1,1,48,48,0.0449233,"\int x^3 (d+e x) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^3*(d + e*x)*(a + b*Log[c*x^n]),x]","\frac{1}{400} x^4 \left(20 a (5 d+4 e x)+20 b (5 d+4 e x) \log \left(c x^n\right)-b n (25 d+16 e x)\right)","\frac{1}{20} \left(5 d x^4+4 e x^5\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{16} b d n x^4-\frac{1}{25} b e n x^5",1,"(x^4*(20*a*(5*d + 4*e*x) - b*n*(25*d + 16*e*x) + 20*b*(5*d + 4*e*x)*Log[c*x^n]))/400","A",1
2,1,45,48,0.0252402,"\int x^2 (d+e x) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^2*(d + e*x)*(a + b*Log[c*x^n]),x]","\frac{1}{144} x^3 \left(48 a d+36 a e x+12 b (4 d+3 e x) \log \left(c x^n\right)-16 b d n-9 b e n x\right)","\frac{1}{12} \left(4 d x^3+3 e x^4\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b d n x^3-\frac{1}{16} b e n x^4",1,"(x^3*(48*a*d - 16*b*d*n + 36*a*e*x - 9*b*e*n*x + 12*b*(4*d + 3*e*x)*Log[c*x^n]))/144","A",1
3,1,48,48,0.0222726,"\int x (d+e x) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x*(d + e*x)*(a + b*Log[c*x^n]),x]","\frac{1}{36} x^2 \left(6 a (3 d+2 e x)+6 b (3 d+2 e x) \log \left(c x^n\right)-b n (9 d+4 e x)\right)","\frac{1}{6} \left(3 d x^2+2 e x^3\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b d n x^2-\frac{1}{9} b e n x^3",1,"(x^2*(6*a*(3*d + 2*e*x) - b*n*(9*d + 4*e*x) + 6*b*(3*d + 2*e*x)*Log[c*x^n]))/36","A",1
4,1,55,48,0.0020971,"\int (d+e x) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(d + e*x)*(a + b*Log[c*x^n]),x]","a d x+\frac{1}{2} a e x^2+b d x \log \left(c x^n\right)+\frac{1}{2} b e x^2 \log \left(c x^n\right)-b d n x-\frac{1}{4} b e n x^2","d x \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} e x^2 \left(a+b \log \left(c x^n\right)\right)-b d n x-\frac{1}{4} b e n x^2",1,"a*d*x - b*d*n*x + (a*e*x^2)/2 - (b*e*n*x^2)/4 + b*d*x*Log[c*x^n] + (b*e*x^2*Log[c*x^n])/2","A",1
5,1,43,44,0.0020656,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[((d + e*x)*(a + b*Log[c*x^n]))/x,x]","a d \log (x)+a e x+\frac{b d \log ^2\left(c x^n\right)}{2 n}+b e x \log \left(c x^n\right)-b e n x","\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}+a e x+b e x \log \left(c x^n\right)-b e n x",1,"a*e*x - b*e*n*x + a*d*Log[x] + b*e*x*Log[c*x^n] + (b*d*Log[c*x^n]^2)/(2*n)","A",1
6,1,48,48,0.026838,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Integrate[((d + e*x)*(a + b*Log[c*x^n]))/x^2,x]","-\frac{d \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}-\frac{b d n}{x}","-\frac{d \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}-\frac{b d n}{x}",1,"-((b*d*n)/x) - (d*(a + b*Log[c*x^n]))/x + (e*(a + b*Log[c*x^n])^2)/(2*b*n)","A",1
7,1,41,60,0.0239322,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Integrate[((d + e*x)*(a + b*Log[c*x^n]))/x^3,x]","-\frac{2 a (d+2 e x)+2 b (d+2 e x) \log \left(c x^n\right)+b n (d+4 e x)}{4 x^2}","-\frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)}{2 d x^2}+\frac{b e^2 n \log (x)}{2 d}-\frac{b d n}{4 x^2}-\frac{b e n}{x}",1,"-1/4*(2*a*(d + 2*e*x) + b*n*(d + 4*e*x) + 2*b*(d + 2*e*x)*Log[c*x^n])/x^2","A",1
8,1,47,57,0.0251582,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Integrate[((d + e*x)*(a + b*Log[c*x^n]))/x^4,x]","-\frac{6 a (2 d+3 e x)+6 b (2 d+3 e x) \log \left(c x^n\right)+b n (4 d+9 e x)}{36 x^3}","-\frac{d \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{e \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{b d n}{9 x^3}-\frac{b e n}{4 x^2}",1,"-1/36*(6*a*(2*d + 3*e*x) + b*n*(4*d + 9*e*x) + 6*b*(2*d + 3*e*x)*Log[c*x^n])/x^3","A",1
9,1,81,74,0.0537038,"\int x^3 (d+e x)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^3*(d + e*x)^2*(a + b*Log[c*x^n]),x]","\frac{x^4 \left(60 a \left(15 d^2+24 d e x+10 e^2 x^2\right)+60 b \left(15 d^2+24 d e x+10 e^2 x^2\right) \log \left(c x^n\right)-b n \left(225 d^2+288 d e x+100 e^2 x^2\right)\right)}{3600}","\frac{1}{60} \left(15 d^2 x^4+24 d e x^5+10 e^2 x^6\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{16} b d^2 n x^4-\frac{2}{25} b d e n x^5-\frac{1}{36} b e^2 n x^6",1,"(x^4*(60*a*(15*d^2 + 24*d*e*x + 10*e^2*x^2) - b*n*(225*d^2 + 288*d*e*x + 100*e^2*x^2) + 60*b*(15*d^2 + 24*d*e*x + 10*e^2*x^2)*Log[c*x^n]))/3600","A",1
10,1,81,74,0.0407563,"\int x^2 (d+e x)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^2*(d + e*x)^2*(a + b*Log[c*x^n]),x]","\frac{x^3 \left(60 a \left(10 d^2+15 d e x+6 e^2 x^2\right)+60 b \left(10 d^2+15 d e x+6 e^2 x^2\right) \log \left(c x^n\right)-b n \left(200 d^2+225 d e x+72 e^2 x^2\right)\right)}{1800}","\frac{1}{30} \left(10 d^2 x^3+15 d e x^4+6 e^2 x^5\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b d^2 n x^3-\frac{1}{8} b d e n x^4-\frac{1}{25} b e^2 n x^5",1,"(x^3*(60*a*(10*d^2 + 15*d*e*x + 6*e^2*x^2) - b*n*(200*d^2 + 225*d*e*x + 72*e^2*x^2) + 60*b*(10*d^2 + 15*d*e*x + 6*e^2*x^2)*Log[c*x^n]))/1800","A",1
11,1,81,74,0.0395965,"\int x (d+e x)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x*(d + e*x)^2*(a + b*Log[c*x^n]),x]","\frac{1}{144} x^2 \left(12 a \left(6 d^2+8 d e x+3 e^2 x^2\right)+12 b \left(6 d^2+8 d e x+3 e^2 x^2\right) \log \left(c x^n\right)-b n \left(36 d^2+32 d e x+9 e^2 x^2\right)\right)","\frac{1}{12} \left(6 d^2 x^2+8 d e x^3+3 e^2 x^4\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b d^2 n x^2-\frac{2}{9} b d e n x^3-\frac{1}{16} b e^2 n x^4",1,"(x^2*(12*a*(6*d^2 + 8*d*e*x + 3*e^2*x^2) - b*n*(36*d^2 + 32*d*e*x + 9*e^2*x^2) + 12*b*(6*d^2 + 8*d*e*x + 3*e^2*x^2)*Log[c*x^n]))/144","A",1
12,1,77,70,0.0459525,"\int (d+e x)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(d + e*x)^2*(a + b*Log[c*x^n]),x]","\frac{1}{18} x \left(6 a \left(3 d^2+3 d e x+e^2 x^2\right)+6 b \left(3 d^2+3 d e x+e^2 x^2\right) \log \left(c x^n\right)-b n \left(18 d^2+9 d e x+2 e^2 x^2\right)\right)","\frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{3 e}-\frac{b d^3 n \log (x)}{3 e}-b d^2 n x-\frac{1}{2} b d e n x^2-\frac{1}{9} b e^2 n x^3",1,"(x*(6*a*(3*d^2 + 3*d*e*x + e^2*x^2) - b*n*(18*d^2 + 9*d*e*x + 2*e^2*x^2) + 6*b*(3*d^2 + 3*d*e*x + e^2*x^2)*Log[c*x^n]))/18","A",1
13,1,83,80,0.048854,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[((d + e*x)^2*(a + b*Log[c*x^n]))/x,x]","\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}+\frac{1}{2} e^2 x^2 \left(a+b \log \left(c x^n\right)\right)+2 a d e x+2 b d e x \log \left(c x^n\right)-2 b d e n x-\frac{1}{4} b e^2 n x^2","d^2 \log (x) \left(a+b \log \left(c x^n\right)\right)+2 d e x \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} e^2 x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} b d^2 n \log ^2(x)-\frac{1}{4} b n (4 d+e x)^2",1,"2*a*d*e*x - 2*b*d*e*n*x - (b*e^2*n*x^2)/4 + 2*b*d*e*x*Log[c*x^n] + (e^2*x^2*(a + b*Log[c*x^n]))/2 + (d^2*(a + b*Log[c*x^n])^2)/(2*b*n)","A",1
14,1,76,78,0.0589635,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Integrate[((d + e*x)^2*(a + b*Log[c*x^n]))/x^2,x]","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{d e \left(a+b \log \left(c x^n\right)\right)^2}{b n}+a e^2 x+b e^2 x \log \left(c x^n\right)-\frac{b d^2 n}{x}-b e^2 n x","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{x}+2 d e \log (x) \left(a+b \log \left(c x^n\right)\right)+e^2 x \left(a+b \log \left(c x^n\right)\right)-\frac{b d^2 n}{x}-b d e n \log ^2(x)-b e^2 n x",1,"-((b*d^2*n)/x) + a*e^2*x - b*e^2*n*x + b*e^2*x*Log[c*x^n] - (d^2*(a + b*Log[c*x^n]))/x + (d*e*(a + b*Log[c*x^n])^2)/(b*n)","A",1
15,1,84,84,0.0589908,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Integrate[((d + e*x)^2*(a + b*Log[c*x^n]))/x^3,x]","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{2 d e \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{e^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}-\frac{b d^2 n}{4 x^2}-\frac{2 b d e n}{x}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{2 d e \left(a+b \log \left(c x^n\right)\right)}{x}+e^2 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{b n (d+4 e x)^2}{4 x^2}-\frac{1}{2} b e^2 n \log ^2(x)",1,"-1/4*(b*d^2*n)/x^2 - (2*b*d*e*n)/x - (d^2*(a + b*Log[c*x^n]))/(2*x^2) - (2*d*e*(a + b*Log[c*x^n]))/x + (e^2*(a + b*Log[c*x^n])^2)/(2*b*n)","A",1
16,1,76,75,0.0421554,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Integrate[((d + e*x)^2*(a + b*Log[c*x^n]))/x^4,x]","-\frac{6 a \left(d^2+3 d e x+3 e^2 x^2\right)+6 b \left(d^2+3 d e x+3 e^2 x^2\right) \log \left(c x^n\right)+b n \left(2 d^2+9 d e x+18 e^2 x^2\right)}{18 x^3}","-\frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{3 d x^3}-\frac{b d^2 n}{9 x^3}+\frac{b e^3 n \log (x)}{3 d}-\frac{b d e n}{2 x^2}-\frac{b e^2 n}{x}",1,"-1/18*(6*a*(d^2 + 3*d*e*x + 3*e^2*x^2) + b*n*(2*d^2 + 9*d*e*x + 18*e^2*x^2) + 6*b*(d^2 + 3*d*e*x + 3*e^2*x^2)*Log[c*x^n])/x^3","A",1
17,1,80,95,0.0444879,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)}{x^5} \, dx","Integrate[((d + e*x)^2*(a + b*Log[c*x^n]))/x^5,x]","-\frac{12 a \left(3 d^2+8 d e x+6 e^2 x^2\right)+12 b \left(3 d^2+8 d e x+6 e^2 x^2\right) \log \left(c x^n\right)+b n \left(9 d^2+32 d e x+36 e^2 x^2\right)}{144 x^4}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{4 x^4}-\frac{2 d e \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{e^2 \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{b d^2 n}{16 x^4}-\frac{2 b d e n}{9 x^3}-\frac{b e^2 n}{4 x^2}",1,"-1/144*(12*a*(3*d^2 + 8*d*e*x + 6*e^2*x^2) + b*n*(9*d^2 + 32*d*e*x + 36*e^2*x^2) + 12*b*(3*d^2 + 8*d*e*x + 6*e^2*x^2)*Log[c*x^n])/x^4","A",1
18,1,80,95,0.0408819,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Integrate[((d + e*x)^2*(a + b*Log[c*x^n]))/x^6,x]","-\frac{60 a \left(6 d^2+15 d e x+10 e^2 x^2\right)+60 b \left(6 d^2+15 d e x+10 e^2 x^2\right) \log \left(c x^n\right)+b n \left(72 d^2+225 d e x+200 e^2 x^2\right)}{1800 x^5}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{d e \left(a+b \log \left(c x^n\right)\right)}{2 x^4}-\frac{e^2 \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{b d^2 n}{25 x^5}-\frac{b d e n}{8 x^4}-\frac{b e^2 n}{9 x^3}",1,"-1/1800*(60*a*(6*d^2 + 15*d*e*x + 10*e^2*x^2) + b*n*(72*d^2 + 225*d*e*x + 200*e^2*x^2) + 60*b*(6*d^2 + 15*d*e*x + 10*e^2*x^2)*Log[c*x^n])/x^5","A",1
19,1,133,100,0.0668937,"\int x^3 (d+e x)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^3*(d + e*x)^3*(a + b*Log[c*x^n]),x]","\frac{1}{4} d^3 x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{3}{5} d^2 e x^5 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} d e^2 x^6 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{7} e^3 x^7 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{16} b d^3 n x^4-\frac{3}{25} b d^2 e n x^5-\frac{1}{12} b d e^2 n x^6-\frac{1}{49} b e^3 n x^7","\frac{1}{140} \left(35 d^3 x^4+84 d^2 e x^5+70 d e^2 x^6+20 e^3 x^7\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{16} b d^3 n x^4-\frac{3}{25} b d^2 e n x^5-\frac{1}{12} b d e^2 n x^6-\frac{1}{49} b e^3 n x^7",1,"-1/16*(b*d^3*n*x^4) - (3*b*d^2*e*n*x^5)/25 - (b*d*e^2*n*x^6)/12 - (b*e^3*n*x^7)/49 + (d^3*x^4*(a + b*Log[c*x^n]))/4 + (3*d^2*e*x^5*(a + b*Log[c*x^n]))/5 + (d*e^2*x^6*(a + b*Log[c*x^n]))/2 + (e^3*x^7*(a + b*Log[c*x^n]))/7","A",1
20,1,133,100,0.0517568,"\int x^2 (d+e x)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^2*(d + e*x)^3*(a + b*Log[c*x^n]),x]","\frac{1}{3} d^3 x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{3}{4} d^2 e x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{3}{5} d e^2 x^5 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{6} e^3 x^6 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b d^3 n x^3-\frac{3}{16} b d^2 e n x^4-\frac{3}{25} b d e^2 n x^5-\frac{1}{36} b e^3 n x^6","\frac{1}{60} \left(20 d^3 x^3+45 d^2 e x^4+36 d e^2 x^5+10 e^3 x^6\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b d^3 n x^3-\frac{3}{16} b d^2 e n x^4-\frac{3}{25} b d e^2 n x^5-\frac{1}{36} b e^3 n x^6",1,"-1/9*(b*d^3*n*x^3) - (3*b*d^2*e*n*x^4)/16 - (3*b*d*e^2*n*x^5)/25 - (b*e^3*n*x^6)/36 + (d^3*x^3*(a + b*Log[c*x^n]))/3 + (3*d^2*e*x^4*(a + b*Log[c*x^n]))/4 + (3*d*e^2*x^5*(a + b*Log[c*x^n]))/5 + (e^3*x^6*(a + b*Log[c*x^n]))/6","A",1
21,1,130,122,0.1239724,"\int x (d+e x)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x*(d + e*x)^3*(a + b*Log[c*x^n]),x]","\frac{1}{2} d^3 x^2 \left(a+b \log \left(c x^n\right)\right)+d^2 e x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{3}{4} d e^2 x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{5} e^3 x^5 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b d^3 n x^2-\frac{1}{3} b d^2 e n x^3-\frac{3}{16} b d e^2 n x^4-\frac{1}{25} b e^3 n x^5","-\frac{1}{20} \left(\frac{5 d (d+e x)^4}{e^2}-\frac{4 (d+e x)^5}{e^2}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{b d^5 n \log (x)}{20 e^2}+\frac{b d^4 n x}{5 e}+\frac{3}{20} b d^3 n x^2+\frac{1}{15} b d^2 e n x^3+\frac{1}{80} b d e^2 n x^4-\frac{b n (d+e x)^5}{25 e^2}",1,"-1/4*(b*d^3*n*x^2) - (b*d^2*e*n*x^3)/3 - (3*b*d*e^2*n*x^4)/16 - (b*e^3*n*x^5)/25 + (d^3*x^2*(a + b*Log[c*x^n]))/2 + d^2*e*x^3*(a + b*Log[c*x^n]) + (3*d*e^2*x^4*(a + b*Log[c*x^n]))/4 + (e^3*x^5*(a + b*Log[c*x^n]))/5","A",1
22,1,110,85,0.0456367,"\int (d+e x)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(d + e*x)^3*(a + b*Log[c*x^n]),x]","\frac{1}{48} x \left(12 a \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)+12 b \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right) \log \left(c x^n\right)-b n \left(48 d^3+36 d^2 e x+16 d e^2 x^2+3 e^3 x^3\right)\right)","\frac{(d+e x)^4 \left(a+b \log \left(c x^n\right)\right)}{4 e}-\frac{b d^4 n \log (x)}{4 e}-b d^3 n x-\frac{3}{4} b d^2 e n x^2-\frac{1}{3} b d e^2 n x^3-\frac{1}{16} b e^3 n x^4",1,"(x*(12*a*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3) - b*n*(48*d^3 + 36*d^2*e*x + 16*d*e^2*x^2 + 3*e^3*x^3) + 12*b*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3)*Log[c*x^n]))/48","A",1
23,1,123,122,0.0625821,"\int \frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[((d + e*x)^3*(a + b*Log[c*x^n]))/x,x]","\frac{d^3 \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}+\frac{3}{2} d e^2 x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{3} e^3 x^3 \left(a+b \log \left(c x^n\right)\right)+3 a d^2 e x+3 b d^2 e x \log \left(c x^n\right)-3 b d^2 e n x-\frac{3}{4} b d e^2 n x^2-\frac{1}{9} b e^3 n x^3","d^3 \log (x) \left(a+b \log \left(c x^n\right)\right)+3 d^2 e x \left(a+b \log \left(c x^n\right)\right)+\frac{3}{2} d e^2 x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{3} e^3 x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} b d^3 n \log ^2(x)-3 b d^2 e n x-\frac{3}{4} b d e^2 n x^2-\frac{1}{9} b e^3 n x^3",1,"3*a*d^2*e*x - 3*b*d^2*e*n*x - (3*b*d*e^2*n*x^2)/4 - (b*e^3*n*x^3)/9 + 3*b*d^2*e*x*Log[c*x^n] + (3*d*e^2*x^2*(a + b*Log[c*x^n]))/2 + (e^3*x^3*(a + b*Log[c*x^n]))/3 + (d^3*(a + b*Log[c*x^n])^2)/(2*b*n)","A",1
24,1,118,119,0.0816605,"\int \frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Integrate[((d + e*x)^3*(a + b*Log[c*x^n]))/x^2,x]","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}+\frac{1}{2} e^3 x^2 \left(a+b \log \left(c x^n\right)\right)+3 a d e^2 x+3 b d e^2 x \log \left(c x^n\right)-\frac{b d^3 n}{x}-3 b d e^2 n x-\frac{1}{4} b e^3 n x^2","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{x}+3 d^2 e \log (x) \left(a+b \log \left(c x^n\right)\right)+3 d e^2 x \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} e^3 x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{b d^3 n}{x}-\frac{3}{2} b d^2 e n \log ^2(x)-3 b d e^2 n x-\frac{1}{4} b e^3 n x^2",1,"-((b*d^3*n)/x) + 3*a*d*e^2*x - 3*b*d*e^2*n*x - (b*e^3*n*x^2)/4 + 3*b*d*e^2*x*Log[c*x^n] - (d^3*(a + b*Log[c*x^n]))/x + (e^3*x^2*(a + b*Log[c*x^n]))/2 + (3*d^2*e*(a + b*Log[c*x^n])^2)/(2*b*n)","A",1
25,1,115,118,0.0806082,"\int \frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Integrate[((d + e*x)^3*(a + b*Log[c*x^n]))/x^3,x]","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{3 d e^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}+a e^3 x+b e^3 x \log \left(c x^n\right)-\frac{b d^3 n}{4 x^2}-\frac{3 b d^2 e n}{x}-b e^3 n x","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{x}+3 d e^2 \log (x) \left(a+b \log \left(c x^n\right)\right)+e^3 x \left(a+b \log \left(c x^n\right)\right)-\frac{b d^3 n}{4 x^2}-\frac{3 b d^2 e n}{x}-\frac{3}{2} b d e^2 n \log ^2(x)-b e^3 n x",1,"-1/4*(b*d^3*n)/x^2 - (3*b*d^2*e*n)/x + a*e^3*x - b*e^3*n*x + b*e^3*x*Log[c*x^n] - (d^3*(a + b*Log[c*x^n]))/(2*x^2) - (3*d^2*e*(a + b*Log[c*x^n]))/x + (3*d*e^2*(a + b*Log[c*x^n])^2)/(2*b*n)","A",1
26,1,122,126,0.0805905,"\int \frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Integrate[((d + e*x)^3*(a + b*Log[c*x^n]))/x^4,x]","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{3 d e^2 \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{e^3 \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}-\frac{b d^3 n}{9 x^3}-\frac{3 b d^2 e n}{4 x^2}-\frac{3 b d e^2 n}{x}","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{3 d e^2 \left(a+b \log \left(c x^n\right)\right)}{x}+e^3 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{b d^3 n}{9 x^3}-\frac{3 b d^2 e n}{4 x^2}-\frac{3 b d e^2 n}{x}-\frac{1}{2} b e^3 n \log ^2(x)",1,"-1/9*(b*d^3*n)/x^3 - (3*b*d^2*e*n)/(4*x^2) - (3*b*d*e^2*n)/x - (d^3*(a + b*Log[c*x^n]))/(3*x^3) - (3*d^2*e*(a + b*Log[c*x^n]))/(2*x^2) - (3*d*e^2*(a + b*Log[c*x^n]))/x + (e^3*(a + b*Log[c*x^n])^2)/(2*b*n)","A",1
27,1,109,90,0.0550037,"\int \frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{x^5} \, dx","Integrate[((d + e*x)^3*(a + b*Log[c*x^n]))/x^5,x]","-\frac{12 a \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)+12 b \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right) \log \left(c x^n\right)+b n \left(3 d^3+16 d^2 e x+36 d e^2 x^2+48 e^3 x^3\right)}{48 x^4}","-\frac{(d+e x)^4 \left(a+b \log \left(c x^n\right)\right)}{4 d x^4}-\frac{b d^3 n}{16 x^4}-\frac{b d^2 e n}{3 x^3}+\frac{b e^4 n \log (x)}{4 d}-\frac{3 b d e^2 n}{4 x^2}-\frac{b e^3 n}{x}",1,"-1/48*(12*a*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) + b*n*(3*d^3 + 16*d^2*e*x + 36*d*e^2*x^2 + 48*e^3*x^3) + 12*b*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3)*Log[c*x^n])/x^4","A",1
28,1,113,142,0.0539798,"\int \frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Integrate[((d + e*x)^3*(a + b*Log[c*x^n]))/x^6,x]","-\frac{60 a \left(4 d^3+15 d^2 e x+20 d e^2 x^2+10 e^3 x^3\right)+60 b \left(4 d^3+15 d^2 e x+20 d e^2 x^2+10 e^3 x^3\right) \log \left(c x^n\right)+b n \left(48 d^3+225 d^2 e x+400 d e^2 x^2+300 e^3 x^3\right)}{1200 x^5}","\frac{e (d+e x)^4 \left(a+b \log \left(c x^n\right)\right)}{20 d^2 x^4}-\frac{(d+e x)^4 \left(a+b \log \left(c x^n\right)\right)}{5 d x^5}-\frac{b e^5 n \log (x)}{20 d^2}-\frac{b n (d+e x)^5}{25 d^2 x^5}+\frac{b d^2 e n}{80 x^4}+\frac{b e^4 n}{5 d x}+\frac{b d e^2 n}{15 x^3}+\frac{3 b e^3 n}{20 x^2}",1,"-1/1200*(60*a*(4*d^3 + 15*d^2*e*x + 20*d*e^2*x^2 + 10*e^3*x^3) + b*n*(48*d^3 + 225*d^2*e*x + 400*d*e^2*x^2 + 300*e^3*x^3) + 60*b*(4*d^3 + 15*d^2*e*x + 20*d*e^2*x^2 + 10*e^3*x^3)*Log[c*x^n])/x^5","A",1
29,1,113,133,0.0554551,"\int \frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{x^7} \, dx","Integrate[((d + e*x)^3*(a + b*Log[c*x^n]))/x^7,x]","-\frac{60 a \left(10 d^3+36 d^2 e x+45 d e^2 x^2+20 e^3 x^3\right)+60 b \left(10 d^3+36 d^2 e x+45 d e^2 x^2+20 e^3 x^3\right) \log \left(c x^n\right)+b n \left(100 d^3+432 d^2 e x+675 d e^2 x^2+400 e^3 x^3\right)}{3600 x^6}","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{6 x^6}-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{3 d e^2 \left(a+b \log \left(c x^n\right)\right)}{4 x^4}-\frac{e^3 \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{b d^3 n}{36 x^6}-\frac{3 b d^2 e n}{25 x^5}-\frac{3 b d e^2 n}{16 x^4}-\frac{b e^3 n}{9 x^3}",1,"-1/3600*(60*a*(10*d^3 + 36*d^2*e*x + 45*d*e^2*x^2 + 20*e^3*x^3) + b*n*(100*d^3 + 432*d^2*e*x + 675*d*e^2*x^2 + 400*e^3*x^3) + 60*b*(10*d^3 + 36*d^2*e*x + 45*d*e^2*x^2 + 20*e^3*x^3)*Log[c*x^n])/x^6","A",1
30,1,113,133,0.0574501,"\int \frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{x^8} \, dx","Integrate[((d + e*x)^3*(a + b*Log[c*x^n]))/x^8,x]","-\frac{420 a \left(20 d^3+70 d^2 e x+84 d e^2 x^2+35 e^3 x^3\right)+420 b \left(20 d^3+70 d^2 e x+84 d e^2 x^2+35 e^3 x^3\right) \log \left(c x^n\right)+b n \left(1200 d^3+4900 d^2 e x+7056 d e^2 x^2+3675 e^3 x^3\right)}{58800 x^7}","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{7 x^7}-\frac{d^2 e \left(a+b \log \left(c x^n\right)\right)}{2 x^6}-\frac{3 d e^2 \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{e^3 \left(a+b \log \left(c x^n\right)\right)}{4 x^4}-\frac{b d^3 n}{49 x^7}-\frac{b d^2 e n}{12 x^6}-\frac{3 b d e^2 n}{25 x^5}-\frac{b e^3 n}{16 x^4}",1,"-1/58800*(420*a*(20*d^3 + 70*d^2*e*x + 84*d*e^2*x^2 + 35*e^3*x^3) + b*n*(1200*d^3 + 4900*d^2*e*x + 7056*d*e^2*x^2 + 3675*e^3*x^3) + 420*b*(20*d^3 + 70*d^2*e*x + 84*d*e^2*x^2 + 35*e^3*x^3)*Log[c*x^n])/x^7","A",1
31,1,142,148,0.0806866,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{d+e x} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/(d + e*x),x]","\frac{-36 a d^3 \log \left(\frac{e x}{d}+1\right)+36 a d^2 e x-18 a d e^2 x^2+12 a e^3 x^3+6 b \log \left(c x^n\right) \left(e x \left(6 d^2-3 d e x+2 e^2 x^2\right)-6 d^3 \log \left(\frac{e x}{d}+1\right)\right)-36 b d^3 n \text{Li}_2\left(-\frac{e x}{d}\right)-36 b d^2 e n x+9 b d e^2 n x^2-4 b e^3 n x^3}{36 e^4}","-\frac{d^3 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}-\frac{d x^2 \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{3 e}+\frac{a d^2 x}{e^3}+\frac{b d^2 x \log \left(c x^n\right)}{e^3}-\frac{b d^3 n \text{Li}_2\left(-\frac{e x}{d}\right)}{e^4}-\frac{b d^2 n x}{e^3}+\frac{b d n x^2}{4 e^2}-\frac{b n x^3}{9 e}",1,"(36*a*d^2*e*x - 36*b*d^2*e*n*x - 18*a*d*e^2*x^2 + 9*b*d*e^2*n*x^2 + 12*a*e^3*x^3 - 4*b*e^3*n*x^3 - 36*a*d^3*Log[1 + (e*x)/d] + 6*b*Log[c*x^n]*(e*x*(6*d^2 - 3*d*e*x + 2*e^2*x^2) - 6*d^3*Log[1 + (e*x)/d]) - 36*b*d^3*n*PolyLog[2, -((e*x)/d)])/(36*e^4)","A",1
32,1,105,107,0.0501055,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{d+e x} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e*x),x]","\frac{4 a d^2 \log \left(\frac{e x}{d}+1\right)-4 a d e x+2 a e^2 x^2+2 b \log \left(c x^n\right) \left(2 d^2 \log \left(\frac{e x}{d}+1\right)+e x (e x-2 d)\right)+4 b d^2 n \text{Li}_2\left(-\frac{e x}{d}\right)+4 b d e n x-b e^2 n x^2}{4 e^3}","\frac{d^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^3}+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{2 e}-\frac{a d x}{e^2}-\frac{b d x \log \left(c x^n\right)}{e^2}+\frac{b d^2 n \text{Li}_2\left(-\frac{e x}{d}\right)}{e^3}+\frac{b d n x}{e^2}-\frac{b n x^2}{4 e}",1,"(-4*a*d*e*x + 4*b*d*e*n*x + 2*a*e^2*x^2 - b*e^2*n*x^2 + 4*a*d^2*Log[1 + (e*x)/d] + 2*b*Log[c*x^n]*(e*x*(-2*d + e*x) + 2*d^2*Log[1 + (e*x)/d]) + 4*b*d^2*n*PolyLog[2, -((e*x)/d)])/(4*e^3)","A",1
33,1,66,69,0.0326806,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{d+e x} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/(d + e*x),x]","\frac{-a d \log \left(\frac{e x}{d}+1\right)+a e x+b \log \left(c x^n\right) \left(e x-d \log \left(\frac{e x}{d}+1\right)\right)-b d n \text{Li}_2\left(-\frac{e x}{d}\right)-b e n x}{e^2}","-\frac{d \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{a x}{e}+\frac{b x \log \left(c x^n\right)}{e}-\frac{b d n \text{Li}_2\left(-\frac{e x}{d}\right)}{e^2}-\frac{b n x}{e}",1,"(a*e*x - b*e*n*x - a*d*Log[1 + (e*x)/d] + b*Log[c*x^n]*(e*x - d*Log[1 + (e*x)/d]) - b*d*n*PolyLog[2, -((e*x)/d)])/e^2","A",1
34,1,37,39,0.0073172,"\int \frac{a+b \log \left(c x^n\right)}{d+e x} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*x),x]","\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+b n \text{Li}_2\left(-\frac{e x}{d}\right)}{e}","\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e}+\frac{b n \text{Li}_2\left(-\frac{e x}{d}\right)}{e}",1,"((a + b*Log[c*x^n])*Log[1 + (e*x)/d] + b*n*PolyLog[2, -((e*x)/d)])/e","A",1
35,1,63,44,0.0348579,"\int \frac{a+b \log \left(c x^n\right)}{x (d+e x)} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x)),x]","\frac{\left(a+b \log \left(c x^n\right)\right) \left(a+b \log \left(c x^n\right)-2 b n \log \left(\frac{e x}{d}+1\right)\right)}{2 b d n}-\frac{b n \text{Li}_2\left(-\frac{e x}{d}\right)}{d}","\frac{b n \text{Li}_2\left(-\frac{d}{e x}\right)}{d}-\frac{\log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d}",1,"((a + b*Log[c*x^n])*(a + b*Log[c*x^n] - 2*b*n*Log[1 + (e*x)/d]))/(2*b*d*n) - (b*n*PolyLog[2, -((e*x)/d)])/d","A",1
36,1,88,74,0.0891453,"\int \frac{a+b \log \left(c x^n\right)}{x^2 (d+e x)} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*(d + e*x)),x]","-\frac{-2 e \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2 d \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{b n}-2 b e n \text{Li}_2\left(-\frac{e x}{d}\right)+\frac{2 b d n}{x}}{2 d^2}","\frac{e \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}-\frac{a+b \log \left(c x^n\right)}{d x}-\frac{b e n \text{Li}_2\left(-\frac{d}{e x}\right)}{d^2}-\frac{b n}{d x}",1,"-1/2*((2*b*d*n)/x + (2*d*(a + b*Log[c*x^n]))/x + (e*(a + b*Log[c*x^n])^2)/(b*n) - 2*e*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 2*b*e*n*PolyLog[2, -((e*x)/d)])/d^2","A",1
37,1,124,110,0.2090545,"\int \frac{a+b \log \left(c x^n\right)}{x^3 (d+e x)} \, dx","Integrate[(a + b*Log[c*x^n])/(x^3*(d + e*x)),x]","-\frac{\frac{2 d^2 \left(a+b \log \left(c x^n\right)\right)}{x^2}+4 e^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{4 d e \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{2 e^2 \left(a+b \log \left(c x^n\right)\right)^2}{b n}+\frac{b d^2 n}{x^2}+4 b e^2 n \text{Li}_2\left(-\frac{e x}{d}\right)-\frac{4 b d e n}{x}}{4 d^3}","-\frac{e^2 \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}+\frac{e \left(a+b \log \left(c x^n\right)\right)}{d^2 x}-\frac{a+b \log \left(c x^n\right)}{2 d x^2}+\frac{b e^2 n \text{Li}_2\left(-\frac{d}{e x}\right)}{d^3}+\frac{b e n}{d^2 x}-\frac{b n}{4 d x^2}",1,"-1/4*((b*d^2*n)/x^2 - (4*b*d*e*n)/x + (2*d^2*(a + b*Log[c*x^n]))/x^2 - (4*d*e*(a + b*Log[c*x^n]))/x - (2*e^2*(a + b*Log[c*x^n])^2)/(b*n) + 4*e^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] + 4*b*e^2*n*PolyLog[2, -((e*x)/d)])/d^3","A",1
38,1,159,150,0.2084766,"\int \frac{a+b \log \left(c x^n\right)}{x^4 (d+e x)} \, dx","Integrate[(a + b*Log[c*x^n])/(x^4*(d + e*x)),x]","\frac{-\frac{12 d^3 \left(a+b \log \left(c x^n\right)\right)}{x^3}+\frac{18 d^2 e \left(a+b \log \left(c x^n\right)\right)}{x^2}+36 e^3 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{36 d e^2 \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{18 e^3 \left(a+b \log \left(c x^n\right)\right)^2}{b n}-\frac{4 b d^3 n}{x^3}+\frac{9 b d^2 e n}{x^2}+36 b e^3 n \text{Li}_2\left(-\frac{e x}{d}\right)-\frac{36 b d e^2 n}{x}}{36 d^4}","\frac{e^3 \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}-\frac{e^2 \left(a+b \log \left(c x^n\right)\right)}{d^3 x}+\frac{e \left(a+b \log \left(c x^n\right)\right)}{2 d^2 x^2}-\frac{a+b \log \left(c x^n\right)}{3 d x^3}-\frac{b e^3 n \text{Li}_2\left(-\frac{d}{e x}\right)}{d^4}-\frac{b e^2 n}{d^3 x}+\frac{b e n}{4 d^2 x^2}-\frac{b n}{9 d x^3}",1,"((-4*b*d^3*n)/x^3 + (9*b*d^2*e*n)/x^2 - (36*b*d*e^2*n)/x - (12*d^3*(a + b*Log[c*x^n]))/x^3 + (18*d^2*e*(a + b*Log[c*x^n]))/x^2 - (36*d*e^2*(a + b*Log[c*x^n]))/x - (18*e^3*(a + b*Log[c*x^n])^2)/(b*n) + 36*e^3*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] + 36*b*e^3*n*PolyLog[2, -((e*x)/d)])/(36*d^4)","A",1
39,1,141,152,0.1410198,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/(d + e*x)^2,x]","\frac{\frac{4 d^3 \left(a+b \log \left(c x^n\right)\right)}{d+e x}+12 d^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+2 e^2 x^2 \left(a+b \log \left(c x^n\right)\right)-8 a d e x-8 b d e x \log \left(c x^n\right)+12 b d^2 n \text{Li}_2\left(-\frac{e x}{d}\right)-4 b d^2 n (\log (x)-\log (d+e x))+8 b d e n x-b e^2 n x^2}{4 e^4}","\frac{d^2 \log \left(\frac{e x}{d}+1\right) \left(3 a+3 b \log \left(c x^n\right)+b n\right)}{e^4}-\frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{e (d+e x)}+\frac{x^2 \left(3 a+3 b \log \left(c x^n\right)+b n\right)}{2 e^2}-\frac{d x (3 a+b n)}{e^3}-\frac{3 b d x \log \left(c x^n\right)}{e^3}+\frac{3 b d^2 n \text{Li}_2\left(-\frac{e x}{d}\right)}{e^4}+\frac{3 b d n x}{e^3}-\frac{3 b n x^2}{4 e^2}",1,"(-8*a*d*e*x + 8*b*d*e*n*x - b*e^2*n*x^2 - 8*b*d*e*x*Log[c*x^n] + 2*e^2*x^2*(a + b*Log[c*x^n]) + (4*d^3*(a + b*Log[c*x^n]))/(d + e*x) - 4*b*d^2*n*(Log[x] - Log[d + e*x]) + 12*d^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] + 12*b*d^2*n*PolyLog[2, -((e*x)/d)])/(4*e^4)","A",1
40,1,98,98,0.0910539,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e*x)^2,x]","\frac{-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{d+e x}-2 d \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+a e x+b e x \log \left(c x^n\right)-2 b d n \text{Li}_2\left(-\frac{e x}{d}\right)+b d n (\log (x)-\log (d+e x))-b e n x}{e^3}","-\frac{d \log \left(\frac{e x}{d}+1\right) \left(2 a+2 b \log \left(c x^n\right)+b n\right)}{e^3}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{e (d+e x)}+\frac{2 x \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{2 b d n \text{Li}_2\left(-\frac{e x}{d}\right)}{e^3}-\frac{b n x}{e^2}",1,"(a*e*x - b*e*n*x + b*e*x*Log[c*x^n] - (d^2*(a + b*Log[c*x^n]))/(d + e*x) + b*d*n*(Log[x] - Log[d + e*x]) - 2*d*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 2*b*d*n*PolyLog[2, -((e*x)/d)])/e^3","A",1
41,1,71,65,0.0621985,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/(d + e*x)^2,x]","\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{d \left(a+b \log \left(c x^n\right)\right)}{d+e x}+b n \text{Li}_2\left(-\frac{e x}{d}\right)-b n (\log (x)-\log (d+e x))}{e^2}","\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)+b n\right)}{e^2}-\frac{x \left(a+b \log \left(c x^n\right)\right)}{e (d+e x)}+\frac{b n \text{Li}_2\left(-\frac{e x}{d}\right)}{e^2}",1,"((d*(a + b*Log[c*x^n]))/(d + e*x) - b*n*(Log[x] - Log[d + e*x]) + (a + b*Log[c*x^n])*Log[1 + (e*x)/d] + b*n*PolyLog[2, -((e*x)/d)])/e^2","A",1
42,1,41,39,0.0295527,"\int \frac{a+b \log \left(c x^n\right)}{(d+e x)^2} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*x)^2,x]","\frac{\frac{b n (\log (x)-\log (d+e x))}{d}-\frac{a+b \log \left(c x^n\right)}{d+e x}}{e}","\frac{x \left(a+b \log \left(c x^n\right)\right)}{d (d+e x)}-\frac{b n \log (d+e x)}{d e}",1,"(-((a + b*Log[c*x^n])/(d + e*x)) + (b*n*(Log[x] - Log[d + e*x]))/d)/e","A",1
43,1,96,80,0.0776566,"\int \frac{a+b \log \left(c x^n\right)}{x (d+e x)^2} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x)^2),x]","\frac{-2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2 d \left(a+b \log \left(c x^n\right)\right)}{d+e x}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{b n}-2 b n \text{Li}_2\left(-\frac{e x}{d}\right)-2 b n (\log (x)-\log (d+e x))}{2 d^2}","-\frac{\log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}-\frac{e x \left(a+b \log \left(c x^n\right)\right)}{d^2 (d+e x)}+\frac{b n \text{Li}_2\left(-\frac{d}{e x}\right)}{d^2}+\frac{b n \log (d+e x)}{d^2}",1,"((2*d*(a + b*Log[c*x^n]))/(d + e*x) + (a + b*Log[c*x^n])^2/(b*n) - 2*b*n*(Log[x] - Log[d + e*x]) - 2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 2*b*n*PolyLog[2, -((e*x)/d)])/(2*d^2)","A",1
44,1,120,114,0.1396657,"\int \frac{a+b \log \left(c x^n\right)}{x^2 (d+e x)^2} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*(d + e*x)^2),x]","-\frac{-2 e \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{d e \left(a+b \log \left(c x^n\right)\right)}{d+e x}+\frac{d \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{b n}-2 b e n \text{Li}_2\left(-\frac{e x}{d}\right)-b e n (\log (x)-\log (d+e x))+\frac{b d n}{x}}{d^3}","\frac{e^2 x \left(a+b \log \left(c x^n\right)\right)}{d^3 (d+e x)}+\frac{2 e \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}-\frac{a+b \log \left(c x^n\right)}{d^2 x}-\frac{2 b e n \text{Li}_2\left(-\frac{d}{e x}\right)}{d^3}-\frac{b e n \log (d+e x)}{d^3}-\frac{b n}{d^2 x}",1,"-(((b*d*n)/x + (d*(a + b*Log[c*x^n]))/x + (d*e*(a + b*Log[c*x^n]))/(d + e*x) + (e*(a + b*Log[c*x^n])^2)/(b*n) - b*e*n*(Log[x] - Log[d + e*x]) - 2*e*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 2*b*e*n*PolyLog[2, -((e*x)/d)])/d^3)","A",1
45,1,165,154,0.2190586,"\int \frac{a+b \log \left(c x^n\right)}{x^3 (d+e x)^2} \, dx","Integrate[(a + b*Log[c*x^n])/(x^3*(d + e*x)^2),x]","-\frac{\frac{2 d^2 \left(a+b \log \left(c x^n\right)\right)}{x^2}-\frac{4 d e^2 \left(a+b \log \left(c x^n\right)\right)}{d+e x}+12 e^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{8 d e \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{6 e^2 \left(a+b \log \left(c x^n\right)\right)^2}{b n}+\frac{b d^2 n}{x^2}+12 b e^2 n \text{Li}_2\left(-\frac{e x}{d}\right)+4 b e^2 n (\log (x)-\log (d+e x))-\frac{8 b d e n}{x}}{4 d^4}","-\frac{e^3 x \left(a+b \log \left(c x^n\right)\right)}{d^4 (d+e x)}-\frac{3 e^2 \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}+\frac{2 e \left(a+b \log \left(c x^n\right)\right)}{d^3 x}-\frac{a+b \log \left(c x^n\right)}{2 d^2 x^2}+\frac{3 b e^2 n \text{Li}_2\left(-\frac{d}{e x}\right)}{d^4}+\frac{b e^2 n \log (d+e x)}{d^4}+\frac{2 b e n}{d^3 x}-\frac{b n}{4 d^2 x^2}",1,"-1/4*((b*d^2*n)/x^2 - (8*b*d*e*n)/x + (2*d^2*(a + b*Log[c*x^n]))/x^2 - (8*d*e*(a + b*Log[c*x^n]))/x - (4*d*e^2*(a + b*Log[c*x^n]))/(d + e*x) - (6*e^2*(a + b*Log[c*x^n])^2)/(b*n) + 4*b*e^2*n*(Log[x] - Log[d + e*x]) + 12*e^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] + 12*b*e^2*n*PolyLog[2, -((e*x)/d)])/d^4","A",1
46,1,150,149,0.1402768,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^3} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/(d + e*x)^3,x]","\frac{\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2}-\frac{6 d^2 \left(a+b \log \left(c x^n\right)\right)}{d+e x}-6 d \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+2 a e x+2 b e x \log \left(c x^n\right)-6 b d n \text{Li}_2\left(-\frac{e x}{d}\right)+6 b d n (\log (x)-\log (d+e x))-b d n \left(\frac{d}{d+e x}-\log (d+e x)+\log (x)\right)-2 b e n x}{2 e^4}","-\frac{d \log \left(\frac{e x}{d}+1\right) \left(6 a+6 b \log \left(c x^n\right)+5 b n\right)}{2 e^4}-\frac{x^2 \left(3 a+3 b \log \left(c x^n\right)+b n\right)}{2 e^2 (d+e x)}-\frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{2 e (d+e x)^2}+\frac{x (6 a+5 b n)}{2 e^3}+\frac{3 b x \log \left(c x^n\right)}{e^3}-\frac{3 b d n \text{Li}_2\left(-\frac{e x}{d}\right)}{e^4}-\frac{3 b n x}{e^3}",1,"(2*a*e*x - 2*b*e*n*x + 2*b*e*x*Log[c*x^n] + (d^3*(a + b*Log[c*x^n]))/(d + e*x)^2 - (6*d^2*(a + b*Log[c*x^n]))/(d + e*x) + 6*b*d*n*(Log[x] - Log[d + e*x]) - b*d*n*(d/(d + e*x) + Log[x] - Log[d + e*x]) - 6*d*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 6*b*d*n*PolyLog[2, -((e*x)/d)])/(2*e^4)","A",1
47,1,122,107,0.1163676,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^3} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e*x)^3,x]","\frac{-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2}+\frac{4 d \left(a+b \log \left(c x^n\right)\right)}{d+e x}+2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+2 b n \text{Li}_2\left(-\frac{e x}{d}\right)-4 b n (\log (x)-\log (d+e x))+b n \left(\frac{d}{d+e x}-\log (d+e x)+\log (x)\right)}{2 e^3}","\frac{\log \left(\frac{e x}{d}+1\right) \left(2 a+2 b \log \left(c x^n\right)+3 b n\right)}{2 e^3}-\frac{x \left(2 a+2 b \log \left(c x^n\right)+b n\right)}{2 e^2 (d+e x)}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{2 e (d+e x)^2}+\frac{b n \text{Li}_2\left(-\frac{e x}{d}\right)}{e^3}",1,"(-((d^2*(a + b*Log[c*x^n]))/(d + e*x)^2) + (4*d*(a + b*Log[c*x^n]))/(d + e*x) - 4*b*n*(Log[x] - Log[d + e*x]) + b*n*(d/(d + e*x) + Log[x] - Log[d + e*x]) + 2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] + 2*b*n*PolyLog[2, -((e*x)/d)])/(2*e^3)","A",1
48,1,75,62,0.1203154,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^3} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/(d + e*x)^3,x]","\frac{b n \log (x)-\frac{a d (d+2 e x)+b d (d+2 e x) \log \left(c x^n\right)+b d n (d+e x)+b n (d+e x)^2 \log (d+e x)}{(d+e x)^2}}{2 d e^2}","\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{2 d (d+e x)^2}-\frac{b n}{2 e^2 (d+e x)}-\frac{b n \log (d+e x)}{2 d e^2}",1,"(b*n*Log[x] - (b*d*n*(d + e*x) + a*d*(d + 2*e*x) + b*d*(d + 2*e*x)*Log[c*x^n] + b*n*(d + e*x)^2*Log[d + e*x])/(d + e*x)^2)/(2*d*e^2)","A",1
49,1,53,76,0.0581122,"\int \frac{a+b \log \left(c x^n\right)}{(d+e x)^3} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*x)^3,x]","\frac{\frac{b n \left(\frac{d}{d+e x}-\log (d+e x)+\log (x)\right)}{d^2}-\frac{a+b \log \left(c x^n\right)}{(d+e x)^2}}{2 e}","-\frac{a+b \log \left(c x^n\right)}{2 e (d+e x)^2}+\frac{b n \log (x)}{2 d^2 e}-\frac{b n \log (d+e x)}{2 d^2 e}+\frac{b n}{2 d e (d+e x)}",1,"(-((a + b*Log[c*x^n])/(d + e*x)^2) + (b*n*(d/(d + e*x) + Log[x] - Log[d + e*x]))/d^2)/(2*e)","A",1
50,1,141,134,0.1305827,"\int \frac{a+b \log \left(c x^n\right)}{x (d+e x)^3} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x)^3),x]","\frac{\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2}+\frac{2 d \left(a+b \log \left(c x^n\right)\right)}{d+e x}-2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{b n}-2 b n \text{Li}_2\left(-\frac{e x}{d}\right)-2 b n (\log (x)-\log (d+e x))+b n \left(-\frac{d}{d+e x}+\log (d+e x)-\log (x)\right)}{2 d^3}","-\frac{\log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}-\frac{e x \left(a+b \log \left(c x^n\right)\right)}{d^3 (d+e x)}+\frac{a+b \log \left(c x^n\right)}{2 d (d+e x)^2}+\frac{b n \text{Li}_2\left(-\frac{d}{e x}\right)}{d^3}+\frac{3 b n \log (d+e x)}{2 d^3}-\frac{b n \log (x)}{2 d^3}-\frac{b n}{2 d^2 (d+e x)}",1,"((d^2*(a + b*Log[c*x^n]))/(d + e*x)^2 + (2*d*(a + b*Log[c*x^n]))/(d + e*x) + (a + b*Log[c*x^n])^2/(b*n) - 2*b*n*(Log[x] - Log[d + e*x]) + b*n*(-(d/(d + e*x)) - Log[x] + Log[d + e*x]) - 2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 2*b*n*PolyLog[2, -((e*x)/d)])/(2*d^3)","A",1
51,1,173,171,0.1765904,"\int \frac{a+b \log \left(c x^n\right)}{x^2 (d+e x)^3} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*(d + e*x)^3),x]","\frac{-\frac{d^2 e \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2}-\frac{4 d e \left(a+b \log \left(c x^n\right)\right)}{d+e x}+6 e \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 d \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{3 e \left(a+b \log \left(c x^n\right)\right)^2}{b n}+6 b e n \text{Li}_2\left(-\frac{e x}{d}\right)+4 b e n (\log (x)-\log (d+e x))+b e n \left(\frac{d}{d+e x}-\log (d+e x)+\log (x)\right)-\frac{2 b d n}{x}}{2 d^4}","\frac{2 e^2 x \left(a+b \log \left(c x^n\right)\right)}{d^4 (d+e x)}+\frac{3 e \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}-\frac{a+b \log \left(c x^n\right)}{d^3 x}-\frac{e \left(a+b \log \left(c x^n\right)\right)}{2 d^2 (d+e x)^2}-\frac{3 b e n \text{Li}_2\left(-\frac{d}{e x}\right)}{d^4}+\frac{b e n \log (x)}{2 d^4}-\frac{5 b e n \log (d+e x)}{2 d^4}+\frac{b e n}{2 d^3 (d+e x)}-\frac{b n}{d^3 x}",1,"((-2*b*d*n)/x - (2*d*(a + b*Log[c*x^n]))/x - (d^2*e*(a + b*Log[c*x^n]))/(d + e*x)^2 - (4*d*e*(a + b*Log[c*x^n]))/(d + e*x) - (3*e*(a + b*Log[c*x^n])^2)/(b*n) + 4*b*e*n*(Log[x] - Log[d + e*x]) + b*e*n*(d/(d + e*x) + Log[x] - Log[d + e*x]) + 6*e*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] + 6*b*e*n*PolyLog[2, -((e*x)/d)])/(2*d^4)","A",1
52,1,227,217,0.4319182,"\int \frac{a+b \log \left(c x^n\right)}{x^3 (d+e x)^3} \, dx","Integrate[(a + b*Log[c*x^n])/(x^3*(d + e*x)^3),x]","-\frac{-\frac{2 d^2 e^2 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2}+\frac{2 d^2 \left(a+b \log \left(c x^n\right)\right)}{x^2}-\frac{12 d e^2 \left(a+b \log \left(c x^n\right)\right)}{d+e x}+24 e^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{12 d e \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{12 e^2 \left(a+b \log \left(c x^n\right)\right)^2}{b n}+\frac{b d^2 n}{x^2}+24 b e^2 n \text{Li}_2\left(-\frac{e x}{d}\right)+12 b e^2 n (\log (x)-\log (d+e x))+\frac{2 b e^2 n (\log (x) (d+e x)-(d+e x) \log (d+e x)+d)}{d+e x}-\frac{12 b d e n}{x}}{4 d^5}","-\frac{3 e^3 x \left(a+b \log \left(c x^n\right)\right)}{d^5 (d+e x)}-\frac{6 e^2 \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^5}+\frac{3 e \left(a+b \log \left(c x^n\right)\right)}{d^4 x}+\frac{e^2 \left(a+b \log \left(c x^n\right)\right)}{2 d^3 (d+e x)^2}-\frac{a+b \log \left(c x^n\right)}{2 d^3 x^2}+\frac{6 b e^2 n \text{Li}_2\left(-\frac{d}{e x}\right)}{d^5}-\frac{b e^2 n \log (x)}{2 d^5}+\frac{7 b e^2 n \log (d+e x)}{2 d^5}-\frac{b e^2 n}{2 d^4 (d+e x)}+\frac{3 b e n}{d^4 x}-\frac{b n}{4 d^3 x^2}",1,"-1/4*((b*d^2*n)/x^2 - (12*b*d*e*n)/x + (2*d^2*(a + b*Log[c*x^n]))/x^2 - (12*d*e*(a + b*Log[c*x^n]))/x - (2*d^2*e^2*(a + b*Log[c*x^n]))/(d + e*x)^2 - (12*d*e^2*(a + b*Log[c*x^n]))/(d + e*x) - (12*e^2*(a + b*Log[c*x^n])^2)/(b*n) + 12*b*e^2*n*(Log[x] - Log[d + e*x]) + (2*b*e^2*n*(d + (d + e*x)*Log[x] - (d + e*x)*Log[d + e*x]))/(d + e*x) + 24*e^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] + 24*b*e^2*n*PolyLog[2, -((e*x)/d)])/d^5","A",1
53,1,249,229,0.3106436,"\int \frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^4} \, dx","Integrate[(x^5*(a + b*Log[c*x^n]))/(d + e*x)^4,x]","\frac{\frac{4 d^5 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^3}-\frac{30 d^4 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2}+\frac{120 d^3 \left(a+b \log \left(c x^n\right)\right)}{d+e x}+120 d^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+6 e^2 x^2 \left(a+b \log \left(c x^n\right)\right)-48 a d e x-48 b d e x \log \left(c x^n\right)+120 b d^2 n \text{Li}_2\left(-\frac{e x}{d}\right)-2 b d^2 n \left(\frac{d (3 d+2 e x)}{(d+e x)^2}-2 \log (d+e x)+2 \log (x)\right)-120 b d^2 n (\log (x)-\log (d+e x))+30 b d^2 n \left(\frac{d}{d+e x}-\log (d+e x)+\log (x)\right)+48 b d e n x-3 b e^2 n x^2}{12 e^6}","\frac{d^2 \log \left(\frac{e x}{d}+1\right) \left(60 a+60 b \log \left(c x^n\right)+47 b n\right)}{6 e^6}-\frac{x^3 \left(20 a+20 b \log \left(c x^n\right)+9 b n\right)}{6 e^3 (d+e x)}-\frac{x^4 \left(5 a+5 b \log \left(c x^n\right)+b n\right)}{6 e^2 (d+e x)^2}-\frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{3 e (d+e x)^3}+\frac{x^2 \left(60 a+60 b \log \left(c x^n\right)+47 b n\right)}{12 e^4}-\frac{d x (60 a+47 b n)}{6 e^5}-\frac{10 b d x \log \left(c x^n\right)}{e^5}+\frac{10 b d^2 n \text{Li}_2\left(-\frac{e x}{d}\right)}{e^6}+\frac{10 b d n x}{e^5}-\frac{5 b n x^2}{2 e^4}",1,"(-48*a*d*e*x + 48*b*d*e*n*x - 3*b*e^2*n*x^2 - 48*b*d*e*x*Log[c*x^n] + 6*e^2*x^2*(a + b*Log[c*x^n]) + (4*d^5*(a + b*Log[c*x^n]))/(d + e*x)^3 - (30*d^4*(a + b*Log[c*x^n]))/(d + e*x)^2 + (120*d^3*(a + b*Log[c*x^n]))/(d + e*x) - 2*b*d^2*n*((d*(3*d + 2*e*x))/(d + e*x)^2 + 2*Log[x] - 2*Log[d + e*x]) - 120*b*d^2*n*(Log[x] - Log[d + e*x]) + 30*b*d^2*n*(d/(d + e*x) + Log[x] - Log[d + e*x]) + 120*d^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] + 120*b*d^2*n*PolyLog[2, -((e*x)/d)])/(12*e^6)","A",1
54,1,207,183,0.226961,"\int \frac{x^4 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^4} \, dx","Integrate[(x^4*(a + b*Log[c*x^n]))/(d + e*x)^4,x]","\frac{-\frac{2 d^4 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^3}+\frac{12 d^3 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2}-\frac{36 d^2 \left(a+b \log \left(c x^n\right)\right)}{d+e x}-24 d \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+6 a e x+6 b e x \log \left(c x^n\right)-24 b d n \text{Li}_2\left(-\frac{e x}{d}\right)+b d n \left(\frac{d (3 d+2 e x)}{(d+e x)^2}-2 \log (d+e x)+2 \log (x)\right)+36 b d n (\log (x)-\log (d+e x))-12 b d n \left(\frac{d}{d+e x}-\log (d+e x)+\log (x)\right)-6 b e n x}{6 e^5}","-\frac{d \log \left(\frac{e x}{d}+1\right) \left(12 a+12 b \log \left(c x^n\right)+13 b n\right)}{3 e^5}-\frac{x^2 \left(12 a+12 b \log \left(c x^n\right)+7 b n\right)}{6 e^3 (d+e x)}-\frac{x^3 \left(4 a+4 b \log \left(c x^n\right)+b n\right)}{6 e^2 (d+e x)^2}-\frac{x^4 \left(a+b \log \left(c x^n\right)\right)}{3 e (d+e x)^3}+\frac{x (12 a+13 b n)}{3 e^4}+\frac{4 b x \log \left(c x^n\right)}{e^4}-\frac{4 b d n \text{Li}_2\left(-\frac{e x}{d}\right)}{e^5}-\frac{4 b n x}{e^4}",1,"(6*a*e*x - 6*b*e*n*x + 6*b*e*x*Log[c*x^n] - (2*d^4*(a + b*Log[c*x^n]))/(d + e*x)^3 + (12*d^3*(a + b*Log[c*x^n]))/(d + e*x)^2 - (36*d^2*(a + b*Log[c*x^n]))/(d + e*x) + b*d*n*((d*(3*d + 2*e*x))/(d + e*x)^2 + 2*Log[x] - 2*Log[d + e*x]) + 36*b*d*n*(Log[x] - Log[d + e*x]) - 12*b*d*n*(d/(d + e*x) + Log[x] - Log[d + e*x]) - 24*d*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 24*b*d*n*PolyLog[2, -((e*x)/d)])/(6*e^5)","A",1
55,1,179,141,0.2381581,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^4} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/(d + e*x)^4,x]","\frac{\frac{2 d^3 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^3}-\frac{9 d^2 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2}+\frac{18 d \left(a+b \log \left(c x^n\right)\right)}{d+e x}+6 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+6 b n \text{Li}_2\left(-\frac{e x}{d}\right)-b n \left(\frac{d (3 d+2 e x)}{(d+e x)^2}-2 \log (d+e x)+2 \log (x)\right)-18 b n (\log (x)-\log (d+e x))+9 b n \left(\frac{d}{d+e x}-\log (d+e x)+\log (x)\right)}{6 e^4}","\frac{\log \left(\frac{e x}{d}+1\right) \left(6 a+6 b \log \left(c x^n\right)+11 b n\right)}{6 e^4}-\frac{x \left(6 a+6 b \log \left(c x^n\right)+5 b n\right)}{6 e^3 (d+e x)}-\frac{x^2 \left(3 a+3 b \log \left(c x^n\right)+b n\right)}{6 e^2 (d+e x)^2}-\frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{3 e (d+e x)^3}+\frac{b n \text{Li}_2\left(-\frac{e x}{d}\right)}{e^4}",1,"((2*d^3*(a + b*Log[c*x^n]))/(d + e*x)^3 - (9*d^2*(a + b*Log[c*x^n]))/(d + e*x)^2 + (18*d*(a + b*Log[c*x^n]))/(d + e*x) - b*n*((d*(3*d + 2*e*x))/(d + e*x)^2 + 2*Log[x] - 2*Log[d + e*x]) - 18*b*n*(Log[x] - Log[d + e*x]) + 9*b*n*(d/(d + e*x) + Log[x] - Log[d + e*x]) + 6*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] + 6*b*n*PolyLog[2, -((e*x)/d)])/(6*e^4)","A",1
56,1,172,79,0.1198843,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^4} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e*x)^4,x]","-\frac{a d^2}{3 e^3 (d+e x)^3}+\frac{a d}{e^3 (d+e x)^2}-\frac{a}{e^3 (d+e x)}-\frac{b d^2 \log \left(c x^n\right)}{3 e^3 (d+e x)^3}+\frac{b d \log \left(c x^n\right)}{e^3 (d+e x)^2}-\frac{b \log \left(c x^n\right)}{e^3 (d+e x)}+\frac{b d n}{6 e^3 (d+e x)^2}-\frac{2 b n}{3 e^3 (d+e x)}+\frac{b n \log (x)}{3 d e^3}-\frac{b n \log (d+e x)}{3 d e^3}","\frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{3 d (d+e x)^3}-\frac{2 b n}{3 e^3 (d+e x)}+\frac{b d n}{6 e^3 (d+e x)^2}-\frac{b n \log (d+e x)}{3 d e^3}",1,"-1/3*(a*d^2)/(e^3*(d + e*x)^3) + (a*d)/(e^3*(d + e*x)^2) + (b*d*n)/(6*e^3*(d + e*x)^2) - a/(e^3*(d + e*x)) - (2*b*n)/(3*e^3*(d + e*x)) + (b*n*Log[x])/(3*d*e^3) - (b*d^2*Log[c*x^n])/(3*e^3*(d + e*x)^3) + (b*d*Log[c*x^n])/(e^3*(d + e*x)^2) - (b*Log[c*x^n])/(e^3*(d + e*x)) - (b*n*Log[d + e*x])/(3*d*e^3)","B",1
57,1,135,117,0.0984147,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^4} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/(d + e*x)^4,x]","-\frac{a+b \log \left(c x^n\right)}{2 e^2 (d+e x)^2}+\frac{d \left(a+b \log \left(c x^n\right)\right)}{3 e^2 (d+e x)^3}-\frac{b n \left(-\frac{2 \log (d+e x)}{d^2}+\frac{2 \log (x)}{d^2}+\frac{2}{d (d+e x)}+\frac{1}{(d+e x)^2}\right)}{6 e^2}+\frac{b n \left(-\frac{\log (d+e x)}{d^2}+\frac{\log (x)}{d^2}+\frac{1}{d (d+e x)}\right)}{2 e^2}","-\frac{a+b \log \left(c x^n\right)}{2 e^2 (d+e x)^2}+\frac{d \left(a+b \log \left(c x^n\right)\right)}{3 e^2 (d+e x)^3}+\frac{b n \log (x)}{6 d^2 e^2}-\frac{b n \log (d+e x)}{6 d^2 e^2}+\frac{b n}{6 d e^2 (d+e x)}-\frac{b n}{6 e^2 (d+e x)^2}",1,"(d*(a + b*Log[c*x^n]))/(3*e^2*(d + e*x)^3) - (a + b*Log[c*x^n])/(2*e^2*(d + e*x)^2) - (b*n*((d + e*x)^(-2) + 2/(d*(d + e*x)) + (2*Log[x])/d^2 - (2*Log[d + e*x])/d^2))/(6*e^2) + (b*n*(1/(d*(d + e*x)) + Log[x]/d^2 - Log[d + e*x]/d^2))/(2*e^2)","A",1
58,1,66,95,0.0862916,"\int \frac{a+b \log \left(c x^n\right)}{(d+e x)^4} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*x)^4,x]","\frac{\frac{b n \left(\frac{d (3 d+2 e x)}{(d+e x)^2}-2 \log (d+e x)+2 \log (x)\right)}{2 d^3}-\frac{a+b \log \left(c x^n\right)}{(d+e x)^3}}{3 e}","-\frac{a+b \log \left(c x^n\right)}{3 e (d+e x)^3}+\frac{b n \log (x)}{3 d^3 e}-\frac{b n \log (d+e x)}{3 d^3 e}+\frac{b n}{3 d^2 e (d+e x)}+\frac{b n}{6 d e (d+e x)^2}",1,"(-((a + b*Log[c*x^n])/(d + e*x)^3) + (b*n*((d*(3*d + 2*e*x))/(d + e*x)^2 + 2*Log[x] - 2*Log[d + e*x]))/(2*d^3))/(3*e)","A",1
59,1,222,174,0.1821736,"\int \frac{a+b \log \left(c x^n\right)}{x (d+e x)^4} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x)^4),x]","\frac{\frac{3 a^2}{b n}+\frac{6 a \log \left(c x^n\right)}{n}+\frac{2 a d^3}{(d+e x)^3}+\frac{3 a d^2}{(d+e x)^2}+\frac{6 a d}{d+e x}-6 a \log \left(\frac{e x}{d}+1\right)+\frac{2 b d^3 \log \left(c x^n\right)}{(d+e x)^3}+\frac{3 b d^2 \log \left(c x^n\right)}{(d+e x)^2}+\frac{6 b d \log \left(c x^n\right)}{d+e x}-6 b \log \left(c x^n\right) \log \left(\frac{e x}{d}+1\right)+\frac{3 b \log ^2\left(c x^n\right)}{n}-\frac{b d^2 n}{(d+e x)^2}-6 b n \text{Li}_2\left(-\frac{e x}{d}\right)-\frac{5 b d n}{d+e x}+11 b n \log (d+e x)-11 b n \log (x)}{6 d^4}","-\frac{\log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}-\frac{e x \left(a+b \log \left(c x^n\right)\right)}{d^4 (d+e x)}+\frac{a+b \log \left(c x^n\right)}{2 d^2 (d+e x)^2}+\frac{a+b \log \left(c x^n\right)}{3 d (d+e x)^3}+\frac{b n \text{Li}_2\left(-\frac{d}{e x}\right)}{d^4}+\frac{11 b n \log (d+e x)}{6 d^4}-\frac{5 b n \log (x)}{6 d^4}-\frac{5 b n}{6 d^3 (d+e x)}-\frac{b n}{6 d^2 (d+e x)^2}",1,"((3*a^2)/(b*n) + (2*a*d^3)/(d + e*x)^3 + (3*a*d^2)/(d + e*x)^2 - (b*d^2*n)/(d + e*x)^2 + (6*a*d)/(d + e*x) - (5*b*d*n)/(d + e*x) - 11*b*n*Log[x] + (6*a*Log[c*x^n])/n + (2*b*d^3*Log[c*x^n])/(d + e*x)^3 + (3*b*d^2*Log[c*x^n])/(d + e*x)^2 + (6*b*d*Log[c*x^n])/(d + e*x) + (3*b*Log[c*x^n]^2)/n + 11*b*n*Log[d + e*x] - 6*a*Log[1 + (e*x)/d] - 6*b*Log[c*x^n]*Log[1 + (e*x)/d] - 6*b*n*PolyLog[2, -((e*x)/d)])/(6*d^4)","A",1
60,1,231,211,0.2761316,"\int \frac{a+b \log \left(c x^n\right)}{x^2 (d+e x)^4} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*(d + e*x)^4),x]","\frac{-\frac{2 d^3 e \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^3}-\frac{6 d^2 e \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2}-\frac{18 d e \left(a+b \log \left(c x^n\right)\right)}{d+e x}+24 e \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{6 d \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{12 e \left(a+b \log \left(c x^n\right)\right)^2}{b n}+24 b e n \text{Li}_2\left(-\frac{e x}{d}\right)+b e n \left(\frac{d (3 d+2 e x)}{(d+e x)^2}-2 \log (d+e x)+2 \log (x)\right)+18 b e n (\log (x)-\log (d+e x))+6 b e n \left(\frac{d}{d+e x}-\log (d+e x)+\log (x)\right)-\frac{6 b d n}{x}}{6 d^5}","\frac{3 e^2 x \left(a+b \log \left(c x^n\right)\right)}{d^5 (d+e x)}+\frac{4 e \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^5}-\frac{a+b \log \left(c x^n\right)}{d^4 x}-\frac{e \left(a+b \log \left(c x^n\right)\right)}{d^3 (d+e x)^2}-\frac{e \left(a+b \log \left(c x^n\right)\right)}{3 d^2 (d+e x)^3}-\frac{4 b e n \text{Li}_2\left(-\frac{d}{e x}\right)}{d^5}+\frac{4 b e n \log (x)}{3 d^5}-\frac{13 b e n \log (d+e x)}{3 d^5}+\frac{4 b e n}{3 d^4 (d+e x)}-\frac{b n}{d^4 x}+\frac{b e n}{6 d^3 (d+e x)^2}",1,"((-6*b*d*n)/x - (6*d*(a + b*Log[c*x^n]))/x - (2*d^3*e*(a + b*Log[c*x^n]))/(d + e*x)^3 - (6*d^2*e*(a + b*Log[c*x^n]))/(d + e*x)^2 - (18*d*e*(a + b*Log[c*x^n]))/(d + e*x) - (12*e*(a + b*Log[c*x^n])^2)/(b*n) + b*e*n*((d*(3*d + 2*e*x))/(d + e*x)^2 + 2*Log[x] - 2*Log[d + e*x]) + 18*b*e*n*(Log[x] - Log[d + e*x]) + 6*b*e*n*(d/(d + e*x) + Log[x] - Log[d + e*x]) + 24*e*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] + 24*b*e*n*PolyLog[2, -((e*x)/d)])/(6*d^5)","A",1
61,1,276,263,0.3808634,"\int \frac{a+b \log \left(c x^n\right)}{x^3 (d+e x)^4} \, dx","Integrate[(a + b*Log[c*x^n])/(x^3*(d + e*x)^4),x]","\frac{\frac{4 d^3 e^2 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^3}+\frac{18 d^2 e^2 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2}-\frac{6 d^2 \left(a+b \log \left(c x^n\right)\right)}{x^2}+\frac{72 d e^2 \left(a+b \log \left(c x^n\right)\right)}{d+e x}-120 e^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{48 d e \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{60 e^2 \left(a+b \log \left(c x^n\right)\right)^2}{b n}-\frac{3 b d^2 n}{x^2}-120 b e^2 n \text{Li}_2\left(-\frac{e x}{d}\right)-\frac{2 b d e^2 n (3 d+2 e x)}{(d+e x)^2}-\frac{18 b d e^2 n}{d+e x}-72 b e^2 n (\log (x)-\log (d+e x))+22 b e^2 n \log (d+e x)+\frac{48 b d e n}{x}-22 b e^2 n \log (x)}{12 d^6}","-\frac{6 e^3 x \left(a+b \log \left(c x^n\right)\right)}{d^6 (d+e x)}-\frac{10 e^2 \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^6}+\frac{4 e \left(a+b \log \left(c x^n\right)\right)}{d^5 x}+\frac{3 e^2 \left(a+b \log \left(c x^n\right)\right)}{2 d^4 (d+e x)^2}-\frac{a+b \log \left(c x^n\right)}{2 d^4 x^2}+\frac{e^2 \left(a+b \log \left(c x^n\right)\right)}{3 d^3 (d+e x)^3}+\frac{10 b e^2 n \text{Li}_2\left(-\frac{d}{e x}\right)}{d^6}-\frac{11 b e^2 n \log (x)}{6 d^6}+\frac{47 b e^2 n \log (d+e x)}{6 d^6}-\frac{11 b e^2 n}{6 d^5 (d+e x)}+\frac{4 b e n}{d^5 x}-\frac{b e^2 n}{6 d^4 (d+e x)^2}-\frac{b n}{4 d^4 x^2}",1,"((-3*b*d^2*n)/x^2 + (48*b*d*e*n)/x - (18*b*d*e^2*n)/(d + e*x) - (2*b*d*e^2*n*(3*d + 2*e*x))/(d + e*x)^2 - 22*b*e^2*n*Log[x] - (6*d^2*(a + b*Log[c*x^n]))/x^2 + (48*d*e*(a + b*Log[c*x^n]))/x + (4*d^3*e^2*(a + b*Log[c*x^n]))/(d + e*x)^3 + (18*d^2*e^2*(a + b*Log[c*x^n]))/(d + e*x)^2 + (72*d*e^2*(a + b*Log[c*x^n]))/(d + e*x) + (60*e^2*(a + b*Log[c*x^n])^2)/(b*n) - 72*b*e^2*n*(Log[x] - Log[d + e*x]) + 22*b*e^2*n*Log[d + e*x] - 120*e^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 120*b*e^2*n*PolyLog[2, -((e*x)/d)])/(12*d^6)","A",1
62,1,403,329,0.4666733,"\int \frac{x^8 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^7} \, dx","Integrate[(x^8*(a + b*Log[c*x^n]))/(d + e*x)^7,x]","\frac{-\frac{60 a d^8}{(d+e x)^6}+\frac{576 a d^7}{(d+e x)^5}-\frac{2520 a d^6}{(d+e x)^4}+\frac{6720 a d^5}{(d+e x)^3}-\frac{12600 a d^4}{(d+e x)^2}+\frac{20160 a d^3}{d+e x}+10080 a d^2 \log \left(\frac{e x}{d}+1\right)-2520 a d e x+180 a e^2 x^2-\frac{60 b d^8 \log \left(c x^n\right)}{(d+e x)^6}+\frac{576 b d^7 \log \left(c x^n\right)}{(d+e x)^5}-\frac{2520 b d^6 \log \left(c x^n\right)}{(d+e x)^4}+\frac{6720 b d^5 \log \left(c x^n\right)}{(d+e x)^3}-\frac{12600 b d^4 \log \left(c x^n\right)}{(d+e x)^2}+\frac{20160 b d^3 \log \left(c x^n\right)}{d+e x}+10080 b d^2 \log \left(c x^n\right) \log \left(\frac{e x}{d}+1\right)-2520 b d e x \log \left(c x^n\right)+180 b e^2 x^2 \log \left(c x^n\right)+\frac{12 b d^7 n}{(d+e x)^5}-\frac{129 b d^6 n}{(d+e x)^4}+\frac{668 b d^5 n}{(d+e x)^3}-\frac{2358 b d^4 n}{(d+e x)^2}+\frac{7884 b d^3 n}{d+e x}+10080 b d^2 n \text{Li}_2\left(-\frac{e x}{d}\right)+12276 b d^2 n \log (d+e x)-12276 b d^2 n \log (x)+2520 b d e n x-90 b e^2 n x^2}{360 e^9}","\frac{d^2 \log \left(\frac{e x}{d}+1\right) \left(280 a+280 b \log \left(c x^n\right)+341 b n\right)}{10 e^9}-\frac{x^3 \left(840 a+840 b \log \left(c x^n\right)+743 b n\right)}{90 e^6 (d+e x)}-\frac{x^4 \left(840 a+840 b \log \left(c x^n\right)+533 b n\right)}{360 e^5 (d+e x)^2}-\frac{x^5 \left(168 a+168 b \log \left(c x^n\right)+73 b n\right)}{180 e^4 (d+e x)^3}-\frac{x^6 \left(56 a+56 b \log \left(c x^n\right)+15 b n\right)}{120 e^3 (d+e x)^4}-\frac{x^7 \left(8 a+8 b \log \left(c x^n\right)+b n\right)}{30 e^2 (d+e x)^5}-\frac{x^8 \left(a+b \log \left(c x^n\right)\right)}{6 e (d+e x)^6}+\frac{x^2 \left(280 a+280 b \log \left(c x^n\right)+341 b n\right)}{20 e^7}-\frac{d x (280 a+341 b n)}{10 e^8}-\frac{28 b d x \log \left(c x^n\right)}{e^8}+\frac{28 b d^2 n \text{Li}_2\left(-\frac{e x}{d}\right)}{e^9}+\frac{28 b d n x}{e^8}-\frac{7 b n x^2}{e^7}",1,"(-2520*a*d*e*x + 2520*b*d*e*n*x + 180*a*e^2*x^2 - 90*b*e^2*n*x^2 - (60*a*d^8)/(d + e*x)^6 + (576*a*d^7)/(d + e*x)^5 + (12*b*d^7*n)/(d + e*x)^5 - (2520*a*d^6)/(d + e*x)^4 - (129*b*d^6*n)/(d + e*x)^4 + (6720*a*d^5)/(d + e*x)^3 + (668*b*d^5*n)/(d + e*x)^3 - (12600*a*d^4)/(d + e*x)^2 - (2358*b*d^4*n)/(d + e*x)^2 + (20160*a*d^3)/(d + e*x) + (7884*b*d^3*n)/(d + e*x) - 12276*b*d^2*n*Log[x] - 2520*b*d*e*x*Log[c*x^n] + 180*b*e^2*x^2*Log[c*x^n] - (60*b*d^8*Log[c*x^n])/(d + e*x)^6 + (576*b*d^7*Log[c*x^n])/(d + e*x)^5 - (2520*b*d^6*Log[c*x^n])/(d + e*x)^4 + (6720*b*d^5*Log[c*x^n])/(d + e*x)^3 - (12600*b*d^4*Log[c*x^n])/(d + e*x)^2 + (20160*b*d^3*Log[c*x^n])/(d + e*x) + 12276*b*d^2*n*Log[d + e*x] + 10080*a*d^2*Log[1 + (e*x)/d] + 10080*b*d^2*Log[c*x^n]*Log[1 + (e*x)/d] + 10080*b*d^2*n*PolyLog[2, -((e*x)/d)])/(360*e^9)","A",1
