(c*f) + d*g)]))/(2*f^4)","A",1
7,1,185,201,0.3078498,"\int (a+b x)^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[(a + b*x)^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","\frac{(a+b x)^5 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-\frac{r \left(-15 b^4 (4 p+5 q) (c+d x)^4 (b c-a d)+40 b^3 (3 p+5 q) (c+d x)^3 (b c-a d)^2-60 b^2 (2 p+5 q) (c+d x)^2 (b c-a d)^3+60 b d x (p+5 q) (b c-a d)^4-60 q (b c-a d)^5 \log (c+d x)+12 b^5 (p+q) (c+d x)^5\right)}{60 d^5}}{5 b}","\frac{q r (b c-a d)^5 \log (c+d x)}{5 b d^5}-\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{(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,"(-1/60*(r*(60*b*d*(b*c - a*d)^4*(p + 5*q)*x - 60*b^2*(b*c - a*d)^3*(2*p + 5*q)*(c + d*x)^2 + 40*b^3*(b*c - a*d)^2*(3*p + 5*q)*(c + d*x)^3 - 15*b^4*(b*c - a*d)*(4*p + 5*q)*(c + d*x)^4 + 12*b^5*(p + q)*(c + d*x)^5 - 60*(b*c - a*d)^5*q*Log[c + d*x]))/d^5 + (a + b*x)^5*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(5*b)","A",1
8,1,154,172,0.215239,"\int (a+b x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[(a + b*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","\frac{\frac{r \left(4 b^3 (3 p+4 q) (c+d x)^3 (b c-a d)-18 b^2 (p+2 q) (c+d x)^2 (b c-a d)^2+12 b d x (p+4 q) (b c-a d)^3-12 q (b c-a d)^4 \log (c+d x)-3 b^4 (p+q) (c+d x)^4\right)}{12 d^4}+(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 (b c-a d)^4 \log (c+d x)}{4 b d^4}+\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{(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,"((r*(12*b*d*(b*c - a*d)^3*(p + 4*q)*x - 18*b^2*(b*c - a*d)^2*(p + 2*q)*(c + d*x)^2 + 4*b^3*(b*c - a*d)*(3*p + 4*q)*(c + d*x)^3 - 3*b^4*(p + q)*(c + d*x)^4 - 12*(b*c - a*d)^4*q*Log[c + d*x]))/(12*d^4) + (a + b*x)^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(4*b)","A",1
9,1,127,143,0.1375448,"\int (a+b x)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[(a + b*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","\frac{(a+b x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-\frac{r \left(-3 b^2 (2 p+3 q) (c+d x)^2 (b c-a d)+6 b d x (p+3 q) (b c-a d)^2-6 q (b c-a d)^3 \log (c+d x)+2 b^3 (p+q) (c+d x)^3\right)}{6 d^3}}{3 b}","\frac{q r (b c-a d)^3 \log (c+d x)}{3 b d^3}-\frac{q r x (b c-a d)^2}{3 d^2}+\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,"(-1/6*(r*(6*b*d*(b*c - a*d)^2*(p + 3*q)*x - 3*b^2*(b*c - a*d)*(2*p + 3*q)*(c + d*x)^2 + 2*b^3*(p + q)*(c + d*x)^3 - 6*(b*c - a*d)^3*q*Log[c + d*x]))/d^3 + (a + b*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(3*b)","A",1
10,1,105,116,0.1997543,"\int (a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[(a + b*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","\frac{a^2 p r \log (a+b x)}{2 b}-\frac{d x \left(r (2 a d (p+2 q)-2 b c q+b d x (p+q))-2 d (2 a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)+2 c q r (b c-2 a d) \log (c+d x)}{4 d^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^2*p*r*Log[a + b*x])/(2*b) - (2*c*(b*c - 2*a*d)*q*r*Log[c + d*x] + d*x*(r*(-2*b*c*q + 2*a*d*(p + 2*q) + b*d*(p + q)*x) - 2*d*(2*a + b*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(4*d^2)","A",1
11,1,93,107,0.1083294,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{a+b x} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(a + b*x),x]","-\frac{\log (a+b x) \left(-2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+2 q r \log \left(\frac{b (c+d x)}{b c-a d}\right)+p r \log (a+b x)\right)+2 q r \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)}{2 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 \text{Li}_2\left(-\frac{d (a+b x)}{b c-a d}\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,"-1/2*(Log[a + b*x]*(p*r*Log[a + b*x] + 2*q*r*Log[(b*(c + d*x))/(b*c - a*d)] - 2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]) + 2*q*r*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/b","A",1
12,1,89,95,0.0554549,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^2} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(a + b*x)^2,x]","\frac{r \left(\frac{d q \log (a+b x)}{b c-a d}-\frac{d q \log (c+d x)}{b c-a d}-\frac{p}{a+b x}\right)}{b}-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{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,"(r*(-(p/(a + b*x)) + (d*q*Log[a + b*x])/(b*c - a*d) - (d*q*Log[c + d*x])/(b*c - a*d)))/b - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(b*(a + b*x))","A",1
13,1,116,135,0.2433486,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^3} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(a + b*x)^3,x]","\frac{r \left(-\frac{d^2 q \log (a+b x)}{(b c-a d)^2}+\frac{d^2 q \log (c+d x)}{(b c-a d)^2}-\frac{p-\frac{2 d q (a+b x)}{a d-b c}}{2 (a+b x)^2}\right)-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^2}}{2 b}","-\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,"(r*(-1/2*(p - (2*d*q*(a + b*x))/(-(b*c) + a*d))/(a + b*x)^2 - (d^2*q*Log[a + b*x])/(b*c - a*d)^2 + (d^2*q*Log[c + d*x])/(b*c - a*d)^2) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(a + b*x)^2)/(2*b)","A",1
14,1,141,164,0.3577704,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^4} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(a + b*x)^4,x]","\frac{r \left(\frac{d^3 q \log (a+b x)}{(b c-a d)^3}-\frac{d^3 q \log (c+d x)}{(b c-a d)^3}+\frac{\frac{6 d^2 q (a+b x)^2}{(b c-a d)^2}+\frac{3 d q (a+b x)}{a d-b c}-2 p}{6 (a+b x)^3}\right)-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^3}}{3 b}","\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{d^2 q r}{3 b (a+b x) (b c-a d)^2}-\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,"(r*((-2*p + (3*d*q*(a + b*x))/(-(b*c) + a*d) + (6*d^2*q*(a + b*x)^2)/(b*c - a*d)^2)/(6*(a + b*x)^3) + (d^3*q*Log[a + b*x])/(b*c - a*d)^3 - (d^3*q*Log[c + d*x])/(b*c - a*d)^3) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(a + b*x)^3)/(3*b)","A",1
15,1,164,193,0.3571518,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^5} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(a + b*x)^5,x]","\frac{r \left(-\frac{d^4 q \log (a+b x)}{(b c-a d)^4}+\frac{d^4 q \log (c+d x)}{(b c-a d)^4}+\frac{-\frac{12 d^3 q (a+b x)^3}{(b c-a d)^3}+\frac{6 d^2 q (a+b x)^2}{(b c-a d)^2}+\frac{4 d q (a+b x)}{a d-b c}-3 p}{12 (a+b x)^4}\right)-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^4}}{4 b}","-\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{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{\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,"(r*((-3*p + (4*d*q*(a + b*x))/(-(b*c) + a*d) + (6*d^2*q*(a + b*x)^2)/(b*c - a*d)^2 - (12*d^3*q*(a + b*x)^3)/(b*c - a*d)^3)/(12*(a + b*x)^4) - (d^4*q*Log[a + b*x])/(b*c - a*d)^4 + (d^4*q*Log[c + d*x])/(b*c - a*d)^4) - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(a + b*x)^4)/(4*b)","A",1
16,1,2508,920,2.8674697,"\int (a+b x)^4 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[(a + b*x)^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2,x]","\text{Result too large to show}","-\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{Li}_2\left(\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,"(2*a^5*p*q*r^2)/b + (2*a*b^3*c^4*p*q*r^2)/(5*d^4) - (2*a^2*b^2*c^3*p*q*r^2)/d^3 + (4*a^3*b*c^2*p*q*r^2)/d^2 - (4*a^4*c*p*q*r^2)/d + (2*a^4*p^2*r^2*x)/25 + (197*a^4*p*q*r^2*x)/150 + (12*b^4*c^4*p*q*r^2*x)/(25*d^4) - (11*a*b^3*c^3*p*q*r^2*x)/(5*d^3) + (59*a^2*b^2*c^2*p*q*r^2*x)/(15*d^2) - (101*a^3*b*c*p*q*r^2*x)/(30*d) + 2*a^4*q^2*r^2*x + (137*b^4*c^4*q^2*r^2*x)/(150*d^4) - (25*a*b^3*c^3*q^2*r^2*x)/(6*d^3) + (22*a^2*b^2*c^2*q^2*r^2*x)/(3*d^2) - (6*a^3*b*c*q^2*r^2*x)/d + (4*a^3*b*p^2*r^2*x^2)/25 + (283*a^3*b*p*q*r^2*x^2)/300 - (7*b^4*c^3*p*q*r^2*x^2)/(50*d^3) + (19*a*b^3*c^2*p*q*r^2*x^2)/(30*d^2) - (67*a^2*b^2*c*p*q*r^2*x^2)/(60*d) + a^3*b*q^2*r^2*x^2 - (77*b^4*c^3*q^2*r^2*x^2)/(300*d^3) + (13*a*b^3*c^2*q^2*r^2*x^2)/(12*d^2) - (5*a^2*b^2*c*q^2*r^2*x^2)/(3*d) + (4*a^2*b^2*p^2*r^2*x^3)/25 + (257*a^2*b^2*p*q*r^2*x^3)/450 + (16*b^4*c^2*p*q*r^2*x^3)/(225*d^2) - (29*a*b^3*c*p*q*r^2*x^3)/(90*d) + (4*a^2*b^2*q^2*r^2*x^3)/9 + (47*b^4*c^2*q^2*r^2*x^3)/(450*d^2) - (7*a*b^3*c*q^2*r^2*x^3)/(18*d) + (2*a*b^3*p^2*r^2*x^4)/25 + (41*a*b^3*p*q*r^2*x^4)/200 - (9*b^4*c*p*q*r^2*x^4)/(200*d) + (a*b^3*q^2*r^2*x^4)/8 - (9*b^4*c*q^2*r^2*x^4)/(200*d) + (2*b^4*p^2*r^2*x^5)/125 + (4*b^4*p*q*r^2*x^5)/125 + (2*b^4*q^2*r^2*x^5)/125 - (a^5*p^2*r^2*Log[a + b*x]^2)/(5*b) + (2*a^5*p*q*r^2*Log[c + d*x])/b - (2*b^4*c^5*p*q*r^2*Log[c + d*x])/(25*d^5) + (2*a*b^3*c^4*p*q*r^2*Log[c + d*x])/(5*d^4) - (4*a^2*b^2*c^3*p*q*r^2*Log[c + d*x])/(5*d^3) + (4*a^3*b*c^2*p*q*r^2*Log[c + d*x])/(5*d^2) - (2*a^4*c*p*q*r^2*Log[c + d*x])/(5*d) - (137*b^4*c^5*q^2*r^2*Log[c + d*x])/(150*d^5) + (25*a*b^3*c^4*q^2*r^2*Log[c + d*x])/(6*d^4) - (22*a^2*b^2*c^3*q^2*r^2*Log[c + d*x])/(3*d^3) + (6*a^3*b*c^2*q^2*r^2*Log[c + d*x])/d^2 - (2*a^4*c*q^2*r^2*Log[c + d*x])/d - (b^4*c^5*q^2*r^2*Log[c + d*x]^2)/(5*d^5) + (a*b^3*c^4*q^2*r^2*Log[c + d*x]^2)/d^4 - (2*a^2*b^2*c^3*q^2*r^2*Log[c + d*x]^2)/d^3 + (2*a^3*b*c^2*q^2*r^2*Log[c + d*x]^2)/d^2 - (a^4*c*q^2*r^2*Log[c + d*x]^2)/d - (2*a^5*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/b - (2*a^4*p*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/5 - 2*a^4*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - (2*b^4*c^4*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(5*d^4) + (2*a*b^3*c^3*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d^3 - (4*a^2*b^2*c^2*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d^2 + (4*a^3*b*c*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d - (4*a^3*b*p*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/5 - 2*a^3*b*q*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + (b^4*c^3*q*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(5*d^3) - (a*b^3*c^2*q*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d^2 + (2*a^2*b^2*c*q*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d - (4*a^2*b^2*p*r*x^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/5 - (4*a^2*b^2*q*r*x^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/3 - (2*b^4*c^2*q*r*x^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(15*d^2) + (2*a*b^3*c*q*r*x^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(3*d) - (2*a*b^3*p*r*x^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/5 - (a*b^3*q*r*x^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/2 + (b^4*c*q*r*x^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(10*d) - (2*b^4*p*r*x^5*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/25 - (2*b^4*q*r*x^5*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/25 + (2*b^4*c^5*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(5*d^5) - (2*a*b^3*c^4*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d^4 + (4*a^2*b^2*c^3*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d^3 - (4*a^3*b*c^2*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d^2 + (2*a^4*c*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d + a^4*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + 2*a^3*b*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + 2*a^2*b^2*x^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + a*b^3*x^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + (b^4*x^5*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2)/5 + (p*r*Log[a + b*x]*(a*d*(a^4*d^4*(288*p - 137*q) - 60*b^4*c^4*q + 270*a*b^3*c^3*d*q - 470*a^2*b^2*c^2*d^2*q + 385*a^3*b*c*d^3*q)*r - 60*b*c*(b^4*c^4 - 5*a*b^3*c^3*d + 10*a^2*b^2*c^2*d^2 - 10*a^3*b*c*d^3 + 5*a^4*d^4)*q*r*Log[c + d*x] + 60*(b*c - a*d)^5*q*r*Log[(b*(c + d*x))/(b*c - a*d)] + 60*a^5*d^5*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(150*b*d^5) + (2*(b*c - a*d)^5*p*q*r^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*d^5)","B",1
17,1,1853,805,2.0862202,"\int (a+b x)^3 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[(a + b*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2,x]","\frac{2 p q r^2 a^4}{b}-\frac{p^2 r^2 \log ^2(a+b x) a^4}{4 b}+\frac{2 p q r^2 \log (c+d x) a^4}{b}-\frac{2 p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a^4}{b}-\frac{3 c p q r^2 a^3}{d}-\frac{c q^2 r^2 \log ^2(c+d x) a^3}{d}+x \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a^3+\frac{1}{8} p^2 r^2 x a^3+2 q^2 r^2 x a^3+\frac{37}{24} p q r^2 x a^3-\frac{2 c q^2 r^2 \log (c+d x) a^3}{d}-\frac{c p q r^2 \log (c+d x) a^3}{2 d}-\frac{1}{2} p r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a^3-2 q r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a^3+\frac{2 c q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a^3}{d}+\frac{2 b c^2 p q r^2 a^2}{d^2}+\frac{3}{16} b p^2 r^2 x^2 a^2+\frac{3}{4} b q^2 r^2 x^2 a^2+\frac{41}{48} b p q r^2 x^2 a^2+\frac{3 b c^2 q^2 r^2 \log ^2(c+d x) a^2}{2 d^2}+\frac{3}{2} b x^2 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a^2-\frac{9 b c q^2 r^2 x a^2}{2 d}-\frac{35 b c p q r^2 x a^2}{12 d}+\frac{9 b c^2 q^2 r^2 \log (c+d x) a^2}{2 d^2}+\frac{3 b c^2 p q r^2 \log (c+d x) a^2}{4 d^2}-\frac{3}{4} b p r x^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a^2-\frac{3}{2} b q r x^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a^2+\frac{3 b c q r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a^2}{d}-\frac{3 b c^2 q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a^2}{d^2}+\frac{1}{8} b^2 p^2 r^2 x^3 a+\frac{2}{9} b^2 q^2 r^2 x^3 a+\frac{25}{72} b^2 p q r^2 x^3 a-\frac{b^2 c^3 p q r^2 a}{2 d^3}-\frac{5 b^2 c q^2 r^2 x^2 a}{6 d}-\frac{2 b^2 c p q r^2 x^2 a}{3 d}-\frac{b^2 c^3 q^2 r^2 \log ^2(c+d x) a}{d^3}+b^2 x^3 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a+\frac{11 b^2 c^2 q^2 r^2 x a}{3 d^2}+\frac{9 b^2 c^2 p q r^2 x a}{4 d^2}-\frac{11 b^2 c^3 q^2 r^2 \log (c+d x) a}{3 d^3}-\frac{b^2 c^3 p q r^2 \log (c+d x) a}{2 d^3}-\frac{1}{2} b^2 p r x^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a-\frac{2}{3} b^2 q r x^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a+\frac{b^2 c q r x^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a}{d}-\frac{2 b^2 c^2 q r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a}{d^2}+\frac{2 b^2 c^3 q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a}{d^3}+\frac{1}{32} b^3 p^2 r^2 x^4+\frac{1}{32} b^3 q^2 r^2 x^4+\frac{1}{16} b^3 p q r^2 x^4-\frac{7 b^3 c q^2 r^2 x^3}{72 d}-\frac{7 b^3 c p q r^2 x^3}{72 d}+\frac{13 b^3 c^2 q^2 r^2 x^2}{48 d^2}+\frac{3 b^3 c^2 p q r^2 x^2}{16 d^2}+\frac{b^3 c^4 q^2 r^2 \log ^2(c+d x)}{4 d^4}+\frac{1}{4} b^3 x^4 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-\frac{25 b^3 c^3 q^2 r^2 x}{24 d^3}-\frac{5 b^3 c^3 p q r^2 x}{8 d^3}+\frac{25 b^3 c^4 q^2 r^2 \log (c+d x)}{24 d^4}+\frac{b^3 c^4 p q r^2 \log (c+d x)}{8 d^4}-\frac{1}{8} b^3 p r x^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-\frac{1}{8} b^3 q r x^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+\frac{b^3 c q r x^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{6 d}-\frac{b^3 c^2 q r x^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{4 d^2}+\frac{b^3 c^3 q r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 d^3}-\frac{b^3 c^4 q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 d^4}+\frac{p r \log (a+b x) \left(12 a^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) d^4+a \left(12 b^3 q c^3-42 a b^2 d q c^2+52 a^2 b d^2 q c+5 a^3 d^3 (9 p-5 q)\right) r d+12 b c \left(b^3 c^3-4 a b^2 d c^2+6 a^2 b d^2 c-4 a^3 d^3\right) q r \log (c+d x)-12 (b c-a d)^4 q r \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)}{24 b d^4}-\frac{(b c-a d)^4 p q r^2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)}{2 b d^4}","\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{Li}_2\left(\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,"(2*a^4*p*q*r^2)/b - (a*b^2*c^3*p*q*r^2)/(2*d^3) + (2*a^2*b*c^2*p*q*r^2)/d^2 - (3*a^3*c*p*q*r^2)/d + (a^3*p^2*r^2*x)/8 + (37*a^3*p*q*r^2*x)/24 - (5*b^3*c^3*p*q*r^2*x)/(8*d^3) + (9*a*b^2*c^2*p*q*r^2*x)/(4*d^2) - (35*a^2*b*c*p*q*r^2*x)/(12*d) + 2*a^3*q^2*r^2*x - (25*b^3*c^3*q^2*r^2*x)/(24*d^3) + (11*a*b^2*c^2*q^2*r^2*x)/(3*d^2) - (9*a^2*b*c*q^2*r^2*x)/(2*d) + (3*a^2*b*p^2*r^2*x^2)/16 + (41*a^2*b*p*q*r^2*x^2)/48 + (3*b^3*c^2*p*q*r^2*x^2)/(16*d^2) - (2*a*b^2*c*p*q*r^2*x^2)/(3*d) + (3*a^2*b*q^2*r^2*x^2)/4 + (13*b^3*c^2*q^2*r^2*x^2)/(48*d^2) - (5*a*b^2*c*q^2*r^2*x^2)/(6*d) + (a*b^2*p^2*r^2*x^3)/8 + (25*a*b^2*p*q*r^2*x^3)/72 - (7*b^3*c*p*q*r^2*x^3)/(72*d) + (2*a*b^2*q^2*r^2*x^3)/9 - (7*b^3*c*q^2*r^2*x^3)/(72*d) + (b^3*p^2*r^2*x^4)/32 + (b^3*p*q*r^2*x^4)/16 + (b^3*q^2*r^2*x^4)/32 - (a^4*p^2*r^2*Log[a + b*x]^2)/(4*b) + (2*a^4*p*q*r^2*Log[c + d*x])/b + (b^3*c^4*p*q*r^2*Log[c + d*x])/(8*d^4) - (a*b^2*c^3*p*q*r^2*Log[c + d*x])/(2*d^3) + (3*a^2*b*c^2*p*q*r^2*Log[c + d*x])/(4*d^2) - (a^3*c*p*q*r^2*Log[c + d*x])/(2*d) + (25*b^3*c^4*q^2*r^2*Log[c + d*x])/(24*d^4) - (11*a*b^2*c^3*q^2*r^2*Log[c + d*x])/(3*d^3) + (9*a^2*b*c^2*q^2*r^2*Log[c + d*x])/(2*d^2) - (2*a^3*c*q^2*r^2*Log[c + d*x])/d + (b^3*c^4*q^2*r^2*Log[c + d*x]^2)/(4*d^4) - (a*b^2*c^3*q^2*r^2*Log[c + d*x]^2)/d^3 + (3*a^2*b*c^2*q^2*r^2*Log[c + d*x]^2)/(2*d^2) - (a^3*c*q^2*r^2*Log[c + d*x]^2)/d - (2*a^4*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/b - (a^3*p*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/2 - 2*a^3*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + (b^3*c^3*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(2*d^3) - (2*a*b^2*c^2*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d^2 + (3*a^2*b*c*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d - (3*a^2*b*p*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/4 - (3*a^2*b*q*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/2 - (b^3*c^2*q*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(4*d^2) + (a*b^2*c*q*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d - (a*b^2*p*r*x^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/2 - (2*a*b^2*q*r*x^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/3 + (b^3*c*q*r*x^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(6*d) - (b^3*p*r*x^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/8 - (b^3*q*r*x^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/8 - (b^3*c^4*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(2*d^4) + (2*a*b^2*c^3*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d^3 - (3*a^2*b*c^2*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d^2 + (2*a^3*c*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d + a^3*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + (3*a^2*b*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2)/2 + a*b^2*x^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + (b^3*x^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2)/4 + (p*r*Log[a + b*x]*(a*d*(5*a^3*d^3*(9*p - 5*q) + 12*b^3*c^3*q - 42*a*b^2*c^2*d*q + 52*a^2*b*c*d^2*q)*r + 12*b*c*(b^3*c^3 - 4*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 4*a^3*d^3)*q*r*Log[c + d*x] - 12*(b*c - a*d)^4*q*r*Log[(b*(c + d*x))/(b*c - a*d)] + 12*a^4*d^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(24*b*d^4) - ((b*c - a*d)^4*p*q*r^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(2*b*d^4)","B",1
18,1,1211,686,1.2871588,"\int (a+b x)^2 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[(a + b*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2,x]","\frac{1}{54} \left(\frac{108 p q r^2 a^3}{b}-\frac{18 p^2 r^2 \log ^2(a+b x) a^3}{b}+\frac{108 p q r^2 \log (c+d x) a^3}{b}-\frac{108 p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a^3}{b}-\frac{108 c p q r^2 a^2}{d}-\frac{54 c q^2 r^2 \log ^2(c+d x) a^2}{d}+54 x \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a^2+12 p^2 r^2 x a^2+108 q^2 r^2 x a^2+102 p q r^2 x a^2-\frac{108 c q^2 r^2 \log (c+d x) a^2}{d}-\frac{36 c p q r^2 \log (c+d x) a^2}{d}-36 p r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a^2-108 q r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a^2+\frac{108 c q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a^2}{d}+\frac{36 b c^2 p q r^2 a}{d^2}+12 b p^2 r^2 x^2 a+27 b q^2 r^2 x^2 a+39 b p q r^2 x^2 a+\frac{54 b c^2 q^2 r^2 \log ^2(c+d x) a}{d^2}+54 b x^2 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a-\frac{162 b c q^2 r^2 x a}{d}-\frac{126 b c p q r^2 x a}{d}+\frac{162 b c^2 q^2 r^2 \log (c+d x) a}{d^2}+\frac{36 b c^2 p q r^2 \log (c+d x) a}{d^2}-36 b p r x^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a-54 b q r x^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a+\frac{108 b c q r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a}{d}-\frac{108 b c^2 q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) a}{d^2}+4 b^2 p^2 r^2 x^3+4 b^2 q^2 r^2 x^3+8 b^2 p q r^2 x^3-\frac{15 b^2 c q^2 r^2 x^2}{d}-\frac{15 b^2 c p q r^2 x^2}{d}-\frac{18 b^2 c^3 q^2 r^2 \log ^2(c+d x)}{d^3}+18 b^2 x^3 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+\frac{66 b^2 c^2 q^2 r^2 x}{d^2}+\frac{48 b^2 c^2 p q r^2 x}{d^2}-\frac{66 b^2 c^3 q^2 r^2 \log (c+d x)}{d^3}-\frac{12 b^2 c^3 p q r^2 \log (c+d x)}{d^3}-12 b^2 p r x^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-12 b^2 q r x^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+\frac{18 b^2 c q r x^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{d}-\frac{36 b^2 c^2 q r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{d^2}+\frac{36 b^2 c^3 q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{d^3}+\frac{6 p r \log (a+b x) \left(6 a^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) d^3+a \left(-6 b^2 q c^2+15 a b d q c+a^2 d^2 (16 p-11 q)\right) r d-6 b c \left(b^2 c^2-3 a b d c+3 a^2 d^2\right) q r \log (c+d x)+6 (b c-a d)^3 q r \log \left(\frac{b (c+d x)}{b c-a d}\right)\right)}{b d^3}+\frac{36 (b c-a d)^3 p q r^2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)}{b d^3}\right)","\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 p q r^2 (b c-a d)^3 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)}{3 b d^3}-\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{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{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{5 q^2 r^2 x (b c-a d)^2}{9 d^2}+\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,"((108*a^3*p*q*r^2)/b + (36*a*b*c^2*p*q*r^2)/d^2 - (108*a^2*c*p*q*r^2)/d + 12*a^2*p^2*r^2*x + 102*a^2*p*q*r^2*x + (48*b^2*c^2*p*q*r^2*x)/d^2 - (126*a*b*c*p*q*r^2*x)/d + 108*a^2*q^2*r^2*x + (66*b^2*c^2*q^2*r^2*x)/d^2 - (162*a*b*c*q^2*r^2*x)/d + 12*a*b*p^2*r^2*x^2 + 39*a*b*p*q*r^2*x^2 - (15*b^2*c*p*q*r^2*x^2)/d + 27*a*b*q^2*r^2*x^2 - (15*b^2*c*q^2*r^2*x^2)/d + 4*b^2*p^2*r^2*x^3 + 8*b^2*p*q*r^2*x^3 + 4*b^2*q^2*r^2*x^3 - (18*a^3*p^2*r^2*Log[a + b*x]^2)/b + (108*a^3*p*q*r^2*Log[c + d*x])/b - (12*b^2*c^3*p*q*r^2*Log[c + d*x])/d^3 + (36*a*b*c^2*p*q*r^2*Log[c + d*x])/d^2 - (36*a^2*c*p*q*r^2*Log[c + d*x])/d - (66*b^2*c^3*q^2*r^2*Log[c + d*x])/d^3 + (162*a*b*c^2*q^2*r^2*Log[c + d*x])/d^2 - (108*a^2*c*q^2*r^2*Log[c + d*x])/d - (18*b^2*c^3*q^2*r^2*Log[c + d*x]^2)/d^3 + (54*a*b*c^2*q^2*r^2*Log[c + d*x]^2)/d^2 - (54*a^2*c*q^2*r^2*Log[c + d*x]^2)/d - (108*a^3*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/b - 36*a^2*p*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 108*a^2*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - (36*b^2*c^2*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d^2 + (108*a*b*c*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d - 36*a*b*p*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 54*a*b*q*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + (18*b^2*c*q*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d - 12*b^2*p*r*x^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 12*b^2*q*r*x^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + (36*b^2*c^3*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d^3 - (108*a*b*c^2*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d^2 + (108*a^2*c*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/d + 54*a^2*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + 54*a*b*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + 18*b^2*x^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + (6*p*r*Log[a + b*x]*(a*d*(a^2*d^2*(16*p - 11*q) - 6*b^2*c^2*q + 15*a*b*c*d*q)*r - 6*b*c*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2)*q*r*Log[c + d*x] + 6*(b*c - a*d)^3*q*r*Log[(b*(c + d*x))/(b*c - a*d)] + 6*a^3*d^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]))/(b*d^3) + (36*(b*c - a*d)^3*p*q*r^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*d^3))/54","A",1