63,1,356,285,0.5174975,"\int \frac{x^7 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^7} \, dx","Integrate[(x^7*(a + b*Log[c*x^n]))/(d + e*x)^7,x]","-\frac{-\frac{60 a d^7}{(d+e x)^6}+\frac{504 a d^6}{(d+e x)^5}-\frac{1890 a d^5}{(d+e x)^4}+\frac{4200 a d^4}{(d+e x)^3}-\frac{6300 a d^3}{(d+e x)^2}+\frac{7560 a d^2}{d+e x}+2520 a d \log \left(\frac{e x}{d}+1\right)-360 a e x-\frac{60 b d^7 \log \left(c x^n\right)}{(d+e x)^6}+\frac{504 b d^6 \log \left(c x^n\right)}{(d+e x)^5}-\frac{1890 b d^5 \log \left(c x^n\right)}{(d+e x)^4}+\frac{4200 b d^4 \log \left(c x^n\right)}{(d+e x)^3}-\frac{6300 b d^3 \log \left(c x^n\right)}{(d+e x)^2}+\frac{7560 b d^2 \log \left(c x^n\right)}{d+e x}+2520 b d \log \left(c x^n\right) \log \left(\frac{e x}{d}+1\right)-360 b e x \log \left(c x^n\right)+\frac{12 b d^6 n}{(d+e x)^5}-\frac{111 b d^5 n}{(d+e x)^4}+\frac{482 b d^4 n}{(d+e x)^3}-\frac{1377 b d^3 n}{(d+e x)^2}+\frac{3546 b d^2 n}{d+e x}+2520 b d n \text{Li}_2\left(-\frac{e x}{d}\right)+4014 b d n \log (d+e x)-4014 b d n \log (x)+360 b e n x}{360 e^8}","-\frac{d \log \left(\frac{e x}{d}+1\right) \left(140 a+140 b \log \left(c x^n\right)+223 b n\right)}{20 e^8}-\frac{x^2 \left(140 a+140 b \log \left(c x^n\right)+153 b n\right)}{40 e^6 (d+e x)}-\frac{x^3 \left(420 a+420 b \log \left(c x^n\right)+319 b n\right)}{360 e^5 (d+e x)^2}-\frac{x^4 \left(210 a+210 b \log \left(c x^n\right)+107 b n\right)}{360 e^4 (d+e x)^3}-\frac{x^5 \left(42 a+42 b \log \left(c x^n\right)+13 b n\right)}{120 e^3 (d+e x)^4}-\frac{x^6 \left(7 a+7 b \log \left(c x^n\right)+b n\right)}{30 e^2 (d+e x)^5}-\frac{x^7 \left(a+b \log \left(c x^n\right)\right)}{6 e (d+e x)^6}+\frac{x (140 a+223 b n)}{20 e^7}+\frac{7 b x \log \left(c x^n\right)}{e^7}-\frac{7 b d n \text{Li}_2\left(-\frac{e x}{d}\right)}{e^8}-\frac{7 b n x}{e^7}",1,"-1/360*(-360*a*e*x + 360*b*e*n*x - (60*a*d^7)/(d + e*x)^6 + (504*a*d^6)/(d + e*x)^5 + (12*b*d^6*n)/(d + e*x)^5 - (1890*a*d^5)/(d + e*x)^4 - (111*b*d^5*n)/(d + e*x)^4 + (4200*a*d^4)/(d + e*x)^3 + (482*b*d^4*n)/(d + e*x)^3 - (6300*a*d^3)/(d + e*x)^2 - (1377*b*d^3*n)/(d + e*x)^2 + (7560*a*d^2)/(d + e*x) + (3546*b*d^2*n)/(d + e*x) - 4014*b*d*n*Log[x] - 360*b*e*x*Log[c*x^n] - (60*b*d^7*Log[c*x^n])/(d + e*x)^6 + (504*b*d^6*Log[c*x^n])/(d + e*x)^5 - (1890*b*d^5*Log[c*x^n])/(d + e*x)^4 + (4200*b*d^4*Log[c*x^n])/(d + e*x)^3 - (6300*b*d^3*Log[c*x^n])/(d + e*x)^2 + (7560*b*d^2*Log[c*x^n])/(d + e*x) + 4014*b*d*n*Log[d + e*x] + 2520*a*d*Log[1 + (e*x)/d] + 2520*b*d*Log[c*x^n]*Log[1 + (e*x)/d] + 2520*b*d*n*PolyLog[2, -((e*x)/d)])/e^8","A",1
64,1,333,243,0.4568191,"\int \frac{x^6 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^7} \, dx","Integrate[(x^6*(a + b*Log[c*x^n]))/(d + e*x)^7,x]","\frac{\frac{-60 a d^6+432 a d^5 (d+e x)-1350 a d^4 (d+e x)^2+2400 a d^3 (d+e x)^3-2700 a d^2 (d+e x)^4+2160 a d (d+e x)^5+360 a (d+e x)^6 \log \left(\frac{e x}{d}+1\right)-60 b d^6 \log \left(c x^n\right)+432 b d^5 (d+e x) \log \left(c x^n\right)-1350 b d^4 (d+e x)^2 \log \left(c x^n\right)+2400 b d^3 (d+e x)^3 \log \left(c x^n\right)-2700 b d^2 (d+e x)^4 \log \left(c x^n\right)+2160 b d (d+e x)^5 \log \left(c x^n\right)+360 b (d+e x)^6 \log \left(c x^n\right) \log \left(\frac{e x}{d}+1\right)+12 b d^5 n (d+e x)-93 b d^4 n (d+e x)^2+326 b d^3 n (d+e x)^3-711 b d^2 n (d+e x)^4+1278 b d n (d+e x)^5+882 b n (d+e x)^6 \log (d+e x)}{(d+e x)^6}+360 b n \text{Li}_2\left(-\frac{e x}{d}\right)-882 b n \log (x)}{360 e^7}","\frac{\log \left(\frac{e x}{d}+1\right) \left(20 a+20 b \log \left(c x^n\right)+49 b n\right)}{20 e^7}-\frac{x \left(20 a+20 b \log \left(c x^n\right)+29 b n\right)}{20 e^6 (d+e x)}-\frac{x^2 \left(20 a+20 b \log \left(c x^n\right)+19 b n\right)}{40 e^5 (d+e x)^2}-\frac{x^3 \left(60 a+60 b \log \left(c x^n\right)+37 b n\right)}{180 e^4 (d+e x)^3}-\frac{x^4 \left(30 a+30 b \log \left(c x^n\right)+11 b n\right)}{120 e^3 (d+e x)^4}-\frac{x^5 \left(6 a+6 b \log \left(c x^n\right)+b n\right)}{30 e^2 (d+e x)^5}-\frac{x^6 \left(a+b \log \left(c x^n\right)\right)}{6 e (d+e x)^6}+\frac{b n \text{Li}_2\left(-\frac{e x}{d}\right)}{e^7}",1,"(-882*b*n*Log[x] + (-60*a*d^6 + 432*a*d^5*(d + e*x) + 12*b*d^5*n*(d + e*x) - 1350*a*d^4*(d + e*x)^2 - 93*b*d^4*n*(d + e*x)^2 + 2400*a*d^3*(d + e*x)^3 + 326*b*d^3*n*(d + e*x)^3 - 2700*a*d^2*(d + e*x)^4 - 711*b*d^2*n*(d + e*x)^4 + 2160*a*d*(d + e*x)^5 + 1278*b*d*n*(d + e*x)^5 - 60*b*d^6*Log[c*x^n] + 432*b*d^5*(d + e*x)*Log[c*x^n] - 1350*b*d^4*(d + e*x)^2*Log[c*x^n] + 2400*b*d^3*(d + e*x)^3*Log[c*x^n] - 2700*b*d^2*(d + e*x)^4*Log[c*x^n] + 2160*b*d*(d + e*x)^5*Log[c*x^n] + 882*b*n*(d + e*x)^6*Log[d + e*x] + 360*a*(d + e*x)^6*Log[1 + (e*x)/d] + 360*b*(d + e*x)^6*Log[c*x^n]*Log[1 + (e*x)/d])/(d + e*x)^6 + 360*b*n*PolyLog[2, -((e*x)/d)])/(360*e^7)","A",1
65,1,335,136,0.2935127,"\int \frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^7} \, dx","Integrate[(x^5*(a + b*Log[c*x^n]))/(d + e*x)^7,x]","-\frac{60 a d^6+360 a d^5 e x+900 a d^4 e^2 x^2+1200 a d^3 e^3 x^3+900 a d^2 e^4 x^4+360 a d e^5 x^5+60 b d \left(d^5+6 d^4 e x+15 d^3 e^2 x^2+20 d^2 e^3 x^3+15 d e^4 x^4+6 e^5 x^5\right) \log \left(c x^n\right)+60 b d^6 n \log (d+e x)+137 b d^6 n+762 b d^5 e n x+360 b d^5 e n x \log (d+e x)+1725 b d^4 e^2 n x^2+900 b d^4 e^2 n x^2 \log (d+e x)+2000 b d^3 e^3 n x^3+1200 b d^3 e^3 n x^3 \log (d+e x)+1200 b d^2 e^4 n x^4+900 b d^2 e^4 n x^4 \log (d+e x)+60 b e^6 n x^6 \log (d+e x)+300 b d e^5 n x^5+360 b d e^5 n x^5 \log (d+e x)-60 b n \log (x) (d+e x)^6}{360 d e^6 (d+e x)^6}","\frac{x^6 \left(a+b \log \left(c x^n\right)\right)}{6 d (d+e x)^6}-\frac{b d^4 n}{30 e^6 (d+e x)^5}+\frac{5 b d^3 n}{24 e^6 (d+e x)^4}-\frac{5 b d^2 n}{9 e^6 (d+e x)^3}-\frac{5 b n}{6 e^6 (d+e x)}+\frac{5 b d n}{6 e^6 (d+e x)^2}-\frac{b n \log (d+e x)}{6 d e^6}",1,"-1/360*(60*a*d^6 + 137*b*d^6*n + 360*a*d^5*e*x + 762*b*d^5*e*n*x + 900*a*d^4*e^2*x^2 + 1725*b*d^4*e^2*n*x^2 + 1200*a*d^3*e^3*x^3 + 2000*b*d^3*e^3*n*x^3 + 900*a*d^2*e^4*x^4 + 1200*b*d^2*e^4*n*x^4 + 360*a*d*e^5*x^5 + 300*b*d*e^5*n*x^5 - 60*b*n*(d + e*x)^6*Log[x] + 60*b*d*(d^5 + 6*d^4*e*x + 15*d^3*e^2*x^2 + 20*d^2*e^3*x^3 + 15*d*e^4*x^4 + 6*e^5*x^5)*Log[c*x^n] + 60*b*d^6*n*Log[d + e*x] + 360*b*d^5*e*n*x*Log[d + e*x] + 900*b*d^4*e^2*n*x^2*Log[d + e*x] + 1200*b*d^3*e^3*n*x^3*Log[d + e*x] + 900*b*d^2*e^4*n*x^4*Log[d + e*x] + 360*b*d*e^5*n*x^5*Log[d + e*x] + 60*b*e^6*n*x^6*Log[d + e*x])/(d*e^6*(d + e*x)^6)","B",1
66,1,316,163,0.3221306,"\int \frac{x^4 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^7} \, dx","Integrate[(x^4*(a + b*Log[c*x^n]))/(d + e*x)^7,x]","-\frac{12 a d^6+72 a d^5 e x+180 a d^4 e^2 x^2+240 a d^3 e^3 x^3+180 a d^2 e^4 x^4+12 b d^2 \left(d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right) \log \left(c x^n\right)+12 b d^6 n \log (d+e x)+13 b d^6 n+66 b d^5 e n x+72 b d^5 e n x \log (d+e x)+129 b d^4 e^2 n x^2+180 b d^4 e^2 n x^2 \log (d+e x)+112 b d^3 e^3 n x^3+240 b d^3 e^3 n x^3 \log (d+e x)+24 b d^2 e^4 n x^4+180 b d^2 e^4 n x^4 \log (d+e x)+12 b e^6 n x^6 \log (d+e x)-12 b d e^5 n x^5+72 b d e^5 n x^5 \log (d+e x)-12 b n \log (x) (d+e x)^6}{360 d^2 e^5 (d+e x)^6}","\frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{30 d^2 (d+e x)^5}+\frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{6 d (d+e x)^6}+\frac{b d^2 n}{120 e^5 (d+e x)^4}-\frac{b n \log (d+e x)}{30 d^2 e^5}-\frac{b n x^5}{30 d^2 (d+e x)^5}-\frac{2 b n}{15 d e^5 (d+e x)}+\frac{b n}{10 e^5 (d+e x)^2}-\frac{2 b d n}{45 e^5 (d+e x)^3}",1,"-1/360*(12*a*d^6 + 13*b*d^6*n + 72*a*d^5*e*x + 66*b*d^5*e*n*x + 180*a*d^4*e^2*x^2 + 129*b*d^4*e^2*n*x^2 + 240*a*d^3*e^3*x^3 + 112*b*d^3*e^3*n*x^3 + 180*a*d^2*e^4*x^4 + 24*b*d^2*e^4*n*x^4 - 12*b*d*e^5*n*x^5 - 12*b*n*(d + e*x)^6*Log[x] + 12*b*d^2*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4)*Log[c*x^n] + 12*b*d^6*n*Log[d + e*x] + 72*b*d^5*e*n*x*Log[d + e*x] + 180*b*d^4*e^2*n*x^2*Log[d + e*x] + 240*b*d^3*e^3*n*x^3*Log[d + e*x] + 180*b*d^2*e^4*n*x^4*Log[d + e*x] + 72*b*d*e^5*n*x^5*Log[d + e*x] + 12*b*e^6*n*x^6*Log[d + e*x])/(d^2*e^5*(d + e*x)^6)","A",1
67,1,281,226,0.2356968,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^7} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/(d + e*x)^7,x]","\frac{a d^3}{6 e^4 (d+e x)^6}-\frac{3 a d^2}{5 e^4 (d+e x)^5}+\frac{3 a d}{4 e^4 (d+e x)^4}-\frac{a}{3 e^4 (d+e x)^3}+\frac{b d^3 \log \left(c x^n\right)}{6 e^4 (d+e x)^6}-\frac{3 b d^2 \log \left(c x^n\right)}{5 e^4 (d+e x)^5}+\frac{3 b d \log \left(c x^n\right)}{4 e^4 (d+e x)^4}-\frac{b \log \left(c x^n\right)}{3 e^4 (d+e x)^3}+\frac{b n \log (x)}{60 d^3 e^4}-\frac{b n \log (d+e x)}{60 d^3 e^4}-\frac{b d^2 n}{30 e^4 (d+e x)^5}+\frac{b n}{60 d^2 e^4 (d+e x)}+\frac{13 b d n}{120 e^4 (d+e x)^4}-\frac{19 b n}{180 e^4 (d+e x)^3}+\frac{b n}{120 d e^4 (d+e x)^2}","\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{6 e^4 (d+e x)^6}-\frac{3 d^2 \left(a+b \log \left(c x^n\right)\right)}{5 e^4 (d+e x)^5}+\frac{3 d \left(a+b \log \left(c x^n\right)\right)}{4 e^4 (d+e x)^4}-\frac{a+b \log \left(c x^n\right)}{3 e^4 (d+e x)^3}+\frac{b n \log (x)}{60 d^3 e^4}-\frac{b n \log (d+e x)}{60 d^3 e^4}-\frac{b d^2 n}{30 e^4 (d+e x)^5}+\frac{b n}{60 d^2 e^4 (d+e x)}+\frac{13 b d n}{120 e^4 (d+e x)^4}-\frac{19 b n}{180 e^4 (d+e x)^3}+\frac{b n}{120 d e^4 (d+e x)^2}",1,"(a*d^3)/(6*e^4*(d + e*x)^6) - (3*a*d^2)/(5*e^4*(d + e*x)^5) - (b*d^2*n)/(30*e^4*(d + e*x)^5) + (3*a*d)/(4*e^4*(d + e*x)^4) + (13*b*d*n)/(120*e^4*(d + e*x)^4) - a/(3*e^4*(d + e*x)^3) - (19*b*n)/(180*e^4*(d + e*x)^3) + (b*n)/(120*d*e^4*(d + e*x)^2) + (b*n)/(60*d^2*e^4*(d + e*x)) + (b*n*Log[x])/(60*d^3*e^4) + (b*d^3*Log[c*x^n])/(6*e^4*(d + e*x)^6) - (3*b*d^2*Log[c*x^n])/(5*e^4*(d + e*x)^5) + (3*b*d*Log[c*x^n])/(4*e^4*(d + e*x)^4) - (b*Log[c*x^n])/(3*e^4*(d + e*x)^3) - (b*n*Log[d + e*x])/(60*d^3*e^4)","A",1
68,1,192,199,0.214694,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^7} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e*x)^7,x]","\frac{-60 a d^6+144 a d^5 (d+e x)-90 a d^4 (d+e x)^2-60 b d^6 \log \left(c x^n\right)+144 b d^5 (d+e x) \log \left(c x^n\right)-90 b d^4 (d+e x)^2 \log \left(c x^n\right)+12 b d^5 n (d+e x)-21 b d^4 n (d+e x)^2+2 b d^3 n (d+e x)^3+3 b d^2 n (d+e x)^4+6 b d n (d+e x)^5+6 b n \log (x) (d+e x)^6-6 b n (d+e x)^6 \log (d+e x)}{360 d^4 e^3 (d+e x)^6}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{6 e^3 (d+e x)^6}+\frac{2 d \left(a+b \log \left(c x^n\right)\right)}{5 e^3 (d+e x)^5}-\frac{a+b \log \left(c x^n\right)}{4 e^3 (d+e x)^4}+\frac{b n \log (x)}{60 d^4 e^3}-\frac{b n \log (d+e x)}{60 d^4 e^3}+\frac{b n}{60 d^3 e^3 (d+e x)}+\frac{b n}{120 d^2 e^3 (d+e x)^2}+\frac{b d n}{30 e^3 (d+e x)^5}-\frac{7 b n}{120 e^3 (d+e x)^4}+\frac{b n}{180 d e^3 (d+e x)^3}",1,"(-60*a*d^6 + 144*a*d^5*(d + e*x) + 12*b*d^5*n*(d + e*x) - 90*a*d^4*(d + e*x)^2 - 21*b*d^4*n*(d + e*x)^2 + 2*b*d^3*n*(d + e*x)^3 + 3*b*d^2*n*(d + e*x)^4 + 6*b*d*n*(d + e*x)^5 + 6*b*n*(d + e*x)^6*Log[x] - 60*b*d^6*Log[c*x^n] + 144*b*d^5*(d + e*x)*Log[c*x^n] - 90*b*d^4*(d + e*x)^2*Log[c*x^n] - 6*b*n*(d + e*x)^6*Log[d + e*x])/(360*d^4*e^3*(d + e*x)^6)","A",1
69,1,160,174,0.148161,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^7} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/(d + e*x)^7,x]","\frac{60 a d^6-72 a d^5 (d+e x)+60 b d^6 \log \left(c x^n\right)-72 b d^5 (d+e x) \log \left(c x^n\right)-12 b d^5 n (d+e x)+3 b d^4 n (d+e x)^2+4 b d^3 n (d+e x)^3+6 b d^2 n (d+e x)^4+12 b d n (d+e x)^5+12 b n \log (x) (d+e x)^6-12 b n (d+e x)^6 \log (d+e x)}{360 d^5 e^2 (d+e x)^6}","-\frac{a+b \log \left(c x^n\right)}{5 e^2 (d+e x)^5}+\frac{d \left(a+b \log \left(c x^n\right)\right)}{6 e^2 (d+e x)^6}+\frac{b n \log (x)}{30 d^5 e^2}-\frac{b n \log (d+e x)}{30 d^5 e^2}+\frac{b n}{30 d^4 e^2 (d+e x)}+\frac{b n}{60 d^3 e^2 (d+e x)^2}+\frac{b n}{90 d^2 e^2 (d+e x)^3}+\frac{b n}{120 d e^2 (d+e x)^4}-\frac{b n}{30 e^2 (d+e x)^5}",1,"(60*a*d^6 - 72*a*d^5*(d + e*x) - 12*b*d^5*n*(d + e*x) + 3*b*d^4*n*(d + e*x)^2 + 4*b*d^3*n*(d + e*x)^3 + 6*b*d^2*n*(d + e*x)^4 + 12*b*d*n*(d + e*x)^5 + 12*b*n*(d + e*x)^6*Log[x] + 60*b*d^6*Log[c*x^n] - 72*b*d^5*(d + e*x)*Log[c*x^n] - 12*b*n*(d + e*x)^6*Log[d + e*x])/(360*d^5*e^2*(d + e*x)^6)","A",1
70,1,99,152,0.1462753,"\int \frac{a+b \log \left(c x^n\right)}{(d+e x)^7} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*x)^7,x]","\frac{\frac{b n \left(\frac{d \left(137 d^4+385 d^3 e x+470 d^2 e^2 x^2+270 d e^3 x^3+60 e^4 x^4\right)}{(d+e x)^5}-60 \log (d+e x)+60 \log (x)\right)}{60 d^6}-\frac{a+b \log \left(c x^n\right)}{(d+e x)^6}}{6 e}","-\frac{a+b \log \left(c x^n\right)}{6 e (d+e x)^6}+\frac{b n \log (x)}{6 d^6 e}-\frac{b n \log (d+e x)}{6 d^6 e}+\frac{b n}{6 d^5 e (d+e x)}+\frac{b n}{12 d^4 e (d+e x)^2}+\frac{b n}{18 d^3 e (d+e x)^3}+\frac{b n}{24 d^2 e (d+e x)^4}+\frac{b n}{30 d e (d+e x)^5}",1,"(-((a + b*Log[c*x^n])/(d + e*x)^6) + (b*n*((d*(137*d^4 + 385*d^3*e*x + 470*d^2*e^2*x^2 + 270*d*e^3*x^3 + 60*e^4*x^4))/(d + e*x)^5 + 60*Log[x] - 60*Log[d + e*x]))/(60*d^6))/(6*e)","A",1
71,1,349,294,0.3716192,"\int \frac{a+b \log \left(c x^n\right)}{x (d+e x)^7} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x)^7),x]","\frac{\frac{360 a \log \left(c x^n\right)}{n}+\frac{60 a d^6}{(d+e x)^6}+\frac{72 a d^5}{(d+e x)^5}+\frac{90 a d^4}{(d+e x)^4}+\frac{120 a d^3}{(d+e x)^3}+\frac{180 a d^2}{(d+e x)^2}+\frac{360 a d}{d+e x}-360 a \log \left(\frac{e x}{d}+1\right)+\frac{60 b d^6 \log \left(c x^n\right)}{(d+e x)^6}+\frac{72 b d^5 \log \left(c x^n\right)}{(d+e x)^5}+\frac{90 b d^4 \log \left(c x^n\right)}{(d+e x)^4}+\frac{120 b d^3 \log \left(c x^n\right)}{(d+e x)^3}+\frac{180 b d^2 \log \left(c x^n\right)}{(d+e x)^2}+\frac{360 b d \log \left(c x^n\right)}{d+e x}-360 b \log \left(c x^n\right) \log \left(\frac{e x}{d}+1\right)+\frac{180 b \log ^2\left(c x^n\right)}{n}-\frac{12 b d^5 n}{(d+e x)^5}-\frac{33 b d^4 n}{(d+e x)^4}-\frac{74 b d^3 n}{(d+e x)^3}-\frac{171 b d^2 n}{(d+e x)^2}-360 b n \text{Li}_2\left(-\frac{e x}{d}\right)-\frac{522 b d n}{d+e x}+882 b n \log (d+e x)-882 b n \log (x)}{360 d^7}","-\frac{\log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^7}-\frac{e x \left(a+b \log \left(c x^n\right)\right)}{d^7 (d+e x)}+\frac{a+b \log \left(c x^n\right)}{2 d^5 (d+e x)^2}+\frac{a+b \log \left(c x^n\right)}{3 d^4 (d+e x)^3}+\frac{a+b \log \left(c x^n\right)}{4 d^3 (d+e x)^4}+\frac{a+b \log \left(c x^n\right)}{5 d^2 (d+e x)^5}+\frac{a+b \log \left(c x^n\right)}{6 d (d+e x)^6}+\frac{b n \text{Li}_2\left(-\frac{d}{e x}\right)}{d^7}+\frac{49 b n \log (d+e x)}{20 d^7}-\frac{29 b n \log (x)}{20 d^7}-\frac{29 b n}{20 d^6 (d+e x)}-\frac{19 b n}{40 d^5 (d+e x)^2}-\frac{37 b n}{180 d^4 (d+e x)^3}-\frac{11 b n}{120 d^3 (d+e x)^4}-\frac{b n}{30 d^2 (d+e x)^5}",1,"((60*a*d^6)/(d + e*x)^6 + (72*a*d^5)/(d + e*x)^5 - (12*b*d^5*n)/(d + e*x)^5 + (90*a*d^4)/(d + e*x)^4 - (33*b*d^4*n)/(d + e*x)^4 + (120*a*d^3)/(d + e*x)^3 - (74*b*d^3*n)/(d + e*x)^3 + (180*a*d^2)/(d + e*x)^2 - (171*b*d^2*n)/(d + e*x)^2 + (360*a*d)/(d + e*x) - (522*b*d*n)/(d + e*x) - 882*b*n*Log[x] + (360*a*Log[c*x^n])/n + (60*b*d^6*Log[c*x^n])/(d + e*x)^6 + (72*b*d^5*Log[c*x^n])/(d + e*x)^5 + (90*b*d^4*Log[c*x^n])/(d + e*x)^4 + (120*b*d^3*Log[c*x^n])/(d + e*x)^3 + (180*b*d^2*Log[c*x^n])/(d + e*x)^2 + (360*b*d*Log[c*x^n])/(d + e*x) + (180*b*Log[c*x^n]^2)/n + 882*b*n*Log[d + e*x] - 360*a*Log[1 + (e*x)/d] - 360*b*Log[c*x^n]*Log[1 + (e*x)/d] - 360*b*n*PolyLog[2, -((e*x)/d)])/(360*d^7)","A",1
72,1,401,339,0.6129679,"\int \frac{a+b \log \left(c x^n\right)}{x^2 (d+e x)^7} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*(d + e*x)^7),x]","-\frac{\frac{2520 a e \log \left(c x^n\right)}{n}+\frac{60 a d^6 e}{(d+e x)^6}+\frac{144 a d^5 e}{(d+e x)^5}+\frac{270 a d^4 e}{(d+e x)^4}+\frac{480 a d^3 e}{(d+e x)^3}+\frac{900 a d^2 e}{(d+e x)^2}+\frac{2160 a d e}{d+e x}-2520 a e \log \left(\frac{e x}{d}+1\right)+\frac{360 a d}{x}+\frac{60 b d^6 e \log \left(c x^n\right)}{(d+e x)^6}+\frac{144 b d^5 e \log \left(c x^n\right)}{(d+e x)^5}+\frac{270 b d^4 e \log \left(c x^n\right)}{(d+e x)^4}+\frac{480 b d^3 e \log \left(c x^n\right)}{(d+e x)^3}+\frac{900 b d^2 e \log \left(c x^n\right)}{(d+e x)^2}+\frac{2160 b d e \log \left(c x^n\right)}{d+e x}-2520 b e \log \left(c x^n\right) \log \left(\frac{e x}{d}+1\right)+\frac{360 b d \log \left(c x^n\right)}{x}+\frac{1260 b e \log ^2\left(c x^n\right)}{n}-\frac{12 b d^5 e n}{(d+e x)^5}-\frac{51 b d^4 e n}{(d+e x)^4}-\frac{158 b d^3 e n}{(d+e x)^3}-\frac{477 b d^2 e n}{(d+e x)^2}-2520 b e n \text{Li}_2\left(-\frac{e x}{d}\right)-\frac{1854 b d e n}{d+e x}+4014 b e n \log (d+e x)+\frac{360 b d n}{x}-4014 b e n \log (x)}{360 d^8}","\frac{6 e^2 x \left(a+b \log \left(c x^n\right)\right)}{d^8 (d+e x)}+\frac{7 e \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^8}-\frac{a+b \log \left(c x^n\right)}{d^7 x}-\frac{5 e \left(a+b \log \left(c x^n\right)\right)}{2 d^6 (d+e x)^2}-\frac{4 e \left(a+b \log \left(c x^n\right)\right)}{3 d^5 (d+e x)^3}-\frac{3 e \left(a+b \log \left(c x^n\right)\right)}{4 d^4 (d+e x)^4}-\frac{2 e \left(a+b \log \left(c x^n\right)\right)}{5 d^3 (d+e x)^5}-\frac{e \left(a+b \log \left(c x^n\right)\right)}{6 d^2 (d+e x)^6}-\frac{7 b e n \text{Li}_2\left(-\frac{d}{e x}\right)}{d^8}+\frac{103 b e n \log (x)}{20 d^8}-\frac{223 b e n \log (d+e x)}{20 d^8}+\frac{103 b e n}{20 d^7 (d+e x)}-\frac{b n}{d^7 x}+\frac{53 b e n}{40 d^6 (d+e x)^2}+\frac{79 b e n}{180 d^5 (d+e x)^3}+\frac{17 b e n}{120 d^4 (d+e x)^4}+\frac{b e n}{30 d^3 (d+e x)^5}",1,"-1/360*((360*a*d)/x + (360*b*d*n)/x + (60*a*d^6*e)/(d + e*x)^6 + (144*a*d^5*e)/(d + e*x)^5 - (12*b*d^5*e*n)/(d + e*x)^5 + (270*a*d^4*e)/(d + e*x)^4 - (51*b*d^4*e*n)/(d + e*x)^4 + (480*a*d^3*e)/(d + e*x)^3 - (158*b*d^3*e*n)/(d + e*x)^3 + (900*a*d^2*e)/(d + e*x)^2 - (477*b*d^2*e*n)/(d + e*x)^2 + (2160*a*d*e)/(d + e*x) - (1854*b*d*e*n)/(d + e*x) - 4014*b*e*n*Log[x] + (2520*a*e*Log[c*x^n])/n + (360*b*d*Log[c*x^n])/x + (60*b*d^6*e*Log[c*x^n])/(d + e*x)^6 + (144*b*d^5*e*Log[c*x^n])/(d + e*x)^5 + (270*b*d^4*e*Log[c*x^n])/(d + e*x)^4 + (480*b*d^3*e*Log[c*x^n])/(d + e*x)^3 + (900*b*d^2*e*Log[c*x^n])/(d + e*x)^2 + (2160*b*d*e*Log[c*x^n])/(d + e*x) + (1260*b*e*Log[c*x^n]^2)/n + 4014*b*e*n*Log[d + e*x] - 2520*a*e*Log[1 + (e*x)/d] - 2520*b*e*Log[c*x^n]*Log[1 + (e*x)/d] - 2520*b*e*n*PolyLog[2, -((e*x)/d)])/d^8","A",1
73,1,486,401,0.6269391,"\int \frac{a+b \log \left(c x^n\right)}{x^3 (d+e x)^7} \, dx","Integrate[(a + b*Log[c*x^n])/(x^3*(d + e*x)^7),x]","\frac{\frac{10080 a e^2 \log \left(c x^n\right)}{n}+\frac{60 a d^6 e^2}{(d+e x)^6}+\frac{216 a d^5 e^2}{(d+e x)^5}+\frac{540 a d^4 e^2}{(d+e x)^4}+\frac{1200 a d^3 e^2}{(d+e x)^3}+\frac{2700 a d^2 e^2}{(d+e x)^2}-\frac{180 a d^2}{x^2}+\frac{7560 a d e^2}{d+e x}-10080 a e^2 \log \left(\frac{e x}{d}+1\right)+\frac{2520 a d e}{x}+\frac{60 b d^6 e^2 \log \left(c x^n\right)}{(d+e x)^6}+\frac{216 b d^5 e^2 \log \left(c x^n\right)}{(d+e x)^5}+\frac{540 b d^4 e^2 \log \left(c x^n\right)}{(d+e x)^4}+\frac{1200 b d^3 e^2 \log \left(c x^n\right)}{(d+e x)^3}+\frac{2700 b d^2 e^2 \log \left(c x^n\right)}{(d+e x)^2}-\frac{180 b d^2 \log \left(c x^n\right)}{x^2}+\frac{7560 b d e^2 \log \left(c x^n\right)}{d+e x}-10080 b e^2 \log \left(c x^n\right) \log \left(\frac{e x}{d}+1\right)+\frac{2520 b d e \log \left(c x^n\right)}{x}+\frac{5040 b e^2 \log ^2\left(c x^n\right)}{n}-\frac{12 b d^5 e^2 n}{(d+e x)^5}-\frac{69 b d^4 e^2 n}{(d+e x)^4}-\frac{272 b d^3 e^2 n}{(d+e x)^3}-\frac{1008 b d^2 e^2 n}{(d+e x)^2}-\frac{90 b d^2 n}{x^2}-10080 b e^2 n \text{Li}_2\left(-\frac{e x}{d}\right)-\frac{4716 b d e^2 n}{d+e x}+12276 b e^2 n \log (d+e x)+\frac{2520 b d e n}{x}-12276 b e^2 n \log (x)}{360 d^9}","-\frac{21 e^3 x \left(a+b \log \left(c x^n\right)\right)}{d^9 (d+e x)}-\frac{28 e^2 \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^9}+\frac{7 e \left(a+b \log \left(c x^n\right)\right)}{d^8 x}+\frac{15 e^2 \left(a+b \log \left(c x^n\right)\right)}{2 d^7 (d+e x)^2}-\frac{a+b \log \left(c x^n\right)}{2 d^7 x^2}+\frac{10 e^2 \left(a+b \log \left(c x^n\right)\right)}{3 d^6 (d+e x)^3}+\frac{3 e^2 \left(a+b \log \left(c x^n\right)\right)}{2 d^5 (d+e x)^4}+\frac{3 e^2 \left(a+b \log \left(c x^n\right)\right)}{5 d^4 (d+e x)^5}+\frac{e^2 \left(a+b \log \left(c x^n\right)\right)}{6 d^3 (d+e x)^6}+\frac{28 b e^2 n \text{Li}_2\left(-\frac{d}{e x}\right)}{d^9}-\frac{131 b e^2 n \log (x)}{10 d^9}+\frac{341 b e^2 n \log (d+e x)}{10 d^9}-\frac{131 b e^2 n}{10 d^8 (d+e x)}+\frac{7 b e n}{d^8 x}-\frac{14 b e^2 n}{5 d^7 (d+e x)^2}-\frac{b n}{4 d^7 x^2}-\frac{34 b e^2 n}{45 d^6 (d+e x)^3}-\frac{23 b e^2 n}{120 d^5 (d+e x)^4}-\frac{b e^2 n}{30 d^4 (d+e x)^5}",1,"((-180*a*d^2)/x^2 - (90*b*d^2*n)/x^2 + (2520*a*d*e)/x + (2520*b*d*e*n)/x + (60*a*d^6*e^2)/(d + e*x)^6 + (216*a*d^5*e^2)/(d + e*x)^5 - (12*b*d^5*e^2*n)/(d + e*x)^5 + (540*a*d^4*e^2)/(d + e*x)^4 - (69*b*d^4*e^2*n)/(d + e*x)^4 + (1200*a*d^3*e^2)/(d + e*x)^3 - (272*b*d^3*e^2*n)/(d + e*x)^3 + (2700*a*d^2*e^2)/(d + e*x)^2 - (1008*b*d^2*e^2*n)/(d + e*x)^2 + (7560*a*d*e^2)/(d + e*x) - (4716*b*d*e^2*n)/(d + e*x) - 12276*b*e^2*n*Log[x] + (10080*a*e^2*Log[c*x^n])/n - (180*b*d^2*Log[c*x^n])/x^2 + (2520*b*d*e*Log[c*x^n])/x + (60*b*d^6*e^2*Log[c*x^n])/(d + e*x)^6 + (216*b*d^5*e^2*Log[c*x^n])/(d + e*x)^5 + (540*b*d^4*e^2*Log[c*x^n])/(d + e*x)^4 + (1200*b*d^3*e^2*Log[c*x^n])/(d + e*x)^3 + (2700*b*d^2*e^2*Log[c*x^n])/(d + e*x)^2 + (7560*b*d*e^2*Log[c*x^n])/(d + e*x) + (5040*b*e^2*Log[c*x^n]^2)/n + 12276*b*e^2*n*Log[d + e*x] - 10080*a*e^2*Log[1 + (e*x)/d] - 10080*b*e^2*Log[c*x^n]*Log[1 + (e*x)/d] - 10080*b*e^2*n*PolyLog[2, -((e*x)/d)])/(360*d^9)","A",1
74,1,12,12,0.0028858,"\int \frac{\log (c x)}{1-c x} \, dx","Integrate[Log[c*x]/(1 - c*x),x]","\frac{\text{Li}_2(1-c x)}{c}","\frac{\text{Li}_2(1-c x)}{c}",1,"PolyLog[2, 1 - c*x]/c","A",1
75,1,11,10,0.002346,"\int \frac{\log \left(\frac{x}{c}\right)}{c-x} \, dx","Integrate[Log[x/c]/(c - x),x]","\text{Li}_2\left(\frac{c-x}{c}\right)","\text{Li}_2\left(1-\frac{x}{c}\right)",1,"PolyLog[2, (c - x)/c]","A",1
76,1,82,109,0.0603319,"\int x^2 (d+e x) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[x^2*(d + e*x)*(a + b*Log[c*x^n])^2,x]","\frac{1}{864} x^3 \left(288 d \left(a+b \log \left(c x^n\right)\right)^2+64 b d n \left(-3 a-3 b \log \left(c x^n\right)+b n\right)+216 e x \left(a+b \log \left(c x^n\right)\right)^2+27 b e n x \left(-4 a-4 b \log \left(c x^n\right)+b n\right)\right)","\frac{1}{3} d x^3 \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{9} b d n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{4} e x^4 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{8} b e n x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{2}{27} b^2 d n^2 x^3+\frac{1}{32} b^2 e n^2 x^4",1,"(x^3*(27*b*e*n*x*(-4*a + b*n - 4*b*Log[c*x^n]) + 64*b*d*n*(-3*a + b*n - 3*b*Log[c*x^n]) + 288*d*(a + b*Log[c*x^n])^2 + 216*e*x*(a + b*Log[c*x^n])^2))/864","A",1
77,1,82,109,0.0557931,"\int x (d+e x) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[x*(d + e*x)*(a + b*Log[c*x^n])^2,x]","\frac{1}{108} x^2 \left(54 d \left(a+b \log \left(c x^n\right)\right)^2+27 b d n \left(-2 a-2 b \log \left(c x^n\right)+b n\right)+36 e x \left(a+b \log \left(c x^n\right)\right)^2+8 b e n x \left(-3 a-3 b \log \left(c x^n\right)+b n\right)\right)","\frac{1}{2} d x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} b d n x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{3} e x^3 \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{9} b e n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{4} b^2 d n^2 x^2+\frac{2}{27} b^2 e n^2 x^3",1,"(x^2*(8*b*e*n*x*(-3*a + b*n - 3*b*Log[c*x^n]) + 27*b*d*n*(-2*a + b*n - 2*b*Log[c*x^n]) + 54*d*(a + b*Log[c*x^n])^2 + 36*e*x*(a + b*Log[c*x^n])^2))/108","A",1
78,1,77,101,0.0489405,"\int (d+e x) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[(d + e*x)*(a + b*Log[c*x^n])^2,x]","\frac{1}{4} x \left(4 d \left(a+b \log \left(c x^n\right)\right)^2-8 b d n \left(a+b \log \left(c x^n\right)-b n\right)+2 e x \left(a+b \log \left(c x^n\right)\right)^2+b e n x \left(-2 a-2 b \log \left(c x^n\right)+b n\right)\right)","d x \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} b e n x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} e x^2 \left(a+b \log \left(c x^n\right)\right)^2-2 a b d n x-2 b^2 d n x \log \left(c x^n\right)+2 b^2 d n^2 x+\frac{1}{4} b^2 e n^2 x^2",1,"(x*(b*e*n*x*(-2*a + b*n - 2*b*Log[c*x^n]) + 4*d*(a + b*Log[c*x^n])^2 + 2*e*x*(a + b*Log[c*x^n])^2 - 8*b*d*n*(a - b*n + b*Log[c*x^n])))/4","A",1
79,1,59,70,0.0217349,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)^2}{x} \, dx","Integrate[((d + e*x)*(a + b*Log[c*x^n])^2)/x,x]","\frac{d \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}+e x \left(a+b \log \left(c x^n\right)\right)^2-2 b e n x \left(a+b \log \left(c x^n\right)-b n\right)","\frac{d \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}+e x \left(a+b \log \left(c x^n\right)\right)^2-2 a b e n x-2 b^2 e n x \log \left(c x^n\right)+2 b^2 e n^2 x",1,"e*x*(a + b*Log[c*x^n])^2 + (d*(a + b*Log[c*x^n])^3)/(3*b*n) - 2*b*e*n*x*(a - b*n + b*Log[c*x^n])","A",1
80,1,63,72,0.0380693,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)^2}{x^2} \, dx","Integrate[((d + e*x)*(a + b*Log[c*x^n])^2)/x^2,x]","-\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{2 b d n \left(a+b \log \left(c x^n\right)+b n\right)}{x}+\frac{e \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}","-\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{2 b d n \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{e \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}-\frac{2 b^2 d n^2}{x}",1,"-((d*(a + b*Log[c*x^n])^2)/x) + (e*(a + b*Log[c*x^n])^3)/(3*b*n) - (2*b*d*n*(a + b*n + b*Log[c*x^n]))/x","A",1
81,1,90,103,0.0481189,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)^2}{x^3} \, dx","Integrate[((d + e*x)*(a + b*Log[c*x^n])^2)/x^3,x]","-\frac{2 a^2 (d+2 e x)+2 b \log \left(c x^n\right) (2 a (d+2 e x)+b n (d+4 e x))+2 a b n (d+4 e x)+2 b^2 (d+2 e x) \log ^2\left(c x^n\right)+b^2 n^2 (d+8 e x)}{4 x^2}","-\frac{b d n \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{2 b e n \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{b^2 d n^2}{4 x^2}-\frac{2 b^2 e n^2}{x}",1,"-1/4*(2*a^2*(d + 2*e*x) + 2*a*b*n*(d + 4*e*x) + b^2*n^2*(d + 8*e*x) + 2*b*(2*a*(d + 2*e*x) + b*n*(d + 4*e*x))*Log[c*x^n] + 2*b^2*(d + 2*e*x)*Log[c*x^n]^2)/x^2","A",1
82,1,82,109,0.0602948,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)^2}{x^4} \, dx","Integrate[((d + e*x)*(a + b*Log[c*x^n])^2)/x^4,x]","-\frac{36 d \left(a+b \log \left(c x^n\right)\right)^2+8 b d n \left(3 a+3 b \log \left(c x^n\right)+b n\right)+54 e x \left(a+b \log \left(c x^n\right)\right)^2+27 b e n x \left(2 a+2 b \log \left(c x^n\right)+b n\right)}{108 x^3}","-\frac{2 b d n \left(a+b \log \left(c x^n\right)\right)}{9 x^3}-\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{3 x^3}-\frac{b e n \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{2 b^2 d n^2}{27 x^3}-\frac{b^2 e n^2}{4 x^2}",1,"-1/108*(36*d*(a + b*Log[c*x^n])^2 + 54*e*x*(a + b*Log[c*x^n])^2 + 27*b*e*n*x*(2*a + b*n + 2*b*Log[c*x^n]) + 8*b*d*n*(3*a + b*n + 3*b*Log[c*x^n]))/x^3","A",1
83,1,82,109,0.0571161,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)^2}{x^5} \, dx","Integrate[((d + e*x)*(a + b*Log[c*x^n])^2)/x^5,x]","-\frac{216 d \left(a+b \log \left(c x^n\right)\right)^2+27 b d n \left(4 a+4 b \log \left(c x^n\right)+b n\right)+288 e x \left(a+b \log \left(c x^n\right)\right)^2+64 b e n x \left(3 a+3 b \log \left(c x^n\right)+b n\right)}{864 x^4}","-\frac{b d n \left(a+b \log \left(c x^n\right)\right)}{8 x^4}-\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{4 x^4}-\frac{2 b e n \left(a+b \log \left(c x^n\right)\right)}{9 x^3}-\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{3 x^3}-\frac{b^2 d n^2}{32 x^4}-\frac{2 b^2 e n^2}{27 x^3}",1,"-1/864*(216*d*(a + b*Log[c*x^n])^2 + 288*e*x*(a + b*Log[c*x^n])^2 + 64*b*e*n*x*(3*a + b*n + 3*b*Log[c*x^n]) + 27*b*d*n*(4*a + b*n + 4*b*Log[c*x^n]))/x^4","A",1
84,1,149,178,0.0998159,"\int x^2 (d+e x)^2 \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[x^2*(d + e*x)^2*(a + b*Log[c*x^n])^2,x]","\frac{1}{3} d^2 x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{2}{27} b d^2 n x^3 \left(-3 a-3 b \log \left(c x^n\right)+b n\right)+\frac{1}{2} d e x^4 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{16} b d e n x^4 \left(-4 a-4 b \log \left(c x^n\right)+b n\right)+\frac{1}{5} e^2 x^5 \left(a+b \log \left(c x^n\right)\right)^2+\frac{2}{125} b e^2 n x^5 \left(-5 a-5 b \log \left(c x^n\right)+b n\right)","\frac{1}{3} d^2 x^3 \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{9} b d^2 n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} d e x^4 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{4} b d e n x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{5} e^2 x^5 \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{25} b e^2 n x^5 \left(a+b \log \left(c x^n\right)\right)+\frac{2}{27} b^2 d^2 n^2 x^3+\frac{1}{16} b^2 d e n^2 x^4+\frac{2}{125} b^2 e^2 n^2 x^5",1,"(2*b*e^2*n*x^5*(-5*a + b*n - 5*b*Log[c*x^n]))/125 + (b*d*e*n*x^4*(-4*a + b*n - 4*b*Log[c*x^n]))/16 + (2*b*d^2*n*x^3*(-3*a + b*n - 3*b*Log[c*x^n]))/27 + (d^2*x^3*(a + b*Log[c*x^n])^2)/3 + (d*e*x^4*(a + b*Log[c*x^n])^2)/2 + (e^2*x^5*(a + b*Log[c*x^n])^2)/5","A",1
85,1,134,178,0.094561,"\int x (d+e x)^2 \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[x*(d + e*x)^2*(a + b*Log[c*x^n])^2,x]","\frac{1}{864} x^2 \left(432 d^2 \left(a+b \log \left(c x^n\right)\right)^2+216 b d^2 n \left(-2 a-2 b \log \left(c x^n\right)+b n\right)+576 d e x \left(a+b \log \left(c x^n\right)\right)^2+128 b d e n x \left(-3 a-3 b \log \left(c x^n\right)+b n\right)+216 e^2 x^2 \left(a+b \log \left(c x^n\right)\right)^2+27 b e^2 n x^2 \left(-4 a-4 b \log \left(c x^n\right)+b n\right)\right)","\frac{1}{2} d^2 x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} b d^2 n x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{2}{3} d e x^3 \left(a+b \log \left(c x^n\right)\right)^2-\frac{4}{9} b d e n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{4} e^2 x^4 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{8} b e^2 n x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{4} b^2 d^2 n^2 x^2+\frac{4}{27} b^2 d e n^2 x^3+\frac{1}{32} b^2 e^2 n^2 x^4",1,"(x^2*(27*b*e^2*n*x^2*(-4*a + b*n - 4*b*Log[c*x^n]) + 128*b*d*e*n*x*(-3*a + b*n - 3*b*Log[c*x^n]) + 216*b*d^2*n*(-2*a + b*n - 2*b*Log[c*x^n]) + 432*d^2*(a + b*Log[c*x^n])^2 + 576*d*e*x*(a + b*Log[c*x^n])^2 + 216*e^2*x^2*(a + b*Log[c*x^n])^2))/864","A",1
86,1,135,173,0.084169,"\int (d+e x)^2 \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[(d + e*x)^2*(a + b*Log[c*x^n])^2,x]","d^2 x \left(a+b \log \left(c x^n\right)\right)^2-2 b d^2 n x \left(a+b \log \left(c x^n\right)-b n\right)+d e x^2 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} b d e n x^2 \left(-2 a-2 b \log \left(c x^n\right)+b n\right)+\frac{1}{3} e^2 x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{2}{27} b e^2 n x^3 \left(-3 a-3 b \log \left(c x^n\right)+b n\right)","-\frac{2 b d^3 n \log (x) \left(a+b \log \left(c x^n\right)\right)}{3 e}-2 b d^2 n x \left(a+b \log \left(c x^n\right)\right)+\frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)^2}{3 e}-b d e n x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{2}{9} b e^2 n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{b^2 d^3 n^2 \log ^2(x)}{3 e}+2 b^2 d^2 n^2 x+\frac{1}{2} b^2 d e n^2 x^2+\frac{2}{27} b^2 e^2 n^2 x^3",1,"(2*b*e^2*n*x^3*(-3*a + b*n - 3*b*Log[c*x^n]))/27 + (b*d*e*n*x^2*(-2*a + b*n - 2*b*Log[c*x^n]))/2 + d^2*x*(a + b*Log[c*x^n])^2 + d*e*x^2*(a + b*Log[c*x^n])^2 + (e^2*x^3*(a + b*Log[c*x^n])^2)/3 - 2*b*d^2*n*x*(a - b*n + b*Log[c*x^n])","A",1
87,1,114,137,0.0404052,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)^2}{x} \, dx","Integrate[((d + e*x)^2*(a + b*Log[c*x^n])^2)/x,x]","\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}+2 d e x \left(a+b \log \left(c x^n\right)\right)^2-4 b d e n x \left(a+b \log \left(c x^n\right)-b n\right)+\frac{1}{2} e^2 x^2 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{4} b e^2 n x^2 \left(-2 a-2 b \log \left(c x^n\right)+b n\right)","\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}+2 d e x \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} e^2 x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} b e^2 n x^2 \left(a+b \log \left(c x^n\right)\right)-4 a b d e n x-4 b^2 d e n x \log \left(c x^n\right)+4 b^2 d e n^2 x+\frac{1}{4} b^2 e^2 n^2 x^2",1,"(b*e^2*n*x^2*(-2*a + b*n - 2*b*Log[c*x^n]))/4 + 2*d*e*x*(a + b*Log[c*x^n])^2 + (e^2*x^2*(a + b*Log[c*x^n])^2)/2 + (d^2*(a + b*Log[c*x^n])^3)/(3*b*n) - 4*b*d*e*n*x*(a - b*n + b*Log[c*x^n])","A",1
88,1,107,133,0.04311,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)^2}{x^2} \, dx","Integrate[((d + e*x)^2*(a + b*Log[c*x^n])^2)/x^2,x]","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{2 b d^2 n \left(a+b \log \left(c x^n\right)+b n\right)}{x}+\frac{2 d e \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}+e^2 x \left(a+b \log \left(c x^n\right)\right)^2-2 b e^2 n x \left(a+b \log \left(c x^n\right)-b n\right)","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{2 b d^2 n \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{2 d e \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}+e^2 x \left(a+b \log \left(c x^n\right)\right)^2-2 a b e^2 n x-2 b^2 e^2 n x \log \left(c x^n\right)-\frac{2 b^2 d^2 n^2}{x}+2 b^2 e^2 n^2 x",1,"-((d^2*(a + b*Log[c*x^n])^2)/x) + e^2*x*(a + b*Log[c*x^n])^2 + (2*d*e*(a + b*Log[c*x^n])^3)/(3*b*n) - 2*b*e^2*n*x*(a - b*n + b*Log[c*x^n]) - (2*b*d^2*n*(a + b*n + b*Log[c*x^n]))/x","A",1
89,1,117,137,0.0853716,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)^2}{x^3} \, dx","Integrate[((d + e*x)^2*(a + b*Log[c*x^n])^2)/x^3,x]","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{b d^2 n \left(2 a+2 b \log \left(c x^n\right)+b n\right)}{4 x^2}-\frac{2 d e \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{4 b d e n \left(a+b \log \left(c x^n\right)+b n\right)}{x}+\frac{e^2 \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{b d^2 n \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{2 d e \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{4 b d e n \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{e^2 \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}-\frac{b^2 d^2 n^2}{4 x^2}-\frac{4 b^2 d e n^2}{x}",1,"-1/2*(d^2*(a + b*Log[c*x^n])^2)/x^2 - (2*d*e*(a + b*Log[c*x^n])^2)/x + (e^2*(a + b*Log[c*x^n])^3)/(3*b*n) - (4*b*d*e*n*(a + b*n + b*Log[c*x^n]))/x - (b*d^2*n*(2*a + b*n + 2*b*Log[c*x^n]))/(4*x^2)","A",1
90,1,131,168,0.0959476,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)^2}{x^4} \, dx","Integrate[((d + e*x)^2*(a + b*Log[c*x^n])^2)/x^4,x]","-\frac{18 d^2 \left(a+b \log \left(c x^n\right)\right)^2+4 b d^2 n \left(3 a+3 b \log \left(c x^n\right)+b n\right)+54 d e x \left(a+b \log \left(c x^n\right)\right)^2+27 b d e n x \left(2 a+2 b \log \left(c x^n\right)+b n\right)+54 e^2 x^2 \left(a+b \log \left(c x^n\right)\right)^2+108 b e^2 n x^2 \left(a+b \log \left(c x^n\right)+b n\right)}{54 x^3}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^2}{3 x^3}-\frac{2 b d^2 n \left(a+b \log \left(c x^n\right)\right)}{9 x^3}-\frac{d e \left(a+b \log \left(c x^n\right)\right)^2}{x^2}-\frac{b d e n \left(a+b \log \left(c x^n\right)\right)}{x^2}-\frac{e^2 \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{2 b e^2 n \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{2 b^2 d^2 n^2}{27 x^3}-\frac{b^2 d e n^2}{2 x^2}-\frac{2 b^2 e^2 n^2}{x}",1,"-1/54*(18*d^2*(a + b*Log[c*x^n])^2 + 54*d*e*x*(a + b*Log[c*x^n])^2 + 54*e^2*x^2*(a + b*Log[c*x^n])^2 + 108*b*e^2*n*x^2*(a + b*n + b*Log[c*x^n]) + 27*b*d*e*n*x*(2*a + b*n + 2*b*Log[c*x^n]) + 4*b*d^2*n*(3*a + b*n + 3*b*Log[c*x^n]))/x^3","A",1
91,1,134,178,0.0977582,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)^2}{x^5} \, dx","Integrate[((d + e*x)^2*(a + b*Log[c*x^n])^2)/x^5,x]","-\frac{216 d^2 \left(a+b \log \left(c x^n\right)\right)^2+27 b d^2 n \left(4 a+4 b \log \left(c x^n\right)+b n\right)+576 d e x \left(a+b \log \left(c x^n\right)\right)^2+128 b d e n x \left(3 a+3 b \log \left(c x^n\right)+b n\right)+432 e^2 x^2 \left(a+b \log \left(c x^n\right)\right)^2+216 b e^2 n x^2 \left(2 a+2 b \log \left(c x^n\right)+b n\right)}{864 x^4}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^2}{4 x^4}-\frac{b d^2 n \left(a+b \log \left(c x^n\right)\right)}{8 x^4}-\frac{2 d e \left(a+b \log \left(c x^n\right)\right)^2}{3 x^3}-\frac{4 b d e n \left(a+b \log \left(c x^n\right)\right)}{9 x^3}-\frac{e^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{b e^2 n \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{b^2 d^2 n^2}{32 x^4}-\frac{4 b^2 d e n^2}{27 x^3}-\frac{b^2 e^2 n^2}{4 x^2}",1,"-1/864*(216*d^2*(a + b*Log[c*x^n])^2 + 576*d*e*x*(a + b*Log[c*x^n])^2 + 432*e^2*x^2*(a + b*Log[c*x^n])^2 + 216*b*e^2*n*x^2*(2*a + b*n + 2*b*Log[c*x^n]) + 128*b*d*e*n*x*(3*a + b*n + 3*b*Log[c*x^n]) + 27*b*d^2*n*(4*a + b*n + 4*b*Log[c*x^n]))/x^4","A",1
92,1,211,271,0.1730877,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)^2}{d+e x} \, dx","Integrate[(x^3*(a + b*Log[c*x^n])^2)/(d + e*x),x]","-\frac{216 b d^3 n \left(\text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \text{Li}_3\left(-\frac{e x}{d}\right)\right)+108 d^3 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-108 d^2 e x \left(a+b \log \left(c x^n\right)\right)^2+216 b d^2 e n x \left(a+b \log \left(c x^n\right)-b n\right)+54 d e^2 x^2 \left(a+b \log \left(c x^n\right)\right)^2+27 b d e^2 n x^2 \left(b n-2 \left(a+b \log \left(c x^n\right)\right)\right)-36 e^3 x^3 \left(a+b \log \left(c x^n\right)\right)^2-8 b e^3 n x^3 \left(b n-3 \left(a+b \log \left(c x^n\right)\right)\right)}{108 e^4}","-\frac{2 b d^3 n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}-\frac{d^3 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^4}+\frac{d^2 x \left(a+b \log \left(c x^n\right)\right)^2}{e^3}-\frac{d x^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 e^2}+\frac{b d n x^2 \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{x^3 \left(a+b \log \left(c x^n\right)\right)^2}{3 e}-\frac{2 b n x^3 \left(a+b \log \left(c x^n\right)\right)}{9 e}-\frac{2 a b d^2 n x}{e^3}-\frac{2 b^2 d^2 n x \log \left(c x^n\right)}{e^3}+\frac{2 b^2 d^3 n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{e^4}+\frac{2 b^2 d^2 n^2 x}{e^3}-\frac{b^2 d n^2 x^2}{4 e^2}+\frac{2 b^2 n^2 x^3}{27 e}",1,"-1/108*(-108*d^2*e*x*(a + b*Log[c*x^n])^2 + 54*d*e^2*x^2*(a + b*Log[c*x^n])^2 - 36*e^3*x^3*(a + b*Log[c*x^n])^2 + 216*b*d^2*e*n*x*(a - b*n + b*Log[c*x^n]) - 8*b*e^3*n*x^3*(b*n - 3*(a + b*Log[c*x^n])) + 27*b*d*e^2*n*x^2*(b*n - 2*(a + b*Log[c*x^n])) + 108*d^3*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] + 216*b*d^3*n*((a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] - b*n*PolyLog[3, -((e*x)/d)]))/e^4","A",1
93,1,158,200,0.1045762,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{d+e x} \, dx","Integrate[(x^2*(a + b*Log[c*x^n])^2)/(d + e*x),x]","\frac{8 b d^2 n \left(\text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \text{Li}_3\left(-\frac{e x}{d}\right)\right)+4 d^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-4 d e x \left(a+b \log \left(c x^n\right)\right)^2+8 b d e n x \left(a+b \log \left(c x^n\right)-b n\right)+2 e^2 x^2 \left(a+b \log \left(c x^n\right)\right)^2+b e^2 n x^2 \left(b n-2 \left(a+b \log \left(c x^n\right)\right)\right)}{4 e^3}","\frac{2 b d^2 n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^3}+\frac{d^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^3}-\frac{d x \left(a+b \log \left(c x^n\right)\right)^2}{e^2}-\frac{b n x^2 \left(a+b \log \left(c x^n\right)\right)}{2 e}+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 e}+\frac{2 a b d n x}{e^2}+\frac{2 b^2 d n x \log \left(c x^n\right)}{e^2}-\frac{2 b^2 d^2 n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{e^3}-\frac{2 b^2 d n^2 x}{e^2}+\frac{b^2 n^2 x^2}{4 e}",1,"(-4*d*e*x*(a + b*Log[c*x^n])^2 + 2*e^2*x^2*(a + b*Log[c*x^n])^2 + 8*b*d*e*n*x*(a - b*n + b*Log[c*x^n]) + b*e^2*n*x^2*(b*n - 2*(a + b*Log[c*x^n])) + 4*d^2*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] + 8*b*d^2*n*((a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] - b*n*PolyLog[3, -((e*x)/d)]))/(4*e^3)","A",1
94,1,103,130,0.0675029,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)^2}{d+e x} \, dx","Integrate[(x*(a + b*Log[c*x^n])^2)/(d + e*x),x]","\frac{-2 b d n \left(\text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \text{Li}_3\left(-\frac{e x}{d}\right)\right)-d \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+e x \left(a+b \log \left(c x^n\right)\right)^2-2 b e n x \left(a+b \log \left(c x^n\right)-b n\right)}{e^2}","-\frac{2 b d n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{d \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^2}+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{e}-\frac{2 a b n x}{e}-\frac{2 b^2 n x \log \left(c x^n\right)}{e}+\frac{2 b^2 d n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{e^2}+\frac{2 b^2 n^2 x}{e}",1,"(e*x*(a + b*Log[c*x^n])^2 - 2*b*e*n*x*(a - b*n + b*Log[c*x^n]) - d*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] - 2*b*d*n*((a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] - b*n*PolyLog[3, -((e*x)/d)]))/e^2","A",1
95,1,68,72,0.0261166,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{d+e x} \, dx","Integrate[(a + b*Log[c*x^n])^2/(d + e*x),x]","\frac{\log \left(\frac{d+e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)^2}{e}-\frac{2 b n \left(b n \text{Li}_3\left(-\frac{e x}{d}\right)-\text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)\right)}{e}","\frac{2 b n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e}+\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e}-\frac{2 b^2 n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{e}",1,"((a + b*Log[c*x^n])^2*Log[(d + e*x)/d])/e - (2*b*n*(-((a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)]) + b*n*PolyLog[3, -((e*x)/d)]))/e","A",1
96,1,94,79,0.0660909,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x (d+e x)} \, dx","Integrate[(a + b*Log[c*x^n])^2/(x*(d + e*x)),x]","-\frac{2 b n \left(\text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \text{Li}_3\left(-\frac{e x}{d}\right)\right)}{d}-\frac{\log \left(\frac{d+e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)^2}{d}+\frac{\left(a+b \log \left(c x^n\right)\right)^3}{3 b d n}","\frac{2 b n \text{Li}_2\left(-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d}-\frac{\log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d}+\frac{2 b^2 n^2 \text{Li}_3\left(-\frac{d}{e x}\right)}{d}",1,"(a + b*Log[c*x^n])^3/(3*b*d*n) - ((a + b*Log[c*x^n])^2*Log[(d + e*x)/d])/d - (2*b*n*((a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] - b*n*PolyLog[3, -((e*x)/d)]))/d","A",1
97,1,130,135,0.1227193,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x^2 (d+e x)} \, dx","Integrate[(a + b*Log[c*x^n])^2/(x^2*(d + e*x)),x]","-\frac{-6 b e n \left(\text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \text{Li}_3\left(-\frac{e x}{d}\right)\right)-3 e \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{3 d \left(a+b \log \left(c x^n\right)\right)^2}{x}+\frac{6 b d n \left(a+b \log \left(c x^n\right)+b n\right)}{x}+\frac{e \left(a+b \log \left(c x^n\right)\right)^3}{b n}}{3 d^2}","-\frac{2 b e n \text{Li}_2\left(-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}+\frac{e \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right)}{d x}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{d x}-\frac{2 b^2 e n^2 \text{Li}_3\left(-\frac{d}{e x}\right)}{d^2}-\frac{2 b^2 n^2}{d x}",1,"-1/3*((3*d*(a + b*Log[c*x^n])^2)/x + (e*(a + b*Log[c*x^n])^3)/(b*n) + (6*b*d*n*(a + b*n + b*Log[c*x^n]))/x - 3*e*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] - 6*b*e*n*((a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] - b*n*PolyLog[3, -((e*x)/d)]))/d^2","A",1
98,1,185,204,0.1394313,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x^3 (d+e x)} \, dx","Integrate[(a + b*Log[c*x^n])^2/(x^3*(d + e*x)),x]","\frac{-\frac{6 d^2 \left(a+b \log \left(c x^n\right)\right)^2}{x^2}-\frac{3 b d^2 n \left(2 a+2 b \log \left(c x^n\right)+b n\right)}{x^2}-24 b e^2 n \left(\text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \text{Li}_3\left(-\frac{e x}{d}\right)\right)-12 e^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{12 d e \left(a+b \log \left(c x^n\right)\right)^2}{x}+\frac{24 b d e n \left(a+b \log \left(c x^n\right)+b n\right)}{x}+\frac{4 e^2 \left(a+b \log \left(c x^n\right)\right)^3}{b n}}{12 d^3}","\frac{2 b e^2 n \text{Li}_2\left(-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}-\frac{e^2 \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^3}+\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{d^2 x}+\frac{2 b e n \left(a+b \log \left(c x^n\right)\right)}{d^2 x}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 d x^2}-\frac{b n \left(a+b \log \left(c x^n\right)\right)}{2 d x^2}+\frac{2 b^2 e^2 n^2 \text{Li}_3\left(-\frac{d}{e x}\right)}{d^3}+\frac{2 b^2 e n^2}{d^2 x}-\frac{b^2 n^2}{4 d x^2}",1,"((-6*d^2*(a + b*Log[c*x^n])^2)/x^2 + (12*d*e*(a + b*Log[c*x^n])^2)/x + (4*e^2*(a + b*Log[c*x^n])^3)/(b*n) + (24*b*d*e*n*(a + b*n + b*Log[c*x^n]))/x - (3*b*d^2*n*(2*a + b*n + 2*b*Log[c*x^n]))/x^2 - 12*e^2*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] - 24*b*e^2*n*((a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] - b*n*PolyLog[3, -((e*x)/d)]))/(12*d^3)","A",1
99,1,237,273,0.1373919,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x^4 (d+e x)} \, dx","Integrate[(a + b*Log[c*x^n])^2/(x^4*(d + e*x)),x]","\frac{-\frac{36 d^3 \left(a+b \log \left(c x^n\right)\right)^2}{x^3}-\frac{8 b d^3 n \left(3 a+3 b \log \left(c x^n\right)+b n\right)}{x^3}+\frac{54 d^2 e \left(a+b \log \left(c x^n\right)\right)^2}{x^2}+\frac{27 b d^2 e n \left(2 a+2 b \log \left(c x^n\right)+b n\right)}{x^2}+216 b e^3 n \left(\text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \text{Li}_3\left(-\frac{e x}{d}\right)\right)+108 e^3 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{108 d e^2 \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{216 b d e^2 n \left(a+b \log \left(c x^n\right)+b n\right)}{x}-\frac{36 e^3 \left(a+b \log \left(c x^n\right)\right)^3}{b n}}{108 d^4}","-\frac{2 b e^3 n \text{Li}_2\left(-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}+\frac{e^3 \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^4}-\frac{e^2 \left(a+b \log \left(c x^n\right)\right)^2}{d^3 x}-\frac{2 b e^2 n \left(a+b \log \left(c x^n\right)\right)}{d^3 x}+\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{2 d^2 x^2}+\frac{b e n \left(a+b \log \left(c x^n\right)\right)}{2 d^2 x^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{3 d x^3}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right)}{9 d x^3}-\frac{2 b^2 e^3 n^2 \text{Li}_3\left(-\frac{d}{e x}\right)}{d^4}-\frac{2 b^2 e^2 n^2}{d^3 x}+\frac{b^2 e n^2}{4 d^2 x^2}-\frac{2 b^2 n^2}{27 d x^3}",1,"((-36*d^3*(a + b*Log[c*x^n])^2)/x^3 + (54*d^2*e*(a + b*Log[c*x^n])^2)/x^2 - (108*d*e^2*(a + b*Log[c*x^n])^2)/x - (36*e^3*(a + b*Log[c*x^n])^3)/(b*n) - (216*b*d*e^2*n*(a + b*n + b*Log[c*x^n]))/x + (27*b*d^2*e*n*(2*a + b*n + 2*b*Log[c*x^n]))/x^2 - (8*b*d^3*n*(3*a + b*n + 3*b*Log[c*x^n]))/x^3 + 108*e^3*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] + 216*b*e^3*n*((a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] - b*n*PolyLog[3, -((e*x)/d)]))/(108*d^4)","A",1
100,1,240,281,0.2046259,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2} \, dx","Integrate[(x^3*(a + b*Log[c*x^n])^2)/(d + e*x)^2,x]","\frac{4 d^2 \left(2 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)-\left(a+b \log \left(c x^n\right)\right) \left(a+b \log \left(c x^n\right)-2 b n \log \left(\frac{e x}{d}+1\right)\right)\right)+\frac{4 d^3 \left(a+b \log \left(c x^n\right)\right)^2}{d+e x}+24 b d^2 n \left(\text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \text{Li}_3\left(-\frac{e x}{d}\right)\right)+12 d^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-8 d e x \left(a+b \log \left(c x^n\right)\right)^2+16 b d e n x \left(a+b \log \left(c x^n\right)-b n\right)+2 e^2 x^2 \left(a+b \log \left(c x^n\right)\right)^2+b e^2 n x^2 \left(b n-2 \left(a+b \log \left(c x^n\right)\right)\right)}{4 e^4}","\frac{6 b d^2 n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}+\frac{2 b d^2 n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}+\frac{3 d^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^4}-\frac{d^2 x \left(a+b \log \left(c x^n\right)\right)^2}{e^3 (d+e x)}-\frac{2 d x \left(a+b \log \left(c x^n\right)\right)^2}{e^3}-\frac{b n x^2 \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 e^2}+\frac{4 a b d n x}{e^3}+\frac{4 b^2 d n x \log \left(c x^n\right)}{e^3}+\frac{2 b^2 d^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{e^4}-\frac{6 b^2 d^2 n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{e^4}-\frac{4 b^2 d n^2 x}{e^3}+\frac{b^2 n^2 x^2}{4 e^2}",1,"(-8*d*e*x*(a + b*Log[c*x^n])^2 + 2*e^2*x^2*(a + b*Log[c*x^n])^2 + (4*d^3*(a + b*Log[c*x^n])^2)/(d + e*x) + 16*b*d*e*n*x*(a - b*n + b*Log[c*x^n]) + b*e^2*n*x^2*(b*n - 2*(a + b*Log[c*x^n])) + 12*d^2*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] + 4*d^2*(-((a + b*Log[c*x^n])*(a + b*Log[c*x^n] - 2*b*n*Log[1 + (e*x)/d])) + 2*b^2*n^2*PolyLog[2, -((e*x)/d)]) + 24*b*d^2*n*((a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] - b*n*PolyLog[3, -((e*x)/d)]))/(4*e^4)","A",1
101,1,186,203,0.161999,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2} \, dx","Integrate[(x^2*(a + b*Log[c*x^n])^2)/(d + e*x)^2,x]","\frac{-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^2}{d+e x}-4 b d n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-2 b d n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)-2 d \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+d \left(a+b \log \left(c x^n\right)\right)^2-2 b e n x \left(a+b \log \left(c x^n\right)-b n\right)+e x \left(a+b \log \left(c x^n\right)\right)^2-2 b^2 d n^2 \text{Li}_2\left(-\frac{e x}{d}\right)+4 b^2 d n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{e^3}","-\frac{4 b d n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^3}-\frac{2 b d n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^3}-\frac{2 d \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^3}+\frac{d x \left(a+b \log \left(c x^n\right)\right)^2}{e^2 (d+e x)}+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{e^2}-\frac{2 a b n x}{e^2}-\frac{2 b^2 n x \log \left(c x^n\right)}{e^2}-\frac{2 b^2 d n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{e^3}+\frac{4 b^2 d n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{e^3}+\frac{2 b^2 n^2 x}{e^2}",1,"(d*(a + b*Log[c*x^n])^2 + e*x*(a + b*Log[c*x^n])^2 - (d^2*(a + b*Log[c*x^n])^2)/(d + e*x) - 2*b*e*n*x*(a - b*n + b*Log[c*x^n]) - 2*b*d*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 2*d*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] - 2*b^2*d*n^2*PolyLog[2, -((e*x)/d)] - 4*b*d*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] + 4*b^2*d*n^2*PolyLog[3, -((e*x)/d)])/e^3","A",1
102,1,142,143,0.1245182,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2} \, dx","Integrate[(x*(a + b*Log[c*x^n])^2)/(d + e*x)^2,x]","\frac{2 b n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)+2 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{d+e x}+\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\left(a+b \log \left(c x^n\right)\right)^2+2 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)-2 b^2 n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{e^2}","\frac{2 b n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{2 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^2}-\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{e (d+e x)}+\frac{2 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{e^2}-\frac{2 b^2 n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{e^2}",1,"(-(a + b*Log[c*x^n])^2 + (d*(a + b*Log[c*x^n])^2)/(d + e*x) + 2*b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] + (a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] + 2*b^2*n^2*PolyLog[2, -((e*x)/d)] + 2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] - 2*b^2*n^2*PolyLog[3, -((e*x)/d)])/e^2","A",1
103,1,81,77,0.0481693,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2} \, dx","Integrate[(a + b*Log[c*x^n])^2/(d + e*x)^2,x]","\frac{\left(a+b \log \left(c x^n\right)\right) \left(a e x+b e x \log \left(c x^n\right)-2 b n (d+e x) \log \left(\frac{e x}{d}+1\right)\right)-2 b^2 n^2 (d+e x) \text{Li}_2\left(-\frac{e x}{d}\right)}{d e (d+e x)}","-\frac{2 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d e}+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{d (d+e x)}-\frac{2 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{d e}",1,"((a + b*Log[c*x^n])*(a*e*x + b*e*x*Log[c*x^n] - 2*b*n*(d + e*x)*Log[1 + (e*x)/d]) - 2*b^2*n^2*(d + e*x)*PolyLog[2, -((e*x)/d)])/(d*e*(d + e*x))","A",1
104,1,166,151,0.1674618,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x (d+e x)^2} \, dx","Integrate[(a + b*Log[c*x^n])^2/(x*(d + e*x)^2),x]","\frac{-6 b n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-3 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{3 d \left(a+b \log \left(c x^n\right)\right)^2}{d+e x}+6 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^3}{b n}-3 \left(a+b \log \left(c x^n\right)\right)^2+6 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)+6 b^2 n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{3 d^2}","\frac{2 b n \text{Li}_2\left(-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}+\frac{2 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}-\frac{\log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2}-\frac{e x \left(a+b \log \left(c x^n\right)\right)^2}{d^2 (d+e x)}+\frac{2 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{d^2}+\frac{2 b^2 n^2 \text{Li}_3\left(-\frac{d}{e x}\right)}{d^2}",1,"(-3*(a + b*Log[c*x^n])^2 + (3*d*(a + b*Log[c*x^n])^2)/(d + e*x) + (a + b*Log[c*x^n])^3/(b*n) + 6*b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 3*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] + 6*b^2*n^2*PolyLog[2, -((e*x)/d)] - 6*b*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] + 6*b^2*n^2*PolyLog[3, -((e*x)/d)])/(3*d^2)","A",1
105,1,223,211,0.3176212,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x^2 (d+e x)^2} \, dx","Integrate[(a + b*Log[c*x^n])^2/(x^2*(d + e*x)^2),x]","-\frac{-12 b e n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-6 e \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{3 d e \left(a+b \log \left(c x^n\right)\right)^2}{d+e x}+6 b e n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{3 d \left(a+b \log \left(c x^n\right)\right)^2}{x}+\frac{6 b d n \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{2 e \left(a+b \log \left(c x^n\right)\right)^3}{b n}-3 e \left(a+b \log \left(c x^n\right)\right)^2+6 b^2 e n^2 \text{Li}_2\left(-\frac{e x}{d}\right)+12 b^2 e n^2 \text{Li}_3\left(-\frac{e x}{d}\right)+\frac{6 b^2 d n^2}{x}}{3 d^3}","\frac{e^2 x \left(a+b \log \left(c x^n\right)\right)^2}{d^3 (d+e x)}-\frac{4 b e n \text{Li}_2\left(-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}-\frac{2 b e n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}+\frac{2 e \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^3}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right)}{d^2 x}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{d^2 x}-\frac{2 b^2 e n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{d^3}-\frac{4 b^2 e n^2 \text{Li}_3\left(-\frac{d}{e x}\right)}{d^3}-\frac{2 b^2 n^2}{d^2 x}",1,"-1/3*((6*b^2*d*n^2)/x + (6*b*d*n*(a + b*Log[c*x^n]))/x - 3*e*(a + b*Log[c*x^n])^2 + (3*d*(a + b*Log[c*x^n])^2)/x + (3*d*e*(a + b*Log[c*x^n])^2)/(d + e*x) + (2*e*(a + b*Log[c*x^n])^3)/(b*n) + 6*b*e*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 6*e*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] + 6*b^2*e*n^2*PolyLog[2, -((e*x)/d)] - 12*b*e*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] + 12*b^2*e*n^2*PolyLog[3, -((e*x)/d)])/d^3","A",1
106,1,268,285,0.1904648,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x^3 (d+e x)^2} \, dx","Integrate[(a + b*Log[c*x^n])^2/(x^3*(d + e*x)^2),x]","\frac{4 e^2 \left(2 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)-\left(a+b \log \left(c x^n\right)\right) \left(a+b \log \left(c x^n\right)-2 b n \log \left(\frac{e x}{d}+1\right)\right)\right)-\frac{2 d^2 \left(a+b \log \left(c x^n\right)\right)^2}{x^2}-\frac{b d^2 n \left(2 a+2 b \log \left(c x^n\right)+b n\right)}{x^2}-24 b e^2 n \left(\text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \text{Li}_3\left(-\frac{e x}{d}\right)\right)-12 e^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{4 d e^2 \left(a+b \log \left(c x^n\right)\right)^2}{d+e x}+\frac{8 d e \left(a+b \log \left(c x^n\right)\right)^2}{x}+\frac{16 b d e n \left(a+b \log \left(c x^n\right)+b n\right)}{x}+\frac{4 e^2 \left(a+b \log \left(c x^n\right)\right)^3}{b n}}{4 d^4}","-\frac{e^3 x \left(a+b \log \left(c x^n\right)\right)^2}{d^4 (d+e x)}+\frac{6 b e^2 n \text{Li}_2\left(-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}-\frac{3 e^2 \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^4}+\frac{2 b e^2 n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}+\frac{2 e \left(a+b \log \left(c x^n\right)\right)^2}{d^3 x}+\frac{4 b e n \left(a+b \log \left(c x^n\right)\right)}{d^3 x}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 d^2 x^2}-\frac{b n \left(a+b \log \left(c x^n\right)\right)}{2 d^2 x^2}+\frac{2 b^2 e^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{d^4}+\frac{6 b^2 e^2 n^2 \text{Li}_3\left(-\frac{d}{e x}\right)}{d^4}+\frac{4 b^2 e n^2}{d^3 x}-\frac{b^2 n^2}{4 d^2 x^2}",1,"((-2*d^2*(a + b*Log[c*x^n])^2)/x^2 + (8*d*e*(a + b*Log[c*x^n])^2)/x + (4*d*e^2*(a + b*Log[c*x^n])^2)/(d + e*x) + (4*e^2*(a + b*Log[c*x^n])^3)/(b*n) + (16*b*d*e*n*(a + b*n + b*Log[c*x^n]))/x - (b*d^2*n*(2*a + b*n + 2*b*Log[c*x^n]))/x^2 - 12*e^2*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] + 4*e^2*(-((a + b*Log[c*x^n])*(a + b*Log[c*x^n] - 2*b*n*Log[1 + (e*x)/d])) + 2*b^2*n^2*PolyLog[2, -((e*x)/d)]) - 24*b*e^2*n*((a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] - b*n*PolyLog[3, -((e*x)/d)]))/(4*d^4)","A",1
107,1,258,296,0.2690683,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^3} \, dx","Integrate[(x^3*(a + b*Log[c*x^n])^2)/(d + e*x)^3,x]","\frac{\frac{d^3 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2}-\frac{6 d^2 \left(a+b \log \left(c x^n\right)\right)^2}{d+e x}-\frac{2 b d^2 n \left(a+b \log \left(c x^n\right)\right)}{d+e x}-12 b d n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-6 d \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-10 b d n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+5 d \left(a+b \log \left(c x^n\right)\right)^2+2 e x \left(a+b \log \left(c x^n\right)\right)^2-4 b e n x \left(a+b \log \left(c x^n\right)-b n\right)-10 b^2 d n^2 \text{Li}_2\left(-\frac{e x}{d}\right)+12 b^2 d n^2 \text{Li}_3\left(-\frac{e x}{d}\right)+2 b^2 d n^2 (\log (x)-\log (d+e x))}{2 e^4}","\frac{d^3 \left(a+b \log \left(c x^n\right)\right)^2}{2 e^4 (d+e x)^2}-\frac{6 b d n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}-\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{2 e^4}-\frac{3 d \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^4}-\frac{5 b d n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}+\frac{3 d x \left(a+b \log \left(c x^n\right)\right)^2}{e^3 (d+e x)}+\frac{b d n x \left(a+b \log \left(c x^n\right)\right)}{e^3 (d+e x)}+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{e^3}-\frac{2 a b n x}{e^3}-\frac{2 b^2 n x \log \left(c x^n\right)}{e^3}-\frac{5 b^2 d n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{e^4}+\frac{6 b^2 d n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{e^4}-\frac{b^2 d n^2 \log (d+e x)}{e^4}+\frac{2 b^2 n^2 x}{e^3}",1,"((-2*b*d^2*n*(a + b*Log[c*x^n]))/(d + e*x) + 5*d*(a + b*Log[c*x^n])^2 + 2*e*x*(a + b*Log[c*x^n])^2 + (d^3*(a + b*Log[c*x^n])^2)/(d + e*x)^2 - (6*d^2*(a + b*Log[c*x^n])^2)/(d + e*x) - 4*b*e*n*x*(a - b*n + b*Log[c*x^n]) + 2*b^2*d*n^2*(Log[x] - Log[d + e*x]) - 10*b*d*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 6*d*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] - 10*b^2*d*n^2*PolyLog[2, -((e*x)/d)] - 12*b*d*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] + 12*b^2*d*n^2*PolyLog[3, -((e*x)/d)])/(2*e^4)","A",1
108,1,212,232,0.279913,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^3} \, dx","Integrate[(x^2*(a + b*Log[c*x^n])^2)/(d + e*x)^3,x]","\frac{-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2}+4 b n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2 b d n \left(a+b \log \left(c x^n\right)\right)}{d+e x}+6 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{4 d \left(a+b \log \left(c x^n\right)\right)^2}{d+e x}+2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-3 \left(a+b \log \left(c x^n\right)\right)^2+6 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)-4 b^2 n^2 \text{Li}_3\left(-\frac{e x}{d}\right)-2 b^2 n^2 (\log (x)-\log (d+e x))}{2 e^3}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 e^3 (d+e x)^2}+\frac{2 b n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^3}+\frac{3 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^3}+\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^3}-\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{e^2 (d+e x)}-\frac{2 x \left(a+b \log \left(c x^n\right)\right)^2}{e^2 (d+e x)}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 e^3}+\frac{3 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{e^3}-\frac{2 b^2 n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{e^3}+\frac{b^2 n^2 \log (d+e x)}{e^3}",1,"((2*b*d*n*(a + b*Log[c*x^n]))/(d + e*x) - 3*(a + b*Log[c*x^n])^2 - (d^2*(a + b*Log[c*x^n])^2)/(d + e*x)^2 + (4*d*(a + b*Log[c*x^n])^2)/(d + e*x) - 2*b^2*n^2*(Log[x] - Log[d + e*x]) + 6*b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] + 2*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] + 6*b^2*n^2*PolyLog[2, -((e*x)/d)] + 4*b*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] - 4*b^2*n^2*PolyLog[3, -((e*x)/d)])/(2*e^3)","A",1
109,1,155,112,0.2364551,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^3} \, dx","Integrate[(x*(a + b*Log[c*x^n])^2)/(d + e*x)^3,x]","\frac{-\frac{2 b n \left(a+b \log \left(c x^n\right)\right)}{d+e x}-\frac{2 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d}-\frac{2 \left(a+b \log \left(c x^n\right)\right)^2}{d+e x}+\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{d}-\frac{2 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{d}+\frac{2 b^2 n^2 (\log (x)-\log (d+e x))}{d}}{2 e^2}","-\frac{b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)+b n\right)}{d e^2}+\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{d e (d+e x)}+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 d (d+e x)^2}-\frac{b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{d e^2}",1,"((-2*b*n*(a + b*Log[c*x^n]))/(d + e*x) + (a + b*Log[c*x^n])^2/d + (d*(a + b*Log[c*x^n])^2)/(d + e*x)^2 - (2*(a + b*Log[c*x^n])^2)/(d + e*x) + (2*b^2*n^2*(Log[x] - Log[d + e*x]))/d - (2*b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d - (2*b^2*n^2*PolyLog[2, -((e*x)/d)])/d)/(2*e^2)","A",1
110,1,146,126,0.1028534,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^3} \, dx","Integrate[(a + b*Log[c*x^n])^2/(d + e*x)^3,x]","\frac{b n \left(-\frac{\log \left(\frac{d+e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 b d^2 n}+\frac{a+b \log \left(c x^n\right)}{d (d+e x)}-\frac{b n \text{Li}_2\left(-\frac{e x}{d}\right)}{d^2}-\frac{b n \left(\frac{\log (x)}{d}-\frac{\log (d+e x)}{d}\right)}{d}\right)}{e}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 e (d+e x)^2}","-\frac{b n \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 e}-\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{d^2 (d+e x)}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 e (d+e x)^2}+\frac{b^2 n^2 \text{Li}_2\left(-\frac{d}{e x}\right)}{d^2 e}+\frac{b^2 n^2 \log (d+e x)}{d^2 e}",1,"-1/2*(a + b*Log[c*x^n])^2/(e*(d + e*x)^2) + (b*n*((a + b*Log[c*x^n])/(d*(d + e*x)) + (a + b*Log[c*x^n])^2/(2*b*d^2*n) - (b*n*(Log[x]/d - Log[d + e*x]/d))/d - ((a + b*Log[c*x^n])*Log[(d + e*x)/d])/d^2 - (b*n*PolyLog[2, -((e*x)/d)])/d^2))/e","A",1
111,1,232,257,0.255656,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x (d+e x)^3} \, dx","Integrate[(a + b*Log[c*x^n])^2/(x*(d + e*x)^3),x]","\frac{\frac{3 d^2 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2}-12 b n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-6 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{6 d \left(a+b \log \left(c x^n\right)\right)^2}{d+e x}+18 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{6 b d n \left(a+b \log \left(c x^n\right)\right)}{d+e x}+\frac{2 \left(a+b \log \left(c x^n\right)\right)^3}{b n}-9 \left(a+b \log \left(c x^n\right)\right)^2+18 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)+12 b^2 n^2 \text{Li}_3\left(-\frac{e x}{d}\right)+6 b^2 n^2 (\log (x)-\log (d+e x))}{6 d^3}","-\frac{2 b n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}-\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^3}-\frac{e x \left(a+b \log \left(c x^n\right)\right)^2}{d^3 (d+e x)}+\frac{3 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}+\frac{b e n x \left(a+b \log \left(c x^n\right)\right)}{d^3 (d+e x)}+\frac{\left(a+b \log \left(c x^n\right)\right)^3}{3 b d^3 n}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 d^3}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 d (d+e x)^2}+\frac{3 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{d^3}+\frac{2 b^2 n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{d^3}-\frac{b^2 n^2 \log (d+e x)}{d^3}",1,"((-6*b*d*n*(a + b*Log[c*x^n]))/(d + e*x) - 9*(a + b*Log[c*x^n])^2 + (3*d^2*(a + b*Log[c*x^n])^2)/(d + e*x)^2 + (6*d*(a + b*Log[c*x^n])^2)/(d + e*x) + (2*(a + b*Log[c*x^n])^3)/(b*n) + 6*b^2*n^2*(Log[x] - Log[d + e*x]) + 18*b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 6*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] + 18*b^2*n^2*PolyLog[2, -((e*x)/d)] - 12*b*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] + 12*b^2*n^2*PolyLog[3, -((e*x)/d)])/(6*d^3)","A",1
112,1,290,322,0.4138522,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x^2 (d+e x)^3} \, dx","Integrate[(a + b*Log[c*x^n])^2/(x^2*(d + e*x)^3),x]","-\frac{\frac{d^2 e \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2}-12 b e n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-6 e \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{4 d e \left(a+b \log \left(c x^n\right)\right)^2}{d+e x}+10 b e n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 b d e n \left(a+b \log \left(c x^n\right)\right)}{d+e x}+\frac{2 d \left(a+b \log \left(c x^n\right)\right)^2}{x}+\frac{4 b d n \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{2 e \left(a+b \log \left(c x^n\right)\right)^3}{b n}-5 e \left(a+b \log \left(c x^n\right)\right)^2+10 b^2 e n^2 \text{Li}_2\left(-\frac{e x}{d}\right)+12 b^2 e n^2 \text{Li}_3\left(-\frac{e x}{d}\right)+2 b^2 e n^2 (\log (x)-\log (d+e x))+\frac{4 b^2 d n^2}{x}}{2 d^4}","\frac{2 e^2 x \left(a+b \log \left(c x^n\right)\right)^2}{d^4 (d+e x)}-\frac{b e^2 n x \left(a+b \log \left(c x^n\right)\right)}{d^4 (d+e x)}+\frac{6 b e n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}-\frac{e \left(a+b \log \left(c x^n\right)\right)^3}{b d^4 n}+\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{2 d^4}+\frac{3 e \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^4}-\frac{5 b e n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{d^3 x}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right)}{d^3 x}-\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{2 d^2 (d+e x)^2}-\frac{5 b^2 e n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{d^4}-\frac{6 b^2 e n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{d^4}+\frac{b^2 e n^2 \log (d+e x)}{d^4}-\frac{2 b^2 n^2}{d^3 x}",1,"-1/2*((4*b^2*d*n^2)/x + (4*b*d*n*(a + b*Log[c*x^n]))/x - (2*b*d*e*n*(a + b*Log[c*x^n]))/(d + e*x) - 5*e*(a + b*Log[c*x^n])^2 + (2*d*(a + b*Log[c*x^n])^2)/x + (d^2*e*(a + b*Log[c*x^n])^2)/(d + e*x)^2 + (4*d*e*(a + b*Log[c*x^n])^2)/(d + e*x) + (2*e*(a + b*Log[c*x^n])^3)/(b*n) + 2*b^2*e*n^2*(Log[x] - Log[d + e*x]) + 10*b*e*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 6*e*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] + 10*b^2*e*n^2*PolyLog[2, -((e*x)/d)] - 12*b*e*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] + 12*b^2*e*n^2*PolyLog[3, -((e*x)/d)])/d^4","A",1
113,1,344,398,0.6544364,"\int \frac{x^4 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^4} \, dx","Integrate[(x^4*(a + b*Log[c*x^n])^2)/(d + e*x)^4,x]","-\frac{\frac{d^4 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^3}-\frac{6 d^3 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2}-\frac{b d^3 n \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2}+\frac{18 d^2 \left(a+b \log \left(c x^n\right)\right)^2}{d+e x}+\frac{10 b d^2 n \left(a+b \log \left(c x^n\right)\right)}{d+e x}+24 b d n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)+12 d \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+26 b d n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)-13 d \left(a+b \log \left(c x^n\right)\right)^2-3 e x \left(a+b \log \left(c x^n\right)\right)^2+6 b e n x \left(a+b \log \left(c x^n\right)-b n\right)+26 b^2 d n^2 \text{Li}_2\left(-\frac{e x}{d}\right)-24 b^2 d n^2 \text{Li}_3\left(-\frac{e x}{d}\right)-10 b^2 d n^2 (\log (x)-\log (d+e x))+\frac{b^2 d n^2 (\log (x) (d+e x)-(d+e x) \log (d+e x)+d)}{d+e x}}{3 e^5}","-\frac{d^4 \left(a+b \log \left(c x^n\right)\right)^2}{3 e^5 (d+e x)^3}+\frac{2 d^3 \left(a+b \log \left(c x^n\right)\right)^2}{e^5 (d+e x)^2}+\frac{b d^3 n \left(a+b \log \left(c x^n\right)\right)}{3 e^5 (d+e x)^2}-\frac{8 b d n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^5}-\frac{5 d \left(a+b \log \left(c x^n\right)\right)^2}{3 e^5}-\frac{4 d \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^5}-\frac{26 b d n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^5}+\frac{6 d x \left(a+b \log \left(c x^n\right)\right)^2}{e^4 (d+e x)}+\frac{10 b d n x \left(a+b \log \left(c x^n\right)\right)}{3 e^4 (d+e x)}+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{e^4}-\frac{2 a b n x}{e^4}-\frac{2 b^2 n x \log \left(c x^n\right)}{e^4}-\frac{b^2 d^2 n^2}{3 e^5 (d+e x)}-\frac{26 b^2 d n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{3 e^5}+\frac{8 b^2 d n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{e^5}-\frac{b^2 d n^2 \log (x)}{3 e^5}-\frac{3 b^2 d n^2 \log (d+e x)}{e^5}+\frac{2 b^2 n^2 x}{e^4}",1,"-1/3*(-((b*d^3*n*(a + b*Log[c*x^n]))/(d + e*x)^2) + (10*b*d^2*n*(a + b*Log[c*x^n]))/(d + e*x) - 13*d*(a + b*Log[c*x^n])^2 - 3*e*x*(a + b*Log[c*x^n])^2 + (d^4*(a + b*Log[c*x^n])^2)/(d + e*x)^3 - (6*d^3*(a + b*Log[c*x^n])^2)/(d + e*x)^2 + (18*d^2*(a + b*Log[c*x^n])^2)/(d + e*x) + 6*b*e*n*x*(a - b*n + b*Log[c*x^n]) - 10*b^2*d*n^2*(Log[x] - Log[d + e*x]) + (b^2*d*n^2*(d + (d + e*x)*Log[x] - (d + e*x)*Log[d + e*x]))/(d + e*x) + 26*b*d*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] + 12*d*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] + 26*b^2*d*n^2*PolyLog[2, -((e*x)/d)] + 24*b*d*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] - 24*b^2*d*n^2*PolyLog[3, -((e*x)/d)])/e^5","A",1
114,1,298,333,0.4977067,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^4} \, dx","Integrate[(x^3*(a + b*Log[c*x^n])^2)/(d + e*x)^4,x]","\frac{\frac{2 d^3 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^3}-\frac{9 d^2 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2}-\frac{2 b d^2 n \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2}+12 b n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{18 d \left(a+b \log \left(c x^n\right)\right)^2}{d+e x}+\frac{14 b d n \left(a+b \log \left(c x^n\right)\right)}{d+e x}+6 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+22 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)-11 \left(a+b \log \left(c x^n\right)\right)^2+22 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)-12 b^2 n^2 \text{Li}_3\left(-\frac{e x}{d}\right)-14 b^2 n^2 (\log (x)-\log (d+e x))+\frac{2 b^2 n^2 (\log (x) (d+e x)-(d+e x) \log (d+e x)+d)}{d+e x}}{6 e^4}","\frac{d^3 \left(a+b \log \left(c x^n\right)\right)^2}{3 e^4 (d+e x)^3}-\frac{3 d^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 e^4 (d+e x)^2}-\frac{b d^2 n \left(a+b \log \left(c x^n\right)\right)}{3 e^4 (d+e x)^2}+\frac{2 b n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}+\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^4}+\frac{11 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^4}-\frac{3 x \left(a+b \log \left(c x^n\right)\right)^2}{e^3 (d+e x)}-\frac{7 b n x \left(a+b \log \left(c x^n\right)\right)}{3 e^3 (d+e x)}+\frac{7 \left(a+b \log \left(c x^n\right)\right)^2}{6 e^4}+\frac{11 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{3 e^4}-\frac{2 b^2 n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{e^4}+\frac{b^2 d n^2}{3 e^4 (d+e x)}+\frac{2 b^2 n^2 \log (d+e x)}{e^4}+\frac{b^2 n^2 \log (x)}{3 e^4}",1,"((-2*b*d^2*n*(a + b*Log[c*x^n]))/(d + e*x)^2 + (14*b*d*n*(a + b*Log[c*x^n]))/(d + e*x) - 11*(a + b*Log[c*x^n])^2 + (2*d^3*(a + b*Log[c*x^n])^2)/(d + e*x)^3 - (9*d^2*(a + b*Log[c*x^n])^2)/(d + e*x)^2 + (18*d*(a + b*Log[c*x^n])^2)/(d + e*x) - 14*b^2*n^2*(Log[x] - Log[d + e*x]) + (2*b^2*n^2*(d + (d + e*x)*Log[x] - (d + e*x)*Log[d + e*x]))/(d + e*x) + 22*b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] + 6*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] + 22*b^2*n^2*PolyLog[2, -((e*x)/d)] + 12*b*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] - 12*b^2*n^2*PolyLog[3, -((e*x)/d)])/(6*e^4)","A",1
115,1,371,161,0.5134432,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^4} \, dx","Integrate[(x^2*(a + b*Log[c*x^n])^2)/(d + e*x)^4,x]","-\frac{\frac{a^2 d^2}{(d+e x)^3}+\frac{3 a^2}{d+e x}-\frac{3 a^2 d}{(d+e x)^2}-\frac{a^2}{d}+\frac{2 a b d^2 \log \left(c x^n\right)}{(d+e x)^3}+\frac{6 a b \log \left(c x^n\right)}{d+e x}-\frac{6 a b d \log \left(c x^n\right)}{(d+e x)^2}-\frac{2 a b \log \left(c x^n\right)}{d}+\frac{4 a b n}{d+e x}-\frac{a b d n}{(d+e x)^2}+\frac{2 a b n \log \left(\frac{e x}{d}+1\right)}{d}+\frac{b^2 d^2 \log ^2\left(c x^n\right)}{(d+e x)^3}+\frac{3 b^2 \log ^2\left(c x^n\right)}{d+e x}-\frac{3 b^2 d \log ^2\left(c x^n\right)}{(d+e x)^2}+\frac{4 b^2 n \log \left(c x^n\right)}{d+e x}-\frac{b^2 d n \log \left(c x^n\right)}{(d+e x)^2}+\frac{2 b^2 n \log \left(c x^n\right) \log \left(\frac{e x}{d}+1\right)}{d}-\frac{b^2 \log ^2\left(c x^n\right)}{d}+\frac{2 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{d}+\frac{b^2 n^2}{d+e x}+\frac{3 b^2 n^2 \log (d+e x)}{d}-\frac{3 b^2 n^2 \log (x)}{d}}{3 e^3}","-\frac{b n \log \left(\frac{e x}{d}+1\right) \left(2 a+2 b \log \left(c x^n\right)+3 b n\right)}{3 d e^3}+\frac{b n x \left(2 a+2 b \log \left(c x^n\right)+b n\right)}{3 d e^2 (d+e x)}+\frac{x^3 \left(a+b \log \left(c x^n\right)\right)^2}{3 d (d+e x)^3}+\frac{b n x^2 \left(a+b \log \left(c x^n\right)\right)}{3 d e (d+e x)^2}-\frac{2 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{3 d e^3}",1,"-1/3*(-(a^2/d) + (a^2*d^2)/(d + e*x)^3 - (3*a^2*d)/(d + e*x)^2 - (a*b*d*n)/(d + e*x)^2 + (3*a^2)/(d + e*x) + (4*a*b*n)/(d + e*x) + (b^2*n^2)/(d + e*x) - (3*b^2*n^2*Log[x])/d - (2*a*b*Log[c*x^n])/d + (2*a*b*d^2*Log[c*x^n])/(d + e*x)^3 - (6*a*b*d*Log[c*x^n])/(d + e*x)^2 - (b^2*d*n*Log[c*x^n])/(d + e*x)^2 + (6*a*b*Log[c*x^n])/(d + e*x) + (4*b^2*n*Log[c*x^n])/(d + e*x) - (b^2*Log[c*x^n]^2)/d + (b^2*d^2*Log[c*x^n]^2)/(d + e*x)^3 - (3*b^2*d*Log[c*x^n]^2)/(d + e*x)^2 + (3*b^2*Log[c*x^n]^2)/(d + e*x) + (3*b^2*n^2*Log[d + e*x])/d + (2*a*b*n*Log[1 + (e*x)/d])/d + (2*b^2*n*Log[c*x^n]*Log[1 + (e*x)/d])/d + (2*b^2*n^2*PolyLog[2, -((e*x)/d)])/d)/e^3","B",1
116,1,281,210,0.2461736,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^4} \, dx","Integrate[(x*(a + b*Log[c*x^n])^2)/(d + e*x)^4,x]","\frac{3 a^2 d e^2 x^2+a^2 e^3 x^3-2 b \log \left(c x^n\right) \left(b n (d+e x)^3 \log \left(\frac{e x}{d}+1\right)-e x (a e x (3 d+e x)+b d n (d+e x))\right)-2 a b d^3 n \log \left(\frac{e x}{d}+1\right)+2 a b d^2 e n x-6 a b d^2 e n x \log \left(\frac{e x}{d}+1\right)-2 a b e^3 n x^3 \log \left(\frac{e x}{d}+1\right)+2 a b d e^2 n x^2-6 a b d e^2 n x^2 \log \left(\frac{e x}{d}+1\right)+b^2 e^2 x^2 (3 d+e x) \log ^2\left(c x^n\right)+2 b^2 d^3 n^2+4 b^2 d^2 e n^2 x+2 b^2 d e^2 n^2 x^2-2 b^2 n^2 (d+e x)^3 \text{Li}_2\left(-\frac{e x}{d}\right)}{6 d^2 e^2 (d+e x)^3}","-\frac{b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^2 e^2}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{6 d^2 e^2}+\frac{b n \left(a+b \log \left(c x^n\right)\right)}{3 d e^2 (d+e x)}-\frac{b n \left(a+b \log \left(c x^n\right)\right)}{3 e^2 (d+e x)^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 e^2 (d+e x)^2}+\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{3 e^2 (d+e x)^3}-\frac{b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{3 d^2 e^2}+\frac{b^2 n^2}{3 d e^2 (d+e x)}",1,"(2*b^2*d^3*n^2 + 2*a*b*d^2*e*n*x + 4*b^2*d^2*e*n^2*x + 3*a^2*d*e^2*x^2 + 2*a*b*d*e^2*n*x^2 + 2*b^2*d*e^2*n^2*x^2 + a^2*e^3*x^3 + b^2*e^2*x^2*(3*d + e*x)*Log[c*x^n]^2 - 2*a*b*d^3*n*Log[1 + (e*x)/d] - 6*a*b*d^2*e*n*x*Log[1 + (e*x)/d] - 6*a*b*d*e^2*n*x^2*Log[1 + (e*x)/d] - 2*a*b*e^3*n*x^3*Log[1 + (e*x)/d] - 2*b*Log[c*x^n]*(-(e*x*(b*d*n*(d + e*x) + a*e*x*(3*d + e*x))) + b*n*(d + e*x)^3*Log[1 + (e*x)/d]) - 2*b^2*n^2*(d + e*x)^3*PolyLog[2, -((e*x)/d)])/(6*d^2*e^2*(d + e*x)^3)","A",1
117,1,211,203,0.1564749,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^4} \, dx","Integrate[(a + b*Log[c*x^n])^2/(d + e*x)^4,x]","\frac{2 b n \left(-\frac{\log \left(\frac{d+e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 b d^3 n}+\frac{a+b \log \left(c x^n\right)}{d^2 (d+e x)}+\frac{a+b \log \left(c x^n\right)}{2 d (d+e x)^2}-\frac{b n \text{Li}_2\left(-\frac{e x}{d}\right)}{d^3}-\frac{b n \left(-\frac{\log (d+e x)}{d^2}+\frac{\log (x)}{d^2}+\frac{1}{d (d+e x)}\right)}{2 d}-\frac{b n \left(\frac{\log (x)}{d}-\frac{\log (d+e x)}{d}\right)}{d^2}\right)}{3 e}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{3 e (d+e x)^3}","-\frac{2 b n \log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^3 e}-\frac{2 b n x \left(a+b \log \left(c x^n\right)\right)}{3 d^3 (d+e x)}+\frac{b n \left(a+b \log \left(c x^n\right)\right)}{3 d e (d+e x)^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{3 e (d+e x)^3}+\frac{2 b^2 n^2 \text{Li}_2\left(-\frac{d}{e x}\right)}{3 d^3 e}-\frac{b^2 n^2 \log (x)}{3 d^3 e}+\frac{b^2 n^2 \log (d+e x)}{d^3 e}-\frac{b^2 n^2}{3 d^2 e (d+e x)}",1,"-1/3*(a + b*Log[c*x^n])^2/(e*(d + e*x)^3) + (2*b*n*((a + b*Log[c*x^n])/(2*d*(d + e*x)^2) + (a + b*Log[c*x^n])/(d^2*(d + e*x)) + (a + b*Log[c*x^n])^2/(2*b*d^3*n) - (b*n*(1/(d*(d + e*x)) + Log[x]/d^2 - Log[d + e*x]/d^2))/(2*d) - (b*n*(Log[x]/d - Log[d + e*x]/d))/d^2 - ((a + b*Log[c*x^n])*Log[(d + e*x)/d])/d^3 - (b*n*PolyLog[2, -((e*x)/d)])/d^3))/(3*e)","A",1
118,1,318,351,0.4323273,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x (d+e x)^4} \, dx","Integrate[(a + b*Log[c*x^n])^2/(x*(d + e*x)^4),x]","\frac{\frac{2 d^3 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^3}+\frac{3 d^2 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2}-\frac{2 b d^2 n \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2}-12 b n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{6 d \left(a+b \log \left(c x^n\right)\right)^2}{d+e x}-\frac{10 b d n \left(a+b \log \left(c x^n\right)\right)}{d+e x}-6 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+22 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2 \left(a+b \log \left(c x^n\right)\right)^3}{b n}-11 \left(a+b \log \left(c x^n\right)\right)^2+22 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)+12 b^2 n^2 \text{Li}_3\left(-\frac{e x}{d}\right)+10 b^2 n^2 (\log (x)-\log (d+e x))+\frac{2 b^2 n^2 (\log (x) (d+e x)-(d+e x) \log (d+e x)+d)}{d+e x}}{6 d^4}","-\frac{2 b n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}-\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^4}-\frac{e x \left(a+b \log \left(c x^n\right)\right)^2}{d^4 (d+e x)}+\frac{11 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^4}+\frac{5 b e n x \left(a+b \log \left(c x^n\right)\right)}{3 d^4 (d+e x)}+\frac{\left(a+b \log \left(c x^n\right)\right)^3}{3 b d^4 n}-\frac{5 \left(a+b \log \left(c x^n\right)\right)^2}{6 d^4}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 d^2 (d+e x)^2}-\frac{b n \left(a+b \log \left(c x^n\right)\right)}{3 d^2 (d+e x)^2}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{3 d (d+e x)^3}+\frac{11 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{3 d^4}+\frac{2 b^2 n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{d^4}-\frac{2 b^2 n^2 \log (d+e x)}{d^4}+\frac{b^2 n^2 \log (x)}{3 d^4}+\frac{b^2 n^2}{3 d^3 (d+e x)}",1,"((-2*b*d^2*n*(a + b*Log[c*x^n]))/(d + e*x)^2 - (10*b*d*n*(a + b*Log[c*x^n]))/(d + e*x) - 11*(a + b*Log[c*x^n])^2 + (2*d^3*(a + b*Log[c*x^n])^2)/(d + e*x)^3 + (3*d^2*(a + b*Log[c*x^n])^2)/(d + e*x)^2 + (6*d*(a + b*Log[c*x^n])^2)/(d + e*x) + (2*(a + b*Log[c*x^n])^3)/(b*n) + 10*b^2*n^2*(Log[x] - Log[d + e*x]) + (2*b^2*n^2*(d + (d + e*x)*Log[x] - (d + e*x)*Log[d + e*x]))/(d + e*x) + 22*b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 6*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] + 22*b^2*n^2*PolyLog[2, -((e*x)/d)] - 12*b*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] + 12*b^2*n^2*PolyLog[3, -((e*x)/d)])/(6*d^4)","A",1
119,1,378,420,0.6695813,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x^2 (d+e x)^4} \, dx","Integrate[(a + b*Log[c*x^n])^2/(x^2*(d + e*x)^4),x]","-\frac{\frac{d^3 e \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^3}+\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2}-\frac{b d^2 e n \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2}-24 b e n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{9 d e \left(a+b \log \left(c x^n\right)\right)^2}{d+e x}-\frac{8 b d e n \left(a+b \log \left(c x^n\right)\right)}{d+e x}-12 e \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+26 b e n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{3 d \left(a+b \log \left(c x^n\right)\right)^2}{x}+\frac{6 b d n \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{4 e \left(a+b \log \left(c x^n\right)\right)^3}{b n}-13 e \left(a+b \log \left(c x^n\right)\right)^2+26 b^2 e n^2 \text{Li}_2\left(-\frac{e x}{d}\right)+24 b^2 e n^2 \text{Li}_3\left(-\frac{e x}{d}\right)+8 b^2 e n^2 (\log (x)-\log (d+e x))+\frac{b^2 e n^2 (\log (x) (d+e x)-(d+e x) \log (d+e x)+d)}{d+e x}+\frac{6 b^2 d n^2}{x}}{3 d^5}","\frac{3 e^2 x \left(a+b \log \left(c x^n\right)\right)^2}{d^5 (d+e x)}-\frac{8 b e^2 n x \left(a+b \log \left(c x^n\right)\right)}{3 d^5 (d+e x)}+\frac{8 b e n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^5}-\frac{4 e \left(a+b \log \left(c x^n\right)\right)^3}{3 b d^5 n}+\frac{4 e \left(a+b \log \left(c x^n\right)\right)^2}{3 d^5}+\frac{4 e \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^5}-\frac{26 b e n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^5}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{d^4 x}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right)}{d^4 x}-\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{d^3 (d+e x)^2}+\frac{b e n \left(a+b \log \left(c x^n\right)\right)}{3 d^3 (d+e x)^2}-\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{3 d^2 (d+e x)^3}-\frac{26 b^2 e n^2 \text{Li}_2\left(-\frac{e x}{d}\right)}{3 d^5}-\frac{8 b^2 e n^2 \text{Li}_3\left(-\frac{e x}{d}\right)}{d^5}-\frac{b^2 e n^2 \log (x)}{3 d^5}+\frac{3 b^2 e n^2 \log (d+e x)}{d^5}-\frac{b^2 e n^2}{3 d^4 (d+e x)}-\frac{2 b^2 n^2}{d^4 x}",1,"-1/3*((6*b^2*d*n^2)/x + (6*b*d*n*(a + b*Log[c*x^n]))/x - (b*d^2*e*n*(a + b*Log[c*x^n]))/(d + e*x)^2 - (8*b*d*e*n*(a + b*Log[c*x^n]))/(d + e*x) - 13*e*(a + b*Log[c*x^n])^2 + (3*d*(a + b*Log[c*x^n])^2)/x + (d^3*e*(a + b*Log[c*x^n])^2)/(d + e*x)^3 + (3*d^2*e*(a + b*Log[c*x^n])^2)/(d + e*x)^2 + (9*d*e*(a + b*Log[c*x^n])^2)/(d + e*x) + (4*e*(a + b*Log[c*x^n])^3)/(b*n) + 8*b^2*e*n^2*(Log[x] - Log[d + e*x]) + (b^2*e*n^2*(d + (d + e*x)*Log[x] - (d + e*x)*Log[d + e*x]))/(d + e*x) + 26*b*e*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 12*e*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] + 26*b^2*e*n^2*PolyLog[2, -((e*x)/d)] - 24*b*e*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] + 24*b^2*e*n^2*PolyLog[3, -((e*x)/d)])/d^5","A",1
120,1,96,107,0.1437105,"\int \frac{x \log ^2(x)}{(d+e x)^4} \, dx","Integrate[(x*Log[x]^2)/(d + e*x)^4,x]","\frac{e^2 x^2 \log ^2(x) (3 d+e x)-2 (d+e x)^3 \text{Li}_2\left(-\frac{e x}{d}\right)+2 d (d+e x)^2-2 \log (x) (d+e x) \left((d+e x)^2 \log \left(\frac{e x}{d}+1\right)-d e x\right)}{6 d^2 e^2 (d+e x)^3}","-\frac{\text{Li}_2\left(-\frac{e x}{d}\right)}{3 d^2 e^2}-\frac{\log (x) \log \left(\frac{e x}{d}+1\right)}{3 d^2 e^2}+\frac{x^2 \log ^2(x) (3 d+e x)}{6 d^2 (d+e x)^3}-\frac{x}{3 d^2 e (d+e x)}+\frac{x \log (x)}{3 d e (d+e x)^2}",1,"(2*d*(d + e*x)^2 + e^2*x^2*(3*d + e*x)*Log[x]^2 - 2*(d + e*x)*Log[x]*(-(d*e*x) + (d + e*x)^2*Log[1 + (e*x)/d]) - 2*(d + e*x)^3*PolyLog[2, -((e*x)/d)])/(6*d^2*e^2*(d + e*x)^3)","A",1
121,1,243,113,0.1966988,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3}{x (d+e x)} \, dx","Integrate[(a + b*Log[c*x^n])^3/(x*(d + e*x)),x]","\frac{-4 b^2 n^2 \left(6 \text{Li}_3\left(-\frac{e x}{d}\right)-6 \log (x) \text{Li}_2\left(-\frac{e x}{d}\right)+\log ^2(x) \left(\log (x)-3 \log \left(\frac{e x}{d}+1\right)\right)\right) \left(-a-b \log \left(c x^n\right)+b n \log (x)\right)+6 b n \left(\log ^2(x)-2 \left(\text{Li}_2\left(-\frac{e x}{d}\right)+\log (x) \log \left(\frac{e x}{d}+1\right)\right)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2-4 \log (d+e x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^3+4 \log (x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^3+b^3 n^3 \left(-24 \text{Li}_4\left(-\frac{e x}{d}\right)-12 \log ^2(x) \text{Li}_2\left(-\frac{e x}{d}\right)+24 \log (x) \text{Li}_3\left(-\frac{e x}{d}\right)-4 \log ^3(x) \log \left(\frac{e x}{d}+1\right)+\log ^4(x)\right)}{4 d}","\frac{6 b^2 n^2 \text{Li}_3\left(-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d}+\frac{3 b n \text{Li}_2\left(-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)^2}{d}-\frac{\log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{d}+\frac{6 b^3 n^3 \text{Li}_4\left(-\frac{d}{e x}\right)}{d}",1,"(4*Log[x]*(a - b*n*Log[x] + b*Log[c*x^n])^3 - 4*(a - b*n*Log[x] + b*Log[c*x^n])^3*Log[d + e*x] + 6*b*n*(a - b*n*Log[x] + b*Log[c*x^n])^2*(Log[x]^2 - 2*(Log[x]*Log[1 + (e*x)/d] + PolyLog[2, -((e*x)/d)])) - 4*b^2*n^2*(-a + b*n*Log[x] - b*Log[c*x^n])*(Log[x]^2*(Log[x] - 3*Log[1 + (e*x)/d]) - 6*Log[x]*PolyLog[2, -((e*x)/d)] + 6*PolyLog[3, -((e*x)/d)]) + b^3*n^3*(Log[x]^4 - 4*Log[x]^3*Log[1 + (e*x)/d] - 12*Log[x]^2*PolyLog[2, -((e*x)/d)] + 24*Log[x]*PolyLog[3, -((e*x)/d)] - 24*PolyLog[4, -((e*x)/d)]))/(4*d)","B",1
122,1,432,217,0.4978742,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3}{x (d+e x)^2} \, dx","Integrate[(a + b*Log[c*x^n])^3/(x*(d + e*x)^2),x]","\frac{4 b^2 n^2 \left(6 (d+e x) \text{Li}_3\left(-\frac{e x}{d}\right)-6 (\log (x)-1) (d+e x) \text{Li}_2\left(-\frac{e x}{d}\right)+\log (x) \left(\log ^2(x) (d+e x)-3 \log (x) \left((d+e x) \log \left(\frac{e x}{d}+1\right)+e x\right)+6 (d+e x) \log \left(\frac{e x}{d}+1\right)\right)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)+6 b n \left(-2 (d+e x) \left(\text{Li}_2\left(-\frac{e x}{d}\right)+\log (x) \log \left(\frac{e x}{d}+1\right)\right)+\log ^2(x) (d+e x)+2 (d+e x) \log (d+e x)-2 e x \log (x)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2+4 \log (x) (d+e x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^3-4 (d+e x) \log (d+e x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^3+4 d \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^3+b^3 n^3 \left(-4 \left(6 (d+e x) \text{Li}_3\left(-\frac{e x}{d}\right)-6 \log (x) (d+e x) \text{Li}_2\left(-\frac{e x}{d}\right)+\log ^2(x) \left(e x \log (x)-3 (d+e x) \log \left(\frac{e x}{d}+1\right)\right)\right)-4 (d+e x) \left(6 \text{Li}_4\left(-\frac{e x}{d}\right)+3 \log ^2(x) \text{Li}_2\left(-\frac{e x}{d}\right)-6 \log (x) \text{Li}_3\left(-\frac{e x}{d}\right)+\log ^3(x) \log \left(\frac{e x}{d}+1\right)\right)+\log ^4(x) (d+e x)\right)}{4 d^2 (d+e x)}","\frac{6 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}+\frac{6 b^2 n^2 \text{Li}_3\left(-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}+\frac{3 b n \text{Li}_2\left(-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2}+\frac{3 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2}-\frac{\log \left(\frac{d}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{d^2}-\frac{e x \left(a+b \log \left(c x^n\right)\right)^3}{d^2 (d+e x)}-\frac{6 b^3 n^3 \text{Li}_3\left(-\frac{e x}{d}\right)}{d^2}+\frac{6 b^3 n^3 \text{Li}_4\left(-\frac{d}{e x}\right)}{d^2}",1,"(4*d*(a - b*n*Log[x] + b*Log[c*x^n])^3 + 4*(d + e*x)*Log[x]*(a - b*n*Log[x] + b*Log[c*x^n])^3 - 4*(d + e*x)*(a - b*n*Log[x] + b*Log[c*x^n])^3*Log[d + e*x] + 6*b*n*(a - b*n*Log[x] + b*Log[c*x^n])^2*(-2*e*x*Log[x] + (d + e*x)*Log[x]^2 + 2*(d + e*x)*Log[d + e*x] - 2*(d + e*x)*(Log[x]*Log[1 + (e*x)/d] + PolyLog[2, -((e*x)/d)])) + 4*b^2*n^2*(a - b*n*Log[x] + b*Log[c*x^n])*(Log[x]*((d + e*x)*Log[x]^2 + 6*(d + e*x)*Log[1 + (e*x)/d] - 3*Log[x]*(e*x + (d + e*x)*Log[1 + (e*x)/d])) - 6*(d + e*x)*(-1 + Log[x])*PolyLog[2, -((e*x)/d)] + 6*(d + e*x)*PolyLog[3, -((e*x)/d)]) + b^3*n^3*((d + e*x)*Log[x]^4 - 4*(Log[x]^2*(e*x*Log[x] - 3*(d + e*x)*Log[1 + (e*x)/d]) - 6*(d + e*x)*Log[x]*PolyLog[2, -((e*x)/d)] + 6*(d + e*x)*PolyLog[3, -((e*x)/d)]) - 4*(d + e*x)*(Log[x]^3*Log[1 + (e*x)/d] + 3*Log[x]^2*PolyLog[2, -((e*x)/d)] - 6*Log[x]*PolyLog[3, -((e*x)/d)] + 6*PolyLog[4, -((e*x)/d)])))/(4*d^2*(d + e*x))","A",1
123,1,706,361,0.9213021,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3}{x (d+e x)^3} \, dx","Integrate[(a + b*Log[c*x^n])^3/(x*(d + e*x)^3),x]","\frac{2 b^2 n^2 \left(6 (d+e x)^2 \text{Li}_2\left(-\frac{e x}{d}\right)-6 (d+e x)^2 \left(-2 \text{Li}_3\left(-\frac{e x}{d}\right)+2 \log (x) \text{Li}_2\left(-\frac{e x}{d}\right)+\log ^2(x) \log \left(\frac{e x}{d}+1\right)\right)-6 (d+e x) \left(\log (x) \left(e x \log (x)-2 (d+e x) \log \left(\frac{e x}{d}+1\right)\right)-2 (d+e x) \text{Li}_2\left(-\frac{e x}{d}\right)\right)+2 \log ^3(x) (d+e x)^2-3 e x \log ^2(x) (2 d+e x)+6 \log (x) (d+e x) \left((d+e x) \log \left(\frac{e x}{d}+1\right)+e x\right)-6 (d+e x)^2 \log (d+e x)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)+2 d^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^3+6 b n \left(-2 (d+e x)^2 \text{Li}_2\left(-\frac{e x}{d}\right)+\log ^2(x) (d+e x)^2+(d+e x) (3 (d+e x) \log (d+e x)-d)-\log (x) \left(e x (4 d+3 e x)+2 (d+e x)^2 \log \left(\frac{e x}{d}+1\right)\right)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2+4 d (d+e x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^3+4 \log (x) (d+e x)^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^3-4 (d+e x)^2 \log (d+e x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^3+b^3 n^3 \left(-4 (d+e x) \left(6 (d+e x) \text{Li}_3\left(-\frac{e x}{d}\right)-6 \log (x) (d+e x) \text{Li}_2\left(-\frac{e x}{d}\right)+\log ^2(x) \left(e x \log (x)-3 (d+e x) \log \left(\frac{e x}{d}+1\right)\right)\right)-2 \left(6 (d+e x)^2 \text{Li}_3\left(-\frac{e x}{d}\right)-6 (\log (x)-1) (d+e x)^2 \text{Li}_2\left(-\frac{e x}{d}\right)+\log (x) \left(e x \log ^2(x) (2 d+e x)+6 (d+e x)^2 \log \left(\frac{e x}{d}+1\right)-3 \log (x) (d+e x) \left((d+e x) \log \left(\frac{e x}{d}+1\right)+e x\right)\right)\right)-4 (d+e x)^2 \left(6 \text{Li}_4\left(-\frac{e x}{d}\right)+3 \log ^2(x) \text{Li}_2\left(-\frac{e x}{d}\right)-6 \log (x) \text{Li}_3\left(-\frac{e x}{d}\right)+\log ^3(x) \log \left(\frac{e x}{d}+1\right)\right)+\log ^4(x) (d+e x)^2\right)}{4 d^3 (d+e x)^2}","\frac{9 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}+\frac{6 b^2 n^2 \text{Li}_3\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}-\frac{3 b^2 n^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}-\frac{3 b n \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^3}-\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{d^3}-\frac{e x \left(a+b \log \left(c x^n\right)\right)^3}{d^3 (d+e x)}+\frac{9 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 d^3}+\frac{3 b e n x \left(a+b \log \left(c x^n\right)\right)^2}{2 d^3 (d+e x)}+\frac{\left(a+b \log \left(c x^n\right)\right)^4}{4 b d^3 n}-\frac{\left(a+b \log \left(c x^n\right)\right)^3}{2 d^3}+\frac{\left(a+b \log \left(c x^n\right)\right)^3}{2 d (d+e x)^2}-\frac{3 b^3 n^3 \text{Li}_2\left(-\frac{e x}{d}\right)}{d^3}-\frac{9 b^3 n^3 \text{Li}_3\left(-\frac{e x}{d}\right)}{d^3}-\frac{6 b^3 n^3 \text{Li}_4\left(-\frac{e x}{d}\right)}{d^3}",1,"(2*d^2*(a - b*n*Log[x] + b*Log[c*x^n])^3 + 4*d*(d + e*x)*(a - b*n*Log[x] + b*Log[c*x^n])^3 + 4*(d + e*x)^2*Log[x]*(a - b*n*Log[x] + b*Log[c*x^n])^3 - 4*(d + e*x)^2*(a - b*n*Log[x] + b*Log[c*x^n])^3*Log[d + e*x] + 6*b*n*(a - b*n*Log[x] + b*Log[c*x^n])^2*((d + e*x)^2*Log[x]^2 + (d + e*x)*(-d + 3*(d + e*x)*Log[d + e*x]) - Log[x]*(e*x*(4*d + 3*e*x) + 2*(d + e*x)^2*Log[1 + (e*x)/d]) - 2*(d + e*x)^2*PolyLog[2, -((e*x)/d)]) + 2*b^2*n^2*(a - b*n*Log[x] + b*Log[c*x^n])*(-3*e*x*(2*d + e*x)*Log[x]^2 + 2*(d + e*x)^2*Log[x]^3 - 6*(d + e*x)^2*Log[d + e*x] + 6*(d + e*x)*Log[x]*(e*x + (d + e*x)*Log[1 + (e*x)/d]) + 6*(d + e*x)^2*PolyLog[2, -((e*x)/d)] - 6*(d + e*x)*(Log[x]*(e*x*Log[x] - 2*(d + e*x)*Log[1 + (e*x)/d]) - 2*(d + e*x)*PolyLog[2, -((e*x)/d)]) - 6*(d + e*x)^2*(Log[x]^2*Log[1 + (e*x)/d] + 2*Log[x]*PolyLog[2, -((e*x)/d)] - 2*PolyLog[3, -((e*x)/d)])) + b^3*n^3*((d + e*x)^2*Log[x]^4 - 4*(d + e*x)*(Log[x]^2*(e*x*Log[x] - 3*(d + e*x)*Log[1 + (e*x)/d]) - 6*(d + e*x)*Log[x]*PolyLog[2, -((e*x)/d)] + 6*(d + e*x)*PolyLog[3, -((e*x)/d)]) - 2*(Log[x]*(e*x*(2*d + e*x)*Log[x]^2 + 6*(d + e*x)^2*Log[1 + (e*x)/d] - 3*(d + e*x)*Log[x]*(e*x + (d + e*x)*Log[1 + (e*x)/d])) - 6*(d + e*x)^2*(-1 + Log[x])*PolyLog[2, -((e*x)/d)] + 6*(d + e*x)^2*PolyLog[3, -((e*x)/d)]) - 4*(d + e*x)^2*(Log[x]^3*Log[1 + (e*x)/d] + 3*Log[x]^2*PolyLog[2, -((e*x)/d)] - 6*Log[x]*PolyLog[3, -((e*x)/d)] + 6*PolyLog[4, -((e*x)/d)])))/(4*d^3*(d + e*x)^2)","A",1
124,1,169,189,0.2813505,"\int (d+e x) \sqrt{a+b \log \left(c x^n\right)} \, dx","Integrate[(d + e*x)*Sqrt[a + b*Log[c*x^n]],x]","\frac{1}{8} x \left(4 (2 d+e x) \sqrt{a+b \log \left(c x^n\right)}-4 \sqrt{\pi } \sqrt{b} d \sqrt{n} e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \text{erfi}\left(\frac{\sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)+\sqrt{2 \pi } \left(-\sqrt{b}\right) e \sqrt{n} x e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)\right)","-\frac{1}{2} \sqrt{\pi } \sqrt{b} d \sqrt{n} x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \text{erfi}\left(\frac{\sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)+d x \sqrt{a+b \log \left(c x^n\right)}-\frac{1}{4} \sqrt{\frac{\pi }{2}} \sqrt{b} e \sqrt{n} x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)+\frac{1}{2} e x^2 \sqrt{a+b \log \left(c x^n\right)}",1,"(x*((-4*Sqrt[b]*d*Sqrt[n]*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[c*x^n]]/(Sqrt[b]*Sqrt[n])])/(E^(a/(b*n))*(c*x^n)^n^(-1)) - (Sqrt[b]*e*Sqrt[n]*Sqrt[2*Pi]*x*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*x^n]])/(Sqrt[b]*Sqrt[n])])/(E^((2*a)/(b*n))*(c*x^n)^(2/n)) + 4*(2*d + e*x)*Sqrt[a + b*Log[c*x^n]]))/8","A",1
125,1,287,298,0.3982632,"\int (d+e x)^2 \sqrt{a+b \log \left(c x^n\right)} \, dx","Integrate[(d + e*x)^2*Sqrt[a + b*Log[c*x^n]],x]","\frac{1}{36} x \left(-18 \sqrt{\pi } \sqrt{b} d^2 \sqrt{n} e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \text{erfi}\left(\frac{\sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)+36 d^2 \sqrt{a+b \log \left(c x^n\right)}-9 \sqrt{2 \pi } \sqrt{b} d e \sqrt{n} x e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)+36 d e x \sqrt{a+b \log \left(c x^n\right)}-2 \sqrt{3 \pi } \sqrt{b} e^2 \sqrt{n} x^2 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)+12 e^2 x^2 \sqrt{a+b \log \left(c x^n\right)}\right)","-\frac{1}{2} \sqrt{\pi } \sqrt{b} d^2 \sqrt{n} x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \text{erfi}\left(\frac{\sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)+d^2 x \sqrt{a+b \log \left(c x^n\right)}-\frac{1}{2} \sqrt{\frac{\pi }{2}} \sqrt{b} d e \sqrt{n} x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)+d e x^2 \sqrt{a+b \log \left(c x^n\right)}-\frac{1}{6} \sqrt{\frac{\pi }{3}} \sqrt{b} e^2 \sqrt{n} x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)+\frac{1}{3} e^2 x^3 \sqrt{a+b \log \left(c x^n\right)}",1,"(x*((-18*Sqrt[b]*d^2*Sqrt[n]*Sqrt[Pi]*Erfi[Sqrt[a + b*Log[c*x^n]]/(Sqrt[b]*Sqrt[n])])/(E^(a/(b*n))*(c*x^n)^n^(-1)) - (9*Sqrt[b]*d*e*Sqrt[n]*Sqrt[2*Pi]*x*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*x^n]])/(Sqrt[b]*Sqrt[n])])/(E^((2*a)/(b*n))*(c*x^n)^(2/n)) - (2*Sqrt[b]*e^2*Sqrt[n]*Sqrt[3*Pi]*x^2*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*x^n]])/(Sqrt[b]*Sqrt[n])])/(E^((3*a)/(b*n))*(c*x^n)^(3/n)) + 36*d^2*Sqrt[a + b*Log[c*x^n]] + 36*d*e*x*Sqrt[a + b*Log[c*x^n]] + 12*e^2*x^2*Sqrt[a + b*Log[c*x^n]]))/36","A",1
126,1,366,402,0.5087256,"\int (d+e x)^3 \sqrt{a+b \log \left(c x^n\right)} \, dx","Integrate[(d + e*x)^3*Sqrt[a + b*Log[c*x^n]],x]","\frac{1}{48} x e^{-\frac{4 a}{b n}} \left(c x^n\right)^{-4/n} \left(-24 \sqrt{\pi } \sqrt{b} d^3 \sqrt{n} e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \text{erfi}\left(\frac{\sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)+2 e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(-9 \sqrt{2 \pi } \sqrt{b} d^2 e \sqrt{n} x e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)+6 e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right) \sqrt{a+b \log \left(c x^n\right)}-4 \sqrt{3 \pi } \sqrt{b} d e^2 \sqrt{n} x^2 \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)\right)-3 \sqrt{\pi } \sqrt{b} e^3 \sqrt{n} x^3 \text{erfi}\left(\frac{2 \sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)\right)","-\frac{1}{2} \sqrt{\pi } \sqrt{b} d^3 \sqrt{n} x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \text{erfi}\left(\frac{\sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)+d^3 x \sqrt{a+b \log \left(c x^n\right)}-\frac{3}{4} \sqrt{\frac{\pi }{2}} \sqrt{b} d^2 e \sqrt{n} x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)+\frac{3}{2} d^2 e x^2 \sqrt{a+b \log \left(c x^n\right)}-\frac{1}{2} \sqrt{\frac{\pi }{3}} \sqrt{b} d e^2 \sqrt{n} x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)+d e^2 x^3 \sqrt{a+b \log \left(c x^n\right)}-\frac{1}{16} \sqrt{\pi } \sqrt{b} e^3 \sqrt{n} x^4 e^{-\frac{4 a}{b n}} \left(c x^n\right)^{-4/n} \text{erfi}\left(\frac{2 \sqrt{a+b \log \left(c x^n\right)}}{\sqrt{b} \sqrt{n}}\right)+\frac{1}{4} e^3 x^4 \sqrt{a+b \log \left(c x^n\right)}",1,"(x*(-24*Sqrt[b]*d^3*E^((3*a)/(b*n))*Sqrt[n]*Sqrt[Pi]*(c*x^n)^(3/n)*Erfi[Sqrt[a + b*Log[c*x^n]]/(Sqrt[b]*Sqrt[n])] - 3*Sqrt[b]*e^3*Sqrt[n]*Sqrt[Pi]*x^3*Erfi[(2*Sqrt[a + b*Log[c*x^n]])/(Sqrt[b]*Sqrt[n])] + 2*E^(a/(b*n))*(c*x^n)^n^(-1)*(-9*Sqrt[b]*d^2*e*E^(a/(b*n))*Sqrt[n]*Sqrt[2*Pi]*x*(c*x^n)^n^(-1)*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*x^n]])/(Sqrt[b]*Sqrt[n])] - 4*Sqrt[b]*d*e^2*Sqrt[n]*Sqrt[3*Pi]*x^2*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*x^n]])/(Sqrt[b]*Sqrt[n])] + 6*E^((3*a)/(b*n))*(c*x^n)^(3/n)*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3)*Sqrt[a + b*Log[c*x^n]])))/(48*E^((4*a)/(b*n))*(c*x^n)^(4/n))","A",1
127,0,0,25,6.3618376,"\int \frac{\sqrt{a+b \log \left(c x^n\right)}}{d+e x} \, dx","Integrate[Sqrt[a + b*Log[c*x^n]]/(d + e*x),x]","\int \frac{\sqrt{a+b \log \left(c x^n\right)}}{d+e x} \, dx","\text{Int}\left(\frac{\sqrt{a+b \log \left(c x^n\right)}}{d+e x},x\right)",0,"Integrate[Sqrt[a + b*Log[c*x^n]]/(d + e*x), x]","A",-1
128,0,0,61,6.7995826,"\int \frac{\sqrt{a+b \log \left(c x^n\right)}}{(d+e x)^2} \, dx","Integrate[Sqrt[a + b*Log[c*x^n]]/(d + e*x)^2,x]","\int \frac{\sqrt{a+b \log \left(c x^n\right)}}{(d+e x)^2} \, dx","\frac{x \sqrt{a+b \log \left(c x^n\right)}}{d (d+e x)}-\frac{b n \text{Int}\left(\frac{1}{(d+e x) \sqrt{a+b \log \left(c x^n\right)}},x\right)}{2 d}",0,"Integrate[Sqrt[a + b*Log[c*x^n]]/(d + e*x)^2, x]","A",-1
129,0,0,66,13.3474042,"\int \frac{\sqrt{a+b \log \left(c x^n\right)}}{(d+e x)^3} \, dx","Integrate[Sqrt[a + b*Log[c*x^n]]/(d + e*x)^3,x]","\int \frac{\sqrt{a+b \log \left(c x^n\right)}}{(d+e x)^3} \, dx","\frac{b n \text{Int}\left(\frac{1}{x (d+e x)^2 \sqrt{a+b \log \left(c x^n\right)}},x\right)}{4 e}-\frac{\sqrt{a+b \log \left(c x^n\right)}}{2 e (d+e x)^2}",0,"Integrate[Sqrt[a + b*Log[c*x^n]]/(d + e*x)^3, x]","A",-1
130,1,183,242,0.4652562,"\int x^3 \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^3*Sqrt[d + e*x]*(a + b*Log[c*x^n]),x]","-\frac{2 \left(\sqrt{d+e x} \left(315 a \left(16 d^4-8 d^3 e x+6 d^2 e^2 x^2-5 d e^3 x^3-35 e^4 x^4\right)+315 b \left(16 d^4-8 d^3 e x+6 d^2 e^2 x^2-5 d e^3 x^3-35 e^4 x^4\right) \log \left(c x^n\right)+2 b n \left(-4388 d^4+934 d^3 e x-543 d^2 e^2 x^2+400 d e^3 x^3+1225 e^4 x^4\right)\right)+10080 b d^{9/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)\right)}{99225 e^4}","-\frac{2 d^3 (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 e^4}+\frac{6 d^2 (d+e x)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e^4}-\frac{6 d (d+e x)^{7/2} \left(a+b \log \left(c x^n\right)\right)}{7 e^4}+\frac{2 (d+e x)^{9/2} \left(a+b \log \left(c x^n\right)\right)}{9 e^4}-\frac{64 b d^{9/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{315 e^4}+\frac{64 b d^4 n \sqrt{d+e x}}{315 e^4}+\frac{64 b d^3 n (d+e x)^{3/2}}{945 e^4}-\frac{356 b d^2 n (d+e x)^{5/2}}{1575 e^4}+\frac{80 b d n (d+e x)^{7/2}}{441 e^4}-\frac{4 b n (d+e x)^{9/2}}{81 e^4}",1,"(-2*(10080*b*d^(9/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + Sqrt[d + e*x]*(315*a*(16*d^4 - 8*d^3*e*x + 6*d^2*e^2*x^2 - 5*d*e^3*x^3 - 35*e^4*x^4) + 2*b*n*(-4388*d^4 + 934*d^3*e*x - 543*d^2*e^2*x^2 + 400*d*e^3*x^3 + 1225*e^4*x^4) + 315*b*(16*d^4 - 8*d^3*e*x + 6*d^2*e^2*x^2 - 5*d*e^3*x^3 - 35*e^4*x^4)*Log[c*x^n])))/(99225*e^4)","A",1
131,1,151,192,0.2184947,"\int x^2 \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^2*Sqrt[d + e*x]*(a + b*Log[c*x^n]),x]","\frac{2 \sqrt{d+e x} \left(105 a \left(8 d^3-4 d^2 e x+3 d e^2 x^2+15 e^3 x^3\right)+105 b \left(8 d^3-4 d^2 e x+3 d e^2 x^2+15 e^3 x^3\right) \log \left(c x^n\right)-2 b n \left(778 d^3-179 d^2 e x+108 d e^2 x^2+225 e^3 x^3\right)\right)+3360 b d^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{11025 e^3}","\frac{2 d^2 (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 e^3}-\frac{4 d (d+e x)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e^3}+\frac{2 (d+e x)^{7/2} \left(a+b \log \left(c x^n\right)\right)}{7 e^3}+\frac{32 b d^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{105 e^3}-\frac{32 b d^3 n \sqrt{d+e x}}{105 e^3}-\frac{32 b d^2 n (d+e x)^{3/2}}{315 e^3}+\frac{36 b d n (d+e x)^{5/2}}{175 e^3}-\frac{4 b n (d+e x)^{7/2}}{49 e^3}",1,"(3360*b*d^(7/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + 2*Sqrt[d + e*x]*(105*a*(8*d^3 - 4*d^2*e*x + 3*d*e^2*x^2 + 15*e^3*x^3) - 2*b*n*(778*d^3 - 179*d^2*e*x + 108*d*e^2*x^2 + 225*e^3*x^3) + 105*b*(8*d^3 - 4*d^2*e*x + 3*d*e^2*x^2 + 15*e^3*x^3)*Log[c*x^n]))/(11025*e^3)","A",1
132,1,116,142,0.1259484,"\int x \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x*Sqrt[d + e*x]*(a + b*Log[c*x^n]),x]","\frac{2 \sqrt{d+e x} \left(15 a \left(-2 d^2+d e x+3 e^2 x^2\right)+15 b \left(-2 d^2+d e x+3 e^2 x^2\right) \log \left(c x^n\right)+2 b n \left(31 d^2-8 d e x-9 e^2 x^2\right)\right)-120 b d^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{225 e^2}","-\frac{2 d (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 e^2}+\frac{2 (d+e x)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e^2}-\frac{8 b d^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{15 e^2}+\frac{8 b d^2 n \sqrt{d+e x}}{15 e^2}+\frac{8 b d n (d+e x)^{3/2}}{45 e^2}-\frac{4 b n (d+e x)^{5/2}}{25 e^2}",1,"(-120*b*d^(5/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + 2*Sqrt[d + e*x]*(2*b*n*(31*d^2 - 8*d*e*x - 9*e^2*x^2) + 15*a*(-2*d^2 + d*e*x + 3*e^2*x^2) + 15*b*(-2*d^2 + d*e*x + 3*e^2*x^2)*Log[c*x^n]))/(225*e^2)","A",1
133,1,77,94,0.0722983,"\int \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Sqrt[d + e*x]*(a + b*Log[c*x^n]),x]","\frac{2 \left(\sqrt{d+e x} \left(3 a (d+e x)+3 b (d+e x) \log \left(c x^n\right)-2 b n (4 d+e x)\right)+6 b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)\right)}{9 e}","\frac{2 (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 e}+\frac{4 b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{3 e}-\frac{4 b d n \sqrt{d+e x}}{3 e}-\frac{4 b n (d+e x)^{3/2}}{9 e}",1,"(2*(6*b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + Sqrt[d + e*x]*(3*a*(d + e*x) - 2*b*n*(4*d + e*x) + 3*b*(d + e*x)*Log[c*x^n])))/(9*e)","A",1
134,1,331,211,0.2182497,"\int \frac{\sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[(Sqrt[d + e*x]*(a + b*Log[c*x^n]))/x,x]","\sqrt{d} \log \left(\sqrt{d}-\sqrt{d+e x}\right) \left(a+b \log \left(c x^n\right)\right)-\sqrt{d} \log \left(\sqrt{d+e x}+\sqrt{d}\right) \left(a+b \log \left(c x^n\right)\right)+2 a \sqrt{d+e x}+2 b \sqrt{d+e x} \log \left(c x^n\right)-\frac{1}{2} b \sqrt{d} n \left(2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)+\log \left(\sqrt{d}-\sqrt{d+e x}\right) \left(\log \left(\sqrt{d}-\sqrt{d+e x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)\right)\right)+\frac{1}{2} b \sqrt{d} n \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)+\log \left(\sqrt{d+e x}+\sqrt{d}\right) \left(\log \left(\sqrt{d+e x}+\sqrt{d}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)\right)\right)-4 b n \left(\sqrt{d+e x}-\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)\right)","2 \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)-2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)-2 b \sqrt{d} n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)-4 b n \sqrt{d+e x}+2 b \sqrt{d} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)^2+4 b \sqrt{d} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)-4 b \sqrt{d} n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)",1,"2*a*Sqrt[d + e*x] - 4*b*n*(Sqrt[d + e*x] - Sqrt[d]*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]) + 2*b*Sqrt[d + e*x]*Log[c*x^n] + Sqrt[d]*(a + b*Log[c*x^n])*Log[Sqrt[d] - Sqrt[d + e*x]] - Sqrt[d]*(a + b*Log[c*x^n])*Log[Sqrt[d] + Sqrt[d + e*x]] - (b*Sqrt[d]*n*(Log[Sqrt[d] - Sqrt[d + e*x]]*(Log[Sqrt[d] - Sqrt[d + e*x]] + 2*Log[(1 + Sqrt[d + e*x]/Sqrt[d])/2]) + 2*PolyLog[2, 1/2 - Sqrt[d + e*x]/(2*Sqrt[d])]))/2 + (b*Sqrt[d]*n*(Log[Sqrt[d] + Sqrt[d + e*x]]*(Log[Sqrt[d] + Sqrt[d + e*x]] + 2*Log[1/2 - Sqrt[d + e*x]/(2*Sqrt[d])]) + 2*PolyLog[2, (1 + Sqrt[d + e*x]/Sqrt[d])/2]))/2","A",1
135,1,392,221,0.335204,"\int \frac{\sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Integrate[(Sqrt[d + e*x]*(a + b*Log[c*x^n]))/x^2,x]","-\frac{4 a \sqrt{d} \sqrt{d+e x}-2 a e x \log \left(\sqrt{d}-\sqrt{d+e x}\right)+2 a e x \log \left(\sqrt{d+e x}+\sqrt{d}\right)-2 b e x \log \left(c x^n\right) \log \left(\sqrt{d}-\sqrt{d+e x}\right)+4 b \sqrt{d} \sqrt{d+e x} \log \left(c x^n\right)+2 b e x \log \left(c x^n\right) \log \left(\sqrt{d+e x}+\sqrt{d}\right)+2 b e n x \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)-2 b e n x \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)+4 b \sqrt{d} n \sqrt{d+e x}+b e n x \log ^2\left(\sqrt{d}-\sqrt{d+e x}\right)-b e n x \log ^2\left(\sqrt{d+e x}+\sqrt{d}\right)+2 b e n x \log \left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right) \log \left(\sqrt{d}-\sqrt{d+e x}\right)-2 b e n x \log \left(\sqrt{d+e x}+\sqrt{d}\right) \log \left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)+4 b e n x \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 \sqrt{d} x}","-\frac{\sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{e \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d}}-\frac{b e n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{\sqrt{d}}-\frac{b n \sqrt{d+e x}}{x}+\frac{b e n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)^2}{\sqrt{d}}-\frac{b e n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{\sqrt{d}}-\frac{2 b e n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{\sqrt{d}}",1,"-1/4*(4*a*Sqrt[d]*Sqrt[d + e*x] + 4*b*Sqrt[d]*n*Sqrt[d + e*x] + 4*b*e*n*x*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + 4*b*Sqrt[d]*Sqrt[d + e*x]*Log[c*x^n] - 2*a*e*x*Log[Sqrt[d] - Sqrt[d + e*x]] - 2*b*e*x*Log[c*x^n]*Log[Sqrt[d] - Sqrt[d + e*x]] + b*e*n*x*Log[Sqrt[d] - Sqrt[d + e*x]]^2 + 2*a*e*x*Log[Sqrt[d] + Sqrt[d + e*x]] + 2*b*e*x*Log[c*x^n]*Log[Sqrt[d] + Sqrt[d + e*x]] - b*e*n*x*Log[Sqrt[d] + Sqrt[d + e*x]]^2 - 2*b*e*n*x*Log[Sqrt[d] + Sqrt[d + e*x]]*Log[1/2 - Sqrt[d + e*x]/(2*Sqrt[d])] + 2*b*e*n*x*Log[Sqrt[d] - Sqrt[d + e*x]]*Log[(1 + Sqrt[d + e*x]/Sqrt[d])/2] + 2*b*e*n*x*PolyLog[2, 1/2 - Sqrt[d + e*x]/(2*Sqrt[d])] - 2*b*e*n*x*PolyLog[2, (1 + Sqrt[d + e*x]/Sqrt[d])/2])/(Sqrt[d]*x)","A",1
136,1,500,298,0.5463231,"\int \frac{\sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Integrate[(Sqrt[d + e*x]*(a + b*Log[c*x^n]))/x^3,x]","-\frac{8 a d^{3/2} \sqrt{d+e x}+2 a e^2 x^2 \log \left(\sqrt{d}-\sqrt{d+e x}\right)-2 a e^2 x^2 \log \left(\sqrt{d+e x}+\sqrt{d}\right)+4 a \sqrt{d} e x \sqrt{d+e x}+8 b d^{3/2} \sqrt{d+e x} \log \left(c x^n\right)+2 b e^2 x^2 \log \left(c x^n\right) \log \left(\sqrt{d}-\sqrt{d+e x}\right)-2 b e^2 x^2 \log \left(c x^n\right) \log \left(\sqrt{d+e x}+\sqrt{d}\right)+4 b \sqrt{d} e x \sqrt{d+e x} \log \left(c x^n\right)+4 b d^{3/2} n \sqrt{d+e x}-2 b e^2 n x^2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)+2 b e^2 n x^2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)-b e^2 n x^2 \log ^2\left(\sqrt{d}-\sqrt{d+e x}\right)+b e^2 n x^2 \log ^2\left(\sqrt{d+e x}+\sqrt{d}\right)+2 b e^2 n x^2 \log \left(\sqrt{d+e x}+\sqrt{d}\right) \log \left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)-2 b e^2 n x^2 \log \left(\sqrt{d}-\sqrt{d+e x}\right) \log \left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)+2 b e^2 n x^2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)+6 b \sqrt{d} e n x \sqrt{d+e x}}{16 d^{3/2} x^2}","\frac{e^2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{4 d^{3/2}}-\frac{e \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{4 d x}-\frac{\sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{2 x^2}+\frac{b e^2 n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{4 d^{3/2}}-\frac{b e^2 n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)^2}{4 d^{3/2}}-\frac{b e^2 n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{8 d^{3/2}}+\frac{b e^2 n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{2 d^{3/2}}-\frac{b n \sqrt{d+e x}}{4 x^2}-\frac{3 b e n \sqrt{d+e x}}{8 d x}",1,"-1/16*(8*a*d^(3/2)*Sqrt[d + e*x] + 4*b*d^(3/2)*n*Sqrt[d + e*x] + 4*a*Sqrt[d]*e*x*Sqrt[d + e*x] + 6*b*Sqrt[d]*e*n*x*Sqrt[d + e*x] + 2*b*e^2*n*x^2*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + 8*b*d^(3/2)*Sqrt[d + e*x]*Log[c*x^n] + 4*b*Sqrt[d]*e*x*Sqrt[d + e*x]*Log[c*x^n] + 2*a*e^2*x^2*Log[Sqrt[d] - Sqrt[d + e*x]] + 2*b*e^2*x^2*Log[c*x^n]*Log[Sqrt[d] - Sqrt[d + e*x]] - b*e^2*n*x^2*Log[Sqrt[d] - Sqrt[d + e*x]]^2 - 2*a*e^2*x^2*Log[Sqrt[d] + Sqrt[d + e*x]] - 2*b*e^2*x^2*Log[c*x^n]*Log[Sqrt[d] + Sqrt[d + e*x]] + b*e^2*n*x^2*Log[Sqrt[d] + Sqrt[d + e*x]]^2 + 2*b*e^2*n*x^2*Log[Sqrt[d] + Sqrt[d + e*x]]*Log[1/2 - Sqrt[d + e*x]/(2*Sqrt[d])] - 2*b*e^2*n*x^2*Log[Sqrt[d] - Sqrt[d + e*x]]*Log[(1 + Sqrt[d + e*x]/Sqrt[d])/2] - 2*b*e^2*n*x^2*PolyLog[2, 1/2 - Sqrt[d + e*x]/(2*Sqrt[d])] + 2*b*e^2*n*x^2*PolyLog[2, (1 + Sqrt[d + e*x]/Sqrt[d])/2])/(d^(3/2)*x^2)","A",1