19,1,781,540,0.6772228,"\int (a+b x) \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[(a + b*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2,x]","\frac{-8 a^2 d^2 p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-2 a^2 d^2 p^2 r^2 \log ^2(a+b x)+8 a^2 d^2 p q r^2 \log (c+d x)+8 a^2 d^2 p q r^2-4 b^2 c^2 q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+2 b^2 d^2 x^2 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-2 b^2 d^2 p r x^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-2 b^2 d^2 q r x^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+4 b^2 c d q r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+4 a b d^2 x \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-4 a b d^2 p r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-8 a b d^2 q r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+8 a b c d q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+2 p r \log (a+b x) \left(a d \left(2 a d \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+3 a d r (p-q)+2 b c q r\right)-2 q r (b c-a d)^2 \log \left(\frac{b (c+d x)}{b c-a d}\right)+2 b c q r (b c-2 a d) \log (c+d x)\right)-4 p q r^2 (b c-a d)^2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)-4 a b c d p q r^2 \log (c+d x)-4 a b c d p q r^2-4 a b c d q^2 r^2 \log ^2(c+d x)-8 a b c d q^2 r^2 \log (c+d x)+2 a b d^2 p^2 r^2 x+10 a b d^2 p q r^2 x+8 a b d^2 q^2 r^2 x+2 b^2 c^2 p q r^2 \log (c+d x)+2 b^2 c^2 q^2 r^2 \log ^2(c+d x)+6 b^2 c^2 q^2 r^2 \log (c+d x)-6 b^2 c d p q r^2 x-6 b^2 c d q^2 r^2 x+b^2 d^2 p^2 r^2 x^2+2 b^2 d^2 p q r^2 x^2+b^2 d^2 q^2 r^2 x^2}{4 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 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\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,"(-4*a*b*c*d*p*q*r^2 + 8*a^2*d^2*p*q*r^2 + 2*a*b*d^2*p^2*r^2*x - 6*b^2*c*d*p*q*r^2*x + 10*a*b*d^2*p*q*r^2*x - 6*b^2*c*d*q^2*r^2*x + 8*a*b*d^2*q^2*r^2*x + b^2*d^2*p^2*r^2*x^2 + 2*b^2*d^2*p*q*r^2*x^2 + b^2*d^2*q^2*r^2*x^2 - 2*a^2*d^2*p^2*r^2*Log[a + b*x]^2 + 2*b^2*c^2*p*q*r^2*Log[c + d*x] - 4*a*b*c*d*p*q*r^2*Log[c + d*x] + 8*a^2*d^2*p*q*r^2*Log[c + d*x] + 6*b^2*c^2*q^2*r^2*Log[c + d*x] - 8*a*b*c*d*q^2*r^2*Log[c + d*x] + 2*b^2*c^2*q^2*r^2*Log[c + d*x]^2 - 4*a*b*c*d*q^2*r^2*Log[c + d*x]^2 - 8*a^2*d^2*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 4*a*b*d^2*p*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 4*b^2*c*d*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 8*a*b*d^2*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 2*b^2*d^2*p*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 2*b^2*d^2*q*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 4*b^2*c^2*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 8*a*b*c*d*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 4*a*b*d^2*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + 2*b^2*d^2*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + 2*p*r*Log[a + b*x]*(2*b*c*(b*c - 2*a*d)*q*r*Log[c + d*x] - 2*(b*c - a*d)^2*q*r*Log[(b*(c + d*x))/(b*c - a*d)] + a*d*(3*a*d*(p - q)*r + 2*b*c*q*r + 2*a*d*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])) - 4*(b*c - a*d)^2*p*q*r^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(4*b*d^2)","A",1
20,1,460,431,0.2032554,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{a+b x} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(a + b*x),x]","\frac{6 q r \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right) \left(\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-p r \log (a+b x)\right)-3 p r \log ^2(a+b x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+3 \log (a+b x) \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-6 q r \log (a+b x) \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+6 q r \log (c+d x) \log \left(\frac{d (a+b x)}{a d-b c}\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+6 p q r^2 \text{Li}_3\left(\frac{d (a+b x)}{a d-b c}\right)-6 p q r^2 \log (a+b x) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)+6 p q r^2 \log ^2(a+b x) \log (c+d x)-3 p q r^2 \log ^2(a+b x) \log \left(\frac{b (c+d x)}{b c-a d}\right)-6 p q r^2 \log (a+b x) \log (c+d x) \log \left(\frac{d (a+b x)}{a d-b c}\right)-6 q^2 r^2 \text{Li}_3\left(\frac{b (c+d x)}{b c-a d}\right)+3 q^2 r^2 \log (a+b x) \log ^2(c+d x)-3 q^2 r^2 \log ^2(c+d x) \log \left(\frac{d (a+b x)}{a d-b c}\right)+p^2 r^2 \log ^3(a+b x)}{3 b}","-\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(\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}+8 \left(\frac{q r \text{Li}_2\left(\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)\right)+\frac{2 p q r^2 \text{Li}_3\left(-\frac{d (a+b x)}{b c-a d}\right)}{b}-\frac{2 q r \text{Li}_2\left(-\frac{d (a+b x)}{b c-a d}\right) \log \left((a+b x)^{p r}\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{2 q^2 r^2 \text{Li}_3\left(\frac{b (c+d x)}{b c-a d}\right)}{b}+\frac{2 q r \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right) \log \left((c+d x)^{q r}\right)}{b}+\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,"(p^2*r^2*Log[a + b*x]^3 + 6*p*q*r^2*Log[a + b*x]^2*Log[c + d*x] - 6*p*q*r^2*Log[a + b*x]*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x] + 3*q^2*r^2*Log[a + b*x]*Log[c + d*x]^2 - 3*q^2*r^2*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x]^2 - 3*p*q*r^2*Log[a + b*x]^2*Log[(b*(c + d*x))/(b*c - a*d)] - 3*p*r*Log[a + b*x]^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 6*q*r*Log[a + b*x]*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 6*q*r*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 3*Log[a + b*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 - 6*p*q*r^2*Log[a + b*x]*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 6*q*r*(-(p*r*Log[a + b*x]) + Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 6*p*q*r^2*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)] - 6*q^2*r^2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])/(3*b)","A",1
21,1,411,465,0.7101526,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^2} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(a + b*x)^2,x]","\frac{-b c \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+a d \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-2 b c p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+2 a d p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-2 a d q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-2 b d q r x \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+2 d q r (a+b x) \log (a+b x) \left(\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-r (p+q) \log \left(\frac{b (c+d x)}{b c-a d}\right)+p r \log (c+d x)+p r\right)-2 d q r^2 (p+q) (a+b x) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)-d p q r^2 (a+b x) \log ^2(a+b x)-2 a d p q r^2 \log (c+d x)+a d q^2 r^2 \log ^2(c+d x)+2 a d p^2 r^2-2 b d p q r^2 x \log (c+d x)+b d q^2 r^2 x \log ^2(c+d x)-2 b c p^2 r^2}{b (a+b x) (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{2 d p q r^2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)}{b (b c-a d)}-\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{2 d q^2 r^2 \text{Li}_2\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*b*c*p^2*r^2 + 2*a*d*p^2*r^2 - d*p*q*r^2*(a + b*x)*Log[a + b*x]^2 - 2*a*d*p*q*r^2*Log[c + d*x] - 2*b*d*p*q*r^2*x*Log[c + d*x] + a*d*q^2*r^2*Log[c + d*x]^2 + b*d*q^2*r^2*x*Log[c + d*x]^2 - 2*b*c*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 2*a*d*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 2*a*d*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 2*b*d*q*r*x*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - b*c*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + a*d*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + 2*d*q*r*(a + b*x)*Log[a + b*x]*(p*r + p*r*Log[c + d*x] - (p + q)*r*Log[(b*(c + d*x))/(b*c - a*d)] + Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]) - 2*d*q*(p + q)*r^2*(a + b*x)*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(b*c - a*d)*(a + b*x))","A",1
22,1,872,632,1.328555,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^3} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(a + b*x)^3,x]","-\frac{c^2 p^2 r^2 b^2+2 d^2 q^2 r^2 x^2 \log ^2(c+d x) b^2+2 c^2 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b^2+6 c d p q r^2 x b^2+4 d^2 q^2 r^2 x^2 \log (c+d x) b^2-2 d^2 p q r^2 x^2 \log (c+d x) b^2+2 c^2 p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b^2+4 c d q r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b^2-4 d^2 q r x^2 \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b^2-2 a c d p^2 r^2 b+6 a c d p q r^2 b+4 a d^2 q^2 r^2 x \log ^2(c+d x) b-4 a c d \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b-6 a d^2 p q r^2 x b+8 a d^2 q^2 r^2 x \log (c+d x) b-4 a d^2 p q r^2 x \log (c+d x) b-4 a c d p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b+4 a c d q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b-4 a d^2 q r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b-8 a d^2 q r x \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b+a^2 d^2 p^2 r^2-6 a^2 d^2 p q r^2-2 d^2 p q r^2 (a+b x)^2 \log ^2(a+b x)+2 a^2 d^2 q^2 r^2 \log ^2(c+d x)+2 a^2 d^2 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+4 a^2 d^2 q^2 r^2 \log (c+d x)-2 a^2 d^2 p q r^2 \log (c+d x)-2 d^2 q r (a+b x)^2 \log (a+b x) \left(-p r+2 q r-2 p \log (c+d x) r+2 (p+q) \log \left(\frac{b (c+d x)}{b c-a d}\right) r-2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)+2 a^2 d^2 p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-4 a^2 d^2 q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-4 a^2 d^2 q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-4 d^2 q (p+q) r^2 (a+b x)^2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)}{4 b (b c-a d)^2 (a+b x)^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 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\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 \text{Li}_2\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,"-1/4*(b^2*c^2*p^2*r^2 - 2*a*b*c*d*p^2*r^2 + a^2*d^2*p^2*r^2 + 6*a*b*c*d*p*q*r^2 - 6*a^2*d^2*p*q*r^2 + 6*b^2*c*d*p*q*r^2*x - 6*a*b*d^2*p*q*r^2*x - 2*d^2*p*q*r^2*(a + b*x)^2*Log[a + b*x]^2 - 2*a^2*d^2*p*q*r^2*Log[c + d*x] + 4*a^2*d^2*q^2*r^2*Log[c + d*x] - 4*a*b*d^2*p*q*r^2*x*Log[c + d*x] + 8*a*b*d^2*q^2*r^2*x*Log[c + d*x] - 2*b^2*d^2*p*q*r^2*x^2*Log[c + d*x] + 4*b^2*d^2*q^2*r^2*x^2*Log[c + d*x] + 2*a^2*d^2*q^2*r^2*Log[c + d*x]^2 + 4*a*b*d^2*q^2*r^2*x*Log[c + d*x]^2 + 2*b^2*d^2*q^2*r^2*x^2*Log[c + d*x]^2 - 2*d^2*q*r*(a + b*x)^2*Log[a + b*x]*(-(p*r) + 2*q*r - 2*p*r*Log[c + d*x] + 2*(p + q)*r*Log[(b*(c + d*x))/(b*c - a*d)] - 2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]) + 2*b^2*c^2*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 4*a*b*c*d*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 2*a^2*d^2*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 4*a*b*c*d*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 4*a^2*d^2*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 4*b^2*c*d*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 4*a*b*d^2*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 4*a^2*d^2*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 8*a*b*d^2*q*r*x*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 4*b^2*d^2*q*r*x^2*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 2*b^2*c^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 - 4*a*b*c*d*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + 2*a^2*d^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 - 4*d^2*q*(p + q)*r^2*(a + b*x)^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(b*c - a*d)^2*(a + b*x)^2)","A",1
23,1,1407,764,1.9450195,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^4} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(a + b*x)^4,x]","-\frac{4 c^3 p^2 r^2 b^3+18 c d^2 q^2 r^2 x^2 b^3-48 c d^2 p q r^2 x^2 b^3-18 d^3 q^2 r^2 x^3 \log ^2(c+d x) b^3+18 c^3 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b^3+15 c^2 d p q r^2 x b^3-54 d^3 q^2 r^2 x^3 \log (c+d x) b^3+12 d^3 p q r^2 x^3 \log (c+d x) b^3-36 c d^2 q r x^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b^3+12 c^3 p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b^3+18 c^2 d q r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b^3+36 d^3 q r x^3 \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b^3-12 a c^2 d p^2 r^2 b^2+15 a c^2 d p q r^2 b^2-18 a d^3 q^2 r^2 x^2 b^2+48 a d^3 p q r^2 x^2 b^2-54 a d^3 q^2 r^2 x^2 \log ^2(c+d x) b^2-54 a c^2 d \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b^2+36 a c d^2 q^2 r^2 x b^2-126 a c d^2 p q r^2 x b^2-162 a d^3 q^2 r^2 x^2 \log (c+d x) b^2+36 a d^3 p q r^2 x^2 \log (c+d x) b^2+36 a d^3 q r x^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b^2-36 a c^2 d p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b^2+18 a c^2 d q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b^2-108 a c d^2 q r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b^2+108 a d^3 q r x^2 \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b^2+12 a^2 c d^2 p^2 r^2 b+18 a^2 c d^2 q^2 r^2 b-78 a^2 c d^2 p q r^2 b-54 a^2 d^3 q^2 r^2 x \log ^2(c+d x) b+54 a^2 c d^2 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b-36 a^2 d^3 q^2 r^2 x b+111 a^2 d^3 p q r^2 x b-162 a^2 d^3 q^2 r^2 x \log (c+d x) b+36 a^2 d^3 p q r^2 x \log (c+d x) b+36 a^2 c d^2 p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b-72 a^2 c d^2 q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b+90 a^2 d^3 q r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b+108 a^2 d^3 q r x \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) b-4 a^3 d^3 p^2 r^2-18 a^3 d^3 q^2 r^2+63 a^3 d^3 p q r^2+18 d^3 p q r^2 (a+b x)^3 \log ^2(a+b x)-18 a^3 d^3 q^2 r^2 \log ^2(c+d x)-18 a^3 d^3 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-54 a^3 d^3 q^2 r^2 \log (c+d x)+12 a^3 d^3 p q r^2 \log (c+d x)-12 a^3 d^3 p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+54 a^3 d^3 q r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+36 a^3 d^3 q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-6 d^3 q r (a+b x)^3 \log (a+b x) \left(2 p r-9 q r+6 p \log (c+d x) r-6 (p+q) \log \left(\frac{b (c+d x)}{b c-a d}\right) r+6 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)+36 d^3 q (p+q) r^2 (a+b x)^3 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)}{54 b (b c-a d)^3 (a+b x)^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^3 p q r^2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)}{3 b (b c-a d)^3}-\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{2 d^3 q^2 r^2 \text{Li}_2\left(-\frac{d (a+b x)}{b c-a d}\right)}{3 b (b c-a d)^3}+\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{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^2 q^2 r^2}{3 b (a+b x) (b c-a d)^2}-\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,"-1/54*(4*b^3*c^3*p^2*r^2 - 12*a*b^2*c^2*d*p^2*r^2 + 12*a^2*b*c*d^2*p^2*r^2 - 4*a^3*d^3*p^2*r^2 + 15*a*b^2*c^2*d*p*q*r^2 - 78*a^2*b*c*d^2*p*q*r^2 + 63*a^3*d^3*p*q*r^2 + 18*a^2*b*c*d^2*q^2*r^2 - 18*a^3*d^3*q^2*r^2 + 15*b^3*c^2*d*p*q*r^2*x - 126*a*b^2*c*d^2*p*q*r^2*x + 111*a^2*b*d^3*p*q*r^2*x + 36*a*b^2*c*d^2*q^2*r^2*x - 36*a^2*b*d^3*q^2*r^2*x - 48*b^3*c*d^2*p*q*r^2*x^2 + 48*a*b^2*d^3*p*q*r^2*x^2 + 18*b^3*c*d^2*q^2*r^2*x^2 - 18*a*b^2*d^3*q^2*r^2*x^2 + 18*d^3*p*q*r^2*(a + b*x)^3*Log[a + b*x]^2 + 12*a^3*d^3*p*q*r^2*Log[c + d*x] - 54*a^3*d^3*q^2*r^2*Log[c + d*x] + 36*a^2*b*d^3*p*q*r^2*x*Log[c + d*x] - 162*a^2*b*d^3*q^2*r^2*x*Log[c + d*x] + 36*a*b^2*d^3*p*q*r^2*x^2*Log[c + d*x] - 162*a*b^2*d^3*q^2*r^2*x^2*Log[c + d*x] + 12*b^3*d^3*p*q*r^2*x^3*Log[c + d*x] - 54*b^3*d^3*q^2*r^2*x^3*Log[c + d*x] - 18*a^3*d^3*q^2*r^2*Log[c + d*x]^2 - 54*a^2*b*d^3*q^2*r^2*x*Log[c + d*x]^2 - 54*a*b^2*d^3*q^2*r^2*x^2*Log[c + d*x]^2 - 18*b^3*d^3*q^2*r^2*x^3*Log[c + d*x]^2 + 12*b^3*c^3*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 36*a*b^2*c^2*d*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 36*a^2*b*c*d^2*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 12*a^3*d^3*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 18*a*b^2*c^2*d*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 72*a^2*b*c*d^2*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 54*a^3*d^3*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 18*b^3*c^2*d*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 108*a*b^2*c*d^2*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 90*a^2*b*d^3*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 36*b^3*c*d^2*q*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 36*a*b^2*d^3*q*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 36*a^3*d^3*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 108*a^2*b*d^3*q*r*x*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 108*a*b^2*d^3*q*r*x^2*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 36*b^3*d^3*q*r*x^3*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 18*b^3*c^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 - 54*a*b^2*c^2*d*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + 54*a^2*b*c*d^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 - 18*a^3*d^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 - 6*d^3*q*r*(a + b*x)^3*Log[a + b*x]*(2*p*r - 9*q*r + 6*p*r*Log[c + d*x] - 6*(p + q)*r*Log[(b*(c + d*x))/(b*c - a*d)] + 6*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]) + 36*d^3*q*(p + q)*r^2*(a + b*x)^3*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(b*c - a*d)^3*(a + b*x)^3)","A",1
24,1,2003,884,3.0013697,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(a+b x)^5} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(a + b*x)^5,x]","\text{Result too large to show}","\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{Li}_2\left(-\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{Li}_2\left(\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,"(-9*b^4*c^4*p^2*r^2 + 36*a*b^3*c^3*d*p^2*r^2 - 54*a^2*b^2*c^2*d^2*p^2*r^2 + 36*a^3*b*c*d^3*p^2*r^2 - 9*a^4*d^4*p^2*r^2 - 28*a*b^3*c^3*d*p*q*r^2 + 138*a^2*b^2*c^2*d^2*p*q*r^2 - 372*a^3*b*c*d^3*p*q*r^2 + 262*a^4*d^4*p*q*r^2 - 24*a^2*b^2*c^2*d^2*q^2*r^2 + 168*a^3*b*c*d^3*q^2*r^2 - 144*a^4*d^4*q^2*r^2 - 28*b^4*c^3*d*p*q*r^2*x + 192*a*b^3*c^2*d^2*p*q*r^2*x - 840*a^2*b^2*c*d^3*p*q*r^2*x + 676*a^3*b*d^4*p*q*r^2*x - 48*a*b^3*c^2*d^2*q^2*r^2*x + 456*a^2*b^2*c*d^3*q^2*r^2*x - 408*a^3*b*d^4*q^2*r^2*x + 54*b^4*c^2*d^2*p*q*r^2*x^2 - 648*a*b^3*c*d^3*p*q*r^2*x^2 + 594*a^2*b^2*d^4*p*q*r^2*x^2 - 24*b^4*c^2*d^2*q^2*r^2*x^2 + 408*a*b^3*c*d^3*q^2*r^2*x^2 - 384*a^2*b^2*d^4*q^2*r^2*x^2 - 180*b^4*c*d^3*p*q*r^2*x^3 + 180*a*b^3*d^4*p*q*r^2*x^3 + 120*b^4*c*d^3*q^2*r^2*x^3 - 120*a*b^3*d^4*q^2*r^2*x^3 + 72*d^4*p*q*r^2*(a + b*x)^4*Log[a + b*x]^2 + 36*a^4*d^4*p*q*r^2*Log[c + d*x] - 264*a^4*d^4*q^2*r^2*Log[c + d*x] + 144*a^3*b*d^4*p*q*r^2*x*Log[c + d*x] - 1056*a^3*b*d^4*q^2*r^2*x*Log[c + d*x] + 216*a^2*b^2*d^4*p*q*r^2*x^2*Log[c + d*x] - 1584*a^2*b^2*d^4*q^2*r^2*x^2*Log[c + d*x] + 144*a*b^3*d^4*p*q*r^2*x^3*Log[c + d*x] - 1056*a*b^3*d^4*q^2*r^2*x^3*Log[c + d*x] + 36*b^4*d^4*p*q*r^2*x^4*Log[c + d*x] - 264*b^4*d^4*q^2*r^2*x^4*Log[c + d*x] - 72*a^4*d^4*q^2*r^2*Log[c + d*x]^2 - 288*a^3*b*d^4*q^2*r^2*x*Log[c + d*x]^2 - 432*a^2*b^2*d^4*q^2*r^2*x^2*Log[c + d*x]^2 - 288*a*b^3*d^4*q^2*r^2*x^3*Log[c + d*x]^2 - 72*b^4*d^4*q^2*r^2*x^4*Log[c + d*x]^2 + 12*d^4*q*r*(a + b*x)^4*Log[a + b*x]*(-3*p*r + 22*q*r - 12*p*r*Log[c + d*x] + 12*(p + q)*r*Log[(b*(c + d*x))/(b*c - a*d)] - 12*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]) - 36*b^4*c^4*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 144*a*b^3*c^3*d*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 216*a^2*b^2*c^2*d^2*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 144*a^3*b*c*d^3*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 36*a^4*d^4*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 48*a*b^3*c^3*d*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 216*a^2*b^2*c^2*d^2*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 432*a^3*b*c*d^3*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 264*a^4*d^4*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 48*b^4*c^3*d*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 288*a*b^3*c^2*d^2*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 864*a^2*b^2*c*d^3*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 624*a^3*b*d^4*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 72*b^4*c^2*d^2*q*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 576*a*b^3*c*d^3*q*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 504*a^2*b^2*d^4*q*r*x^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 144*b^4*c*d^3*q*r*x^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 144*a*b^3*d^4*q*r*x^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 144*a^4*d^4*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 576*a^3*b*d^4*q*r*x*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 864*a^2*b^2*d^4*q*r*x^2*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 576*a*b^3*d^4*q*r*x^3*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 144*b^4*d^4*q*r*x^4*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 72*b^4*c^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + 288*a*b^3*c^3*d*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 - 432*a^2*b^2*c^2*d^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + 288*a^3*b*c*d^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 - 72*a^4*d^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + 144*d^4*q*(p + q)*r^2*(a + b*x)^4*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(288*b*(b*c - a*d)^4*(a + b*x)^4)","B",1