137,1,187,263,0.3414756,"\int x^3 (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^3*(d + e*x)^(3/2)*(a + b*Log[c*x^n]),x]","\frac{2 \sqrt{d+e x} \left(-3465 a \left(16 d^3-40 d^2 e x+70 d e^2 x^2-105 e^3 x^3\right) (d+e x)^2-3465 b \left(16 d^3-40 d^2 e x+70 d e^2 x^2-105 e^3 x^3\right) (d+e x)^2 \log \left(c x^n\right)+2 b n \left(53308 d^5-12794 d^4 e x+7863 d^3 e^2 x^2-5975 d^2 e^3 x^3-57575 d e^4 x^4-33075 e^5 x^5\right)\right)-221760 b d^{11/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4002075 e^4}","-\frac{2 d^3 (d+e x)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e^4}+\frac{6 d^2 (d+e x)^{7/2} \left(a+b \log \left(c x^n\right)\right)}{7 e^4}-\frac{2 d (d+e x)^{9/2} \left(a+b \log \left(c x^n\right)\right)}{3 e^4}+\frac{2 (d+e x)^{11/2} \left(a+b \log \left(c x^n\right)\right)}{11 e^4}-\frac{64 b d^{11/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{1155 e^4}+\frac{64 b d^5 n \sqrt{d+e x}}{1155 e^4}+\frac{64 b d^4 n (d+e x)^{3/2}}{3465 e^4}+\frac{64 b d^3 n (d+e x)^{5/2}}{5775 e^4}-\frac{172 b d^2 n (d+e x)^{7/2}}{1617 e^4}+\frac{32 b d n (d+e x)^{9/2}}{297 e^4}-\frac{4 b n (d+e x)^{11/2}}{121 e^4}",1,"(-221760*b*d^(11/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + 2*Sqrt[d + e*x]*(-3465*a*(d + e*x)^2*(16*d^3 - 40*d^2*e*x + 70*d*e^2*x^2 - 105*e^3*x^3) + 2*b*n*(53308*d^5 - 12794*d^4*e*x + 7863*d^3*e^2*x^2 - 5975*d^2*e^3*x^3 - 57575*d*e^4*x^4 - 33075*e^5*x^5) - 3465*b*(d + e*x)^2*(16*d^3 - 40*d^2*e*x + 70*d*e^2*x^2 - 105*e^3*x^3)*Log[c*x^n]))/(4002075*e^4)","A",1
138,1,153,213,0.237506,"\int x^2 (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^2*(d + e*x)^(3/2)*(a + b*Log[c*x^n]),x]","\frac{2 \left(\sqrt{d+e x} \left(315 a \left(8 d^2-20 d e x+35 e^2 x^2\right) (d+e x)^2+315 b \left(8 d^2-20 d e x+35 e^2 x^2\right) (d+e x)^2 \log \left(c x^n\right)-2 b n \left(2614 d^4-677 d^3 e x+429 d^2 e^2 x^2+2425 d e^3 x^3+1225 e^4 x^4\right)\right)+5040 b d^{9/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)\right)}{99225 e^3}","\frac{2 d^2 (d+e x)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e^3}-\frac{4 d (d+e x)^{7/2} \left(a+b \log \left(c x^n\right)\right)}{7 e^3}+\frac{2 (d+e x)^{9/2} \left(a+b \log \left(c x^n\right)\right)}{9 e^3}+\frac{32 b d^{9/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{315 e^3}-\frac{32 b d^4 n \sqrt{d+e x}}{315 e^3}-\frac{32 b d^3 n (d+e x)^{3/2}}{945 e^3}-\frac{32 b d^2 n (d+e x)^{5/2}}{1575 e^3}+\frac{44 b d n (d+e x)^{7/2}}{441 e^3}-\frac{4 b n (d+e x)^{9/2}}{81 e^3}",1,"(2*(5040*b*d^(9/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + Sqrt[d + e*x]*(315*a*(d + e*x)^2*(8*d^2 - 20*d*e*x + 35*e^2*x^2) - 2*b*n*(2614*d^4 - 677*d^3*e*x + 429*d^2*e^2*x^2 + 2425*d*e^3*x^3 + 1225*e^4*x^4) + 315*b*(d + e*x)^2*(8*d^2 - 20*d*e*x + 35*e^2*x^2)*Log[c*x^n])))/(99225*e^3)","A",1
139,1,120,163,0.1777735,"\int x (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x*(d + e*x)^(3/2)*(a + b*Log[c*x^n]),x]","-\frac{2 \left(\sqrt{d+e x} \left(105 a (2 d-5 e x) (d+e x)^2+105 b (2 d-5 e x) (d+e x)^2 \log \left(c x^n\right)+2 b n \left(-247 d^3+71 d^2 e x+183 d e^2 x^2+75 e^3 x^3\right)\right)+420 b d^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)\right)}{3675 e^2}","-\frac{2 d (d+e x)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e^2}+\frac{2 (d+e x)^{7/2} \left(a+b \log \left(c x^n\right)\right)}{7 e^2}-\frac{8 b d^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{35 e^2}+\frac{8 b d^3 n \sqrt{d+e x}}{35 e^2}+\frac{8 b d^2 n (d+e x)^{3/2}}{105 e^2}+\frac{8 b d n (d+e x)^{5/2}}{175 e^2}-\frac{4 b n (d+e x)^{7/2}}{49 e^2}",1,"(-2*(420*b*d^(7/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + Sqrt[d + e*x]*(105*a*(2*d - 5*e*x)*(d + e*x)^2 + 2*b*n*(-247*d^3 + 71*d^2*e*x + 183*d*e^2*x^2 + 75*e^3*x^3) + 105*b*(2*d - 5*e*x)*(d + e*x)^2*Log[c*x^n])))/(3675*e^2)","A",1
140,1,87,115,0.1063419,"\int (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(d + e*x)^(3/2)*(a + b*Log[c*x^n]),x]","\frac{2 \left((d+e x)^{5/2} \left(a+b \log \left(c x^n\right)\right)+2 b d^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)-\frac{2}{15} b n \sqrt{d+e x} \left(23 d^2+11 d e x+3 e^2 x^2\right)\right)}{5 e}","\frac{2 (d+e x)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e}+\frac{4 b d^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{5 e}-\frac{4 b d^2 n \sqrt{d+e x}}{5 e}-\frac{4 b d n (d+e x)^{3/2}}{15 e}-\frac{4 b n (d+e x)^{5/2}}{25 e}",1,"(2*((-2*b*n*Sqrt[d + e*x]*(23*d^2 + 11*d*e*x + 3*e^2*x^2))/15 + 2*b*d^(5/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + (d + e*x)^(5/2)*(a + b*Log[c*x^n])))/(5*e)","A",1
141,1,375,255,0.3020786,"\int \frac{(d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[((d + e*x)^(3/2)*(a + b*Log[c*x^n]))/x,x]","d^{3/2} \log \left(\sqrt{d}-\sqrt{d+e x}\right) \left(a+b \log \left(c x^n\right)\right)-d^{3/2} \log \left(\sqrt{d+e x}+\sqrt{d}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2}{3} (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)+2 a d \sqrt{d+e x}+2 b d \sqrt{d+e x} \log \left(c x^n\right)-\frac{1}{2} b d^{3/2} n \left(2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)+\log \left(\sqrt{d}-\sqrt{d+e x}\right) \left(\log \left(\sqrt{d}-\sqrt{d+e x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)\right)\right)+\frac{1}{2} b d^{3/2} n \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)+\log \left(\sqrt{d+e x}+\sqrt{d}\right) \left(\log \left(\sqrt{d+e x}+\sqrt{d}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)\right)\right)-\frac{4}{9} b n (d+e x)^{3/2}+\frac{16}{3} b d n \left(\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)-\sqrt{d+e x}\right)","-2 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2}{3} (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)+2 d \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)-2 b d^{3/2} n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)+2 b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)^2+\frac{16}{3} b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)-4 b d^{3/2} n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)-\frac{4}{9} b n (d+e x)^{3/2}-\frac{16}{3} b d n \sqrt{d+e x}",1,"2*a*d*Sqrt[d + e*x] - (4*b*n*(d + e*x)^(3/2))/9 + (16*b*d*n*(-Sqrt[d + e*x] + Sqrt[d]*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]))/3 + 2*b*d*Sqrt[d + e*x]*Log[c*x^n] + (2*(d + e*x)^(3/2)*(a + b*Log[c*x^n]))/3 + d^(3/2)*(a + b*Log[c*x^n])*Log[Sqrt[d] - Sqrt[d + e*x]] - d^(3/2)*(a + b*Log[c*x^n])*Log[Sqrt[d] + Sqrt[d + e*x]] - (b*d^(3/2)*n*(Log[Sqrt[d] - Sqrt[d + e*x]]*(Log[Sqrt[d] - Sqrt[d + e*x]] + 2*Log[(1 + Sqrt[d + e*x]/Sqrt[d])/2]) + 2*PolyLog[2, 1/2 - Sqrt[d + e*x]/(2*Sqrt[d])]))/2 + (b*d^(3/2)*n*(Log[Sqrt[d] + Sqrt[d + e*x]]*(Log[Sqrt[d] + Sqrt[d + e*x]] + 2*Log[1/2 - Sqrt[d + e*x]/(2*Sqrt[d])]) + 2*PolyLog[2, (1 + Sqrt[d + e*x]/Sqrt[d])/2]))/2","A",1
142,1,480,259,0.3409095,"\int \frac{(d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Integrate[((d + e*x)^(3/2)*(a + b*Log[c*x^n]))/x^2,x]","\frac{-4 a d \sqrt{d+e x}+8 a e x \sqrt{d+e x}+6 a \sqrt{d} e x \log \left(\sqrt{d}-\sqrt{d+e x}\right)-6 a \sqrt{d} e x \log \left(\sqrt{d+e x}+\sqrt{d}\right)+6 b \sqrt{d} e x \log \left(c x^n\right) \log \left(\sqrt{d}-\sqrt{d+e x}\right)-4 b d \sqrt{d+e x} \log \left(c x^n\right)+8 b e x \sqrt{d+e x} \log \left(c x^n\right)-6 b \sqrt{d} e x \log \left(c x^n\right) \log \left(\sqrt{d+e x}+\sqrt{d}\right)-6 b \sqrt{d} e n x \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)+6 b \sqrt{d} e n x \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)-4 b d n \sqrt{d+e x}-16 b e n x \sqrt{d+e x}-3 b \sqrt{d} e n x \log ^2\left(\sqrt{d}-\sqrt{d+e x}\right)+3 b \sqrt{d} e n x \log ^2\left(\sqrt{d+e x}+\sqrt{d}\right)-6 b \sqrt{d} e n x \log \left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right) \log \left(\sqrt{d}-\sqrt{d+e x}\right)+6 b \sqrt{d} e n x \log \left(\sqrt{d+e x}+\sqrt{d}\right) \log \left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)+12 b \sqrt{d} e n x \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 x}","-\frac{(d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x}+3 e \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)-3 \sqrt{d} e \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)-3 b \sqrt{d} e n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)-4 b e n \sqrt{d+e x}-\frac{b d n \sqrt{d+e x}}{x}+3 b \sqrt{d} e n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)^2+3 b \sqrt{d} e n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)-6 b \sqrt{d} e n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)",1,"(-4*a*d*Sqrt[d + e*x] - 4*b*d*n*Sqrt[d + e*x] + 8*a*e*x*Sqrt[d + e*x] - 16*b*e*n*x*Sqrt[d + e*x] + 12*b*Sqrt[d]*e*n*x*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] - 4*b*d*Sqrt[d + e*x]*Log[c*x^n] + 8*b*e*x*Sqrt[d + e*x]*Log[c*x^n] + 6*a*Sqrt[d]*e*x*Log[Sqrt[d] - Sqrt[d + e*x]] + 6*b*Sqrt[d]*e*x*Log[c*x^n]*Log[Sqrt[d] - Sqrt[d + e*x]] - 3*b*Sqrt[d]*e*n*x*Log[Sqrt[d] - Sqrt[d + e*x]]^2 - 6*a*Sqrt[d]*e*x*Log[Sqrt[d] + Sqrt[d + e*x]] - 6*b*Sqrt[d]*e*x*Log[c*x^n]*Log[Sqrt[d] + Sqrt[d + e*x]] + 3*b*Sqrt[d]*e*n*x*Log[Sqrt[d] + Sqrt[d + e*x]]^2 + 6*b*Sqrt[d]*e*n*x*Log[Sqrt[d] + Sqrt[d + e*x]]*Log[1/2 - Sqrt[d + e*x]/(2*Sqrt[d])] - 6*b*Sqrt[d]*e*n*x*Log[Sqrt[d] - Sqrt[d + e*x]]*Log[(1 + Sqrt[d + e*x]/Sqrt[d])/2] - 6*b*Sqrt[d]*e*n*x*PolyLog[2, 1/2 - Sqrt[d + e*x]/(2*Sqrt[d])] + 6*b*Sqrt[d]*e*n*x*PolyLog[2, (1 + Sqrt[d + e*x]/Sqrt[d])/2])/(4*x)","A",1
143,1,501,293,0.6032733,"\int \frac{(d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Integrate[((d + e*x)^(3/2)*(a + b*Log[c*x^n]))/x^3,x]","-\frac{8 a d^{3/2} \sqrt{d+e x}-6 a e^2 x^2 \log \left(\sqrt{d}-\sqrt{d+e x}\right)+6 a e^2 x^2 \log \left(\sqrt{d+e x}+\sqrt{d}\right)+20 a \sqrt{d} e x \sqrt{d+e x}+8 b d^{3/2} \sqrt{d+e x} \log \left(c x^n\right)-6 b e^2 x^2 \log \left(c x^n\right) \log \left(\sqrt{d}-\sqrt{d+e x}\right)+6 b e^2 x^2 \log \left(c x^n\right) \log \left(\sqrt{d+e x}+\sqrt{d}\right)+20 b \sqrt{d} e x \sqrt{d+e x} \log \left(c x^n\right)+4 b d^{3/2} n \sqrt{d+e x}+6 b e^2 n x^2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)-6 b e^2 n x^2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)+3 b e^2 n x^2 \log ^2\left(\sqrt{d}-\sqrt{d+e x}\right)-3 b e^2 n x^2 \log ^2\left(\sqrt{d+e x}+\sqrt{d}\right)-6 b e^2 n x^2 \log \left(\sqrt{d+e x}+\sqrt{d}\right) \log \left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)+6 b e^2 n x^2 \log \left(\sqrt{d}-\sqrt{d+e x}\right) \log \left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)+18 b e^2 n x^2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)+22 b \sqrt{d} e n x \sqrt{d+e x}}{16 \sqrt{d} x^2}","-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{4 \sqrt{d}}-\frac{3 e \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{4 x}-\frac{(d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{3 b e^2 n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{4 \sqrt{d}}+\frac{3 b e^2 n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)^2}{4 \sqrt{d}}-\frac{9 b e^2 n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{8 \sqrt{d}}-\frac{3 b e^2 n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{2 \sqrt{d}}-\frac{b d n \sqrt{d+e x}}{4 x^2}-\frac{11 b e n \sqrt{d+e x}}{8 x}",1,"-1/16*(8*a*d^(3/2)*Sqrt[d + e*x] + 4*b*d^(3/2)*n*Sqrt[d + e*x] + 20*a*Sqrt[d]*e*x*Sqrt[d + e*x] + 22*b*Sqrt[d]*e*n*x*Sqrt[d + e*x] + 18*b*e^2*n*x^2*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + 8*b*d^(3/2)*Sqrt[d + e*x]*Log[c*x^n] + 20*b*Sqrt[d]*e*x*Sqrt[d + e*x]*Log[c*x^n] - 6*a*e^2*x^2*Log[Sqrt[d] - Sqrt[d + e*x]] - 6*b*e^2*x^2*Log[c*x^n]*Log[Sqrt[d] - Sqrt[d + e*x]] + 3*b*e^2*n*x^2*Log[Sqrt[d] - Sqrt[d + e*x]]^2 + 6*a*e^2*x^2*Log[Sqrt[d] + Sqrt[d + e*x]] + 6*b*e^2*x^2*Log[c*x^n]*Log[Sqrt[d] + Sqrt[d + e*x]] - 3*b*e^2*n*x^2*Log[Sqrt[d] + Sqrt[d + e*x]]^2 - 6*b*e^2*n*x^2*Log[Sqrt[d] + Sqrt[d + e*x]]*Log[1/2 - Sqrt[d + e*x]/(2*Sqrt[d])] + 6*b*e^2*n*x^2*Log[Sqrt[d] - Sqrt[d + e*x]]*Log[(1 + Sqrt[d + e*x]/Sqrt[d])/2] + 6*b*e^2*n*x^2*PolyLog[2, 1/2 - Sqrt[d + e*x]/(2*Sqrt[d])] - 6*b*e^2*n*x^2*PolyLog[2, (1 + Sqrt[d + e*x]/Sqrt[d])/2])/(Sqrt[d]*x^2)","A",1
144,1,150,217,0.2319327,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d+e x}} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/Sqrt[d + e*x],x]","-\frac{2 \left(\sqrt{d+e x} \left(105 a \left(16 d^3-8 d^2 e x+6 d e^2 x^2-5 e^3 x^3\right)+105 b \left(16 d^3-8 d^2 e x+6 d e^2 x^2-5 e^3 x^3\right) \log \left(c x^n\right)+2 b n \left(-1276 d^3+218 d^2 e x-111 d e^2 x^2+75 e^3 x^3\right)\right)+3360 b d^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)\right)}{3675 e^4}","-\frac{2 d^3 \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{e^4}+\frac{2 d^2 (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{e^4}-\frac{6 d (d+e x)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e^4}+\frac{2 (d+e x)^{7/2} \left(a+b \log \left(c x^n\right)\right)}{7 e^4}-\frac{64 b d^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{35 e^4}+\frac{64 b d^3 n \sqrt{d+e x}}{35 e^4}-\frac{76 b d^2 n (d+e x)^{3/2}}{105 e^4}+\frac{64 b d n (d+e x)^{5/2}}{175 e^4}-\frac{4 b n (d+e x)^{7/2}}{49 e^4}",1,"(-2*(3360*b*d^(7/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + Sqrt[d + e*x]*(105*a*(16*d^3 - 8*d^2*e*x + 6*d*e^2*x^2 - 5*e^3*x^3) + 2*b*n*(-1276*d^3 + 218*d^2*e*x - 111*d*e^2*x^2 + 75*e^3*x^3) + 105*b*(16*d^3 - 8*d^2*e*x + 6*d*e^2*x^2 - 5*e^3*x^3)*Log[c*x^n])))/(3675*e^4)","A",1
145,1,118,169,0.1800947,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d+e x}} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(15 a \left(8 d^2-4 d e x+3 e^2 x^2\right)+15 b \left(8 d^2-4 d e x+3 e^2 x^2\right) \log \left(c x^n\right)-2 b n \left(94 d^2-17 d e x+9 e^2 x^2\right)\right)+480 b d^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{225 e^3}","\frac{2 d^2 \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{e^3}-\frac{4 d (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 e^3}+\frac{2 (d+e x)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e^3}+\frac{32 b d^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{15 e^3}-\frac{32 b d^2 n \sqrt{d+e x}}{15 e^3}+\frac{28 b d n (d+e x)^{3/2}}{45 e^3}-\frac{4 b n (d+e x)^{5/2}}{25 e^3}",1,"(480*b*d^(5/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + 2*Sqrt[d + e*x]*(15*a*(8*d^2 - 4*d*e*x + 3*e^2*x^2) - 2*b*n*(94*d^2 - 17*d*e*x + 9*e^2*x^2) + 15*b*(8*d^2 - 4*d*e*x + 3*e^2*x^2)*Log[c*x^n]))/(225*e^3)","A",1
146,1,80,119,0.1110603,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d+e x}} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/Sqrt[d + e*x],x]","-\frac{2 \left(\sqrt{d+e x} \left(6 a d-3 a e x+b (6 d-3 e x) \log \left(c x^n\right)-10 b d n+2 b e n x\right)+12 b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)\right)}{9 e^2}","-\frac{2 d \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{2 (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 e^2}-\frac{8 b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{3 e^2}+\frac{8 b d n \sqrt{d+e x}}{3 e^2}-\frac{4 b n (d+e x)^{3/2}}{9 e^2}",1,"(-2*(12*b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + Sqrt[d + e*x]*(6*a*d - 10*b*d*n - 3*a*e*x + 2*b*e*n*x + b*(6*d - 3*e*x)*Log[c*x^n])))/(9*e^2)","A",1
147,1,55,69,0.0431055,"\int \frac{a+b \log \left(c x^n\right)}{\sqrt{d+e x}} \, dx","Integrate[(a + b*Log[c*x^n])/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(a+b \log \left(c x^n\right)-2 b n\right)+4 b \sqrt{d} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{e}","\frac{2 \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{4 b n \sqrt{d+e x}}{e}+\frac{4 b \sqrt{d} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{e}",1,"(4*b*Sqrt[d]*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + 2*Sqrt[d + e*x]*(a - 2*b*n + b*Log[c*x^n]))/e","A",1
148,1,249,152,0.0991031,"\int \frac{a+b \log \left(c x^n\right)}{x \sqrt{d+e x}} \, dx","Integrate[(a + b*Log[c*x^n])/(x*Sqrt[d + e*x]),x]","\frac{2 \log \left(\sqrt{d}-\sqrt{d+e x}\right) \left(a+b \log \left(c x^n\right)\right)-2 \log \left(\sqrt{d+e x}+\sqrt{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \left(2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)+\log \left(\sqrt{d}-\sqrt{d+e x}\right) \left(\log \left(\sqrt{d}-\sqrt{d+e x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)\right)\right)+b n \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)+\log \left(\sqrt{d+e x}+\sqrt{d}\right) \left(\log \left(\sqrt{d+e x}+\sqrt{d}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)\right)\right)}{2 \sqrt{d}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d}}-\frac{2 b n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{\sqrt{d}}+\frac{2 b n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)^2}{\sqrt{d}}-\frac{4 b n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{\sqrt{d}}",1,"(2*(a + b*Log[c*x^n])*Log[Sqrt[d] - Sqrt[d + e*x]] - 2*(a + b*Log[c*x^n])*Log[Sqrt[d] + Sqrt[d + e*x]] - b*n*(Log[Sqrt[d] - Sqrt[d + e*x]]*(Log[Sqrt[d] - Sqrt[d + e*x]] + 2*Log[(1 + Sqrt[d + e*x]/Sqrt[d])/2]) + 2*PolyLog[2, 1/2 - Sqrt[d + e*x]/(2*Sqrt[d])]) + b*n*(Log[Sqrt[d] + Sqrt[d + e*x]]*(Log[Sqrt[d] + Sqrt[d + e*x]] + 2*Log[1/2 - Sqrt[d + e*x]/(2*Sqrt[d])]) + 2*PolyLog[2, (1 + Sqrt[d + e*x]/Sqrt[d])/2]))/(2*Sqrt[d])","A",1
149,1,392,226,0.2606595,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \sqrt{d+e x}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*Sqrt[d + e*x]),x]","-\frac{4 a \sqrt{d} \sqrt{d+e x}+2 a e x \log \left(\sqrt{d}-\sqrt{d+e x}\right)-2 a e x \log \left(\sqrt{d+e x}+\sqrt{d}\right)+2 b e x \log \left(c x^n\right) \log \left(\sqrt{d}-\sqrt{d+e x}\right)+4 b \sqrt{d} \sqrt{d+e x} \log \left(c x^n\right)-2 b e x \log \left(c x^n\right) \log \left(\sqrt{d+e x}+\sqrt{d}\right)-2 b e n x \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)+2 b e n x \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)+4 b \sqrt{d} n \sqrt{d+e x}-b e n x \log ^2\left(\sqrt{d}-\sqrt{d+e x}\right)+b e n x \log ^2\left(\sqrt{d+e x}+\sqrt{d}\right)-2 b e n x \log \left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right) \log \left(\sqrt{d}-\sqrt{d+e x}\right)+2 b e n x \log \left(\sqrt{d+e x}+\sqrt{d}\right) \log \left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)+4 b e n x \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 d^{3/2} x}","\frac{e \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{d^{3/2}}-\frac{\sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{d x}+\frac{b e n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{d^{3/2}}-\frac{b e n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)^2}{d^{3/2}}-\frac{b e n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{d^{3/2}}+\frac{2 b e n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{b n \sqrt{d+e x}}{d x}",1,"-1/4*(4*a*Sqrt[d]*Sqrt[d + e*x] + 4*b*Sqrt[d]*n*Sqrt[d + e*x] + 4*b*e*n*x*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + 4*b*Sqrt[d]*Sqrt[d + e*x]*Log[c*x^n] + 2*a*e*x*Log[Sqrt[d] - Sqrt[d + e*x]] + 2*b*e*x*Log[c*x^n]*Log[Sqrt[d] - Sqrt[d + e*x]] - b*e*n*x*Log[Sqrt[d] - Sqrt[d + e*x]]^2 - 2*a*e*x*Log[Sqrt[d] + Sqrt[d + e*x]] - 2*b*e*x*Log[c*x^n]*Log[Sqrt[d] + Sqrt[d + e*x]] + b*e*n*x*Log[Sqrt[d] + Sqrt[d + e*x]]^2 + 2*b*e*n*x*Log[Sqrt[d] + Sqrt[d + e*x]]*Log[1/2 - Sqrt[d + e*x]/(2*Sqrt[d])] - 2*b*e*n*x*Log[Sqrt[d] - Sqrt[d + e*x]]*Log[(1 + Sqrt[d + e*x]/Sqrt[d])/2] - 2*b*e*n*x*PolyLog[2, 1/2 - Sqrt[d + e*x]/(2*Sqrt[d])] + 2*b*e*n*x*PolyLog[2, (1 + Sqrt[d + e*x]/Sqrt[d])/2])/(d^(3/2)*x)","A",1
150,1,501,304,0.4255026,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \sqrt{d+e x}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^3*Sqrt[d + e*x]),x]","\frac{-8 a d^{3/2} \sqrt{d+e x}+6 a e^2 x^2 \log \left(\sqrt{d}-\sqrt{d+e x}\right)-6 a e^2 x^2 \log \left(\sqrt{d+e x}+\sqrt{d}\right)+12 a \sqrt{d} e x \sqrt{d+e x}-8 b d^{3/2} \sqrt{d+e x} \log \left(c x^n\right)+6 b e^2 x^2 \log \left(c x^n\right) \log \left(\sqrt{d}-\sqrt{d+e x}\right)-6 b e^2 x^2 \log \left(c x^n\right) \log \left(\sqrt{d+e x}+\sqrt{d}\right)+12 b \sqrt{d} e x \sqrt{d+e x} \log \left(c x^n\right)-4 b d^{3/2} n \sqrt{d+e x}-6 b e^2 n x^2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)+6 b e^2 n x^2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)-3 b e^2 n x^2 \log ^2\left(\sqrt{d}-\sqrt{d+e x}\right)+3 b e^2 n x^2 \log ^2\left(\sqrt{d+e x}+\sqrt{d}\right)+6 b e^2 n x^2 \log \left(\sqrt{d+e x}+\sqrt{d}\right) \log \left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)-6 b e^2 n x^2 \log \left(\sqrt{d}-\sqrt{d+e x}\right) \log \left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)+14 b e^2 n x^2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)+10 b \sqrt{d} e n x \sqrt{d+e x}}{16 d^{5/2} x^2}","-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{4 d^{5/2}}+\frac{3 e \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{4 d^2 x}-\frac{\sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{2 d x^2}-\frac{3 b e^2 n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{4 d^{5/2}}+\frac{3 b e^2 n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)^2}{4 d^{5/2}}+\frac{7 b e^2 n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{8 d^{5/2}}-\frac{3 b e^2 n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{2 d^{5/2}}+\frac{5 b e n \sqrt{d+e x}}{8 d^2 x}-\frac{b n \sqrt{d+e x}}{4 d x^2}",1,"(-8*a*d^(3/2)*Sqrt[d + e*x] - 4*b*d^(3/2)*n*Sqrt[d + e*x] + 12*a*Sqrt[d]*e*x*Sqrt[d + e*x] + 10*b*Sqrt[d]*e*n*x*Sqrt[d + e*x] + 14*b*e^2*n*x^2*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] - 8*b*d^(3/2)*Sqrt[d + e*x]*Log[c*x^n] + 12*b*Sqrt[d]*e*x*Sqrt[d + e*x]*Log[c*x^n] + 6*a*e^2*x^2*Log[Sqrt[d] - Sqrt[d + e*x]] + 6*b*e^2*x^2*Log[c*x^n]*Log[Sqrt[d] - Sqrt[d + e*x]] - 3*b*e^2*n*x^2*Log[Sqrt[d] - Sqrt[d + e*x]]^2 - 6*a*e^2*x^2*Log[Sqrt[d] + Sqrt[d + e*x]] - 6*b*e^2*x^2*Log[c*x^n]*Log[Sqrt[d] + Sqrt[d + e*x]] + 3*b*e^2*n*x^2*Log[Sqrt[d] + Sqrt[d + e*x]]^2 + 6*b*e^2*n*x^2*Log[Sqrt[d] + Sqrt[d + e*x]]*Log[1/2 - Sqrt[d + e*x]/(2*Sqrt[d])] - 6*b*e^2*n*x^2*Log[Sqrt[d] - Sqrt[d + e*x]]*Log[(1 + Sqrt[d + e*x]/Sqrt[d])/2] - 6*b*e^2*n*x^2*PolyLog[2, 1/2 - Sqrt[d + e*x]/(2*Sqrt[d])] + 6*b*e^2*n*x^2*PolyLog[2, (1 + Sqrt[d + e*x]/Sqrt[d])/2])/(16*d^(5/2)*x^2)","A",1
151,1,159,194,0.1311639,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^{3/2}} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/(d + e*x)^(3/2),x]","\frac{480 a d^3+240 a d^2 e x-60 a d e^2 x^2+30 a e^3 x^3+30 b \left(16 d^3+8 d^2 e x-2 d e^2 x^2+e^3 x^3\right) \log \left(c x^n\right)+960 b d^{5/2} n \sqrt{d+e x} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)-592 b d^3 n-536 b d^2 e n x+44 b d e^2 n x^2-12 b e^3 n x^3}{75 e^4 \sqrt{d+e x}}","\frac{2 d^3 \left(a+b \log \left(c x^n\right)\right)}{e^4 \sqrt{d+e x}}+\frac{6 d^2 \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{e^4}-\frac{2 d (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{e^4}+\frac{2 (d+e x)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e^4}+\frac{64 b d^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{5 e^4}-\frac{44 b d^2 n \sqrt{d+e x}}{5 e^4}+\frac{16 b d n (d+e x)^{3/2}}{15 e^4}-\frac{4 b n (d+e x)^{5/2}}{25 e^4}",1,"(480*a*d^3 - 592*b*d^3*n + 240*a*d^2*e*x - 536*b*d^2*e*n*x - 60*a*d*e^2*x^2 + 44*b*d*e^2*n*x^2 + 30*a*e^3*x^3 - 12*b*e^3*n*x^3 + 960*b*d^(5/2)*n*Sqrt[d + e*x]*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + 30*b*(16*d^3 + 8*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3)*Log[c*x^n])/(75*e^4*Sqrt[d + e*x])","A",1
152,1,124,146,0.0968387,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^{3/2}} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e*x)^(3/2),x]","\frac{-48 a d^2-24 a d e x+6 a e^2 x^2-6 b \left(8 d^2+4 d e x-e^2 x^2\right) \log \left(c x^n\right)-96 b d^{3/2} n \sqrt{d+e x} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)+56 b d^2 n+52 b d e n x-4 b e^2 n x^2}{9 e^3 \sqrt{d+e x}}","-\frac{2 d^2 \left(a+b \log \left(c x^n\right)\right)}{e^3 \sqrt{d+e x}}-\frac{4 d \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{e^3}+\frac{2 (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 e^3}-\frac{32 b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{3 e^3}+\frac{20 b d n \sqrt{d+e x}}{3 e^3}-\frac{4 b n (d+e x)^{3/2}}{9 e^3}",1,"(-48*a*d^2 + 56*b*d^2*n - 24*a*d*e*x + 52*b*d*e*n*x + 6*a*e^2*x^2 - 4*b*e^2*n*x^2 - 96*b*d^(3/2)*n*Sqrt[d + e*x]*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] - 6*b*(8*d^2 + 4*d*e*x - e^2*x^2)*Log[c*x^n])/(9*e^3*Sqrt[d + e*x])","A",1
153,1,83,94,0.0712274,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^{3/2}} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/(d + e*x)^(3/2),x]","\frac{2 \left(2 a d+a e x+b (2 d+e x) \log \left(c x^n\right)+4 b \sqrt{d} n \sqrt{d+e x} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)-2 b d n-2 b e n x\right)}{e^2 \sqrt{d+e x}}","\frac{2 \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{2 d \left(a+b \log \left(c x^n\right)\right)}{e^2 \sqrt{d+e x}}-\frac{4 b n \sqrt{d+e x}}{e^2}+\frac{8 b \sqrt{d} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{e^2}",1,"(2*(2*a*d - 2*b*d*n + a*e*x - 2*b*e*n*x + 4*b*Sqrt[d]*n*Sqrt[d + e*x]*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + b*(2*d + e*x)*Log[c*x^n]))/(e^2*Sqrt[d + e*x])","A",1
154,1,53,53,0.0434356,"\int \frac{a+b \log \left(c x^n\right)}{(d+e x)^{3/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*x)^(3/2),x]","-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{e \sqrt{d+e x}}-\frac{4 b n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{\sqrt{d} e}","-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{e \sqrt{d+e x}}-\frac{4 b n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{\sqrt{d} e}",1,"(-4*b*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(Sqrt[d]*e) - (2*(a + b*Log[c*x^n]))/(e*Sqrt[d + e*x])","A",1
155,1,295,201,0.2792312,"\int \frac{a+b \log \left(c x^n\right)}{x (d+e x)^{3/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x)^(3/2)),x]","\frac{\frac{4 \sqrt{d} \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d+e x}}+2 \log \left(\sqrt{d}-\sqrt{d+e x}\right) \left(a+b \log \left(c x^n\right)\right)-2 \log \left(\sqrt{d+e x}+\sqrt{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \left(2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)+\log \left(\sqrt{d}-\sqrt{d+e x}\right) \left(\log \left(\sqrt{d}-\sqrt{d+e x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)\right)\right)+b n \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt{d+e x}}{\sqrt{d}}+1\right)\right)+\log \left(\sqrt{d+e x}+\sqrt{d}\right) \left(\log \left(\sqrt{d+e x}+\sqrt{d}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{d+e x}}{2 \sqrt{d}}\right)\right)\right)+8 b n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{2 d^{3/2}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{d^{3/2}}+\frac{2 \left(a+b \log \left(c x^n\right)\right)}{d \sqrt{d+e x}}-\frac{2 b n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{d^{3/2}}+\frac{2 b n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)^2}{d^{3/2}}+\frac{4 b n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{4 b n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{d^{3/2}}",1,"(8*b*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + (4*Sqrt[d]*(a + b*Log[c*x^n]))/Sqrt[d + e*x] + 2*(a + b*Log[c*x^n])*Log[Sqrt[d] - Sqrt[d + e*x]] - 2*(a + b*Log[c*x^n])*Log[Sqrt[d] + Sqrt[d + e*x]] - b*n*(Log[Sqrt[d] - Sqrt[d + e*x]]*(Log[Sqrt[d] - Sqrt[d + e*x]] + 2*Log[(1 + Sqrt[d + e*x]/Sqrt[d])/2]) + 2*PolyLog[2, 1/2 - Sqrt[d + e*x]/(2*Sqrt[d])]) + b*n*(Log[Sqrt[d] + Sqrt[d + e*x]]*(Log[Sqrt[d] + Sqrt[d + e*x]] + 2*Log[1/2 - Sqrt[d + e*x]/(2*Sqrt[d])]) + 2*PolyLog[2, (1 + Sqrt[d + e*x]/Sqrt[d])/2]))/(2*d^(3/2))","A",1
156,1,506,253,0.4929999,"\int \frac{a+b \log \left(c x^n\right)}{x^2 (d+e x)^{3/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*(d + e*x)^(3/2)),x]","2 e \left(-\frac{3 \log \left(\sqrt{d}-\sqrt{d+e x}\right) \left(a+b \log \left(c x^n\right)\right)}{4 d^{5/2}}+\frac{3 \log \left(\sqrt{d+e x}+\sqrt{d}\right) \left(a+b \log \left(c x^n\right)\right)}{4 d^{5/2}}-\frac{a+b \log \left(c x^n\right)}{d^2 \sqrt{d+e x}}+\frac{a+b \log \left(c x^n\right)}{4 d^2 \left(\sqrt{d}-\sqrt{d+e x}\right)}-\frac{a+b \log \left(c x^n\right)}{4 d^2 \left(\sqrt{d+e x}+\sqrt{d}\right)}+\frac{3 b n \left(2 \text{Li}_2\left(\frac{\sqrt{d}-\sqrt{d+e x}}{2 \sqrt{d}}\right)+\log ^2\left(\sqrt{d}-\sqrt{d+e x}\right)+2 \log \left(\frac{\sqrt{d+e x}+\sqrt{d}}{2 \sqrt{d}}\right) \log \left(\sqrt{d}-\sqrt{d+e x}\right)\right)}{8 d^{5/2}}-\frac{3 b n \left(2 \text{Li}_2\left(\frac{\sqrt{d}+\sqrt{d+e x}}{2 \sqrt{d}}\right)+\log ^2\left(\sqrt{d+e x}+\sqrt{d}\right)+2 \log \left(\frac{\sqrt{d}-\sqrt{d+e x}}{2 \sqrt{d}}\right) \log \left(\sqrt{d+e x}+\sqrt{d}\right)\right)}{8 d^{5/2}}-\frac{2 b n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{d^{5/2}}+\frac{b n \left(\frac{1}{\sqrt{d}-\sqrt{d+e x}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{\sqrt{d}}\right)}{4 d^2}-\frac{b n \left(\frac{1}{\sqrt{d+e x}+\sqrt{d}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{\sqrt{d}}\right)}{4 d^2}\right)","\frac{3 e \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{d^{5/2}}-\frac{3 e \left(a+b \log \left(c x^n\right)\right)}{d^2 \sqrt{d+e x}}-\frac{a+b \log \left(c x^n\right)}{d x \sqrt{d+e x}}+\frac{3 b e n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{d^{5/2}}-\frac{3 b e n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)^2}{d^{5/2}}-\frac{5 b e n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{d^{5/2}}+\frac{6 b e n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{d^{5/2}}-\frac{b n \sqrt{d+e x}}{d^2 x}",1,"2*e*((-2*b*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/d^(5/2) + (b*n*((Sqrt[d] - Sqrt[d + e*x])^(-1) - ArcTanh[Sqrt[d + e*x]/Sqrt[d]]/Sqrt[d]))/(4*d^2) - (b*n*((Sqrt[d] + Sqrt[d + e*x])^(-1) + ArcTanh[Sqrt[d + e*x]/Sqrt[d]]/Sqrt[d]))/(4*d^2) - (a + b*Log[c*x^n])/(d^2*Sqrt[d + e*x]) + (a + b*Log[c*x^n])/(4*d^2*(Sqrt[d] - Sqrt[d + e*x])) - (a + b*Log[c*x^n])/(4*d^2*(Sqrt[d] + Sqrt[d + e*x])) - (3*(a + b*Log[c*x^n])*Log[Sqrt[d] - Sqrt[d + e*x]])/(4*d^(5/2)) + (3*(a + b*Log[c*x^n])*Log[Sqrt[d] + Sqrt[d + e*x]])/(4*d^(5/2)) + (3*b*n*(Log[Sqrt[d] - Sqrt[d + e*x]]^2 + 2*Log[Sqrt[d] - Sqrt[d + e*x]]*Log[(Sqrt[d] + Sqrt[d + e*x])/(2*Sqrt[d])] + 2*PolyLog[2, (Sqrt[d] - Sqrt[d + e*x])/(2*Sqrt[d])]))/(8*d^(5/2)) - (3*b*n*(2*Log[(Sqrt[d] - Sqrt[d + e*x])/(2*Sqrt[d])]*Log[Sqrt[d] + Sqrt[d + e*x]] + Log[Sqrt[d] + Sqrt[d + e*x]]^2 + 2*PolyLog[2, (Sqrt[d] + Sqrt[d + e*x])/(2*Sqrt[d])]))/(8*d^(5/2)))","A",1
157,0,0,26,1.3454331,"\int \frac{x^2}{(d+e x) \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[x^2/((d + e*x)*(a + b*Log[c*x^n])),x]","\int \frac{x^2}{(d+e x) \left(a+b \log \left(c x^n\right)\right)} \, dx","\text{Int}\left(\frac{x^2}{(d+e x) \left(a+b \log \left(c x^n\right)\right)},x\right)",0,"Integrate[x^2/((d + e*x)*(a + b*Log[c*x^n])), x]","A",-1
158,0,0,24,0.761258,"\int \frac{x}{(d+e x) \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[x/((d + e*x)*(a + b*Log[c*x^n])),x]","\int \frac{x}{(d+e x) \left(a+b \log \left(c x^n\right)\right)} \, dx","\text{Int}\left(\frac{x}{(d+e x) \left(a+b \log \left(c x^n\right)\right)},x\right)",0,"Integrate[x/((d + e*x)*(a + b*Log[c*x^n])), x]","A",-1
159,0,0,23,0.0221965,"\int \frac{1}{(d+e x) \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/((d + e*x)*(a + b*Log[c*x^n])),x]","\int \frac{1}{(d+e x) \left(a+b \log \left(c x^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{(d+e x) \left(a+b \log \left(c x^n\right)\right)},x\right)",0,"Integrate[1/((d + e*x)*(a + b*Log[c*x^n])), x]","A",-1
160,0,0,26,0.2732171,"\int \frac{1}{x (d+e x) \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x*(d + e*x)*(a + b*Log[c*x^n])),x]","\int \frac{1}{x (d+e x) \left(a+b \log \left(c x^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{x (d+e x) \left(a+b \log \left(c x^n\right)\right)},x\right)",0,"Integrate[1/(x*(d + e*x)*(a + b*Log[c*x^n])), x]","A",-1
161,0,0,26,0.6414283,"\int \frac{1}{x^2 (d+e x) \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x^2*(d + e*x)*(a + b*Log[c*x^n])),x]","\int \frac{1}{x^2 (d+e x) \left(a+b \log \left(c x^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 (d+e x) \left(a+b \log \left(c x^n\right)\right)},x\right)",0,"Integrate[1/(x^2*(d + e*x)*(a + b*Log[c*x^n])), x]","A",-1
162,1,152,211,0.2358896,"\int (f x)^m (d+e x)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^m*(d + e*x)^3*(a + b*Log[c*x^n]),x]","x (f x)^m \left(\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{m+1}+\frac{3 d^2 e x \left(a+b \log \left(c x^n\right)\right)}{m+2}+\frac{3 d e^2 x^2 \left(a+b \log \left(c x^n\right)\right)}{m+3}+\frac{e^3 x^3 \left(a+b \log \left(c x^n\right)\right)}{m+4}-\frac{b d^3 n}{(m+1)^2}-\frac{3 b d^2 e n x}{(m+2)^2}-\frac{3 b d e^2 n x^2}{(m+3)^2}-\frac{b e^3 n x^3}{(m+4)^2}\right)","\frac{d^3 (f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+1)}+\frac{3 d^2 e (f x)^{m+2} \left(a+b \log \left(c x^n\right)\right)}{f^2 (m+2)}+\frac{3 d e^2 (f x)^{m+3} \left(a+b \log \left(c x^n\right)\right)}{f^3 (m+3)}+\frac{e^3 (f x)^{m+4} \left(a+b \log \left(c x^n\right)\right)}{f^4 (m+4)}-\frac{b d^3 n (f x)^{m+1}}{f (m+1)^2}-\frac{3 b d^2 e n (f x)^{m+2}}{f^2 (m+2)^2}-\frac{3 b d e^2 n (f x)^{m+3}}{f^3 (m+3)^2}-\frac{b e^3 n (f x)^{m+4}}{f^4 (m+4)^2}",1,"x*(f*x)^m*(-((b*d^3*n)/(1 + m)^2) - (3*b*d^2*e*n*x)/(2 + m)^2 - (3*b*d*e^2*n*x^2)/(3 + m)^2 - (b*e^3*n*x^3)/(4 + m)^2 + (d^3*(a + b*Log[c*x^n]))/(1 + m) + (3*d^2*e*x*(a + b*Log[c*x^n]))/(2 + m) + (3*d*e^2*x^2*(a + b*Log[c*x^n]))/(3 + m) + (e^3*x^3*(a + b*Log[c*x^n]))/(4 + m))","A",1
163,1,108,153,0.1449139,"\int (f x)^m (d+e x)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^m*(d + e*x)^2*(a + b*Log[c*x^n]),x]","x (f x)^m \left(\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{m+1}+\frac{2 d e x \left(a+b \log \left(c x^n\right)\right)}{m+2}+\frac{e^2 x^2 \left(a+b \log \left(c x^n\right)\right)}{m+3}-\frac{b d^2 n}{(m+1)^2}-\frac{2 b d e n x}{(m+2)^2}-\frac{b e^2 n x^2}{(m+3)^2}\right)","\frac{d^2 (f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+1)}+\frac{2 d e (f x)^{m+2} \left(a+b \log \left(c x^n\right)\right)}{f^2 (m+2)}+\frac{e^2 (f x)^{m+3} \left(a+b \log \left(c x^n\right)\right)}{f^3 (m+3)}-\frac{b d^2 n (f x)^{m+1}}{f (m+1)^2}-\frac{2 b d e n (f x)^{m+2}}{f^2 (m+2)^2}-\frac{b e^2 n (f x)^{m+3}}{f^3 (m+3)^2}",1,"x*(f*x)^m*(-((b*d^2*n)/(1 + m)^2) - (2*b*d*e*n*x)/(2 + m)^2 - (b*e^2*n*x^2)/(3 + m)^2 + (d^2*(a + b*Log[c*x^n]))/(1 + m) + (2*d*e*x*(a + b*Log[c*x^n]))/(2 + m) + (e^2*x^2*(a + b*Log[c*x^n]))/(3 + m))","A",1
164,1,64,95,0.0706671,"\int (f x)^m (d+e x) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^m*(d + e*x)*(a + b*Log[c*x^n]),x]","x (f x)^m \left(\frac{d \left(a+b \log \left(c x^n\right)\right)}{m+1}+\frac{e x \left(a+b \log \left(c x^n\right)\right)}{m+2}-\frac{b d n}{(m+1)^2}-\frac{b e n x}{(m+2)^2}\right)","\frac{d (f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+1)}+\frac{e (f x)^{m+2} \left(a+b \log \left(c x^n\right)\right)}{f^2 (m+2)}-\frac{b d n (f x)^{m+1}}{f (m+1)^2}-\frac{b e n (f x)^{m+2}}{f^2 (m+2)^2}",1,"x*(f*x)^m*(-((b*d*n)/(1 + m)^2) - (b*e*n*x)/(2 + m)^2 + (d*(a + b*Log[c*x^n]))/(1 + m) + (e*x*(a + b*Log[c*x^n]))/(2 + m))","A",1
165,1,32,46,0.0134723,"\int (f x)^m \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^m*(a + b*Log[c*x^n]),x]","\frac{x (f x)^m \left(a m+a+b (m+1) \log \left(c x^n\right)-b n\right)}{(m+1)^2}","\frac{(f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+1)}-\frac{b n (f x)^{m+1}}{f (m+1)^2}",1,"(x*(f*x)^m*(a + a*m - b*n + b*(1 + m)*Log[c*x^n]))/(1 + m)^2","A",1
166,1,72,26,0.1047142,"\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{d+e x} \, dx","Integrate[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x),x]","\frac{x (f x)^m \left((m+1) \, _2F_1\left(1,m+1;m+2;-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \, _3F_2\left(1,m+1,m+1;m+2,m+2;-\frac{e x}{d}\right)\right)}{d (m+1)^2}","\text{Int}\left(\frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{d+e x},x\right)",0,"(x*(f*x)^m*(-(b*n*HypergeometricPFQ[{1, 1 + m, 1 + m}, {2 + m, 2 + m}, -((e*x)/d)]) + (1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((e*x)/d)]*(a + b*Log[c*x^n])))/(d*(1 + m)^2)","B",0
167,1,72,26,0.1070258,"\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2} \, dx","Integrate[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x)^2,x]","\frac{x (f x)^m \left((m+1) \, _2F_1\left(2,m+1;m+2;-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \, _3F_2\left(2,m+1,m+1;m+2,m+2;-\frac{e x}{d}\right)\right)}{d^2 (m+1)^2}","\text{Int}\left(\frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2},x\right)",0,"(x*(f*x)^m*(-(b*n*HypergeometricPFQ[{2, 1 + m, 1 + m}, {2 + m, 2 + m}, -((e*x)/d)]) + (1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, -((e*x)/d)]*(a + b*Log[c*x^n])))/(d^2*(1 + m)^2)","B",0
168,1,173,18,0.2506162,"\int x (a+b x)^m \log \left(c x^n\right) \, dx","Integrate[x*(a + b*x)^m*Log[c*x^n],x]","\frac{(a+b x)^m \left(\frac{b x}{a}+1\right)^{-m} \left(a b (m+2) n x \, _3F_2\left(1,1,-m-1;2,2;-\frac{b x}{a}\right)+\left(-a^2 \left(\left(\frac{b x}{a}+1\right)^m-1\right)+b^2 (m+1) x^2 \left(\frac{b x}{a}+1\right)^m+a b m x \left(\frac{b x}{a}+1\right)^m\right) \log \left(c x^n\right)-n \left(a^2 \left(\left(\frac{b x}{a}+1\right)^m-1\right)+b^2 x^2 \left(\frac{b x}{a}+1\right)^m+2 a b x \left(\frac{b x}{a}+1\right)^m\right)\right)}{b^2 (m+1) (m+2)}","\text{Int}\left(x (a+b x)^m \log \left(c x^n\right),x\right)",0,"((a + b*x)^m*(-(n*(2*a*b*x*(1 + (b*x)/a)^m + b^2*x^2*(1 + (b*x)/a)^m + a^2*(-1 + (1 + (b*x)/a)^m))) + a*b*(2 + m)*n*x*HypergeometricPFQ[{1, 1, -1 - m}, {2, 2}, -((b*x)/a)] + (a*b*m*x*(1 + (b*x)/a)^m + b^2*(1 + m)*x^2*(1 + (b*x)/a)^m - a^2*(-1 + (1 + (b*x)/a)^m))*Log[c*x^n]))/(b^2*(1 + m)*(2 + m)*(1 + (b*x)/a)^m)","B",1
169,1,61,68,0.0218624,"\int (a+b x)^m \log \left(c x^n\right) \, dx","Integrate[(a + b*x)^m*Log[c*x^n],x]","\frac{(a+b x)^{m+1} \left(n (a+b x) \, _2F_1\left(1,m+2;m+3;\frac{b x}{a}+1\right)+a (m+2) \log \left(c x^n\right)\right)}{a b (m+1) (m+2)}","\frac{(a+b x)^{m+1} \log \left(c x^n\right)}{b (m+1)}+\frac{n (a+b x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{b x}{a}+1\right)}{a b \left(m^2+3 m+2\right)}",1,"((a + b*x)^(1 + m)*(n*(a + b*x)*Hypergeometric2F1[1, 2 + m, 3 + m, 1 + (b*x)/a] + a*(2 + m)*Log[c*x^n]))/(a*b*(1 + m)*(2 + m))","A",1
170,1,89,20,0.0644198,"\int \frac{(a+b x)^m \log \left(c x^n\right)}{x} \, dx","Integrate[((a + b*x)^m*Log[c*x^n])/x,x]","\frac{\left(\frac{a}{b x}+1\right)^{-m} (a+b x)^m \left(m \log \left(c x^n\right) \, _2F_1\left(-m,-m;1-m;-\frac{a}{b x}\right)-n \, _3F_2\left(-m,-m,-m;1-m,1-m;-\frac{a}{b x}\right)\right)}{m^2}","\text{Int}\left(\frac{(a+b x)^m \log \left(c x^n\right)}{x},x\right)",0,"((a + b*x)^m*(-(n*HypergeometricPFQ[{-m, -m, -m}, {1 - m, 1 - m}, -(a/(b*x))]) + m*Hypergeometric2F1[-m, -m, 1 - m, -(a/(b*x))]*Log[c*x^n]))/(m^2*(1 + a/(b*x))^m)","B",0
171,1,69,48,0.0032421,"\int x^5 \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^5*(d + e*x^2)*(a + b*Log[c*x^n]),x]","\frac{1}{6} a d x^6+\frac{1}{8} a e x^8+\frac{1}{6} b d x^6 \log \left(c x^n\right)+\frac{1}{8} b e x^8 \log \left(c x^n\right)-\frac{1}{36} b d n x^6-\frac{1}{64} b e n x^8","\frac{1}{24} \left(4 d x^6+3 e x^8\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{36} b d n x^6-\frac{1}{64} b e n x^8",1,"(a*d*x^6)/6 - (b*d*n*x^6)/36 + (a*e*x^8)/8 - (b*e*n*x^8)/64 + (b*d*x^6*Log[c*x^n])/6 + (b*e*x^8*Log[c*x^n])/8","A",1
172,1,69,48,0.0024399,"\int x^3 \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^3*(d + e*x^2)*(a + b*Log[c*x^n]),x]","\frac{1}{4} a d x^4+\frac{1}{6} a e x^6+\frac{1}{4} b d x^4 \log \left(c x^n\right)+\frac{1}{6} b e x^6 \log \left(c x^n\right)-\frac{1}{16} b d n x^4-\frac{1}{36} b e n x^6","\frac{1}{12} \left(3 d x^4+2 e x^6\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{16} b d n x^4-\frac{1}{36} b e n x^6",1,"(a*d*x^4)/4 - (b*d*n*x^4)/16 + (a*e*x^6)/6 - (b*e*n*x^6)/36 + (b*d*x^4*Log[c*x^n])/4 + (b*e*x^6*Log[c*x^n])/6","A",1
173,1,69,47,0.0022461,"\int x \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x*(d + e*x^2)*(a + b*Log[c*x^n]),x]","\frac{1}{2} a d x^2+\frac{1}{4} a e x^4+\frac{1}{2} b d x^2 \log \left(c x^n\right)+\frac{1}{4} b e x^4 \log \left(c x^n\right)-\frac{1}{4} b d n x^2-\frac{1}{16} b e n x^4","\frac{1}{4} \left(2 d x^2+e x^4\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b d n x^2-\frac{1}{16} b e n x^4",1,"(a*d*x^2)/2 - (b*d*n*x^2)/4 + (a*e*x^4)/4 - (b*e*n*x^4)/16 + (b*d*x^2*Log[c*x^n])/2 + (b*e*x^4*Log[c*x^n])/4","A",1
174,1,57,52,0.0032304,"\int \frac{\left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[((d + e*x^2)*(a + b*Log[c*x^n]))/x,x]","a d \log (x)+\frac{1}{2} a e x^2+\frac{b d \log ^2\left(c x^n\right)}{2 n}+\frac{1}{2} b e x^2 \log \left(c x^n\right)-\frac{1}{4} b e n x^2","\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}+\frac{1}{2} e x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b e n x^2",1,"(a*e*x^2)/2 - (b*e*n*x^2)/4 + a*d*Log[x] + (b*e*x^2*Log[c*x^n])/2 + (b*d*Log[c*x^n]^2)/(2*n)","A",1
175,1,57,52,0.0038406,"\int \frac{\left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Integrate[((d + e*x^2)*(a + b*Log[c*x^n]))/x^3,x]","-\frac{a d}{2 x^2}+a e \log (x)-\frac{b d \log \left(c x^n\right)}{2 x^2}+\frac{b e \log ^2\left(c x^n\right)}{2 n}-\frac{b d n}{4 x^2}","-\frac{d \left(a+b \log \left(c x^n\right)\right)}{2 x^2}+\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}-\frac{b d n}{4 x^2}",1,"-1/2*(a*d)/x^2 - (b*d*n)/(4*x^2) + a*e*Log[x] - (b*d*Log[c*x^n])/(2*x^2) + (b*e*Log[c*x^n]^2)/(2*n)","A",1
176,1,69,57,0.0030479,"\int \frac{\left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right)}{x^5} \, dx","Integrate[((d + e*x^2)*(a + b*Log[c*x^n]))/x^5,x]","-\frac{a d}{4 x^4}-\frac{a e}{2 x^2}-\frac{b d \log \left(c x^n\right)}{4 x^4}-\frac{b e \log \left(c x^n\right)}{2 x^2}-\frac{b d n}{16 x^4}-\frac{b e n}{4 x^2}","-\frac{d \left(a+b \log \left(c x^n\right)\right)}{4 x^4}-\frac{e \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{b d n}{16 x^4}-\frac{b e n}{4 x^2}",1,"-1/4*(a*d)/x^4 - (b*d*n)/(16*x^4) - (a*e)/(2*x^2) - (b*e*n)/(4*x^2) - (b*d*Log[c*x^n])/(4*x^4) - (b*e*Log[c*x^n])/(2*x^2)","A",1
177,1,69,48,0.0025868,"\int x^4 \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^4*(d + e*x^2)*(a + b*Log[c*x^n]),x]","\frac{1}{5} a d x^5+\frac{1}{7} a e x^7+\frac{1}{5} b d x^5 \log \left(c x^n\right)+\frac{1}{7} b e x^7 \log \left(c x^n\right)-\frac{1}{25} b d n x^5-\frac{1}{49} b e n x^7","\frac{1}{35} \left(7 d x^5+5 e x^7\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{25} b d n x^5-\frac{1}{49} b e n x^7",1,"(a*d*x^5)/5 - (b*d*n*x^5)/25 + (a*e*x^7)/7 - (b*e*n*x^7)/49 + (b*d*x^5*Log[c*x^n])/5 + (b*e*x^7*Log[c*x^n])/7","A",1
178,1,69,48,0.0034619,"\int x^2 \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^2*(d + e*x^2)*(a + b*Log[c*x^n]),x]","\frac{1}{3} a d x^3+\frac{1}{5} a e x^5+\frac{1}{3} b d x^3 \log \left(c x^n\right)+\frac{1}{5} b e x^5 \log \left(c x^n\right)-\frac{1}{9} b d n x^3-\frac{1}{25} b e n x^5","\frac{1}{15} \left(5 d x^3+3 e x^5\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b d n x^3-\frac{1}{25} b e n x^5",1,"(a*d*x^3)/3 - (b*d*n*x^3)/9 + (a*e*x^5)/5 - (b*e*n*x^5)/25 + (b*d*x^3*Log[c*x^n])/3 + (b*e*x^5*Log[c*x^n])/5","A",1
179,1,55,48,0.0015808,"\int \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(d + e*x^2)*(a + b*Log[c*x^n]),x]","a d x+\frac{1}{3} a e x^3+b d x \log \left(c x^n\right)+\frac{1}{3} b e x^3 \log \left(c x^n\right)-b d n x-\frac{1}{9} b e n x^3","d x \left(a+b \log \left(c x^n\right)\right)+\frac{1}{3} e x^3 \left(a+b \log \left(c x^n\right)\right)-b d n x-\frac{1}{9} b e n x^3",1,"a*d*x - b*d*n*x + (a*e*x^3)/3 - (b*e*n*x^3)/9 + b*d*x*Log[c*x^n] + (b*e*x^3*Log[c*x^n])/3","A",1
180,1,49,44,0.0021351,"\int \frac{\left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Integrate[((d + e*x^2)*(a + b*Log[c*x^n]))/x^2,x]","-\frac{a d}{x}+a e x-\frac{b d \log \left(c x^n\right)}{x}+b e x \log \left(c x^n\right)-\frac{b d n}{x}-b e n x","-\frac{d \left(a+b \log \left(c x^n\right)\right)}{x}+e x \left(a+b \log \left(c x^n\right)\right)-\frac{b d n}{x}-b e n x",1,"-((a*d)/x) - (b*d*n)/x + a*e*x - b*e*n*x - (b*d*Log[c*x^n])/x + b*e*x*Log[c*x^n]","A",1
181,1,63,53,0.0029397,"\int \frac{\left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Integrate[((d + e*x^2)*(a + b*Log[c*x^n]))/x^4,x]","-\frac{a d}{3 x^3}-\frac{a e}{x}-\frac{b d \log \left(c x^n\right)}{3 x^3}-\frac{b e \log \left(c x^n\right)}{x}-\frac{b d n}{9 x^3}-\frac{b e n}{x}","-\frac{d \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{e \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{b d n}{9 x^3}-\frac{b e n}{x}",1,"-1/3*(a*d)/x^3 - (b*d*n)/(9*x^3) - (a*e)/x - (b*e*n)/x - (b*d*Log[c*x^n])/(3*x^3) - (b*e*Log[c*x^n])/x","A",1
182,1,69,57,0.0025115,"\int \frac{\left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Integrate[((d + e*x^2)*(a + b*Log[c*x^n]))/x^6,x]","-\frac{a d}{5 x^5}-\frac{a e}{3 x^3}-\frac{b d \log \left(c x^n\right)}{5 x^5}-\frac{b e \log \left(c x^n\right)}{3 x^3}-\frac{b d n}{25 x^5}-\frac{b e n}{9 x^3}","-\frac{d \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{e \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{b d n}{25 x^5}-\frac{b e n}{9 x^3}",1,"-1/5*(a*d)/x^5 - (b*d*n)/(25*x^5) - (a*e)/(3*x^3) - (b*e*n)/(9*x^3) - (b*d*Log[c*x^n])/(5*x^5) - (b*e*Log[c*x^n])/(3*x^3)","A",1
183,1,84,74,0.0430437,"\int x^5 \left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^5*(d + e*x^2)^2*(a + b*Log[c*x^n]),x]","\frac{x^6 \left(1200 d^2 \left(a+b \log \left(c x^n\right)\right)+1800 d e x^2 \left(a+b \log \left(c x^n\right)\right)+720 e^2 x^4 \left(a+b \log \left(c x^n\right)\right)-200 b d^2 n-225 b d e n x^2-72 b e^2 n x^4\right)}{7200}","\frac{1}{60} \left(10 d^2 x^6+15 d e x^8+6 e^2 x^{10}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{36} b d^2 n x^6-\frac{1}{32} b d e n x^8-\frac{1}{100} b e^2 n x^{10}",1,"(x^6*(-200*b*d^2*n - 225*b*d*e*n*x^2 - 72*b*e^2*n*x^4 + 1200*d^2*(a + b*Log[c*x^n]) + 1800*d*e*x^2*(a + b*Log[c*x^n]) + 720*e^2*x^4*(a + b*Log[c*x^n])))/7200","A",1
184,1,87,74,0.0593373,"\int x^3 \left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^3*(d + e*x^2)^2*(a + b*Log[c*x^n]),x]","\frac{1}{576} x^4 \left(24 a \left(6 d^2+8 d e x^2+3 e^2 x^4\right)+24 b \left(6 d^2+8 d e x^2+3 e^2 x^4\right) \log \left(c x^n\right)-b n \left(36 d^2+32 d e x^2+9 e^2 x^4\right)\right)","\frac{1}{24} \left(6 d^2 x^4+8 d e x^6+3 e^2 x^8\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{16} b d^2 n x^4-\frac{1}{18} b d e n x^6-\frac{1}{64} b e^2 n x^8",1,"(x^4*(24*a*(6*d^2 + 8*d*e*x^2 + 3*e^2*x^4) - b*n*(36*d^2 + 32*d*e*x^2 + 9*e^2*x^4) + 24*b*(6*d^2 + 8*d*e*x^2 + 3*e^2*x^4)*Log[c*x^n]))/576","A",1
185,1,85,76,0.0477843,"\int x \left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x*(d + e*x^2)^2*(a + b*Log[c*x^n]),x]","\frac{1}{72} x^2 \left(12 a \left(3 d^2+3 d e x^2+e^2 x^4\right)+12 b \left(3 d^2+3 d e x^2+e^2 x^4\right) \log \left(c x^n\right)-b n \left(18 d^2+9 d e x^2+2 e^2 x^4\right)\right)","\frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{6 e}-\frac{b d^3 n \log (x)}{6 e}-\frac{1}{4} b d^2 n x^2-\frac{1}{8} b d e n x^4-\frac{1}{36} b e^2 n x^6",1,"(x^2*(12*a*(3*d^2 + 3*d*e*x^2 + e^2*x^4) - b*n*(18*d^2 + 9*d*e*x^2 + 2*e^2*x^4) + 12*b*(3*d^2 + 3*d*e*x^2 + e^2*x^4)*Log[c*x^n]))/72","A",1
186,1,82,89,0.081684,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[((d + e*x^2)^2*(a + b*Log[c*x^n]))/x,x]","\frac{1}{16} \left(\frac{8 d^2 \left(a+b \log \left(c x^n\right)\right)^2}{b n}+16 d e x^2 \left(a+b \log \left(c x^n\right)\right)+4 e^2 x^4 \left(a+b \log \left(c x^n\right)\right)-8 b d e n x^2-b e^2 n x^4\right)","d^2 \log (x) \left(a+b \log \left(c x^n\right)\right)+d e x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{4} e^2 x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} b d^2 n \log ^2(x)-\frac{1}{2} b d e n x^2-\frac{1}{16} b e^2 n x^4",1,"(-8*b*d*e*n*x^2 - b*e^2*n*x^4 + 16*d*e*x^2*(a + b*Log[c*x^n]) + 4*e^2*x^4*(a + b*Log[c*x^n]) + (8*d^2*(a + b*Log[c*x^n])^2)/(b*n))/16","A",1
187,1,83,91,0.0607318,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Integrate[((d + e*x^2)^2*(a + b*Log[c*x^n]))/x^3,x]","\frac{1}{4} \left(-\frac{2 d^2 \left(a+b \log \left(c x^n\right)\right)}{x^2}+\frac{4 d e \left(a+b \log \left(c x^n\right)\right)^2}{b n}+2 e^2 x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{b d^2 n}{x^2}-b e^2 n x^2\right)","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{2 x^2}+2 d e \log (x) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} e^2 x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{b d^2 n}{4 x^2}-b d e n \log ^2(x)-\frac{1}{4} b e^2 n x^2",1,"(-((b*d^2*n)/x^2) - b*e^2*n*x^2 - (2*d^2*(a + b*Log[c*x^n]))/x^2 + 2*e^2*x^2*(a + b*Log[c*x^n]) + (4*d*e*(a + b*Log[c*x^n])^2)/(b*n))/4","A",1
188,1,82,90,0.0565103,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^5} \, dx","Integrate[((d + e*x^2)^2*(a + b*Log[c*x^n]))/x^5,x]","\frac{1}{16} \left(-\frac{4 d^2 \left(a+b \log \left(c x^n\right)\right)}{x^4}-\frac{16 d e \left(a+b \log \left(c x^n\right)\right)}{x^2}+\frac{8 e^2 \left(a+b \log \left(c x^n\right)\right)^2}{b n}-\frac{b d^2 n}{x^4}-\frac{8 b d e n}{x^2}\right)","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{4 x^4}-\frac{d e \left(a+b \log \left(c x^n\right)\right)}{x^2}+e^2 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{b d^2 n}{16 x^4}-\frac{b d e n}{2 x^2}-\frac{1}{2} b e^2 n \log ^2(x)",1,"(-((b*d^2*n)/x^4) - (8*b*d*e*n)/x^2 - (4*d^2*(a + b*Log[c*x^n]))/x^4 - (16*d*e*(a + b*Log[c*x^n]))/x^2 + (8*e^2*(a + b*Log[c*x^n])^2)/(b*n))/16","A",1
189,1,95,74,0.0356494,"\int x^4 \left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^4*(d + e*x^2)^2*(a + b*Log[c*x^n]),x]","\frac{1}{5} d^2 x^5 \left(a+b \log \left(c x^n\right)\right)+\frac{2}{7} d e x^7 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{9} e^2 x^9 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{25} b d^2 n x^5-\frac{2}{49} b d e n x^7-\frac{1}{81} b e^2 n x^9","\frac{1}{315} \left(63 d^2 x^5+90 d e x^7+35 e^2 x^9\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{25} b d^2 n x^5-\frac{2}{49} b d e n x^7-\frac{1}{81} b e^2 n x^9",1,"-1/25*(b*d^2*n*x^5) - (2*b*d*e*n*x^7)/49 - (b*e^2*n*x^9)/81 + (d^2*x^5*(a + b*Log[c*x^n]))/5 + (2*d*e*x^7*(a + b*Log[c*x^n]))/7 + (e^2*x^9*(a + b*Log[c*x^n]))/9","A",1
190,1,95,74,0.0349724,"\int x^2 \left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^2*(d + e*x^2)^2*(a + b*Log[c*x^n]),x]","\frac{1}{3} d^2 x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{2}{5} d e x^5 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{7} e^2 x^7 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b d^2 n x^3-\frac{2}{25} b d e n x^5-\frac{1}{49} b e^2 n x^7","\frac{1}{105} \left(35 d^2 x^3+42 d e x^5+15 e^2 x^7\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b d^2 n x^3-\frac{2}{25} b d e n x^5-\frac{1}{49} b e^2 n x^7",1,"-1/9*(b*d^2*n*x^3) - (2*b*d*e*n*x^5)/25 - (b*e^2*n*x^7)/49 + (d^2*x^3*(a + b*Log[c*x^n]))/3 + (2*d*e*x^5*(a + b*Log[c*x^n]))/5 + (e^2*x^7*(a + b*Log[c*x^n]))/7","A",1
191,1,89,86,0.0347514,"\int \left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(d + e*x^2)^2*(a + b*Log[c*x^n]),x]","\frac{2}{3} d e x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{5} e^2 x^5 \left(a+b \log \left(c x^n\right)\right)+a d^2 x+b d^2 x \log \left(c x^n\right)-b d^2 n x-\frac{2}{9} b d e n x^3-\frac{1}{25} b e^2 n x^5","d^2 x \left(a+b \log \left(c x^n\right)\right)+\frac{2}{3} d e x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{5} e^2 x^5 \left(a+b \log \left(c x^n\right)\right)-b d^2 n x-\frac{2}{9} b d e n x^3-\frac{1}{25} b e^2 n x^5",1,"a*d^2*x - b*d^2*n*x - (2*b*d*e*n*x^3)/9 - (b*e^2*n*x^5)/25 + b*d^2*x*Log[c*x^n] + (2*d*e*x^3*(a + b*Log[c*x^n]))/3 + (e^2*x^5*(a + b*Log[c*x^n]))/5","A",1
192,1,86,83,0.0352879,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Integrate[((d + e*x^2)^2*(a + b*Log[c*x^n]))/x^2,x]","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{1}{3} e^2 x^3 \left(a+b \log \left(c x^n\right)\right)+2 a d e x+2 b d e x \log \left(c x^n\right)-\frac{b d^2 n}{x}-2 b d e n x-\frac{1}{9} b e^2 n x^3","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{x}+2 d e x \left(a+b \log \left(c x^n\right)\right)+\frac{1}{3} e^2 x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{b d^2 n}{x}-2 b d e n x-\frac{1}{9} b e^2 n x^3",1,"-((b*d^2*n)/x) + 2*a*d*e*x - 2*b*d*e*n*x - (b*e^2*n*x^3)/9 + 2*b*d*e*x*Log[c*x^n] - (d^2*(a + b*Log[c*x^n]))/x + (e^2*x^3*(a + b*Log[c*x^n]))/3","A",1
193,1,80,82,0.0399142,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Integrate[((d + e*x^2)^2*(a + b*Log[c*x^n]))/x^4,x]","-\frac{3 a \left(d^2+6 d e x^2-3 e^2 x^4\right)+3 b \left(d^2+6 d e x^2-3 e^2 x^4\right) \log \left(c x^n\right)+b n \left(d^2+18 d e x^2+9 e^2 x^4\right)}{9 x^3}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{2 d e \left(a+b \log \left(c x^n\right)\right)}{x}+e^2 x \left(a+b \log \left(c x^n\right)\right)-\frac{b d^2 n}{9 x^3}-\frac{2 b d e n}{x}-b e^2 n x",1,"-1/9*(3*a*(d^2 + 6*d*e*x^2 - 3*e^2*x^4) + b*n*(d^2 + 18*d*e*x^2 + 9*e^2*x^4) + 3*b*(d^2 + 6*d*e*x^2 - 3*e^2*x^4)*Log[c*x^n])/x^3","A",1
194,1,86,91,0.0419191,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Integrate[((d + e*x^2)^2*(a + b*Log[c*x^n]))/x^6,x]","-\frac{15 a \left(3 d^2+10 d e x^2+15 e^2 x^4\right)+15 b \left(3 d^2+10 d e x^2+15 e^2 x^4\right) \log \left(c x^n\right)+b n \left(9 d^2+50 d e x^2+225 e^2 x^4\right)}{225 x^5}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{2 d e \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{e^2 \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{b d^2 n}{25 x^5}-\frac{2 b d e n}{9 x^3}-\frac{b e^2 n}{x}",1,"-1/225*(15*a*(3*d^2 + 10*d*e*x^2 + 15*e^2*x^4) + b*n*(9*d^2 + 50*d*e*x^2 + 225*e^2*x^4) + 15*b*(3*d^2 + 10*d*e*x^2 + 15*e^2*x^4)*Log[c*x^n])/x^5","A",1
195,1,95,95,0.0458167,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^8} \, dx","Integrate[((d + e*x^2)^2*(a + b*Log[c*x^n]))/x^8,x]","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{7 x^7}-\frac{2 d e \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{e^2 \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{b d^2 n}{49 x^7}-\frac{2 b d e n}{25 x^5}-\frac{b e^2 n}{9 x^3}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{7 x^7}-\frac{2 d e \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{e^2 \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{b d^2 n}{49 x^7}-\frac{2 b d e n}{25 x^5}-\frac{b e^2 n}{9 x^3}",1,"-1/49*(b*d^2*n)/x^7 - (2*b*d*e*n)/(25*x^5) - (b*e^2*n)/(9*x^3) - (d^2*(a + b*Log[c*x^n]))/(7*x^7) - (2*d*e*(a + b*Log[c*x^n]))/(5*x^5) - (e^2*(a + b*Log[c*x^n]))/(3*x^3)","A",1
196,1,120,100,0.054504,"\int x^5 \left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^5*(d + e*x^2)^3*(a + b*Log[c*x^n]),x]","\frac{x^6 \left(120 a \left(20 d^3+45 d^2 e x^2+36 d e^2 x^4+10 e^3 x^6\right)+120 b \left(20 d^3+45 d^2 e x^2+36 d e^2 x^4+10 e^3 x^6\right) \log \left(c x^n\right)-b n \left(400 d^3+675 d^2 e x^2+432 d e^2 x^4+100 e^3 x^6\right)\right)}{14400}","\frac{1}{120} \left(20 d^3 x^6+45 d^2 e x^8+36 d e^2 x^{10}+10 e^3 x^{12}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{36} b d^3 n x^6-\frac{3}{64} b d^2 e n x^8-\frac{3}{100} b d e^2 n x^{10}-\frac{1}{144} b e^3 n x^{12}",1,"(x^6*(120*a*(20*d^3 + 45*d^2*e*x^2 + 36*d*e^2*x^4 + 10*e^3*x^6) - b*n*(400*d^3 + 675*d^2*e*x^2 + 432*d*e^2*x^4 + 100*e^3*x^6) + 120*b*(20*d^3 + 45*d^2*e*x^2 + 36*d*e^2*x^4 + 10*e^3*x^6)*Log[c*x^n]))/14400","A",1