25,1,275,334,0.3324131,"\int (g+h x)^4 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[(g + h*x)^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","\frac{-\frac{p r \left(15 b^4 (g+h x)^4 (b g-a h)+20 b^3 (g+h x)^3 (b g-a h)^2+30 b^2 (g+h x)^2 (b g-a h)^3+60 b h x (b g-a h)^4+60 (b g-a h)^5 \log (a+b x)+12 b^5 (g+h x)^5\right)}{60 b^5}+(g+h x)^5 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-\frac{q r \left(15 d^4 (g+h x)^4 (d g-c h)+20 d^3 (g+h x)^3 (d g-c h)^2+30 d^2 (g+h x)^2 (d g-c h)^3+60 d h x (d g-c h)^4+60 (d g-c h)^5 \log (c+d x)+12 d^5 (g+h x)^5\right)}{60 d^5}}{5 h}","-\frac{p r (b g-a h)^5 \log (a+b x)}{5 b^5 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{(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 (d g-c h)^5 \log (c+d x)}{5 d^5 h}-\frac{q r x (d g-c h)^4}{5 d^4}-\frac{q r (g+h x)^2 (d g-c h)^3}{10 d^3 h}-\frac{q r (g+h x)^3 (d g-c h)^2}{15 d^2 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,"(-1/60*(p*r*(60*b*h*(b*g - a*h)^4*x + 30*b^2*(b*g - a*h)^3*(g + h*x)^2 + 20*b^3*(b*g - a*h)^2*(g + h*x)^3 + 15*b^4*(b*g - a*h)*(g + h*x)^4 + 12*b^5*(g + h*x)^5 + 60*(b*g - a*h)^5*Log[a + b*x]))/b^5 - (q*r*(60*d*h*(d*g - c*h)^4*x + 30*d^2*(d*g - c*h)^3*(g + h*x)^2 + 20*d^3*(d*g - c*h)^2*(g + h*x)^3 + 15*d^4*(d*g - c*h)*(g + h*x)^4 + 12*d^5*(g + h*x)^5 + 60*(d*g - c*h)^5*Log[c + d*x]))/(60*d^5) + (g + h*x)^5*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(5*h)","A",1
26,1,231,276,0.2922075,"\int (g+h x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[(g + h*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","\frac{\frac{1}{12} r \left(-\frac{p \left(4 b^3 (g+h x)^3 (b g-a h)+6 b^2 (g+h x)^2 (b g-a h)^2+12 b h x (b g-a h)^3+12 (b g-a h)^4 \log (a+b x)+3 b^4 (g+h x)^4\right)}{b^4}-\frac{q \left(4 d^3 (g+h x)^3 (d g-c h)+6 d^2 (g+h x)^2 (d g-c h)^2+12 d h x (d g-c h)^3+12 (d g-c h)^4 \log (c+d x)+3 d^4 (g+h x)^4\right)}{d^4}\right)+(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 (b g-a h)^4 \log (a+b x)}{4 b^4 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{(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 (d g-c h)^4 \log (c+d x)}{4 d^4 h}-\frac{q r x (d g-c h)^3}{4 d^3}-\frac{q r (g+h x)^2 (d g-c h)^2}{8 d^2 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,"((r*(-((p*(12*b*h*(b*g - a*h)^3*x + 6*b^2*(b*g - a*h)^2*(g + h*x)^2 + 4*b^3*(b*g - a*h)*(g + h*x)^3 + 3*b^4*(g + h*x)^4 + 12*(b*g - a*h)^4*Log[a + b*x]))/b^4) - (q*(12*d*h*(d*g - c*h)^3*x + 6*d^2*(d*g - c*h)^2*(g + h*x)^2 + 4*d^3*(d*g - c*h)*(g + h*x)^3 + 3*d^4*(g + h*x)^4 + 12*(d*g - c*h)^4*Log[c + d*x]))/d^4))/12 + (g + h*x)^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(4*h)","A",1
27,1,209,218,0.2444652,"\int (g+h x)^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[(g + h*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","\frac{(g+h x)^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-\frac{r \left(b \left(6 a^2 d^3 h^3 p x-3 a b d^3 h p \left(g^2+6 g h x+h^2 x^2\right)+b^2 d \left(6 c^2 h^3 q x-3 c d h q \left(g^2+6 g h x+h^2 x^2\right)+d^2 (p+q) \left(5 g^3+18 g^2 h x+9 g h^2 x^2+2 h^3 x^3\right)\right)+6 b^2 q (d g-c h)^3 \log (c+d x)\right)+6 d^3 p (b g-a h)^3 \log (a+b x)\right)}{6 b^3 d^3}}{3 h}","-\frac{p r (b g-a h)^3 \log (a+b x)}{3 b^3 h}-\frac{p r x (b g-a h)^2}{3 b^2}+\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 (d g-c h)^3 \log (c+d x)}{3 d^3 h}-\frac{q r x (d g-c h)^2}{3 d^2}-\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,"(-1/6*(r*(6*d^3*(b*g - a*h)^3*p*Log[a + b*x] + b*(6*a^2*d^3*h^3*p*x - 3*a*b*d^3*h*p*(g^2 + 6*g*h*x + h^2*x^2) + b^2*d*(6*c^2*h^3*q*x - 3*c*d*h*q*(g^2 + 6*g*h*x + h^2*x^2) + d^2*(p + q)*(5*g^3 + 18*g^2*h*x + 9*g*h^2*x^2 + 2*h^3*x^3)) + 6*b^2*(d*g - c*h)^3*q*Log[c + d*x])))/(b^3*d^3) + (g + h*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/(3*h)","A",1
28,1,120,160,0.2064587,"\int (g+h x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[(g + h*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","-\frac{b \left(d x \left(r (-2 a d h p-2 b c h q+b d (p+q) (4 g+h x))-2 b d (2 g+h x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)+2 b c q r (c h-2 d g) \log (c+d x)\right)+2 a d^2 p r (a h-2 b g) \log (a+b x)}{4 b^2 d^2}","-\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,"-1/4*(2*a*d^2*(-2*b*g + a*h)*p*r*Log[a + b*x] + b*(2*b*c*(-2*d*g + c*h)*q*r*Log[c + d*x] + d*x*(r*(-2*a*d*h*p - 2*b*c*h*q + b*d*(p + q)*(4*g + h*x)) - 2*b*d*(2*g + h*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])))/(b^2*d^2)","A",1
29,1,57,61,0.0699245,"\int \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r],x]","x \left(\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-r (p+q)\right)+\frac{a p r \log (a+b x)}{b}+\frac{c q r \log (c+d x)}{d}","\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,"(a*p*r*Log[a + b*x])/b + (c*q*r*Log[c + d*x])/d + x*(-((p + q)*r) + Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])","A",1
30,1,163,148,0.0961888,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{g+h x} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(g + h*x),x]","\frac{\log (g+h x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+p r \text{Li}_2\left(\frac{h (a+b x)}{a h-b g}\right)-p r \log (a+b x) \log (g+h x)+p r \log (a+b x) \log \left(\frac{b (g+h x)}{b g-a h}\right)+q r \text{Li}_2\left(\frac{h (c+d x)}{c h-d g}\right)-q r \log (c+d x) \log (g+h x)+q r \log (c+d x) \log \left(\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 \text{Li}_2\left(\frac{b (g+h x)}{b g-a h}\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 \text{Li}_2\left(\frac{d (g+h x)}{d g-c 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[a + b*x]*Log[g + h*x]) - q*r*Log[c + d*x]*Log[g + h*x] + Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[g + h*x] + p*r*Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)] + q*r*Log[c + d*x]*Log[(d*(g + h*x))/(d*g - c*h)] + p*r*PolyLog[2, (h*(a + b*x))/(-(b*g) + a*h)] + q*r*PolyLog[2, (h*(c + d*x))/(-(d*g) + c*h)])/h","A",1
31,1,93,128,0.1891394,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g+h x)^2} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(g + h*x)^2,x]","\frac{-\frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{g+h x}+\frac{b p r (\log (a+b x)-\log (g+h x))}{b g-a h}+\frac{d q r (\log (c+d x)-\log (g+h x))}{d g-c h}}{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,"(-(Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(g + h*x)) + (b*p*r*(Log[a + b*x] - Log[g + h*x]))/(b*g - a*h) + (d*q*r*(Log[c + d*x] - Log[g + h*x]))/(d*g - c*h))/h","A",1
32,1,206,202,0.5296131,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g+h x)^3} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(g + h*x)^3,x]","\frac{\frac{r (g+h x) \left((b c-a d) (b g-a h) (d g-c h) (b d g (p+q)-h (a d q+b c p))-(g+h x) \left(d^2 q (a d-b c) (b g-a h)^2 (\log (c+d x)-\log (g+h x))-b^2 p (b c-a d) (d g-c h)^2 (\log (a+b x)-\log (g+h x))\right)\right)}{(b c-a d) (b g-a h)^2 (d g-c h)^2}-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{2 h (g+h x)^2}","\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,"(-Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + (r*(g + h*x)*((b*c - a*d)*(b*g - a*h)*(d*g - c*h)*(b*d*g*(p + q) - h*(b*c*p + a*d*q)) - (g + h*x)*(-(b^2*(b*c - a*d)*(d*g - c*h)^2*p*(Log[a + b*x] - Log[g + h*x])) + d^2*(-(b*c) + a*d)*(b*g - a*h)^2*q*(Log[c + d*x] - Log[g + h*x]))))/((b*c - a*d)*(b*g - a*h)^2*(d*g - c*h)^2))/(2*h*(g + h*x)^2)","A",1
33,1,254,260,0.7627787,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g+h x)^4} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(g + h*x)^4,x]","\frac{\frac{r (g+h x) \left((b g-a h)^2 (d g-c h)^2 (b d g (p+q)-h (a d q+b c p))-(g+h x) \left((b g-a h) (d g-c h) \left(-2 a^2 d^2 h^2 q+4 a b d^2 g h q-2 b^2 \left(c^2 h^2 p-2 c d g h p+d^2 g^2 (p+q)\right)\right)-2 (g+h x) \left(b^3 p (d g-c h)^3 (\log (a+b x)-\log (g+h x))+d^3 q (b g-a h)^3 (\log (c+d x)-\log (g+h x))\right)\right)\right)}{(b g-a h)^3 (d g-c h)^3}-2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{6 h (g+h x)^3}","\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{b^2 p r}{3 h (g+h x) (b g-a h)^2}-\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^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^2 q r}{3 h (g+h x) (d g-c h)^2}+\frac{d q r}{6 h (g+h x)^2 (d g-c h)}",1,"(-2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + (r*(g + h*x)*((b*g - a*h)^2*(d*g - c*h)^2*(b*d*g*(p + q) - h*(b*c*p + a*d*q)) - (g + h*x)*((b*g - a*h)*(d*g - c*h)*(4*a*b*d^2*g*h*q - 2*a^2*d^2*h^2*q - 2*b^2*(-2*c*d*g*h*p + c^2*h^2*p + d^2*g^2*(p + q))) - 2*(g + h*x)*(b^3*(d*g - c*h)^3*p*(Log[a + b*x] - Log[g + h*x]) + d^3*(b*g - a*h)^3*q*(Log[c + d*x] - Log[g + h*x])))))/((b*g - a*h)^3*(d*g - c*h)^3))/(6*h*(g + h*x)^3)","A",1
34,1,480,318,1.4926042,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g+h x)^5} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(g + h*x)^5,x]","\frac{\frac{r (g+h x) \left(2 (b g-a h)^3 (d g-c h)^3 (b d g (p+q)-h (a d q+b c p))-(g+h x) \left((b g-a h)^2 (d g-c h)^2 \left(-3 a^2 d^2 h^2 q+6 a b d^2 g h q-3 b^2 \left(c^2 h^2 p-2 c d g h p+d^2 g^2 (p+q)\right)\right)+6 (g+h x) \left(-\left((b g-a h) (c h-d g) \left(a^3 d^3 h^3 q-3 a^2 b d^3 g h^2 q+3 a b^2 d^3 g^2 h q-\left(b^3 \left(-c^3 h^3 p+3 c^2 d g h^2 p-3 c d^2 g^2 h p+d^3 g^3 (p+q)\right)\right)\right)\right)-(g+h x) \left(-\log (g+h x) \left(a^4 d^4 h^4 q-4 a^3 b d^4 g h^3 q+6 a^2 b^2 d^4 g^2 h^2 q-4 a b^3 d^4 g^3 h q+b^4 \left(c^4 h^4 p-4 c^3 d g h^3 p+6 c^2 d^2 g^2 h^2 p-4 c d^3 g^3 h p+d^4 g^4 (p+q)\right)\right)+b^4 p \log (a+b x) (d g-c h)^4+d^4 q (b g-a h)^4 \log (c+d x)\right)\right)\right)\right)}{(b g-a h)^4 (d g-c h)^4}-6 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{24 h (g+h x)^4}","\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{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{\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^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^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 q r}{12 h (g+h x)^3 (d g-c h)}",1,"(-6*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + (r*(g + h*x)*(2*(b*g - a*h)^3*(d*g - c*h)^3*(b*d*g*(p + q) - h*(b*c*p + a*d*q)) - (g + h*x)*((b*g - a*h)^2*(d*g - c*h)^2*(6*a*b*d^2*g*h*q - 3*a^2*d^2*h^2*q - 3*b^2*(-2*c*d*g*h*p + c^2*h^2*p + d^2*g^2*(p + q))) + 6*(g + h*x)*(-((b*g - a*h)*(-(d*g) + c*h)*(3*a*b^2*d^3*g^2*h*q - 3*a^2*b*d^3*g*h^2*q + a^3*d^3*h^3*q - b^3*(-3*c*d^2*g^2*h*p + 3*c^2*d*g*h^2*p - c^3*h^3*p + d^3*g^3*(p + q)))) - (g + h*x)*(b^4*(d*g - c*h)^4*p*Log[a + b*x] + d^4*(b*g - a*h)^4*q*Log[c + d*x] - (-4*a*b^3*d^4*g^3*h*q + 6*a^2*b^2*d^4*g^2*h^2*q - 4*a^3*b*d^4*g*h^3*q + a^4*d^4*h^4*q + b^4*(-4*c*d^3*g^3*h*p + 6*c^2*d^2*g^2*h^2*p - 4*c^3*d*g*h^3*p + c^4*h^4*p + d^4*g^4*(p + q)))*Log[g + h*x])))))/((b*g - a*h)^4*(d*g - c*h)^4))/(24*h*(g + h*x)^4)","A",1
35,1,1386,2240,3.3941978,"\int (g+h x)^3 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[(g + h*x)^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2,x]","\frac{72 a \left(-4 b^3 g^3+6 a b^2 h g^2-4 a^2 b h^2 g+a^3 h^3\right) p^2 r^2 \log ^2(a+b x) d^4+12 p r \log (a+b x) \left(12 c \left(-4 d^3 g^3+6 c d^2 h g^2-4 c^2 d h^2 g+c^3 h^3\right) q r \log (c+d x) b^4-12 \left(c \left(-4 d^3 g^3+6 c d^2 h g^2-4 c^2 d h^2 g+c^3 h^3\right) b^4+4 a d^4 g^3 b^3-6 a^2 d^4 g^2 h b^2+4 a^3 d^4 g h^2 b-a^4 d^4 h^3\right) q r \log \left(\frac{b (c+d x)}{b c-a d}\right)+a d \left(12 \left(4 b^3 g^3-6 a b^2 h g^2+4 a^2 b h^2 g-a^3 h^3\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) d^3+\left(12 \left(-4 d^3 g^3+6 c d^2 h g^2-4 c^2 d h^2 g+c^3 h^3\right) q b^3+6 a d h \left(6 d^2 (3 p+q) g^2-4 c d h q g+c^2 h^2 q\right) b^2-4 a^2 d^2 h^2 (22 d g p+4 d g q-c h q) b+a^3 d^3 h^3 (25 p+3 q)\right) r\right)\right)+b \left(72 c \left(-4 d^3 g^3+6 c d^2 h g^2-4 c^2 d h^2 g+c^3 h^3\right) q^2 r^2 \log ^2(c+d x) b^3+12 q r \log (c+d x) \left(\left(c \left(-48 d^3 (p+q) g^3+36 c d^2 h (p+3 q) g^2-8 c^2 d h^2 (2 p+11 q) g+c^3 h^3 (3 p+25 q)\right) b^3+4 a d \left(12 d^3 g^3+18 c d^2 h g^2-6 c^2 d h^2 g+c^3 h^3\right) p b^2+6 a^2 c d^2 h^2 (c h-8 d g) p b+12 a^3 c d^3 h^3 p\right) r-12 b^3 c \left(-4 d^3 g^3+6 c d^2 h g^2-4 c^2 d h^2 g+c^3 h^3\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)+d \left(72 b^3 x \left(4 g^3+6 h x g^2+4 h^2 x^2 g+h^3 x^3\right) \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) d^3+r^2 \left(x \left((p+q)^2 \left(576 g^3+216 h x g^2+64 h^2 x^2 g+9 h^3 x^3\right) d^3-4 c h q (p+q) \left(324 g^2+60 h x g+7 h^2 x^2\right) d^2+6 c^2 h^2 q (16 g (8 p+11 q)+h (9 p+13 q) x) d-60 c^3 h^3 q (3 p+5 q)\right) b^3-4 a p \left(\left(-144 q g^3+324 h (p+q) x g^2+60 h^2 (p+q) x^2 g+7 h^3 (p+q) x^3\right) d^3-12 c h q \left(-18 g^2+12 h x g+h^2 x^2\right) d^2+6 c^2 h^2 q (5 h x-24 g) d+36 c^3 h^3 q\right) b^2+6 a^2 d^2 h^2 p x (-20 c h q+16 d g (11 p+8 q)+d h (13 p+9 q) x) b-60 a^3 d^3 h^3 p (5 p+3 q) x\right)+12 r \left(-x \left((p+q) \left(48 g^3+36 h x g^2+16 h^2 x^2 g+3 h^3 x^3\right) d^3-4 c h q \left(18 g^2+6 h x g+h^2 x^2\right) d^2+6 c^2 h^2 q (8 g+h x) d-12 c^3 h^3 q\right) b^3+4 a d^3 p \left(-12 g^3+18 h x g^2+6 h^2 x^2 g+h^3 x^3\right) b^2-6 a^2 d^3 h^2 p x (8 g+h x) b+12 a^3 d^3 h^3 p x\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)\right)-144 \left(c \left(-4 d^3 g^3+6 c d^2 h g^2-4 c^2 d h^2 g+c^3 h^3\right) b^4+4 a d^4 g^3 b^3-6 a^2 d^4 g^2 h b^2+4 a^3 d^4 g h^2 b-a^4 d^4 h^3\right) p q r^2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)}{288 b^4 d^4}","-\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{Li}_2\left(\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{Li}_2\left(-\frac{d (a+b x)}{b c-a d}\right)}{2 d^4 h}",1,"(72*a*d^4*(-4*b^3*g^3 + 6*a*b^2*g^2*h - 4*a^2*b*g*h^2 + a^3*h^3)*p^2*r^2*Log[a + b*x]^2 + 12*p*r*Log[a + b*x]*(12*b^4*c*(-4*d^3*g^3 + 6*c*d^2*g^2*h - 4*c^2*d*g*h^2 + c^3*h^3)*q*r*Log[c + d*x] - 12*(4*a*b^3*d^4*g^3 - 6*a^2*b^2*d^4*g^2*h + 4*a^3*b*d^4*g*h^2 - a^4*d^4*h^3 + b^4*c*(-4*d^3*g^3 + 6*c*d^2*g^2*h - 4*c^2*d*g*h^2 + c^3*h^3))*q*r*Log[(b*(c + d*x))/(b*c - a*d)] + a*d*((12*b^3*(-4*d^3*g^3 + 6*c*d^2*g^2*h - 4*c^2*d*g*h^2 + c^3*h^3)*q + a^3*d^3*h^3*(25*p + 3*q) - 4*a^2*b*d^2*h^2*(22*d*g*p + 4*d*g*q - c*h*q) + 6*a*b^2*d*h*(-4*c*d*g*h*q + c^2*h^2*q + 6*d^2*g^2*(3*p + q)))*r + 12*d^3*(4*b^3*g^3 - 6*a*b^2*g^2*h + 4*a^2*b*g*h^2 - a^3*h^3)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])) + b*(72*b^3*c*(-4*d^3*g^3 + 6*c*d^2*g^2*h - 4*c^2*d*g*h^2 + c^3*h^3)*q^2*r^2*Log[c + d*x]^2 + 12*q*r*Log[c + d*x]*((12*a^3*c*d^3*h^3*p + 6*a^2*b*c*d^2*h^2*(-8*d*g + c*h)*p + 4*a*b^2*d*(12*d^3*g^3 + 18*c*d^2*g^2*h - 6*c^2*d*g*h^2 + c^3*h^3)*p + b^3*c*(-48*d^3*g^3*(p + q) + 36*c*d^2*g^2*h*(p + 3*q) - 8*c^2*d*g*h^2*(2*p + 11*q) + c^3*h^3*(3*p + 25*q)))*r - 12*b^3*c*(-4*d^3*g^3 + 6*c*d^2*g^2*h - 4*c^2*d*g*h^2 + c^3*h^3)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]) + d*(r^2*(-60*a^3*d^3*h^3*p*(5*p + 3*q)*x + 6*a^2*b*d^2*h^2*p*x*(-20*c*h*q + 16*d*g*(11*p + 8*q) + d*h*(13*p + 9*q)*x) + b^3*x*(-60*c^3*h^3*q*(3*p + 5*q) + 6*c^2*d*h^2*q*(16*g*(8*p + 11*q) + h*(9*p + 13*q)*x) - 4*c*d^2*h*q*(p + q)*(324*g^2 + 60*g*h*x + 7*h^2*x^2) + d^3*(p + q)^2*(576*g^3 + 216*g^2*h*x + 64*g*h^2*x^2 + 9*h^3*x^3)) - 4*a*b^2*p*(36*c^3*h^3*q + 6*c^2*d*h^2*q*(-24*g + 5*h*x) - 12*c*d^2*h*q*(-18*g^2 + 12*g*h*x + h^2*x^2) + d^3*(-144*g^3*q + 324*g^2*h*(p + q)*x + 60*g*h^2*(p + q)*x^2 + 7*h^3*(p + q)*x^3))) + 12*r*(12*a^3*d^3*h^3*p*x - 6*a^2*b*d^3*h^2*p*x*(8*g + h*x) + 4*a*b^2*d^3*p*(-12*g^3 + 18*g^2*h*x + 6*g*h^2*x^2 + h^3*x^3) - b^3*x*(-12*c^3*h^3*q + 6*c^2*d*h^2*q*(8*g + h*x) - 4*c*d^2*h*q*(18*g^2 + 6*g*h*x + h^2*x^2) + d^3*(p + q)*(48*g^3 + 36*g^2*h*x + 16*g*h^2*x^2 + 3*h^3*x^3)))*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 72*b^3*d^3*x*(4*g^3 + 6*g^2*h*x + 4*g*h^2*x^2 + h^3*x^3)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2)) - 144*(4*a*b^3*d^4*g^3 - 6*a^2*b^2*d^4*g^2*h + 4*a^3*b*d^4*g*h^2 - a^4*d^4*h^3 + b^4*c*(-4*d^3*g^3 + 6*c*d^2*g^2*h - 4*c^2*d*g*h^2 + c^3*h^3))*p*q*r^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(288*b^4*d^4)","A",1
36,1,899,1645,2.0325786,"\int (g+h x)^2 \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[(g + h*x)^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2,x]","\frac{-18 a \left(3 b^2 g^2-3 a b h g+a^2 h^2\right) p^2 r^2 \log ^2(a+b x) d^3-6 p r \log (a+b x) \left(6 c \left(3 d^2 g^2-3 c d h g+c^2 h^2\right) q r \log (c+d x) b^3-6 (b c-a d) \left(\left(3 d^2 g^2-3 c d h g+c^2 h^2\right) b^2+a d h (c h-3 d g) b+a^2 d^2 h^2\right) q r \log \left(\frac{b (c+d x)}{b c-a d}\right)+a d \left(\left(6 \left(3 d^2 g^2-3 c d h g+c^2 h^2\right) q b^2-3 a d h (3 d g (3 p+q)-c h q) b+a^2 d^2 h^2 (11 p+2 q)\right) r-6 d^2 \left(3 b^2 g^2-3 a b h g+a^2 h^2\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)\right)+b \left(-18 b^2 c \left(3 d^2 g^2-3 c d h g+c^2 h^2\right) q^2 r^2 \log ^2(c+d x)-6 q r \left(\left(c \left(18 d^2 (p+q) g^2-9 c d h (p+3 q) g+c^2 h^2 (2 p+11 q)\right) b^2-3 a d \left(6 d^2 g^2+6 c d h g-c^2 h^2\right) p b+6 a^2 c d^2 h^2 p\right) r-6 b^2 c \left(3 d^2 g^2-3 c d h g+c^2 h^2\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right) \log (c+d x)+d \left(\left(x \left(6 c^2 q (8 p+11 q) h^2-3 c d q (p+q) (54 g+5 h x) h+d^2 (p+q)^2 \left(108 g^2+27 h x g+4 h^2 x^2\right)\right) b^2-3 a p \left(\left(-36 q g^2+54 h (p+q) x g+5 h^2 (p+q) x^2\right) d^2-12 c h q (h x-3 g) d-12 c^2 h^2 q\right) b+6 a^2 d^2 h^2 p (11 p+8 q) x\right) r^2-6 \left(x \left((p+q) \left(18 g^2+9 h x g+2 h^2 x^2\right) d^2-3 c h q (6 g+h x) d+6 c^2 h^2 q\right) b^2+3 a d^2 p \left(6 g^2-6 h x g-h^2 x^2\right) b+6 a^2 d^2 h^2 p x\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) r+18 b^2 d^2 x \left(3 g^2+3 h x g+h^2 x^2\right) \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)\right)+36 (b c-a d) \left(\left(3 d^2 g^2-3 c d h g+c^2 h^2\right) b^2+a d h (c h-3 d g) b+a^2 d^2 h^2\right) p q r^2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)}{54 b^3 d^3}","-\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{Li}_2\left(\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{Li}_2\left(-\frac{d (a+b x)}{b c-a d}\right)}{3 d^3 h}",1,"(-18*a*d^3*(3*b^2*g^2 - 3*a*b*g*h + a^2*h^2)*p^2*r^2*Log[a + b*x]^2 - 6*p*r*Log[a + b*x]*(6*b^3*c*(3*d^2*g^2 - 3*c*d*g*h + c^2*h^2)*q*r*Log[c + d*x] - 6*(b*c - a*d)*(a^2*d^2*h^2 + a*b*d*h*(-3*d*g + c*h) + b^2*(3*d^2*g^2 - 3*c*d*g*h + c^2*h^2))*q*r*Log[(b*(c + d*x))/(b*c - a*d)] + a*d*((6*b^2*(3*d^2*g^2 - 3*c*d*g*h + c^2*h^2)*q + a^2*d^2*h^2*(11*p + 2*q) - 3*a*b*d*h*(-(c*h*q) + 3*d*g*(3*p + q)))*r - 6*d^2*(3*b^2*g^2 - 3*a*b*g*h + a^2*h^2)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])) + b*(-18*b^2*c*(3*d^2*g^2 - 3*c*d*g*h + c^2*h^2)*q^2*r^2*Log[c + d*x]^2 - 6*q*r*Log[c + d*x]*((6*a^2*c*d^2*h^2*p - 3*a*b*d*(6*d^2*g^2 + 6*c*d*g*h - c^2*h^2)*p + b^2*c*(18*d^2*g^2*(p + q) - 9*c*d*g*h*(p + 3*q) + c^2*h^2*(2*p + 11*q)))*r - 6*b^2*c*(3*d^2*g^2 - 3*c*d*g*h + c^2*h^2)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]) + d*(r^2*(6*a^2*d^2*h^2*p*(11*p + 8*q)*x + b^2*x*(6*c^2*h^2*q*(8*p + 11*q) - 3*c*d*h*q*(p + q)*(54*g + 5*h*x) + d^2*(p + q)^2*(108*g^2 + 27*g*h*x + 4*h^2*x^2)) - 3*a*b*p*(-12*c^2*h^2*q - 12*c*d*h*q*(-3*g + h*x) + d^2*(-36*g^2*q + 54*g*h*(p + q)*x + 5*h^2*(p + q)*x^2))) - 6*r*(6*a^2*d^2*h^2*p*x + 3*a*b*d^2*p*(6*g^2 - 6*g*h*x - h^2*x^2) + b^2*x*(6*c^2*h^2*q - 3*c*d*h*q*(6*g + h*x) + d^2*(p + q)*(18*g^2 + 9*g*h*x + 2*h^2*x^2)))*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 18*b^2*d^2*x*(3*g^2 + 3*g*h*x + h^2*x^2)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2)) + 36*(b*c - a*d)*(a^2*d^2*h^2 + a*b*d*h*(-3*d*g + c*h) + b^2*(3*d^2*g^2 - 3*c*d*g*h + c^2*h^2))*p*q*r^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(54*b^3*d^3)","A",1
37,1,480,1063,0.928135,"\int (g+h x) \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[(g + h*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2,x]","\frac{2 p r \log (a+b x) \left(a d \left((4 b d g-2 a d h) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+a d h r (3 p+q)+2 b q r (c h-2 d g)\right)-2 q r (b c-a d) (a d h+b c h-2 b d g) \log \left(\frac{b (c+d x)}{b c-a d}\right)+2 b^2 c q r (c h-2 d g) \log (c+d x)\right)+b \left(d \left(2 b d x (2 g+h x) \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-2 r (2 a d p (2 g-h x)+b x (d (p+q) (4 g+h x)-2 c h q)) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+r^2 (b x (p+q) (d (p+q) (8 g+h x)-6 c h q)-2 a p (2 c h q-4 d g q+3 d h x (p+q)))\right)+2 q r \log (c+d x) \left(-2 b c (c h-2 d g) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+2 a d p r (c h+2 d g)+b c r (c h (p+3 q)-4 d g (p+q))\right)+2 b c q^2 r^2 (c h-2 d g) \log ^2(c+d x)\right)-4 p q r^2 (b c-a d) (a d h+b c h-2 b d g) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)+2 a d^2 p^2 r^2 (a h-2 b g) \log ^2(a+b x)}{4 b^2 d^2}","-\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{Li}_2\left(\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{Li}_2\left(-\frac{d (a+b x)}{b c-a d}\right)}{d^2 h}",1,"(2*a*d^2*(-2*b*g + a*h)*p^2*r^2*Log[a + b*x]^2 + 2*p*r*Log[a + b*x]*(2*b^2*c*(-2*d*g + c*h)*q*r*Log[c + d*x] - 2*(b*c - a*d)*(-2*b*d*g + b*c*h + a*d*h)*q*r*Log[(b*(c + d*x))/(b*c - a*d)] + a*d*(2*b*(-2*d*g + c*h)*q*r + a*d*h*(3*p + q)*r + (4*b*d*g - 2*a*d*h)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])) + b*(2*b*c*(-2*d*g + c*h)*q^2*r^2*Log[c + d*x]^2 + 2*q*r*Log[c + d*x]*(2*a*d*(2*d*g + c*h)*p*r + b*c*(-4*d*g*(p + q) + c*h*(p + 3*q))*r - 2*b*c*(-2*d*g + c*h)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]) + d*(r^2*(-2*a*p*(-4*d*g*q + 2*c*h*q + 3*d*h*(p + q)*x) + b*(p + q)*x*(-6*c*h*q + d*(p + q)*(8*g + h*x))) - 2*r*(2*a*d*p*(2*g - h*x) + b*x*(-2*c*h*q + d*(p + q)*(4*g + h*x)))*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 2*b*d*x*(2*g + h*x)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2)) - 4*(b*c - a*d)*(-2*b*d*g + b*c*h + a*d*h)*p*q*r^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(4*b^2*d^2)","A",1