197,1,120,130,0.0542524,"\int x^3 \left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^3*(d + e*x^2)^3*(a + b*Log[c*x^n]),x]","\frac{x^4 \left(120 a \left(10 d^3+20 d^2 e x^2+15 d e^2 x^4+4 e^3 x^6\right)+120 b \left(10 d^3+20 d^2 e x^2+15 d e^2 x^4+4 e^3 x^6\right) \log \left(c x^n\right)-b n \left(300 d^3+400 d^2 e x^2+225 d e^2 x^4+48 e^3 x^6\right)\right)}{4800}","-\frac{1}{40} \left(\frac{5 d \left(d+e x^2\right)^4}{e^2}-\frac{4 \left(d+e x^2\right)^5}{e^2}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{b d^5 n \log (x)}{40 e^2}+\frac{b d^4 n x^2}{20 e}+\frac{3}{80} b d^3 n x^4+\frac{1}{60} b d^2 e n x^6+\frac{1}{320} b d e^2 n x^8-\frac{b n \left(d+e x^2\right)^5}{100 e^2}",1,"(x^4*(120*a*(10*d^3 + 20*d^2*e*x^2 + 15*d*e^2*x^4 + 4*e^3*x^6) - b*n*(300*d^3 + 400*d^2*e*x^2 + 225*d*e^2*x^4 + 48*e^3*x^6) + 120*b*(10*d^3 + 20*d^2*e*x^2 + 15*d*e^2*x^4 + 4*e^3*x^6)*Log[c*x^n]))/4800","A",1
198,1,118,91,0.0511096,"\int x \left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x*(d + e*x^2)^3*(a + b*Log[c*x^n]),x]","\frac{1}{192} x^2 \left(24 a \left(4 d^3+6 d^2 e x^2+4 d e^2 x^4+e^3 x^6\right)+24 b \left(4 d^3+6 d^2 e x^2+4 d e^2 x^4+e^3 x^6\right) \log \left(c x^n\right)-b n \left(48 d^3+36 d^2 e x^2+16 d e^2 x^4+3 e^3 x^6\right)\right)","\frac{\left(d+e x^2\right)^4 \left(a+b \log \left(c x^n\right)\right)}{8 e}-\frac{b d^4 n \log (x)}{8 e}-\frac{1}{4} b d^3 n x^2-\frac{3}{16} b d^2 e n x^4-\frac{1}{12} b d e^2 n x^6-\frac{1}{64} b e^3 n x^8",1,"(x^2*(24*a*(4*d^3 + 6*d^2*e*x^2 + 4*d*e^2*x^4 + e^3*x^6) - b*n*(48*d^3 + 36*d^2*e*x^2 + 16*d*e^2*x^4 + 3*e^3*x^6) + 24*b*(4*d^3 + 6*d^2*e*x^2 + 4*d*e^2*x^4 + e^3*x^6)*Log[c*x^n]))/192","A",1
199,1,116,130,0.0646534,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[((d + e*x^2)^3*(a + b*Log[c*x^n]))/x,x]","\frac{1}{144} \left(\frac{72 d^3 \left(a+b \log \left(c x^n\right)\right)^2}{b n}+216 d^2 e x^2 \left(a+b \log \left(c x^n\right)\right)+108 d e^2 x^4 \left(a+b \log \left(c x^n\right)\right)+24 e^3 x^6 \left(a+b \log \left(c x^n\right)\right)-108 b d^2 e n x^2-27 b d e^2 n x^4-4 b e^3 n x^6\right)","d^3 \log (x) \left(a+b \log \left(c x^n\right)\right)+\frac{3}{2} d^2 e x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{3}{4} d e^2 x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{6} e^3 x^6 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} b d^3 n \log ^2(x)-\frac{3}{4} b d^2 e n x^2-\frac{3}{16} b d e^2 n x^4-\frac{1}{36} b e^3 n x^6",1,"(-108*b*d^2*e*n*x^2 - 27*b*d*e^2*n*x^4 - 4*b*e^3*n*x^6 + 216*d^2*e*x^2*(a + b*Log[c*x^n]) + 108*d*e^2*x^4*(a + b*Log[c*x^n]) + 24*e^3*x^6*(a + b*Log[c*x^n]) + (72*d^3*(a + b*Log[c*x^n])^2)/(b*n))/144","A",1
200,1,115,131,0.0865809,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Integrate[((d + e*x^2)^3*(a + b*Log[c*x^n]))/x^3,x]","\frac{1}{16} \left(-\frac{8 d^3 \left(a+b \log \left(c x^n\right)\right)}{x^2}+\frac{24 d^2 e \left(a+b \log \left(c x^n\right)\right)^2}{b n}+24 d e^2 x^2 \left(a+b \log \left(c x^n\right)\right)+4 e^3 x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{4 b d^3 n}{x^2}-12 b d e^2 n x^2-b e^3 n x^4\right)","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{2 x^2}+3 d^2 e \log (x) \left(a+b \log \left(c x^n\right)\right)+\frac{3}{2} d e^2 x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{4} e^3 x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{b d^3 n}{4 x^2}-\frac{3}{2} b d^2 e n \log ^2(x)-\frac{3}{4} b d e^2 n x^2-\frac{1}{16} b e^3 n x^4",1,"((-4*b*d^3*n)/x^2 - 12*b*d*e^2*n*x^2 - b*e^3*n*x^4 - (8*d^3*(a + b*Log[c*x^n]))/x^2 + 24*d*e^2*x^2*(a + b*Log[c*x^n]) + 4*e^3*x^4*(a + b*Log[c*x^n]) + (24*d^2*e*(a + b*Log[c*x^n])^2)/(b*n))/16","A",1
201,1,115,131,0.0854284,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^5} \, dx","Integrate[((d + e*x^2)^3*(a + b*Log[c*x^n]))/x^5,x]","\frac{1}{16} \left(-\frac{4 d^3 \left(a+b \log \left(c x^n\right)\right)}{x^4}-\frac{24 d^2 e \left(a+b \log \left(c x^n\right)\right)}{x^2}+\frac{24 d e^2 \left(a+b \log \left(c x^n\right)\right)^2}{b n}+8 e^3 x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{b d^3 n}{x^4}-\frac{12 b d^2 e n}{x^2}-4 b e^3 n x^2\right)","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{4 x^4}-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{2 x^2}+3 d e^2 \log (x) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} e^3 x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{b d^3 n}{16 x^4}-\frac{3 b d^2 e n}{4 x^2}-\frac{3}{2} b d e^2 n \log ^2(x)-\frac{1}{4} b e^3 n x^2",1,"(-((b*d^3*n)/x^4) - (12*b*d^2*e*n)/x^2 - 4*b*e^3*n*x^2 - (4*d^3*(a + b*Log[c*x^n]))/x^4 - (24*d^2*e*(a + b*Log[c*x^n]))/x^2 + 8*e^3*x^2*(a + b*Log[c*x^n]) + (24*d*e^2*(a + b*Log[c*x^n])^2)/(b*n))/16","A",1
202,1,133,100,0.0495269,"\int x^4 \left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^4*(d + e*x^2)^3*(a + b*Log[c*x^n]),x]","\frac{1}{5} d^3 x^5 \left(a+b \log \left(c x^n\right)\right)+\frac{3}{7} d^2 e x^7 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{3} d e^2 x^9 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{11} e^3 x^{11} \left(a+b \log \left(c x^n\right)\right)-\frac{1}{25} b d^3 n x^5-\frac{3}{49} b d^2 e n x^7-\frac{1}{27} b d e^2 n x^9-\frac{1}{121} b e^3 n x^{11}","\frac{\left(231 d^3 x^5+495 d^2 e x^7+385 d e^2 x^9+105 e^3 x^{11}\right) \left(a+b \log \left(c x^n\right)\right)}{1155}-\frac{1}{25} b d^3 n x^5-\frac{3}{49} b d^2 e n x^7-\frac{1}{27} b d e^2 n x^9-\frac{1}{121} b e^3 n x^{11}",1,"-1/25*(b*d^3*n*x^5) - (3*b*d^2*e*n*x^7)/49 - (b*d*e^2*n*x^9)/27 - (b*e^3*n*x^11)/121 + (d^3*x^5*(a + b*Log[c*x^n]))/5 + (3*d^2*e*x^7*(a + b*Log[c*x^n]))/7 + (d*e^2*x^9*(a + b*Log[c*x^n]))/3 + (e^3*x^11*(a + b*Log[c*x^n]))/11","A",1
203,1,133,100,0.0474987,"\int x^2 \left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^2*(d + e*x^2)^3*(a + b*Log[c*x^n]),x]","\frac{1}{3} d^3 x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{3}{5} d^2 e x^5 \left(a+b \log \left(c x^n\right)\right)+\frac{3}{7} d e^2 x^7 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{9} e^3 x^9 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b d^3 n x^3-\frac{3}{25} b d^2 e n x^5-\frac{3}{49} b d e^2 n x^7-\frac{1}{81} b e^3 n x^9","\frac{1}{315} \left(105 d^3 x^3+189 d^2 e x^5+135 d e^2 x^7+35 e^3 x^9\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b d^3 n x^3-\frac{3}{25} b d^2 e n x^5-\frac{3}{49} b d e^2 n x^7-\frac{1}{81} b e^3 n x^9",1,"-1/9*(b*d^3*n*x^3) - (3*b*d^2*e*n*x^5)/25 - (3*b*d*e^2*n*x^7)/49 - (b*e^3*n*x^9)/81 + (d^3*x^3*(a + b*Log[c*x^n]))/3 + (3*d^2*e*x^5*(a + b*Log[c*x^n]))/5 + (3*d*e^2*x^7*(a + b*Log[c*x^n]))/7 + (e^3*x^9*(a + b*Log[c*x^n]))/9","A",1
204,1,124,121,0.0452953,"\int \left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(d + e*x^2)^3*(a + b*Log[c*x^n]),x]","d^2 e x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{3}{5} d e^2 x^5 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{7} e^3 x^7 \left(a+b \log \left(c x^n\right)\right)+a d^3 x+b d^3 x \log \left(c x^n\right)-b d^3 n x-\frac{1}{3} b d^2 e n x^3-\frac{3}{25} b d e^2 n x^5-\frac{1}{49} b e^3 n x^7","d^3 x \left(a+b \log \left(c x^n\right)\right)+d^2 e x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{3}{5} d e^2 x^5 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{7} e^3 x^7 \left(a+b \log \left(c x^n\right)\right)-b d^3 n x-\frac{1}{3} b d^2 e n x^3-\frac{3}{25} b d e^2 n x^5-\frac{1}{49} b e^3 n x^7",1,"a*d^3*x - b*d^3*n*x - (b*d^2*e*n*x^3)/3 - (3*b*d*e^2*n*x^5)/25 - (b*e^3*n*x^7)/49 + b*d^3*x*Log[c*x^n] + d^2*e*x^3*(a + b*Log[c*x^n]) + (3*d*e^2*x^5*(a + b*Log[c*x^n]))/5 + (e^3*x^7*(a + b*Log[c*x^n]))/7","A",1
205,1,123,118,0.0567524,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Integrate[((d + e*x^2)^3*(a + b*Log[c*x^n]))/x^2,x]","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{x}+d e^2 x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{5} e^3 x^5 \left(a+b \log \left(c x^n\right)\right)+3 a d^2 e x+3 b d^2 e x \log \left(c x^n\right)-\frac{b d^3 n}{x}-3 b d^2 e n x-\frac{1}{3} b d e^2 n x^3-\frac{1}{25} b e^3 n x^5","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{x}+3 d^2 e x \left(a+b \log \left(c x^n\right)\right)+d e^2 x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{5} e^3 x^5 \left(a+b \log \left(c x^n\right)\right)-\frac{b d^3 n}{x}-3 b d^2 e n x-\frac{1}{3} b d e^2 n x^3-\frac{1}{25} b e^3 n x^5",1,"-((b*d^3*n)/x) + 3*a*d^2*e*x - 3*b*d^2*e*n*x - (b*d*e^2*n*x^3)/3 - (b*e^3*n*x^5)/25 + 3*b*d^2*e*x*Log[c*x^n] - (d^3*(a + b*Log[c*x^n]))/x + d*e^2*x^3*(a + b*Log[c*x^n]) + (e^3*x^5*(a + b*Log[c*x^n]))/5","A",1
206,1,112,121,0.0551332,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Integrate[((d + e*x^2)^3*(a + b*Log[c*x^n]))/x^4,x]","-\frac{3 a \left(d^3+9 d^2 e x^2-9 d e^2 x^4-e^3 x^6\right)+3 b \left(d^3+9 d^2 e x^2-9 d e^2 x^4-e^3 x^6\right) \log \left(c x^n\right)+b n \left(d^3+27 d^2 e x^2+27 d e^2 x^4+e^3 x^6\right)}{9 x^3}","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{x}+3 d e^2 x \left(a+b \log \left(c x^n\right)\right)+\frac{1}{3} e^3 x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{b d^3 n}{9 x^3}-\frac{3 b d^2 e n}{x}-3 b d e^2 n x-\frac{1}{9} b e^3 n x^3",1,"-1/9*(3*a*(d^3 + 9*d^2*e*x^2 - 9*d*e^2*x^4 - e^3*x^6) + b*n*(d^3 + 27*d^2*e*x^2 + 27*d*e^2*x^4 + e^3*x^6) + 3*b*(d^3 + 9*d^2*e*x^2 - 9*d*e^2*x^4 - e^3*x^6)*Log[c*x^n])/x^3","A",1
207,1,115,118,0.056201,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Integrate[((d + e*x^2)^3*(a + b*Log[c*x^n]))/x^6,x]","-\frac{15 a \left(d^3+5 d^2 e x^2+15 d e^2 x^4-5 e^3 x^6\right)+15 b \left(d^3+5 d^2 e x^2+15 d e^2 x^4-5 e^3 x^6\right) \log \left(c x^n\right)+b n \left(3 d^3+25 d^2 e x^2+225 d e^2 x^4+75 e^3 x^6\right)}{75 x^5}","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{d^2 e \left(a+b \log \left(c x^n\right)\right)}{x^3}-\frac{3 d e^2 \left(a+b \log \left(c x^n\right)\right)}{x}+e^3 x \left(a+b \log \left(c x^n\right)\right)-\frac{b d^3 n}{25 x^5}-\frac{b d^2 e n}{3 x^3}-\frac{3 b d e^2 n}{x}-b e^3 n x",1,"-1/75*(15*a*(d^3 + 5*d^2*e*x^2 + 15*d*e^2*x^4 - 5*e^3*x^6) + b*n*(3*d^3 + 25*d^2*e*x^2 + 225*d*e^2*x^4 + 75*e^3*x^6) + 15*b*(d^3 + 5*d^2*e*x^2 + 15*d*e^2*x^4 - 5*e^3*x^6)*Log[c*x^n])/x^5","A",1
208,1,127,127,0.0610578,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^8} \, dx","Integrate[((d + e*x^2)^3*(a + b*Log[c*x^n]))/x^8,x]","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{7 x^7}-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{d e^2 \left(a+b \log \left(c x^n\right)\right)}{x^3}-\frac{e^3 \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{b d^3 n}{49 x^7}-\frac{3 b d^2 e n}{25 x^5}-\frac{b d e^2 n}{3 x^3}-\frac{b e^3 n}{x}","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{7 x^7}-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{d e^2 \left(a+b \log \left(c x^n\right)\right)}{x^3}-\frac{e^3 \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{b d^3 n}{49 x^7}-\frac{3 b d^2 e n}{25 x^5}-\frac{b d e^2 n}{3 x^3}-\frac{b e^3 n}{x}",1,"-1/49*(b*d^3*n)/x^7 - (3*b*d^2*e*n)/(25*x^5) - (b*d*e^2*n)/(3*x^3) - (b*e^3*n)/x - (d^3*(a + b*Log[c*x^n]))/(7*x^7) - (3*d^2*e*(a + b*Log[c*x^n]))/(5*x^5) - (d*e^2*(a + b*Log[c*x^n]))/x^3 - (e^3*(a + b*Log[c*x^n]))/x","A",1
209,1,133,133,0.0614143,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^{10}} \, dx","Integrate[((d + e*x^2)^3*(a + b*Log[c*x^n]))/x^10,x]","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{9 x^9}-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{7 x^7}-\frac{3 d e^2 \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{e^3 \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{b d^3 n}{81 x^9}-\frac{3 b d^2 e n}{49 x^7}-\frac{3 b d e^2 n}{25 x^5}-\frac{b e^3 n}{9 x^3}","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{9 x^9}-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{7 x^7}-\frac{3 d e^2 \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{e^3 \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{b d^3 n}{81 x^9}-\frac{3 b d^2 e n}{49 x^7}-\frac{3 b d e^2 n}{25 x^5}-\frac{b e^3 n}{9 x^3}",1,"-1/81*(b*d^3*n)/x^9 - (3*b*d^2*e*n)/(49*x^7) - (3*b*d*e^2*n)/(25*x^5) - (b*e^3*n)/(9*x^3) - (d^3*(a + b*Log[c*x^n]))/(9*x^9) - (3*d^2*e*(a + b*Log[c*x^n]))/(7*x^7) - (3*d*e^2*(a + b*Log[c*x^n]))/(5*x^5) - (e^3*(a + b*Log[c*x^n]))/(3*x^3)","A",1
210,1,174,121,0.123294,"\int \frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{d+e x^2} \, dx","Integrate[(x^5*(a + b*Log[c*x^n]))/(d + e*x^2),x]","\frac{8 d^2 \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)+8 d^2 \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)-8 d e x^2 \left(a+b \log \left(c x^n\right)\right)+4 e^2 x^4 \left(a+b \log \left(c x^n\right)\right)+8 b d^2 n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)+8 b d^2 n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)+4 b d e n x^2-b e^2 n x^4}{16 e^3}","\frac{d^2 \log \left(\frac{e x^2}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^3}-\frac{d x^2 \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{x^4 \left(a+b \log \left(c x^n\right)\right)}{4 e}+\frac{b d^2 n \text{Li}_2\left(-\frac{e x^2}{d}\right)}{4 e^3}+\frac{b d n x^2}{4 e^2}-\frac{b n x^4}{16 e}",1,"(4*b*d*e*n*x^2 - b*e^2*n*x^4 - 8*d*e*x^2*(a + b*Log[c*x^n]) + 4*e^2*x^4*(a + b*Log[c*x^n]) + 8*d^2*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]] + 8*d^2*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)] + 8*b*d^2*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]] + 8*b*d^2*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(16*e^3)","A",1
211,1,135,83,0.0728379,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{d+e x^2} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/(d + e*x^2),x]","-\frac{2 d \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)+2 d \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)-2 e x^2 \left(a+b \log \left(c x^n\right)\right)+2 b d n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)+2 b d n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)+b e n x^2}{4 e^2}","-\frac{d \log \left(\frac{e x^2}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{2 e}-\frac{b d n \text{Li}_2\left(-\frac{e x^2}{d}\right)}{4 e^2}-\frac{b n x^2}{4 e}",1,"-1/4*(b*e*n*x^2 - 2*e*x^2*(a + b*Log[c*x^n]) + 2*d*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]] + 2*d*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)] + 2*b*d*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]] + 2*b*d*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/e^2","A",1
212,1,94,49,0.0342703,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{d+e x^2} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/(d + e*x^2),x]","\frac{\left(\log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right)+\log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right)\right) \left(a+b \log \left(c x^n\right)\right)+b n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)+b n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)}{2 e}","\frac{\log \left(\frac{e x^2}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 e}+\frac{b n \text{Li}_2\left(-\frac{e x^2}{d}\right)}{4 e}",1,"((a + b*Log[c*x^n])*(Log[1 + (Sqrt[e]*x)/Sqrt[-d]] + Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)]) + b*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]] + b*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(2*e)","A",1
213,1,126,49,0.1014274,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^2\right)} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x^2)),x]","-\frac{-\left(a+b \log \left(c x^n\right)\right) \left(a+b \log \left(c x^n\right)-b n \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right)-b n \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right)\right)+b^2 n^2 \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)+b^2 n^2 \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)}{2 b d n}","\frac{b n \text{Li}_2\left(-\frac{d}{e x^2}\right)}{4 d}-\frac{\log \left(\frac{d}{e x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 d}",1,"-1/2*(-((a + b*Log[c*x^n])*(a + b*Log[c*x^n] - b*n*Log[1 + (Sqrt[e]*x)/Sqrt[-d]] - b*n*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)])) + b^2*n^2*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]] + b^2*n^2*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(b*d*n)","B",1
214,1,157,83,0.1344058,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^2\right)} \, dx","Integrate[(a + b*Log[c*x^n])/(x^3*(d + e*x^2)),x]","\frac{2 e \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)+2 e \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 d \left(a+b \log \left(c x^n\right)\right)}{x^2}-\frac{2 e \left(a+b \log \left(c x^n\right)\right)^2}{b n}+2 b e n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)+2 b e n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)-\frac{b d n}{x^2}}{4 d^2}","\frac{e \log \left(\frac{d}{e x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 d^2}-\frac{a+b \log \left(c x^n\right)}{2 d x^2}-\frac{b e n \text{Li}_2\left(-\frac{d}{e x^2}\right)}{4 d^2}-\frac{b n}{4 d x^2}",1,"(-((b*d*n)/x^2) - (2*d*(a + b*Log[c*x^n]))/x^2 - (2*e*(a + b*Log[c*x^n])^2)/(b*n) + 2*e*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]] + 2*e*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)] + 2*b*e*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]] + 2*b*e*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(4*d^2)","A",1
215,1,196,121,0.1996691,"\int \frac{a+b \log \left(c x^n\right)}{x^5 \left(d+e x^2\right)} \, dx","Integrate[(a + b*Log[c*x^n])/(x^5*(d + e*x^2)),x]","-\frac{\frac{4 d^2 \left(a+b \log \left(c x^n\right)\right)}{x^4}+8 e^2 \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)+8 e^2 \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{8 d e \left(a+b \log \left(c x^n\right)\right)}{x^2}-\frac{8 e^2 \left(a+b \log \left(c x^n\right)\right)^2}{b n}+\frac{b d^2 n}{x^4}+8 b e^2 n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)+8 b e^2 n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)-\frac{4 b d e n}{x^2}}{16 d^3}","-\frac{e^2 \log \left(\frac{d}{e x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 d^3}+\frac{e \left(a+b \log \left(c x^n\right)\right)}{2 d^2 x^2}-\frac{a+b \log \left(c x^n\right)}{4 d x^4}+\frac{b e^2 n \text{Li}_2\left(-\frac{d}{e x^2}\right)}{4 d^3}+\frac{b e n}{4 d^2 x^2}-\frac{b n}{16 d x^4}",1,"-1/16*((b*d^2*n)/x^4 - (4*b*d*e*n)/x^2 + (4*d^2*(a + b*Log[c*x^n]))/x^4 - (8*d*e*(a + b*Log[c*x^n]))/x^2 - (8*e^2*(a + b*Log[c*x^n])^2)/(b*n) + 8*e^2*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]] + 8*e^2*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)] + 8*b*e^2*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]] + 8*b*e^2*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/d^3","A",1
216,1,208,167,0.1643937,"\int \frac{x^4 \left(a+b \log \left(c x^n\right)\right)}{d+e x^2} \, dx","Integrate[(x^4*(a + b*Log[c*x^n]))/(d + e*x^2),x]","\frac{9 \sqrt{-d} d \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)+9 (-d)^{3/2} \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)+6 e^{3/2} x^3 \left(a+b \log \left(c x^n\right)\right)-18 a d \sqrt{e} x-18 b d \sqrt{e} x \log \left(c x^n\right)+9 b (-d)^{3/2} n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)-9 b (-d)^{3/2} n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)+18 b d \sqrt{e} n x-2 b e^{3/2} n x^3}{18 e^{5/2}}","\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{e^{5/2}}+\frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{3 e}-\frac{a d x}{e^2}-\frac{b d x \log \left(c x^n\right)}{e^2}-\frac{i b d^{3/2} n \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 e^{5/2}}+\frac{i b d^{3/2} n \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 e^{5/2}}+\frac{b d n x}{e^2}-\frac{b n x^3}{9 e}",1,"(-18*a*d*Sqrt[e]*x + 18*b*d*Sqrt[e]*n*x - 2*b*e^(3/2)*n*x^3 - 18*b*d*Sqrt[e]*x*Log[c*x^n] + 6*e^(3/2)*x^3*(a + b*Log[c*x^n]) + 9*Sqrt[-d]*d*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]] + 9*(-d)^(3/2)*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)] + 9*b*(-d)^(3/2)*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]] - 9*b*(-d)^(3/2)*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(18*e^(5/2))","A",1
217,1,170,132,0.1101652,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{d+e x^2} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e*x^2),x]","\frac{-\sqrt{-d} \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)+\sqrt{-d} \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)+2 a \sqrt{e} x+2 b \sqrt{e} x \log \left(c x^n\right)+b \sqrt{-d} n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)-b \sqrt{-d} n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)-2 b \sqrt{e} n x}{2 e^{3/2}}","-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{e^{3/2}}+\frac{a x}{e}+\frac{b x \log \left(c x^n\right)}{e}+\frac{i b \sqrt{d} n \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 e^{3/2}}-\frac{i b \sqrt{d} n \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 e^{3/2}}-\frac{b n x}{e}",1,"(2*a*Sqrt[e]*x - 2*b*Sqrt[e]*n*x + 2*b*Sqrt[e]*x*Log[c*x^n] - Sqrt[-d]*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]] + Sqrt[-d]*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)] + b*Sqrt[-d]*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]] - b*Sqrt[-d]*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(2*e^(3/2))","A",1
218,1,107,105,0.047181,"\int \frac{a+b \log \left(c x^n\right)}{d+e x^2} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*x^2),x]","\frac{-\left(\left(\log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right)-\log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right)\right) \left(a+b \log \left(c x^n\right)\right)\right)+b n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)-b n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)}{2 \sqrt{-d} \sqrt{e}}","\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d} \sqrt{e}}-\frac{i b n \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 \sqrt{d} \sqrt{e}}+\frac{i b n \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 \sqrt{d} \sqrt{e}}",1,"(-((a + b*Log[c*x^n])*(Log[1 + (Sqrt[e]*x)/Sqrt[-d]] - Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)])) + b*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]] - b*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(2*Sqrt[-d]*Sqrt[e])","A",1
219,1,173,134,0.1417934,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^2\right)} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*(d + e*x^2)),x]","\frac{d \left(-d \sqrt{e} x \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)+d \sqrt{e} x \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)+2 d \sqrt{-d} \left(a+b \log \left(c x^n\right)\right)+b d \sqrt{e} n x \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)-b d \sqrt{e} n x \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)-2 b (-d)^{3/2} n\right)}{2 (-d)^{7/2} x}","-\frac{\sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{d^{3/2}}-\frac{a+b \log \left(c x^n\right)}{d x}+\frac{i b \sqrt{e} n \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2}}-\frac{i b \sqrt{e} n \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2}}-\frac{b n}{d x}",1,"(d*(-2*b*(-d)^(3/2)*n + 2*Sqrt[-d]*d*(a + b*Log[c*x^n]) - d*Sqrt[e]*x*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]] + d*Sqrt[e]*x*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)] + b*d*Sqrt[e]*n*x*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]] - b*d*Sqrt[e]*n*x*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)]))/(2*(-d)^(7/2)*x)","A",1
220,1,211,165,0.1847238,"\int \frac{a+b \log \left(c x^n\right)}{x^4 \left(d+e x^2\right)} \, dx","Integrate[(a + b*Log[c*x^n])/(x^4*(d + e*x^2)),x]","\frac{1}{18} \left(\frac{18 e \left(a+b \log \left(c x^n\right)\right)}{d^2 x}-\frac{9 e^{3/2} \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{5/2}}+\frac{9 e^{3/2} \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{5/2}}-\frac{6 \left(a+b \log \left(c x^n\right)\right)}{d x^3}+\frac{18 b e n}{d^2 x}+\frac{9 b e^{3/2} n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{(-d)^{5/2}}-\frac{9 b e^{3/2} n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)}{(-d)^{5/2}}-\frac{2 b n}{d x^3}\right)","\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{d^{5/2}}+\frac{e \left(a+b \log \left(c x^n\right)\right)}{d^2 x}-\frac{a+b \log \left(c x^n\right)}{3 d x^3}-\frac{i b e^{3/2} n \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 d^{5/2}}+\frac{i b e^{3/2} n \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 d^{5/2}}+\frac{b e n}{d^2 x}-\frac{b n}{9 d x^3}",1,"((-2*b*n)/(d*x^3) + (18*b*e*n)/(d^2*x) - (6*(a + b*Log[c*x^n]))/(d*x^3) + (18*e*(a + b*Log[c*x^n]))/(d^2*x) - (9*e^(3/2)*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(5/2) + (9*e^(3/2)*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(5/2) + (9*b*e^(3/2)*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(5/2) - (9*b*e^(3/2)*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(5/2))/18","A",1
221,1,287,129,0.5087041,"\int \frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^2} \, dx","Integrate[(x^5*(a + b*Log[c*x^n]))/(d + e*x^2)^2,x]","\frac{-\frac{2 d^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{d+e x^2}-4 d \log \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)+2 e x^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)+b n \left(-4 d \left(\text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)+\log (x) \log \left(1+\frac{i \sqrt{e} x}{\sqrt{d}}\right)\right)-4 d \left(\text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)+\log (x) \log \left(1-\frac{i \sqrt{e} x}{\sqrt{d}}\right)\right)+\frac{d \sqrt{e} x \log (x)}{\sqrt{e} x-i \sqrt{d}}+\frac{d \sqrt{e} x \log (x)}{\sqrt{e} x+i \sqrt{d}}-d \log \left(-\sqrt{e} x+i \sqrt{d}\right)-d \log \left(\sqrt{e} x+i \sqrt{d}\right)+e x^2 (2 \log (x)-1)\right)}{4 e^3}","-\frac{d \log \left(\frac{e x^2}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^3}+\frac{d x^2 \left(a+b \log \left(c x^n\right)\right)}{2 e^2 \left(d+e x^2\right)}+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{b d n \text{Li}_2\left(-\frac{e x^2}{d}\right)}{2 e^3}-\frac{b d n \log \left(d+e x^2\right)}{4 e^3}-\frac{b n x^2}{4 e^2}",1,"(2*e*x^2*(a - b*n*Log[x] + b*Log[c*x^n]) - (2*d^2*(a - b*n*Log[x] + b*Log[c*x^n]))/(d + e*x^2) - 4*d*(a - b*n*Log[x] + b*Log[c*x^n])*Log[d + e*x^2] + b*n*((d*Sqrt[e]*x*Log[x])/((-I)*Sqrt[d] + Sqrt[e]*x) + (d*Sqrt[e]*x*Log[x])/(I*Sqrt[d] + Sqrt[e]*x) + e*x^2*(-1 + 2*Log[x]) - d*Log[I*Sqrt[d] - Sqrt[e]*x] - d*Log[I*Sqrt[d] + Sqrt[e]*x] - 4*d*(Log[x]*Log[1 + (I*Sqrt[e]*x)/Sqrt[d]] + PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]]) - 4*d*(Log[x]*Log[1 - (I*Sqrt[e]*x)/Sqrt[d]] + PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])))/(4*e^3)","C",1
222,1,321,95,0.2434567,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^2} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/(d + e*x^2)^2,x]","\frac{2 \log \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)+\frac{2 d \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{d+e x^2}+\frac{b n \left(2 \left(d+e x^2\right) \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)+2 \left(d+e x^2\right) \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)+e x^2 \log \left(-\sqrt{e} x+i \sqrt{d}\right)+e x^2 \log \left(\sqrt{e} x+i \sqrt{d}\right)+2 e x^2 \log (x) \log \left(1-\frac{i \sqrt{e} x}{\sqrt{d}}\right)+2 e x^2 \log (x) \log \left(1+\frac{i \sqrt{e} x}{\sqrt{d}}\right)+d \log \left(-\sqrt{e} x+i \sqrt{d}\right)+d \log \left(\sqrt{e} x+i \sqrt{d}\right)+2 d \log (x) \log \left(1-\frac{i \sqrt{e} x}{\sqrt{d}}\right)+2 d \log (x) \log \left(1+\frac{i \sqrt{e} x}{\sqrt{d}}\right)-2 e x^2 \log (x)\right)}{d+e x^2}}{4 e^2}","\frac{\log \left(\frac{e x^2}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{2 e \left(d+e x^2\right)}+\frac{b n \text{Li}_2\left(-\frac{e x^2}{d}\right)}{4 e^2}+\frac{b n \log \left(d+e x^2\right)}{4 e^2}",1,"((2*d*(a - b*n*Log[x] + b*Log[c*x^n]))/(d + e*x^2) + 2*(a - b*n*Log[x] + b*Log[c*x^n])*Log[d + e*x^2] + (b*n*(-2*e*x^2*Log[x] + d*Log[I*Sqrt[d] - Sqrt[e]*x] + e*x^2*Log[I*Sqrt[d] - Sqrt[e]*x] + d*Log[I*Sqrt[d] + Sqrt[e]*x] + e*x^2*Log[I*Sqrt[d] + Sqrt[e]*x] + 2*d*Log[x]*Log[1 - (I*Sqrt[e]*x)/Sqrt[d]] + 2*e*x^2*Log[x]*Log[1 - (I*Sqrt[e]*x)/Sqrt[d]] + 2*d*Log[x]*Log[1 + (I*Sqrt[e]*x)/Sqrt[d]] + 2*e*x^2*Log[x]*Log[1 + (I*Sqrt[e]*x)/Sqrt[d]] + 2*(d + e*x^2)*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]] + 2*(d + e*x^2)*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]]))/(d + e*x^2))/(4*e^2)","C",1
223,1,74,50,0.0655834,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^2} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/(d + e*x^2)^2,x]","-\frac{2 a d+2 b d \log \left(c x^n\right)+b e n x^2 \log \left(d+e x^2\right)-2 b n \log (x) \left(d+e x^2\right)+b d n \log \left(d+e x^2\right)}{4 d e \left(d+e x^2\right)}","\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{2 d \left(d+e x^2\right)}-\frac{b n \log \left(d+e x^2\right)}{4 d e}",1,"-1/4*(2*a*d - 2*b*n*(d + e*x^2)*Log[x] + 2*b*d*Log[c*x^n] + b*d*n*Log[d + e*x^2] + b*e*n*x^2*Log[d + e*x^2])/(d*e*(d + e*x^2))","A",1
224,1,279,82,0.4239659,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^2\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x^2)^2),x]","-\frac{\log \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{2 d^2}+\frac{a+b \log \left(c x^n\right)-b n \log (x)}{2 d^2+2 d e x^2}+\frac{\log (x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{d^2}+\frac{b n \left(-2 \left(\text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)+\log (x) \log \left(1+\frac{i \sqrt{e} x}{\sqrt{d}}\right)\right)-2 \left(\text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)+\log (x) \log \left(1-\frac{i \sqrt{e} x}{\sqrt{d}}\right)\right)+\frac{\sqrt{e} x \log (x)}{-\sqrt{e} x+i \sqrt{d}}-\frac{\sqrt{e} x \log (x)}{\sqrt{e} x+i \sqrt{d}}+\log \left(-\sqrt{e} x+i \sqrt{d}\right)+\log \left(\sqrt{e} x+i \sqrt{d}\right)+2 \log ^2(x)\right)}{4 d^2}","-\frac{\log \left(\frac{d}{e x^2}+1\right) \left(2 a+2 b \log \left(c x^n\right)-b n\right)}{4 d^2}+\frac{a+b \log \left(c x^n\right)}{2 d \left(d+e x^2\right)}+\frac{b n \text{Li}_2\left(-\frac{d}{e x^2}\right)}{4 d^2}",1,"(a - b*n*Log[x] + b*Log[c*x^n])/(2*d^2 + 2*d*e*x^2) + (Log[x]*(a - b*n*Log[x] + b*Log[c*x^n]))/d^2 - ((a - b*n*Log[x] + b*Log[c*x^n])*Log[d + e*x^2])/(2*d^2) + (b*n*((Sqrt[e]*x*Log[x])/(I*Sqrt[d] - Sqrt[e]*x) - (Sqrt[e]*x*Log[x])/(I*Sqrt[d] + Sqrt[e]*x) + 2*Log[x]^2 + Log[I*Sqrt[d] - Sqrt[e]*x] + Log[I*Sqrt[d] + Sqrt[e]*x] - 2*(Log[x]*Log[1 + (I*Sqrt[e]*x)/Sqrt[d]] + PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]]) - 2*(Log[x]*Log[1 - (I*Sqrt[e]*x)/Sqrt[d]] + PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])))/(4*d^2)","C",1
225,1,334,126,0.5690551,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^2\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])/(x^3*(d + e*x^2)^2),x]","\frac{4 e \log \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-\frac{2 d e \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{d+e x^2}-\frac{2 d \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{x^2}-8 e \log (x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)+b n \left(\frac{e^{3/2} x \log (x)}{\sqrt{e} x-i \sqrt{d}}+\frac{e \left(-\sqrt{d}+i \sqrt{e} x\right) \log \left(\sqrt{e} x+i \sqrt{d}\right)-i e^{3/2} x \log (x)}{\sqrt{d}-i \sqrt{e} x}+4 e \left(\text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)+\log (x) \log \left(1+\frac{i \sqrt{e} x}{\sqrt{d}}\right)\right)+4 e \left(\text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)+\log (x) \log \left(1-\frac{i \sqrt{e} x}{\sqrt{d}}\right)\right)-e \log \left(-\sqrt{e} x+i \sqrt{d}\right)-\frac{2 d \log (x)+d}{x^2}-4 e \log ^2(x)\right)}{4 d^3}","\frac{e \log \left(\frac{d}{e x^2}+1\right) \left(4 a+4 b \log \left(c x^n\right)-b n\right)}{4 d^3}-\frac{4 a+4 b \log \left(c x^n\right)-b n}{4 d^2 x^2}+\frac{a+b \log \left(c x^n\right)}{2 d x^2 \left(d+e x^2\right)}-\frac{b e n \text{Li}_2\left(-\frac{d}{e x^2}\right)}{2 d^3}-\frac{b n}{2 d^2 x^2}",1,"((-2*d*(a - b*n*Log[x] + b*Log[c*x^n]))/x^2 - (2*d*e*(a - b*n*Log[x] + b*Log[c*x^n]))/(d + e*x^2) - 8*e*Log[x]*(a - b*n*Log[x] + b*Log[c*x^n]) + 4*e*(a - b*n*Log[x] + b*Log[c*x^n])*Log[d + e*x^2] + b*n*((e^(3/2)*x*Log[x])/((-I)*Sqrt[d] + Sqrt[e]*x) - 4*e*Log[x]^2 - (d + 2*d*Log[x])/x^2 - e*Log[I*Sqrt[d] - Sqrt[e]*x] + ((-I)*e^(3/2)*x*Log[x] + e*(-Sqrt[d] + I*Sqrt[e]*x)*Log[I*Sqrt[d] + Sqrt[e]*x])/(Sqrt[d] - I*Sqrt[e]*x) + 4*e*(Log[x]*Log[1 + (I*Sqrt[e]*x)/Sqrt[d]] + PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]]) + 4*e*(Log[x]*Log[1 - (I*Sqrt[e]*x)/Sqrt[d]] + PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])))/(4*d^3)","C",1
226,1,296,191,0.5587489,"\int \frac{x^4 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^2} \, dx","Integrate[(x^4*(a + b*Log[c*x^n]))/(d + e*x^2)^2,x]","\frac{-\frac{d \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-d}-\sqrt{e} x}+\frac{d \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-d}+\sqrt{e} x}-3 \sqrt{-d} \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)+3 \sqrt{-d} \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)+4 a \sqrt{e} x+4 b \sqrt{e} x \log \left(c x^n\right)+3 b \sqrt{-d} n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)-3 b \sqrt{-d} n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)+\frac{b d n \left(\log (x)-\log \left(\sqrt{-d}-\sqrt{e} x\right)\right)}{\sqrt{-d}}+b \sqrt{-d} n \left(\log (x)-\log \left(\sqrt{-d}+\sqrt{e} x\right)\right)-4 b \sqrt{e} n x}{4 e^{5/2}}","-\frac{3 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^{5/2}}+\frac{d x \left(a+b \log \left(c x^n\right)\right)}{2 e^2 \left(d+e x^2\right)}+\frac{a x}{e^2}+\frac{b x \log \left(c x^n\right)}{e^2}+\frac{3 i b \sqrt{d} n \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 e^{5/2}}-\frac{3 i b \sqrt{d} n \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 e^{5/2}}-\frac{b \sqrt{d} n \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 e^{5/2}}-\frac{b n x}{e^2}",1,"(4*a*Sqrt[e]*x - 4*b*Sqrt[e]*n*x + 4*b*Sqrt[e]*x*Log[c*x^n] - (d*(a + b*Log[c*x^n]))/(Sqrt[-d] - Sqrt[e]*x) + (d*(a + b*Log[c*x^n]))/(Sqrt[-d] + Sqrt[e]*x) + (b*d*n*(Log[x] - Log[Sqrt[-d] - Sqrt[e]*x]))/Sqrt[-d] + b*Sqrt[-d]*n*(Log[x] - Log[Sqrt[-d] + Sqrt[e]*x]) - 3*Sqrt[-d]*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]] + 3*Sqrt[-d]*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)] + 3*b*Sqrt[-d]*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]] - 3*b*Sqrt[-d]*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(4*e^(5/2))","A",1
227,1,258,164,0.4933656,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^2} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e*x^2)^2,x]","\frac{\frac{d \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{3/2}}+\frac{\log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-d}}+\frac{a+b \log \left(c x^n\right)}{\sqrt{-d}-\sqrt{e} x}-\frac{a+b \log \left(c x^n\right)}{\sqrt{-d}+\sqrt{e} x}+\frac{b n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{\sqrt{-d}}+\frac{b d n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)}{(-d)^{3/2}}+\frac{b d n \left(\log (x)-\log \left(\sqrt{-d}-\sqrt{e} x\right)\right)}{(-d)^{3/2}}+\frac{b n \left(\log (x)-\log \left(\sqrt{-d}+\sqrt{e} x\right)\right)}{\sqrt{-d}}}{4 e^{3/2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 \sqrt{d} e^{3/2}}-\frac{x \left(a+b \log \left(c x^n\right)\right)}{2 e \left(d+e x^2\right)}-\frac{i b n \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 \sqrt{d} e^{3/2}}+\frac{i b n \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 \sqrt{d} e^{3/2}}+\frac{b n \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 \sqrt{d} e^{3/2}}",1,"((a + b*Log[c*x^n])/(Sqrt[-d] - Sqrt[e]*x) - (a + b*Log[c*x^n])/(Sqrt[-d] + Sqrt[e]*x) + (b*d*n*(Log[x] - Log[Sqrt[-d] - Sqrt[e]*x]))/(-d)^(3/2) + (b*n*(Log[x] - Log[Sqrt[-d] + Sqrt[e]*x]))/Sqrt[-d] + (d*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(3/2) + ((a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)])/Sqrt[-d] + (b*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]])/Sqrt[-d] + (b*d*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(3/2))/(4*e^(3/2))","A",1
228,1,289,164,0.5767555,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+e x^2\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*x^2)^2,x]","\frac{1}{4} \left(\frac{\log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{3/2} \sqrt{e}}+\frac{d \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{5/2} \sqrt{e}}+\frac{a+b \log \left(c x^n\right)}{d \left(\sqrt{-d} \sqrt{e}+e x\right)}+\frac{a+b \log \left(c x^n\right)}{d e x+(-d)^{3/2} \sqrt{e}}+\frac{b d n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{(-d)^{5/2} \sqrt{e}}+\frac{b n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)}{(-d)^{3/2} \sqrt{e}}+\frac{b d n \left(\log (x)-\log \left(\sqrt{-d}-\sqrt{e} x\right)\right)}{(-d)^{5/2} \sqrt{e}}+\frac{b n \left(\log (x)-\log \left(\sqrt{-d}+\sqrt{e} x\right)\right)}{(-d)^{3/2} \sqrt{e}}\right)","\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 d^{3/2} \sqrt{e}}+\frac{x \left(a+b \log \left(c x^n\right)\right)}{2 d \left(d+e x^2\right)}-\frac{i b n \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{3/2} \sqrt{e}}+\frac{i b n \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{3/2} \sqrt{e}}-\frac{b n \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2} \sqrt{e}}",1,"((a + b*Log[c*x^n])/(d*(Sqrt[-d]*Sqrt[e] + e*x)) + (a + b*Log[c*x^n])/((-d)^(3/2)*Sqrt[e] + d*e*x) + (b*d*n*(Log[x] - Log[Sqrt[-d] - Sqrt[e]*x]))/((-d)^(5/2)*Sqrt[e]) + (b*n*(Log[x] - Log[Sqrt[-d] + Sqrt[e]*x]))/((-d)^(3/2)*Sqrt[e]) + ((a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]])/((-d)^(3/2)*Sqrt[e]) + (d*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)])/((-d)^(5/2)*Sqrt[e]) + (b*d*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]])/((-d)^(5/2)*Sqrt[e]) + (b*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/((-d)^(3/2)*Sqrt[e]))/4","A",1
229,1,328,183,0.7295014,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^2\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*(d + e*x^2)^2),x]","\frac{1}{4} \left(\frac{\sqrt{e} \left(a+b \log \left(c x^n\right)\right)}{d^2 \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{\sqrt{e} \left(a+b \log \left(c x^n\right)\right)}{d^2 \left(\sqrt{-d}+\sqrt{e} x\right)}-\frac{4 \left(a+b \log \left(c x^n\right)\right)}{d^2 x}+\frac{3 \sqrt{e} \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{5/2}}-\frac{3 \sqrt{e} \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{5/2}}-\frac{4 b n}{d^2 x}-\frac{3 b \sqrt{e} n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{(-d)^{5/2}}+\frac{3 b \sqrt{e} n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)}{(-d)^{5/2}}+\frac{b \sqrt{e} n \left(\log \left(\sqrt{-d}-\sqrt{e} x\right)-\log (x)\right)}{(-d)^{5/2}}+\frac{b \sqrt{e} n \left(\log (x)-\log \left(\sqrt{-d}+\sqrt{e} x\right)\right)}{(-d)^{5/2}}\right)","-\frac{\sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(3 a+3 b \log \left(c x^n\right)-b n\right)}{2 d^{5/2}}-\frac{3 a+3 b \log \left(c x^n\right)-b n}{2 d^2 x}+\frac{a+b \log \left(c x^n\right)}{2 d x \left(d+e x^2\right)}+\frac{3 i b \sqrt{e} n \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{5/2}}-\frac{3 i b \sqrt{e} n \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{5/2}}-\frac{3 b n}{2 d^2 x}",1,"((-4*b*n)/(d^2*x) - (4*(a + b*Log[c*x^n]))/(d^2*x) + (Sqrt[e]*(a + b*Log[c*x^n]))/(d^2*(Sqrt[-d] - Sqrt[e]*x)) - (Sqrt[e]*(a + b*Log[c*x^n]))/(d^2*(Sqrt[-d] + Sqrt[e]*x)) + (b*Sqrt[e]*n*(-Log[x] + Log[Sqrt[-d] - Sqrt[e]*x]))/(-d)^(5/2) + (b*Sqrt[e]*n*(Log[x] - Log[Sqrt[-d] + Sqrt[e]*x]))/(-d)^(5/2) + (3*Sqrt[e]*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(5/2) - (3*Sqrt[e]*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(5/2) - (3*b*Sqrt[e]*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(5/2) + (3*b*Sqrt[e]*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(5/2))/4","A",1
230,1,361,224,0.7108547,"\int \frac{a+b \log \left(c x^n\right)}{x^4 \left(d+e x^2\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])/(x^4*(d + e*x^2)^2),x]","\frac{1}{36} \left(-\frac{9 e^{3/2} \left(a+b \log \left(c x^n\right)\right)}{d^3 \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{9 e^{3/2} \left(a+b \log \left(c x^n\right)\right)}{d^3 \left(\sqrt{-d}+\sqrt{e} x\right)}+\frac{72 e \left(a+b \log \left(c x^n\right)\right)}{d^3 x}-\frac{12 \left(a+b \log \left(c x^n\right)\right)}{d^2 x^3}+\frac{45 e^{3/2} \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{7/2}}-\frac{45 e^{3/2} \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{7/2}}+\frac{72 b e n}{d^3 x}-\frac{4 b n}{d^2 x^3}-\frac{45 b e^{3/2} n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{(-d)^{7/2}}+\frac{45 b e^{3/2} n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)}{(-d)^{7/2}}-\frac{9 b e^{3/2} n \left(\log (x)-\log \left(\sqrt{-d}-\sqrt{e} x\right)\right)}{(-d)^{7/2}}+\frac{9 b e^{3/2} n \left(\log (x)-\log \left(\sqrt{-d}+\sqrt{e} x\right)\right)}{(-d)^{7/2}}\right)","\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(5 a+5 b \log \left(c x^n\right)-b n\right)}{2 d^{7/2}}+\frac{e \left(5 a+5 b \log \left(c x^n\right)-b n\right)}{2 d^3 x}-\frac{5 a+5 b \log \left(c x^n\right)-b n}{6 d^2 x^3}+\frac{a+b \log \left(c x^n\right)}{2 d x^3 \left(d+e x^2\right)}-\frac{5 i b e^{3/2} n \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{7/2}}+\frac{5 i b e^{3/2} n \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{7/2}}+\frac{5 b e n}{2 d^3 x}-\frac{5 b n}{18 d^2 x^3}",1,"((-4*b*n)/(d^2*x^3) + (72*b*e*n)/(d^3*x) - (12*(a + b*Log[c*x^n]))/(d^2*x^3) + (72*e*(a + b*Log[c*x^n]))/(d^3*x) - (9*e^(3/2)*(a + b*Log[c*x^n]))/(d^3*(Sqrt[-d] - Sqrt[e]*x)) + (9*e^(3/2)*(a + b*Log[c*x^n]))/(d^3*(Sqrt[-d] + Sqrt[e]*x)) - (9*b*e^(3/2)*n*(Log[x] - Log[Sqrt[-d] - Sqrt[e]*x]))/(-d)^(7/2) + (9*b*e^(3/2)*n*(Log[x] - Log[Sqrt[-d] + Sqrt[e]*x]))/(-d)^(7/2) + (45*e^(3/2)*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(7/2) - (45*e^(3/2)*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(7/2) - (45*b*e^(3/2)*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(7/2) + (45*b*e^(3/2)*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(7/2))/36","A",1
231,1,498,152,0.6013591,"\int \frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^3} \, dx","Integrate[(x^5*(a + b*Log[c*x^n]))/(d + e*x^2)^3,x]","\frac{-2 d^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)+8 d \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)+4 \left(d+e x^2\right)^2 \log \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)+b n \left(3 d^2 \log \left(-\sqrt{e} x+i \sqrt{d}\right)+3 d^2 \log \left(\sqrt{e} x+i \sqrt{d}\right)+4 d^2 \log (x) \log \left(1-\frac{i \sqrt{e} x}{\sqrt{d}}\right)+4 d^2 \log (x) \log \left(1+\frac{i \sqrt{e} x}{\sqrt{d}}\right)+d^2+3 e^2 x^4 \log \left(-\sqrt{e} x+i \sqrt{d}\right)+3 e^2 x^4 \log \left(\sqrt{e} x+i \sqrt{d}\right)+4 e^2 x^4 \log (x) \log \left(1-\frac{i \sqrt{e} x}{\sqrt{d}}\right)+4 e^2 x^4 \log (x) \log \left(1+\frac{i \sqrt{e} x}{\sqrt{d}}\right)+4 \left(d+e x^2\right)^2 \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)+4 \left(d+e x^2\right)^2 \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)+d e x^2-4 d e x^2 \log (x)+6 d e x^2 \log \left(-\sqrt{e} x+i \sqrt{d}\right)+6 d e x^2 \log \left(\sqrt{e} x+i \sqrt{d}\right)+8 d e x^2 \log (x) \log \left(1-\frac{i \sqrt{e} x}{\sqrt{d}}\right)+8 d e x^2 \log (x) \log \left(1+\frac{i \sqrt{e} x}{\sqrt{d}}\right)-6 e^2 x^4 \log (x)\right)}{8 e^3 \left(d+e x^2\right)^2}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{4 e^3 \left(d+e x^2\right)^2}+\frac{\log \left(\frac{e x^2}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^3}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{e^2 \left(d+e x^2\right)}+\frac{b n \text{Li}_2\left(-\frac{e x^2}{d}\right)}{4 e^3}+\frac{b d n}{8 e^3 \left(d+e x^2\right)}+\frac{3 b n \log \left(d+e x^2\right)}{8 e^3}+\frac{b n \log (x)}{4 e^3}",1,"(-2*d^2*(a - b*n*Log[x] + b*Log[c*x^n]) + 8*d*(d + e*x^2)*(a - b*n*Log[x] + b*Log[c*x^n]) + 4*(d + e*x^2)^2*(a - b*n*Log[x] + b*Log[c*x^n])*Log[d + e*x^2] + b*n*(d^2 + d*e*x^2 - 4*d*e*x^2*Log[x] - 6*e^2*x^4*Log[x] + 3*d^2*Log[I*Sqrt[d] - Sqrt[e]*x] + 6*d*e*x^2*Log[I*Sqrt[d] - Sqrt[e]*x] + 3*e^2*x^4*Log[I*Sqrt[d] - Sqrt[e]*x] + 3*d^2*Log[I*Sqrt[d] + Sqrt[e]*x] + 6*d*e*x^2*Log[I*Sqrt[d] + Sqrt[e]*x] + 3*e^2*x^4*Log[I*Sqrt[d] + Sqrt[e]*x] + 4*d^2*Log[x]*Log[1 - (I*Sqrt[e]*x)/Sqrt[d]] + 8*d*e*x^2*Log[x]*Log[1 - (I*Sqrt[e]*x)/Sqrt[d]] + 4*e^2*x^4*Log[x]*Log[1 - (I*Sqrt[e]*x)/Sqrt[d]] + 4*d^2*Log[x]*Log[1 + (I*Sqrt[e]*x)/Sqrt[d]] + 8*d*e*x^2*Log[x]*Log[1 + (I*Sqrt[e]*x)/Sqrt[d]] + 4*e^2*x^4*Log[x]*Log[1 + (I*Sqrt[e]*x)/Sqrt[d]] + 4*(d + e*x^2)^2*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]] + 4*(d + e*x^2)^2*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]]))/(8*e^3*(d + e*x^2)^2)","C",1
232,1,129,68,0.150617,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^3} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/(d + e*x^2)^3,x]","-\frac{2 a d^2+4 a d e x^2+2 b d \left(d+2 e x^2\right) \log \left(c x^n\right)+b d^2 n \log \left(d+e x^2\right)+b d^2 n+b e^2 n x^4 \log \left(d+e x^2\right)+b d e n x^2+2 b d e n x^2 \log \left(d+e x^2\right)-2 b n \log (x) \left(d+e x^2\right)^2}{8 d e^2 \left(d+e x^2\right)^2}","\frac{x^4 \left(a+b \log \left(c x^n\right)\right)}{4 d \left(d+e x^2\right)^2}-\frac{b n}{8 e^2 \left(d+e x^2\right)}-\frac{b n \log \left(d+e x^2\right)}{8 d e^2}",1,"-1/8*(2*a*d^2 + b*d^2*n + 4*a*d*e*x^2 + b*d*e*n*x^2 - 2*b*n*(d + e*x^2)^2*Log[x] + 2*b*d*(d + 2*e*x^2)*Log[c*x^n] + b*d^2*n*Log[d + e*x^2] + 2*b*d*e*n*x^2*Log[d + e*x^2] + b*e^2*n*x^4*Log[d + e*x^2])/(d*e^2*(d + e*x^2)^2)","A",1
233,1,111,82,0.0705852,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^3} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/(d + e*x^2)^3,x]","\frac{-a-b \left(\log \left(c x^n\right)-n \log (x)\right)}{4 e \left(d+e x^2\right)^2}-\frac{b n \log \left(d+e x^2\right)}{8 d^2 e}+\frac{b n \log (x)}{4 d^2 e}+\frac{b n}{8 d e \left(d+e x^2\right)}-\frac{b n \log (x)}{4 e \left(d+e x^2\right)^2}","-\frac{a+b \log \left(c x^n\right)}{4 e \left(d+e x^2\right)^2}-\frac{b n \log \left(d+e x^2\right)}{8 d^2 e}+\frac{b n \log (x)}{4 d^2 e}+\frac{b n}{8 d e \left(d+e x^2\right)}",1,"(b*n)/(8*d*e*(d + e*x^2)) + (b*n*Log[x])/(4*d^2*e) - (b*n*Log[x])/(4*e*(d + e*x^2)^2) + (-a - b*(-(n*Log[x]) + Log[c*x^n]))/(4*e*(d + e*x^2)^2) - (b*n*Log[d + e*x^2])/(8*d^2*e)","A",1
234,1,396,115,1.0213709,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^2\right)^3} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x^2)^3),x]","\frac{\frac{4 d^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{\left(d+e x^2\right)^2}+\frac{8 d \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{d+e x^2}-8 \log \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)+16 \log (x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-b n \left(8 \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)+8 \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)+\frac{d}{d-i \sqrt{d} \sqrt{e} x}+\frac{d}{d+i \sqrt{d} \sqrt{e} x}+8 \log (x) \log \left(1-\frac{i \sqrt{e} x}{\sqrt{d}}\right)+8 \log (x) \log \left(1+\frac{i \sqrt{e} x}{\sqrt{d}}\right)+\frac{5 \sqrt{e} x \log (x)}{\sqrt{e} x-i \sqrt{d}}+\frac{5 \sqrt{e} x \log (x)}{\sqrt{e} x+i \sqrt{d}}-\frac{d \log (x)}{\left(\sqrt{d}-i \sqrt{e} x\right)^2}-\frac{d \log (x)}{\left(\sqrt{d}+i \sqrt{e} x\right)^2}-6 \log \left(-\sqrt{e} x+i \sqrt{d}\right)-6 \log \left(\sqrt{e} x+i \sqrt{d}\right)-8 \log ^2(x)+2 \log (x)\right)}{16 d^3}","-\frac{\log \left(\frac{d}{e x^2}+1\right) \left(4 a+4 b \log \left(c x^n\right)-3 b n\right)}{8 d^3}+\frac{4 a+4 b \log \left(c x^n\right)-b n}{8 d^2 \left(d+e x^2\right)}+\frac{a+b \log \left(c x^n\right)}{4 d \left(d+e x^2\right)^2}+\frac{b n \text{Li}_2\left(-\frac{d}{e x^2}\right)}{4 d^3}",1,"((4*d^2*(a - b*n*Log[x] + b*Log[c*x^n]))/(d + e*x^2)^2 + (8*d*(a - b*n*Log[x] + b*Log[c*x^n]))/(d + e*x^2) + 16*Log[x]*(a - b*n*Log[x] + b*Log[c*x^n]) - 8*(a - b*n*Log[x] + b*Log[c*x^n])*Log[d + e*x^2] - b*n*(d/(d - I*Sqrt[d]*Sqrt[e]*x) + d/(d + I*Sqrt[d]*Sqrt[e]*x) + 2*Log[x] - (d*Log[x])/(Sqrt[d] - I*Sqrt[e]*x)^2 - (d*Log[x])/(Sqrt[d] + I*Sqrt[e]*x)^2 + (5*Sqrt[e]*x*Log[x])/((-I)*Sqrt[d] + Sqrt[e]*x) + (5*Sqrt[e]*x*Log[x])/(I*Sqrt[d] + Sqrt[e]*x) - 8*Log[x]^2 - 6*Log[I*Sqrt[d] - Sqrt[e]*x] - 6*Log[I*Sqrt[d] + Sqrt[e]*x] + 8*Log[x]*Log[1 - (I*Sqrt[e]*x)/Sqrt[d]] + 8*Log[x]*Log[1 + (I*Sqrt[e]*x)/Sqrt[d]] + 8*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]] + 8*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]]))/(16*d^3)","C",1
235,1,507,162,1.2718392,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^2\right)^3} \, dx","Integrate[(a + b*Log[c*x^n])/(x^3*(d + e*x^2)^3),x]","\frac{-\frac{4 d^2 e \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{\left(d+e x^2\right)^2}-\frac{16 d e \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{d+e x^2}+24 e \log \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-\frac{8 d \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{x^2}-48 e \log (x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)+b n \left(\frac{9 e^{3/2} x \log (x)}{\sqrt{e} x-i \sqrt{d}}+\frac{9 i e \left(\sqrt{e} x+i \sqrt{d}\right) \log \left(\sqrt{e} x+i \sqrt{d}\right)-9 i e^{3/2} x \log (x)}{\sqrt{d}-i \sqrt{e} x}+24 e \left(\text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)+\log (x) \log \left(1+\frac{i \sqrt{e} x}{\sqrt{d}}\right)\right)+24 e \left(\text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)+\log (x) \log \left(1-\frac{i \sqrt{e} x}{\sqrt{d}}\right)\right)+e \left(\frac{d}{d+i \sqrt{d} \sqrt{e} x}-\frac{d \log (x)}{\left(\sqrt{d}+i \sqrt{e} x\right)^2}-\log \left(-\sqrt{e} x+i \sqrt{d}\right)+\log (x)\right)-9 e \log \left(-\sqrt{e} x+i \sqrt{d}\right)+e \left(\frac{d}{d-i \sqrt{d} \sqrt{e} x}-\frac{d \log (x)}{\left(\sqrt{d}-i \sqrt{e} x\right)^2}-\log \left(\sqrt{e} x+i \sqrt{d}\right)+\log (x)\right)-\frac{4 d (2 \log (x)+1)}{x^2}-24 e \log ^2(x)\right)}{16 d^4}","\frac{e \log \left(\frac{d}{e x^2}+1\right) \left(12 a+12 b \log \left(c x^n\right)-5 b n\right)}{8 d^4}-\frac{12 a+12 b \log \left(c x^n\right)-5 b n}{8 d^3 x^2}+\frac{6 a+6 b \log \left(c x^n\right)-b n}{8 d^2 x^2 \left(d+e x^2\right)}+\frac{a+b \log \left(c x^n\right)}{4 d x^2 \left(d+e x^2\right)^2}-\frac{3 b e n \text{Li}_2\left(-\frac{d}{e x^2}\right)}{4 d^4}-\frac{3 b n}{4 d^3 x^2}",1,"((-8*d*(a - b*n*Log[x] + b*Log[c*x^n]))/x^2 - (4*d^2*e*(a - b*n*Log[x] + b*Log[c*x^n]))/(d + e*x^2)^2 - (16*d*e*(a - b*n*Log[x] + b*Log[c*x^n]))/(d + e*x^2) - 48*e*Log[x]*(a - b*n*Log[x] + b*Log[c*x^n]) + 24*e*(a - b*n*Log[x] + b*Log[c*x^n])*Log[d + e*x^2] + b*n*((9*e^(3/2)*x*Log[x])/((-I)*Sqrt[d] + Sqrt[e]*x) - 24*e*Log[x]^2 - (4*d*(1 + 2*Log[x]))/x^2 + e*(d/(d + I*Sqrt[d]*Sqrt[e]*x) + Log[x] - (d*Log[x])/(Sqrt[d] + I*Sqrt[e]*x)^2 - Log[I*Sqrt[d] - Sqrt[e]*x]) - 9*e*Log[I*Sqrt[d] - Sqrt[e]*x] + e*(d/(d - I*Sqrt[d]*Sqrt[e]*x) + Log[x] - (d*Log[x])/(Sqrt[d] - I*Sqrt[e]*x)^2 - Log[I*Sqrt[d] + Sqrt[e]*x]) + ((-9*I)*e^(3/2)*x*Log[x] + (9*I)*e*(I*Sqrt[d] + Sqrt[e]*x)*Log[I*Sqrt[d] + Sqrt[e]*x])/(Sqrt[d] - I*Sqrt[e]*x) + 24*e*(Log[x]*Log[1 + (I*Sqrt[e]*x)/Sqrt[d]] + PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]]) + 24*e*(Log[x]*Log[1 - (I*Sqrt[e]*x)/Sqrt[d]] + PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])))/(16*d^4)","C",1
236,1,495,211,1.2679141,"\int \frac{x^4 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^3} \, dx","Integrate[(x^4*(a + b*Log[c*x^n]))/(d + e*x^2)^3,x]","\frac{-\frac{3 \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-d}}+\frac{3 \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-d}}+\frac{5 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-d}-\sqrt{e} x}-\frac{5 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-d}+\sqrt{e} x}-\frac{\sqrt{-d} \left(a+b \log \left(c x^n\right)\right)}{\left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{\sqrt{-d} \left(a+b \log \left(c x^n\right)\right)}{\left(\sqrt{-d}+\sqrt{e} x\right)^2}+\frac{3 b n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{\sqrt{-d}}-\frac{3 b n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)}{\sqrt{-d}}-\frac{5 b n \left(\log (x)-\log \left(\sqrt{-d}-\sqrt{e} x\right)\right)}{\sqrt{-d}}+\frac{5 b n \left(\log (x)-\log \left(\sqrt{-d}+\sqrt{e} x\right)\right)}{\sqrt{-d}}-\frac{b n \left(\log (x) \left(d-\sqrt{-d} \sqrt{e} x\right)+\left(\sqrt{-d} \sqrt{e} x-d\right) \log \left(\sqrt{-d}+\sqrt{e} x\right)+d\right)}{d \left(\sqrt{-d}+\sqrt{e} x\right)}+\frac{b n \left(\log (x) \left(\sqrt{-d} \sqrt{e} x+d\right)-\left(\sqrt{-d} \sqrt{e} x+d\right) \log \left(d \sqrt{e} x+(-d)^{3/2}\right)+d\right)}{d \left(\sqrt{-d}-\sqrt{e} x\right)}}{16 e^{5/2}}","\frac{3 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{8 \sqrt{d} e^{5/2}}-\frac{5 x \left(a+b \log \left(c x^n\right)\right)}{8 e^2 \left(d+e x^2\right)}+\frac{d x \left(a+b \log \left(c x^n\right)\right)}{4 e^2 \left(d+e x^2\right)^2}-\frac{3 i b n \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 \sqrt{d} e^{5/2}}+\frac{3 i b n \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 \sqrt{d} e^{5/2}}+\frac{b n \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 \sqrt{d} e^{5/2}}-\frac{b n x}{8 e^2 \left(d+e x^2\right)}",1,"(-((Sqrt[-d]*(a + b*Log[c*x^n]))/(Sqrt[-d] - Sqrt[e]*x)^2) + (5*(a + b*Log[c*x^n]))/(Sqrt[-d] - Sqrt[e]*x) + (Sqrt[-d]*(a + b*Log[c*x^n]))/(Sqrt[-d] + Sqrt[e]*x)^2 - (5*(a + b*Log[c*x^n]))/(Sqrt[-d] + Sqrt[e]*x) - (5*b*n*(Log[x] - Log[Sqrt[-d] - Sqrt[e]*x]))/Sqrt[-d] + (5*b*n*(Log[x] - Log[Sqrt[-d] + Sqrt[e]*x]))/Sqrt[-d] - (b*n*(d + (d - Sqrt[-d]*Sqrt[e]*x)*Log[x] + (-d + Sqrt[-d]*Sqrt[e]*x)*Log[Sqrt[-d] + Sqrt[e]*x]))/(d*(Sqrt[-d] + Sqrt[e]*x)) - (3*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]])/Sqrt[-d] + (b*n*(d + (d + Sqrt[-d]*Sqrt[e]*x)*Log[x] - (d + Sqrt[-d]*Sqrt[e]*x)*Log[(-d)^(3/2) + d*Sqrt[e]*x]))/(d*(Sqrt[-d] - Sqrt[e]*x)) + (3*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)])/Sqrt[-d] + (3*b*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]])/Sqrt[-d] - (3*b*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/Sqrt[-d])/(16*e^(5/2))","B",1
237,1,497,187,1.0814636,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^3} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e*x^2)^3,x]","\frac{\frac{\log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{3/2}}+\frac{d \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{5/2}}-\frac{a+b \log \left(c x^n\right)}{\sqrt{-d} d-d \sqrt{e} x}+\frac{a+b \log \left(c x^n\right)}{d \sqrt{e} x+\sqrt{-d} d}+\frac{d \left(a+b \log \left(c x^n\right)\right)}{(-d)^{3/2} \left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{a+b \log \left(c x^n\right)}{\sqrt{-d} \left(\sqrt{-d}+\sqrt{e} x\right)^2}+\frac{b n \left(\log (x) \left(d-\sqrt{-d} \sqrt{e} x\right)+\left(\sqrt{-d} \sqrt{e} x-d\right) \log \left(\sqrt{-d}+\sqrt{e} x\right)+d\right)}{d^2 \left(\sqrt{-d}+\sqrt{e} x\right)}-\frac{b n \left(\log (x) \left(\sqrt{-d} \sqrt{e} x+d\right)-\left(\sqrt{-d} \sqrt{e} x+d\right) \log \left(d \sqrt{e} x+(-d)^{3/2}\right)+d\right)}{d^2 \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{b d n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{(-d)^{5/2}}+\frac{b n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)}{(-d)^{3/2}}+\frac{b d n \left(\log (x)-\log \left(\sqrt{-d}-\sqrt{e} x\right)\right)}{(-d)^{5/2}}+\frac{b n \left(\log (x)-\log \left(\sqrt{-d}+\sqrt{e} x\right)\right)}{(-d)^{3/2}}}{16 e^{3/2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{8 d^{3/2} e^{3/2}}+\frac{x \left(a+b \log \left(c x^n\right)\right)}{8 d e \left(d+e x^2\right)}-\frac{x \left(a+b \log \left(c x^n\right)\right)}{4 e \left(d+e x^2\right)^2}-\frac{i b n \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{3/2} e^{3/2}}+\frac{i b n \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{3/2} e^{3/2}}+\frac{b n x}{8 d e \left(d+e x^2\right)}",1,"((d*(a + b*Log[c*x^n]))/((-d)^(3/2)*(Sqrt[-d] - Sqrt[e]*x)^2) + (a + b*Log[c*x^n])/(Sqrt[-d]*(Sqrt[-d] + Sqrt[e]*x)^2) - (a + b*Log[c*x^n])/(Sqrt[-d]*d - d*Sqrt[e]*x) + (a + b*Log[c*x^n])/(Sqrt[-d]*d + d*Sqrt[e]*x) + (b*d*n*(Log[x] - Log[Sqrt[-d] - Sqrt[e]*x]))/(-d)^(5/2) + (b*n*(Log[x] - Log[Sqrt[-d] + Sqrt[e]*x]))/(-d)^(3/2) + (b*n*(d + (d - Sqrt[-d]*Sqrt[e]*x)*Log[x] + (-d + Sqrt[-d]*Sqrt[e]*x)*Log[Sqrt[-d] + Sqrt[e]*x]))/(d^2*(Sqrt[-d] + Sqrt[e]*x)) + ((a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(3/2) - (b*n*(d + (d + Sqrt[-d]*Sqrt[e]*x)*Log[x] - (d + Sqrt[-d]*Sqrt[e]*x)*Log[(-d)^(3/2) + d*Sqrt[e]*x]))/(d^2*(Sqrt[-d] - Sqrt[e]*x)) + (d*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(5/2) + (b*d*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(5/2) + (b*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(3/2))/(16*e^(3/2))","B",1