38,1,389,269,0.2347922,"\int \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2,x]","\frac{b d x \log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-2 p r \log (a+b x) \left(a d \left(q r-\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)\right)+q r (a d-b c) \log \left(\frac{b (c+d x)}{b c-a d}\right)+b c q r \log (c+d x)\right)-2 a d p r \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-2 b d p r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-2 b d q r x \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+2 b c q r \log (c+d x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+2 p q r^2 (b c-a d) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)-a d p^2 r^2 \log ^2(a+b x)+2 a d p q r^2 \log (c+d x)+2 a d p q r^2-2 b c p q r^2 \log (c+d x)-b c q^2 r^2 \log ^2(c+d x)-2 b c q^2 r^2 \log (c+d x)+2 b d p^2 r^2 x+4 b d p q r^2 x+2 b d q^2 r^2 x}{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 p q r^2 (b c-a d) \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\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*a*d*p*q*r^2 + 2*b*d*p^2*r^2*x + 4*b*d*p*q*r^2*x + 2*b*d*q^2*r^2*x - a*d*p^2*r^2*Log[a + b*x]^2 - 2*b*c*p*q*r^2*Log[c + d*x] + 2*a*d*p*q*r^2*Log[c + d*x] - 2*b*c*q^2*r^2*Log[c + d*x] - b*c*q^2*r^2*Log[c + d*x]^2 - 2*p*r*Log[a + b*x]*(b*c*q*r*Log[c + d*x] + (-(b*c) + a*d)*q*r*Log[(b*(c + d*x))/(b*c - a*d)] + a*d*(q*r - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])) - 2*a*d*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 2*b*d*p*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 2*b*d*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 2*b*c*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + b*d*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + 2*(b*c - a*d)*p*q*r^2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*d)","A",1
39,1,1370,1471,0.2939263,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{g+h x} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(g + h*x),x]","\frac{p q \log \left(\frac{a d-b c}{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+p^2 \log ^2(a+b x) \log (g+h x) r^2+q^2 \log ^2(c+d x) \log (g+h x) r^2+2 p q \log (a+b x) \log (c+d x) \log (g+h x) r^2-p^2 \log ^2(a+b x) \log \left(\frac{b (g+h x)}{b g-a h}\right) r^2+p q \log ^2\left(\frac{h (c+d x)}{c h-d g}\right) \log \left(\frac{b (g+h x)}{b g-a h}\right) r^2+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^2-2 p q \log (a+b x) \log \left(\frac{h (c+d x)}{c h-d g}\right) \log \left(\frac{b (g+h x)}{b g-a h}\right) r^2-2 p q \log \left(\frac{h (c+d x)}{c h-d g}\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-q^2 \log ^2(c+d x) \log \left(\frac{d (g+h x)}{d g-c h}\right) r^2-p q \log ^2\left(\frac{h (c+d x)}{c h-d g}\right) \log \left(\frac{d (g+h x)}{d g-c h}\right) r^2-2 p q \log (a+b x) \log (c+d x) \log \left(\frac{d (g+h x)}{d g-c h}\right) r^2+2 p q \log (a+b x) \log \left(\frac{h (c+d x)}{c h-d g}\right) \log \left(\frac{d (g+h x)}{d g-c h}\right) r^2+2 p q \log \left(\frac{h (c+d x)}{c h-d g}\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-p q \log ^2\left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right) \log \left(\frac{(a d-b c) (g+h x)}{(d g-c h) (a+b x)}\right) r^2+2 p q \log \left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right) \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right) r^2-2 p q \log \left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right) \text{Li}_2\left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right) r^2-2 p^2 \text{Li}_3\left(\frac{h (a+b x)}{a h-b g}\right) r^2-2 p q \text{Li}_3\left(\frac{h (a+b x)}{a h-b g}\right) r^2-2 q^2 \text{Li}_3\left(\frac{h (c+d x)}{c h-d g}\right) r^2-2 p q \text{Li}_3\left(\frac{h (c+d x)}{c h-d g}\right) r^2-2 p q \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right) r^2+2 p q \text{Li}_3\left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right) r^2-2 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-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+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+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+2 p \left(\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-q r \log \left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right)\right) \text{Li}_2\left(\frac{h (a+b x)}{a h-b g}\right) r+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{Li}_2\left(\frac{h (c+d x)}{c h-d g}\right) r+\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \log (g+h x)}{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{Li}_2\left(\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{Li}_2\left(\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}\right) r^2}{h}-\frac{2 p^2 \text{Li}_3\left(-\frac{h (a+b x)}{b g-a h}\right) r^2}{h}-\frac{2 p q \text{Li}_3\left(-\frac{h (a+b x)}{b g-a h}\right) r^2}{h}-\frac{2 q^2 \text{Li}_3\left(-\frac{h (c+d x)}{d g-c h}\right) r^2}{h}-\frac{2 p q \text{Li}_3\left(-\frac{h (c+d x)}{d g-c h}\right) r^2}{h}-\frac{2 p q \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right) r^2}{h}+\frac{2 p q \text{Li}_3\left(\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{Li}_2\left(-\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{Li}_2\left(-\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,"(p*q*r^2*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]^2 + p^2*r^2*Log[a + b*x]^2*Log[g + h*x] + 2*p*q*r^2*Log[a + b*x]*Log[c + d*x]*Log[g + h*x] + q^2*r^2*Log[c + d*x]^2*Log[g + h*x] - 2*p*r*Log[a + b*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[g + h*x] - 2*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[g + h*x] + Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2*Log[g + h*x] - p^2*r^2*Log[a + b*x]^2*Log[(b*(g + h*x))/(b*g - a*h)] - 2*p*q*r^2*Log[a + b*x]*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(b*(g + h*x))/(b*g - a*h)] + p*q*r^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]^2*Log[(b*(g + h*x))/(b*g - a*h)] - 2*p*q*r^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Log[(b*(g + h*x))/(b*g - a*h)] + p*q*r^2*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]^2*Log[(b*(g + h*x))/(b*g - a*h)] + 2*p*r*Log[a + b*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[(b*(g + h*x))/(b*g - a*h)] - 2*p*q*r^2*Log[a + b*x]*Log[c + d*x]*Log[(d*(g + h*x))/(d*g - c*h)] - q^2*r^2*Log[c + d*x]^2*Log[(d*(g + h*x))/(d*g - c*h)] + 2*p*q*r^2*Log[a + b*x]*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(d*(g + h*x))/(d*g - c*h)] - p*q*r^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]^2*Log[(d*(g + h*x))/(d*g - c*h)] + 2*p*q*r^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Log[(d*(g + h*x))/(d*g - c*h)] + 2*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[(d*(g + h*x))/(d*g - c*h)] - p*q*r^2*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]^2*Log[((-(b*c) + a*d)*(g + h*x))/((d*g - c*h)*(a + b*x))] + 2*p*r*(-(q*r*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]) + Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])*PolyLog[2, (h*(a + b*x))/(-(b*g) + a*h)] + 2*q*r*(p*r*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] + Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])*PolyLog[2, (h*(c + d*x))/(-(d*g) + c*h)] + 2*p*q*r^2*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 2*p*q*r^2*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*PolyLog[2, ((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] - 2*p^2*r^2*PolyLog[3, (h*(a + b*x))/(-(b*g) + a*h)] - 2*p*q*r^2*PolyLog[3, (h*(a + b*x))/(-(b*g) + a*h)] - 2*p*q*r^2*PolyLog[3, (h*(c + d*x))/(-(d*g) + c*h)] - 2*q^2*r^2*PolyLog[3, (h*(c + d*x))/(-(d*g) + c*h)] - 2*p*q*r^2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))] + 2*p*q*r^2*PolyLog[3, ((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))])/h","A",1
40,1,2930,832,1.3439774,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g+h x)^2} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(g + h*x)^2,x]","\text{Result too large to show}","\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{Li}_2\left(-\frac{b g-a h}{h (a+b x)}\right) r^2}{h (b g-a h)}+\frac{2 d p q \text{Li}_2\left(-\frac{d (a+b x)}{b c-a d}\right) r^2}{h (d g-c h)}-\frac{2 d p q \text{Li}_2\left(-\frac{h (a+b x)}{b g-a h}\right) r^2}{h (d g-c h)}+\frac{2 d q^2 \text{Li}_2\left(-\frac{d g-c h}{h (c+d x)}\right) r^2}{h (d g-c h)}+\frac{2 b p q \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right) r^2}{h (b g-a h)}-\frac{2 b p q \text{Li}_2\left(-\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*d*g^2*p^2*r^2*Log[a + b*x]^2) + b*c*g*h*p^2*r^2*Log[a + b*x]^2 - b*d*g*h*p^2*r^2*x*Log[a + b*x]^2 + b*c*h^2*p^2*r^2*x*Log[a + b*x]^2 - 2*b*d*g^2*p*q*r^2*Log[a + b*x]*Log[c + d*x] + 2*a*d*g*h*p*q*r^2*Log[a + b*x]*Log[c + d*x] - 2*b*d*g*h*p*q*r^2*x*Log[a + b*x]*Log[c + d*x] + 2*a*d*h^2*p*q*r^2*x*Log[a + b*x]*Log[c + d*x] - b*d*g^2*q^2*r^2*Log[c + d*x]^2 + a*d*g*h*q^2*r^2*Log[c + d*x]^2 - b*d*g*h*q^2*r^2*x*Log[c + d*x]^2 + a*d*h^2*q^2*r^2*x*Log[c + d*x]^2 + 2*b*c*g*h*p*q*r^2*Log[a + b*x]*Log[(h*(c + d*x))/(-(d*g) + c*h)] - 2*a*d*g*h*p*q*r^2*Log[a + b*x]*Log[(h*(c + d*x))/(-(d*g) + c*h)] + 2*b*c*h^2*p*q*r^2*x*Log[a + b*x]*Log[(h*(c + d*x))/(-(d*g) + c*h)] - 2*a*d*h^2*p*q*r^2*x*Log[a + b*x]*Log[(h*(c + d*x))/(-(d*g) + c*h)] - b*c*g*h*p*q*r^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]^2 + a*d*g*h*p*q*r^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]^2 - b*c*h^2*p*q*r^2*x*Log[(h*(c + d*x))/(-(d*g) + c*h)]^2 + a*d*h^2*p*q*r^2*x*Log[(h*(c + d*x))/(-(d*g) + c*h)]^2 + 2*b*c*g*h*p*q*r^2*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] - 2*a*d*g*h*p*q*r^2*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] + 2*b*c*h^2*p*q*r^2*x*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] - 2*a*d*h^2*p*q*r^2*x*Log[(-(b*c) + a*d)/(d*(a + b*x))]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] + 2*b*c*g*h*p*q*r^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] - 2*a*d*g*h*p*q*r^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] + 2*b*c*h^2*p*q*r^2*x*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] - 2*a*d*h^2*p*q*r^2*x*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))] - b*c*g*h*p*q*r^2*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]^2 + a*d*g*h*p*q*r^2*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]^2 - b*c*h^2*p*q*r^2*x*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]^2 + a*d*h^2*p*q*r^2*x*Log[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]^2 + 2*b*d*g^2*p*r*Log[a + b*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 2*b*c*g*h*p*r*Log[a + b*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 2*b*d*g*h*p*r*x*Log[a + b*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 2*b*c*h^2*p*r*x*Log[a + b*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 2*b*d*g^2*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 2*a*d*g*h*q*r*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + 2*b*d*g*h*q*r*x*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 2*a*d*h^2*q*r*x*Log[c + d*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - b*d*g^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + b*c*g*h*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 + a*d*g*h*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 - a*c*h^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2 - 2*b*d*g^2*p*q*r^2*Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)] + 2*a*d*g*h*p*q*r^2*Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)] - 2*b*d*g*h*p*q*r^2*x*Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)] + 2*a*d*h^2*p*q*r^2*x*Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)] + 2*b*d*g^2*p*q*r^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(b*(g + h*x))/(b*g - a*h)] - 2*b*c*g*h*p*q*r^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(b*(g + h*x))/(b*g - a*h)] + 2*b*d*g*h*p*q*r^2*x*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(b*(g + h*x))/(b*g - a*h)] - 2*b*c*h^2*p*q*r^2*x*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(b*(g + h*x))/(b*g - a*h)] - 2*b*d*g^2*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[(b*(g + h*x))/(b*g - a*h)] + 2*b*c*g*h*p*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[(b*(g + h*x))/(b*g - a*h)] - 2*b*d*g*h*p*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[(b*(g + h*x))/(b*g - a*h)] + 2*b*c*h^2*p*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[(b*(g + h*x))/(b*g - a*h)] + 2*b*d*g^2*p*q*r^2*Log[a + b*x]*Log[(d*(g + h*x))/(d*g - c*h)] - 2*a*d*g*h*p*q*r^2*Log[a + b*x]*Log[(d*(g + h*x))/(d*g - c*h)] + 2*b*d*g*h*p*q*r^2*x*Log[a + b*x]*Log[(d*(g + h*x))/(d*g - c*h)] - 2*a*d*h^2*p*q*r^2*x*Log[a + b*x]*Log[(d*(g + h*x))/(d*g - c*h)] - 2*b*d*g^2*p*q*r^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(d*(g + h*x))/(d*g - c*h)] + 2*b*c*g*h*p*q*r^2*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(d*(g + h*x))/(d*g - c*h)] - 2*b*d*g*h*p*q*r^2*x*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(d*(g + h*x))/(d*g - c*h)] + 2*b*c*h^2*p*q*r^2*x*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[(d*(g + h*x))/(d*g - c*h)] - 2*b*d*g^2*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[(d*(g + h*x))/(d*g - c*h)] + 2*a*d*g*h*q*r*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[(d*(g + h*x))/(d*g - c*h)] - 2*b*d*g*h*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[(d*(g + h*x))/(d*g - c*h)] + 2*a*d*h^2*q*r*x*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[(d*(g + h*x))/(d*g - c*h)] + 2*p*(b*c*h*p + a*d*h*q - b*d*g*(p + q))*r^2*(g + h*x)*PolyLog[2, (h*(a + b*x))/(-(b*g) + a*h)] + 2*q*(b*c*h*p + a*d*h*q - b*d*g*(p + q))*r^2*(g + h*x)*PolyLog[2, (h*(c + d*x))/(-(d*g) + c*h)] + 2*b*c*g*h*p*q*r^2*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 2*a*d*g*h*p*q*r^2*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] + 2*b*c*h^2*p*q*r^2*x*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 2*a*d*h^2*p*q*r^2*x*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))])/(h*(-(b*g) + a*h)*(-(d*g) + c*h)*(g + h*x))","B",1
41,1,15960,1304,6.3118401,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g+h x)^3} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(g + h*x)^3,x]","\text{Result too large to show}","\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{Li}_2\left(-\frac{b g-a h}{h (a+b x)}\right) b^2}{h (b g-a h)^2}+\frac{p q r^2 \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right) b^2}{h (b g-a h)^2}-\frac{p q r^2 \text{Li}_2\left(-\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{Li}_2\left(-\frac{d (a+b x)}{b c-a d}\right)}{h (d g-c h)^2}-\frac{d^2 p q r^2 \text{Li}_2\left(-\frac{h (a+b x)}{b g-a h}\right)}{h (d g-c h)^2}+\frac{d^2 q^2 r^2 \text{Li}_2\left(-\frac{d g-c h}{h (c+d x)}\right)}{h (d g-c h)^2}",1,"Result too large to show","B",1
42,1,47127,1957,6.5292207,"\int \frac{\log ^2\left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{(g+h x)^4} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^2/(g + h*x)^4,x]","\text{Result too large to show}","-\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{Li}_2\left(-\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{Li}_2\left(\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{Li}_2\left(-\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{Li}_2\left(-\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{Li}_2\left(-\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{Li}_2\left(-\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,"Result too large to show","B",1
43,1,42,42,0.03183,"\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","Integrate[(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",1
44,1,37,37,0.0089411,"\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","Integrate[(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,"-1/4*(a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^4/(b*c)","A",1
45,1,37,37,0.0105322,"\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","Integrate[(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,"-1/3*(a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3/(b*c)","A",1
46,1,37,37,0.0068663,"\int \frac{a+b \log \left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)}{1-c^2 x^2} \, dx","Integrate[(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,"-1/2*(a + b*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2/(b*c)","A",1
47,1,34,34,0.0372645,"\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","Integrate[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",1
48,1,34,34,0.0101934,"\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","Integrate[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",1
49,1,37,37,0.0106325,"\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","Integrate[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",1
50,1,30,30,0.009106,"\int \frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Integrate[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,"-1/2*Log[Sqrt[1 - a*x]/Sqrt[1 + a*x]]^2/a","A",1
51,1,22595,410,7.4875174,"\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","Integrate[(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]","\text{Result too large to show}","\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 \text{Li}_2\left(\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{Li}_3\left(\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{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{2 n^2 p r t^2 \text{Li}_4\left(\frac{b (g+h x)}{b g-a h}\right)}{h k}-\frac{q r \text{Li}_2\left(\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{Li}_3\left(\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{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{2 n^2 q r t^2 \text{Li}_4\left(\frac{d (g+h x)}{d g-c h}\right)}{h k}",1,"Result too large to show","B",1
52,1,436,306,1.5408702,"\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","Integrate[(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{2 t \log (g+h x) \log \left(i (g+h x)^n\right) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-n t \log ^2(g+h x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+2 s \log (g+h x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-2 p r \text{Li}_2\left(\frac{b (g+h x)}{b g-a h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)-2 p r t \log (g+h x) \log \left(\frac{h (a+b x)}{a h-b g}\right) \log \left(i (g+h x)^n\right)+2 n p r t \text{Li}_3\left(\frac{b (g+h x)}{b g-a h}\right)+n p r t \log ^2(g+h x) \log \left(\frac{h (a+b x)}{a h-b g}\right)-2 p r s \log (g+h x) \log \left(\frac{h (a+b x)}{a h-b g}\right)-2 q r \text{Li}_2\left(\frac{d (g+h x)}{d g-c h}\right) \left(t \log \left(i (g+h x)^n\right)+s\right)-2 q r t \log (g+h x) \log \left(\frac{h (c+d x)}{c h-d g}\right) \log \left(i (g+h x)^n\right)+2 n q r t \text{Li}_3\left(\frac{d (g+h x)}{d g-c h}\right)+n q r t \log ^2(g+h x) \log \left(\frac{h (c+d x)}{c h-d g}\right)-2 q r s \log (g+h x) \log \left(\frac{h (c+d x)}{c h-d g}\right)}{2 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 \text{Li}_2\left(\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{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{n p r t \text{Li}_3\left(\frac{b (g+h x)}{b g-a h}\right)}{h k}-\frac{q r \text{Li}_2\left(\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{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{n q r t \text{Li}_3\left(\frac{d (g+h x)}{d g-c h}\right)}{h k}",1,"(-2*p*r*s*Log[(h*(a + b*x))/(-(b*g) + a*h)]*Log[g + h*x] - 2*q*r*s*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[g + h*x] + 2*s*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[g + h*x] + n*p*r*t*Log[(h*(a + b*x))/(-(b*g) + a*h)]*Log[g + h*x]^2 + n*q*r*t*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[g + h*x]^2 - n*t*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[g + h*x]^2 - 2*p*r*t*Log[(h*(a + b*x))/(-(b*g) + a*h)]*Log[g + h*x]*Log[i*(g + h*x)^n] - 2*q*r*t*Log[(h*(c + d*x))/(-(d*g) + c*h)]*Log[g + h*x]*Log[i*(g + h*x)^n] + 2*t*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[g + h*x]*Log[i*(g + h*x)^n] - 2*p*r*(s + t*Log[i*(g + h*x)^n])*PolyLog[2, (b*(g + h*x))/(b*g - a*h)] - 2*q*r*(s + t*Log[i*(g + h*x)^n])*PolyLog[2, (d*(g + h*x))/(d*g - c*h)] + 2*n*p*r*t*PolyLog[3, (b*(g + h*x))/(b*g - a*h)] + 2*n*q*r*t*PolyLog[3, (d*(g + h*x))/(d*g - c*h)])/(2*h*k)","A",1
53,1,166,172,0.0901241,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{g k+h k x} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(g*k + h*k*x),x]","\frac{\log (g+h x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)+p r \text{Li}_2\left(\frac{h (a+b x)}{a h-b g}\right)-p r \log (a+b x) \log (g+h x)+p r \log (a+b x) \log \left(\frac{b (g+h x)}{b g-a h}\right)+q r \text{Li}_2\left(\frac{h (c+d x)}{c h-d g}\right)-q r \log (c+d x) \log (g+h x)+q r \log (c+d x) \log \left(\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 \text{Li}_2\left(\frac{b (g+h x)}{b g-a h}\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 \text{Li}_2\left(\frac{d (g+h x)}{d g-c 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[a + b*x]*Log[g + h*x]) - q*r*Log[c + d*x]*Log[g + h*x] + Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]*Log[g + h*x] + p*r*Log[a + b*x]*Log[(b*(g + h*x))/(b*g - a*h)] + q*r*Log[c + d*x]*Log[(d*(g + h*x))/(d*g - c*h)] + p*r*PolyLog[2, (h*(a + b*x))/(-(b*g) + a*h)] + q*r*PolyLog[2, (h*(c + d*x))/(-(d*g) + c*h)])/(h*k)","A",1
54,0,0,51,0.3858081,"\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","Integrate[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,"Integrate[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",-1
55,0,0,51,2.8724632,"\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","Integrate[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,"Integrate[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",-1
56,1,1241,328,1.8418074,"\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","Integrate[(Log[i*(j*(h*x)^t)^u]^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/x,x]","-p r t^3 u^3 \log (a+b x) \log ^4(h x)+\frac{1}{4} p r t^3 u^3 \log \left(\frac{b x}{a}+1\right) \log ^4(h x)-q r t^3 u^3 \log (c+d x) \log ^4(h x)+\frac{3}{4} t^3 u^3 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \log ^4(h x)+\frac{1}{4} q r t^3 u^3 \log \left(\frac{d x}{c}+1\right) \log ^4(h x)+p r t^3 u^3 \log (x) \log (a+b x) \log ^3(h x)+3 p r t^2 u^2 \log \left(i \left(j (h x)^t\right)^u\right) \log (a+b x) \log ^3(h x)-p r t^2 u^2 \log \left(i \left(j (h x)^t\right)^u\right) \log \left(\frac{b x}{a}+1\right) \log ^3(h x)+q r t^3 u^3 \log (x) \log (c+d x) \log ^3(h x)+3 q r t^2 u^2 \log \left(i \left(j (h x)^t\right)^u\right) \log (c+d x) \log ^3(h x)-t^3 u^3 \log (x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \log ^3(h x)-2 t^2 u^2 \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) \log ^3(h x)-q r t^2 u^2 \log \left(i \left(j (h x)^t\right)^u\right) \log \left(\frac{d x}{c}+1\right) \log ^3(h x)-3 p r t u \log ^2\left(i \left(j (h x)^t\right)^u\right) \log (a+b x) \log ^2(h x)-3 p r t^2 u^2 \log (x) \log \left(i \left(j (h x)^t\right)^u\right) \log (a+b x) \log ^2(h x)+\frac{3}{2} p r t u \log ^2\left(i \left(j (h x)^t\right)^u\right) \log \left(\frac{b x}{a}+1\right) \log ^2(h x)-3 q r t u \log ^2\left(i \left(j (h x)^t\right)^u\right) \log (c+d x) \log ^2(h x)-3 q r t^2 u^2 \log (x) \log \left(i \left(j (h x)^t\right)^u\right) \log (c+d x) \log ^2(h x)+\frac{3}{2} t u \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) \log ^2(h x)+3 t^2 u^2 \log (x) \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) \log ^2(h x)+\frac{3}{2} q r t u \log ^2\left(i \left(j (h x)^t\right)^u\right) \log \left(\frac{d x}{c}+1\right) \log ^2(h x)+p r \log ^3\left(i \left(j (h x)^t\right)^u\right) \log (a+b x) \log (h x)+3 p r t u \log (x) \log ^2\left(i \left(j (h x)^t\right)^u\right) \log (a+b x) \log (h x)-p r \log ^3\left(i \left(j (h x)^t\right)^u\right) \log \left(\frac{b x}{a}+1\right) \log (h x)+q r \log ^3\left(i \left(j (h x)^t\right)^u\right) \log (c+d x) \log (h x)+3 q r t u \log (x) \log ^2\left(i \left(j (h x)^t\right)^u\right) \log (c+d x) \log (h x)-3 t u \log (x) \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) \log (h x)-q r \log ^3\left(i \left(j (h x)^t\right)^u\right) \log \left(\frac{d x}{c}+1\right) \log (h x)-p r \log (x) \log ^3\left(i \left(j (h x)^t\right)^u\right) \log (a+b x)-q r \log (x) \log ^3\left(i \left(j (h x)^t\right)^u\right) \log (c+d x)+\log (x) \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)-p r \log ^3\left(i \left(j (h x)^t\right)^u\right) \text{Li}_2\left(-\frac{b x}{a}\right)-q r \log ^3\left(i \left(j (h x)^t\right)^u\right) \text{Li}_2\left(-\frac{d x}{c}\right)+3 p r t u \log ^2\left(i \left(j (h x)^t\right)^u\right) \text{Li}_3\left(-\frac{b x}{a}\right)+3 q r t u \log ^2\left(i \left(j (h x)^t\right)^u\right) \text{Li}_3\left(-\frac{d x}{c}\right)-6 p r t^2 u^2 \log \left(i \left(j (h x)^t\right)^u\right) \text{Li}_4\left(-\frac{b x}{a}\right)-6 q r t^2 u^2 \log \left(i \left(j (h x)^t\right)^u\right) \text{Li}_4\left(-\frac{d x}{c}\right)+6 p r t^3 u^3 \text{Li}_5\left(-\frac{b x}{a}\right)+6 q r t^3 u^3 \text{Li}_5\left(-\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}-6 p r t^2 u^2 \text{Li}_4\left(-\frac{b x}{a}\right) \log \left(i \left(j (h x)^t\right)^u\right)-p r \text{Li}_2\left(-\frac{b x}{a}\right) \log ^3\left(i \left(j (h x)^t\right)^u\right)+3 p r t u \text{Li}_3\left(-\frac{b x}{a}\right) \log ^2\left(i \left(j (h x)^t\right)^u\right)-\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}+6 p r t^3 u^3 \text{Li}_5\left(-\frac{b x}{a}\right)-6 q r t^2 u^2 \text{Li}_4\left(-\frac{d x}{c}\right) \log \left(i \left(j (h x)^t\right)^u\right)-q r \text{Li}_2\left(-\frac{d x}{c}\right) \log ^3\left(i \left(j (h x)^t\right)^u\right)+3 q r t u \text{Li}_3\left(-\frac{d x}{c}\right) \log ^2\left(i \left(j (h x)^t\right)^u\right)-\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 q r t^3 u^3 \text{Li}_5\left(-\frac{d x}{c}\right)",1,"p*r*t^3*u^3*Log[x]*Log[h*x]^3*Log[a + b*x] - p*r*t^3*u^3*Log[h*x]^4*Log[a + b*x] - 3*p*r*t^2*u^2*Log[x]*Log[h*x]^2*Log[i*(j*(h*x)^t)^u]*Log[a + b*x] + 3*p*r*t^2*u^2*Log[h*x]^3*Log[i*(j*(h*x)^t)^u]*Log[a + b*x] + 3*p*r*t*u*Log[x]*Log[h*x]*Log[i*(j*(h*x)^t)^u]^2*Log[a + b*x] - 3*p*r*t*u*Log[h*x]^2*Log[i*(j*(h*x)^t)^u]^2*Log[a + b*x] - p*r*Log[x]*Log[i*(j*(h*x)^t)^u]^3*Log[a + b*x] + p*r*Log[h*x]*Log[i*(j*(h*x)^t)^u]^3*Log[a + b*x] + (p*r*t^3*u^3*Log[h*x]^4*Log[1 + (b*x)/a])/4 - p*r*t^2*u^2*Log[h*x]^3*Log[i*(j*(h*x)^t)^u]*Log[1 + (b*x)/a] + (3*p*r*t*u*Log[h*x]^2*Log[i*(j*(h*x)^t)^u]^2*Log[1 + (b*x)/a])/2 - p*r*Log[h*x]*Log[i*(j*(h*x)^t)^u]^3*Log[1 + (b*x)/a] + q*r*t^3*u^3*Log[x]*Log[h*x]^3*Log[c + d*x] - q*r*t^3*u^3*Log[h*x]^4*Log[c + d*x] - 3*q*r*t^2*u^2*Log[x]*Log[h*x]^2*Log[i*(j*(h*x)^t)^u]*Log[c + d*x] + 3*q*r*t^2*u^2*Log[h*x]^3*Log[i*(j*(h*x)^t)^u]*Log[c + d*x] + 3*q*r*t*u*Log[x]*Log[h*x]*Log[i*(j*(h*x)^t)^u]^2*Log[c + d*x] - 3*q*r*t*u*Log[h*x]^2*Log[i*(j*(h*x)^t)^u]^2*Log[c + d*x] - q*r*Log[x]*Log[i*(j*(h*x)^t)^u]^3*Log[c + d*x] + q*r*Log[h*x]*Log[i*(j*(h*x)^t)^u]^3*Log[c + d*x] - t^3*u^3*Log[x]*Log[h*x]^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + (3*t^3*u^3*Log[h*x]^4*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/4 + 3*t^2*u^2*Log[x]*Log[h*x]^2*Log[i*(j*(h*x)^t)^u]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 2*t^2*u^2*Log[h*x]^3*Log[i*(j*(h*x)^t)^u]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - 3*t*u*Log[x]*Log[h*x]*Log[i*(j*(h*x)^t)^u]^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + (3*t*u*Log[h*x]^2*Log[i*(j*(h*x)^t)^u]^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/2 + Log[x]*Log[i*(j*(h*x)^t)^u]^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + (q*r*t^3*u^3*Log[h*x]^4*Log[1 + (d*x)/c])/4 - q*r*t^2*u^2*Log[h*x]^3*Log[i*(j*(h*x)^t)^u]*Log[1 + (d*x)/c] + (3*q*r*t*u*Log[h*x]^2*Log[i*(j*(h*x)^t)^u]^2*Log[1 + (d*x)/c])/2 - q*r*Log[h*x]*Log[i*(j*(h*x)^t)^u]^3*Log[1 + (d*x)/c] - 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)]","B",1
57,1,839,262,0.8829509,"\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","Integrate[(Log[i*(j*(h*x)^t)^u]^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/x,x]","p r t^2 u^2 \log (a+b x) \log ^3(h x)-\frac{1}{3} p r t^2 u^2 \log \left(\frac{b x}{a}+1\right) \log ^3(h x)+q r t^2 u^2 \log (c+d x) \log ^3(h x)-\frac{2}{3} t^2 u^2 \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \log ^3(h x)-\frac{1}{3} q r t^2 u^2 \log \left(\frac{d x}{c}+1\right) \log ^3(h x)-p r t^2 u^2 \log (x) \log (a+b x) \log ^2(h x)-2 p r t u \log \left(i \left(j (h x)^t\right)^u\right) \log (a+b x) \log ^2(h x)+p r t u \log \left(i \left(j (h x)^t\right)^u\right) \log \left(\frac{b x}{a}+1\right) \log ^2(h x)-q r t^2 u^2 \log (x) \log (c+d x) \log ^2(h x)-2 q r t u \log \left(i \left(j (h x)^t\right)^u\right) \log (c+d x) \log ^2(h x)+t^2 u^2 \log (x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right) \log ^2(h x)+t u \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) \log ^2(h x)+q r t u \log \left(i \left(j (h x)^t\right)^u\right) \log \left(\frac{d x}{c}+1\right) \log ^2(h x)+p r \log ^2\left(i \left(j (h x)^t\right)^u\right) \log (a+b x) \log (h x)+2 p r t u \log (x) \log \left(i \left(j (h x)^t\right)^u\right) \log (a+b x) \log (h x)-p r \log ^2\left(i \left(j (h x)^t\right)^u\right) \log \left(\frac{b x}{a}+1\right) \log (h x)+q r \log ^2\left(i \left(j (h x)^t\right)^u\right) \log (c+d x) \log (h x)+2 q r t u \log (x) \log \left(i \left(j (h x)^t\right)^u\right) \log (c+d x) \log (h x)-2 t u \log (x) \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) \log (h x)-q r \log ^2\left(i \left(j (h x)^t\right)^u\right) \log \left(\frac{d x}{c}+1\right) \log (h x)-p r \log (x) \log ^2\left(i \left(j (h x)^t\right)^u\right) \log (a+b x)-q r \log (x) \log ^2\left(i \left(j (h x)^t\right)^u\right) \log (c+d x)+\log (x) \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)-p r \log ^2\left(i \left(j (h x)^t\right)^u\right) \text{Li}_2\left(-\frac{b x}{a}\right)-q r \log ^2\left(i \left(j (h x)^t\right)^u\right) \text{Li}_2\left(-\frac{d x}{c}\right)+2 p r t u \log \left(i \left(j (h x)^t\right)^u\right) \text{Li}_3\left(-\frac{b x}{a}\right)+2 q r t u \log \left(i \left(j (h x)^t\right)^u\right) \text{Li}_3\left(-\frac{d x}{c}\right)-2 p r t^2 u^2 \text{Li}_4\left(-\frac{b x}{a}\right)-2 q r t^2 u^2 \text{Li}_4\left(-\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}-p r \text{Li}_2\left(-\frac{b x}{a}\right) \log ^2\left(i \left(j (h x)^t\right)^u\right)+2 p r t u \text{Li}_3\left(-\frac{b x}{a}\right) \log \left(i \left(j (h x)^t\right)^u\right)-\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}-2 p r t^2 u^2 \text{Li}_4\left(-\frac{b x}{a}\right)-q r \text{Li}_2\left(-\frac{d x}{c}\right) \log ^2\left(i \left(j (h x)^t\right)^u\right)+2 q r t u \text{Li}_3\left(-\frac{d x}{c}\right) \log \left(i \left(j (h x)^t\right)^u\right)-\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}-2 q r t^2 u^2 \text{Li}_4\left(-\frac{d x}{c}\right)",1,"-(p*r*t^2*u^2*Log[x]*Log[h*x]^2*Log[a + b*x]) + p*r*t^2*u^2*Log[h*x]^3*Log[a + b*x] + 2*p*r*t*u*Log[x]*Log[h*x]*Log[i*(j*(h*x)^t)^u]*Log[a + b*x] - 2*p*r*t*u*Log[h*x]^2*Log[i*(j*(h*x)^t)^u]*Log[a + b*x] - p*r*Log[x]*Log[i*(j*(h*x)^t)^u]^2*Log[a + b*x] + p*r*Log[h*x]*Log[i*(j*(h*x)^t)^u]^2*Log[a + b*x] - (p*r*t^2*u^2*Log[h*x]^3*Log[1 + (b*x)/a])/3 + p*r*t*u*Log[h*x]^2*Log[i*(j*(h*x)^t)^u]*Log[1 + (b*x)/a] - p*r*Log[h*x]*Log[i*(j*(h*x)^t)^u]^2*Log[1 + (b*x)/a] - q*r*t^2*u^2*Log[x]*Log[h*x]^2*Log[c + d*x] + q*r*t^2*u^2*Log[h*x]^3*Log[c + d*x] + 2*q*r*t*u*Log[x]*Log[h*x]*Log[i*(j*(h*x)^t)^u]*Log[c + d*x] - 2*q*r*t*u*Log[h*x]^2*Log[i*(j*(h*x)^t)^u]*Log[c + d*x] - q*r*Log[x]*Log[i*(j*(h*x)^t)^u]^2*Log[c + d*x] + q*r*Log[h*x]*Log[i*(j*(h*x)^t)^u]^2*Log[c + d*x] + t^2*u^2*Log[x]*Log[h*x]^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - (2*t^2*u^2*Log[h*x]^3*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/3 - 2*t*u*Log[x]*Log[h*x]*Log[i*(j*(h*x)^t)^u]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + t*u*Log[h*x]^2*Log[i*(j*(h*x)^t)^u]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + Log[x]*Log[i*(j*(h*x)^t)^u]^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - (q*r*t^2*u^2*Log[h*x]^3*Log[1 + (d*x)/c])/3 + q*r*t*u*Log[h*x]^2*Log[i*(j*(h*x)^t)^u]*Log[1 + (d*x)/c] - q*r*Log[h*x]*Log[i*(j*(h*x)^t)^u]^2*Log[1 + (d*x)/c] - 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)]","B",1
58,1,451,194,0.4332084,"\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","Integrate[(Log[i*(j*(h*x)^t)^u]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/x,x]","\log (x) \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)+\frac{1}{2} t u \log ^2(h x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-t u \log (x) \log (h x) \log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-p r \text{Li}_2\left(-\frac{b x}{a}\right) \log \left(i \left(j (h x)^t\right)^u\right)+p r \log (h x) \log (a+b x) \log \left(i \left(j (h x)^t\right)^u\right)-p r \log (h x) \log \left(\frac{b x}{a}+1\right) \log \left(i \left(j (h x)^t\right)^u\right)-p r \log (x) \log (a+b x) \log \left(i \left(j (h x)^t\right)^u\right)-p r t u \log ^2(h x) \log (a+b x)+\frac{1}{2} p r t u \log ^2(h x) \log \left(\frac{b x}{a}+1\right)+p r t u \log (x) \log (h x) \log (a+b x)+p r t u \text{Li}_3\left(-\frac{b x}{a}\right)-q r \text{Li}_2\left(-\frac{d x}{c}\right) \log \left(i \left(j (h x)^t\right)^u\right)+q r \log (h x) \log (c+d x) \log \left(i \left(j (h x)^t\right)^u\right)-q r \log (h x) \log \left(\frac{d x}{c}+1\right) \log \left(i \left(j (h x)^t\right)^u\right)-q r \log (x) \log (c+d x) \log \left(i \left(j (h x)^t\right)^u\right)-q r t u \log ^2(h x) \log (c+d x)+\frac{1}{2} q r t u \log ^2(h x) \log \left(\frac{d x}{c}+1\right)+q r t u \log (x) \log (h x) \log (c+d x)+q r t u \text{Li}_3\left(-\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}-p r \text{Li}_2\left(-\frac{b x}{a}\right) \log \left(i \left(j (h x)^t\right)^u\right)-\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}+p r t u \text{Li}_3\left(-\frac{b x}{a}\right)-q r \text{Li}_2\left(-\frac{d x}{c}\right) \log \left(i \left(j (h x)^t\right)^u\right)-\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}+q r t u \text{Li}_3\left(-\frac{d x}{c}\right)",1,"p*r*t*u*Log[x]*Log[h*x]*Log[a + b*x] - p*r*t*u*Log[h*x]^2*Log[a + b*x] - p*r*Log[x]*Log[i*(j*(h*x)^t)^u]*Log[a + b*x] + p*r*Log[h*x]*Log[i*(j*(h*x)^t)^u]*Log[a + b*x] + (p*r*t*u*Log[h*x]^2*Log[1 + (b*x)/a])/2 - p*r*Log[h*x]*Log[i*(j*(h*x)^t)^u]*Log[1 + (b*x)/a] + q*r*t*u*Log[x]*Log[h*x]*Log[c + d*x] - q*r*t*u*Log[h*x]^2*Log[c + d*x] - q*r*Log[x]*Log[i*(j*(h*x)^t)^u]*Log[c + d*x] + q*r*Log[h*x]*Log[i*(j*(h*x)^t)^u]*Log[c + d*x] - t*u*Log[x]*Log[h*x]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + (t*u*Log[h*x]^2*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r])/2 + Log[x]*Log[i*(j*(h*x)^t)^u]*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] + (q*r*t*u*Log[h*x]^2*Log[1 + (d*x)/c])/2 - q*r*Log[h*x]*Log[i*(j*(h*x)^t)^u]*Log[1 + (d*x)/c] - 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)]","B",1
59,1,78,81,0.0749189,"\int \frac{\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)}{x} \, dx","Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/x,x]","\log (x) \left(\log \left(e \left(f (a+b x)^p (c+d x)^q\right)^r\right)-p r \log \left(\frac{b x}{a}+1\right)-q r \log \left(\frac{d x}{c}+1\right)\right)-p r \text{Li}_2\left(-\frac{b x}{a}\right)-q r \text{Li}_2\left(-\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 \text{Li}_2\left(-\frac{b x}{a}\right)-p r \log (x) \log \left(\frac{b x}{a}+1\right)-q r \text{Li}_2\left(-\frac{d x}{c}\right)-q r \log (x) \log \left(\frac{d x}{c}+1\right)",1,"Log[x]*(-(p*r*Log[1 + (b*x)/a]) + Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r] - q*r*Log[1 + (d*x)/c]) - p*r*PolyLog[2, -((b*x)/a)] - q*r*PolyLog[2, -((d*x)/c)]","A",1
60,0,0,42,0.4865162,"\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","Integrate[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,"Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(x*Log[i*(j*(h*x)^t)^u]), x]","A",-1
61,0,0,42,2.5463319,"\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","Integrate[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,"Integrate[Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]/(x*Log[i*(j*(h*x)^t)^u]^2), x]","A",-1
62,0,0,31,5.0951281,"\int \frac{\log (x) \log ^3\left(\frac{a+b x}{(b c-a d) x}\right)}{x} \, dx","Integrate[(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,"Integrate[(Log[x]*Log[(a + b*x)/((b*c - a*d)*x)]^3)/x, x]","A",-1
63,0,0,31,5.088036,"\int \frac{\log (x) \log ^2\left(\frac{a+b x}{(b c-a d) x}\right)}{x} \, dx","Integrate[(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,"Integrate[(Log[x]*Log[(a + b*x)/((b*c - a*d)*x)]^2)/x, x]","A",-1
64,1,66,82,5.0325623,"\int \frac{\log (x) \log \left(\frac{a+b x}{(b c-a d) x}\right)}{x} \, dx","Integrate[(Log[x]*Log[(a + b*x)/((b*c - a*d)*x)])/x,x]","\frac{1}{6} \log ^2(x) \left(3 \log \left(\frac{a+b x}{b c x-a d x}\right)-3 \log \left(\frac{b x}{a}+1\right)+\log (x)\right)+\text{Li}_3\left(-\frac{b x}{a}\right)-\log (x) \text{Li}_2\left(-\frac{b x}{a}\right)","\frac{1}{2} \log ^2(x) \log \left(\frac{a}{x (b c-a d)}+\frac{b}{b c-a d}\right)+\text{Li}_3\left(-\frac{a}{b x}\right)+\log (x) \text{Li}_2\left(-\frac{a}{b x}\right)-\frac{1}{2} \log ^2(x) \log \left(\frac{a}{b x}+1\right)",1,"(Log[x]^2*(Log[x] - 3*Log[1 + (b*x)/a] + 3*Log[(a + b*x)/(b*c*x - a*d*x)]))/6 - Log[x]*PolyLog[2, -((b*x)/a)] + PolyLog[3, -((b*x)/a)]","A",1
65,0,0,31,5.1004344,"\int \frac{\log (x)}{x \log \left(\frac{a+b x}{(b c-a d) x}\right)} \, dx","Integrate[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,"Integrate[Log[x]/(x*Log[(a + b*x)/((b*c - a*d)*x)]), x]","A",-1
66,0,0,31,33.6575542,"\int \frac{\log (x)}{x \log ^2\left(\frac{a+b x}{(b c-a d) x}\right)} \, dx","Integrate[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,"Integrate[Log[x]/(x*Log[(a + b*x)/((b*c - a*d)*x)]^2), x]","A",-1
67,1,18164,620,22.1533998,"\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","Integrate[(Log[e*((a + b*x)/(c + d*x))^n]^3*Log[h*(f + g*x)^m])/((a + b*x)*(c + d*x)),x]","\text{Result too large to show}","\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{6 m n^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{Li}_4\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{b c-a d}-\frac{m \log ^3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\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{Li}_3\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{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{6 m n^2 \text{Li}_4\left(\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{Li}_2\left(\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{Li}_3\left(\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{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^3 \text{Li}_5\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{b c-a d}-\frac{6 m n^3 \text{Li}_5\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b c-a d}",1,"Result too large to show","B",0
68,1,9211,496,10.2108747,"\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","Integrate[(Log[e*((a + b*x)/(c + d*x))^n]^2*Log[h*(f + g*x)^m])/((a + b*x)*(c + d*x)),x]","\text{Result too large to show}","\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 ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{b c-a d}+\frac{2 m n \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{Li}_3\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{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 \text{Li}_2\left(\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{Li}_3\left(\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 \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{2 m n^2 \text{Li}_4\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{b c-a d}+\frac{2 m n^2 \text{Li}_4\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b c-a d}",1,"Result too large to show","B",0
69,1,1408,371,3.1656334,"\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","Integrate[(Log[e*((a + b*x)/(c + d*x))^n]*Log[h*(f + g*x)^m])/((a + b*x)*(c + d*x)),x]","\frac{-m n \log (f+g x) \log ^2\left(\frac{a}{b}+x\right)+n \log \left(h (f+g x)^m\right) \log ^2\left(\frac{a}{b}+x\right)+2 m n \log (a+b x) \log (f+g x) \log \left(\frac{a}{b}+x\right)+2 m \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log (f+g x) \log \left(\frac{a}{b}+x\right)-2 m n \log \left(\frac{a+b x}{c+d x}\right) \log (f+g x) \log \left(\frac{a}{b}+x\right)-2 m n \log (c+d x) \log (f+g x) \log \left(\frac{a}{b}+x\right)+2 m n \log \left(\frac{b (c+d x)}{b c-a d}\right) \log (f+g x) \log \left(\frac{a}{b}+x\right)-2 m \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(\frac{b (f+g x)}{b f-a g}\right) \log \left(\frac{a}{b}+x\right)+2 m n \log \left(\frac{a+b x}{c+d x}\right) \log \left(\frac{b (f+g x)}{b f-a g}\right) \log \left(\frac{a}{b}+x\right)-2 n \log (a+b x) \log \left(h (f+g x)^m\right) \log \left(\frac{a}{b}+x\right)+2 n \log (c+d x) \log \left(h (f+g x)^m\right) \log \left(\frac{a}{b}+x\right)-2 n \log \left(\frac{b (c+d x)}{b c-a d}\right) \log \left(h (f+g x)^m\right) \log \left(\frac{a}{b}+x\right)+m n \log ^2\left(\frac{a+b x}{c+d x}\right) \log \left(\frac{b c-a d}{b c+b d x}\right)-m n \log ^2\left(\frac{c}{d}+x\right) \log (f+g x)+m n \log ^2\left(\frac{a+b x}{c+d x}\right) \log (f+g x)-2 m n \log \left(\frac{c}{d}+x\right) \log (a+b x) \log (f+g x)+2 m n \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right) \log (f+g x)-2 m \log \left(\frac{c}{d}+x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log (f+g x)-2 m \log (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log (f+g x)+2 m n \log \left(\frac{c}{d}+x\right) \log \left(\frac{a+b x}{c+d x}\right) \log (f+g x)+2 m n \log \left(\frac{c}{d}+x\right) \log (c+d x) \log (f+g x)+2 m \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log (c+d x) \log (f+g x)+2 m \log \left(\frac{c}{d}+x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(\frac{d (f+g x)}{d f-c g}\right)-2 m n \log \left(\frac{c}{d}+x\right) \log \left(\frac{a+b x}{c+d x}\right) \log \left(\frac{d (f+g x)}{d f-c g}\right)-m n \log ^2\left(\frac{a+b x}{c+d x}\right) \log \left(\frac{(b c-a d) (f+g x)}{(b f-a g) (c+d x)}\right)+n \log ^2\left(\frac{c}{d}+x\right) \log \left(h (f+g x)^m\right)+2 n \log \left(\frac{c}{d}+x\right) \log (a+b x) \log \left(h (f+g x)^m\right)-2 n \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right) \log \left(h (f+g x)^m\right)+2 \log (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(h (f+g x)^m\right)-2 n \log \left(\frac{c}{d}+x\right) \log (c+d x) \log \left(h (f+g x)^m\right)-2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log (c+d x) \log \left(h (f+g x)^m\right)+2 n \left(m \log (f+g x)-\log \left(h (f+g x)^m\right)\right) \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)-2 m \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right) \text{Li}_2\left(\frac{g (a+b x)}{a g-b f}\right)+2 m n \log \left(\frac{a+b x}{c+d x}\right) \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right)-2 m n \log \left(\frac{a+b x}{c+d x}\right) \text{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)+2 m n \log (f+g x) \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)-2 n \log \left(h (f+g x)^m\right) \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+2 m \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{Li}_2\left(\frac{g (c+d x)}{c g-d f}\right)-2 m n \log \left(\frac{a+b x}{c+d x}\right) \text{Li}_2\left(\frac{g (c+d x)}{c g-d f}\right)-2 m n \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)+2 m n \text{Li}_3\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{2 b c-2 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 \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \text{Li}_2\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{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 \text{Li}_2\left(\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 \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 n \text{Li}_3\left(\frac{(d f-c g) (a+b x)}{(b f-a g) (c+d x)}\right)}{b c-a d}-\frac{m n \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)}{b c-a d}",1,"(m*n*Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] - m*n*Log[a/b + x]^2*Log[f + g*x] - m*n*Log[c/d + x]^2*Log[f + g*x] + 2*m*n*Log[a/b + x]*Log[a + b*x]*Log[f + g*x] - 2*m*n*Log[c/d + x]*Log[a + b*x]*Log[f + g*x] + 2*m*n*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[f + g*x] + 2*m*Log[a/b + x]*Log[e*((a + b*x)/(c + d*x))^n]*Log[f + g*x] - 2*m*Log[c/d + x]*Log[e*((a + b*x)/(c + d*x))^n]*Log[f + g*x] - 2*m*Log[a + b*x]*Log[e*((a + b*x)/(c + d*x))^n]*Log[f + g*x] - 2*m*n*Log[a/b + x]*Log[(a + b*x)/(c + d*x)]*Log[f + g*x] + 2*m*n*Log[c/d + x]*Log[(a + b*x)/(c + d*x)]*Log[f + g*x] + m*n*Log[(a + b*x)/(c + d*x)]^2*Log[f + g*x] - 2*m*n*Log[a/b + x]*Log[c + d*x]*Log[f + g*x] + 2*m*n*Log[c/d + x]*Log[c + d*x]*Log[f + g*x] + 2*m*Log[e*((a + b*x)/(c + d*x))^n]*Log[c + d*x]*Log[f + g*x] + 2*m*n*Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)]*Log[f + g*x] - 2*m*Log[a/b + x]*Log[e*((a + b*x)/(c + d*x))^n]*Log[(b*(f + g*x))/(b*f - a*g)] + 2*m*n*Log[a/b + x]*Log[(a + b*x)/(c + d*x)]*Log[(b*(f + g*x))/(b*f - a*g)] + 2*m*Log[c/d + x]*Log[e*((a + b*x)/(c + d*x))^n]*Log[(d*(f + g*x))/(d*f - c*g)] - 2*m*n*Log[c/d + x]*Log[(a + b*x)/(c + d*x)]*Log[(d*(f + g*x))/(d*f - c*g)] - m*n*Log[(a + b*x)/(c + d*x)]^2*Log[((b*c - a*d)*(f + g*x))/((b*f - a*g)*(c + d*x))] + n*Log[a/b + x]^2*Log[h*(f + g*x)^m] + n*Log[c/d + x]^2*Log[h*(f + g*x)^m] - 2*n*Log[a/b + x]*Log[a + b*x]*Log[h*(f + g*x)^m] + 2*n*Log[c/d + x]*Log[a + b*x]*Log[h*(f + g*x)^m] - 2*n*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[h*(f + g*x)^m] + 2*Log[a + b*x]*Log[e*((a + b*x)/(c + d*x))^n]*Log[h*(f + g*x)^m] + 2*n*Log[a/b + x]*Log[c + d*x]*Log[h*(f + g*x)^m] - 2*n*Log[c/d + x]*Log[c + d*x]*Log[h*(f + g*x)^m] - 2*Log[e*((a + b*x)/(c + d*x))^n]*Log[c + d*x]*Log[h*(f + g*x)^m] - 2*n*Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)]*Log[h*(f + g*x)^m] + 2*n*(m*Log[f + g*x] - Log[h*(f + g*x)^m])*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] - 2*m*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])*PolyLog[2, (g*(a + b*x))/(-(b*f) + a*g)] + 2*m*n*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 2*m*n*Log[(a + b*x)/(c + d*x)]*PolyLog[2, ((d*f - c*g)*(a + b*x))/((b*f - a*g)*(c + d*x))] + 2*m*n*Log[f + g*x]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] - 2*n*Log[h*(f + g*x)^m]*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 2*m*Log[e*((a + b*x)/(c + d*x))^n]*PolyLog[2, (g*(c + d*x))/(-(d*f) + c*g)] - 2*m*n*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (g*(c + d*x))/(-(d*f) + c*g)] - 2*m*n*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] + 2*m*n*PolyLog[3, ((d*f - c*g)*(a + b*x))/((b*f - a*g)*(c + d*x))])/(2*b*c - 2*a*d)","B",1