238,1,544,210,0.9546289,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+e x^2\right)^3} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*x^2)^3,x]","\frac{1}{16} \left(\frac{3 \left(a+b \log \left(c x^n\right)\right)}{d^2 e x+(-d)^{5/2} \sqrt{e}}+\frac{3 \left(a+b \log \left(c x^n\right)\right)}{d^2 e x+(-d)^{3/2} d \sqrt{e}}-\frac{3 \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{5/2} \sqrt{e}}+\frac{3 \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{5/2} \sqrt{e}}+\frac{d \left(a+b \log \left(c x^n\right)\right)}{(-d)^{5/2} \sqrt{e} \left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{a+b \log \left(c x^n\right)}{(-d)^{3/2} \sqrt{e} \left(\sqrt{-d}+\sqrt{e} x\right)^2}-\frac{b n \left(\log (x) \left(d-\sqrt{-d} \sqrt{e} x\right)+\left(\sqrt{-d} \sqrt{e} x-d\right) \log \left(\sqrt{-d}+\sqrt{e} x\right)+d\right)}{d^3 \left(\sqrt{-d} \sqrt{e}+e x\right)}-\frac{b n \left(\log (x) \left(\sqrt{-d} \sqrt{e} x+d\right)-\left(\sqrt{-d} \sqrt{e} x+d\right) \log \left(d \sqrt{e} x+(-d)^{3/2}\right)+d\right)}{d^3 e x+(-d)^{7/2} \sqrt{e}}+\frac{3 b n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{(-d)^{5/2} \sqrt{e}}-\frac{3 b n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)}{(-d)^{5/2} \sqrt{e}}+\frac{3 b n \left(\log (x)-\log \left(\sqrt{-d}-\sqrt{e} x\right)\right)}{(-d)^{5/2} \sqrt{e}}-\frac{3 b n \left(\log (x)-\log \left(\sqrt{-d}+\sqrt{e} x\right)\right)}{(-d)^{5/2} \sqrt{e}}\right)","\frac{3 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{8 d^{5/2} \sqrt{e}}+\frac{3 x \left(a+b \log \left(c x^n\right)\right)}{8 d^2 \left(d+e x^2\right)}+\frac{x \left(a+b \log \left(c x^n\right)\right)}{4 d \left(d+e x^2\right)^2}-\frac{3 i b n \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{5/2} \sqrt{e}}+\frac{3 i b n \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{5/2} \sqrt{e}}-\frac{b n \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{5/2} \sqrt{e}}-\frac{b n x}{8 d^2 \left(d+e x^2\right)}",1,"((d*(a + b*Log[c*x^n]))/((-d)^(5/2)*Sqrt[e]*(Sqrt[-d] - Sqrt[e]*x)^2) + (a + b*Log[c*x^n])/((-d)^(3/2)*Sqrt[e]*(Sqrt[-d] + Sqrt[e]*x)^2) + (3*(a + b*Log[c*x^n]))/((-d)^(5/2)*Sqrt[e] + d^2*e*x) + (3*(a + b*Log[c*x^n]))/((-d)^(3/2)*d*Sqrt[e] + d^2*e*x) + (3*b*n*(Log[x] - Log[Sqrt[-d] - Sqrt[e]*x]))/((-d)^(5/2)*Sqrt[e]) - (3*b*n*(Log[x] - Log[Sqrt[-d] + Sqrt[e]*x]))/((-d)^(5/2)*Sqrt[e]) - (b*n*(d + (d - Sqrt[-d]*Sqrt[e]*x)*Log[x] + (-d + Sqrt[-d]*Sqrt[e]*x)*Log[Sqrt[-d] + Sqrt[e]*x]))/(d^3*(Sqrt[-d]*Sqrt[e] + e*x)) - (3*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]])/((-d)^(5/2)*Sqrt[e]) - (b*n*(d + (d + Sqrt[-d]*Sqrt[e]*x)*Log[x] - (d + Sqrt[-d]*Sqrt[e]*x)*Log[(-d)^(3/2) + d*Sqrt[e]*x]))/((-d)^(7/2)*Sqrt[e] + d^3*e*x) + (3*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)])/((-d)^(5/2)*Sqrt[e]) + (3*b*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]])/((-d)^(5/2)*Sqrt[e]) - (3*b*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/((-d)^(5/2)*Sqrt[e]))/16","B",1
239,1,552,219,1.6133815,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^2\right)^3} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*(d + e*x^2)^3),x]","\frac{1}{16} \left(\frac{7 \sqrt{e} \left(a+b \log \left(c x^n\right)\right)}{d^3 \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{7 \sqrt{e} \left(a+b \log \left(c x^n\right)\right)}{d^3 \left(\sqrt{-d}+\sqrt{e} x\right)}-\frac{16 \left(a+b \log \left(c x^n\right)\right)}{d^3 x}+\frac{d \sqrt{e} \left(a+b \log \left(c x^n\right)\right)}{(-d)^{7/2} \left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{\sqrt{e} \left(a+b \log \left(c x^n\right)\right)}{(-d)^{5/2} \left(\sqrt{-d}+\sqrt{e} x\right)^2}-\frac{15 \sqrt{e} \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{7/2}}+\frac{15 \sqrt{e} \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{7/2}}-\frac{16 b n}{d^3 x}+\frac{15 b \sqrt{e} n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{(-d)^{7/2}}-\frac{15 b \sqrt{e} n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)}{(-d)^{7/2}}+\frac{7 b \sqrt{e} n \left(\log (x)-\log \left(\sqrt{-d}-\sqrt{e} x\right)\right)}{(-d)^{7/2}}-\frac{7 b \sqrt{e} n \left(\log (x)-\log \left(\sqrt{-d}+\sqrt{e} x\right)\right)}{(-d)^{7/2}}+\frac{b d \sqrt{e} n \left(\frac{1}{\sqrt{-d} \left(\sqrt{-d}+\sqrt{e} x\right)}+\frac{\log \left(\sqrt{-d}+\sqrt{e} x\right)}{d}-\frac{\log (x)}{d}\right)}{(-d)^{7/2}}+\frac{b \sqrt{e} n \left(\frac{1}{\sqrt{-d} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{\log \left(d \sqrt{e} x+(-d)^{3/2}\right)}{d}-\frac{\log (x)}{d}\right)}{(-d)^{5/2}}\right)","-\frac{\sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(15 a+15 b \log \left(c x^n\right)-8 b n\right)}{8 d^{7/2}}-\frac{15 a+15 b \log \left(c x^n\right)-8 b n}{8 d^3 x}+\frac{5 a+5 b \log \left(c x^n\right)-b n}{8 d^2 x \left(d+e x^2\right)}+\frac{a+b \log \left(c x^n\right)}{4 d x \left(d+e x^2\right)^2}+\frac{15 i b \sqrt{e} n \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{7/2}}-\frac{15 i b \sqrt{e} n \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{7/2}}-\frac{15 b n}{8 d^3 x}",1,"((-16*b*n)/(d^3*x) - (16*(a + b*Log[c*x^n]))/(d^3*x) + (d*Sqrt[e]*(a + b*Log[c*x^n]))/((-d)^(7/2)*(Sqrt[-d] - Sqrt[e]*x)^2) + (7*Sqrt[e]*(a + b*Log[c*x^n]))/(d^3*(Sqrt[-d] - Sqrt[e]*x)) + (Sqrt[e]*(a + b*Log[c*x^n]))/((-d)^(5/2)*(Sqrt[-d] + Sqrt[e]*x)^2) - (7*Sqrt[e]*(a + b*Log[c*x^n]))/(d^3*(Sqrt[-d] + Sqrt[e]*x)) + (7*b*Sqrt[e]*n*(Log[x] - Log[Sqrt[-d] - Sqrt[e]*x]))/(-d)^(7/2) - (7*b*Sqrt[e]*n*(Log[x] - Log[Sqrt[-d] + Sqrt[e]*x]))/(-d)^(7/2) + (b*d*Sqrt[e]*n*(1/(Sqrt[-d]*(Sqrt[-d] + Sqrt[e]*x)) - Log[x]/d + Log[Sqrt[-d] + Sqrt[e]*x]/d))/(-d)^(7/2) - (15*Sqrt[e]*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(7/2) + (b*Sqrt[e]*n*(1/(Sqrt[-d]*(Sqrt[-d] - Sqrt[e]*x)) - Log[x]/d + Log[(-d)^(3/2) + d*Sqrt[e]*x]/d))/(-d)^(5/2) + (15*Sqrt[e]*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(7/2) + (15*b*Sqrt[e]*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(7/2) - (15*b*Sqrt[e]*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(7/2))/16","B",1
240,1,584,260,1.6682927,"\int \frac{a+b \log \left(c x^n\right)}{x^4 \left(d+e x^2\right)^3} \, dx","Integrate[(a + b*Log[c*x^n])/(x^4*(d + e*x^2)^3),x]","\frac{1}{144} \left(-\frac{99 e^{3/2} \left(a+b \log \left(c x^n\right)\right)}{d^4 \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{99 e^{3/2} \left(a+b \log \left(c x^n\right)\right)}{d^4 \left(\sqrt{-d}+\sqrt{e} x\right)}+\frac{432 e \left(a+b \log \left(c x^n\right)\right)}{d^4 x}-\frac{48 \left(a+b \log \left(c x^n\right)\right)}{d^3 x^3}-\frac{9 e^{3/2} \left(a+b \log \left(c x^n\right)\right)}{(-d)^{7/2} \left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{9 e^{3/2} \left(a+b \log \left(c x^n\right)\right)}{(-d)^{7/2} \left(\sqrt{-d}+\sqrt{e} x\right)^2}-\frac{315 e^{3/2} \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{9/2}}+\frac{315 e^{3/2} \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{9/2}}+\frac{432 b e n}{d^4 x}-\frac{16 b n}{d^3 x^3}+\frac{315 b e^{3/2} n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{(-d)^{9/2}}-\frac{315 b e^{3/2} n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)}{(-d)^{9/2}}+\frac{99 b e^{3/2} n \left(\log (x)-\log \left(\sqrt{-d}-\sqrt{e} x\right)\right)}{(-d)^{9/2}}-\frac{99 b e^{3/2} n \left(\log (x)-\log \left(\sqrt{-d}+\sqrt{e} x\right)\right)}{(-d)^{9/2}}-\frac{9 b e^{3/2} n \left(\frac{1}{\sqrt{-d} \left(\sqrt{-d}+\sqrt{e} x\right)}+\frac{\log \left(\sqrt{-d}+\sqrt{e} x\right)}{d}-\frac{\log (x)}{d}\right)}{(-d)^{7/2}}+\frac{9 b e^{3/2} n \left(\frac{1}{\sqrt{-d} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{\log \left(d \sqrt{e} x+(-d)^{3/2}\right)}{d}-\frac{\log (x)}{d}\right)}{(-d)^{7/2}}\right)","\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(35 a+35 b \log \left(c x^n\right)-12 b n\right)}{8 d^{9/2}}+\frac{e \left(35 a+35 b \log \left(c x^n\right)-12 b n\right)}{8 d^4 x}-\frac{35 a+35 b \log \left(c x^n\right)-12 b n}{24 d^3 x^3}+\frac{7 a+7 b \log \left(c x^n\right)-b n}{8 d^2 x^3 \left(d+e x^2\right)}+\frac{a+b \log \left(c x^n\right)}{4 d x^3 \left(d+e x^2\right)^2}-\frac{35 i b e^{3/2} n \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{9/2}}+\frac{35 i b e^{3/2} n \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{9/2}}+\frac{35 b e n}{8 d^4 x}-\frac{35 b n}{72 d^3 x^3}",1,"((-16*b*n)/(d^3*x^3) + (432*b*e*n)/(d^4*x) - (48*(a + b*Log[c*x^n]))/(d^3*x^3) + (432*e*(a + b*Log[c*x^n]))/(d^4*x) - (9*e^(3/2)*(a + b*Log[c*x^n]))/((-d)^(7/2)*(Sqrt[-d] - Sqrt[e]*x)^2) - (99*e^(3/2)*(a + b*Log[c*x^n]))/(d^4*(Sqrt[-d] - Sqrt[e]*x)) + (9*e^(3/2)*(a + b*Log[c*x^n]))/((-d)^(7/2)*(Sqrt[-d] + Sqrt[e]*x)^2) + (99*e^(3/2)*(a + b*Log[c*x^n]))/(d^4*(Sqrt[-d] + Sqrt[e]*x)) + (99*b*e^(3/2)*n*(Log[x] - Log[Sqrt[-d] - Sqrt[e]*x]))/(-d)^(9/2) - (99*b*e^(3/2)*n*(Log[x] - Log[Sqrt[-d] + Sqrt[e]*x]))/(-d)^(9/2) - (9*b*e^(3/2)*n*(1/(Sqrt[-d]*(Sqrt[-d] + Sqrt[e]*x)) - Log[x]/d + Log[Sqrt[-d] + Sqrt[e]*x]/d))/(-d)^(7/2) - (315*e^(3/2)*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(9/2) + (9*b*e^(3/2)*n*(1/(Sqrt[-d]*(Sqrt[-d] - Sqrt[e]*x)) - Log[x]/d + Log[(-d)^(3/2) + d*Sqrt[e]*x]/d))/(-d)^(7/2) + (315*e^(3/2)*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(9/2) + (315*b*e^(3/2)*n*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(9/2) - (315*b*e^(3/2)*n*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(9/2))/144","B",1
241,1,17,17,0.0048112,"\int \frac{x \log \left(c x^2\right)}{1-c x^2} \, dx","Integrate[(x*Log[c*x^2])/(1 - c*x^2),x]","\frac{\text{Li}_2\left(1-c x^2\right)}{2 c}","\frac{\text{Li}_2\left(1-c x^2\right)}{2 c}",1,"PolyLog[2, 1 - c*x^2]/(2*c)","A",1
242,1,17,16,0.0044143,"\int \frac{x \log \left(\frac{x^2}{c}\right)}{c-x^2} \, dx","Integrate[(x*Log[x^2/c])/(c - x^2),x]","\frac{1}{2} \text{Li}_2\left(\frac{c-x^2}{c}\right)","\frac{1}{2} \text{Li}_2\left(1-\frac{x^2}{c}\right)",1,"PolyLog[2, (c - x^2)/c]/2","A",1
243,1,31,22,0.0062033,"\int \frac{\log (x)}{1-x^2} \, dx","Integrate[Log[x]/(1 - x^2),x]","\frac{\text{Li}_2(1-x)}{2}+\frac{\text{Li}_2(-x)}{2}+\frac{1}{2} \log (x) \log (x+1)","\frac{\text{Li}_2(-x)}{2}-\frac{\text{Li}_2(x)}{2}+\log (x) \tanh ^{-1}(x)",1,"(Log[x]*Log[1 + x])/2 + PolyLog[2, 1 - x]/2 + PolyLog[2, -x]/2","A",1
244,1,65,32,0.0084984,"\int \frac{\log (x)}{1+x^2} \, dx","Integrate[Log[x]/(1 + x^2),x]","-\frac{1}{2} i \text{Li}_2(-i x)+\frac{1}{2} i \text{Li}_2(i x)-\frac{1}{2} i \log (-i (-x+i)) \log (x)+\frac{1}{2} i \log (-i (x+i)) \log (x)","-\frac{1}{2} i \text{Li}_2(-i x)+\frac{1}{2} i \text{Li}_2(i x)+\log (x) \tan ^{-1}(x)",1,"(-1/2*I)*Log[(-I)*(I - x)]*Log[x] + (I/2)*Log[x]*Log[(-I)*(I + x)] - (I/2)*PolyLog[2, (-I)*x] + (I/2)*PolyLog[2, I*x]","B",1
245,1,68,62,0.0306028,"\int \frac{a+b \log (c x)}{1-e x^2} \, dx","Integrate[(a + b*Log[c*x])/(1 - e*x^2),x]","\frac{-\left(\left(\log \left(1-\sqrt{e} x\right)-\log \left(\sqrt{e} x+1\right)\right) (a+b \log (c x))\right)+b \text{Li}_2\left(-\sqrt{e} x\right)-b \text{Li}_2\left(\sqrt{e} x\right)}{2 \sqrt{e}}","\frac{\tanh ^{-1}\left(\sqrt{e} x\right) (a+b \log (c x))}{\sqrt{e}}+\frac{b \text{Li}_2\left(-\sqrt{e} x\right)}{2 \sqrt{e}}-\frac{b \text{Li}_2\left(\sqrt{e} x\right)}{2 \sqrt{e}}",1,"(-((a + b*Log[c*x])*(Log[1 - Sqrt[e]*x] - Log[1 + Sqrt[e]*x])) + b*PolyLog[2, -(Sqrt[e]*x)] - b*PolyLog[2, Sqrt[e]*x])/(2*Sqrt[e])","A",1
246,1,72,66,0.0257513,"\int \frac{a+b \log \left(c x^n\right)}{1-e x^2} \, dx","Integrate[(a + b*Log[c*x^n])/(1 - e*x^2),x]","\frac{-\left(\left(\log \left(1-\sqrt{e} x\right)-\log \left(\sqrt{e} x+1\right)\right) \left(a+b \log \left(c x^n\right)\right)\right)+b n \text{Li}_2\left(-\sqrt{e} x\right)-b n \text{Li}_2\left(\sqrt{e} x\right)}{2 \sqrt{e}}","\frac{\tanh ^{-1}\left(\sqrt{e} x\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{e}}+\frac{b n \text{Li}_2\left(-\sqrt{e} x\right)}{2 \sqrt{e}}-\frac{b n \text{Li}_2\left(\sqrt{e} x\right)}{2 \sqrt{e}}",1,"(-((a + b*Log[c*x^n])*(Log[1 - Sqrt[e]*x] - Log[1 + Sqrt[e]*x])) + b*n*PolyLog[2, -(Sqrt[e]*x)] - b*n*PolyLog[2, Sqrt[e]*x])/(2*Sqrt[e])","A",1
247,1,432,509,0.7844253,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{\left(d+e x^2\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])^2/(d + e*x^2)^2,x]","\frac{-\frac{2 b n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{3/2}}+\frac{2 b n \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{3/2}}-\frac{2 b n \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{3/2}}+\frac{2 b n \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{(-d)^{3/2}}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{d \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{d \left(\sqrt{-d}+\sqrt{e} x\right)}+\frac{\log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{(-d)^{3/2}}+\frac{d \log \left(\frac{d \sqrt{e} x}{(-d)^{3/2}}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{(-d)^{5/2}}+\frac{2 b^2 n^2 \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{(-d)^{3/2}}-\frac{2 b^2 n^2 \text{Li}_2\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)}{(-d)^{3/2}}+\frac{2 b^2 n^2 \text{Li}_3\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{(-d)^{3/2}}-\frac{2 b^2 n^2 \text{Li}_3\left(\frac{d \sqrt{e} x}{(-d)^{3/2}}\right)}{(-d)^{3/2}}}{4 \sqrt{e}}","\frac{b n \text{Li}_2\left(-\frac{\sqrt{e} x}{\sqrt{-d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 (-d)^{3/2} \sqrt{e}}-\frac{b n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 (-d)^{3/2} \sqrt{e}}+\frac{b n \log \left(1-\frac{\sqrt{e} x}{\sqrt{-d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 (-d)^{3/2} \sqrt{e}}-\frac{b n \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 (-d)^{3/2} \sqrt{e}}+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{4 (-d)^{3/2} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{4 (-d)^{3/2} \left(\sqrt{-d}+\sqrt{e} x\right)}-\frac{\log \left(1-\frac{\sqrt{e} x}{\sqrt{-d}}\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 (-d)^{3/2} \sqrt{e}}+\frac{\log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 (-d)^{3/2} \sqrt{e}}-\frac{b^2 n^2 \text{Li}_2\left(-\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}+\frac{b^2 n^2 \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}-\frac{b^2 n^2 \text{Li}_3\left(-\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}+\frac{b^2 n^2 \text{Li}_3\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}",1,"(-((a + b*Log[c*x^n])^2/(d*(Sqrt[-d] - Sqrt[e]*x))) + (a + b*Log[c*x^n])^2/(d*(Sqrt[-d] + Sqrt[e]*x)) - (2*b*n*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(3/2) + ((a + b*Log[c*x^n])^2*Log[1 + (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(3/2) + (2*b*n*(a + b*Log[c*x^n])*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(3/2) + (d*(a + b*Log[c*x^n])^2*Log[1 + (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(5/2) + (2*b^2*n^2*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(3/2) - (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(3/2) - (2*b^2*n^2*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(3/2) + (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(3/2) + (2*b^2*n^2*PolyLog[3, (Sqrt[e]*x)/Sqrt[-d]])/(-d)^(3/2) - (2*b^2*n^2*PolyLog[3, (d*Sqrt[e]*x)/(-d)^(3/2)])/(-d)^(3/2))/(4*Sqrt[e])","A",1
248,1,1073,711,2.4618701,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3}{\left(d+e x^2\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])^3/(d + e*x^2)^2,x]","\frac{\frac{i b^3 \left(\log \left(1-\frac{i \sqrt{e} x}{\sqrt{d}}\right) \log ^3(x)-\log \left(\frac{i \sqrt{e} x}{\sqrt{d}}+1\right) \log ^3(x)+\frac{\sqrt{d} \log ^3(x)}{i \sqrt{e} x+\sqrt{d}}+\frac{\sqrt{e} x \log ^3(x)}{\sqrt{e} x+i \sqrt{d}}-\log ^3(x)-3 \log \left(1-\frac{i \sqrt{e} x}{\sqrt{d}}\right) \log ^2(x)+3 \log \left(\frac{i \sqrt{e} x}{\sqrt{d}}+1\right) \log ^2(x)-3 (\log (x)-2) \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right) \log (x)+3 (\log (x)-2) \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right) \log (x)+6 \text{Li}_3\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right) \log (x)-6 \text{Li}_3\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right) \log (x)-6 \text{Li}_3\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)+6 \text{Li}_3\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)-6 \text{Li}_4\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)+6 \text{Li}_4\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)\right) n^3}{\sqrt{e}}+3 b^2 \left(a-b n \log (x)+b \log \left(c x^n\right)\right) \left(\frac{\log (x) \left(\sqrt{e} x \log (x)+2 i \left(i \sqrt{e} x+\sqrt{d}\right) \log \left(\frac{i \sqrt{e} x}{\sqrt{d}}+1\right)\right)+2 i \left(i \sqrt{e} x+\sqrt{d}\right) \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{i e x+\sqrt{d} \sqrt{e}}+\frac{\log (x) \left(\sqrt{e} x \log (x)-2 i \left(\sqrt{d}-i \sqrt{e} x\right) \log \left(1-\frac{i \sqrt{e} x}{\sqrt{d}}\right)\right)-2 \left(\sqrt{e} x+i \sqrt{d}\right) \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \sqrt{e}-i e x}-\frac{i \left(\log \left(\frac{i \sqrt{e} x}{\sqrt{d}}+1\right) \log ^2(x)+2 \text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right) \log (x)-2 \text{Li}_3\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)\right)}{\sqrt{e}}+\frac{i \left(\log \left(1-\frac{i \sqrt{e} x}{\sqrt{d}}\right) \log ^2(x)+2 \text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right) \log (x)-2 \text{Li}_3\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)\right)}{\sqrt{e}}\right) n^2+3 b \left(a-b n \log (x)+b \log \left(c x^n\right)\right)^2 \left(\frac{\sqrt{e} x \log (x)+i \left(i \sqrt{e} x+\sqrt{d}\right) \log \left(i \sqrt{d}-\sqrt{e} x\right)}{i e x+\sqrt{d} \sqrt{e}}+\frac{\sqrt{e} x \log (x)+\left(-\sqrt{e} x-i \sqrt{d}\right) \log \left(\sqrt{e} x+i \sqrt{d}\right)}{\sqrt{d} \sqrt{e}-i e x}-\frac{i \left(\log (x) \log \left(\frac{i \sqrt{e} x}{\sqrt{d}}+1\right)+\text{Li}_2\left(-\frac{i \sqrt{e} x}{\sqrt{d}}\right)\right)}{\sqrt{e}}+\frac{i \left(\log (x) \log \left(1-\frac{i \sqrt{e} x}{\sqrt{d}}\right)+\text{Li}_2\left(\frac{i \sqrt{e} x}{\sqrt{d}}\right)\right)}{\sqrt{e}}\right) n+\frac{2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a-b n \log (x)+b \log \left(c x^n\right)\right)^3}{\sqrt{e}}+\frac{2 \sqrt{d} x \left(a-b n \log (x)+b \log \left(c x^n\right)\right)^3}{e x^2+d}}{4 d^{3/2}}","-\frac{3 b^2 n^2 \text{Li}_2\left(-\frac{\sqrt{e} x}{\sqrt{-d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 (-d)^{3/2} \sqrt{e}}+\frac{3 b^2 n^2 \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 (-d)^{3/2} \sqrt{e}}-\frac{3 b^2 n^2 \text{Li}_3\left(-\frac{\sqrt{e} x}{\sqrt{-d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 (-d)^{3/2} \sqrt{e}}+\frac{3 b^2 n^2 \text{Li}_3\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 (-d)^{3/2} \sqrt{e}}+\frac{3 b n \text{Li}_2\left(-\frac{\sqrt{e} x}{\sqrt{-d}}\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 (-d)^{3/2} \sqrt{e}}-\frac{3 b n \text{Li}_2\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 (-d)^{3/2} \sqrt{e}}+\frac{3 b n \log \left(1-\frac{\sqrt{e} x}{\sqrt{-d}}\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 (-d)^{3/2} \sqrt{e}}-\frac{3 b n \log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 (-d)^{3/2} \sqrt{e}}+\frac{x \left(a+b \log \left(c x^n\right)\right)^3}{4 (-d)^{3/2} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{x \left(a+b \log \left(c x^n\right)\right)^3}{4 (-d)^{3/2} \left(\sqrt{-d}+\sqrt{e} x\right)}-\frac{\log \left(1-\frac{\sqrt{e} x}{\sqrt{-d}}\right) \left(a+b \log \left(c x^n\right)\right)^3}{4 (-d)^{3/2} \sqrt{e}}+\frac{\log \left(\frac{\sqrt{e} x}{\sqrt{-d}}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{4 (-d)^{3/2} \sqrt{e}}+\frac{3 b^3 n^3 \text{Li}_3\left(-\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}-\frac{3 b^3 n^3 \text{Li}_3\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}+\frac{3 b^3 n^3 \text{Li}_4\left(-\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}-\frac{3 b^3 n^3 \text{Li}_4\left(\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}",1,"((2*Sqrt[d]*x*(a - b*n*Log[x] + b*Log[c*x^n])^3)/(d + e*x^2) + (2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(a - b*n*Log[x] + b*Log[c*x^n])^3)/Sqrt[e] + 3*b*n*(a - b*n*Log[x] + b*Log[c*x^n])^2*((Sqrt[e]*x*Log[x] + I*(Sqrt[d] + I*Sqrt[e]*x)*Log[I*Sqrt[d] - Sqrt[e]*x])/(Sqrt[d]*Sqrt[e] + I*e*x) + (Sqrt[e]*x*Log[x] + ((-I)*Sqrt[d] - Sqrt[e]*x)*Log[I*Sqrt[d] + Sqrt[e]*x])/(Sqrt[d]*Sqrt[e] - I*e*x) - (I*(Log[x]*Log[1 + (I*Sqrt[e]*x)/Sqrt[d]] + PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]]))/Sqrt[e] + (I*(Log[x]*Log[1 - (I*Sqrt[e]*x)/Sqrt[d]] + PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]]))/Sqrt[e]) + 3*b^2*n^2*(a - b*n*Log[x] + b*Log[c*x^n])*((Log[x]*(Sqrt[e]*x*Log[x] + (2*I)*(Sqrt[d] + I*Sqrt[e]*x)*Log[1 + (I*Sqrt[e]*x)/Sqrt[d]]) + (2*I)*(Sqrt[d] + I*Sqrt[e]*x)*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*Sqrt[e] + I*e*x) + (Log[x]*(Sqrt[e]*x*Log[x] - (2*I)*(Sqrt[d] - I*Sqrt[e]*x)*Log[1 - (I*Sqrt[e]*x)/Sqrt[d]]) - 2*(I*Sqrt[d] + Sqrt[e]*x)*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*Sqrt[e] - I*e*x) - (I*(Log[x]^2*Log[1 + (I*Sqrt[e]*x)/Sqrt[d]] + 2*Log[x]*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]] - 2*PolyLog[3, ((-I)*Sqrt[e]*x)/Sqrt[d]]))/Sqrt[e] + (I*(Log[x]^2*Log[1 - (I*Sqrt[e]*x)/Sqrt[d]] + 2*Log[x]*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]] - 2*PolyLog[3, (I*Sqrt[e]*x)/Sqrt[d]]))/Sqrt[e]) + (I*b^3*n^3*(-Log[x]^3 + (Sqrt[d]*Log[x]^3)/(Sqrt[d] + I*Sqrt[e]*x) + (Sqrt[e]*x*Log[x]^3)/(I*Sqrt[d] + Sqrt[e]*x) - 3*Log[x]^2*Log[1 - (I*Sqrt[e]*x)/Sqrt[d]] + Log[x]^3*Log[1 - (I*Sqrt[e]*x)/Sqrt[d]] + 3*Log[x]^2*Log[1 + (I*Sqrt[e]*x)/Sqrt[d]] - Log[x]^3*Log[1 + (I*Sqrt[e]*x)/Sqrt[d]] - 3*(-2 + Log[x])*Log[x]*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]] + 3*(-2 + Log[x])*Log[x]*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]] - 6*PolyLog[3, ((-I)*Sqrt[e]*x)/Sqrt[d]] + 6*Log[x]*PolyLog[3, ((-I)*Sqrt[e]*x)/Sqrt[d]] + 6*PolyLog[3, (I*Sqrt[e]*x)/Sqrt[d]] - 6*Log[x]*PolyLog[3, (I*Sqrt[e]*x)/Sqrt[d]] - 6*PolyLog[4, ((-I)*Sqrt[e]*x)/Sqrt[d]] + 6*PolyLog[4, (I*Sqrt[e]*x)/Sqrt[d]]))/Sqrt[e])/(4*d^(3/2))","C",1
249,0,0,25,2.8787639,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/((d + e*x^2)^2*(a + b*Log[c*x^n])),x]","\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)},x\right)",0,"Integrate[1/((d + e*x^2)^2*(a + b*Log[c*x^n])), x]","A",-1
250,0,0,25,14.4934275,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[1/((d + e*x^2)^2*(a + b*Log[c*x^n])^2),x]","\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)^2},x\right)",0,"Integrate[1/((d + e*x^2)^2*(a + b*Log[c*x^n])^2), x]","A",-1
251,1,251,208,0.2046155,"\int x^5 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^5*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]),x]","\sqrt{d+e x^2} \left(\frac{2 d^3 \left(420 a+420 b \left(\log \left(c x^n\right)-n \log (x)\right)-389 b n\right)}{11025 e^3}-\frac{d^2 x^2 \left(420 a+420 b \left(\log \left(c x^n\right)-n \log (x)\right)-179 b n\right)}{11025 e^2}+\frac{d x^4 \left(35 a+35 b \left(\log \left(c x^n\right)-n \log (x)\right)-12 b n\right)}{1225 e}+\frac{1}{49} x^6 \left(7 a+7 b \left(\log \left(c x^n\right)-n \log (x)\right)-b n\right)\right)+\frac{8 b d^{7/2} n \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)}{105 e^3}-\frac{8 b d^{7/2} n \log (x)}{105 e^3}+\frac{b n \log (x) \sqrt{d+e x^2} \left(8 d^3-4 d^2 e x^2+3 d e^2 x^4+15 e^3 x^6\right)}{105 e^3}","\frac{d^2 \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 e^3}-\frac{2 d \left(d+e x^2\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e^3}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \log \left(c x^n\right)\right)}{7 e^3}+\frac{8 b d^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{105 e^3}-\frac{8 b d^3 n \sqrt{d+e x^2}}{105 e^3}-\frac{8 b d^2 n \left(d+e x^2\right)^{3/2}}{315 e^3}+\frac{9 b d n \left(d+e x^2\right)^{5/2}}{175 e^3}-\frac{b n \left(d+e x^2\right)^{7/2}}{49 e^3}",1,"(-8*b*d^(7/2)*n*Log[x])/(105*e^3) + (b*n*Sqrt[d + e*x^2]*(8*d^3 - 4*d^2*e*x^2 + 3*d*e^2*x^4 + 15*e^3*x^6)*Log[x])/(105*e^3) + Sqrt[d + e*x^2]*((x^6*(7*a - b*n + 7*b*(-(n*Log[x]) + Log[c*x^n])))/49 + (d*x^4*(35*a - 12*b*n + 35*b*(-(n*Log[x]) + Log[c*x^n])))/(1225*e) + (2*d^3*(420*a - 389*b*n + 420*b*(-(n*Log[x]) + Log[c*x^n])))/(11025*e^3) - (d^2*x^2*(420*a - 179*b*n + 420*b*(-(n*Log[x]) + Log[c*x^n])))/(11025*e^2)) + (8*b*d^(7/2)*n*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/(105*e^3)","A",1
252,1,204,154,0.1560172,"\int x^3 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^3*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]),x]","\sqrt{d+e x^2} \left(-\frac{d^2 \left(30 a+30 b \left(\log \left(c x^n\right)-n \log (x)\right)-31 b n\right)}{225 e^2}+\frac{d x^2 \left(15 a+15 b \left(\log \left(c x^n\right)-n \log (x)\right)-8 b n\right)}{225 e}+\frac{1}{25} x^4 \left(5 a+5 b \left(\log \left(c x^n\right)-n \log (x)\right)-b n\right)\right)-\frac{2 b d^{5/2} n \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)}{15 e^2}+\frac{2 b d^{5/2} n \log (x)}{15 e^2}-\frac{b n \log (x) \sqrt{d+e x^2} \left(2 d^2-d e x^2-3 e^2 x^4\right)}{15 e^2}","-\frac{d \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 e^2}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e^2}-\frac{2 b d^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{15 e^2}+\frac{2 b d^2 n \sqrt{d+e x^2}}{15 e^2}+\frac{2 b d n \left(d+e x^2\right)^{3/2}}{45 e^2}-\frac{b n \left(d+e x^2\right)^{5/2}}{25 e^2}",1,"(2*b*d^(5/2)*n*Log[x])/(15*e^2) - (b*n*Sqrt[d + e*x^2]*(2*d^2 - d*e*x^2 - 3*e^2*x^4)*Log[x])/(15*e^2) + Sqrt[d + e*x^2]*((x^4*(5*a - b*n + 5*b*(-(n*Log[x]) + Log[c*x^n])))/25 + (d*x^2*(15*a - 8*b*n + 15*b*(-(n*Log[x]) + Log[c*x^n])))/(225*e) - (d^2*(30*a - 31*b*n + 30*b*(-(n*Log[x]) + Log[c*x^n])))/(225*e^2)) - (2*b*d^(5/2)*n*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/(15*e^2)","A",1
253,1,136,102,0.1110623,"\int x \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]),x]","\frac{3 a e x^2 \sqrt{d+e x^2}+3 a d \sqrt{d+e x^2}+3 b \left(d+e x^2\right)^{3/2} \log \left(c x^n\right)+3 b d^{3/2} n \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)-3 b d^{3/2} n \log (x)-b e n x^2 \sqrt{d+e x^2}-4 b d n \sqrt{d+e x^2}}{9 e}","\frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 e}+\frac{b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{3 e}-\frac{b d n \sqrt{d+e x^2}}{3 e}-\frac{b n \left(d+e x^2\right)^{3/2}}{9 e}",1,"(3*a*d*Sqrt[d + e*x^2] - 4*b*d*n*Sqrt[d + e*x^2] + 3*a*e*x^2*Sqrt[d + e*x^2] - b*e*n*x^2*Sqrt[d + e*x^2] - 3*b*d^(3/2)*n*Log[x] + 3*b*(d + e*x^2)^(3/2)*Log[c*x^n] + 3*b*d^(3/2)*n*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/(9*e)","A",1
254,1,203,220,0.3319734,"\int \frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[(Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/x,x]","\frac{b n \sqrt{d+e x^2} \left(-\, _3F_2\left(-\frac{1}{2},-\frac{1}{2},-\frac{1}{2};\frac{1}{2},\frac{1}{2};-\frac{d}{e x^2}\right)+\log (x) \sqrt{\frac{d}{e x^2}+1}-\frac{\sqrt{d} \log (x) \sinh ^{-1}\left(\frac{\sqrt{d}}{\sqrt{e} x}\right)}{\sqrt{e} x}\right)}{\sqrt{\frac{d}{e x^2}+1}}+\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-\sqrt{d} \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)+\sqrt{d} \log (x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)","\left(\sqrt{d+e x^2}-\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} b \sqrt{d} n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^2+d}}\right)-b n \sqrt{d+e x^2}+\frac{1}{2} b \sqrt{d} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)^2+b \sqrt{d} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)-b \sqrt{d} n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)",1,"(b*n*Sqrt[d + e*x^2]*(-HypergeometricPFQ[{-1/2, -1/2, -1/2}, {1/2, 1/2}, -(d/(e*x^2))] + Sqrt[1 + d/(e*x^2)]*Log[x] - (Sqrt[d]*ArcSinh[Sqrt[d]/(Sqrt[e]*x)]*Log[x])/(Sqrt[e]*x)))/Sqrt[1 + d/(e*x^2)] + Sqrt[d + e*x^2]*(a - b*n*Log[x] + b*Log[c*x^n]) + Sqrt[d]*Log[x]*(a - b*n*Log[x] + b*Log[c*x^n]) - Sqrt[d]*(a - b*n*Log[x] + b*Log[c*x^n])*Log[d + Sqrt[d]*Sqrt[d + e*x^2]]","C",1
255,1,303,252,0.5584406,"\int \frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Integrate[(Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/x^3,x]","\frac{-2 b \sqrt{d} n \sqrt{d+e x^2} \, _3F_2\left(\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-\frac{d}{e x^2}\right)+\sqrt{\frac{d}{e x^2}+1} \left(2 e x^2 \log (x) \left(a+b \log \left(c x^n\right)+b n \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)\right)-2 a \sqrt{d} \sqrt{d+e x^2}-2 a e x^2 \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)-2 b \log \left(c x^n\right) \left(\sqrt{d} \sqrt{d+e x^2}+e x^2 \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)\right)-b \sqrt{d} n \sqrt{d+e x^2}-2 b e n x^2 \log ^2(x)\right)-b \sqrt{e} n x (2 \log (x)+1) \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{d}}{\sqrt{e} x}\right)}{4 \sqrt{d} x^2 \sqrt{\frac{d}{e x^2}+1}}","-\frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{e \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 \sqrt{d}}-\frac{b e n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^2+d}}\right)}{4 \sqrt{d}}-\frac{b n \sqrt{d+e x^2}}{4 x^2}+\frac{b e n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)^2}{4 \sqrt{d}}-\frac{b e n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{4 \sqrt{d}}-\frac{b e n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{2 \sqrt{d}}",1,"(-2*b*Sqrt[d]*n*Sqrt[d + e*x^2]*HypergeometricPFQ[{1/2, 1/2, 1/2}, {3/2, 3/2}, -(d/(e*x^2))] - b*Sqrt[e]*n*x*Sqrt[d + e*x^2]*ArcSinh[Sqrt[d]/(Sqrt[e]*x)]*(1 + 2*Log[x]) + Sqrt[1 + d/(e*x^2)]*(-2*a*Sqrt[d]*Sqrt[d + e*x^2] - b*Sqrt[d]*n*Sqrt[d + e*x^2] - 2*b*e*n*x^2*Log[x]^2 - 2*a*e*x^2*Log[d + Sqrt[d]*Sqrt[d + e*x^2]] + 2*e*x^2*Log[x]*(a + b*Log[c*x^n] + b*n*Log[d + Sqrt[d]*Sqrt[d + e*x^2]]) - 2*b*Log[c*x^n]*(Sqrt[d]*Sqrt[d + e*x^2] + e*x^2*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])))/(4*Sqrt[d]*Sqrt[1 + d/(e*x^2)]*x^2)","C",1
256,1,276,469,0.614384,"\int x^4 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^4*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]),x]","\frac{-48 b e^{5/2} n x^5 \sqrt{d+e x^2} \, _3F_2\left(-\frac{1}{2},\frac{5}{2},\frac{5}{2};\frac{7}{2},\frac{7}{2};-\frac{e x^2}{d}\right)+25 \sqrt{\frac{e x^2}{d}+1} \left(3 d^3 \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right) (a-b n \log (x))+a \sqrt{e} x \sqrt{d+e x^2} \left(-3 d^2+2 d e x^2+8 e^2 x^4\right)+b \log \left(c x^n\right) \left(3 d^3 \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)+\sqrt{e} x \sqrt{d+e x^2} \left(-3 d^2+2 d e x^2+8 e^2 x^4\right)\right)\right)+75 b d^{5/2} n \log (x) \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{1200 e^{5/2} \sqrt{\frac{e x^2}{d}+1}}","\frac{d^{5/2} \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{16 e^{5/2} \sqrt{\frac{e x^2}{d}+1}}-\frac{d^2 x \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{16 e^2}+\frac{1}{6} x^5 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)+\frac{d x^3 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{24 e}-\frac{b d^{5/2} n \sqrt{d+e x^2} \text{Li}_2\left(e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{32 e^{5/2} \sqrt{\frac{e x^2}{d}+1}}+\frac{b d^{5/2} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{32 e^{5/2} \sqrt{\frac{e x^2}{d}+1}}+\frac{5 b d^{5/2} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{192 e^{5/2} \sqrt{\frac{e x^2}{d}+1}}-\frac{b d^{5/2} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{16 e^{5/2} \sqrt{\frac{e x^2}{d}+1}}+\frac{7 b d^2 n x \sqrt{d+e x^2}}{192 e^2}-\frac{1}{36} b n x^5 \sqrt{d+e x^2}-\frac{5 b d n x^3 \sqrt{d+e x^2}}{288 e}",1,"(-48*b*e^(5/2)*n*x^5*Sqrt[d + e*x^2]*HypergeometricPFQ[{-1/2, 5/2, 5/2}, {7/2, 7/2}, -((e*x^2)/d)] + 75*b*d^(5/2)*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[x] + 25*Sqrt[1 + (e*x^2)/d]*(a*Sqrt[e]*x*Sqrt[d + e*x^2]*(-3*d^2 + 2*d*e*x^2 + 8*e^2*x^4) + 3*d^3*(a - b*n*Log[x])*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]] + b*Log[c*x^n]*(Sqrt[e]*x*Sqrt[d + e*x^2]*(-3*d^2 + 2*d*e*x^2 + 8*e^2*x^4) + 3*d^3*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])))/(1200*e^(5/2)*Sqrt[1 + (e*x^2)/d])","C",1
257,1,250,409,0.4621681,"\int x^2 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^2*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]),x]","\frac{-8 b e^{3/2} n x^3 \sqrt{d+e x^2} \, _3F_2\left(-\frac{1}{2},\frac{3}{2},\frac{3}{2};\frac{5}{2},\frac{5}{2};-\frac{e x^2}{d}\right)+9 \sqrt{\frac{e x^2}{d}+1} \left(d^2 \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right) (b n \log (x)-a)+a \sqrt{e} x \sqrt{d+e x^2} \left(d+2 e x^2\right)+b \log \left(c x^n\right) \left(\sqrt{e} x \sqrt{d+e x^2} \left(d+2 e x^2\right)-d^2 \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)\right)\right)-9 b d^{3/2} n \log (x) \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{72 e^{3/2} \sqrt{\frac{e x^2}{d}+1}}","-\frac{d^{3/2} \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{8 e^{3/2} \sqrt{\frac{e x^2}{d}+1}}+\frac{d x \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{8 e}+\frac{1}{4} x^3 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)+\frac{b d^{3/2} n \sqrt{d+e x^2} \text{Li}_2\left(e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{16 e^{3/2} \sqrt{\frac{e x^2}{d}+1}}-\frac{b d^{3/2} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{16 e^{3/2} \sqrt{\frac{e x^2}{d}+1}}-\frac{b d^{3/2} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{32 e^{3/2} \sqrt{\frac{e x^2}{d}+1}}+\frac{b d^{3/2} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{8 e^{3/2} \sqrt{\frac{e x^2}{d}+1}}-\frac{3 b d n x \sqrt{d+e x^2}}{32 e}-\frac{1}{16} b n x^3 \sqrt{d+e x^2}",1,"(-8*b*e^(3/2)*n*x^3*Sqrt[d + e*x^2]*HypergeometricPFQ[{-1/2, 3/2, 3/2}, {5/2, 5/2}, -((e*x^2)/d)] - 9*b*d^(3/2)*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[x] + 9*Sqrt[1 + (e*x^2)/d]*(a*Sqrt[e]*x*Sqrt[d + e*x^2]*(d + 2*e*x^2) + d^2*(-a + b*n*Log[x])*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]] + b*Log[c*x^n]*(Sqrt[e]*x*Sqrt[d + e*x^2]*(d + 2*e*x^2) - d^2*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])))/(72*e^(3/2)*Sqrt[1 + (e*x^2)/d])","C",1
258,1,237,330,0.3606675,"\int \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Sqrt[d + e*x^2]*(a + b*Log[c*x^n]),x]","\frac{-2 b \sqrt{e} n x \sqrt{d+e x^2} \, _3F_2\left(\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-\frac{e x^2}{d}\right)+\sqrt{\frac{e x^2}{d}+1} \left(\sqrt{e} x (2 a-b n) \sqrt{d+e x^2}+2 d \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right) (a-b n \log (x))+2 b \log \left(c x^n\right) \left(\sqrt{e} x \sqrt{d+e x^2}+d \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)\right)\right)+b \sqrt{d} n (2 \log (x)-1) \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{4 \sqrt{e} \sqrt{\frac{e x^2}{d}+1}}","\frac{d^{3/2} \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 \sqrt{e} \sqrt{d+e x^2}}+\frac{1}{2} x \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)-\frac{b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \text{Li}_2\left(e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{4 \sqrt{e} \sqrt{d+e x^2}}+\frac{b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{4 \sqrt{e} \sqrt{d+e x^2}}-\frac{b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 \sqrt{e} \sqrt{d+e x^2}}-\frac{1}{4} b n x \sqrt{d+e x^2}-\frac{b d n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{4 \sqrt{e}}",1,"(-2*b*Sqrt[e]*n*x*Sqrt[d + e*x^2]*HypergeometricPFQ[{1/2, 1/2, 1/2}, {3/2, 3/2}, -((e*x^2)/d)] + b*Sqrt[d]*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*(-1 + 2*Log[x]) + Sqrt[1 + (e*x^2)/d]*(Sqrt[e]*(2*a - b*n)*x*Sqrt[d + e*x^2] + 2*d*(a - b*n*Log[x])*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]] + 2*b*Log[c*x^n]*(Sqrt[e]*x*Sqrt[d + e*x^2] + d*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])))/(4*Sqrt[e]*Sqrt[1 + (e*x^2)/d])","C",1
259,1,183,345,0.6589373,"\int \frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Integrate[(Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/x^2,x]","\frac{b n \sqrt{d+e x^2} \left(-\, _3F_2\left(-\frac{1}{2},-\frac{1}{2},-\frac{1}{2};\frac{1}{2},\frac{1}{2};-\frac{e x^2}{d}\right)-\log (x) \sqrt{\frac{e x^2}{d}+1}+\frac{\sqrt{e} x \log (x) \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d}}\right)}{x \sqrt{\frac{e x^2}{d}+1}}-\frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{x}+\sqrt{e} \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)","-\frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{\sqrt{e} \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d} \sqrt{\frac{e x^2}{d}+1}}-\frac{b \sqrt{e} n \sqrt{d+e x^2} \text{Li}_2\left(e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 \sqrt{d} \sqrt{\frac{e x^2}{d}+1}}-\frac{b n \sqrt{d+e x^2}}{x}+\frac{b \sqrt{e} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{2 \sqrt{d} \sqrt{\frac{e x^2}{d}+1}}+\frac{b \sqrt{e} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \sqrt{\frac{e x^2}{d}+1}}-\frac{b \sqrt{e} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{\sqrt{d} \sqrt{\frac{e x^2}{d}+1}}",1,"(b*n*Sqrt[d + e*x^2]*(-HypergeometricPFQ[{-1/2, -1/2, -1/2}, {1/2, 1/2}, -((e*x^2)/d)] - Sqrt[1 + (e*x^2)/d]*Log[x] + (Sqrt[e]*x*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[x])/Sqrt[d]))/(x*Sqrt[1 + (e*x^2)/d]) - (Sqrt[d + e*x^2]*(a - b*n*Log[x] + b*Log[c*x^n]))/x + Sqrt[e]*(a - b*n*Log[x] + b*Log[c*x^n])*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]]","C",1
260,1,99,112,0.1468455,"\int \frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Integrate[(Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/x^4,x]","-\frac{\sqrt{d+e x^2} \left(3 a \left(d+e x^2\right)+b n \left(d+4 e x^2\right)\right)+3 b \left(d+e x^2\right)^{3/2} \log \left(c x^n\right)-3 b e^{3/2} n x^3 \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)}{9 d x^3}","-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 d x^3}+\frac{b e^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{3 d}-\frac{b e n \sqrt{d+e x^2}}{3 d x}-\frac{b n \left(d+e x^2\right)^{3/2}}{9 d x^3}",1,"-1/9*(Sqrt[d + e*x^2]*(3*a*(d + e*x^2) + b*n*(d + 4*e*x^2)) + 3*b*(d + e*x^2)^(3/2)*Log[c*x^n] - 3*b*e^(3/2)*n*x^3*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(d*x^3)","A",1
261,1,145,170,0.196819,"\int \frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Integrate[(Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/x^6,x]","-\frac{\sqrt{d+e x^2} \left(15 a \left(3 d^2+d e x^2-2 e^2 x^4\right)+b n \left(9 d^2+8 d e x^2-31 e^2 x^4\right)\right)+15 b \sqrt{d+e x^2} \left(3 d^2+d e x^2-2 e^2 x^4\right) \log \left(c x^n\right)+30 b e^{5/2} n x^5 \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)}{225 d^2 x^5}","\frac{2 e \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{15 d^2 x^3}-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{5 d x^5}-\frac{2 b e^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{15 d^2}+\frac{2 b e^2 n \sqrt{d+e x^2}}{15 d^2 x}-\frac{b n \left(d+e x^2\right)^{5/2}}{25 d^2 x^5}+\frac{2 b e n \left(d+e x^2\right)^{3/2}}{45 d^2 x^3}",1,"-1/225*(Sqrt[d + e*x^2]*(b*n*(9*d^2 + 8*d*e*x^2 - 31*e^2*x^4) + 15*a*(3*d^2 + d*e*x^2 - 2*e^2*x^4)) + 15*b*Sqrt[d + e*x^2]*(3*d^2 + d*e*x^2 - 2*e^2*x^4)*Log[c*x^n] + 30*b*e^(5/2)*n*x^5*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(d^2*x^5)","A",1
262,1,180,230,0.2439617,"\int \frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{x^8} \, dx","Integrate[(Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/x^8,x]","-\frac{\sqrt{d+e x^2} \left(105 a \left(15 d^3+3 d^2 e x^2-4 d e^2 x^4+8 e^3 x^6\right)+b n \left(225 d^3+108 d^2 e x^2-179 d e^2 x^4+778 e^3 x^6\right)\right)+105 b \sqrt{d+e x^2} \left(15 d^3+3 d^2 e x^2-4 d e^2 x^4+8 e^3 x^6\right) \log \left(c x^n\right)-840 b e^{7/2} n x^7 \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)}{11025 d^3 x^7}","-\frac{8 e^2 \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{105 d^3 x^3}+\frac{4 e \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{35 d^2 x^5}-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{7 d x^7}+\frac{8 b e^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{105 d^3}-\frac{8 b e^3 n \sqrt{d+e x^2}}{105 d^3 x}-\frac{8 b e^2 n \left(d+e x^2\right)^{3/2}}{315 d^3 x^3}+\frac{38 b e n \left(d+e x^2\right)^{5/2}}{1225 d^3 x^5}-\frac{b n \left(d+e x^2\right)^{5/2}}{49 d^2 x^7}",1,"-1/11025*(Sqrt[d + e*x^2]*(105*a*(15*d^3 + 3*d^2*e*x^2 - 4*d*e^2*x^4 + 8*e^3*x^6) + b*n*(225*d^3 + 108*d^2*e*x^2 - 179*d*e^2*x^4 + 778*e^3*x^6)) + 105*b*Sqrt[d + e*x^2]*(15*d^3 + 3*d^2*e*x^2 - 4*d*e^2*x^4 + 8*e^3*x^6)*Log[c*x^n] - 840*b*e^(7/2)*n*x^7*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(d^3*x^7)","A",1
263,1,256,231,0.3589074,"\int x^5 \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^5*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]),x]","\frac{\sqrt{d+e x^2} \left(2 d^4 \left(1260 a+1260 b \left(\log \left(c x^n\right)-n \log (x)\right)-1307 b n\right)-d^3 e x^2 \left(1260 a+1260 b \left(\log \left(c x^n\right)-n \log (x)\right)-677 b n\right)+3 d^2 e^2 x^4 \left(315 a+315 b \left(\log \left(c x^n\right)-n \log (x)\right)-143 b n\right)+25 d e^3 x^6 \left(630 a+630 b \left(\log \left(c x^n\right)-n \log (x)\right)-97 b n\right)+1225 e^4 x^8 \left(9 a+9 b \log \left(c x^n\right)-9 b n \log (x)-b n\right)\right)+2520 b d^{9/2} n \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)-2520 b d^{9/2} n \log (x)+315 b n \log (x) \left(d+e x^2\right)^{5/2} \left(8 d^2-20 d e x^2+35 e^2 x^4\right)}{99225 e^3}","\frac{d^2 \left(d+e x^2\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e^3}-\frac{2 d \left(d+e x^2\right)^{7/2} \left(a+b \log \left(c x^n\right)\right)}{7 e^3}+\frac{\left(d+e x^2\right)^{9/2} \left(a+b \log \left(c x^n\right)\right)}{9 e^3}+\frac{8 b d^{9/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{315 e^3}-\frac{8 b d^4 n \sqrt{d+e x^2}}{315 e^3}-\frac{8 b d^3 n \left(d+e x^2\right)^{3/2}}{945 e^3}-\frac{8 b d^2 n \left(d+e x^2\right)^{5/2}}{1575 e^3}+\frac{11 b d n \left(d+e x^2\right)^{7/2}}{441 e^3}-\frac{b n \left(d+e x^2\right)^{9/2}}{81 e^3}",1,"(-2520*b*d^(9/2)*n*Log[x] + 315*b*n*(d + e*x^2)^(5/2)*(8*d^2 - 20*d*e*x^2 + 35*e^2*x^4)*Log[x] + Sqrt[d + e*x^2]*(1225*e^4*x^8*(9*a - b*n - 9*b*n*Log[x] + 9*b*Log[c*x^n]) + 3*d^2*e^2*x^4*(315*a - 143*b*n + 315*b*(-(n*Log[x]) + Log[c*x^n])) + 25*d*e^3*x^6*(630*a - 97*b*n + 630*b*(-(n*Log[x]) + Log[c*x^n])) + 2*d^4*(1260*a - 1307*b*n + 1260*b*(-(n*Log[x]) + Log[c*x^n])) - d^3*e*x^2*(1260*a - 677*b*n + 1260*b*(-(n*Log[x]) + Log[c*x^n]))) + 2520*b*d^(9/2)*n*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/(99225*e^3)","A",1
264,1,227,177,0.210159,"\int x^3 \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^3*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]),x]","\sqrt{d+e x^2} \left(-\frac{d^3 \left(210 a+210 b \left(\log \left(c x^n\right)-n \log (x)\right)-247 b n\right)}{3675 e^2}+\frac{d^2 x^2 \left(105 a+105 b \left(\log \left(c x^n\right)-n \log (x)\right)-71 b n\right)}{3675 e}+\frac{d x^4 \left(280 a+280 b \left(\log \left(c x^n\right)-n \log (x)\right)-61 b n\right)}{1225}+\frac{1}{49} e x^6 \left(7 a+7 b \left(\log \left(c x^n\right)-n \log (x)\right)-b n\right)\right)-\frac{2 b d^{7/2} n \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)}{35 e^2}+\frac{2 b d^{7/2} n \log (x)}{35 e^2}-\frac{b n \log (x) \left(2 d-5 e x^2\right) \left(d+e x^2\right)^{5/2}}{35 e^2}","-\frac{d \left(d+e x^2\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e^2}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \log \left(c x^n\right)\right)}{7 e^2}-\frac{2 b d^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{35 e^2}+\frac{2 b d^3 n \sqrt{d+e x^2}}{35 e^2}+\frac{2 b d^2 n \left(d+e x^2\right)^{3/2}}{105 e^2}+\frac{2 b d n \left(d+e x^2\right)^{5/2}}{175 e^2}-\frac{b n \left(d+e x^2\right)^{7/2}}{49 e^2}",1,"(2*b*d^(7/2)*n*Log[x])/(35*e^2) - (b*n*(2*d - 5*e*x^2)*(d + e*x^2)^(5/2)*Log[x])/(35*e^2) + Sqrt[d + e*x^2]*((e*x^6*(7*a - b*n + 7*b*(-(n*Log[x]) + Log[c*x^n])))/49 + (d^2*x^2*(105*a - 71*b*n + 105*b*(-(n*Log[x]) + Log[c*x^n])))/(3675*e) - (d^3*(210*a - 247*b*n + 210*b*(-(n*Log[x]) + Log[c*x^n])))/(3675*e^2) + (d*x^4*(280*a - 61*b*n + 280*b*(-(n*Log[x]) + Log[c*x^n])))/1225) - (2*b*d^(7/2)*n*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/(35*e^2)","A",1
265,1,181,125,0.1527313,"\int x \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]),x]","\sqrt{d+e x^2} \left(\frac{d^2 \left(15 a+15 b \left(\log \left(c x^n\right)-n \log (x)\right)-23 b n\right)}{75 e}+\frac{1}{75} d x^2 \left(30 a+30 b \left(\log \left(c x^n\right)-n \log (x)\right)-11 b n\right)+\frac{1}{25} e x^4 \left(5 a+5 b \left(\log \left(c x^n\right)-n \log (x)\right)-b n\right)\right)+\frac{b d^{5/2} n \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)}{5 e}-\frac{b d^{5/2} n \log (x)}{5 e}+\frac{b n \log (x) \left(d+e x^2\right)^{5/2}}{5 e}","\frac{\left(d+e x^2\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e}+\frac{b d^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{5 e}-\frac{b d^2 n \sqrt{d+e x^2}}{5 e}-\frac{b d n \left(d+e x^2\right)^{3/2}}{15 e}-\frac{b n \left(d+e x^2\right)^{5/2}}{25 e}",1,"-1/5*(b*d^(5/2)*n*Log[x])/e + (b*n*(d + e*x^2)^(5/2)*Log[x])/(5*e) + Sqrt[d + e*x^2]*((e*x^4*(5*a - b*n + 5*b*(-(n*Log[x]) + Log[c*x^n])))/25 + (d^2*(15*a - 23*b*n + 15*b*(-(n*Log[x]) + Log[c*x^n])))/(75*e) + (d*x^2*(30*a - 11*b*n + 30*b*(-(n*Log[x]) + Log[c*x^n])))/75) + (b*d^(5/2)*n*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/(5*e)","A",1
266,1,301,260,0.83802,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/x,x]","\frac{b e n x^2 \sqrt{d+e x^2} \left(\frac{d \log (x) \left(\left(\frac{e x^2}{d}+1\right)^{3/2}-1\right)}{3 e x^2}-\frac{1}{4} \, _3F_2\left(-\frac{1}{2},1,1;2,2;-\frac{e x^2}{d}\right)\right)}{\sqrt{\frac{e x^2}{d}+1}}+\frac{b d n \sqrt{d+e x^2} \left(-\, _3F_2\left(-\frac{1}{2},-\frac{1}{2},-\frac{1}{2};\frac{1}{2},\frac{1}{2};-\frac{d}{e x^2}\right)+\log (x) \sqrt{\frac{d}{e x^2}+1}-\frac{\sqrt{d} \log (x) \sinh ^{-1}\left(\frac{\sqrt{d}}{\sqrt{e} x}\right)}{\sqrt{e} x}\right)}{\sqrt{\frac{d}{e x^2}+1}}-d^{3/2} \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)+d^{3/2} \log (x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)+\frac{1}{3} \sqrt{d+e x^2} \left(4 d+e x^2\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)","\frac{1}{3} \left(-3 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)+3 d \sqrt{d+e x^2}+\left(d+e x^2\right)^{3/2}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} b d^{3/2} n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^2+d}}\right)+\frac{1}{2} b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)^2+\frac{4}{3} b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)-b d^{3/2} n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)-\frac{1}{9} b n \left(d+e x^2\right)^{3/2}-\frac{4}{3} b d n \sqrt{d+e x^2}",1,"(b*e*n*x^2*Sqrt[d + e*x^2]*(-1/4*HypergeometricPFQ[{-1/2, 1, 1}, {2, 2}, -((e*x^2)/d)] + (d*(-1 + (1 + (e*x^2)/d)^(3/2))*Log[x])/(3*e*x^2)))/Sqrt[1 + (e*x^2)/d] + (b*d*n*Sqrt[d + e*x^2]*(-HypergeometricPFQ[{-1/2, -1/2, -1/2}, {1/2, 1/2}, -(d/(e*x^2))] + Sqrt[1 + d/(e*x^2)]*Log[x] - (Sqrt[d]*ArcSinh[Sqrt[d]/(Sqrt[e]*x)]*Log[x])/(Sqrt[e]*x)))/Sqrt[1 + d/(e*x^2)] + (Sqrt[d + e*x^2]*(4*d + e*x^2)*(a - b*n*Log[x] + b*Log[c*x^n]))/3 + d^(3/2)*Log[x]*(a - b*n*Log[x] + b*Log[c*x^n]) - d^(3/2)*(a - b*n*Log[x] + b*Log[c*x^n])*Log[d + Sqrt[d]*Sqrt[d + e*x^2]]","C",1
267,1,349,295,0.9642124,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Integrate[((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/x^3,x]","\frac{b e n \sqrt{d+e x^2} \left(-\, _3F_2\left(-\frac{1}{2},-\frac{1}{2},-\frac{1}{2};\frac{1}{2},\frac{1}{2};-\frac{d}{e x^2}\right)+\log (x) \sqrt{\frac{d}{e x^2}+1}-\frac{\sqrt{d} \log (x) \sinh ^{-1}\left(\frac{\sqrt{d}}{\sqrt{e} x}\right)}{\sqrt{e} x}\right)}{\sqrt{\frac{d}{e x^2}+1}}-\frac{b \sqrt{d} n \sqrt{d+e x^2} \left(2 \sqrt{d} \, _3F_2\left(\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-\frac{d}{e x^2}\right)+(2 \log (x)+1) \left(\sqrt{d} \sqrt{\frac{d}{e x^2}+1}+\sqrt{e} x \sinh ^{-1}\left(\frac{\sqrt{d}}{\sqrt{e} x}\right)\right)\right)}{4 x^2 \sqrt{\frac{d}{e x^2}+1}}+\frac{3}{2} \sqrt{d} e \log (x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-\frac{\left(d-2 e x^2\right) \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{2 x^2}-\frac{3}{2} \sqrt{d} e \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)","-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{2 x^2}+\frac{3}{2} e \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)-\frac{3}{2} \sqrt{d} e \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3}{4} b \sqrt{d} e n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^2+d}}\right)-b e n \sqrt{d+e x^2}-\frac{b d n \sqrt{d+e x^2}}{4 x^2}+\frac{3}{4} b \sqrt{d} e n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)^2+\frac{3}{4} b \sqrt{d} e n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)-\frac{3}{2} b \sqrt{d} e n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)",1,"(b*e*n*Sqrt[d + e*x^2]*(-HypergeometricPFQ[{-1/2, -1/2, -1/2}, {1/2, 1/2}, -(d/(e*x^2))] + Sqrt[1 + d/(e*x^2)]*Log[x] - (Sqrt[d]*ArcSinh[Sqrt[d]/(Sqrt[e]*x)]*Log[x])/(Sqrt[e]*x)))/Sqrt[1 + d/(e*x^2)] - (b*Sqrt[d]*n*Sqrt[d + e*x^2]*(2*Sqrt[d]*HypergeometricPFQ[{1/2, 1/2, 1/2}, {3/2, 3/2}, -(d/(e*x^2))] + (Sqrt[d]*Sqrt[1 + d/(e*x^2)] + Sqrt[e]*x*ArcSinh[Sqrt[d]/(Sqrt[e]*x)])*(1 + 2*Log[x])))/(4*Sqrt[1 + d/(e*x^2)]*x^2) - ((d - 2*e*x^2)*Sqrt[d + e*x^2]*(a - b*n*Log[x] + b*Log[c*x^n]))/(2*x^2) + (3*Sqrt[d]*e*Log[x]*(a - b*n*Log[x] + b*Log[c*x^n]))/2 - (3*Sqrt[d]*e*(a - b*n*Log[x] + b*Log[c*x^n])*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/2","C",1
268,1,331,464,1.1936823,"\int x^2 \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^2*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]),x]","\frac{-144 b e^{5/2} n x^5 \sqrt{d+e x^2} \, _3F_2\left(-\frac{1}{2},\frac{5}{2},\frac{5}{2};\frac{7}{2},\frac{7}{2};-\frac{e x^2}{d}\right)-400 b d e^{3/2} n x^3 \sqrt{d+e x^2} \, _3F_2\left(-\frac{1}{2},\frac{3}{2},\frac{3}{2};\frac{5}{2},\frac{5}{2};-\frac{e x^2}{d}\right)-75 \left(\sqrt{\frac{e x^2}{d}+1} \left(3 d^3 \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right) (a-b n \log (x))-a \sqrt{e} x \sqrt{d+e x^2} \left(3 d^2+14 d e x^2+8 e^2 x^4\right)-b \log \left(c x^n\right) \left(\sqrt{e} x \sqrt{d+e x^2} \left(3 d^2+14 d e x^2+8 e^2 x^4\right)-3 d^3 \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)\right)\right)+3 b d^{5/2} n \log (x) \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)\right)}{3600 e^{3/2} \sqrt{\frac{e x^2}{d}+1}}","-\frac{d^{5/2} \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{16 e^{3/2} \sqrt{\frac{e x^2}{d}+1}}+\frac{d^2 x \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{16 e}+\frac{1}{6} x^3 \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)+\frac{1}{8} d x^3 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)+\frac{b d^{5/2} n \sqrt{d+e x^2} \text{Li}_2\left(e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{32 e^{3/2} \sqrt{\frac{e x^2}{d}+1}}-\frac{b d^{5/2} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{32 e^{3/2} \sqrt{\frac{e x^2}{d}+1}}-\frac{b d^{5/2} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{192 e^{3/2} \sqrt{\frac{e x^2}{d}+1}}+\frac{b d^{5/2} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{16 e^{3/2} \sqrt{\frac{e x^2}{d}+1}}-\frac{11 b d^2 n x \sqrt{d+e x^2}}{192 e}-\frac{1}{36} b e n x^5 \sqrt{d+e x^2}-\frac{23}{288} b d n x^3 \sqrt{d+e x^2}",1,"(-400*b*d*e^(3/2)*n*x^3*Sqrt[d + e*x^2]*HypergeometricPFQ[{-1/2, 3/2, 3/2}, {5/2, 5/2}, -((e*x^2)/d)] - 144*b*e^(5/2)*n*x^5*Sqrt[d + e*x^2]*HypergeometricPFQ[{-1/2, 5/2, 5/2}, {7/2, 7/2}, -((e*x^2)/d)] - 75*(3*b*d^(5/2)*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[x] + Sqrt[1 + (e*x^2)/d]*(-(a*Sqrt[e]*x*Sqrt[d + e*x^2]*(3*d^2 + 14*d*e*x^2 + 8*e^2*x^4)) + 3*d^3*(a - b*n*Log[x])*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]] - b*Log[c*x^n]*(Sqrt[e]*x*Sqrt[d + e*x^2]*(3*d^2 + 14*d*e*x^2 + 8*e^2*x^4) - 3*d^3*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]]))))/(3600*e^(3/2)*Sqrt[1 + (e*x^2)/d])","C",1
269,1,314,378,1.0324287,"\int \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]),x]","\frac{9 \left(-4 b d \sqrt{e} n x \sqrt{d+e x^2} \, _3F_2\left(\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-\frac{e x^2}{d}\right)+\sqrt{\frac{e x^2}{d}+1} \left(3 d^2 \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right) (a-b n \log (x))+\sqrt{e} x \sqrt{d+e x^2} \left(5 a d+2 a e x^2-2 b d n\right)+b \log \left(c x^n\right) \left(3 d^2 \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)+\sqrt{e} x \sqrt{d+e x^2} \left(5 d+2 e x^2\right)\right)\right)+b d^{3/2} n (3 \log (x)-2) \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)\right)-8 b e^{3/2} n x^3 \sqrt{d+e x^2} \, _3F_2\left(-\frac{1}{2},\frac{3}{2},\frac{3}{2};\frac{5}{2},\frac{5}{2};-\frac{e x^2}{d}\right)}{72 \sqrt{e} \sqrt{\frac{e x^2}{d}+1}}","\frac{3 d^{5/2} \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{8 \sqrt{e} \sqrt{d+e x^2}}+\frac{3}{8} d x \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)+\frac{1}{4} x \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^{5/2} n \sqrt{\frac{e x^2}{d}+1} \text{Li}_2\left(e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{16 \sqrt{e} \sqrt{d+e x^2}}+\frac{3 b d^{5/2} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{16 \sqrt{e} \sqrt{d+e x^2}}-\frac{3 b d^{5/2} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{8 \sqrt{e} \sqrt{d+e x^2}}-\frac{9 b d^2 n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{32 \sqrt{e}}-\frac{9}{32} b d n x \sqrt{d+e x^2}-\frac{1}{16} b n x \left(d+e x^2\right)^{3/2}",1,"(-8*b*e^(3/2)*n*x^3*Sqrt[d + e*x^2]*HypergeometricPFQ[{-1/2, 3/2, 3/2}, {5/2, 5/2}, -((e*x^2)/d)] + 9*(-4*b*d*Sqrt[e]*n*x*Sqrt[d + e*x^2]*HypergeometricPFQ[{1/2, 1/2, 1/2}, {3/2, 3/2}, -((e*x^2)/d)] + b*d^(3/2)*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*(-2 + 3*Log[x]) + Sqrt[1 + (e*x^2)/d]*(Sqrt[e]*x*Sqrt[d + e*x^2]*(5*a*d - 2*b*d*n + 2*a*e*x^2) + 3*d^2*(a - b*n*Log[x])*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]] + b*Log[c*x^n]*(Sqrt[e]*x*Sqrt[d + e*x^2]*(5*d + 2*e*x^2) + 3*d^2*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]]))))/(72*Sqrt[e]*Sqrt[1 + (e*x^2)/d])","C",1