70,0,0,108,2.0140373,"\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","Integrate[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,"Integrate[Log[h*(f + g*x)^m]/((a + b*x)*(c + d*x)*Log[e*((a + b*x)/(c + d*x))^n]), x]","A",-1
71,0,0,93,1.3254147,"\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","Integrate[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,"Integrate[Log[h*(f + g*x)^m]/((a + b*x)*(c + d*x)*Log[e*((a + b*x)/(c + d*x))^n]^2), x]","A",-1
72,0,0,114,0.6502854,"\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","Integrate[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,"Integrate[Log[1 - (a + b*x)/(c + d*x)]/((a + b*x)*(c + d*x)*Log[(a + b*x)/(c + d*x)]^2), x]","A",-1
73,0,0,114,0.6386134,"\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","Integrate[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,"Integrate[Log[1 - (c + d*x)/(a + b*x)]/((a + b*x)*(c + d*x)*Log[(a + b*x)/(c + d*x)]^2), x]","A",-1
74,1,44,45,0.3191032,"\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","Integrate[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]","\frac{\log \left(1-\frac{a+b x}{c+d x}\right)}{(a d-b c) \log \left(\frac{a+b x}{c+d x}\right)}","-\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,"Log[1 - (a + b*x)/(c + d*x)]/((-(b*c) + a*d)*Log[(a + b*x)/(c + d*x)])","A",1
75,1,45,45,0.0891919,"\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","Integrate[-(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]","-\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)}","-\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,"-(Log[1 - (c + d*x)/(a + b*x)]/((b*c - a*d)*Log[(a + b*x)/(c + d*x)]))","A",1
76,1,461,560,0.3857538,"\int \frac{x^3 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f-g x^2} \, dx","Integrate[(x^3*Log[e*((a + b*x)/(c + d*x))^n])/(f - g*x^2),x]","\frac{\frac{g n \left(a^2 d^2 \log (a+b x)-b \left(d x (a d-b c)+b c^2 \log (c+d x)\right)\right)}{b^2 d^2}-f \log \left(\sqrt{f}-\sqrt{g} x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-f \log \left(\sqrt{f}+\sqrt{g} x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-g x^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+f n \left(\log \left(\sqrt{f}-\sqrt{g} x\right) \left(\log \left(\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)-\log \left(\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)\right)+\text{Li}_2\left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{\sqrt{g} a+b \sqrt{f}}\right)-\text{Li}_2\left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{\sqrt{g} c+d \sqrt{f}}\right)\right)+f n \left(\log \left(\sqrt{f}+\sqrt{g} x\right) \left(\log \left(-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)-\log \left(-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)\right)+\text{Li}_2\left(\frac{b \left(\sqrt{g} x+\sqrt{f}\right)}{b \sqrt{f}-a \sqrt{g}}\right)-\text{Li}_2\left(\frac{d \left(\sqrt{g} x+\sqrt{f}\right)}{d \sqrt{f}-c \sqrt{g}}\right)\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 \text{Li}_2\left(-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 g^2}-\frac{f n \text{Li}_2\left(\frac{\sqrt{g} (a+b x)}{\sqrt{g} a+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)}{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 \text{Li}_2\left(-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 g^2}+\frac{f n \text{Li}_2\left(\frac{\sqrt{g} (c+d x)}{\sqrt{g} c+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)}{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,"(-(g*x^2*Log[e*((a + b*x)/(c + d*x))^n]) + (g*n*(a^2*d^2*Log[a + b*x] - b*(d*(-(b*c) + a*d)*x + b*c^2*Log[c + d*x])))/(b^2*d^2) - f*Log[e*((a + b*x)/(c + d*x))^n]*Log[Sqrt[f] - Sqrt[g]*x] - f*Log[e*((a + b*x)/(c + d*x))^n]*Log[Sqrt[f] + Sqrt[g]*x] + f*n*((Log[(Sqrt[g]*(a + b*x))/(b*Sqrt[f] + a*Sqrt[g])] - Log[(Sqrt[g]*(c + d*x))/(d*Sqrt[f] + c*Sqrt[g])])*Log[Sqrt[f] - Sqrt[g]*x] + PolyLog[2, (b*(Sqrt[f] - Sqrt[g]*x))/(b*Sqrt[f] + a*Sqrt[g])] - PolyLog[2, (d*(Sqrt[f] - Sqrt[g]*x))/(d*Sqrt[f] + c*Sqrt[g])]) + f*n*((Log[-((Sqrt[g]*(a + b*x))/(b*Sqrt[f] - a*Sqrt[g]))] - Log[-((Sqrt[g]*(c + d*x))/(d*Sqrt[f] - c*Sqrt[g]))])*Log[Sqrt[f] + Sqrt[g]*x] + PolyLog[2, (b*(Sqrt[f] + Sqrt[g]*x))/(b*Sqrt[f] - a*Sqrt[g])] - PolyLog[2, (d*(Sqrt[f] + Sqrt[g]*x))/(d*Sqrt[f] - c*Sqrt[g])]))/(2*g^2)","A",1
77,1,467,550,0.2549884,"\int \frac{x^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f-g x^2} \, dx","Integrate[(x^2*Log[e*((a + b*x)/(c + d*x))^n])/(f - g*x^2),x]","\frac{-\sqrt{f} \log \left(\sqrt{f}-\sqrt{g} x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+\sqrt{f} \log \left(\sqrt{f}+\sqrt{g} x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-\frac{2 \sqrt{g} (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b}+\sqrt{f} n \left(\log \left(\sqrt{f}-\sqrt{g} x\right) \left(\log \left(\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)-\log \left(\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)\right)+\text{Li}_2\left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{\sqrt{g} a+b \sqrt{f}}\right)-\text{Li}_2\left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{\sqrt{g} c+d \sqrt{f}}\right)\right)-\sqrt{f} n \left(\log \left(\sqrt{f}+\sqrt{g} x\right) \left(\log \left(-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)-\log \left(-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)\right)+\text{Li}_2\left(\frac{b \left(\sqrt{g} x+\sqrt{f}\right)}{b \sqrt{f}-a \sqrt{g}}\right)-\text{Li}_2\left(\frac{d \left(\sqrt{g} x+\sqrt{f}\right)}{d \sqrt{f}-c \sqrt{g}}\right)\right)+\frac{2 \sqrt{g} n (b c-a d) \log (c+d x)}{b d}}{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 \text{Li}_2\left(-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 g^{3/2}}-\frac{\sqrt{f} n \text{Li}_2\left(\frac{\sqrt{g} (a+b x)}{\sqrt{g} a+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)}{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 \text{Li}_2\left(-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 g^{3/2}}+\frac{\sqrt{f} n \text{Li}_2\left(\frac{\sqrt{g} (c+d x)}{\sqrt{g} c+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)}{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,"((-2*Sqrt[g]*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/b + (2*(b*c - a*d)*Sqrt[g]*n*Log[c + d*x])/(b*d) - Sqrt[f]*Log[e*((a + b*x)/(c + d*x))^n]*Log[Sqrt[f] - Sqrt[g]*x] + Sqrt[f]*Log[e*((a + b*x)/(c + d*x))^n]*Log[Sqrt[f] + Sqrt[g]*x] + Sqrt[f]*n*((Log[(Sqrt[g]*(a + b*x))/(b*Sqrt[f] + a*Sqrt[g])] - Log[(Sqrt[g]*(c + d*x))/(d*Sqrt[f] + c*Sqrt[g])])*Log[Sqrt[f] - Sqrt[g]*x] + PolyLog[2, (b*(Sqrt[f] - Sqrt[g]*x))/(b*Sqrt[f] + a*Sqrt[g])] - PolyLog[2, (d*(Sqrt[f] - Sqrt[g]*x))/(d*Sqrt[f] + c*Sqrt[g])]) - Sqrt[f]*n*((Log[-((Sqrt[g]*(a + b*x))/(b*Sqrt[f] - a*Sqrt[g]))] - Log[-((Sqrt[g]*(c + d*x))/(d*Sqrt[f] - c*Sqrt[g]))])*Log[Sqrt[f] + Sqrt[g]*x] + PolyLog[2, (b*(Sqrt[f] + Sqrt[g]*x))/(b*Sqrt[f] - a*Sqrt[g])] - PolyLog[2, (d*(Sqrt[f] + Sqrt[g]*x))/(d*Sqrt[f] - c*Sqrt[g])]))/(2*g^(3/2))","A",1
78,1,413,403,0.1300264,"\int \frac{x \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f-g x^2} \, dx","Integrate[(x*Log[e*((a + b*x)/(c + d*x))^n])/(f - g*x^2),x]","-\frac{\log \left(\sqrt{f}-\sqrt{g} x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+\log \left(\sqrt{f}+\sqrt{g} x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \text{Li}_2\left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{\sqrt{g} a+b \sqrt{f}}\right)-n \text{Li}_2\left(\frac{b \left(\sqrt{g} x+\sqrt{f}\right)}{b \sqrt{f}-a \sqrt{g}}\right)-n \log \left(\sqrt{f}-\sqrt{g} x\right) \log \left(\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)-n \log \left(\sqrt{f}+\sqrt{g} x\right) \log \left(-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)+n \text{Li}_2\left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{\sqrt{g} c+d \sqrt{f}}\right)+n \text{Li}_2\left(\frac{d \left(\sqrt{g} x+\sqrt{f}\right)}{d \sqrt{f}-c \sqrt{g}}\right)+n \log \left(\sqrt{f}-\sqrt{g} x\right) \log \left(\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)+n \log \left(\sqrt{f}+\sqrt{g} x\right) \log \left(-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\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 \text{Li}_2\left(-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 g}-\frac{n \text{Li}_2\left(\frac{\sqrt{g} (a+b x)}{\sqrt{g} a+b \sqrt{f}}\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 \text{Li}_2\left(-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 g}+\frac{n \text{Li}_2\left(\frac{\sqrt{g} (c+d x)}{\sqrt{g} c+d \sqrt{f}}\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,"-1/2*(-(n*Log[(Sqrt[g]*(a + b*x))/(b*Sqrt[f] + a*Sqrt[g])]*Log[Sqrt[f] - Sqrt[g]*x]) + Log[e*((a + b*x)/(c + d*x))^n]*Log[Sqrt[f] - Sqrt[g]*x] + n*Log[(Sqrt[g]*(c + d*x))/(d*Sqrt[f] + c*Sqrt[g])]*Log[Sqrt[f] - Sqrt[g]*x] - n*Log[-((Sqrt[g]*(a + b*x))/(b*Sqrt[f] - a*Sqrt[g]))]*Log[Sqrt[f] + Sqrt[g]*x] + Log[e*((a + b*x)/(c + d*x))^n]*Log[Sqrt[f] + Sqrt[g]*x] + n*Log[-((Sqrt[g]*(c + d*x))/(d*Sqrt[f] - c*Sqrt[g]))]*Log[Sqrt[f] + Sqrt[g]*x] - n*PolyLog[2, (b*(Sqrt[f] - Sqrt[g]*x))/(b*Sqrt[f] + a*Sqrt[g])] + n*PolyLog[2, (d*(Sqrt[f] - Sqrt[g]*x))/(d*Sqrt[f] + c*Sqrt[g])] - n*PolyLog[2, (b*(Sqrt[f] + Sqrt[g]*x))/(b*Sqrt[f] - a*Sqrt[g])] + n*PolyLog[2, (d*(Sqrt[f] + Sqrt[g]*x))/(d*Sqrt[f] - c*Sqrt[g])])/g","A",1
79,1,421,291,0.1094271,"\int \frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f-g x^2} \, dx","Integrate[Log[e*((a + b*x)/(c + d*x))^n]/(f - g*x^2),x]","\frac{-\log \left(\sqrt{f}-\sqrt{g} x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+\log \left(\sqrt{f}+\sqrt{g} x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \text{Li}_2\left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{\sqrt{g} a+b \sqrt{f}}\right)-n \text{Li}_2\left(\frac{b \left(\sqrt{g} x+\sqrt{f}\right)}{b \sqrt{f}-a \sqrt{g}}\right)+n \log \left(\sqrt{f}-\sqrt{g} x\right) \log \left(\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)-n \log \left(\sqrt{f}+\sqrt{g} x\right) \log \left(-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)-n \text{Li}_2\left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{\sqrt{g} c+d \sqrt{f}}\right)+n \text{Li}_2\left(\frac{d \left(\sqrt{g} x+\sqrt{f}\right)}{d \sqrt{f}-c \sqrt{g}}\right)-n \log \left(\sqrt{f}-\sqrt{g} x\right) \log \left(\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)+n \log \left(\sqrt{f}+\sqrt{g} x\right) \log \left(-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\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}}+\frac{n \text{Li}_2\left(\frac{\left(d \sqrt{f}-c \sqrt{g}\right) (a+b x)}{\left(b \sqrt{f}-a \sqrt{g}\right) (c+d x)}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{n \text{Li}_2\left(\frac{\left(\sqrt{g} c+d \sqrt{f}\right) (a+b x)}{\left(\sqrt{g} a+b \sqrt{f}\right) (c+d x)}\right)}{2 \sqrt{f} \sqrt{g}}",1,"(n*Log[(Sqrt[g]*(a + b*x))/(b*Sqrt[f] + a*Sqrt[g])]*Log[Sqrt[f] - Sqrt[g]*x] - Log[e*((a + b*x)/(c + d*x))^n]*Log[Sqrt[f] - Sqrt[g]*x] - n*Log[(Sqrt[g]*(c + d*x))/(d*Sqrt[f] + c*Sqrt[g])]*Log[Sqrt[f] - Sqrt[g]*x] - n*Log[-((Sqrt[g]*(a + b*x))/(b*Sqrt[f] - a*Sqrt[g]))]*Log[Sqrt[f] + Sqrt[g]*x] + Log[e*((a + b*x)/(c + d*x))^n]*Log[Sqrt[f] + Sqrt[g]*x] + n*Log[-((Sqrt[g]*(c + d*x))/(d*Sqrt[f] - c*Sqrt[g]))]*Log[Sqrt[f] + Sqrt[g]*x] + n*PolyLog[2, (b*(Sqrt[f] - Sqrt[g]*x))/(b*Sqrt[f] + a*Sqrt[g])] - n*PolyLog[2, (d*(Sqrt[f] - Sqrt[g]*x))/(d*Sqrt[f] + c*Sqrt[g])] - n*PolyLog[2, (b*(Sqrt[f] + Sqrt[g]*x))/(b*Sqrt[f] - a*Sqrt[g])] + n*PolyLog[2, (d*(Sqrt[f] + Sqrt[g]*x))/(d*Sqrt[f] - c*Sqrt[g])])/(2*Sqrt[f]*Sqrt[g])","A",1
80,1,487,518,0.1961445,"\int \frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{x \left(f-g x^2\right)} \, dx","Integrate[Log[e*((a + b*x)/(c + d*x))^n]/(x*(f - g*x^2)),x]","-\frac{\log \left(\sqrt{f}-\sqrt{g} x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+\log \left(\sqrt{f}+\sqrt{g} x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-2 \log (x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \text{Li}_2\left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{\sqrt{g} a+b \sqrt{f}}\right)-n \text{Li}_2\left(\frac{b \left(\sqrt{g} x+\sqrt{f}\right)}{b \sqrt{f}-a \sqrt{g}}\right)-n \log \left(\sqrt{f}-\sqrt{g} x\right) \log \left(\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)-n \log \left(\sqrt{f}+\sqrt{g} x\right) \log \left(-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)+2 n \text{Li}_2\left(-\frac{b x}{a}\right)+2 n \log (x) \log \left(\frac{b x}{a}+1\right)+n \text{Li}_2\left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{\sqrt{g} c+d \sqrt{f}}\right)+n \text{Li}_2\left(\frac{d \left(\sqrt{g} x+\sqrt{f}\right)}{d \sqrt{f}-c \sqrt{g}}\right)+n \log \left(\sqrt{f}-\sqrt{g} x\right) \log \left(\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)+n \log \left(\sqrt{f}+\sqrt{g} x\right) \log \left(-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)-2 n \text{Li}_2\left(-\frac{d x}{c}\right)-2 n \log (x) \log \left(\frac{d x}{c}+1\right)}{2 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 \text{Li}_2\left(-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 f}-\frac{n \text{Li}_2\left(\frac{\sqrt{g} (a+b x)}{\sqrt{g} a+b \sqrt{f}}\right)}{2 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 \text{Li}_2\left(\frac{b x}{a}+1\right)}{f}+\frac{n \log \left(-\frac{b x}{a}\right) \log (a+b x)}{f}+\frac{n \text{Li}_2\left(-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 f}+\frac{n \text{Li}_2\left(\frac{\sqrt{g} (c+d x)}{\sqrt{g} c+d \sqrt{f}}\right)}{2 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 \text{Li}_2\left(\frac{d x}{c}+1\right)}{f}-\frac{n \log \left(-\frac{d x}{c}\right) \log (c+d x)}{f}",1,"-1/2*(2*n*Log[x]*Log[1 + (b*x)/a] - 2*Log[x]*Log[e*((a + b*x)/(c + d*x))^n] - 2*n*Log[x]*Log[1 + (d*x)/c] - n*Log[(Sqrt[g]*(a + b*x))/(b*Sqrt[f] + a*Sqrt[g])]*Log[Sqrt[f] - Sqrt[g]*x] + Log[e*((a + b*x)/(c + d*x))^n]*Log[Sqrt[f] - Sqrt[g]*x] + n*Log[(Sqrt[g]*(c + d*x))/(d*Sqrt[f] + c*Sqrt[g])]*Log[Sqrt[f] - Sqrt[g]*x] - n*Log[-((Sqrt[g]*(a + b*x))/(b*Sqrt[f] - a*Sqrt[g]))]*Log[Sqrt[f] + Sqrt[g]*x] + Log[e*((a + b*x)/(c + d*x))^n]*Log[Sqrt[f] + Sqrt[g]*x] + n*Log[-((Sqrt[g]*(c + d*x))/(d*Sqrt[f] - c*Sqrt[g]))]*Log[Sqrt[f] + Sqrt[g]*x] + 2*n*PolyLog[2, -((b*x)/a)] - 2*n*PolyLog[2, -((d*x)/c)] - n*PolyLog[2, (b*(Sqrt[f] - Sqrt[g]*x))/(b*Sqrt[f] + a*Sqrt[g])] + n*PolyLog[2, (d*(Sqrt[f] - Sqrt[g]*x))/(d*Sqrt[f] + c*Sqrt[g])] - n*PolyLog[2, (b*(Sqrt[f] + Sqrt[g]*x))/(b*Sqrt[f] - a*Sqrt[g])] + n*PolyLog[2, (d*(Sqrt[f] + Sqrt[g]*x))/(d*Sqrt[f] - c*Sqrt[g])])/f","A",1
81,1,479,596,0.4015283,"\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","Integrate[Log[e*((a + b*x)/(c + d*x))^n]/(x^2*(f - g*x^2)),x]","\frac{-\sqrt{g} \log \left(\sqrt{f}-\sqrt{g} x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+\sqrt{g} \log \left(\sqrt{f}+\sqrt{g} x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-\frac{2 \sqrt{f} \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{x}+\sqrt{g} n \left(\log \left(\sqrt{f}-\sqrt{g} x\right) \left(\log \left(\frac{\sqrt{g} (a+b x)}{a \sqrt{g}+b \sqrt{f}}\right)-\log \left(\frac{\sqrt{g} (c+d x)}{c \sqrt{g}+d \sqrt{f}}\right)\right)+\text{Li}_2\left(\frac{b \left(\sqrt{f}-\sqrt{g} x\right)}{\sqrt{g} a+b \sqrt{f}}\right)-\text{Li}_2\left(\frac{d \left(\sqrt{f}-\sqrt{g} x\right)}{\sqrt{g} c+d \sqrt{f}}\right)\right)-\sqrt{g} n \left(\log \left(\sqrt{f}+\sqrt{g} x\right) \left(\log \left(-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)-\log \left(-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)\right)+\text{Li}_2\left(\frac{b \left(\sqrt{g} x+\sqrt{f}\right)}{b \sqrt{f}-a \sqrt{g}}\right)-\text{Li}_2\left(\frac{d \left(\sqrt{g} x+\sqrt{f}\right)}{d \sqrt{f}-c \sqrt{g}}\right)\right)+\frac{2 \sqrt{f} n (\log (x) (b c-a d)-b c \log (a+b x)+a d \log (c+d x))}{a c}}{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 \text{Li}_2\left(-\frac{\sqrt{g} (a+b x)}{b \sqrt{f}-a \sqrt{g}}\right)}{2 f^{3/2}}-\frac{\sqrt{g} n \text{Li}_2\left(\frac{\sqrt{g} (a+b x)}{\sqrt{g} a+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)}{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 \text{Li}_2\left(-\frac{\sqrt{g} (c+d x)}{d \sqrt{f}-c \sqrt{g}}\right)}{2 f^{3/2}}+\frac{\sqrt{g} n \text{Li}_2\left(\frac{\sqrt{g} (c+d x)}{\sqrt{g} c+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)}{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,"((-2*Sqrt[f]*Log[e*((a + b*x)/(c + d*x))^n])/x + (2*Sqrt[f]*n*((b*c - a*d)*Log[x] - b*c*Log[a + b*x] + a*d*Log[c + d*x]))/(a*c) - Sqrt[g]*Log[e*((a + b*x)/(c + d*x))^n]*Log[Sqrt[f] - Sqrt[g]*x] + Sqrt[g]*Log[e*((a + b*x)/(c + d*x))^n]*Log[Sqrt[f] + Sqrt[g]*x] + Sqrt[g]*n*((Log[(Sqrt[g]*(a + b*x))/(b*Sqrt[f] + a*Sqrt[g])] - Log[(Sqrt[g]*(c + d*x))/(d*Sqrt[f] + c*Sqrt[g])])*Log[Sqrt[f] - Sqrt[g]*x] + PolyLog[2, (b*(Sqrt[f] - Sqrt[g]*x))/(b*Sqrt[f] + a*Sqrt[g])] - PolyLog[2, (d*(Sqrt[f] - Sqrt[g]*x))/(d*Sqrt[f] + c*Sqrt[g])]) - Sqrt[g]*n*((Log[-((Sqrt[g]*(a + b*x))/(b*Sqrt[f] - a*Sqrt[g]))] - Log[-((Sqrt[g]*(c + d*x))/(d*Sqrt[f] - c*Sqrt[g]))])*Log[Sqrt[f] + Sqrt[g]*x] + PolyLog[2, (b*(Sqrt[f] + Sqrt[g]*x))/(b*Sqrt[f] - a*Sqrt[g])] - PolyLog[2, (d*(Sqrt[f] + Sqrt[g]*x))/(d*Sqrt[f] - c*Sqrt[g])]))/(2*f^(3/2))","A",1
82,1,1240,1046,1.4786701,"\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","Integrate[(x^3*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x + h*x^2),x]","\frac{x^2 \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) h^2+\frac{n \left(b \left(b \log (c+d x) c^2+d (a d-b c) x\right)-a^2 d^2 \log (a+b x)\right) h^2}{b^2 d^2}-\frac{2 g (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) h}{b}+\frac{2 (b c-a d) g n \log (c+d x) h}{b d}+\frac{2 f g \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(g+2 h x-\sqrt{g^2-4 f h}\right) h}{\sqrt{g^2-4 f h}}-\frac{2 f g \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(g+2 h x+\sqrt{g^2-4 f h}\right) h}{\sqrt{g^2-4 f h}}-\frac{2 f g n \left(\left(\log \left(\frac{2 h (a+b x)}{-g b+\sqrt{g^2-4 f h} b+2 a h}\right)-\log \left(\frac{2 h (c+d x)}{-g d+\sqrt{g^2-4 f h} d+2 c h}\right)\right) \log \left(g+2 h x-\sqrt{g^2-4 f h}\right)+\text{Li}_2\left(\frac{b \left(-g-2 h x+\sqrt{g^2-4 f h}\right)}{-g b+\sqrt{g^2-4 f h} b+2 a h}\right)-\text{Li}_2\left(\frac{d \left(-g-2 h x+\sqrt{g^2-4 f h}\right)}{2 c h+d \left(\sqrt{g^2-4 f h}-g\right)}\right)\right) h}{\sqrt{g^2-4 f h}}+\frac{2 f g n \left(\left(\log \left(\frac{2 h (a+b x)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right)-\log \left(\frac{2 h (c+d x)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)\right) \log \left(g+2 h x+\sqrt{g^2-4 f h}\right)+\text{Li}_2\left(\frac{b \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{b \left(g+\sqrt{g^2-4 f h}\right)-2 a h}\right)-\text{Li}_2\left(\frac{d \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{d \left(g+\sqrt{g^2-4 f h}\right)-2 c h}\right)\right) h}{\sqrt{g^2-4 f h}}+\left(g^2-f h\right) \left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(g+2 h x-\sqrt{g^2-4 f h}\right)+\left(g^2-f h\right) \left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right) \log \left(g+2 h x+\sqrt{g^2-4 f h}\right)-\frac{\left(g^2-f h\right) \left(\sqrt{g^2-4 f h}-g\right) n \left(\left(\log \left(\frac{2 h (a+b x)}{-g b+\sqrt{g^2-4 f h} b+2 a h}\right)-\log \left(\frac{2 h (c+d x)}{-g d+\sqrt{g^2-4 f h} d+2 c h}\right)\right) \log \left(g+2 h x-\sqrt{g^2-4 f h}\right)+\text{Li}_2\left(\frac{b \left(-g-2 h x+\sqrt{g^2-4 f h}\right)}{-g b+\sqrt{g^2-4 f h} b+2 a h}\right)-\text{Li}_2\left(\frac{d \left(-g-2 h x+\sqrt{g^2-4 f h}\right)}{2 c h+d \left(\sqrt{g^2-4 f h}-g\right)}\right)\right)}{\sqrt{g^2-4 f h}}-\frac{\left(g^2-f h\right) \left(g+\sqrt{g^2-4 f h}\right) n \left(\left(\log \left(\frac{2 h (a+b x)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right)-\log \left(\frac{2 h (c+d x)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)\right) \log \left(g+2 h x+\sqrt{g^2-4 f h}\right)+\text{Li}_2\left(\frac{b \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{b \left(g+\sqrt{g^2-4 f h}\right)-2 a h}\right)-\text{Li}_2\left(\frac{d \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{d \left(g+\sqrt{g^2-4 f h}\right)-2 c h}\right)\right)}{\sqrt{g^2-4 f h}}}{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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\frac{2 h (c+d x)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 h^3}",1,"(h^2*x^2*Log[e*((a + b*x)/(c + d*x))^n] - (2*g*h*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n])/b + (2*(b*c - a*d)*g*h*n*Log[c + d*x])/(b*d) + (h^2*n*(-(a^2*d^2*Log[a + b*x]) + b*(d*(-(b*c) + a*d)*x + b*c^2*Log[c + d*x])))/(b^2*d^2) + (2*f*g*h*Log[e*((a + b*x)/(c + d*x))^n]*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x])/Sqrt[g^2 - 4*f*h] + (g^2 - f*h)*(1 - g/Sqrt[g^2 - 4*f*h])*Log[e*((a + b*x)/(c + d*x))^n]*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x] - (2*f*g*h*Log[e*((a + b*x)/(c + d*x))^n]*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x])/Sqrt[g^2 - 4*f*h] + (g^2 - f*h)*(1 + g/Sqrt[g^2 - 4*f*h])*Log[e*((a + b*x)/(c + d*x))^n]*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x] - (2*f*g*h*n*((Log[(2*h*(a + b*x))/(-(b*g) + 2*a*h + b*Sqrt[g^2 - 4*f*h])] - Log[(2*h*(c + d*x))/(-(d*g) + 2*c*h + d*Sqrt[g^2 - 4*f*h])])*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x] + PolyLog[2, (b*(-g + Sqrt[g^2 - 4*f*h] - 2*h*x))/(-(b*g) + 2*a*h + b*Sqrt[g^2 - 4*f*h])] - PolyLog[2, (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] - ((g^2 - f*h)*(-g + Sqrt[g^2 - 4*f*h])*n*((Log[(2*h*(a + b*x))/(-(b*g) + 2*a*h + b*Sqrt[g^2 - 4*f*h])] - Log[(2*h*(c + d*x))/(-(d*g) + 2*c*h + d*Sqrt[g^2 - 4*f*h])])*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x] + PolyLog[2, (b*(-g + Sqrt[g^2 - 4*f*h] - 2*h*x))/(-(b*g) + 2*a*h + b*Sqrt[g^2 - 4*f*h])] - PolyLog[2, (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] + (2*f*g*h*n*((Log[(2*h*(a + b*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h]))] - Log[(2*h*(c + d*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h]))])*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x] + PolyLog[2, (b*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(-2*a*h + b*(g + Sqrt[g^2 - 4*f*h]))] - PolyLog[2, (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] - ((g^2 - f*h)*(g + Sqrt[g^2 - 4*f*h])*n*((Log[(2*h*(a + b*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h]))] - Log[(2*h*(c + d*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h]))])*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x] + PolyLog[2, (b*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(-2*a*h + b*(g + Sqrt[g^2 - 4*f*h]))] - PolyLog[2, (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])/(2*h^3)","A",1
83,1,1105,831,4.1067909,"\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","Integrate[(x^2*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x + h*x^2),x]","\frac{2 d h \sqrt{g^2-4 f h} (a+b x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-2 b d f h \log \left(g+2 h x-\sqrt{g^2-4 f h}\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+b d g \left(g-\sqrt{g^2-4 f h}\right) \log \left(g+2 h x-\sqrt{g^2-4 f h}\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 b d f h \log \left(g+2 h x+\sqrt{g^2-4 f h}\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-b d g \left(g+\sqrt{g^2-4 f h}\right) \log \left(g+2 h x+\sqrt{g^2-4 f h}\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-2 (b c-a d) h \sqrt{g^2-4 f h} n \log (c+d x)+2 b d f h n \left(\left(\log \left(\frac{2 h (a+b x)}{-g b+\sqrt{g^2-4 f h} b+2 a h}\right)-\log \left(\frac{2 h (c+d x)}{-g d+\sqrt{g^2-4 f h} d+2 c h}\right)\right) \log \left(g+2 h x-\sqrt{g^2-4 f h}\right)+\text{Li}_2\left(\frac{b \left(-g-2 h x+\sqrt{g^2-4 f h}\right)}{-g b+\sqrt{g^2-4 f h} b+2 a h}\right)-\text{Li}_2\left(\frac{d \left(-g-2 h x+\sqrt{g^2-4 f h}\right)}{2 c h+d \left(\sqrt{g^2-4 f h}-g\right)}\right)\right)-b d g \left(g-\sqrt{g^2-4 f h}\right) n \left(\left(\log \left(\frac{2 h (a+b x)}{-g b+\sqrt{g^2-4 f h} b+2 a h}\right)-\log \left(\frac{2 h (c+d x)}{-g d+\sqrt{g^2-4 f h} d+2 c h}\right)\right) \log \left(g+2 h x-\sqrt{g^2-4 f h}\right)+\text{Li}_2\left(\frac{b \left(-g-2 h x+\sqrt{g^2-4 f h}\right)}{-g b+\sqrt{g^2-4 f h} b+2 a h}\right)-\text{Li}_2\left(\frac{d \left(-g-2 h x+\sqrt{g^2-4 f h}\right)}{2 c h+d \left(\sqrt{g^2-4 f h}-g\right)}\right)\right)-2 b d f h n \left(\left(\log \left(\frac{2 h (a+b x)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right)-\log \left(\frac{2 h (c+d x)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)\right) \log \left(g+2 h x+\sqrt{g^2-4 f h}\right)+\text{Li}_2\left(\frac{b \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{b \left(g+\sqrt{g^2-4 f h}\right)-2 a h}\right)-\text{Li}_2\left(\frac{d \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{d \left(g+\sqrt{g^2-4 f h}\right)-2 c h}\right)\right)+b d g \left(g+\sqrt{g^2-4 f h}\right) n \left(\left(\log \left(\frac{2 h (a+b x)}{2 a h-b \left(g+\sqrt{g^2-4 f h}\right)}\right)-\log \left(\frac{2 h (c+d x)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)\right) \log \left(g+2 h x+\sqrt{g^2-4 f h}\right)+\text{Li}_2\left(\frac{b \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{b \left(g+\sqrt{g^2-4 f h}\right)-2 a h}\right)-\text{Li}_2\left(\frac{d \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{d \left(g+\sqrt{g^2-4 f h}\right)-2 c h}\right)\right)}{2 b d h^2 \sqrt{g^2-4 f h}}","\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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\frac{2 h (c+d x)}{2 c h-d \left(g+\sqrt{g^2-4 f h}\right)}\right)}{2 h^2}",1,"(2*d*h*Sqrt[g^2 - 4*f*h]*(a + b*x)*Log[e*((a + b*x)/(c + d*x))^n] - 2*(b*c - a*d)*h*Sqrt[g^2 - 4*f*h]*n*Log[c + d*x] - 2*b*d*f*h*Log[e*((a + b*x)/(c + d*x))^n]*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x] + b*d*g*(g - Sqrt[g^2 - 4*f*h])*Log[e*((a + b*x)/(c + d*x))^n]*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x] + 2*b*d*f*h*Log[e*((a + b*x)/(c + d*x))^n]*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x] - b*d*g*(g + Sqrt[g^2 - 4*f*h])*Log[e*((a + b*x)/(c + d*x))^n]*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x] + 2*b*d*f*h*n*((Log[(2*h*(a + b*x))/(-(b*g) + 2*a*h + b*Sqrt[g^2 - 4*f*h])] - Log[(2*h*(c + d*x))/(-(d*g) + 2*c*h + d*Sqrt[g^2 - 4*f*h])])*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x] + PolyLog[2, (b*(-g + Sqrt[g^2 - 4*f*h] - 2*h*x))/(-(b*g) + 2*a*h + b*Sqrt[g^2 - 4*f*h])] - PolyLog[2, (d*(-g + Sqrt[g^2 - 4*f*h] - 2*h*x))/(2*c*h + d*(-g + Sqrt[g^2 - 4*f*h]))]) - b*d*g*(g - Sqrt[g^2 - 4*f*h])*n*((Log[(2*h*(a + b*x))/(-(b*g) + 2*a*h + b*Sqrt[g^2 - 4*f*h])] - Log[(2*h*(c + d*x))/(-(d*g) + 2*c*h + d*Sqrt[g^2 - 4*f*h])])*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x] + PolyLog[2, (b*(-g + Sqrt[g^2 - 4*f*h] - 2*h*x))/(-(b*g) + 2*a*h + b*Sqrt[g^2 - 4*f*h])] - PolyLog[2, (d*(-g + Sqrt[g^2 - 4*f*h] - 2*h*x))/(2*c*h + d*(-g + Sqrt[g^2 - 4*f*h]))]) - 2*b*d*f*h*n*((Log[(2*h*(a + b*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h]))] - Log[(2*h*(c + d*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h]))])*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x] + PolyLog[2, (b*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(-2*a*h + b*(g + Sqrt[g^2 - 4*f*h]))] - PolyLog[2, (d*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(-2*c*h + d*(g + Sqrt[g^2 - 4*f*h]))]) + b*d*g*(g + Sqrt[g^2 - 4*f*h])*n*((Log[(2*h*(a + b*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h]))] - Log[(2*h*(c + d*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h]))])*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x] + PolyLog[2, (b*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(-2*a*h + b*(g + Sqrt[g^2 - 4*f*h]))] - PolyLog[2, (d*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(-2*c*h + d*(g + Sqrt[g^2 - 4*f*h]))]))/(2*b*d*h^2*Sqrt[g^2 - 4*f*h])","A",1
84,1,539,685,0.730458,"\int \frac{x \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f+g x+h x^2} \, dx","Integrate[(x*Log[e*((a + b*x)/(c + d*x))^n])/(f + g*x + h*x^2),x]","\frac{\left(\sqrt{g^2-4 f h}-g\right) \log \left(-\sqrt{g^2-4 f h}+g+2 h x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+\left(\sqrt{g^2-4 f h}+g\right) \log \left(\sqrt{g^2-4 f h}+g+2 h x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n \left(g-\sqrt{g^2-4 f h}\right) \left(\log \left(-\sqrt{g^2-4 f h}+g+2 h x\right) \left(\log \left(\frac{2 h (a+b x)}{2 a h+b \sqrt{g^2-4 f h}+b (-g)}\right)-\log \left(\frac{2 h (c+d x)}{2 c h+d \sqrt{g^2-4 f h}+d (-g)}\right)\right)+\text{Li}_2\left(\frac{b \left(-g-2 h x+\sqrt{g^2-4 f h}\right)}{-g b+\sqrt{g^2-4 f h} b+2 a h}\right)-\text{Li}_2\left(\frac{d \left(-g-2 h x+\sqrt{g^2-4 f h}\right)}{2 c h+d \left(\sqrt{g^2-4 f h}-g\right)}\right)\right)-n \left(\sqrt{g^2-4 f h}+g\right) \left(\log \left(\sqrt{g^2-4 f h}+g+2 h x\right) \left(\log \left(\frac{2 h (a+b x)}{2 a h-b \left(\sqrt{g^2-4 f h}+g\right)}\right)-\log \left(\frac{2 h (c+d x)}{2 c h-d \left(\sqrt{g^2-4 f h}+g\right)}\right)\right)+\text{Li}_2\left(\frac{b \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{b \left(g+\sqrt{g^2-4 f h}\right)-2 a h}\right)-\text{Li}_2\left(\frac{d \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{d \left(g+\sqrt{g^2-4 f h}\right)-2 c h}\right)\right)}{2 h \sqrt{g^2-4 f 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) \text{Li}_2\left(\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{Li}_2\left(\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(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) \text{Li}_2\left(\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{Li}_2\left(\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(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 + Sqrt[g^2 - 4*f*h])*Log[e*((a + b*x)/(c + d*x))^n]*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x] + (g + Sqrt[g^2 - 4*f*h])*Log[e*((a + b*x)/(c + d*x))^n]*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x] + (g - Sqrt[g^2 - 4*f*h])*n*((Log[(2*h*(a + b*x))/(-(b*g) + 2*a*h + b*Sqrt[g^2 - 4*f*h])] - Log[(2*h*(c + d*x))/(-(d*g) + 2*c*h + d*Sqrt[g^2 - 4*f*h])])*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x] + PolyLog[2, (b*(-g + Sqrt[g^2 - 4*f*h] - 2*h*x))/(-(b*g) + 2*a*h + b*Sqrt[g^2 - 4*f*h])] - PolyLog[2, (d*(-g + Sqrt[g^2 - 4*f*h] - 2*h*x))/(2*c*h + d*(-g + Sqrt[g^2 - 4*f*h]))]) - (g + Sqrt[g^2 - 4*f*h])*n*((Log[(2*h*(a + b*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h]))] - Log[(2*h*(c + d*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h]))])*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x] + PolyLog[2, (b*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(-2*a*h + b*(g + Sqrt[g^2 - 4*f*h]))] - PolyLog[2, (d*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(-2*c*h + d*(g + Sqrt[g^2 - 4*f*h]))]))/(2*h*Sqrt[g^2 - 4*f*h])","A",1
85,1,515,401,0.3527773,"\int \frac{\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{f+g x+h x^2} \, dx","Integrate[Log[e*((a + b*x)/(c + d*x))^n]/(f + g*x + h*x^2),x]","\frac{\log \left(-\sqrt{g^2-4 f h}+g+2 h x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-\log \left(\sqrt{g^2-4 f h}+g+2 h x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \text{Li}_2\left(\frac{b \left(-g-2 h x+\sqrt{g^2-4 f h}\right)}{2 a h+b \left(\sqrt{g^2-4 f h}-g\right)}\right)+n \text{Li}_2\left(\frac{b \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{b \left(g+\sqrt{g^2-4 f h}\right)-2 a h}\right)-n \log \left(-\sqrt{g^2-4 f h}+g+2 h x\right) \log \left(\frac{2 h (a+b x)}{2 a h+b \sqrt{g^2-4 f h}+b (-g)}\right)+n \log \left(\sqrt{g^2-4 f h}+g+2 h x\right) \log \left(\frac{2 h (a+b x)}{2 a h-b \left(\sqrt{g^2-4 f h}+g\right)}\right)+n \text{Li}_2\left(\frac{d \left(-g-2 h x+\sqrt{g^2-4 f h}\right)}{-g d+\sqrt{g^2-4 f h} d+2 c h}\right)-n \text{Li}_2\left(\frac{d \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{d \left(g+\sqrt{g^2-4 f h}\right)-2 c h}\right)+n \log \left(-\sqrt{g^2-4 f h}+g+2 h x\right) \log \left(\frac{2 h (c+d x)}{2 c h+d \sqrt{g^2-4 f h}+d (-g)}\right)-n \log \left(\sqrt{g^2-4 f h}+g+2 h x\right) \log \left(\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{\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}}-\frac{n \text{Li}_2\left(\frac{2 \left(h c^2-d g c+d^2 f\right) (a+b x)}{\left(-\sqrt{g^2-4 f h} (b c-a d)+2 b d f-b c g-a d g+2 a c h\right) (c+d x)}\right)}{\sqrt{g^2-4 f h}}+\frac{n \text{Li}_2\left(\frac{2 \left(h c^2-d g c+d^2 f\right) (a+b x)}{\left(\sqrt{g^2-4 f h} (b c-a d)+2 b d f-b c g-a d g+2 a c h\right) (c+d x)}\right)}{\sqrt{g^2-4 f h}}",1,"(-(n*Log[(2*h*(a + b*x))/(-(b*g) + 2*a*h + b*Sqrt[g^2 - 4*f*h])]*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x]) + Log[e*((a + b*x)/(c + d*x))^n]*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x] + n*Log[(2*h*(c + d*x))/(-(d*g) + 2*c*h + d*Sqrt[g^2 - 4*f*h])]*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x] + n*Log[(2*h*(a + b*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h]))]*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x] - Log[e*((a + b*x)/(c + d*x))^n]*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x] - n*Log[(2*h*(c + d*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h]))]*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x] + n*PolyLog[2, (d*(-g + Sqrt[g^2 - 4*f*h] - 2*h*x))/(-(d*g) + 2*c*h + d*Sqrt[g^2 - 4*f*h])] - n*PolyLog[2, (b*(-g + Sqrt[g^2 - 4*f*h] - 2*h*x))/(2*a*h + b*(-g + Sqrt[g^2 - 4*f*h]))] + n*PolyLog[2, (b*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(-2*a*h + b*(g + Sqrt[g^2 - 4*f*h]))] - n*PolyLog[2, (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]","A",1
86,1,625,800,0.9368945,"\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","Integrate[Log[e*((a + b*x)/(c + d*x))^n]/(x*(f + g*x + h*x^2)),x]","\frac{-\left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) \log \left(-\sqrt{g^2-4 f h}+g+2 h x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-\left(1-\frac{g}{\sqrt{g^2-4 f h}}\right) \log \left(\sqrt{g^2-4 f h}+g+2 h x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+2 \log (x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+\frac{n \left(\sqrt{g^2-4 f h}+g\right) \left(\log \left(-\sqrt{g^2-4 f h}+g+2 h x\right) \left(\log \left(\frac{2 h (a+b x)}{2 a h+b \sqrt{g^2-4 f h}+b (-g)}\right)-\log \left(\frac{2 h (c+d x)}{2 c h+d \sqrt{g^2-4 f h}+d (-g)}\right)\right)+\text{Li}_2\left(\frac{b \left(-g-2 h x+\sqrt{g^2-4 f h}\right)}{-g b+\sqrt{g^2-4 f h} b+2 a h}\right)-\text{Li}_2\left(\frac{d \left(-g-2 h x+\sqrt{g^2-4 f h}\right)}{2 c h+d \left(\sqrt{g^2-4 f h}-g\right)}\right)\right)}{\sqrt{g^2-4 f h}}+\frac{n \left(\sqrt{g^2-4 f h}-g\right) \left(\log \left(\sqrt{g^2-4 f h}+g+2 h x\right) \left(\log \left(\frac{2 h (a+b x)}{2 a h-b \left(\sqrt{g^2-4 f h}+g\right)}\right)-\log \left(\frac{2 h (c+d x)}{2 c h-d \left(\sqrt{g^2-4 f h}+g\right)}\right)\right)+\text{Li}_2\left(\frac{b \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{b \left(g+\sqrt{g^2-4 f h}\right)-2 a h}\right)-\text{Li}_2\left(\frac{d \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{d \left(g+\sqrt{g^2-4 f h}\right)-2 c h}\right)\right)}{\sqrt{g^2-4 f h}}-2 n \left(\log (x) \left(\log \left(\frac{b x}{a}+1\right)-\log \left(\frac{d x}{c}+1\right)\right)+\text{Li}_2\left(-\frac{b x}{a}\right)-\text{Li}_2\left(-\frac{d x}{c}\right)\right)}{2 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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\frac{b x}{a}+1\right)}{f}+\frac{\left(\frac{g}{\sqrt{g^2-4 f h}}+1\right) n \text{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\frac{d x}{c}+1\right)}{f}",1,"(2*Log[x]*Log[e*((a + b*x)/(c + d*x))^n] - (1 + g/Sqrt[g^2 - 4*f*h])*Log[e*((a + b*x)/(c + d*x))^n]*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x] - (1 - g/Sqrt[g^2 - 4*f*h])*Log[e*((a + b*x)/(c + d*x))^n]*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x] - 2*n*(Log[x]*(Log[1 + (b*x)/a] - Log[1 + (d*x)/c]) + PolyLog[2, -((b*x)/a)] - PolyLog[2, -((d*x)/c)]) + ((g + Sqrt[g^2 - 4*f*h])*n*((Log[(2*h*(a + b*x))/(-(b*g) + 2*a*h + b*Sqrt[g^2 - 4*f*h])] - Log[(2*h*(c + d*x))/(-(d*g) + 2*c*h + d*Sqrt[g^2 - 4*f*h])])*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x] + PolyLog[2, (b*(-g + Sqrt[g^2 - 4*f*h] - 2*h*x))/(-(b*g) + 2*a*h + b*Sqrt[g^2 - 4*f*h])] - PolyLog[2, (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] + ((-g + Sqrt[g^2 - 4*f*h])*n*((Log[(2*h*(a + b*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h]))] - Log[(2*h*(c + d*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h]))])*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x] + PolyLog[2, (b*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(-2*a*h + b*(g + Sqrt[g^2 - 4*f*h]))] - PolyLog[2, (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])/(2*f)","A",1
87,1,721,995,0.8831962,"\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","Integrate[Log[e*((a + b*x)/(c + d*x))^n]/(x^2*(f + g*x + h*x^2)),x]","\frac{\left(\frac{g^2-2 f h}{\sqrt{g^2-4 f h}}+g\right) \log \left(-\sqrt{g^2-4 f h}+g+2 h x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+\left(\frac{2 f h-g^2}{\sqrt{g^2-4 f h}}+g\right) \log \left(\sqrt{g^2-4 f h}+g+2 h x\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-\frac{2 f \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{x}-2 g \log (x) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-\frac{n \left(g \sqrt{g^2-4 f h}-2 f h+g^2\right) \left(\log \left(-\sqrt{g^2-4 f h}+g+2 h x\right) \left(\log \left(\frac{2 h (a+b x)}{2 a h+b \sqrt{g^2-4 f h}+b (-g)}\right)-\log \left(\frac{2 h (c+d x)}{2 c h+d \sqrt{g^2-4 f h}+d (-g)}\right)\right)+\text{Li}_2\left(\frac{b \left(-g-2 h x+\sqrt{g^2-4 f h}\right)}{-g b+\sqrt{g^2-4 f h} b+2 a h}\right)-\text{Li}_2\left(\frac{d \left(-g-2 h x+\sqrt{g^2-4 f h}\right)}{2 c h+d \left(\sqrt{g^2-4 f h}-g\right)}\right)\right)}{\sqrt{g^2-4 f h}}+\frac{n \left(-g \sqrt{g^2-4 f h}-2 f h+g^2\right) \left(\log \left(\sqrt{g^2-4 f h}+g+2 h x\right) \left(\log \left(\frac{2 h (a+b x)}{2 a h-b \left(\sqrt{g^2-4 f h}+g\right)}\right)-\log \left(\frac{2 h (c+d x)}{2 c h-d \left(\sqrt{g^2-4 f h}+g\right)}\right)\right)+\text{Li}_2\left(\frac{b \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{b \left(g+\sqrt{g^2-4 f h}\right)-2 a h}\right)-\text{Li}_2\left(\frac{d \left(g+2 h x+\sqrt{g^2-4 f h}\right)}{d \left(g+\sqrt{g^2-4 f h}\right)-2 c h}\right)\right)}{\sqrt{g^2-4 f h}}+\frac{2 f n (\log (x) (b c-a d)-b c \log (a+b x)+a d \log (c+d x))}{a c}+2 g n \left(\log (x) \left(\log \left(\frac{b x}{a}+1\right)-\log \left(\frac{d x}{c}+1\right)\right)+\text{Li}_2\left(-\frac{b x}{a}\right)-\text{Li}_2\left(-\frac{d x}{c}\right)\right)}{2 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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\frac{d x}{c}+1\right)}{f^2}",1,"((-2*f*Log[e*((a + b*x)/(c + d*x))^n])/x - 2*g*Log[x]*Log[e*((a + b*x)/(c + d*x))^n] + (2*f*n*((b*c - a*d)*Log[x] - b*c*Log[a + b*x] + a*d*Log[c + d*x]))/(a*c) + (g + (g^2 - 2*f*h)/Sqrt[g^2 - 4*f*h])*Log[e*((a + b*x)/(c + d*x))^n]*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x] + (g + (-g^2 + 2*f*h)/Sqrt[g^2 - 4*f*h])*Log[e*((a + b*x)/(c + d*x))^n]*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x] + 2*g*n*(Log[x]*(Log[1 + (b*x)/a] - Log[1 + (d*x)/c]) + PolyLog[2, -((b*x)/a)] - PolyLog[2, -((d*x)/c)]) - ((g^2 - 2*f*h + g*Sqrt[g^2 - 4*f*h])*n*((Log[(2*h*(a + b*x))/(-(b*g) + 2*a*h + b*Sqrt[g^2 - 4*f*h])] - Log[(2*h*(c + d*x))/(-(d*g) + 2*c*h + d*Sqrt[g^2 - 4*f*h])])*Log[g - Sqrt[g^2 - 4*f*h] + 2*h*x] + PolyLog[2, (b*(-g + Sqrt[g^2 - 4*f*h] - 2*h*x))/(-(b*g) + 2*a*h + b*Sqrt[g^2 - 4*f*h])] - PolyLog[2, (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] + ((g^2 - 2*f*h - g*Sqrt[g^2 - 4*f*h])*n*((Log[(2*h*(a + b*x))/(2*a*h - b*(g + Sqrt[g^2 - 4*f*h]))] - Log[(2*h*(c + d*x))/(2*c*h - d*(g + Sqrt[g^2 - 4*f*h]))])*Log[g + Sqrt[g^2 - 4*f*h] + 2*h*x] + PolyLog[2, (b*(g + Sqrt[g^2 - 4*f*h] + 2*h*x))/(-2*a*h + b*(g + Sqrt[g^2 - 4*f*h]))] - PolyLog[2, (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])/(2*f^2)","A",1
88,1,84,46,0.0162839,"\int \frac{\log \left(\frac{c x}{a+b x}\right)}{a+b x} \, dx","Integrate[Log[(c*x)/(a + b*x)]/(a + b*x),x]","-\frac{\log \left(\frac{a}{a+b x}\right) \log \left(\frac{c x}{a+b x}\right)}{b}-\frac{\text{Li}_2\left(\frac{a+b x}{a}\right)}{b}+\frac{\log ^2\left(\frac{a}{a+b x}\right)}{2 b}+\frac{\log \left(-\frac{b x}{a}\right) \log \left(\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{Li}_2\left(1-\frac{a}{a+b x}\right)}{b}",1,"(Log[-((b*x)/a)]*Log[a/(a + b*x)])/b + Log[a/(a + b*x)]^2/(2*b) - (Log[a/(a + b*x)]*Log[(c*x)/(a + b*x)])/b - PolyLog[2, (a + b*x)/a]/b","A",1
89,1,20,20,0.1023307,"\int \frac{\log ^2\left(\frac{c x}{a+b x}\right)}{x (a+b x)} \, dx","Integrate[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
90,1,76,82,0.0140854,"\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","Integrate[(Log[a/(a + b*x)]*Log[(c*x)/(a + b*x)]^2)/(x*(a + b*x)),x]","-\frac{\text{Li}_2\left(\frac{b x}{a+b x}\right) \log ^2\left(\frac{c x}{a+b x}\right)}{a}+\frac{2 \text{Li}_3\left(\frac{b x}{a+b x}\right) \log \left(\frac{c x}{a+b x}\right)}{a}-\frac{2 \text{Li}_4\left(\frac{b x}{a+b x}\right)}{a}","-\frac{\text{Li}_2\left(1-\frac{a}{a+b x}\right) \log ^2\left(\frac{c x}{a+b x}\right)}{a}+\frac{2 \text{Li}_3\left(1-\frac{a}{a+b x}\right) \log \left(\frac{c x}{a+b x}\right)}{a}-\frac{2 \text{Li}_4\left(1-\frac{a}{a+b x}\right)}{a}",1,"-((Log[(c*x)/(a + b*x)]^2*PolyLog[2, (b*x)/(a + b*x)])/a) + (2*Log[(c*x)/(a + b*x)]*PolyLog[3, (b*x)/(a + b*x)])/a - (2*PolyLog[4, (b*x)/(a + b*x)])/a","A",1
91,1,110,150,0.0375429,"\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","Integrate[(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{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right) \log ^2\left(\frac{e (a+b x)}{c+d x}\right)+2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right) \log \left(\frac{e (a+b x)}{c+d x}\right)-2 \text{Li}_4\left(\frac{d (a+b x)}{b (c+d x)}\right)}{g (b c-a d)}","-\frac{\text{Li}_2\left(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{Li}_3\left(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{Li}_4\left(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, (d*(a + b*x))/(b*(c + d*x))]) + 2*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] - 2*PolyLog[4, (d*(a + b*x))/(b*(c + d*x))])/((b*c - a*d)*g)","A",1
92,1,559,160,0.4541455,"\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","Integrate[(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{\log \left(\frac{a+b x}{c+d x}\right) \log \left(\frac{b c-a d}{b c+b d x}\right) \left(3 \log ^2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-3 n \log \left(\frac{a+b x}{c+d x}\right) \log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)+n^2 \log ^2\left(\frac{a+b x}{c+d x}\right)\right)+3 n \left(-2 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right)+2 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right) \log \left(\frac{a+b x}{c+d x}\right)+\log \left(\frac{b c-a d}{b c+b d x}\right) \log ^2\left(\frac{a+b x}{c+d x}\right)\right) \left(n \log \left(\frac{a+b x}{c+d x}\right)-\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)\right)+\frac{3}{2} \left(2 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right)-2 \log \left(\frac{a}{b}+x\right) \log (c+d x)+2 \log (c+d x) \log \left(\frac{a+b x}{c+d x}\right)+2 \log \left(\frac{a}{b}+x\right) \log \left(\frac{b (c+d x)}{b c-a d}\right)-\log ^2\left(\frac{c}{d}+x\right)+2 \log (c+d x) \log \left(\frac{c}{d}+x\right)\right) \left(\log \left(e \left(\frac{a+b x}{c+d x}\right)^n\right)-n \log \left(\frac{a+b x}{c+d x}\right)\right)^2-\left(n^2 \left(6 \text{Li}_4\left(\frac{d (a+b x)}{b (c+d x)}\right)+3 \text{Li}_2\left(\frac{d (a+b x)}{b (c+d x)}\right) \log ^2\left(\frac{a+b x}{c+d x}\right)-6 \text{Li}_3\left(\frac{d (a+b x)}{b (c+d x)}\right) \log \left(\frac{a+b x}{c+d x}\right)+\log \left(\frac{b c-a d}{b c+b d x}\right) \log ^3\left(\frac{a+b x}{c+d x}\right)\right)\right)}{3 g (b c-a d)}","-\frac{\text{Li}_2\left(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{Li}_3\left(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{Li}_4\left(1-\frac{b c-a d}{b (c+d x)}\right)}{g (b c-a d)}",1,"(Log[(a + b*x)/(c + d*x)]*(3*Log[e*((a + b*x)/(c + d*x))^n]^2 - 3*n*Log[e*((a + b*x)/(c + d*x))^n]*Log[(a + b*x)/(c + d*x)] + n^2*Log[(a + b*x)/(c + d*x)]^2)*Log[(b*c - a*d)/(b*c + b*d*x)] + (3*(Log[e*((a + b*x)/(c + d*x))^n] - n*Log[(a + b*x)/(c + d*x)])^2*(-Log[c/d + x]^2 - 2*Log[a/b + x]*Log[c + d*x] + 2*Log[c/d + x]*Log[c + d*x] + 2*Log[(a + b*x)/(c + d*x)]*Log[c + d*x] + 2*Log[a/b + x]*Log[(b*(c + d*x))/(b*c - a*d)] + 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]))/2 + 3*n*(-Log[e*((a + b*x)/(c + d*x))^n] + n*Log[(a + b*x)/(c + d*x)])*(Log[(a + b*x)/(c + d*x)]^2*Log[(b*c - a*d)/(b*c + b*d*x)] + 2*Log[(a + b*x)/(c + d*x)]*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 2*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))]) - n^2*(Log[(a + b*x)/(c + d*x)]^3*Log[(b*c - a*d)/(b*c + b*d*x)] + 3*Log[(a + b*x)/(c + d*x)]^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))] - 6*Log[(a + b*x)/(c + d*x)]*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))] + 6*PolyLog[4, (d*(a + b*x))/(b*(c + d*x))]))/(3*(b*c - a*d)*g)","B",1