270,1,329,400,1.1539595,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Integrate[((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/x^2,x]","-\frac{b \sqrt{d} n \sqrt{d+e x^2} \left(\sqrt{d} \, _3F_2\left(-\frac{1}{2},-\frac{1}{2},-\frac{1}{2};\frac{1}{2},\frac{1}{2};-\frac{e x^2}{d}\right)+\log (x) \left(\sqrt{d} \sqrt{\frac{e x^2}{d}+1}-\sqrt{e} x \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)\right)\right)}{x \sqrt{\frac{e x^2}{d}+1}}+\frac{b \sqrt{e} n \sqrt{d+e x^2} \left((2 \log (x)-1) \left(\sqrt{e} x \sqrt{\frac{e x^2}{d}+1}+\sqrt{d} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)\right)-2 \sqrt{e} x \, _3F_2\left(\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-\frac{e x^2}{d}\right)\right)}{4 \sqrt{\frac{e x^2}{d}+1}}-\frac{\left(2 d-e x^2\right) \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{2 x}+\frac{3}{2} d \sqrt{e} \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)","-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{3}{2} e x \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)+\frac{3 \sqrt{d} \sqrt{e} \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 \sqrt{\frac{e x^2}{d}+1}}-\frac{3 b \sqrt{d} \sqrt{e} n \sqrt{d+e x^2} \text{Li}_2\left(e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{4 \sqrt{\frac{e x^2}{d}+1}}-\frac{1}{4} b e n x \sqrt{d+e x^2}-\frac{b d n \sqrt{d+e x^2}}{x}+\frac{3 b \sqrt{d} \sqrt{e} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{4 \sqrt{\frac{e x^2}{d}+1}}+\frac{3 b \sqrt{d} \sqrt{e} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{4 \sqrt{\frac{e x^2}{d}+1}}-\frac{3 b \sqrt{d} \sqrt{e} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 \sqrt{\frac{e x^2}{d}+1}}",1,"-((b*Sqrt[d]*n*Sqrt[d + e*x^2]*(Sqrt[d]*HypergeometricPFQ[{-1/2, -1/2, -1/2}, {1/2, 1/2}, -((e*x^2)/d)] + (Sqrt[d]*Sqrt[1 + (e*x^2)/d] - Sqrt[e]*x*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])*Log[x]))/(x*Sqrt[1 + (e*x^2)/d])) + (b*Sqrt[e]*n*Sqrt[d + e*x^2]*(-2*Sqrt[e]*x*HypergeometricPFQ[{1/2, 1/2, 1/2}, {3/2, 3/2}, -((e*x^2)/d)] + (Sqrt[e]*x*Sqrt[1 + (e*x^2)/d] + Sqrt[d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])*(-1 + 2*Log[x])))/(4*Sqrt[1 + (e*x^2)/d]) - ((2*d - e*x^2)*Sqrt[d + e*x^2]*(a - b*n*Log[x] + b*Log[c*x^n]))/(2*x) + (3*d*Sqrt[e]*(a - b*n*Log[x] + b*Log[c*x^n])*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/2","C",1
271,1,269,400,0.7751344,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Integrate[((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/x^4,x]","\frac{b e n \sqrt{d+e x^2} \left(-\, _3F_2\left(-\frac{1}{2},-\frac{1}{2},-\frac{1}{2};\frac{1}{2},\frac{1}{2};-\frac{e x^2}{d}\right)-\log (x) \sqrt{\frac{e x^2}{d}+1}+\frac{\sqrt{e} x \log (x) \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d}}\right)}{x \sqrt{\frac{e x^2}{d}+1}}+e^{3/2} \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-\frac{\sqrt{d+e x^2} \left(d+4 e x^2\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{3 x^3}+\frac{b d n \sqrt{d+e x^2} \left(-\, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};-\frac{e x^2}{d}\right)-3 \log (x) \left(\frac{e x^2}{d}+1\right)^{3/2}\right)}{9 x^3 \sqrt{\frac{e x^2}{d}+1}}","\frac{e^{3/2} \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d} \sqrt{\frac{e x^2}{d}+1}}-\frac{e \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{b e^{3/2} n \sqrt{d+e x^2} \text{Li}_2\left(e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 \sqrt{d} \sqrt{\frac{e x^2}{d}+1}}+\frac{b e^{3/2} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{2 \sqrt{d} \sqrt{\frac{e x^2}{d}+1}}+\frac{4 b e^{3/2} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 \sqrt{d} \sqrt{\frac{e x^2}{d}+1}}-\frac{b e^{3/2} n \sqrt{d+e x^2} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{\sqrt{d} \sqrt{\frac{e x^2}{d}+1}}-\frac{4 b e n \sqrt{d+e x^2}}{3 x}-\frac{b n \left(d+e x^2\right)^{3/2}}{9 x^3}",1,"(b*d*n*Sqrt[d + e*x^2]*(-Hypergeometric2F1[-3/2, -3/2, -1/2, -((e*x^2)/d)] - 3*(1 + (e*x^2)/d)^(3/2)*Log[x]))/(9*x^3*Sqrt[1 + (e*x^2)/d]) + (b*e*n*Sqrt[d + e*x^2]*(-HypergeometricPFQ[{-1/2, -1/2, -1/2}, {1/2, 1/2}, -((e*x^2)/d)] - Sqrt[1 + (e*x^2)/d]*Log[x] + (Sqrt[e]*x*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[x])/Sqrt[d]))/(x*Sqrt[1 + (e*x^2)/d]) - (Sqrt[d + e*x^2]*(d + 4*e*x^2)*(a - b*n*Log[x] + b*Log[c*x^n]))/(3*x^3) + e^(3/2)*(a - b*n*Log[x] + b*Log[c*x^n])*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]]","C",1
272,1,114,138,0.2127193,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Integrate[((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/x^6,x]","-\frac{\sqrt{d+e x^2} \left(15 a \left(d+e x^2\right)^2+b n \left(3 d^2+11 d e x^2+23 e^2 x^4\right)\right)+15 b \left(d+e x^2\right)^{5/2} \log \left(c x^n\right)-15 b e^{5/2} n x^5 \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)}{75 d x^5}","-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 d x^5}+\frac{b e^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{5 d}-\frac{b e^2 n \sqrt{d+e x^2}}{5 d x}-\frac{b n \left(d+e x^2\right)^{5/2}}{25 d x^5}-\frac{b e n \left(d+e x^2\right)^{3/2}}{15 d x^3}",1,"-1/75*(Sqrt[d + e*x^2]*(15*a*(d + e*x^2)^2 + b*n*(3*d^2 + 11*d*e*x^2 + 23*e^2*x^4)) + 15*b*(d + e*x^2)^(5/2)*Log[c*x^n] - 15*b*e^(5/2)*n*x^5*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(d*x^5)","A",1
273,1,145,196,0.2386199,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x^8} \, dx","Integrate[((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/x^8,x]","-\frac{\sqrt{d+e x^2} \left(105 a \left(5 d-2 e x^2\right) \left(d+e x^2\right)^2+b n \left(75 d^3+183 d^2 e x^2+71 d e^2 x^4-247 e^3 x^6\right)\right)+105 b \left(5 d-2 e x^2\right) \left(d+e x^2\right)^{5/2} \log \left(c x^n\right)+210 b e^{7/2} n x^7 \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)}{3675 d^2 x^7}","\frac{2 e \left(d+e x^2\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{35 d^2 x^5}-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{7 d x^7}-\frac{2 b e^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{35 d^2}+\frac{2 b e^3 n \sqrt{d+e x^2}}{35 d^2 x}+\frac{2 b e^2 n \left(d+e x^2\right)^{3/2}}{105 d^2 x^3}-\frac{b n \left(d+e x^2\right)^{7/2}}{49 d^2 x^7}+\frac{2 b e n \left(d+e x^2\right)^{5/2}}{175 d^2 x^5}",1,"-1/3675*(Sqrt[d + e*x^2]*(105*a*(5*d - 2*e*x^2)*(d + e*x^2)^2 + b*n*(75*d^3 + 183*d^2*e*x^2 + 71*d*e^2*x^4 - 247*e^3*x^6)) + 105*b*(5*d - 2*e*x^2)*(d + e*x^2)^(5/2)*Log[c*x^n] + 210*b*e^(7/2)*n*x^7*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(d^2*x^7)","A",1
274,1,178,256,0.2813172,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x^{10}} \, dx","Integrate[((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/x^10,x]","-\frac{\sqrt{d+e x^2} \left(315 a \left(35 d^2-20 d e x^2+8 e^2 x^4\right) \left(d+e x^2\right)^2+b n \left(1225 d^4+2425 d^3 e x^2+429 d^2 e^2 x^4-677 d e^3 x^6+2614 e^4 x^8\right)\right)+315 b \left(d+e x^2\right)^{5/2} \left(35 d^2-20 d e x^2+8 e^2 x^4\right) \log \left(c x^n\right)-2520 b e^{9/2} n x^9 \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)}{99225 d^3 x^9}","-\frac{8 e^2 \left(d+e x^2\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{315 d^3 x^5}+\frac{4 e \left(d+e x^2\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{63 d^2 x^7}-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{9 d x^9}+\frac{8 b e^{9/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{315 d^3}-\frac{8 b e^4 n \sqrt{d+e x^2}}{315 d^3 x}-\frac{8 b e^3 n \left(d+e x^2\right)^{3/2}}{945 d^3 x^3}-\frac{8 b e^2 n \left(d+e x^2\right)^{5/2}}{1575 d^3 x^5}+\frac{50 b e n \left(d+e x^2\right)^{7/2}}{3969 d^3 x^7}-\frac{b n \left(d+e x^2\right)^{7/2}}{81 d^2 x^9}",1,"-1/99225*(Sqrt[d + e*x^2]*(315*a*(d + e*x^2)^2*(35*d^2 - 20*d*e*x^2 + 8*e^2*x^4) + b*n*(1225*d^4 + 2425*d^3*e*x^2 + 429*d^2*e^2*x^4 - 677*d*e^3*x^6 + 2614*e^4*x^8)) + 315*b*(d + e*x^2)^(5/2)*(35*d^2 - 20*d*e*x^2 + 8*e^2*x^4)*Log[c*x^n] - 2520*b*e^(9/2)*n*x^9*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(d^3*x^9)","A",1
275,1,53,60,0.0445951,"\int x \sqrt{4+x^2} \log (x) \, dx","Integrate[x*Sqrt[4 + x^2]*Log[x],x]","\frac{1}{3} \left(-\frac{1}{3} \left(x^2+16\right) \sqrt{x^2+4}+\left(x^2+4\right)^{3/2} \log (x)+8 \log \left(\sqrt{x^2+4}+2\right)-8 \log (x)\right)","-\frac{1}{9} \left(x^2+4\right)^{3/2}-\frac{4 \sqrt{x^2+4}}{3}+\frac{1}{3} \left(x^2+4\right)^{3/2} \log (x)+\frac{8}{3} \tanh ^{-1}\left(\frac{\sqrt{x^2+4}}{2}\right)",1,"(-1/3*(Sqrt[4 + x^2]*(16 + x^2)) - 8*Log[x] + (4 + x^2)^(3/2)*Log[x] + 8*Log[2 + Sqrt[4 + x^2]])/3","A",1
276,1,204,182,0.2081071,"\int \frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d+e x^2}} \, dx","Integrate[(x^5*(a + b*Log[c*x^n]))/Sqrt[d + e*x^2],x]","\frac{120 a d^2 \sqrt{d+e x^2}+45 a e^2 x^4 \sqrt{d+e x^2}-60 a d e x^2 \sqrt{d+e x^2}+15 b \sqrt{d+e x^2} \left(8 d^2-4 d e x^2+3 e^2 x^4\right) \log \left(c x^n\right)+120 b d^{5/2} n \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)-120 b d^{5/2} n \log (x)-94 b d^2 n \sqrt{d+e x^2}-9 b e^2 n x^4 \sqrt{d+e x^2}+17 b d e n x^2 \sqrt{d+e x^2}}{225 e^3}","\frac{d^2 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{e^3}-\frac{2 d \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 e^3}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e^3}+\frac{8 b d^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{15 e^3}-\frac{8 b d^2 n \sqrt{d+e x^2}}{15 e^3}+\frac{7 b d n \left(d+e x^2\right)^{3/2}}{45 e^3}-\frac{b n \left(d+e x^2\right)^{5/2}}{25 e^3}",1,"(120*a*d^2*Sqrt[d + e*x^2] - 94*b*d^2*n*Sqrt[d + e*x^2] - 60*a*d*e*x^2*Sqrt[d + e*x^2] + 17*b*d*e*n*x^2*Sqrt[d + e*x^2] + 45*a*e^2*x^4*Sqrt[d + e*x^2] - 9*b*e^2*n*x^4*Sqrt[d + e*x^2] - 120*b*d^(5/2)*n*Log[x] + 15*b*Sqrt[d + e*x^2]*(8*d^2 - 4*d*e*x^2 + 3*e^2*x^4)*Log[c*x^n] + 120*b*d^(5/2)*n*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/(225*e^3)","A",1
277,1,145,129,0.1655306,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d+e x^2}} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/Sqrt[d + e*x^2],x]","\frac{3 a e x^2 \sqrt{d+e x^2}-6 a d \sqrt{d+e x^2}+3 b \left(e x^2-2 d\right) \sqrt{d+e x^2} \log \left(c x^n\right)-6 b d^{3/2} n \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)+6 b d^{3/2} n \log (x)-b e n x^2 \sqrt{d+e x^2}+5 b d n \sqrt{d+e x^2}}{9 e^2}","-\frac{d \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 e^2}-\frac{2 b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{3 e^2}+\frac{2 b d n \sqrt{d+e x^2}}{3 e^2}-\frac{b n \left(d+e x^2\right)^{3/2}}{9 e^2}",1,"(-6*a*d*Sqrt[d + e*x^2] + 5*b*d*n*Sqrt[d + e*x^2] + 3*a*e*x^2*Sqrt[d + e*x^2] - b*e*n*x^2*Sqrt[d + e*x^2] + 6*b*d^(3/2)*n*Log[x] + 3*b*(-2*d + e*x^2)*Sqrt[d + e*x^2]*Log[c*x^n] - 6*b*d^(3/2)*n*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/(9*e^2)","A",1
278,1,91,73,0.0903042,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d+e x^2}} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/Sqrt[d + e*x^2],x]","\frac{a \sqrt{d+e x^2}+b \sqrt{d+e x^2} \log \left(c x^n\right)-b n \sqrt{d+e x^2}+b \sqrt{d} n \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)-b \sqrt{d} n \log (x)}{e}","\frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{b n \sqrt{d+e x^2}}{e}+\frac{b \sqrt{d} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{e}",1,"(a*Sqrt[d + e*x^2] - b*n*Sqrt[d + e*x^2] - b*Sqrt[d]*n*Log[x] + b*Sqrt[d + e*x^2]*Log[c*x^n] + b*Sqrt[d]*n*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/e","A",1
279,1,162,166,0.2104785,"\int \frac{a+b \log \left(c x^n\right)}{x \sqrt{d+e x^2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x*Sqrt[d + e*x^2]),x]","\frac{b n \sqrt{\frac{d}{e x^2}+1} \left(-\, _3F_2\left(\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-\frac{d}{e x^2}\right)-\frac{\sqrt{e} x \log (x) \sinh ^{-1}\left(\frac{\sqrt{d}}{\sqrt{e} x}\right)}{\sqrt{d}}\right)}{\sqrt{d+e x^2}}+\frac{\log \left(\sqrt{d} \sqrt{d+e x^2}+d\right) \left(-a-b \left(\log \left(c x^n\right)-n \log (x)\right)\right)}{\sqrt{d}}-\frac{\log (x) \left(-a-b \left(\log \left(c x^n\right)-n \log (x)\right)\right)}{\sqrt{d}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d}}-\frac{b n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^2+d}}\right)}{2 \sqrt{d}}+\frac{b n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)^2}{2 \sqrt{d}}-\frac{b n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{\sqrt{d}}",1,"(b*n*Sqrt[1 + d/(e*x^2)]*(-HypergeometricPFQ[{1/2, 1/2, 1/2}, {3/2, 3/2}, -(d/(e*x^2))] - (Sqrt[e]*x*ArcSinh[Sqrt[d]/(Sqrt[e]*x)]*Log[x])/Sqrt[d]))/Sqrt[d + e*x^2] - (Log[x]*(-a - b*(-(n*Log[x]) + Log[c*x^n])))/Sqrt[d] + ((-a - b*(-(n*Log[x]) + Log[c*x^n]))*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/Sqrt[d]","C",1
280,1,229,258,1.1045347,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \sqrt{d+e x^2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^3*Sqrt[d + e*x^2]),x]","\frac{\frac{b n \sqrt{\frac{d}{e x^2}+1} \left(2 d^{3/2} \, _3F_2\left(\frac{3}{2},\frac{3}{2},\frac{3}{2};\frac{5}{2},\frac{5}{2};-\frac{d}{e x^2}\right)+9 e x^2 (2 \log (x)+1) \left(\sqrt{e} x \sinh ^{-1}\left(\frac{\sqrt{d}}{\sqrt{e} x}\right)-\sqrt{d} \sqrt{\frac{d}{e x^2}+1}\right)\right)}{x^2 \sqrt{d+e x^2}}-\frac{18 \sqrt{d} \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{x^2}+18 e \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-18 e \log (x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{36 d^{3/2}}","\frac{e \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 d^{3/2}}-\frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{2 d x^2}+\frac{b e n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^2+d}}\right)}{4 d^{3/2}}-\frac{b e n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)^2}{4 d^{3/2}}-\frac{b e n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{4 d^{3/2}}+\frac{b e n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{2 d^{3/2}}-\frac{b n \sqrt{d+e x^2}}{4 d x^2}",1,"((b*n*Sqrt[1 + d/(e*x^2)]*(2*d^(3/2)*HypergeometricPFQ[{3/2, 3/2, 3/2}, {5/2, 5/2}, -(d/(e*x^2))] + 9*e*x^2*(-(Sqrt[d]*Sqrt[1 + d/(e*x^2)]) + Sqrt[e]*x*ArcSinh[Sqrt[d]/(Sqrt[e]*x)])*(1 + 2*Log[x])))/(x^2*Sqrt[d + e*x^2]) - (18*Sqrt[d]*Sqrt[d + e*x^2]*(a - b*n*Log[x] + b*Log[c*x^n]))/x^2 - 18*e*Log[x]*(a - b*n*Log[x] + b*Log[c*x^n]) + 18*e*(a - b*n*Log[x] + b*Log[c*x^n])*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/(36*d^(3/2))","C",1
281,1,205,359,0.7900167,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d+e x^2}} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/Sqrt[d + e*x^2],x]","\frac{\frac{b n \sqrt{\frac{e x^2}{d}+1} \left(2 e^2 x^3 \, _3F_2\left(\frac{3}{2},\frac{3}{2},\frac{3}{2};\frac{5}{2},\frac{5}{2};-\frac{e x^2}{d}\right)+9 d \sqrt{e} (2 \log (x)-1) \left(\sqrt{e} x \sqrt{\frac{e x^2}{d}+1}-\sqrt{d} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)\right)\right)}{\sqrt{d+e x^2}}+18 e x \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-18 d \sqrt{e} \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{36 e^2}","-\frac{d^{3/2} \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^{3/2} \sqrt{d+e x^2}}+\frac{x \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{2 e}+\frac{b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \text{Li}_2\left(e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{4 e^{3/2} \sqrt{d+e x^2}}-\frac{b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{4 e^{3/2} \sqrt{d+e x^2}}-\frac{b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{4 e^{3/2} \sqrt{d+e x^2}}+\frac{b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 e^{3/2} \sqrt{d+e x^2}}-\frac{b n x \sqrt{d+e x^2}}{4 e}",1,"((b*n*Sqrt[1 + (e*x^2)/d]*(2*e^2*x^3*HypergeometricPFQ[{3/2, 3/2, 3/2}, {5/2, 5/2}, -((e*x^2)/d)] + 9*d*Sqrt[e]*(Sqrt[e]*x*Sqrt[1 + (e*x^2)/d] - Sqrt[d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])*(-1 + 2*Log[x])))/Sqrt[d + e*x^2] + 18*e*x*Sqrt[d + e*x^2]*(a - b*n*Log[x] + b*Log[c*x^n]) - 18*d*Sqrt[e]*(a - b*n*Log[x] + b*Log[c*x^n])*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(36*e^2)","C",1
282,1,186,250,0.6078346,"\int \frac{a+b \log \left(c x^n\right)}{\sqrt{d+e x^2}} \, dx","Integrate[(a + b*Log[c*x^n])/Sqrt[d + e*x^2],x]","\frac{\log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{\sqrt{e}}+\frac{b n \sqrt{\frac{e x^2}{d}+1} \left(\text{Li}_2\left(e^{-2 \sinh ^{-1}\left(\sqrt{\frac{e}{d}} x\right)}\right)+2 \log (x) \log \left(\sqrt{\frac{e x^2}{d}+1}+x \sqrt{\frac{e}{d}}\right)-\sinh ^{-1}\left(x \sqrt{\frac{e}{d}}\right)^2-2 \sinh ^{-1}\left(x \sqrt{\frac{e}{d}}\right) \log \left(1-e^{-2 \sinh ^{-1}\left(x \sqrt{\frac{e}{d}}\right)}\right)\right)}{2 \sqrt{\frac{e}{d}} \sqrt{d+e x^2}}","\frac{\sqrt{d} \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{e} \sqrt{d+e x^2}}-\frac{b \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \text{Li}_2\left(e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 \sqrt{e} \sqrt{d+e x^2}}+\frac{b \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{2 \sqrt{e} \sqrt{d+e x^2}}-\frac{b \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{\sqrt{e} \sqrt{d+e x^2}}",1,"((a - b*n*Log[x] + b*Log[c*x^n])*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/Sqrt[e] + (b*n*Sqrt[1 + (e*x^2)/d]*(-ArcSinh[Sqrt[e/d]*x]^2 - 2*ArcSinh[Sqrt[e/d]*x]*Log[1 - E^(-2*ArcSinh[Sqrt[e/d]*x])] + 2*Log[x]*Log[Sqrt[e/d]*x + Sqrt[1 + (e*x^2)/d]] + PolyLog[2, E^(-2*ArcSinh[Sqrt[e/d]*x])]))/(2*Sqrt[e/d]*Sqrt[d + e*x^2])","A",0
283,1,77,81,0.1072949,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \sqrt{d+e x^2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*Sqrt[d + e*x^2]),x]","\frac{(a+b n) \left(-\sqrt{d+e x^2}\right)-b \sqrt{d+e x^2} \log \left(c x^n\right)+b \sqrt{e} n x \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)}{d x}","-\frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{d x}-\frac{b n \sqrt{d+e x^2}}{d x}+\frac{b \sqrt{e} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{d}",1,"(-((a + b*n)*Sqrt[d + e*x^2]) - b*Sqrt[d + e*x^2]*Log[c*x^n] + b*Sqrt[e]*n*x*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(d*x)","A",1
284,1,110,144,0.1524458,"\int \frac{a+b \log \left(c x^n\right)}{x^4 \sqrt{d+e x^2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^4*Sqrt[d + e*x^2]),x]","\frac{\sqrt{d+e x^2} \left(-3 a d+6 a e x^2-b d n+5 b e n x^2\right)-3 b \left(d-2 e x^2\right) \sqrt{d+e x^2} \log \left(c x^n\right)-6 b e^{3/2} n x^3 \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)}{9 d^2 x^3}","\frac{2 e \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{3 d^2 x}-\frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{3 d x^3}-\frac{2 b e^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{3 d^2}+\frac{2 b e n \sqrt{d+e x^2}}{3 d^2 x}-\frac{b n \left(d+e x^2\right)^{3/2}}{9 d^2 x^3}",1,"(Sqrt[d + e*x^2]*(-3*a*d - b*d*n + 6*a*e*x^2 + 5*b*e*n*x^2) - 3*b*(d - 2*e*x^2)*Sqrt[d + e*x^2]*Log[c*x^n] - 6*b*e^(3/2)*n*x^3*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(9*d^2*x^3)","A",1
285,1,147,204,0.2337583,"\int \frac{a+b \log \left(c x^n\right)}{x^6 \sqrt{d+e x^2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^6*Sqrt[d + e*x^2]),x]","-\frac{\sqrt{d+e x^2} \left(15 a \left(3 d^2-4 d e x^2+8 e^2 x^4\right)+b n \left(9 d^2-17 d e x^2+94 e^2 x^4\right)\right)+15 b \sqrt{d+e x^2} \left(3 d^2-4 d e x^2+8 e^2 x^4\right) \log \left(c x^n\right)-120 b e^{5/2} n x^5 \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)}{225 d^3 x^5}","-\frac{8 e^2 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{15 d^3 x}+\frac{4 e \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{15 d^2 x^3}-\frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{5 d x^5}+\frac{8 b e^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{15 d^3}-\frac{8 b e^2 n \sqrt{d+e x^2}}{15 d^3 x}+\frac{26 b e n \left(d+e x^2\right)^{3/2}}{225 d^3 x^3}-\frac{b n \left(d+e x^2\right)^{3/2}}{25 d^2 x^5}",1,"-1/225*(Sqrt[d + e*x^2]*(15*a*(3*d^2 - 4*d*e*x^2 + 8*e^2*x^4) + b*n*(9*d^2 - 17*d*e*x^2 + 94*e^2*x^4)) + 15*b*Sqrt[d + e*x^2]*(3*d^2 - 4*d*e*x^2 + 8*e^2*x^4)*Log[c*x^n] - 120*b*e^(5/2)*n*x^5*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(d^3*x^5)","A",1
286,1,195,209,0.2207966,"\int \frac{x^7 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Integrate[(x^7*(a + b*Log[c*x^n]))/(d + e*x^2)^(3/2),x]","\frac{240 a d^3+120 a d^2 e x^2-30 a d e^2 x^4+15 a e^3 x^6+15 b \left(16 d^3+8 d^2 e x^2-2 d e^2 x^4+e^3 x^6\right) \log \left(c x^n\right)-240 b d^{5/2} n \log (x) \sqrt{d+e x^2}+240 b d^{5/2} n \sqrt{d+e x^2} \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)-148 b d^3 n-134 b d^2 e n x^2+11 b d e^2 n x^4-3 b e^3 n x^6}{75 e^4 \sqrt{d+e x^2}}","\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{e^4 \sqrt{d+e x^2}}+\frac{3 d^2 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{e^4}-\frac{d \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{e^4}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e^4}+\frac{16 b d^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{5 e^4}-\frac{11 b d^2 n \sqrt{d+e x^2}}{5 e^4}+\frac{4 b d n \left(d+e x^2\right)^{3/2}}{15 e^4}-\frac{b n \left(d+e x^2\right)^{5/2}}{25 e^4}",1,"(240*a*d^3 - 148*b*d^3*n + 120*a*d^2*e*x^2 - 134*b*d^2*e*n*x^2 - 30*a*d*e^2*x^4 + 11*b*d*e^2*n*x^4 + 15*a*e^3*x^6 - 3*b*e^3*n*x^6 - 240*b*d^(5/2)*n*Sqrt[d + e*x^2]*Log[x] + 15*b*(16*d^3 + 8*d^2*e*x^2 - 2*d*e^2*x^4 + e^3*x^6)*Log[c*x^n] + 240*b*d^(5/2)*n*Sqrt[d + e*x^2]*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/(75*e^4*Sqrt[d + e*x^2])","A",1
287,1,160,158,0.1874795,"\int \frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Integrate[(x^5*(a + b*Log[c*x^n]))/(d + e*x^2)^(3/2),x]","\frac{-24 a d^2-12 a d e x^2+3 a e^2 x^4-3 b \left(8 d^2+4 d e x^2-e^2 x^4\right) \log \left(c x^n\right)+24 b d^{3/2} n \log (x) \sqrt{d+e x^2}-24 b d^{3/2} n \sqrt{d+e x^2} \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)+14 b d^2 n+13 b d e n x^2-b e^2 n x^4}{9 e^3 \sqrt{d+e x^2}}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{e^3 \sqrt{d+e x^2}}-\frac{2 d \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{e^3}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 e^3}-\frac{8 b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{3 e^3}+\frac{5 b d n \sqrt{d+e x^2}}{3 e^3}-\frac{b n \left(d+e x^2\right)^{3/2}}{9 e^3}",1,"(-24*a*d^2 + 14*b*d^2*n - 12*a*d*e*x^2 + 13*b*d*e*n*x^2 + 3*a*e^2*x^4 - b*e^2*n*x^4 + 24*b*d^(3/2)*n*Sqrt[d + e*x^2]*Log[x] - 3*b*(8*d^2 + 4*d*e*x^2 - e^2*x^4)*Log[c*x^n] - 24*b*d^(3/2)*n*Sqrt[d + e*x^2]*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/(9*e^3*Sqrt[d + e*x^2])","A",1
288,1,118,100,0.1492116,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/(d + e*x^2)^(3/2),x]","\frac{2 a d+a e x^2+b \left(2 d+e x^2\right) \log \left(c x^n\right)-2 b \sqrt{d} n \log (x) \sqrt{d+e x^2}+2 b \sqrt{d} n \sqrt{d+e x^2} \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)-b d n-b e n x^2}{e^2 \sqrt{d+e x^2}}","\frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{d \left(a+b \log \left(c x^n\right)\right)}{e^2 \sqrt{d+e x^2}}-\frac{b n \sqrt{d+e x^2}}{e^2}+\frac{2 b \sqrt{d} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{e^2}",1,"(2*a*d - b*d*n + a*e*x^2 - b*e*n*x^2 - 2*b*Sqrt[d]*n*Sqrt[d + e*x^2]*Log[x] + b*(2*d + e*x^2)*Log[c*x^n] + 2*b*Sqrt[d]*n*Sqrt[d + e*x^2]*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/(e^2*Sqrt[d + e*x^2])","A",1
289,1,77,57,0.142985,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/(d + e*x^2)^(3/2),x]","-\frac{\frac{a}{\sqrt{d+e x^2}}+\frac{b \log \left(c x^n\right)}{\sqrt{d+e x^2}}+\frac{b n \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)}{\sqrt{d}}-\frac{b n \log (x)}{\sqrt{d}}}{e}","-\frac{a+b \log \left(c x^n\right)}{e \sqrt{d+e x^2}}-\frac{b n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{\sqrt{d} e}",1,"-((a/Sqrt[d + e*x^2] - (b*n*Log[x])/Sqrt[d] + (b*Log[c*x^n])/Sqrt[d + e*x^2] + (b*n*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/Sqrt[d])/e)","A",1
290,1,241,209,0.3863546,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^2\right)^{3/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x^2)^(3/2)),x]","\frac{9 e x^2 \left(\log (x) \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)+b n \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)\right)+\left(\sqrt{d}-\sqrt{d+e x^2} \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)\right) \left(a+b \log \left(c x^n\right)\right)-b n \log ^2(x) \sqrt{d+e x^2}-b \sqrt{e} n x \log (x) \sqrt{\frac{d}{e x^2}+1} \sinh ^{-1}\left(\frac{\sqrt{d}}{\sqrt{e} x}\right)\right)-b d^{3/2} n \sqrt{\frac{d}{e x^2}+1} \, _3F_2\left(\frac{3}{2},\frac{3}{2},\frac{3}{2};\frac{5}{2},\frac{5}{2};-\frac{d}{e x^2}\right)}{9 d^{3/2} e x^2 \sqrt{d+e x^2}}","\left(\frac{1}{d \sqrt{d+e x^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{d^{3/2}}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^2+d}}\right)}{2 d^{3/2}}+\frac{b n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)^2}{2 d^{3/2}}+\frac{b n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{b n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{d^{3/2}}",1,"(-(b*d^(3/2)*n*Sqrt[1 + d/(e*x^2)]*HypergeometricPFQ[{3/2, 3/2, 3/2}, {5/2, 5/2}, -(d/(e*x^2))]) + 9*e*x^2*(-(b*Sqrt[e]*n*Sqrt[1 + d/(e*x^2)]*x*ArcSinh[Sqrt[d]/(Sqrt[e]*x)]*Log[x]) - b*n*Sqrt[d + e*x^2]*Log[x]^2 + Sqrt[d + e*x^2]*Log[x]*(a + b*Log[c*x^n] + b*n*Log[d + Sqrt[d]*Sqrt[d + e*x^2]]) + (a + b*Log[c*x^n])*(Sqrt[d] - Sqrt[d + e*x^2]*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])))/(9*d^(3/2)*e*x^2*Sqrt[d + e*x^2])","C",1
291,1,218,287,0.3592075,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^2\right)^{3/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^3*(d + e*x^2)^(3/2)),x]","\frac{3 b d^{5/2} n \sqrt{\frac{d}{e x^2}+1} \, _3F_2\left(\frac{5}{2},\frac{5}{2},\frac{5}{2};\frac{7}{2},\frac{7}{2};-\frac{d}{e x^2}\right)-25 e x^2 \left(\sqrt{d} \left(d+3 e x^2\right)+3 e x^2 \log (x) \sqrt{d+e x^2}-3 e x^2 \sqrt{d+e x^2} \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-5 b d^{5/2} n (2 \log (x)+1) \sqrt{\frac{d}{e x^2}+1} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};-\frac{d}{e x^2}\right)}{50 d^{5/2} e x^4 \sqrt{d+e x^2}}","\frac{3 e \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 d^{5/2}}-\frac{3 e \left(a+b \log \left(c x^n\right)\right)}{2 d^2 \sqrt{d+e x^2}}-\frac{a+b \log \left(c x^n\right)}{2 d x^2 \sqrt{d+e x^2}}+\frac{3 b e n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^2+d}}\right)}{4 d^{5/2}}-\frac{3 b e n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)^2}{4 d^{5/2}}-\frac{5 b e n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{4 d^{5/2}}+\frac{3 b e n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{2 d^{5/2}}-\frac{b n \sqrt{d+e x^2}}{4 d^2 x^2}",1,"(3*b*d^(5/2)*n*Sqrt[1 + d/(e*x^2)]*HypergeometricPFQ[{5/2, 5/2, 5/2}, {7/2, 7/2}, -(d/(e*x^2))] - 5*b*d^(5/2)*n*Sqrt[1 + d/(e*x^2)]*Hypergeometric2F1[3/2, 5/2, 7/2, -(d/(e*x^2))]*(1 + 2*Log[x]) - 25*e*x^2*(a - b*n*Log[x] + b*Log[c*x^n])*(Sqrt[d]*(d + 3*e*x^2) + 3*e*x^2*Sqrt[d + e*x^2]*Log[x] - 3*e*x^2*Sqrt[d + e*x^2]*Log[d + Sqrt[d]*Sqrt[d + e*x^2]]))/(50*d^(5/2)*e*x^4*Sqrt[d + e*x^2])","C",0
292,1,217,328,0.4791071,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e*x^2)^(3/2),x]","-\frac{b n \sqrt{\frac{e x^2}{d}+1} \left(e^{3/2} x^3 \left(d+e x^2\right) \, _3F_2\left(\frac{3}{2},\frac{3}{2},\frac{3}{2};\frac{5}{2},\frac{5}{2};-\frac{e x^2}{d}\right)-9 d^{3/2} \log (x) \left(d+e x^2\right) \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)+9 d^2 \sqrt{e} x \log (x) \sqrt{\frac{e x^2}{d}+1}\right)}{9 d e^{3/2} \left(d+e x^2\right)^{3/2}}+\frac{\log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{e^{3/2}}-\frac{x \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{e \sqrt{d+e x^2}}","\frac{\sqrt{d} \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{e^{3/2} \sqrt{d+e x^2}}-\frac{x \left(a+b \log \left(c x^n\right)\right)}{e \sqrt{d+e x^2}}-\frac{b \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \text{Li}_2\left(e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 e^{3/2} \sqrt{d+e x^2}}+\frac{b \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{2 e^{3/2} \sqrt{d+e x^2}}+\frac{b \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{e^{3/2} \sqrt{d+e x^2}}-\frac{b \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{e^{3/2} \sqrt{d+e x^2}}",1,"-1/9*(b*n*Sqrt[1 + (e*x^2)/d]*(e^(3/2)*x^3*(d + e*x^2)*HypergeometricPFQ[{3/2, 3/2, 3/2}, {5/2, 5/2}, -((e*x^2)/d)] + 9*d^2*Sqrt[e]*x*Sqrt[1 + (e*x^2)/d]*Log[x] - 9*d^(3/2)*(d + e*x^2)*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[x]))/(d*e^(3/2)*(d + e*x^2)^(3/2)) - (x*(a - b*n*Log[x] + b*Log[c*x^n]))/(e*Sqrt[d + e*x^2]) + ((a - b*n*Log[x] + b*Log[c*x^n])*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/e^(3/2)","C",1
293,1,70,58,0.1035685,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*x^2)^(3/2),x]","\frac{\frac{a x}{\sqrt{d+e x^2}}+\frac{b x \log \left(c x^n\right)}{\sqrt{d+e x^2}}-\frac{b n \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)}{\sqrt{e}}}{d}","\frac{x \left(a+b \log \left(c x^n\right)\right)}{d \sqrt{d+e x^2}}-\frac{b n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{d \sqrt{e}}",1,"((a*x)/Sqrt[d + e*x^2] + (b*x*Log[c*x^n])/Sqrt[d + e*x^2] - (b*n*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/Sqrt[e])/d","A",1
294,1,103,110,0.1311361,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^2\right)^{3/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*(d + e*x^2)^(3/2)),x]","\frac{-a d-2 a e x^2-b \left(d+2 e x^2\right) \log \left(c x^n\right)+2 b \sqrt{e} n x \sqrt{d+e x^2} \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)-b d n-b e n x^2}{d^2 x \sqrt{d+e x^2}}","-\frac{2 e x \left(a+b \log \left(c x^n\right)\right)}{d^2 \sqrt{d+e x^2}}-\frac{a+b \log \left(c x^n\right)}{d x \sqrt{d+e x^2}}-\frac{b n \sqrt{d+e x^2}}{d^2 x}+\frac{2 b \sqrt{e} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{d^2}",1,"(-(a*d) - b*d*n - 2*a*e*x^2 - b*e*n*x^2 - b*(d + 2*e*x^2)*Log[c*x^n] + 2*b*Sqrt[e]*n*x*Sqrt[d + e*x^2]*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(d^2*x*Sqrt[d + e*x^2])","A",1
295,1,144,176,0.1681525,"\int \frac{a+b \log \left(c x^n\right)}{x^4 \left(d+e x^2\right)^{3/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^4*(d + e*x^2)^(3/2)),x]","\frac{-3 a d^2+12 a d e x^2+24 a e^2 x^4-3 b \left(d^2-4 d e x^2-8 e^2 x^4\right) \log \left(c x^n\right)-b d^2 n-24 b e^{3/2} n x^3 \sqrt{d+e x^2} \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)+13 b d e n x^2+14 b e^2 n x^4}{9 d^3 x^3 \sqrt{d+e x^2}}","\frac{8 e^2 x \left(a+b \log \left(c x^n\right)\right)}{3 d^3 \sqrt{d+e x^2}}+\frac{4 e \left(a+b \log \left(c x^n\right)\right)}{3 d^2 x \sqrt{d+e x^2}}-\frac{a+b \log \left(c x^n\right)}{3 d x^3 \sqrt{d+e x^2}}-\frac{8 b e^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{3 d^3}+\frac{14 b e n \sqrt{d+e x^2}}{9 d^3 x}-\frac{b n \sqrt{d+e x^2}}{9 d^2 x^3}",1,"(-3*a*d^2 - b*d^2*n + 12*a*d*e*x^2 + 13*b*d*e*n*x^2 + 24*a*e^2*x^4 + 14*b*e^2*n*x^4 - 3*b*(d^2 - 4*d*e*x^2 - 8*e^2*x^4)*Log[c*x^n] - 24*b*e^(3/2)*n*x^3*Sqrt[d + e*x^2]*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(9*d^3*x^3*Sqrt[d + e*x^2])","A",1
296,1,180,236,0.2041978,"\int \frac{a+b \log \left(c x^n\right)}{x^6 \left(d+e x^2\right)^{3/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^6*(d + e*x^2)^(3/2)),x]","\frac{-15 a d^3+30 a d^2 e x^2-120 a d e^2 x^4-240 a e^3 x^6-15 b \left(d^3-2 d^2 e x^2+8 d e^2 x^4+16 e^3 x^6\right) \log \left(c x^n\right)-3 b d^3 n+11 b d^2 e n x^2+240 b e^{5/2} n x^5 \sqrt{d+e x^2} \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)-134 b d e^2 n x^4-148 b e^3 n x^6}{75 d^4 x^5 \sqrt{d+e x^2}}","-\frac{16 e^3 x \left(a+b \log \left(c x^n\right)\right)}{5 d^4 \sqrt{d+e x^2}}-\frac{8 e^2 \left(a+b \log \left(c x^n\right)\right)}{5 d^3 x \sqrt{d+e x^2}}+\frac{2 e \left(a+b \log \left(c x^n\right)\right)}{5 d^2 x^3 \sqrt{d+e x^2}}-\frac{a+b \log \left(c x^n\right)}{5 d x^5 \sqrt{d+e x^2}}+\frac{16 b e^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{5 d^4}-\frac{148 b e^2 n \sqrt{d+e x^2}}{75 d^4 x}+\frac{14 b e n \sqrt{d+e x^2}}{75 d^3 x^3}-\frac{b n \sqrt{d+e x^2}}{25 d^2 x^5}",1,"(-15*a*d^3 - 3*b*d^3*n + 30*a*d^2*e*x^2 + 11*b*d^2*e*n*x^2 - 120*a*d*e^2*x^4 - 134*b*d*e^2*n*x^4 - 240*a*e^3*x^6 - 148*b*e^3*n*x^6 - 15*b*(d^3 - 2*d^2*e*x^2 + 8*d*e^2*x^4 + 16*e^3*x^6)*Log[c*x^n] + 240*b*e^(5/2)*n*x^5*Sqrt[d + e*x^2]*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(75*d^4*x^5*Sqrt[d + e*x^2])","A",1
297,1,240,212,0.2654018,"\int \frac{x^7 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Integrate[(x^7*(a + b*Log[c*x^n]))/(d + e*x^2)^(5/2),x]","\frac{-48 a d^3-72 a d^2 e x^2-18 a d e^2 x^4+3 a e^3 x^6-3 b \left(16 d^3+24 d^2 e x^2+6 d e^2 x^4-e^3 x^6\right) \log \left(c x^n\right)-48 b d^{3/2} e n x^2 \sqrt{d+e x^2} \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)+48 b d^{3/2} n \log (x) \left(d+e x^2\right)^{3/2}-48 b d^{5/2} n \sqrt{d+e x^2} \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)+20 b d^3 n+42 b d^2 e n x^2+21 b d e^2 n x^4-b e^3 n x^6}{9 e^4 \left(d+e x^2\right)^{3/2}}","\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{3 e^4 \left(d+e x^2\right)^{3/2}}-\frac{3 d^2 \left(a+b \log \left(c x^n\right)\right)}{e^4 \sqrt{d+e x^2}}-\frac{3 d \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{e^4}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 e^4}-\frac{16 b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{3 e^4}-\frac{b d^2 n}{3 e^4 \sqrt{d+e x^2}}+\frac{8 b d n \sqrt{d+e x^2}}{3 e^4}-\frac{b n \left(d+e x^2\right)^{3/2}}{9 e^4}",1,"(-48*a*d^3 + 20*b*d^3*n - 72*a*d^2*e*x^2 + 42*b*d^2*e*n*x^2 - 18*a*d*e^2*x^4 + 21*b*d*e^2*n*x^4 + 3*a*e^3*x^6 - b*e^3*n*x^6 + 48*b*d^(3/2)*n*(d + e*x^2)^(3/2)*Log[x] - 3*b*(16*d^3 + 24*d^2*e*x^2 + 6*d*e^2*x^4 - e^3*x^6)*Log[c*x^n] - 48*b*d^(5/2)*n*Sqrt[d + e*x^2]*Log[d + Sqrt[d]*Sqrt[d + e*x^2]] - 48*b*d^(3/2)*e*n*x^2*Sqrt[d + e*x^2]*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/(9*e^4*(d + e*x^2)^(3/2))","A",1
298,1,205,155,0.2189451,"\int \frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Integrate[(x^5*(a + b*Log[c*x^n]))/(d + e*x^2)^(5/2),x]","\sqrt{d+e x^2} \left(-\frac{d^2 \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)}{3 e^3 \left(d+e x^2\right)^2}+\frac{d \left(6 a+6 b \left(\log \left(c x^n\right)-n \log (x)\right)+b n\right)}{3 e^3 \left(d+e x^2\right)}+\frac{a+b \left(\log \left(c x^n\right)-n \log (x)\right)-b n}{e^3}\right)+\frac{b n \log (x) \left(8 d^2+12 d e x^2+3 e^2 x^4\right)}{3 e^3 \left(d+e x^2\right)^{3/2}}+\frac{8 b \sqrt{d} n \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)}{3 e^3}-\frac{8 b \sqrt{d} n \log (x)}{3 e^3}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{3 e^3 \left(d+e x^2\right)^{3/2}}+\frac{2 d \left(a+b \log \left(c x^n\right)\right)}{e^3 \sqrt{d+e x^2}}+\frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{e^3}+\frac{b d n}{3 e^3 \sqrt{d+e x^2}}-\frac{b n \sqrt{d+e x^2}}{e^3}+\frac{8 b \sqrt{d} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{3 e^3}",1,"(-8*b*Sqrt[d]*n*Log[x])/(3*e^3) + (b*n*(8*d^2 + 12*d*e*x^2 + 3*e^2*x^4)*Log[x])/(3*e^3*(d + e*x^2)^(3/2)) + Sqrt[d + e*x^2]*(-1/3*(d^2*(a + b*(-(n*Log[x]) + Log[c*x^n])))/(e^3*(d + e*x^2)^2) + (a - b*n + b*(-(n*Log[x]) + Log[c*x^n]))/e^3 + (d*(6*a + b*n + 6*b*(-(n*Log[x]) + Log[c*x^n])))/(3*e^3*(d + e*x^2))) + (8*b*Sqrt[d]*n*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/(3*e^3)","A",1
299,1,137,108,0.2805442,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/(d + e*x^2)^(5/2),x]","\frac{\frac{d \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-\left(d+e x^2\right) \left(3 a+3 b \log \left(c x^n\right)-3 b n \log (x)+b n\right)}{\left(d+e x^2\right)^{3/2}}-\frac{b n \log (x) \left(2 d+3 e x^2\right)}{\left(d+e x^2\right)^{3/2}}-\frac{2 b n \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)}{\sqrt{d}}+\frac{2 b n \log (x)}{\sqrt{d}}}{3 e^2}","-\frac{a+b \log \left(c x^n\right)}{e^2 \sqrt{d+e x^2}}+\frac{d \left(a+b \log \left(c x^n\right)\right)}{3 e^2 \left(d+e x^2\right)^{3/2}}-\frac{b n}{3 e^2 \sqrt{d+e x^2}}-\frac{2 b n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{3 \sqrt{d} e^2}",1,"((2*b*n*Log[x])/Sqrt[d] - (b*n*(2*d + 3*e*x^2)*Log[x])/(d + e*x^2)^(3/2) + (d*(a - b*n*Log[x] + b*Log[c*x^n]) - (d + e*x^2)*(3*a + b*n - 3*b*n*Log[x] + 3*b*Log[c*x^n]))/(d + e*x^2)^(3/2) - (2*b*n*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/Sqrt[d])/(3*e^2)","A",1
300,1,97,84,0.2407757,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/(d + e*x^2)^(5/2),x]","-\frac{\frac{a}{\left(d+e x^2\right)^{3/2}}+\frac{b \log \left(c x^n\right)}{\left(d+e x^2\right)^{3/2}}+\frac{b n \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)}{d^{3/2}}-\frac{b n \log (x)}{d^{3/2}}-\frac{b n}{d \sqrt{d+e x^2}}}{3 e}","-\frac{a+b \log \left(c x^n\right)}{3 e \left(d+e x^2\right)^{3/2}}-\frac{b n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{3 d^{3/2} e}+\frac{b n}{3 d e \sqrt{d+e x^2}}",1,"-1/3*(a/(d + e*x^2)^(3/2) - (b*n)/(d*Sqrt[d + e*x^2]) - (b*n*Log[x])/d^(3/2) + (b*Log[c*x^n])/(d + e*x^2)^(3/2) + (b*n*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/d^(3/2))/e","A",1
301,1,273,251,0.4465536,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^2\right)^{5/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x^2)^(5/2)),x]","\frac{b n \sqrt{\frac{d}{e x^2}+1} \left(-3 d^{5/2} \left(d+e x^2\right)^2 \, _3F_2\left(\frac{5}{2},\frac{5}{2},\frac{5}{2};\frac{7}{2},\frac{7}{2};-\frac{d}{e x^2}\right)-75 e^{5/2} x^5 \log (x) \left(d+e x^2\right)^2 \sinh ^{-1}\left(\frac{\sqrt{d}}{\sqrt{e} x}\right)+25 \sqrt{d} e^3 x^6 \log (x) \sqrt{\frac{d}{e x^2}+1} \left(4 d+3 e x^2\right)\right)}{75 d^{5/2} e^2 x^4 \left(d+e x^2\right)^{5/2}}-\frac{\log \left(\sqrt{d} \sqrt{d+e x^2}+d\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{d^{5/2}}+\frac{\log (x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{d^{5/2}}+\frac{\left(4 d+3 e x^2\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{3 d^2 \left(d+e x^2\right)^{3/2}}","\frac{1}{3} \left(-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{d^{5/2}}+\frac{3}{d^2 \sqrt{d+e x^2}}+\frac{1}{d \left(d+e x^2\right)^{3/2}}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^2+d}}\right)}{2 d^{5/2}}+\frac{b n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)^2}{2 d^{5/2}}+\frac{4 b n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{3 d^{5/2}}-\frac{b n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{d^{5/2}}-\frac{b n}{3 d^2 \sqrt{d+e x^2}}",1,"(b*n*Sqrt[1 + d/(e*x^2)]*(-3*d^(5/2)*(d + e*x^2)^2*HypergeometricPFQ[{5/2, 5/2, 5/2}, {7/2, 7/2}, -(d/(e*x^2))] + 25*Sqrt[d]*e^3*Sqrt[1 + d/(e*x^2)]*x^6*(4*d + 3*e*x^2)*Log[x] - 75*e^(5/2)*x^5*(d + e*x^2)^2*ArcSinh[Sqrt[d]/(Sqrt[e]*x)]*Log[x]))/(75*d^(5/2)*e^2*x^4*(d + e*x^2)^(5/2)) + ((4*d + 3*e*x^2)*(a - b*n*Log[x] + b*Log[c*x^n]))/(3*d^2*(d + e*x^2)^(3/2)) + (Log[x]*(a - b*n*Log[x] + b*Log[c*x^n]))/d^(5/2) - ((a - b*n*Log[x] + b*Log[c*x^n])*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/d^(5/2)","C",1
302,1,227,337,0.285328,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^2\right)^{5/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^3*(d + e*x^2)^(5/2)),x]","\frac{b n \sqrt{\frac{d}{e x^2}+1} \left(5 \, _3F_2\left(\frac{7}{2},\frac{7}{2},\frac{7}{2};\frac{9}{2},\frac{9}{2};-\frac{d}{e x^2}\right)-7 (2 \log (x)+1) \, _2F_1\left(\frac{5}{2},\frac{7}{2};\frac{9}{2};-\frac{d}{e x^2}\right)\right)}{98 e^2 x^6 \sqrt{d+e x^2}}-\frac{5 e \log (x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{2 d^{7/2}}+\frac{5 e \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{2 d^{7/2}}-\frac{\left(3 d^2+20 d e x^2+15 e^2 x^4\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{6 d^3 x^2 \left(d+e x^2\right)^{3/2}}","\frac{5 e \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 d^{7/2}}-\frac{5 e \left(a+b \log \left(c x^n\right)\right)}{2 d^3 \sqrt{d+e x^2}}-\frac{5 e \left(a+b \log \left(c x^n\right)\right)}{6 d^2 \left(d+e x^2\right)^{3/2}}-\frac{a+b \log \left(c x^n\right)}{2 d x^2 \left(d+e x^2\right)^{3/2}}+\frac{5 b e n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^2+d}}\right)}{4 d^{7/2}}-\frac{5 b e n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)^2}{4 d^{7/2}}-\frac{31 b e n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{12 d^{7/2}}+\frac{5 b e n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{2 d^{7/2}}-\frac{b n \sqrt{d+e x^2}}{4 d^3 x^2}+\frac{b e n}{3 d^3 \sqrt{d+e x^2}}",1,"(b*n*Sqrt[1 + d/(e*x^2)]*(5*HypergeometricPFQ[{7/2, 7/2, 7/2}, {9/2, 9/2}, -(d/(e*x^2))] - 7*Hypergeometric2F1[5/2, 7/2, 9/2, -(d/(e*x^2))]*(1 + 2*Log[x])))/(98*e^2*x^6*Sqrt[d + e*x^2]) - ((3*d^2 + 20*d*e*x^2 + 15*e^2*x^4)*(a - b*n*Log[x] + b*Log[c*x^n]))/(6*d^3*x^2*(d + e*x^2)^(3/2)) - (5*e*Log[x]*(a - b*n*Log[x] + b*Log[c*x^n]))/(2*d^(7/2)) + (5*e*(a - b*n*Log[x] + b*Log[c*x^n])*Log[d + Sqrt[d]*Sqrt[d + e*x^2]])/(2*d^(7/2))","C",0
303,1,199,443,0.2809855,"\int \frac{x^6 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Integrate[(x^6*(a + b*Log[c*x^n]))/(d + e*x^2)^(5/2),x]","\frac{b n x^7 \sqrt{\frac{e x^2}{d}+1} \left(5 \, _3F_2\left(\frac{7}{2},\frac{7}{2},\frac{7}{2};\frac{9}{2},\frac{9}{2};-\frac{e x^2}{d}\right)+7 (2 \log (x)-1) \, _2F_1\left(\frac{5}{2},\frac{7}{2};\frac{9}{2};-\frac{e x^2}{d}\right)\right)}{98 d^2 \sqrt{d+e x^2}}+\frac{x \left(15 d^2+20 d e x^2+3 e^2 x^4\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{6 e^3 \left(d+e x^2\right)^{3/2}}-\frac{5 d \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{2 e^{7/2}}","-\frac{5 d^{3/2} \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^{7/2} \sqrt{d+e x^2}}+\frac{5 x \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{2 e^3}-\frac{5 x^3 \left(a+b \log \left(c x^n\right)\right)}{3 e^2 \sqrt{d+e x^2}}-\frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{3 e \left(d+e x^2\right)^{3/2}}+\frac{5 b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \text{Li}_2\left(e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{4 e^{7/2} \sqrt{d+e x^2}}-\frac{5 b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{4 e^{7/2} \sqrt{d+e x^2}}-\frac{31 b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{12 e^{7/2} \sqrt{d+e x^2}}+\frac{5 b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 e^{7/2} \sqrt{d+e x^2}}-\frac{b n x \sqrt{d+e x^2}}{4 e^3}+\frac{b d n x}{3 e^3 \sqrt{d+e x^2}}",1,"(b*n*x^7*Sqrt[1 + (e*x^2)/d]*(5*HypergeometricPFQ[{7/2, 7/2, 7/2}, {9/2, 9/2}, -((e*x^2)/d)] + 7*Hypergeometric2F1[5/2, 7/2, 9/2, -((e*x^2)/d)]*(-1 + 2*Log[x])))/(98*d^2*Sqrt[d + e*x^2]) + (x*(15*d^2 + 20*d*e*x^2 + 3*e^2*x^4)*(a - b*n*Log[x] + b*Log[c*x^n]))/(6*e^3*(d + e*x^2)^(3/2)) - (5*d*(a - b*n*Log[x] + b*Log[c*x^n])*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(2*e^(7/2))","C",0
304,1,244,383,0.8667253,"\int \frac{x^4 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Integrate[(x^4*(a + b*Log[c*x^n]))/(d + e*x^2)^(5/2),x]","-\frac{b n \sqrt{\frac{e x^2}{d}+1} \left(3 e^{5/2} x^5 \left(d+e x^2\right)^2 \, _3F_2\left(\frac{5}{2},\frac{5}{2},\frac{5}{2};\frac{7}{2},\frac{7}{2};-\frac{e x^2}{d}\right)-75 d^{5/2} \log (x) \left(d+e x^2\right)^2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)+25 d^3 \sqrt{e} x \log (x) \left(3 d+4 e x^2\right) \sqrt{\frac{e x^2}{d}+1}\right)}{75 d^2 e^{5/2} \left(d+e x^2\right)^{5/2}}+\frac{\log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{e^{5/2}}-\frac{x \left(3 d+4 e x^2\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{3 e^2 \left(d+e x^2\right)^{3/2}}","\frac{\sqrt{d} \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{e^{5/2} \sqrt{d+e x^2}}-\frac{x \left(a+b \log \left(c x^n\right)\right)}{e^2 \sqrt{d+e x^2}}-\frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{3 e \left(d+e x^2\right)^{3/2}}-\frac{b \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \text{Li}_2\left(e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 e^{5/2} \sqrt{d+e x^2}}+\frac{b \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{2 e^{5/2} \sqrt{d+e x^2}}+\frac{4 b \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 e^{5/2} \sqrt{d+e x^2}}-\frac{b \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{e^{5/2} \sqrt{d+e x^2}}-\frac{b n x}{3 e^2 \sqrt{d+e x^2}}",1,"-1/75*(b*n*Sqrt[1 + (e*x^2)/d]*(3*e^(5/2)*x^5*(d + e*x^2)^2*HypergeometricPFQ[{5/2, 5/2, 5/2}, {7/2, 7/2}, -((e*x^2)/d)] + 25*d^3*Sqrt[e]*x*(3*d + 4*e*x^2)*Sqrt[1 + (e*x^2)/d]*Log[x] - 75*d^(5/2)*(d + e*x^2)^2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[x]))/(d^2*e^(5/2)*(d + e*x^2)^(5/2)) - (x*(3*d + 4*e*x^2)*(a - b*n*Log[x] + b*Log[c*x^n]))/(3*e^2*(d + e*x^2)^(3/2)) + ((a - b*n*Log[x] + b*Log[c*x^n])*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/e^(5/2)","C",1
305,1,101,89,0.1545328,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e*x^2)^(5/2),x]","\frac{\sqrt{e} x \left(a e x^2+b n \left(d+e x^2\right)\right)+b e^{3/2} x^3 \log \left(c x^n\right)-b n \left(d+e x^2\right)^{3/2} \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)}{3 d e^{3/2} \left(d+e x^2\right)^{3/2}}","\frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{3 d \left(d+e x^2\right)^{3/2}}-\frac{b n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{3 d e^{3/2}}+\frac{b n x}{3 d e \sqrt{d+e x^2}}",1,"(Sqrt[e]*x*(a*e*x^2 + b*n*(d + e*x^2)) + b*e^(3/2)*x^3*Log[c*x^n] - b*n*(d + e*x^2)^(3/2)*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(3*d*e^(3/2)*(d + e*x^2)^(3/2))","A",1
306,1,116,113,0.1390094,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*x^2)^(5/2),x]","\frac{\sqrt{e} x \left(a \left(3 d+2 e x^2\right)-b n \left(d+e x^2\right)\right)+b \sqrt{e} x \left(3 d+2 e x^2\right) \log \left(c x^n\right)-2 b n \left(d+e x^2\right)^{3/2} \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)}{3 d^2 \sqrt{e} \left(d+e x^2\right)^{3/2}}","\frac{2 x \left(a+b \log \left(c x^n\right)\right)}{3 d^2 \sqrt{d+e x^2}}+\frac{x \left(a+b \log \left(c x^n\right)\right)}{3 d \left(d+e x^2\right)^{3/2}}-\frac{b n x}{3 d^2 \sqrt{d+e x^2}}-\frac{2 b n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{3 d^2 \sqrt{e}}",1,"(Sqrt[e]*x*(-(b*n*(d + e*x^2)) + a*(3*d + 2*e*x^2)) + b*Sqrt[e]*x*(3*d + 2*e*x^2)*Log[c*x^n] - 2*b*n*(d + e*x^2)^(3/2)*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(3*d^2*Sqrt[e]*(d + e*x^2)^(3/2))","A",1
307,1,144,166,0.190568,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^2\right)^{5/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*(d + e*x^2)^(5/2)),x]","\frac{-3 a d^2-12 a d e x^2-8 a e^2 x^4-b \left(3 d^2+12 d e x^2+8 e^2 x^4\right) \log \left(c x^n\right)-3 b d^2 n-5 b d e n x^2+8 b \sqrt{e} n x \left(d+e x^2\right)^{3/2} \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)-2 b e^2 n x^4}{3 d^3 x \left(d+e x^2\right)^{3/2}}","-\frac{8 e x \left(a+b \log \left(c x^n\right)\right)}{3 d^3 \sqrt{d+e x^2}}-\frac{4 e x \left(a+b \log \left(c x^n\right)\right)}{3 d^2 \left(d+e x^2\right)^{3/2}}-\frac{a+b \log \left(c x^n\right)}{d x \left(d+e x^2\right)^{3/2}}-\frac{2 b e n x}{3 d^3 \sqrt{d+e x^2}}+\frac{8 b \sqrt{e} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{3 d^3}-\frac{b n}{d^2 x \sqrt{d+e x^2}}",1,"(-3*a*d^2 - 3*b*d^2*n - 12*a*d*e*x^2 - 5*b*d*e*n*x^2 - 8*a*e^2*x^4 - 2*b*e^2*n*x^4 - b*(3*d^2 + 12*d*e*x^2 + 8*e^2*x^4)*Log[c*x^n] + 8*b*Sqrt[e]*n*x*(d + e*x^2)^(3/2)*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(3*d^3*x*(d + e*x^2)^(3/2))","A",1
308,1,182,230,0.2260223,"\int \frac{a+b \log \left(c x^n\right)}{x^4 \left(d+e x^2\right)^{5/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^4*(d + e*x^2)^(5/2)),x]","\frac{-3 a d^3+18 a d^2 e x^2+72 a d e^2 x^4+48 a e^3 x^6+3 b \left(-d^3+6 d^2 e x^2+24 d e^2 x^4+16 e^3 x^6\right) \log \left(c x^n\right)-b d^3 n+21 b d^2 e n x^2-48 b e^{3/2} n x^3 \left(d+e x^2\right)^{3/2} \log \left(\sqrt{e} \sqrt{d+e x^2}+e x\right)+42 b d e^2 n x^4+20 b e^3 n x^6}{9 d^4 x^3 \left(d+e x^2\right)^{3/2}}","\frac{16 e^2 x \left(a+b \log \left(c x^n\right)\right)}{3 d^4 \sqrt{d+e x^2}}+\frac{8 e^2 x \left(a+b \log \left(c x^n\right)\right)}{3 d^3 \left(d+e x^2\right)^{3/2}}+\frac{2 e \left(a+b \log \left(c x^n\right)\right)}{d^2 x \left(d+e x^2\right)^{3/2}}-\frac{a+b \log \left(c x^n\right)}{3 d x^3 \left(d+e x^2\right)^{3/2}}-\frac{16 b e^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{3 d^4}-\frac{b e^2 n x}{3 d^4 \sqrt{d+e x^2}}+\frac{23 b e n \sqrt{d+e x^2}}{9 d^4 x}-\frac{b n \sqrt{d+e x^2}}{9 d^3 x^3}",1,"(-3*a*d^3 - b*d^3*n + 18*a*d^2*e*x^2 + 21*b*d^2*e*n*x^2 + 72*a*d*e^2*x^4 + 42*b*d*e^2*n*x^4 + 48*a*e^3*x^6 + 20*b*e^3*n*x^6 + 3*b*(-d^3 + 6*d^2*e*x^2 + 24*d*e^2*x^4 + 16*e^3*x^6)*Log[c*x^n] - 48*b*e^(3/2)*n*x^3*(d + e*x^2)^(3/2)*Log[e*x + Sqrt[e]*Sqrt[d + e*x^2]])/(9*d^4*x^3*(d + e*x^2)^(3/2))","A",1
309,1,163,251,0.403782,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d-e x} \sqrt{d+e x}} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/(Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{\sqrt{d-e x} \sqrt{d+e x} \left(d^2 \left(6 a+6 b \log \left(c x^n\right)-6 b n \log (x)-5 b n\right)+e^2 x^2 \left(3 a+3 b \log \left(c x^n\right)-3 b n \log (x)-b n\right)\right)+6 b d^3 n \log \left(\sqrt{d-e x} \sqrt{d+e x}+d\right)-6 b d^3 n \log (x)+3 b n \log (x) \sqrt{d-e x} \sqrt{d+e x} \left(2 d^2+e^2 x^2\right)}{9 e^4}","-\frac{d^2 \left(d^2-e^2 x^2\right) \left(a+b \log \left(c x^n\right)\right)}{e^4 \sqrt{d-e x} \sqrt{d+e x}}+\frac{\left(d^2-e^2 x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)}{3 e^4 \sqrt{d-e x} \sqrt{d+e x}}+\frac{2 b d^2 n \left(d^2-e^2 x^2\right)}{3 e^4 \sqrt{d-e x} \sqrt{d+e x}}-\frac{b n \left(d^2-e^2 x^2\right)^2}{9 e^4 \sqrt{d-e x} \sqrt{d+e x}}-\frac{2 b d^4 n \sqrt{1-\frac{e^2 x^2}{d^2}} \tanh ^{-1}\left(\sqrt{1-\frac{e^2 x^2}{d^2}}\right)}{3 e^4 \sqrt{d-e x} \sqrt{d+e x}}",1,"-1/9*(-6*b*d^3*n*Log[x] + 3*b*n*Sqrt[d - e*x]*Sqrt[d + e*x]*(2*d^2 + e^2*x^2)*Log[x] + Sqrt[d - e*x]*Sqrt[d + e*x]*(e^2*x^2*(3*a - b*n - 3*b*n*Log[x] + 3*b*Log[c*x^n]) + d^2*(6*a - 5*b*n - 6*b*n*Log[x] + 6*b*Log[c*x^n])) + 6*b*d^3*n*Log[d + Sqrt[d - e*x]*Sqrt[d + e*x]])/e^4","A",1
310,1,113,148,0.1841196,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d-e x} \sqrt{d+e x}} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/(Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{\sqrt{d-e x} \sqrt{d+e x} \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)-b n\right)}{e^2}+\frac{b d n \log (x)}{e^2}-\frac{b n \log (x) \sqrt{d-e x} \sqrt{d+e x}}{e^2}-\frac{b d n \log \left(\sqrt{d-e x} \sqrt{d+e x}+d\right)}{e^2}","-\frac{\left(d^2-e^2 x^2\right) \left(a+b \log \left(c x^n\right)\right)}{e^2 \sqrt{d-e x} \sqrt{d+e x}}+\frac{b n \left(d^2-e^2 x^2\right)}{e^2 \sqrt{d-e x} \sqrt{d+e x}}-\frac{b d^2 n \sqrt{1-\frac{e^2 x^2}{d^2}} \tanh ^{-1}\left(\sqrt{1-\frac{e^2 x^2}{d^2}}\right)}{e^2 \sqrt{d-e x} \sqrt{d+e x}}",1,"(b*d*n*Log[x])/e^2 - (b*n*Sqrt[d - e*x]*Sqrt[d + e*x]*Log[x])/e^2 - (Sqrt[d - e*x]*Sqrt[d + e*x]*(a - b*n + b*(-(n*Log[x]) + Log[c*x^n])))/e^2 - (b*d*n*Log[d + Sqrt[d - e*x]*Sqrt[d + e*x]])/e^2","A",1
311,1,310,301,1.8264428,"\int \frac{a+b \log \left(c x^n\right)}{x \sqrt{d-e x} \sqrt{d+e x}} \, dx","Integrate[(a + b*Log[c*x^n])/(x*Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{\log \left(\sqrt{d-e x} \sqrt{d+e x}+d\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{d}+\frac{\log (x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{d}+\frac{b n \sqrt{e^2 x^2-d^2} \left(\frac{\sqrt{1-\frac{e^2 x^2}{d^2}} \left(-4 \text{Li}_2\left(\frac{1}{2}-\frac{1}{2} \sqrt{1-\frac{e^2 x^2}{d^2}}\right)+\log ^2\left(\frac{e^2 x^2}{d^2}\right)+2 \log ^2\left(\frac{1}{2} \left(\sqrt{1-\frac{e^2 x^2}{d^2}}+1\right)\right)-4 \log \left(\frac{1}{2} \left(\sqrt{1-\frac{e^2 x^2}{d^2}}+1\right)\right) \log \left(\frac{e^2 x^2}{d^2}\right)\right)}{\sqrt{e^2 x^2-d^2}}-\frac{4 \left(2 \log (x)-\log \left(\frac{e^2 x^2}{d^2}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{e^2 x^2-d^2}}{\sqrt{-d^2}}\right)}{\sqrt{-d^2}}\right)}{8 \sqrt{d-e x} \sqrt{d+e x}}","-\frac{\sqrt{1-\frac{e^2 x^2}{d^2}} \tanh ^{-1}\left(\sqrt{1-\frac{e^2 x^2}{d^2}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d-e x} \sqrt{d+e x}}-\frac{b n \sqrt{1-\frac{e^2 x^2}{d^2}} \text{Li}_2\left(-\frac{\sqrt{1-\frac{e^2 x^2}{d^2}}+1}{1-\sqrt{1-\frac{e^2 x^2}{d^2}}}\right)}{2 \sqrt{d-e x} \sqrt{d+e x}}+\frac{b n \sqrt{1-\frac{e^2 x^2}{d^2}} \tanh ^{-1}\left(\sqrt{1-\frac{e^2 x^2}{d^2}}\right)^2}{2 \sqrt{d-e x} \sqrt{d+e x}}-\frac{b n \sqrt{1-\frac{e^2 x^2}{d^2}} \log \left(\frac{2}{1-\sqrt{1-\frac{e^2 x^2}{d^2}}}\right) \tanh ^{-1}\left(\sqrt{1-\frac{e^2 x^2}{d^2}}\right)}{\sqrt{d-e x} \sqrt{d+e x}}",1,"(Log[x]*(a - b*n*Log[x] + b*Log[c*x^n]))/d - ((a - b*n*Log[x] + b*Log[c*x^n])*Log[d + Sqrt[d - e*x]*Sqrt[d + e*x]])/d + (b*n*Sqrt[-d^2 + e^2*x^2]*((-4*ArcTanh[Sqrt[-d^2 + e^2*x^2]/Sqrt[-d^2]]*(2*Log[x] - Log[(e^2*x^2)/d^2]))/Sqrt[-d^2] + (Sqrt[1 - (e^2*x^2)/d^2]*(Log[(e^2*x^2)/d^2]^2 - 4*Log[(e^2*x^2)/d^2]*Log[(1 + Sqrt[1 - (e^2*x^2)/d^2])/2] + 2*Log[(1 + Sqrt[1 - (e^2*x^2)/d^2])/2]^2 - 4*PolyLog[2, 1/2 - Sqrt[1 - (e^2*x^2)/d^2]/2]))/Sqrt[-d^2 + e^2*x^2]))/(8*Sqrt[d - e*x]*Sqrt[d + e*x])","A",1
312,1,255,489,0.8841714,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \sqrt{d-e x} \sqrt{d+e x}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^3*Sqrt[d - e*x]*Sqrt[d + e*x]),x]","\frac{\frac{b n \left(e^2 x^2-d^2\right) \left(2 d^3 \, _3F_2\left(\frac{3}{2},\frac{3}{2},\frac{3}{2};\frac{5}{2},\frac{5}{2};\frac{d^2}{e^2 x^2}\right)+9 e^2 x^2 (2 \log (x)+1) \left(d \sqrt{1-\frac{d^2}{e^2 x^2}}-e x \sin ^{-1}\left(\frac{d}{e x}\right)\right)\right)}{e^2 x^4 \sqrt{1-\frac{d^2}{e^2 x^2}} \sqrt{d-e x} \sqrt{d+e x}}-18 e^2 \log \left(\sqrt{d-e x} \sqrt{d+e x}+d\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-\frac{18 d \sqrt{d-e x} \sqrt{d+e x} \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{x^2}+18 e^2 \log (x) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{36 d^3}","-\frac{\left(d^2-e^2 x^2\right) \left(a+b \log \left(c x^n\right)\right)}{2 d^2 x^2 \sqrt{d-e x} \sqrt{d+e x}}-\frac{e^2 \sqrt{1-\frac{e^2 x^2}{d^2}} \tanh ^{-1}\left(\sqrt{1-\frac{e^2 x^2}{d^2}}\right) \left(a+b \log \left(c x^n\right)\right)}{2 d^2 \sqrt{d-e x} \sqrt{d+e x}}-\frac{b e^2 n \sqrt{1-\frac{e^2 x^2}{d^2}} \text{Li}_2\left(-\frac{\sqrt{1-\frac{e^2 x^2}{d^2}}+1}{1-\sqrt{1-\frac{e^2 x^2}{d^2}}}\right)}{4 d^2 \sqrt{d-e x} \sqrt{d+e x}}-\frac{b n \left(d^2-e^2 x^2\right)}{4 d^2 x^2 \sqrt{d-e x} \sqrt{d+e x}}+\frac{b e^2 n \sqrt{1-\frac{e^2 x^2}{d^2}} \tanh ^{-1}\left(\sqrt{1-\frac{e^2 x^2}{d^2}}\right)^2}{4 d^2 \sqrt{d-e x} \sqrt{d+e x}}+\frac{b e^2 n \sqrt{1-\frac{e^2 x^2}{d^2}} \tanh ^{-1}\left(\sqrt{1-\frac{e^2 x^2}{d^2}}\right)}{4 d^2 \sqrt{d-e x} \sqrt{d+e x}}-\frac{b e^2 n \sqrt{1-\frac{e^2 x^2}{d^2}} \log \left(\frac{2}{1-\sqrt{1-\frac{e^2 x^2}{d^2}}}\right) \tanh ^{-1}\left(\sqrt{1-\frac{e^2 x^2}{d^2}}\right)}{2 d^2 \sqrt{d-e x} \sqrt{d+e x}}",1,"((b*n*(-d^2 + e^2*x^2)*(2*d^3*HypergeometricPFQ[{3/2, 3/2, 3/2}, {5/2, 5/2}, d^2/(e^2*x^2)] + 9*e^2*x^2*(d*Sqrt[1 - d^2/(e^2*x^2)] - e*x*ArcSin[d/(e*x)])*(1 + 2*Log[x])))/(e^2*Sqrt[1 - d^2/(e^2*x^2)]*x^4*Sqrt[d - e*x]*Sqrt[d + e*x]) - (18*d*Sqrt[d - e*x]*Sqrt[d + e*x]*(a - b*n*Log[x] + b*Log[c*x^n]))/x^2 + 18*e^2*Log[x]*(a - b*n*Log[x] + b*Log[c*x^n]) - 18*e^2*(a - b*n*Log[x] + b*Log[c*x^n])*Log[d + Sqrt[d - e*x]*Sqrt[d + e*x]])/(36*d^3)","C",1
313,1,316,406,2.7912857,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d-e x} \sqrt{d+e x}} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/(Sqrt[d - e*x]*Sqrt[d + e*x]),x]","\frac{2 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d-e x} \sqrt{d+e x}}\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-2 e x \sqrt{d-e x} \sqrt{d+e x} \left(a+b \log \left(c x^n\right)-b n \log (x)\right)+\frac{b n \left(e x (2 \log (x)-1) \left(e^2 x^2-d^2\right)+\frac{e^3 \sqrt{1-\frac{e^2 x^2}{d^2}} \left(-\text{Li}_2\left(e^{-2 \sinh ^{-1}\left(\sqrt{-\frac{e^2}{d^2}} x\right)}\right)-2 \log (x) \log \left(\sqrt{1-\frac{e^2 x^2}{d^2}}+x \sqrt{-\frac{e^2}{d^2}}\right)+\sinh ^{-1}\left(x \sqrt{-\frac{e^2}{d^2}}\right)^2+2 \sinh ^{-1}\left(x \sqrt{-\frac{e^2}{d^2}}\right) \log \left(1-e^{-2 \sinh ^{-1}\left(x \sqrt{-\frac{e^2}{d^2}}\right)}\right)\right)}{\left(-\frac{e^2}{d^2}\right)^{3/2}}+d^3 \sqrt{1-\frac{e^2 x^2}{d^2}} \sin ^{-1}\left(\frac{e x}{d}\right)\right)}{\sqrt{d-e x} \sqrt{d+e x}}}{4 e^3}","-\frac{x \left(d^2-e^2 x^2\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^2 \sqrt{d-e x} \sqrt{d+e x}}+\frac{d^3 \sqrt{1-\frac{e^2 x^2}{d^2}} \sin ^{-1}\left(\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^3 \sqrt{d-e x} \sqrt{d+e x}}+\frac{b n x \left(d^2-e^2 x^2\right)}{4 e^2 \sqrt{d-e x} \sqrt{d+e x}}+\frac{i b d^3 n \sqrt{1-\frac{e^2 x^2}{d^2}} \text{Li}_2\left(e^{2 i \sin ^{-1}\left(\frac{e x}{d}\right)}\right)}{4 e^3 \sqrt{d-e x} \sqrt{d+e x}}+\frac{i b d^3 n \sqrt{1-\frac{e^2 x^2}{d^2}} \sin ^{-1}\left(\frac{e x}{d}\right)^2}{4 e^3 \sqrt{d-e x} \sqrt{d+e x}}+\frac{b d^3 n \sqrt{1-\frac{e^2 x^2}{d^2}} \sin ^{-1}\left(\frac{e x}{d}\right)}{4 e^3 \sqrt{d-e x} \sqrt{d+e x}}-\frac{b d^3 n \sqrt{1-\frac{e^2 x^2}{d^2}} \sin ^{-1}\left(\frac{e x}{d}\right) \log \left(1-e^{2 i \sin ^{-1}\left(\frac{e x}{d}\right)}\right)}{2 e^3 \sqrt{d-e x} \sqrt{d+e x}}",1,"(-2*e*x*Sqrt[d - e*x]*Sqrt[d + e*x]*(a - b*n*Log[x] + b*Log[c*x^n]) + 2*d^2*ArcTan[(e*x)/(Sqrt[d - e*x]*Sqrt[d + e*x])]*(a - b*n*Log[x] + b*Log[c*x^n]) + (b*n*(d^3*Sqrt[1 - (e^2*x^2)/d^2]*ArcSin[(e*x)/d] + e*x*(-d^2 + e^2*x^2)*(-1 + 2*Log[x]) + (e^3*Sqrt[1 - (e^2*x^2)/d^2]*(ArcSinh[Sqrt[-(e^2/d^2)]*x]^2 + 2*ArcSinh[Sqrt[-(e^2/d^2)]*x]*Log[1 - E^(-2*ArcSinh[Sqrt[-(e^2/d^2)]*x])] - 2*Log[x]*Log[Sqrt[-(e^2/d^2)]*x + Sqrt[1 - (e^2*x^2)/d^2]] - PolyLog[2, E^(-2*ArcSinh[Sqrt[-(e^2/d^2)]*x])]))/(-(e^2/d^2))^(3/2)))/(Sqrt[d - e*x]*Sqrt[d + e*x]))/(4*e^3)","A",0