93,1,28,25,0.0049002,"\int \log \left(\frac{c (b+a x)}{x}\right) \, dx","Integrate[Log[(c*(b + a*x))/x],x]","\frac{(a x+b) \log \left(\frac{c (a x+b)}{x}\right)}{a}+\frac{b \log (x)}{a}","x \log \left(a c+\frac{b c}{x}\right)+\frac{b \log (a x+b)}{a}",1,"(b*Log[x])/a + ((b + a*x)*Log[(c*(b + a*x))/x])/a","A",1
94,1,63,67,0.0162094,"\int \log ^2\left(\frac{c (b+a x)}{x}\right) \, dx","Integrate[Log[(c*(b + a*x))/x]^2,x]","\frac{\log \left(\frac{c (a x+b)}{x}\right) \left((a x+b) \log \left(\frac{c (a x+b)}{x}\right)-2 b \log \left(-\frac{b}{a x}\right)\right)-2 b \text{Li}_2\left(\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{Li}_2\left(\frac{b}{a x}+1\right)}{a}",1,"(Log[(c*(b + a*x))/x]*(-2*b*Log[-(b/(a*x))] + (b + a*x)*Log[(c*(b + a*x))/x]) - 2*b*PolyLog[2, 1 + b/(a*x)])/a","A",1
95,1,91,97,0.0261048,"\int \log ^3\left(\frac{c (b+a x)}{x}\right) \, dx","Integrate[Log[(c*(b + a*x))/x]^3,x]","\frac{-6 b \text{Li}_2\left(\frac{b}{a x}+1\right) \log \left(\frac{c (a x+b)}{x}\right)+\left((a x+b) \log \left(\frac{c (a x+b)}{x}\right)-3 b \log \left(-\frac{b}{a x}\right)\right) \log ^2\left(\frac{c (a x+b)}{x}\right)+6 b \text{Li}_3\left(\frac{b}{a x}+1\right)}{a}","-\frac{6 b \text{Li}_2\left(\frac{b}{a x}+1\right) \log \left(c \left(a+\frac{b}{x}\right)\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{Li}_3\left(\frac{b}{a x}+1\right)}{a}",1,"(Log[(c*(b + a*x))/x]^2*(-3*b*Log[-(b/(a*x))] + (b + a*x)*Log[(c*(b + a*x))/x]) - 6*b*Log[(c*(b + a*x))/x]*PolyLog[2, 1 + b/(a*x)] + 6*b*PolyLog[3, 1 + b/(a*x)])/a","A",1
96,1,28,28,0.0028029,"\int \log \left(\frac{c (b+a x)^2}{x^2}\right) \, dx","Integrate[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",1
97,1,106,67,0.0161368,"\int \log ^2\left(\frac{c (b+a x)^2}{x^2}\right) \, dx","Integrate[Log[(c*(b + a*x)^2)/x^2]^2,x]","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{Li}_2\left(\frac{b+a x}{b}\right)}{a}-\frac{4 b \log ^2\left(\frac{b}{a x+b}\right)}{a}-\frac{8 b \log \left(-\frac{a x}{b}\right) \log \left(\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{Li}_2\left(1-\frac{b}{b+a x}\right)}{a}",1,"(-8*b*Log[-((a*x)/b)]*Log[b/(b + a*x)])/a - (4*b*Log[b/(b + a*x)]^2)/a - (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, (b + a*x)/b])/a","A",1
98,1,98,102,0.0250592,"\int \log ^3\left(\frac{c (b+a x)^2}{x^2}\right) \, dx","Integrate[Log[(c*(b + a*x)^2)/x^2]^3,x]","\frac{24 b \text{Li}_2\left(\frac{a x}{b+a x}\right) \log \left(\frac{c (a x+b)^2}{x^2}\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{48 b \text{Li}_3\left(\frac{a x}{b+a x}\right)}{a}","\frac{24 b \text{Li}_2\left(\frac{a x}{b+a x}\right) \log \left(\frac{c (a x+b)^2}{x^2}\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}+\frac{48 b \text{Li}_3\left(\frac{a x}{b+a x}\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, (a*x)/(b + a*x)])/a + (48*b*PolyLog[3, (a*x)/(b + a*x)])/a","A",1
99,1,28,28,0.0030696,"\int \log \left(\frac{c x^2}{(b+a x)^2}\right) \, dx","Integrate[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",1
100,1,106,67,0.0144439,"\int \log ^2\left(\frac{c x^2}{(b+a x)^2}\right) \, dx","Integrate[Log[(c*x^2)/(b + a*x)^2]^2,x]","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{Li}_2\left(\frac{b+a x}{b}\right)}{a}-\frac{4 b \log ^2\left(\frac{b}{a x+b}\right)}{a}-\frac{8 b \log \left(-\frac{a x}{b}\right) \log \left(\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{Li}_2\left(1-\frac{b}{b+a x}\right)}{a}",1,"x*Log[(c*x^2)/(b + a*x)^2]^2 - (8*b*Log[-((a*x)/b)]*Log[b/(b + a*x)])/a + (4*b*Log[(c*x^2)/(b + a*x)^2]*Log[b/(b + a*x)])/a - (4*b*Log[b/(b + a*x)]^2)/a + (8*b*PolyLog[2, (b + a*x)/b])/a","A",1
101,1,98,98,0.0262202,"\int \log ^3\left(\frac{c x^2}{(b+a x)^2}\right) \, dx","Integrate[Log[(c*x^2)/(b + a*x)^2]^3,x]","\frac{24 b \text{Li}_2\left(\frac{a x}{b+a x}\right) \log \left(\frac{c x^2}{(a x+b)^2}\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{48 b \text{Li}_3\left(\frac{a x}{b+a x}\right)}{a}","\frac{24 b \text{Li}_2\left(\frac{a x}{b+a x}\right) \log \left(\frac{c x^2}{(a x+b)^2}\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{48 b \text{Li}_3\left(\frac{a x}{b+a x}\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, (a*x)/(b + a*x)])/a - (48*b*PolyLog[3, (a*x)/(b + a*x)])/a","A",1
102,1,30,35,0.0122649,"\int \frac{\text{Li}_2\left(1+\frac{b c-a d}{d (a+b x)}\right)}{(a+b x) (c+d x)} \, dx","Integrate[PolyLog[2, 1 + (b*c - a*d)/(d*(a + b*x))]/((a + b*x)*(c + d*x)),x]","\frac{\text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{a d-b c}","-\frac{\text{Li}_3\left(\frac{b c-a d}{d (a+b x)}+1\right)}{b c-a d}",1,"PolyLog[3, (b*(c + d*x))/(d*(a + b*x))]/(-(b*c) + a*d)","A",1
103,1,68,85,0.0252693,"\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","Integrate[(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{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right) \log \left(\frac{e (c+d x)}{a+b x}\right)-\text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b c-a d}","\frac{\text{Li}_2\left(\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{Li}_3\left(\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, (b*(c + d*x))/(d*(a + b*x))] - PolyLog[3, (b*(c + d*x))/(d*(a + b*x))])/(b*c - a*d)","A",1
104,1,135,140,0.0430434,"\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","Integrate[Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]^2/(a + b*x),x]","\frac{-2 \text{Li}_2\left(\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)-\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)+2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b}","-\frac{2 \text{Li}_2\left(\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{\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}+\frac{2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\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) - 2*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] + 2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))])/b","A",1
105,1,96,109,0.02692,"\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","Integrate[(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{Li}_2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)-\text{Li}_3\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{b c-a d}","\frac{\log \left(\frac{e (c+d x)}{a+b x}\right) \text{Li}_2\left(\frac{(b c-a d) (e+f x)}{(d e-c f) (a+b x)}+1\right)}{b c-a d}-\frac{\text{Li}_3\left(\frac{(b c-a d) (e+f x)}{(d e-c f) (a+b x)}+1\right)}{b c-a d}",1,"(Log[(e*(c + d*x))/(a + b*x)]*PolyLog[2, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))] - PolyLog[3, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))])/(b*c - a*d)","A",1
106,1,1636,204,0.5212427,"\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","Integrate[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 \log ^3\left(\frac{a}{b}+x\right)+3 \log (a+b x) \log ^2\left(\frac{a}{b}+x\right)+3 \log \left(\frac{b (c+d x)}{b c-a d}\right) \log ^2\left(\frac{a}{b}+x\right)-3 \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log ^2\left(\frac{a}{b}+x\right)-3 \log (e+f x) \log ^2\left(\frac{a}{b}+x\right)+3 \log \left(\frac{b (e+f x)}{b e-a f}\right) \log ^2\left(\frac{a}{b}+x\right)-6 \log \left(\frac{c}{d}+x\right) \log (a+b x) \log \left(\frac{a}{b}+x\right)+6 \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right) \log \left(\frac{a}{b}+x\right)+6 \log (a+b x) \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log \left(\frac{a}{b}+x\right)+6 \log \left(\frac{c}{d}+x\right) \log (e+f x) \log \left(\frac{a}{b}+x\right)-6 \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log (e+f x) \log \left(\frac{a}{b}+x\right)-6 \log \left(\frac{f (c+d x)}{c f-d e}\right) \log \left(\frac{b (e+f x)}{b e-a f}\right) \log \left(\frac{a}{b}+x\right)+6 \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) \log \left(\frac{a}{b}+x\right)-6 \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (e+f x)}{d e-c f}\right) \log \left(\frac{a}{b}+x\right)+6 \log \left(\frac{f (c+d x)}{c f-d e}\right) \log \left(\frac{d (e+f x)}{d e-c f}\right) \log \left(\frac{a}{b}+x\right)+6 \text{Li}_2\left(\frac{d (a+b x)}{a d-b c}\right) \log \left(\frac{a}{b}+x\right)+3 \log \left(\frac{a d-b c}{d (a+b x)}\right) \log ^2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)+3 \log (a+b x) \log ^2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)+3 \log ^2\left(\frac{c}{d}+x\right) \log (a+b x)-3 \log ^2\left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right)-6 \log \left(\frac{c}{d}+x\right) \log (a+b x) \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)+6 \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (a+b x)}{a d-b c}\right) \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)-3 \log ^2\left(\frac{c}{d}+x\right) \log (e+f x)-3 \log ^2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log (e+f x)+6 \log \left(\frac{c}{d}+x\right) \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log (e+f x)+3 \log ^2\left(\frac{f (c+d x)}{c f-d e}\right) \log \left(\frac{b (e+f x)}{b e-a f}\right)+3 \log ^2\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)-6 \log \left(\frac{f (c+d x)}{c f-d e}\right) \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)+3 \log ^2\left(\frac{c}{d}+x\right) \log \left(\frac{d (e+f x)}{d e-c f}\right)-3 \log ^2\left(\frac{f (c+d x)}{c f-d e}\right) \log \left(\frac{d (e+f x)}{d e-c f}\right)-6 \log \left(\frac{c}{d}+x\right) \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log \left(\frac{d (e+f x)}{d e-c f}\right)+6 \log \left(\frac{f (c+d x)}{c f-d e}\right) \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log \left(\frac{d (e+f x)}{d e-c f}\right)-3 \log ^2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log \left(\frac{(a d-b c) (e+f x)}{(d e-c f) (a+b x)}\right)+6 \left(\log \left(\frac{a}{b}+x\right)+\log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)\right) \text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+6 \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)-6 \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \text{Li}_2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)-6 \text{Li}_3\left(\frac{d (a+b x)}{a d-b c}\right)-6 \text{Li}_3\left(\frac{b (c+d x)}{b c-a d}\right)-6 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)+6 \text{Li}_3\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{3 b e-3 a f}","\frac{2 \text{Li}_3\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{b e-a f}-\frac{2 \text{Li}_2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log \left(\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,"(-2*Log[a/b + x]^3 + 3*Log[a/b + x]^2*Log[a + b*x] - 6*Log[a/b + x]*Log[c/d + x]*Log[a + b*x] + 3*Log[c/d + x]^2*Log[a + b*x] + 6*Log[a/b + x]*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] - 3*Log[c/d + x]^2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 3*Log[a/b + x]^2*Log[(b*(c + d*x))/(b*c - a*d)] - 3*Log[a/b + x]^2*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))] + 6*Log[a/b + x]*Log[a + b*x]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))] - 6*Log[c/d + x]*Log[a + b*x]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))] + 6*Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))] + 3*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 + 3*Log[a + b*x]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]^2 - 3*Log[a/b + x]^2*Log[e + f*x] + 6*Log[a/b + x]*Log[c/d + x]*Log[e + f*x] - 3*Log[c/d + x]^2*Log[e + f*x] - 6*Log[a/b + x]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[e + f*x] + 6*Log[c/d + x]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[e + f*x] - 3*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]^2*Log[e + f*x] + 3*Log[a/b + x]^2*Log[(b*(e + f*x))/(b*e - a*f)] - 6*Log[a/b + x]*Log[(f*(c + d*x))/(-(d*e) + c*f)]*Log[(b*(e + f*x))/(b*e - a*f)] + 3*Log[(f*(c + d*x))/(-(d*e) + c*f)]^2*Log[(b*(e + f*x))/(b*e - a*f)] + 6*Log[a/b + x]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[(b*(e + f*x))/(b*e - a*f)] - 6*Log[(f*(c + d*x))/(-(d*e) + c*f)]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[(b*(e + f*x))/(b*e - a*f)] + 3*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)] - 6*Log[a/b + x]*Log[c/d + x]*Log[(d*(e + f*x))/(d*e - c*f)] + 3*Log[c/d + x]^2*Log[(d*(e + f*x))/(d*e - c*f)] + 6*Log[a/b + x]*Log[(f*(c + d*x))/(-(d*e) + c*f)]*Log[(d*(e + f*x))/(d*e - c*f)] - 3*Log[(f*(c + d*x))/(-(d*e) + c*f)]^2*Log[(d*(e + f*x))/(d*e - c*f)] - 6*Log[c/d + x]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[(d*(e + f*x))/(d*e - c*f)] + 6*Log[(f*(c + d*x))/(-(d*e) + c*f)]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[(d*(e + f*x))/(d*e - c*f)] - 3*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))] + 6*Log[a/b + x]*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 6*(Log[a/b + x] + Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))])*PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + 6*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] - 6*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*PolyLog[2, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))] - 6*PolyLog[3, (d*(a + b*x))/(-(b*c) + a*d)] - 6*PolyLog[3, (b*(c + d*x))/(b*c - a*d)] - 6*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))] + 6*PolyLog[3, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))])/(3*b*e - 3*a*f)","B",1
107,1,1080,322,0.2825272,"\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","Integrate[Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]^2/(e + f*x),x]","\frac{\log (e+f x) \log ^2\left(\frac{a}{b}+x\right)-\log \left(\frac{b (e+f x)}{b e-a f}\right) \log ^2\left(\frac{a}{b}+x\right)-2 \log \left(\frac{c}{d}+x\right) \log (e+f x) \log \left(\frac{a}{b}+x\right)+2 \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log (e+f x) \log \left(\frac{a}{b}+x\right)+2 \log \left(\frac{f (c+d x)}{c f-d e}\right) \log \left(\frac{b (e+f x)}{b e-a f}\right) \log \left(\frac{a}{b}+x\right)-2 \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) \log \left(\frac{a}{b}+x\right)+2 \log \left(\frac{c}{d}+x\right) \log \left(\frac{d (e+f x)}{d e-c f}\right) \log \left(\frac{a}{b}+x\right)-2 \log \left(\frac{f (c+d x)}{c f-d e}\right) \log \left(\frac{d (e+f x)}{d e-c f}\right) \log \left(\frac{a}{b}+x\right)-\log \left(\frac{a d-b c}{d (a+b x)}\right) \log ^2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)+\log ^2\left(\frac{c}{d}+x\right) \log (e+f x)+\log ^2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log (e+f x)-2 \log \left(\frac{c}{d}+x\right) \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log (e+f x)-\log ^2\left(\frac{f (c+d x)}{c f-d e}\right) \log \left(\frac{b (e+f x)}{b e-a f}\right)-\log ^2\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)+2 \log \left(\frac{f (c+d x)}{c f-d e}\right) \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)-\log ^2\left(\frac{c}{d}+x\right) \log \left(\frac{d (e+f x)}{d e-c f}\right)+\log ^2\left(\frac{f (c+d x)}{c f-d e}\right) \log \left(\frac{d (e+f x)}{d e-c f}\right)+2 \log \left(\frac{c}{d}+x\right) \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log \left(\frac{d (e+f x)}{d e-c f}\right)-2 \log \left(\frac{f (c+d x)}{c f-d e}\right) \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log \left(\frac{d (e+f x)}{d e-c f}\right)+\log ^2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log \left(\frac{(a d-b c) (e+f x)}{(d e-c f) (a+b x)}\right)-2 \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)+2 \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \text{Li}_2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)+2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)-2 \text{Li}_3\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{f}","-\frac{2 \text{Li}_3\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{f}-\frac{2 \text{Li}_2\left(\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 \text{Li}_2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log \left(\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}\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}+\frac{2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{f}",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) + Log[a/b + x]^2*Log[e + f*x] - 2*Log[a/b + x]*Log[c/d + x]*Log[e + f*x] + Log[c/d + x]^2*Log[e + f*x] + 2*Log[a/b + x]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[e + f*x] - 2*Log[c/d + x]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[e + f*x] + Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]^2*Log[e + f*x] - Log[a/b + x]^2*Log[(b*(e + f*x))/(b*e - a*f)] + 2*Log[a/b + x]*Log[(f*(c + d*x))/(-(d*e) + c*f)]*Log[(b*(e + f*x))/(b*e - a*f)] - Log[(f*(c + d*x))/(-(d*e) + c*f)]^2*Log[(b*(e + f*x))/(b*e - a*f)] - 2*Log[a/b + x]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[(b*(e + f*x))/(b*e - a*f)] + 2*Log[(f*(c + d*x))/(-(d*e) + c*f)]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[(b*(e + f*x))/(b*e - a*f)] - 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*Log[a/b + x]*Log[c/d + x]*Log[(d*(e + f*x))/(d*e - c*f)] - Log[c/d + x]^2*Log[(d*(e + f*x))/(d*e - c*f)] - 2*Log[a/b + x]*Log[(f*(c + d*x))/(-(d*e) + c*f)]*Log[(d*(e + f*x))/(d*e - c*f)] + Log[(f*(c + d*x))/(-(d*e) + c*f)]^2*Log[(d*(e + f*x))/(d*e - c*f)] + 2*Log[c/d + x]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[(d*(e + f*x))/(d*e - c*f)] - 2*Log[(f*(c + d*x))/(-(d*e) + c*f)]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[(d*(e + f*x))/(d*e - c*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))/((d*e - c*f)*(a + b*x))] - 2*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] + 2*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*PolyLog[2, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))] + 2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))] - 2*PolyLog[3, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))])/f","B",1
108,1,908,433,0.8152165,"\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","Integrate[(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{\log \left(\frac{b (e+f x)}{b e-a f}\right) \log ^2(c+d x)-\log \left(\frac{d (e+f x)}{d e-c f}\right) \log ^2(c+d x)-2 \log (a+b x) \log \left(\frac{b (e+f x)}{b e-a f}\right) \log (c+d x)-2 \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) \log (c+d x)+2 \log (a+b x) \log \left(\frac{d (e+f x)}{d e-c f}\right) \log (c+d x)+2 \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log \left(\frac{d (e+f x)}{d e-c f}\right) \log (c+d x)-\log \left(\frac{a d-b c}{d (a+b x)}\right) \log ^2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)-\log ^2\left(\frac{f (c+d x)}{c f-d e}\right) \log \left(\frac{b (e+f x)}{b e-a f}\right)-\log ^2\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)+2 \log (a+b x) \log \left(\frac{f (c+d x)}{c f-d e}\right) \log \left(\frac{b (e+f x)}{b e-a f}\right)+2 \log \left(\frac{f (c+d x)}{c f-d e}\right) \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)+\log ^2\left(\frac{f (c+d x)}{c f-d e}\right) \log \left(\frac{d (e+f x)}{d e-c f}\right)-2 \log (a+b x) \log \left(\frac{f (c+d x)}{c f-d e}\right) \log \left(\frac{d (e+f x)}{d e-c f}\right)-2 \log \left(\frac{f (c+d x)}{c f-d e}\right) \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log \left(\frac{d (e+f x)}{d e-c f}\right)+\log ^2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \log \left(\frac{(a d-b c) (e+f x)}{(d e-c f) (a+b x)}\right)-2 \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \text{Li}_2\left(\frac{b (c+d x)}{d (a+b x)}\right)+2 \log \left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right) \text{Li}_2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)+2 \text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)-2 \text{Li}_3\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{2 b c-2 a d}","-\frac{\text{Li}_3\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{b c-a d}-\frac{\text{Li}_2\left(\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{\text{Li}_2\left(\frac{(b e-a f) (c+d x)}{(d e-c f) (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{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)}+\frac{\text{Li}_3\left(\frac{b (c+d x)}{d (a+b x)}\right)}{b c-a d}",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) - 2*Log[a + b*x]*Log[c + d*x]*Log[(b*(e + f*x))/(b*e - a*f)] + Log[c + d*x]^2*Log[(b*(e + f*x))/(b*e - a*f)] + 2*Log[a + b*x]*Log[(f*(c + d*x))/(-(d*e) + c*f)]*Log[(b*(e + f*x))/(b*e - a*f)] - Log[(f*(c + d*x))/(-(d*e) + c*f)]^2*Log[(b*(e + f*x))/(b*e - a*f)] - 2*Log[c + d*x]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[(b*(e + f*x))/(b*e - a*f)] + 2*Log[(f*(c + d*x))/(-(d*e) + c*f)]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[(b*(e + f*x))/(b*e - a*f)] - 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*Log[a + b*x]*Log[c + d*x]*Log[(d*(e + f*x))/(d*e - c*f)] - Log[c + d*x]^2*Log[(d*(e + f*x))/(d*e - c*f)] - 2*Log[a + b*x]*Log[(f*(c + d*x))/(-(d*e) + c*f)]*Log[(d*(e + f*x))/(d*e - c*f)] + Log[(f*(c + d*x))/(-(d*e) + c*f)]^2*Log[(d*(e + f*x))/(d*e - c*f)] + 2*Log[c + d*x]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[(d*(e + f*x))/(d*e - c*f)] - 2*Log[(f*(c + d*x))/(-(d*e) + c*f)]*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Log[(d*(e + f*x))/(d*e - c*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))/((d*e - c*f)*(a + b*x))] - 2*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] + 2*Log[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*PolyLog[2, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))] + 2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))] - 2*PolyLog[3, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))])/(2*b*c - 2*a*d)","B",1