314,1,217,248,0.5491386,"\int \frac{a+b \log \left(c x^n\right)}{\sqrt{d-e x} \sqrt{d+e x}} \, dx","Integrate[(a + b*Log[c*x^n])/(Sqrt[d - e*x]*Sqrt[d + e*x]),x]","\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d-e x} \sqrt{d+e x}}\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{e}-\frac{b n \sqrt{1-\frac{e^2 x^2}{d^2}} \left(-\text{Li}_2\left(e^{-2 \sinh ^{-1}\left(\sqrt{-\frac{e^2}{d^2}} x\right)}\right)-2 \log (x) \log \left(\sqrt{1-\frac{e^2 x^2}{d^2}}+x \sqrt{-\frac{e^2}{d^2}}\right)+\sinh ^{-1}\left(x \sqrt{-\frac{e^2}{d^2}}\right)^2+2 \sinh ^{-1}\left(x \sqrt{-\frac{e^2}{d^2}}\right) \log \left(1-e^{-2 \sinh ^{-1}\left(x \sqrt{-\frac{e^2}{d^2}}\right)}\right)\right)}{2 \sqrt{-\frac{e^2}{d^2}} \sqrt{d-e x} \sqrt{d+e x}}","\frac{d \sqrt{1-\frac{e^2 x^2}{d^2}} \sin ^{-1}\left(\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e \sqrt{d-e x} \sqrt{d+e x}}+\frac{i b d n \sqrt{1-\frac{e^2 x^2}{d^2}} \text{Li}_2\left(e^{2 i \sin ^{-1}\left(\frac{e x}{d}\right)}\right)}{2 e \sqrt{d-e x} \sqrt{d+e x}}+\frac{i b d n \sqrt{1-\frac{e^2 x^2}{d^2}} \sin ^{-1}\left(\frac{e x}{d}\right)^2}{2 e \sqrt{d-e x} \sqrt{d+e x}}-\frac{b d n \sqrt{1-\frac{e^2 x^2}{d^2}} \sin ^{-1}\left(\frac{e x}{d}\right) \log \left(1-e^{2 i \sin ^{-1}\left(\frac{e x}{d}\right)}\right)}{e \sqrt{d-e x} \sqrt{d+e x}}",1,"(ArcTan[(e*x)/(Sqrt[d - e*x]*Sqrt[d + e*x])]*(a - b*n*Log[x] + b*Log[c*x^n]))/e - (b*n*Sqrt[1 - (e^2*x^2)/d^2]*(ArcSinh[Sqrt[-(e^2/d^2)]*x]^2 + 2*ArcSinh[Sqrt[-(e^2/d^2)]*x]*Log[1 - E^(-2*ArcSinh[Sqrt[-(e^2/d^2)]*x])] - 2*Log[x]*Log[Sqrt[-(e^2/d^2)]*x + Sqrt[1 - (e^2*x^2)/d^2]] - PolyLog[2, E^(-2*ArcSinh[Sqrt[-(e^2/d^2)]*x])]))/(2*Sqrt[-(e^2/d^2)]*Sqrt[d - e*x]*Sqrt[d + e*x])","A",0
315,1,70,142,0.2279959,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \sqrt{d-e x} \sqrt{d+e x}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{\sqrt{d-e x} \sqrt{d+e x} \left(a+b \log \left(c x^n\right)+b n\right)+b e n x \tan ^{-1}\left(\frac{e x}{\sqrt{d-e x} \sqrt{d+e x}}\right)}{d^2 x}","-\frac{\left(d^2-e^2 x^2\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 x \sqrt{d-e x} \sqrt{d+e x}}-\frac{b n \left(d^2-e^2 x^2\right)}{d^2 x \sqrt{d-e x} \sqrt{d+e x}}-\frac{b e n \sqrt{1-\frac{e^2 x^2}{d^2}} \sin ^{-1}\left(\frac{e x}{d}\right)}{d \sqrt{d-e x} \sqrt{d+e x}}",1,"-((b*e*n*x*ArcTan[(e*x)/(Sqrt[d - e*x]*Sqrt[d + e*x])] + Sqrt[d - e*x]*Sqrt[d + e*x]*(a + b*n + b*Log[c*x^n]))/(d^2*x))","A",1
316,1,116,252,0.3083146,"\int \frac{a+b \log \left(c x^n\right)}{x^4 \sqrt{d-e x} \sqrt{d+e x}} \, dx","Integrate[(a + b*Log[c*x^n])/(x^4*Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{\sqrt{d-e x} \sqrt{d+e x} \left(3 a \left(d^2+2 e^2 x^2\right)+3 b \left(d^2+2 e^2 x^2\right) \log \left(c x^n\right)+b n \left(d^2+5 e^2 x^2\right)\right)+6 b e^3 n x^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d-e x} \sqrt{d+e x}}\right)}{9 d^4 x^3}","-\frac{\left(d^2-e^2 x^2\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^2 x^3 \sqrt{d-e x} \sqrt{d+e x}}-\frac{2 e^2 \left(d^2-e^2 x^2\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^4 x \sqrt{d-e x} \sqrt{d+e x}}-\frac{2 b e^2 n \left(d^2-e^2 x^2\right)}{3 d^4 x \sqrt{d-e x} \sqrt{d+e x}}-\frac{b n \left(d^2-e^2 x^2\right)^2}{9 d^4 x^3 \sqrt{d-e x} \sqrt{d+e x}}-\frac{2 b e^3 n \sqrt{1-\frac{e^2 x^2}{d^2}} \sin ^{-1}\left(\frac{e x}{d}\right)}{3 d^3 \sqrt{d-e x} \sqrt{d+e x}}",1,"-1/9*(6*b*e^3*n*x^3*ArcTan[(e*x)/(Sqrt[d - e*x]*Sqrt[d + e*x])] + Sqrt[d - e*x]*Sqrt[d + e*x]*(3*a*(d^2 + 2*e^2*x^2) + b*n*(d^2 + 5*e^2*x^2) + 3*b*(d^2 + 2*e^2*x^2)*Log[c*x^n]))/(d^4*x^3)","A",1
317,1,27,34,0.0269003,"\int \frac{x \log (x)}{\sqrt{-1+x^2}} \, dx","Integrate[(x*Log[x])/Sqrt[-1 + x^2],x]","\sqrt{x^2-1} (\log (x)-1)-\tan ^{-1}\left(\frac{1}{\sqrt{x^2-1}}\right)","-\sqrt{x^2-1}+\sqrt{x^2-1} \log (x)+\tan ^{-1}\left(\sqrt{x^2-1}\right)",1,"-ArcTan[1/Sqrt[-1 + x^2]] + Sqrt[-1 + x^2]*(-1 + Log[x])","A",1
318,1,156,211,0.2688798,"\int (f x)^m \left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^m*(d + e*x^2)^3*(a + b*Log[c*x^n]),x]","x (f x)^m \left(\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{m+1}+\frac{3 d^2 e x^2 \left(a+b \log \left(c x^n\right)\right)}{m+3}+\frac{3 d e^2 x^4 \left(a+b \log \left(c x^n\right)\right)}{m+5}+\frac{e^3 x^6 \left(a+b \log \left(c x^n\right)\right)}{m+7}-\frac{b d^3 n}{(m+1)^2}-\frac{3 b d^2 e n x^2}{(m+3)^2}-\frac{3 b d e^2 n x^4}{(m+5)^2}-\frac{b e^3 n x^6}{(m+7)^2}\right)","\frac{d^3 (f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+1)}+\frac{3 d^2 e (f x)^{m+3} \left(a+b \log \left(c x^n\right)\right)}{f^3 (m+3)}+\frac{3 d e^2 (f x)^{m+5} \left(a+b \log \left(c x^n\right)\right)}{f^5 (m+5)}+\frac{e^3 (f x)^{m+7} \left(a+b \log \left(c x^n\right)\right)}{f^7 (m+7)}-\frac{b d^3 n (f x)^{m+1}}{f (m+1)^2}-\frac{3 b d^2 e n (f x)^{m+3}}{f^3 (m+3)^2}-\frac{3 b d e^2 n (f x)^{m+5}}{f^5 (m+5)^2}-\frac{b e^3 n (f x)^{m+7}}{f^7 (m+7)^2}",1,"x*(f*x)^m*(-((b*d^3*n)/(1 + m)^2) - (3*b*d^2*e*n*x^2)/(3 + m)^2 - (3*b*d*e^2*n*x^4)/(5 + m)^2 - (b*e^3*n*x^6)/(7 + m)^2 + (d^3*(a + b*Log[c*x^n]))/(1 + m) + (3*d^2*e*x^2*(a + b*Log[c*x^n]))/(3 + m) + (3*d*e^2*x^4*(a + b*Log[c*x^n]))/(5 + m) + (e^3*x^6*(a + b*Log[c*x^n]))/(7 + m))","A",1
319,1,112,153,0.1983278,"\int (f x)^m \left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^m*(d + e*x^2)^2*(a + b*Log[c*x^n]),x]","x (f x)^m \left(\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{m+1}+\frac{2 d e x^2 \left(a+b \log \left(c x^n\right)\right)}{m+3}+\frac{e^2 x^4 \left(a+b \log \left(c x^n\right)\right)}{m+5}-\frac{b d^2 n}{(m+1)^2}-\frac{2 b d e n x^2}{(m+3)^2}-\frac{b e^2 n x^4}{(m+5)^2}\right)","\frac{d^2 (f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+1)}+\frac{2 d e (f x)^{m+3} \left(a+b \log \left(c x^n\right)\right)}{f^3 (m+3)}+\frac{e^2 (f x)^{m+5} \left(a+b \log \left(c x^n\right)\right)}{f^5 (m+5)}-\frac{b d^2 n (f x)^{m+1}}{f (m+1)^2}-\frac{2 b d e n (f x)^{m+3}}{f^3 (m+3)^2}-\frac{b e^2 n (f x)^{m+5}}{f^5 (m+5)^2}",1,"x*(f*x)^m*(-((b*d^2*n)/(1 + m)^2) - (2*b*d*e*n*x^2)/(3 + m)^2 - (b*e^2*n*x^4)/(5 + m)^2 + (d^2*(a + b*Log[c*x^n]))/(1 + m) + (2*d*e*x^2*(a + b*Log[c*x^n]))/(3 + m) + (e^2*x^4*(a + b*Log[c*x^n]))/(5 + m))","A",1
320,1,68,95,0.0803044,"\int (f x)^m \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^m*(d + e*x^2)*(a + b*Log[c*x^n]),x]","x (f x)^m \left(\frac{d \left(a+b \log \left(c x^n\right)\right)}{m+1}+\frac{e x^2 \left(a+b \log \left(c x^n\right)\right)}{m+3}-\frac{b d n}{(m+1)^2}-\frac{b e n x^2}{(m+3)^2}\right)","\frac{d (f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+1)}+\frac{e (f x)^{m+3} \left(a+b \log \left(c x^n\right)\right)}{f^3 (m+3)}-\frac{b d n (f x)^{m+1}}{f (m+1)^2}-\frac{b e n (f x)^{m+3}}{f^3 (m+3)^2}",1,"x*(f*x)^m*(-((b*d*n)/(1 + m)^2) - (b*e*n*x^2)/(3 + m)^2 + (d*(a + b*Log[c*x^n]))/(1 + m) + (e*x^2*(a + b*Log[c*x^n]))/(3 + m))","A",1
321,1,32,46,0.0132653,"\int (f x)^m \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^m*(a + b*Log[c*x^n]),x]","\frac{x (f x)^m \left(a m+a+b (m+1) \log \left(c x^n\right)-b n\right)}{(m+1)^2}","\frac{(f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+1)}-\frac{b n (f x)^{m+1}}{f (m+1)^2}",1,"(x*(f*x)^m*(a + a*m - b*n + b*(1 + m)*Log[c*x^n]))/(1 + m)^2","A",1
322,1,108,28,0.2081451,"\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{d+e x^2} \, dx","Integrate[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x^2),x]","\frac{x (f x)^m \left((m+1) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{e x^2}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \, _3F_2\left(1,\frac{m}{2}+\frac{1}{2},\frac{m}{2}+\frac{1}{2};\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};-\frac{e x^2}{d}\right)\right)}{d (m+1)^2}","\text{Int}\left(\frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{d+e x^2},x\right)",0,"(x*(f*x)^m*(-(b*n*HypergeometricPFQ[{1, 1/2 + m/2, 1/2 + m/2}, {3/2 + m/2, 3/2 + m/2}, -((e*x^2)/d)]) + (1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((e*x^2)/d)]*(a + b*Log[c*x^n])))/(d*(1 + m)^2)","B",0
323,1,108,28,0.1288381,"\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^2} \, dx","Integrate[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x^2)^2,x]","\frac{x (f x)^m \left((m+1) \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{e x^2}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \, _3F_2\left(2,\frac{m}{2}+\frac{1}{2},\frac{m}{2}+\frac{1}{2};\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};-\frac{e x^2}{d}\right)\right)}{d^2 (m+1)^2}","\text{Int}\left(\frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^2},x\right)",0,"(x*(f*x)^m*(-(b*n*HypergeometricPFQ[{2, 1/2 + m/2, 1/2 + m/2}, {3/2 + m/2, 3/2 + m/2}, -((e*x^2)/d)]) + (1 + m)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, -((e*x^2)/d)]*(a + b*Log[c*x^n])))/(d^2*(1 + m)^2)","B",0
324,1,2215,1198,7.8022841,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3}{\left(d+e x^3\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])^3/(d + e*x^3)^2,x]","\text{Result too large to show}","\frac{2 b^3 \text{Li}_3\left(-\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^3}{3 d^{5/3} \sqrt[3]{e}}-\frac{6 \sqrt[3]{-1} b^3 \text{Li}_3\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^3}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \sqrt[3]{e}}-\frac{2 \sqrt[3]{-1} b^3 \text{Li}_3\left(-\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^3}{3 d^{5/3} \sqrt[3]{e}}+\frac{4 b^3 \text{Li}_4\left(-\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^3}{3 d^{5/3} \sqrt[3]{e}}-\frac{12 i \sqrt{3} b^3 \text{Li}_4\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^3}{\left(1+\sqrt[3]{-1}\right)^5 d^{5/3} \sqrt[3]{e}}+\frac{12 b^3 \text{Li}_4\left(-\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^3}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \sqrt[3]{e}}-\frac{2 b^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^2}{3 d^{5/3} \sqrt[3]{e}}+\frac{6 \sqrt[3]{-1} b^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^2}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \sqrt[3]{e}}+\frac{2 \sqrt[3]{-1} b^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^2}{3 d^{5/3} \sqrt[3]{e}}-\frac{4 b^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(-\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^2}{3 d^{5/3} \sqrt[3]{e}}+\frac{12 i \sqrt{3} b^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^2}{\left(1+\sqrt[3]{-1}\right)^5 d^{5/3} \sqrt[3]{e}}-\frac{12 b^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(-\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^2}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \sqrt[3]{e}}-\frac{b \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}+1\right) n}{3 d^{5/3} \sqrt[3]{e}}+\frac{3 \sqrt[3]{-1} b \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \sqrt[3]{e}}+\frac{\sqrt[3]{-1} b \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}+1\right) n}{3 d^{5/3} \sqrt[3]{e}}+\frac{2 b \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(-\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}\right) n}{3 d^{5/3} \sqrt[3]{e}}-\frac{6 i \sqrt{3} b \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n}{\left(1+\sqrt[3]{-1}\right)^5 d^{5/3} \sqrt[3]{e}}+\frac{6 b \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(-\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \sqrt[3]{e}}+\frac{x \left(a+b \log \left(c x^n\right)\right)^3}{9 d^{5/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}-\frac{\sqrt[3]{-1} x \left(a+b \log \left(c x^n\right)\right)^3}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \left(\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}\right)}+\frac{x \left(a+b \log \left(c x^n\right)\right)^3}{9 d^{5/3} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}+\frac{2 \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}+1\right)}{9 d^{5/3} \sqrt[3]{e}}-\frac{2 i \sqrt{3} \left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right)}{\left(1+\sqrt[3]{-1}\right)^5 d^{5/3} \sqrt[3]{e}}+\frac{2 \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}+1\right)}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \sqrt[3]{e}}",1,"(x*(a + b*(-(n*Log[x]) + Log[c*x^n]))^3)/(3*d*(d + e*x^3)) + (2*ArcTan[(-d^(1/3) + 2*e^(1/3)*x)/(Sqrt[3]*d^(1/3))]*(a + b*(-(n*Log[x]) + Log[c*x^n]))^3)/(3*Sqrt[3]*d^(5/3)*e^(1/3)) + (2*(a + b*(-(n*Log[x]) + Log[c*x^n]))^3*Log[d^(1/3) + e^(1/3)*x])/(9*d^(5/3)*e^(1/3)) - ((a + b*(-(n*Log[x]) + Log[c*x^n]))^3*Log[d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2])/(9*d^(5/3)*e^(1/3)) + 3*b*n*(a + b*(-(n*Log[x]) + Log[c*x^n]))^2*(-1/3*((-1 + (-1)^(1/3))*((-((-1)^(1/3)/d^(1/3)) - ((-1)^(2/3)*d^(1/3) + e^(1/3)*x)^(-1))*Log[x] + ((-1)^(1/3)*Log[-((-1)^(2/3)*d^(1/3)) - e^(1/3)*x])/d^(1/3)))/((1 + (-1)^(1/3))^2*d^(4/3)*e^(1/3)) + ((-1)^(1/3)*((d^(-1/3) - (d^(1/3) + e^(1/3)*x)^(-1))*Log[x] - Log[d^(1/3) + e^(1/3)*x]/d^(1/3)))/(3*(1 + (-1)^(1/3))^2*d^(4/3)*e^(1/3)) - (Log[x]/(e^(1/3)*((-1)^(1/3)*d^(1/3) - e^(1/3)*x)) - (-(((-1)^(2/3)*Log[x])/d^(1/3)) + ((-1)^(2/3)*Log[d^(1/3) + (-1)^(2/3)*e^(1/3)*x])/d^(1/3))/e^(1/3))/(3*(1 + (-1)^(1/3))^2*d^(4/3)) + (2*(-1)^(1/3)*(Log[x]*Log[1 + (e^(1/3)*x)/d^(1/3)] + PolyLog[2, -((e^(1/3)*x)/d^(1/3))]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3)) - (2*(Log[x]*Log[1 - ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)] + PolyLog[2, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3)) - (2*(-1 + (-1)^(1/3))*(Log[x]*Log[1 + ((-1)^(2/3)*e^(1/3)*x)/d^(1/3)] + PolyLog[2, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3))) + 3*b^2*n^2*(a + b*(-(n*Log[x]) + Log[c*x^n]))*(((-1)^(1/3)*(Log[x]*((e^(1/3)*x*Log[x])/(d^(1/3) + e^(1/3)*x) - 2*Log[1 + (e^(1/3)*x)/d^(1/3)]) - 2*PolyLog[2, -((e^(1/3)*x)/d^(1/3))]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3)) - ((-1 + (-1)^(1/3))*(Log[x]*((-((-1)^(1/3)/d^(1/3)) - ((-1)^(2/3)*d^(1/3) + e^(1/3)*x)^(-1))*Log[x] + (2*(-1)^(1/3)*Log[1 - ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/d^(1/3)) + (2*(-1)^(1/3)*PolyLog[2, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/d^(1/3)))/(3*(1 + (-1)^(1/3))^2*d^(4/3)*e^(1/3)) - (Log[x]*((-1)^(2/3)*e^(1/3)*x*Log[x] - 2*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)*Log[1 + ((-1)^(2/3)*e^(1/3)*x)/d^(1/3)]) - 2*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)*PolyLog[2, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))])/(3*(1 + (-1)^(1/3))^2*d^(4/3)*(-((-1)^(1/3)*d^(2/3)*e^(1/3)) + d^(1/3)*e^(2/3)*x)) + (2*(-1)^(1/3)*(Log[x]^2*Log[1 + (e^(1/3)*x)/d^(1/3)] + 2*Log[x]*PolyLog[2, -((e^(1/3)*x)/d^(1/3))] - 2*PolyLog[3, -((e^(1/3)*x)/d^(1/3))]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3)) - (2*(Log[x]^2*Log[1 - ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)] + 2*Log[x]*PolyLog[2, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)] - 2*PolyLog[3, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3)) - (2*(-1 + (-1)^(1/3))*(Log[x]^2*Log[1 + ((-1)^(2/3)*e^(1/3)*x)/d^(1/3)] + 2*Log[x]*PolyLog[2, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))] - 2*PolyLog[3, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3))) + b^3*n^3*(((-1)^(1/3)*(Log[x]^2*((d^(-1/3) - (d^(1/3) + e^(1/3)*x)^(-1))*Log[x] - (3*Log[1 + (e^(1/3)*x)/d^(1/3)])/d^(1/3)) - (6*Log[x]*PolyLog[2, -((e^(1/3)*x)/d^(1/3))])/d^(1/3) + (6*PolyLog[3, -((e^(1/3)*x)/d^(1/3))])/d^(1/3)))/(3*(1 + (-1)^(1/3))^2*d^(4/3)*e^(1/3)) - ((-1 + (-1)^(1/3))*(-(((-1)^(1/3)*Log[x]^3)/d^(1/3)) - Log[x]^3/((-1)^(2/3)*d^(1/3) + e^(1/3)*x) + (3*(-1)^(1/3)*Log[x]^2*Log[1 - ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/d^(1/3) + (6*(-1)^(1/3)*(Log[x]*PolyLog[2, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)] - PolyLog[3, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)]))/d^(1/3)))/(3*(1 + (-1)^(1/3))^2*d^(4/3)*e^(1/3)) - (((-1)^(2/3)*Log[x]^3)/d^(1/3) + Log[x]^3/((-1)^(1/3)*d^(1/3) - e^(1/3)*x) - (3*(-1)^(2/3)*Log[x]^2*Log[1 + ((-1)^(2/3)*e^(1/3)*x)/d^(1/3)])/d^(1/3) - (6*(-1)^(2/3)*(Log[x]*PolyLog[2, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))] - PolyLog[3, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))]))/d^(1/3))/(3*(1 + (-1)^(1/3))^2*d^(4/3)*e^(1/3)) + (2*(-1)^(1/3)*(Log[x]^3*Log[1 + (e^(1/3)*x)/d^(1/3)] + 3*Log[x]^2*PolyLog[2, -((e^(1/3)*x)/d^(1/3))] - 6*Log[x]*PolyLog[3, -((e^(1/3)*x)/d^(1/3))] + 6*PolyLog[4, -((e^(1/3)*x)/d^(1/3))]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3)) - (2*(Log[x]^3*Log[1 - ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)] + 3*Log[x]^2*PolyLog[2, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)] - 6*Log[x]*PolyLog[3, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)] + 6*PolyLog[4, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3)) - (2*(-1 + (-1)^(1/3))*(Log[x]^3*Log[1 + ((-1)^(2/3)*e^(1/3)*x)/d^(1/3)] + 3*Log[x]^2*PolyLog[2, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))] - 6*Log[x]*PolyLog[3, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))] + 6*PolyLog[4, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3)))","A",0
325,1,1379,860,6.1582513,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{\left(d+e x^3\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])^2/(d + e*x^3)^2,x]","b^2 \left(\frac{\sqrt[3]{-1} \left(\log (x) \left(\frac{\sqrt[3]{e} x \log (x)}{\sqrt[3]{e} x+\sqrt[3]{d}}-2 \log \left(\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}+1\right)\right)-2 \text{Li}_2\left(-\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}\right)\right)}{3 \left(1+\sqrt[3]{-1}\right)^2 d^{5/3} \sqrt[3]{e}}-\frac{\left(-1+\sqrt[3]{-1}\right) \left(\log (x) \left(\left(-\frac{1}{\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}}-\frac{\sqrt[3]{-1}}{\sqrt[3]{d}}\right) \log (x)+\frac{2 \sqrt[3]{-1} \log \left(1-\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right)}{\sqrt[3]{d}}\right)+\frac{2 \sqrt[3]{-1} \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right)}{\sqrt[3]{d}}\right)}{3 \left(1+\sqrt[3]{-1}\right)^2 d^{4/3} \sqrt[3]{e}}-\frac{\log (x) \left((-1)^{2/3} \sqrt[3]{e} x \log (x)-2 \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right) \log \left(\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}+1\right)\right)-2 \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right) \text{Li}_2\left(-\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}\right)}{3 \left(1+\sqrt[3]{-1}\right)^2 d^{4/3} \left(\sqrt[3]{d} e^{2/3} x-\sqrt[3]{-1} d^{2/3} \sqrt[3]{e}\right)}+\frac{2 \sqrt[3]{-1} \left(\log \left(\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}+1\right) \log ^2(x)+2 \text{Li}_2\left(-\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}\right) \log (x)-2 \text{Li}_3\left(-\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}\right)\right)}{3 \left(1+\sqrt[3]{-1}\right)^2 d^{5/3} \sqrt[3]{e}}-\frac{2 \left(\log \left(1-\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) \log ^2(x)+2 \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) \log (x)-2 \text{Li}_3\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right)\right)}{3 \left(1+\sqrt[3]{-1}\right)^2 d^{5/3} \sqrt[3]{e}}-\frac{2 \left(-1+\sqrt[3]{-1}\right) \left(\log \left(\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}+1\right) \log ^2(x)+2 \text{Li}_2\left(-\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) \log (x)-2 \text{Li}_3\left(-\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}\right)\right)}{3 \left(1+\sqrt[3]{-1}\right)^2 d^{5/3} \sqrt[3]{e}}\right) n^2+2 b \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right) \left(-\frac{\left(-1+\sqrt[3]{-1}\right) \left(\left(-\frac{1}{\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}}-\frac{\sqrt[3]{-1}}{\sqrt[3]{d}}\right) \log (x)+\frac{\sqrt[3]{-1} \log \left(-\sqrt[3]{e} x-(-1)^{2/3} \sqrt[3]{d}\right)}{\sqrt[3]{d}}\right)}{3 \left(1+\sqrt[3]{-1}\right)^2 d^{4/3} \sqrt[3]{e}}+\frac{\sqrt[3]{-1} \left(\left(\frac{1}{\sqrt[3]{d}}-\frac{1}{\sqrt[3]{e} x+\sqrt[3]{d}}\right) \log (x)-\frac{\log \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\sqrt[3]{d}}\right)}{3 \left(1+\sqrt[3]{-1}\right)^2 d^{4/3} \sqrt[3]{e}}-\frac{\frac{\log (x)}{\sqrt[3]{e} \left(\sqrt[3]{-1} \sqrt[3]{d}-\sqrt[3]{e} x\right)}-\frac{\frac{(-1)^{2/3} \log \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\sqrt[3]{d}}-\frac{(-1)^{2/3} \log (x)}{\sqrt[3]{d}}}{\sqrt[3]{e}}}{3 \left(1+\sqrt[3]{-1}\right)^2 d^{4/3}}+\frac{2 \sqrt[3]{-1} \left(\log (x) \log \left(\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}+1\right)+\text{Li}_2\left(-\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}\right)\right)}{3 \left(1+\sqrt[3]{-1}\right)^2 d^{5/3} \sqrt[3]{e}}-\frac{2 \left(\log (x) \log \left(1-\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right)+\text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right)\right)}{3 \left(1+\sqrt[3]{-1}\right)^2 d^{5/3} \sqrt[3]{e}}-\frac{2 \left(-1+\sqrt[3]{-1}\right) \left(\log (x) \log \left(\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}+1\right)+\text{Li}_2\left(-\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}\right)\right)}{3 \left(1+\sqrt[3]{-1}\right)^2 d^{5/3} \sqrt[3]{e}}\right) n+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{e} x-\sqrt[3]{d}}{\sqrt{3} \sqrt[3]{d}}\right) \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)^2}{3 \sqrt{3} d^{5/3} \sqrt[3]{e}}+\frac{x \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)^2}{3 d \left(e x^3+d\right)}+\frac{2 \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)^2 \log \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{9 d^{5/3} \sqrt[3]{e}}-\frac{\left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)^2 \log \left(e^{2/3} x^2-\sqrt[3]{d} \sqrt[3]{e} x+d^{2/3}\right)}{9 d^{5/3} \sqrt[3]{e}}","-\frac{2 b^2 \text{Li}_2\left(-\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^2}{9 d^{5/3} \sqrt[3]{e}}+\frac{2 \sqrt[3]{-1} b^2 \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^2}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \sqrt[3]{e}}+\frac{2 \sqrt[3]{-1} b^2 \text{Li}_2\left(-\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^2}{9 d^{5/3} \sqrt[3]{e}}-\frac{4 b^2 \text{Li}_3\left(-\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^2}{9 d^{5/3} \sqrt[3]{e}}+\frac{4 i \sqrt{3} b^2 \text{Li}_3\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^2}{\left(1+\sqrt[3]{-1}\right)^5 d^{5/3} \sqrt[3]{e}}-\frac{4 b^2 \text{Li}_3\left(-\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n^2}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \sqrt[3]{e}}-\frac{2 b \left(a+b \log \left(c x^n\right)\right) \log \left(\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}+1\right) n}{9 d^{5/3} \sqrt[3]{e}}+\frac{2 \sqrt[3]{-1} b \left(a+b \log \left(c x^n\right)\right) \log \left(1-\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \sqrt[3]{e}}+\frac{2 \sqrt[3]{-1} b \left(a+b \log \left(c x^n\right)\right) \log \left(\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}+1\right) n}{9 d^{5/3} \sqrt[3]{e}}+\frac{4 b \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}\right) n}{9 d^{5/3} \sqrt[3]{e}}-\frac{4 i \sqrt{3} b \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n}{\left(1+\sqrt[3]{-1}\right)^5 d^{5/3} \sqrt[3]{e}}+\frac{4 b \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) n}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \sqrt[3]{e}}+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{9 d^{5/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}-\frac{\sqrt[3]{-1} x \left(a+b \log \left(c x^n\right)\right)^2}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \left(\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}\right)}+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{9 d^{5/3} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}+\frac{2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}+1\right)}{9 d^{5/3} \sqrt[3]{e}}-\frac{2 i \sqrt{3} \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right)}{\left(1+\sqrt[3]{-1}\right)^5 d^{5/3} \sqrt[3]{e}}+\frac{2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}+1\right)}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \sqrt[3]{e}}",1,"(x*(a + b*(-(n*Log[x]) + Log[c*x^n]))^2)/(3*d*(d + e*x^3)) + (2*ArcTan[(-d^(1/3) + 2*e^(1/3)*x)/(Sqrt[3]*d^(1/3))]*(a + b*(-(n*Log[x]) + Log[c*x^n]))^2)/(3*Sqrt[3]*d^(5/3)*e^(1/3)) + (2*(a + b*(-(n*Log[x]) + Log[c*x^n]))^2*Log[d^(1/3) + e^(1/3)*x])/(9*d^(5/3)*e^(1/3)) - ((a + b*(-(n*Log[x]) + Log[c*x^n]))^2*Log[d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2])/(9*d^(5/3)*e^(1/3)) + 2*b*n*(a + b*(-(n*Log[x]) + Log[c*x^n]))*(-1/3*((-1 + (-1)^(1/3))*((-((-1)^(1/3)/d^(1/3)) - ((-1)^(2/3)*d^(1/3) + e^(1/3)*x)^(-1))*Log[x] + ((-1)^(1/3)*Log[-((-1)^(2/3)*d^(1/3)) - e^(1/3)*x])/d^(1/3)))/((1 + (-1)^(1/3))^2*d^(4/3)*e^(1/3)) + ((-1)^(1/3)*((d^(-1/3) - (d^(1/3) + e^(1/3)*x)^(-1))*Log[x] - Log[d^(1/3) + e^(1/3)*x]/d^(1/3)))/(3*(1 + (-1)^(1/3))^2*d^(4/3)*e^(1/3)) - (Log[x]/(e^(1/3)*((-1)^(1/3)*d^(1/3) - e^(1/3)*x)) - (-(((-1)^(2/3)*Log[x])/d^(1/3)) + ((-1)^(2/3)*Log[d^(1/3) + (-1)^(2/3)*e^(1/3)*x])/d^(1/3))/e^(1/3))/(3*(1 + (-1)^(1/3))^2*d^(4/3)) + (2*(-1)^(1/3)*(Log[x]*Log[1 + (e^(1/3)*x)/d^(1/3)] + PolyLog[2, -((e^(1/3)*x)/d^(1/3))]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3)) - (2*(Log[x]*Log[1 - ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)] + PolyLog[2, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3)) - (2*(-1 + (-1)^(1/3))*(Log[x]*Log[1 + ((-1)^(2/3)*e^(1/3)*x)/d^(1/3)] + PolyLog[2, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3))) + b^2*n^2*(((-1)^(1/3)*(Log[x]*((e^(1/3)*x*Log[x])/(d^(1/3) + e^(1/3)*x) - 2*Log[1 + (e^(1/3)*x)/d^(1/3)]) - 2*PolyLog[2, -((e^(1/3)*x)/d^(1/3))]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3)) - ((-1 + (-1)^(1/3))*(Log[x]*((-((-1)^(1/3)/d^(1/3)) - ((-1)^(2/3)*d^(1/3) + e^(1/3)*x)^(-1))*Log[x] + (2*(-1)^(1/3)*Log[1 - ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/d^(1/3)) + (2*(-1)^(1/3)*PolyLog[2, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/d^(1/3)))/(3*(1 + (-1)^(1/3))^2*d^(4/3)*e^(1/3)) - (Log[x]*((-1)^(2/3)*e^(1/3)*x*Log[x] - 2*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)*Log[1 + ((-1)^(2/3)*e^(1/3)*x)/d^(1/3)]) - 2*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)*PolyLog[2, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))])/(3*(1 + (-1)^(1/3))^2*d^(4/3)*(-((-1)^(1/3)*d^(2/3)*e^(1/3)) + d^(1/3)*e^(2/3)*x)) + (2*(-1)^(1/3)*(Log[x]^2*Log[1 + (e^(1/3)*x)/d^(1/3)] + 2*Log[x]*PolyLog[2, -((e^(1/3)*x)/d^(1/3))] - 2*PolyLog[3, -((e^(1/3)*x)/d^(1/3))]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3)) - (2*(Log[x]^2*Log[1 - ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)] + 2*Log[x]*PolyLog[2, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)] - 2*PolyLog[3, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3)) - (2*(-1 + (-1)^(1/3))*(Log[x]^2*Log[1 + ((-1)^(2/3)*e^(1/3)*x)/d^(1/3)] + 2*Log[x]*PolyLog[2, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))] - 2*PolyLog[3, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))]))/(3*(1 + (-1)^(1/3))^2*d^(5/3)*e^(1/3)))","A",1
326,1,571,520,1.874065,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+e x^3\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*x^3)^2,x]","\frac{-\frac{\log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{\sqrt[3]{e}}+\frac{3 d^{2/3} x \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{d+e x^3}+\frac{2 \log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{\sqrt[3]{e}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{e} x}{\sqrt[3]{d}}}{\sqrt{3}}\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{\sqrt[3]{e}}+\frac{3 b n \left(\frac{\left(\sqrt[3]{-1}-1\right) \left(\left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right) \log \left(-(-1)^{2/3} \sqrt[3]{d}-\sqrt[3]{e} x\right)+\sqrt[3]{-1} \sqrt[3]{e} x \log (x)\right)}{(-1)^{2/3} \sqrt[3]{d} \sqrt[3]{e}+e^{2/3} x}+\frac{\left(\sqrt[3]{d}+(-1)^{2/3} \sqrt[3]{e} x\right) \log \left(\sqrt[3]{d}+(-1)^{2/3} \sqrt[3]{e} x\right)-(-1)^{2/3} \sqrt[3]{e} x \log (x)}{e^{2/3} x-\sqrt[3]{-1} \sqrt[3]{d} \sqrt[3]{e}}+\frac{2 \sqrt[3]{-1} \left(\text{Li}_2\left(-\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}\right)+\log (x) \log \left(\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}+1\right)\right)}{\sqrt[3]{e}}-\frac{2 \left(\text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right)+\log (x) \log \left(1-\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right)\right)}{\sqrt[3]{e}}-\frac{2 \left(\sqrt[3]{-1}-1\right) \left(\text{Li}_2\left(-\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}\right)+\log (x) \log \left(\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}+1\right)\right)}{\sqrt[3]{e}}+\sqrt[3]{-1} \left(\frac{x \log (x)}{\sqrt[3]{d}+\sqrt[3]{e} x}-\frac{\log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\sqrt[3]{e}}\right)\right)}{\left(1+\sqrt[3]{-1}\right)^2}}{9 d^{5/3}}","\frac{2 \log \left(\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{9 d^{5/3} \sqrt[3]{e}}-\frac{2 i \sqrt{3} \log \left(1-\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{\left(1+\sqrt[3]{-1}\right)^5 d^{5/3} \sqrt[3]{e}}+\frac{2 \log \left(\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \sqrt[3]{e}}+\frac{x \left(a+b \log \left(c x^n\right)\right)}{9 d^{5/3} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}-\frac{\sqrt[3]{-1} x \left(a+b \log \left(c x^n\right)\right)}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \left((-1)^{2/3} \sqrt[3]{d}+\sqrt[3]{e} x\right)}+\frac{x \left(a+b \log \left(c x^n\right)\right)}{9 d^{5/3} \left(\sqrt[3]{d}+(-1)^{2/3} \sqrt[3]{e} x\right)}+\frac{2 b n \text{Li}_2\left(-\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}\right)}{9 d^{5/3} \sqrt[3]{e}}-\frac{2 i \sqrt{3} b n \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x}{\sqrt[3]{d}}\right)}{\left(1+\sqrt[3]{-1}\right)^5 d^{5/3} \sqrt[3]{e}}+\frac{2 b n \text{Li}_2\left(-\frac{(-1)^{2/3} \sqrt[3]{e} x}{\sqrt[3]{d}}\right)}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \sqrt[3]{e}}+\frac{\sqrt[3]{-1} b n \log \left(-(-1)^{2/3} \sqrt[3]{d}-\sqrt[3]{e} x\right)}{\left(1+\sqrt[3]{-1}\right)^4 d^{5/3} \sqrt[3]{e}}-\frac{b n \log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{9 d^{5/3} \sqrt[3]{e}}+\frac{\sqrt[3]{-1} b n \log \left(\sqrt[3]{d}+(-1)^{2/3} \sqrt[3]{e} x\right)}{9 d^{5/3} \sqrt[3]{e}}",1,"((3*d^(2/3)*x*(a - b*n*Log[x] + b*Log[c*x^n]))/(d + e*x^3) - (2*Sqrt[3]*ArcTan[(1 - (2*e^(1/3)*x)/d^(1/3))/Sqrt[3]]*(a - b*n*Log[x] + b*Log[c*x^n]))/e^(1/3) + (2*(a - b*n*Log[x] + b*Log[c*x^n])*Log[d^(1/3) + e^(1/3)*x])/e^(1/3) - ((a - b*n*Log[x] + b*Log[c*x^n])*Log[d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2])/e^(1/3) + (3*b*n*(((-1 + (-1)^(1/3))*((-1)^(1/3)*e^(1/3)*x*Log[x] + (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*Log[-((-1)^(2/3)*d^(1/3)) - e^(1/3)*x]))/((-1)^(2/3)*d^(1/3)*e^(1/3) + e^(2/3)*x) + (-1)^(1/3)*((x*Log[x])/(d^(1/3) + e^(1/3)*x) - Log[d^(1/3) + e^(1/3)*x]/e^(1/3)) + (-((-1)^(2/3)*e^(1/3)*x*Log[x]) + (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)*Log[d^(1/3) + (-1)^(2/3)*e^(1/3)*x])/(-((-1)^(1/3)*d^(1/3)*e^(1/3)) + e^(2/3)*x) + (2*(-1)^(1/3)*(Log[x]*Log[1 + (e^(1/3)*x)/d^(1/3)] + PolyLog[2, -((e^(1/3)*x)/d^(1/3))]))/e^(1/3) - (2*(Log[x]*Log[1 - ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)] + PolyLog[2, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)]))/e^(1/3) - (2*(-1 + (-1)^(1/3))*(Log[x]*Log[1 + ((-1)^(2/3)*e^(1/3)*x)/d^(1/3)] + PolyLog[2, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))]))/e^(1/3)))/(1 + (-1)^(1/3))^2)/(9*d^(5/3))","A",1
327,0,0,25,5.6283073,"\int \frac{1}{\left(d+e x^3\right)^2 \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/((d + e*x^3)^2*(a + b*Log[c*x^n])),x]","\int \frac{1}{\left(d+e x^3\right)^2 \left(a+b \log \left(c x^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^3\right)^2 \left(a+b \log \left(c x^n\right)\right)},x\right)",0,"Integrate[1/((d + e*x^3)^2*(a + b*Log[c*x^n])), x]","A",-1
328,0,0,25,25.6735081,"\int \frac{1}{\left(d+e x^3\right)^2 \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[1/((d + e*x^3)^2*(a + b*Log[c*x^n])^2),x]","\int \frac{1}{\left(d+e x^3\right)^2 \left(a+b \log \left(c x^n\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^3\right)^2 \left(a+b \log \left(c x^n\right)\right)^2},x\right)",0,"Integrate[1/((d + e*x^3)^2*(a + b*Log[c*x^n])^2), x]","A",-1
329,1,171,185,0.1066402,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{d+\frac{e}{x}} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/(d + e/x),x]","\frac{36 d^4 x^4 \left(a+b \log \left(c x^n\right)\right)-48 d^3 e x^3 \left(a+b \log \left(c x^n\right)\right)+72 d^2 e^2 x^2 \left(a+b \log \left(c x^n\right)\right)+144 e^4 \log \left(\frac{d x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)-144 a d e^3 x-144 b d e^3 x \log \left(c x^n\right)-9 b d^4 n x^4+16 b d^3 e n x^3-36 b d^2 e^2 n x^2+144 b e^4 n \text{Li}_2\left(-\frac{d x}{e}\right)+144 b d e^3 n x}{144 d^5}","\frac{e^4 \log \left(\frac{d x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^5}+\frac{e^2 x^2 \left(a+b \log \left(c x^n\right)\right)}{2 d^3}-\frac{e x^3 \left(a+b \log \left(c x^n\right)\right)}{3 d^2}+\frac{x^4 \left(a+b \log \left(c x^n\right)\right)}{4 d}-\frac{a e^3 x}{d^4}-\frac{b e^3 x \log \left(c x^n\right)}{d^4}+\frac{b e^4 n \text{Li}_2\left(-\frac{d x}{e}\right)}{d^5}+\frac{b e^3 n x}{d^4}-\frac{b e^2 n x^2}{4 d^3}+\frac{b e n x^3}{9 d^2}-\frac{b n x^4}{16 d}",1,"(-144*a*d*e^3*x + 144*b*d*e^3*n*x - 36*b*d^2*e^2*n*x^2 + 16*b*d^3*e*n*x^3 - 9*b*d^4*n*x^4 - 144*b*d*e^3*x*Log[c*x^n] + 72*d^2*e^2*x^2*(a + b*Log[c*x^n]) - 48*d^3*e*x^3*(a + b*Log[c*x^n]) + 36*d^4*x^4*(a + b*Log[c*x^n]) + 144*e^4*(a + b*Log[c*x^n])*Log[1 + (d*x)/e] + 144*b*e^4*n*PolyLog[2, -((d*x)/e)])/(144*d^5)","A",1
330,1,142,148,0.0726189,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{d+\frac{e}{x}} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e/x),x]","\frac{12 a d^3 x^3-18 a d^2 e x^2-36 a e^3 \log \left(\frac{d x}{e}+1\right)+36 a d e^2 x+6 b \log \left(c x^n\right) \left(d x \left(2 d^2 x^2-3 d e x+6 e^2\right)-6 e^3 \log \left(\frac{d x}{e}+1\right)\right)-4 b d^3 n x^3+9 b d^2 e n x^2-36 b e^3 n \text{Li}_2\left(-\frac{d x}{e}\right)-36 b d e^2 n x}{36 d^4}","-\frac{e^3 \log \left(\frac{d x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}-\frac{e x^2 \left(a+b \log \left(c x^n\right)\right)}{2 d^2}+\frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{3 d}+\frac{a e^2 x}{d^3}+\frac{b e^2 x \log \left(c x^n\right)}{d^3}-\frac{b e^3 n \text{Li}_2\left(-\frac{d x}{e}\right)}{d^4}-\frac{b e^2 n x}{d^3}+\frac{b e n x^2}{4 d^2}-\frac{b n x^3}{9 d}",1,"(36*a*d*e^2*x - 36*b*d*e^2*n*x - 18*a*d^2*e*x^2 + 9*b*d^2*e*n*x^2 + 12*a*d^3*x^3 - 4*b*d^3*n*x^3 - 36*a*e^3*Log[1 + (d*x)/e] + 6*b*Log[c*x^n]*(d*x*(6*e^2 - 3*d*e*x + 2*d^2*x^2) - 6*e^3*Log[1 + (d*x)/e]) - 36*b*e^3*n*PolyLog[2, -((d*x)/e)])/(36*d^4)","A",1
331,1,105,107,0.0504932,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{d+\frac{e}{x}} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/(d + e/x),x]","\frac{2 a d^2 x^2+4 a e^2 \log \left(\frac{d x}{e}+1\right)-4 a d e x+2 b \log \left(c x^n\right) \left(2 e^2 \log \left(\frac{d x}{e}+1\right)+d x (d x-2 e)\right)-b d^2 n x^2+4 b e^2 n \text{Li}_2\left(-\frac{d x}{e}\right)+4 b d e n x}{4 d^3}","\frac{e^2 \log \left(\frac{d x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{2 d}-\frac{a e x}{d^2}-\frac{b e x \log \left(c x^n\right)}{d^2}+\frac{b e^2 n \text{Li}_2\left(-\frac{d x}{e}\right)}{d^3}+\frac{b e n x}{d^2}-\frac{b n x^2}{4 d}",1,"(-4*a*d*e*x + 4*b*d*e*n*x + 2*a*d^2*x^2 - b*d^2*n*x^2 + 4*a*e^2*Log[1 + (d*x)/e] + 2*b*Log[c*x^n]*(d*x*(-2*e + d*x) + 2*e^2*Log[1 + (d*x)/e]) + 4*b*e^2*n*PolyLog[2, -((d*x)/e)])/(4*d^3)","A",1
332,1,66,69,0.0327729,"\int \frac{a+b \log \left(c x^n\right)}{d+\frac{e}{x}} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e/x),x]","\frac{-a e \log \left(\frac{d x}{e}+1\right)+a d x+b \log \left(c x^n\right) \left(d x-e \log \left(\frac{d x}{e}+1\right)\right)-b e n \text{Li}_2\left(-\frac{d x}{e}\right)-b d n x}{d^2}","-\frac{e \log \left(\frac{d x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}+\frac{a x}{d}+\frac{b x \log \left(c x^n\right)}{d}-\frac{b e n \text{Li}_2\left(-\frac{d x}{e}\right)}{d^2}-\frac{b n x}{d}",1,"(a*d*x - b*d*n*x - a*e*Log[1 + (d*x)/e] + b*Log[c*x^n]*(d*x - e*Log[1 + (d*x)/e]) - b*e*n*PolyLog[2, -((d*x)/e)])/d^2","A",1
333,1,37,39,0.0073245,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+\frac{e}{x}\right) x} \, dx","Integrate[(a + b*Log[c*x^n])/((d + e/x)*x),x]","\frac{\log \left(\frac{d x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)+b n \text{Li}_2\left(-\frac{d x}{e}\right)}{d}","\frac{\log \left(\frac{d x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d}+\frac{b n \text{Li}_2\left(-\frac{d x}{e}\right)}{d}",1,"((a + b*Log[c*x^n])*Log[1 + (d*x)/e] + b*n*PolyLog[2, -((d*x)/e)])/d","A",1
334,1,63,44,0.0342698,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+\frac{e}{x}\right) x^2} \, dx","Integrate[(a + b*Log[c*x^n])/((d + e/x)*x^2),x]","\frac{\left(a+b \log \left(c x^n\right)\right) \left(a+b \log \left(c x^n\right)-2 b n \log \left(\frac{d x}{e}+1\right)\right)}{2 b e n}-\frac{b n \text{Li}_2\left(-\frac{d x}{e}\right)}{e}","\frac{b n \text{Li}_2\left(-\frac{e}{d x}\right)}{e}-\frac{\log \left(\frac{e}{d x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e}",1,"((a + b*Log[c*x^n])*(a + b*Log[c*x^n] - 2*b*n*Log[1 + (d*x)/e]))/(2*b*e*n) - (b*n*PolyLog[2, -((d*x)/e)])/e","A",1
335,1,88,95,0.0884978,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+\frac{e}{x}\right) x^3} \, dx","Integrate[(a + b*Log[c*x^n])/((d + e/x)*x^3),x]","-\frac{-2 d \log \left(\frac{d x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{b n}+\frac{2 e \left(a+b \log \left(c x^n\right)\right)}{x}-2 b d n \text{Li}_2\left(-\frac{d x}{e}\right)+\frac{2 b e n}{x}}{2 e^2}","-\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{2 b e^2 n}+\frac{d \log \left(\frac{d x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{a+b \log \left(c x^n\right)}{e x}+\frac{b d n \text{Li}_2\left(-\frac{d x}{e}\right)}{e^2}-\frac{b n}{e x}",1,"-1/2*((2*b*e*n)/x + (2*e*(a + b*Log[c*x^n]))/x + (d*(a + b*Log[c*x^n])^2)/(b*n) - 2*d*(a + b*Log[c*x^n])*Log[1 + (d*x)/e] - 2*b*d*n*PolyLog[2, -((d*x)/e)])/e^2","A",1
336,1,124,135,0.2082885,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+\frac{e}{x}\right) x^4} \, dx","Integrate[(a + b*Log[c*x^n])/((d + e/x)*x^4),x]","-\frac{4 d^2 \log \left(\frac{d x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 d^2 \left(a+b \log \left(c x^n\right)\right)^2}{b n}-\frac{4 d e \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{2 e^2 \left(a+b \log \left(c x^n\right)\right)}{x^2}+4 b d^2 n \text{Li}_2\left(-\frac{d x}{e}\right)-\frac{4 b d e n}{x}+\frac{b e^2 n}{x^2}}{4 e^3}","\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 b e^3 n}-\frac{d^2 \log \left(\frac{d x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^3}+\frac{d \left(a+b \log \left(c x^n\right)\right)}{e^2 x}-\frac{a+b \log \left(c x^n\right)}{2 e x^2}-\frac{b d^2 n \text{Li}_2\left(-\frac{d x}{e}\right)}{e^3}+\frac{b d n}{e^2 x}-\frac{b n}{4 e x^2}",1,"-1/4*((b*e^2*n)/x^2 - (4*b*d*e*n)/x + (2*e^2*(a + b*Log[c*x^n]))/x^2 - (4*d*e*(a + b*Log[c*x^n]))/x - (2*d^2*(a + b*Log[c*x^n])^2)/(b*n) + 4*d^2*(a + b*Log[c*x^n])*Log[1 + (d*x)/e] + 4*b*d^2*n*PolyLog[2, -((d*x)/e)])/e^3","A",1
337,1,156,170,0.0822498,"\int \frac{x^3 (a+b \log (c x))}{d+\frac{e}{x}} \, dx","Integrate[(x^3*(a + b*Log[c*x]))/(d + e/x),x]","\frac{36 d^4 x^4 (a+b \log (c x))-48 d^3 e x^3 (a+b \log (c x))+72 d^2 e^2 x^2 (a+b \log (c x))+144 e^4 \log \left(\frac{d x}{e}+1\right) (a+b \log (c x))-144 a d e^3 x-144 b d e^3 x \log (c x)-9 b d^4 x^4+16 b d^3 e x^3-36 b d^2 e^2 x^2+144 b e^4 \text{Li}_2\left(-\frac{d x}{e}\right)+144 b d e^3 x}{144 d^5}","\frac{e^4 \log \left(\frac{d x}{e}+1\right) (a+b \log (c x))}{d^5}+\frac{e^2 x^2 (a+b \log (c x))}{2 d^3}-\frac{e x^3 (a+b \log (c x))}{3 d^2}+\frac{x^4 (a+b \log (c x))}{4 d}-\frac{a e^3 x}{d^4}-\frac{b e^3 x \log (c x)}{d^4}+\frac{b e^4 \text{Li}_2\left(-\frac{d x}{e}\right)}{d^5}+\frac{b e^3 x}{d^4}-\frac{b e^2 x^2}{4 d^3}+\frac{b e x^3}{9 d^2}-\frac{b x^4}{16 d}",1,"(-144*a*d*e^3*x + 144*b*d*e^3*x - 36*b*d^2*e^2*x^2 + 16*b*d^3*e*x^3 - 9*b*d^4*x^4 - 144*b*d*e^3*x*Log[c*x] + 72*d^2*e^2*x^2*(a + b*Log[c*x]) - 48*d^3*e*x^3*(a + b*Log[c*x]) + 36*d^4*x^4*(a + b*Log[c*x]) + 144*e^4*(a + b*Log[c*x])*Log[1 + (d*x)/e] + 144*b*e^4*PolyLog[2, -((d*x)/e)])/(144*d^5)","A",1
338,1,125,136,0.0662327,"\int \frac{x^2 (a+b \log (c x))}{d+\frac{e}{x}} \, dx","Integrate[(x^2*(a + b*Log[c*x]))/(d + e/x),x]","\frac{12 d^3 x^3 (a+b \log (c x))-18 d^2 e x^2 (a+b \log (c x))-36 e^3 \log \left(\frac{d x}{e}+1\right) (a+b \log (c x))+36 a d e^2 x+36 b d e^2 x \log (c x)-4 b d^3 x^3+9 b d^2 e x^2-36 b e^3 \text{Li}_2\left(-\frac{d x}{e}\right)-36 b d e^2 x}{36 d^4}","-\frac{e^3 \log \left(\frac{d x}{e}+1\right) (a+b \log (c x))}{d^4}-\frac{e x^2 (a+b \log (c x))}{2 d^2}+\frac{x^3 (a+b \log (c x))}{3 d}+\frac{a e^2 x}{d^3}+\frac{b e^2 x \log (c x)}{d^3}-\frac{b e^3 \text{Li}_2\left(-\frac{d x}{e}\right)}{d^4}-\frac{b e^2 x}{d^3}+\frac{b e x^2}{4 d^2}-\frac{b x^3}{9 d}",1,"(36*a*d*e^2*x - 36*b*d*e^2*x + 9*b*d^2*e*x^2 - 4*b*d^3*x^3 + 36*b*d*e^2*x*Log[c*x] - 18*d^2*e*x^2*(a + b*Log[c*x]) + 12*d^3*x^3*(a + b*Log[c*x]) - 36*e^3*(a + b*Log[c*x])*Log[1 + (d*x)/e] - 36*b*e^3*PolyLog[2, -((d*x)/e)])/(36*d^4)","A",1
339,1,99,98,0.0432305,"\int \frac{x (a+b \log (c x))}{d+\frac{e}{x}} \, dx","Integrate[(x*(a + b*Log[c*x]))/(d + e/x),x]","\frac{e^2 \log \left(\frac{d x+e}{e}\right) (a+b \log (c x))}{d^3}+\frac{x^2 (a+b \log (c x))}{2 d}-\frac{a e x}{d^2}-\frac{b e x \log (c x)}{d^2}+\frac{b e^2 \text{Li}_2\left(-\frac{d x}{e}\right)}{d^3}+\frac{b e x}{d^2}-\frac{b x^2}{4 d}","\frac{e^2 \log \left(\frac{d x}{e}+1\right) (a+b \log (c x))}{d^3}+\frac{x^2 (a+b \log (c x))}{2 d}-\frac{a e x}{d^2}-\frac{b e x \log (c x)}{d^2}+\frac{b e^2 \text{Li}_2\left(-\frac{d x}{e}\right)}{d^3}+\frac{b e x}{d^2}-\frac{b x^2}{4 d}",1,"-((a*e*x)/d^2) + (b*e*x)/d^2 - (b*x^2)/(4*d) - (b*e*x*Log[c*x])/d^2 + (x^2*(a + b*Log[c*x]))/(2*d) + (e^2*(a + b*Log[c*x])*Log[(e + d*x)/e])/d^3 + (b*e^2*PolyLog[2, -((d*x)/e)])/d^3","A",1
340,1,64,63,0.0288991,"\int \frac{a+b \log (c x)}{d+\frac{e}{x}} \, dx","Integrate[(a + b*Log[c*x])/(d + e/x),x]","-\frac{e \log \left(\frac{d x+e}{e}\right) (a+b \log (c x))}{d^2}+\frac{a x}{d}+\frac{b x \log (c x)}{d}-\frac{b e \text{Li}_2\left(-\frac{d x}{e}\right)}{d^2}-\frac{b x}{d}","-\frac{e \log \left(\frac{d x}{e}+1\right) (a+b \log (c x))}{d^2}+\frac{a x}{d}+\frac{b x \log (c x)}{d}-\frac{b e \text{Li}_2\left(-\frac{d x}{e}\right)}{d^2}-\frac{b x}{d}",1,"(a*x)/d - (b*x)/d + (b*x*Log[c*x])/d - (e*(a + b*Log[c*x])*Log[(e + d*x)/e])/d^2 - (b*e*PolyLog[2, -((d*x)/e)])/d^2","A",1
341,1,34,36,0.006689,"\int \frac{a+b \log (c x)}{\left(d+\frac{e}{x}\right) x} \, dx","Integrate[(a + b*Log[c*x])/((d + e/x)*x),x]","\frac{\log \left(\frac{d x}{e}+1\right) (a+b \log (c x))+b \text{Li}_2\left(-\frac{d x}{e}\right)}{d}","\frac{\log \left(\frac{d x}{e}+1\right) (a+b \log (c x))}{d}+\frac{b \text{Li}_2\left(-\frac{d x}{e}\right)}{d}",1,"((a + b*Log[c*x])*Log[1 + (d*x)/e] + b*PolyLog[2, -((d*x)/e)])/d","A",1
342,1,54,41,0.0252263,"\int \frac{a+b \log (c x)}{\left(d+\frac{e}{x}\right) x^2} \, dx","Integrate[(a + b*Log[c*x])/((d + e/x)*x^2),x]","\frac{(a+b \log (c x)) \left(a+b \log (c x)-2 b \log \left(\frac{d x}{e}+1\right)\right)-2 b^2 \text{Li}_2\left(-\frac{d x}{e}\right)}{2 b e}","\frac{b \text{Li}_2\left(-\frac{e}{d x}\right)}{e}-\frac{\log \left(\frac{e}{d x}+1\right) (a+b \log (c x))}{e}",1,"((a + b*Log[c*x])*(a + b*Log[c*x] - 2*b*Log[1 + (d*x)/e]) - 2*b^2*PolyLog[2, -((d*x)/e)])/(2*b*e)","A",1
343,1,77,84,0.0892911,"\int \frac{a+b \log (c x)}{\left(d+\frac{e}{x}\right) x^3} \, dx","Integrate[(a + b*Log[c*x])/((d + e/x)*x^3),x]","-\frac{-2 d \log \left(\frac{d x}{e}+1\right) (a+b \log (c x))+\frac{d (a+b \log (c x))^2}{b}+\frac{2 e (a+b \log (c x))}{x}-2 b d \text{Li}_2\left(-\frac{d x}{e}\right)+\frac{2 b e}{x}}{2 e^2}","-\frac{d (a+b \log (c x))^2}{2 b e^2}+\frac{d \log \left(\frac{d x}{e}+1\right) (a+b \log (c x))}{e^2}-\frac{a+b \log (c x)}{e x}+\frac{b d \text{Li}_2\left(-\frac{d x}{e}\right)}{e^2}-\frac{b}{e x}",1,"-1/2*((2*b*e)/x + (2*e*(a + b*Log[c*x]))/x + (d*(a + b*Log[c*x])^2)/b - 2*d*(a + b*Log[c*x])*Log[1 + (d*x)/e] - 2*b*d*PolyLog[2, -((d*x)/e)])/e^2","A",1
344,1,110,121,0.1472163,"\int \frac{a+b \log (c x)}{\left(d+\frac{e}{x}\right) x^4} \, dx","Integrate[(a + b*Log[c*x])/((d + e/x)*x^4),x]","-\frac{4 d^2 \log \left(\frac{d x}{e}+1\right) (a+b \log (c x))-\frac{2 d^2 (a+b \log (c x))^2}{b}-\frac{4 d e (a+b \log (c x))}{x}+\frac{2 e^2 (a+b \log (c x))}{x^2}+4 b d^2 \text{Li}_2\left(-\frac{d x}{e}\right)-\frac{4 b d e}{x}+\frac{b e^2}{x^2}}{4 e^3}","\frac{d^2 (a+b \log (c x))^2}{2 b e^3}-\frac{d^2 \log \left(\frac{d x}{e}+1\right) (a+b \log (c x))}{e^3}+\frac{d (a+b \log (c x))}{e^2 x}-\frac{a+b \log (c x)}{2 e x^2}-\frac{b d^2 \text{Li}_2\left(-\frac{d x}{e}\right)}{e^3}+\frac{b d}{e^2 x}-\frac{b}{4 e x^2}",1,"-1/4*((b*e^2)/x^2 - (4*b*d*e)/x + (2*e^2*(a + b*Log[c*x]))/x^2 - (4*d*e*(a + b*Log[c*x]))/x - (2*d^2*(a + b*Log[c*x])^2)/b + 4*d^2*(a + b*Log[c*x])*Log[1 + (d*x)/e] + 4*b*d^2*PolyLog[2, -((d*x)/e)])/e^3","A",1
345,1,17,17,0.0111461,"\int \frac{x^{-1+n} \log \left(e x^n\right)}{1-e x^n} \, dx","Integrate[(x^(-1 + n)*Log[e*x^n])/(1 - e*x^n),x]","\frac{\text{Li}_2\left(1-e x^n\right)}{e n}","\frac{\text{Li}_2\left(1-e x^n\right)}{e n}",1,"PolyLog[2, 1 - e*x^n]/(e*n)","A",1
346,1,17,16,0.0100853,"\int \frac{x^{-1+n} \log \left(\frac{x^n}{d}\right)}{d-x^n} \, dx","Integrate[(x^(-1 + n)*Log[x^n/d])/(d - x^n),x]","\frac{\text{Li}_2\left(\frac{d-x^n}{d}\right)}{n}","\frac{\text{Li}_2\left(1-\frac{x^n}{d}\right)}{n}",1,"PolyLog[2, (d - x^n)/d]/n","A",1
347,1,21,20,0.0104459,"\int \frac{x^{-1+n} \log \left(-\frac{e x^n}{d}\right)}{d+e x^n} \, dx","Integrate[(x^(-1 + n)*Log[-((e*x^n)/d)])/(d + e*x^n),x]","-\frac{\text{Li}_2\left(\frac{e x^n+d}{d}\right)}{e n}","-\frac{\text{Li}_2\left(\frac{e x^n}{d}+1\right)}{e n}",1,"-(PolyLog[2, (d + e*x^n)/d]/(e*n))","A",1
348,1,16,14,0.0041849,"\int \frac{\log \left(\frac{a}{x}\right)}{a x-x^2} \, dx","Integrate[Log[a/x]/(a*x - x^2),x]","\frac{\text{Li}_2\left(-\frac{a-x}{x}\right)}{a}","\frac{\text{Li}_2\left(1-\frac{a}{x}\right)}{a}",1,"PolyLog[2, -((a - x)/x)]/a","A",1
349,1,21,17,0.004748,"\int \frac{\log \left(\frac{a}{x^2}\right)}{a x-x^3} \, dx","Integrate[Log[a/x^2]/(a*x - x^3),x]","\frac{\text{Li}_2\left(-\frac{a-x^2}{x^2}\right)}{2 a}","\frac{\text{Li}_2\left(1-\frac{a}{x^2}\right)}{2 a}",1,"PolyLog[2, -((a - x^2)/x^2)]/(2*a)","A",1
350,1,23,26,0.0099457,"\int \frac{\log \left(a x^{1-n}\right)}{a x-x^n} \, dx","Integrate[Log[a*x^(1 - n)]/(a*x - x^n),x]","\frac{\text{Li}_2\left(1-a x^{1-n}\right)}{a (n-1)}","-\frac{\text{Li}_2\left(1-a x^{1-n}\right)}{a (1-n)}",1,"PolyLog[2, 1 - a*x^(1 - n)]/(a*(-1 + n))","A",1
351,1,140,171,0.1567478,"\int (f x)^{-1+m} \left(d+e x^m\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^(-1 + m)*(d + e*x^m)^3*(a + b*Log[c*x^n]),x]","\frac{(f x)^m \left(12 a m \left(4 d^3+6 d^2 e x^m+4 d e^2 x^{2 m}+e^3 x^{3 m}\right)+12 b m \log \left(c x^n\right) \left(4 d^3+6 d^2 e x^m+4 d e^2 x^{2 m}+e^3 x^{3 m}\right)-b n \left(48 d^3+36 d^2 e x^m+16 d e^2 x^{2 m}+3 e^3 x^{3 m}\right)\right)}{48 f m^2}","\frac{x^{1-m} (f x)^{m-1} \left(d+e x^m\right)^4 \left(a+b \log \left(c x^n\right)\right)}{4 e m}-\frac{b d^4 n x^{1-m} \log (x) (f x)^{m-1}}{4 e m}-\frac{b d^3 n x (f x)^{m-1}}{m^2}-\frac{3 b d^2 e n x^{m+1} (f x)^{m-1}}{4 m^2}-\frac{b d e^2 n x^{2 m+1} (f x)^{m-1}}{3 m^2}-\frac{b e^3 n x^{3 m+1} (f x)^{m-1}}{16 m^2}",1,"((f*x)^m*(12*a*m*(4*d^3 + 6*d^2*e*x^m + 4*d*e^2*x^(2*m) + e^3*x^(3*m)) - b*n*(48*d^3 + 36*d^2*e*x^m + 16*d*e^2*x^(2*m) + 3*e^3*x^(3*m)) + 12*b*m*(4*d^3 + 6*d^2*e*x^m + 4*d*e^2*x^(2*m) + e^3*x^(3*m))*Log[c*x^n]))/(48*f*m^2)","A",1
352,1,101,142,0.1160966,"\int (f x)^{-1+m} \left(d+e x^m\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^(-1 + m)*(d + e*x^m)^2*(a + b*Log[c*x^n]),x]","\frac{(f x)^m \left(6 a m \left(3 d^2+3 d e x^m+e^2 x^{2 m}\right)+6 b m \log \left(c x^n\right) \left(3 d^2+3 d e x^m+e^2 x^{2 m}\right)-b n \left(18 d^2+9 d e x^m+2 e^2 x^{2 m}\right)\right)}{18 f m^2}","\frac{x^{1-m} (f x)^{m-1} \left(d+e x^m\right)^3 \left(a+b \log \left(c x^n\right)\right)}{3 e m}-\frac{b d^3 n x^{1-m} \log (x) (f x)^{m-1}}{3 e m}-\frac{b d^2 n x (f x)^{m-1}}{m^2}-\frac{b d e n x^{m+1} (f x)^{m-1}}{2 m^2}-\frac{b e^2 n x^{2 m+1} (f x)^{m-1}}{9 m^2}",1,"((f*x)^m*(6*a*m*(3*d^2 + 3*d*e*x^m + e^2*x^(2*m)) - b*n*(18*d^2 + 9*d*e*x^m + 2*e^2*x^(2*m)) + 6*b*m*(3*d^2 + 3*d*e*x^m + e^2*x^(2*m))*Log[c*x^n]))/(18*f*m^2)","A",1
353,1,61,90,0.0656712,"\int (f x)^{-1+m} \left(d+e x^m\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^(-1 + m)*(d + e*x^m)*(a + b*Log[c*x^n]),x]","\frac{(f x)^m \left(2 a m \left(2 d+e x^m\right)+2 b m \log \left(c x^n\right) \left(2 d+e x^m\right)-b n \left(4 d+e x^m\right)\right)}{4 f m^2}","\frac{d (f x)^m \left(a+b \log \left(c x^n\right)\right)}{f m}+\frac{e x^m (f x)^m \left(a+b \log \left(c x^n\right)\right)}{2 f m}-\frac{b d n (f x)^m}{f m^2}-\frac{b e n x^m (f x)^m}{4 f m^2}",1,"((f*x)^m*(2*a*m*(2*d + e*x^m) - b*n*(4*d + e*x^m) + 2*b*m*(2*d + e*x^m)*Log[c*x^n]))/(4*f*m^2)","A",1
354,1,29,38,0.0099224,"\int (f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^(-1 + m)*(a + b*Log[c*x^n]),x]","\frac{(f x)^m \left(a m+b m \log \left(c x^n\right)-b n\right)}{f m^2}","\frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{f m}-\frac{b n (f x)^m}{f m^2}",1,"((f*x)^m*(a*m - b*n + b*m*Log[c*x^n]))/(f*m^2)","A",1
355,1,141,77,0.1460856,"\int \frac{(f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right)}{d+e x^m} \, dx","Integrate[((f*x)^(-1 + m)*(a + b*Log[c*x^n]))/(d + e*x^m),x]","\frac{x^{-m} (f x)^m \left(m \log (x) \left(a m+b m \log \left(c x^n\right)+b n \log \left(d+e x^m\right)-b n \log \left(d-d x^m\right)\right)+a m \log \left(d-d x^m\right)+b m \log \left(c x^n\right) \log \left(d-d x^m\right)-b n \text{Li}_2\left(\frac{e x^m}{d}+1\right)-b n \log \left(-\frac{e x^m}{d}\right) \log \left(d+e x^m\right)-b m^2 n \log ^2(x)\right)}{e f m^2}","\frac{x^{1-m} (f x)^{m-1} \log \left(\frac{e x^m}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e m}+\frac{b n x^{1-m} (f x)^{m-1} \text{Li}_2\left(-\frac{e x^m}{d}\right)}{e m^2}",1,"((f*x)^m*(-(b*m^2*n*Log[x]^2) + a*m*Log[d - d*x^m] + b*m*Log[c*x^n]*Log[d - d*x^m] - b*n*Log[-((e*x^m)/d)]*Log[d + e*x^m] + m*Log[x]*(a*m + b*m*Log[c*x^n] - b*n*Log[d - d*x^m] + b*n*Log[d + e*x^m]) - b*n*PolyLog[2, 1 + (e*x^m)/d]))/(e*f*m^2*x^m)","A",0
356,1,89,69,0.1220073,"\int \frac{(f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^m\right)^2} \, dx","Integrate[((f*x)^(-1 + m)*(a + b*Log[c*x^n]))/(d + e*x^m)^2,x]","-\frac{x^{-m} (f x)^m \left(a d m+b d m \log \left(c x^n\right)+b e n x^m \log \left(d+e x^m\right)-b m n \log (x) \left(d+e x^m\right)+b d n \log \left(d+e x^m\right)\right)}{d e f m^2 \left(d+e x^m\right)}","\frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{d f m \left(d+e x^m\right)}-\frac{b n x^{-m} (f x)^m \log \left(d+e x^m\right)}{d e f m^2}",1,"-(((f*x)^m*(a*d*m - b*m*n*(d + e*x^m)*Log[x] + b*d*m*Log[c*x^n] + b*d*n*Log[d + e*x^m] + b*e*n*x^m*Log[d + e*x^m]))/(d*e*f*m^2*x^m*(d + e*x^m)))","A",1
357,1,137,150,0.149647,"\int \frac{(f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^m\right)^3} \, dx","Integrate[((f*x)^(-1 + m)*(a + b*Log[c*x^n]))/(d + e*x^m)^3,x]","\frac{x^{-m} (f x)^m \left(-a d^2 m-b d^2 m \log \left(c x^n\right)-b d^2 n \log \left(d+e x^m\right)+b d^2 n-b e^2 n x^{2 m} \log \left(d+e x^m\right)+b d e n x^m-2 b d e n x^m \log \left(d+e x^m\right)+b m n \log (x) \left(d+e x^m\right)^2\right)}{2 d^2 e f m^2 \left(d+e x^m\right)^2}","-\frac{x^{1-m} (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{2 e m \left(d+e x^m\right)^2}-\frac{b n x^{1-m} (f x)^{m-1} \log \left(d+e x^m\right)}{2 d^2 e m^2}+\frac{b n x^{1-m} \log (x) (f x)^{m-1}}{2 d^2 e m}+\frac{b n x^{1-m} (f x)^{m-1}}{2 d e m^2 \left(d+e x^m\right)}",1,"((f*x)^m*(-(a*d^2*m) + b*d^2*n + b*d*e*n*x^m + b*m*n*(d + e*x^m)^2*Log[x] - b*d^2*m*Log[c*x^n] - b*d^2*n*Log[d + e*x^m] - 2*b*d*e*n*x^m*Log[d + e*x^m] - b*e^2*n*x^(2*m)*Log[d + e*x^m]))/(2*d^2*e*f*m^2*x^m*(d + e*x^m)^2)","A",1
358,1,178,188,0.1612026,"\int \frac{(f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^m\right)^4} \, dx","Integrate[((f*x)^(-1 + m)*(a + b*Log[c*x^n]))/(d + e*x^m)^4,x]","\frac{x^{-m} (f x)^m \left(-2 a d^3 m-2 b d^3 m \log \left(c x^n\right)-2 b d^3 n \log \left(d+e x^m\right)+3 b d^3 n+5 b d^2 e n x^m-6 b d^2 e n x^m \log \left(d+e x^m\right)-2 b e^3 n x^{3 m} \log \left(d+e x^m\right)+2 b d e^2 n x^{2 m}-6 b d e^2 n x^{2 m} \log \left(d+e x^m\right)+2 b m n \log (x) \left(d+e x^m\right)^3\right)}{6 d^3 e f m^2 \left(d+e x^m\right)^3}","-\frac{x^{1-m} (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{3 e m \left(d+e x^m\right)^3}-\frac{b n x^{1-m} (f x)^{m-1} \log \left(d+e x^m\right)}{3 d^3 e m^2}+\frac{b n x^{1-m} \log (x) (f x)^{m-1}}{3 d^3 e m}+\frac{b n x^{1-m} (f x)^{m-1}}{3 d^2 e m^2 \left(d+e x^m\right)}+\frac{b n x^{1-m} (f x)^{m-1}}{6 d e m^2 \left(d+e x^m\right)^2}",1,"((f*x)^m*(-2*a*d^3*m + 3*b*d^3*n + 5*b*d^2*e*n*x^m + 2*b*d*e^2*n*x^(2*m) + 2*b*m*n*(d + e*x^m)^3*Log[x] - 2*b*d^3*m*Log[c*x^n] - 2*b*d^3*n*Log[d + e*x^m] - 6*b*d^2*e*n*x^m*Log[d + e*x^m] - 6*b*d*e^2*n*x^(2*m)*Log[d + e*x^m] - 2*b*e^3*n*x^(3*m)*Log[d + e*x^m]))/(6*d^3*e*f*m^2*x^m*(d + e*x^m)^3)","A",1
359,1,285,372,0.2586756,"\int (f x)^{-1+m} \left(d+e x^m\right)^3 \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[(f*x)^(-1 + m)*(d + e*x^m)^3*(a + b*Log[c*x^n])^2,x]","\frac{(f x)^m \left(72 a^2 m^2 \left(4 d^3+6 d^2 e x^m+4 d e^2 x^{2 m}+e^3 x^{3 m}\right)+12 b m \log \left(c x^n\right) \left(12 a m \left(4 d^3+6 d^2 e x^m+4 d e^2 x^{2 m}+e^3 x^{3 m}\right)-b n \left(48 d^3+36 d^2 e x^m+16 d e^2 x^{2 m}+3 e^3 x^{3 m}\right)\right)-12 a b m n \left(48 d^3+36 d^2 e x^m+16 d e^2 x^{2 m}+3 e^3 x^{3 m}\right)+72 b^2 m^2 \log ^2\left(c x^n\right) \left(4 d^3+6 d^2 e x^m+4 d e^2 x^{2 m}+e^3 x^{3 m}\right)+b^2 n^2 \left(576 d^3+216 d^2 e x^m+64 d e^2 x^{2 m}+9 e^3 x^{3 m}\right)\right)}{288 f m^3}","-\frac{b d^4 n x^{1-m} \log (x) (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{2 e m}-\frac{2 b d^3 n x (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{m^2}-\frac{3 b d^2 e n x^{m+1} (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{2 m^2}-\frac{2 b d e^2 n x^{2 m+1} (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{3 m^2}+\frac{x^{1-m} (f x)^{m-1} \left(d+e x^m\right)^4 \left(a+b \log \left(c x^n\right)\right)^2}{4 e m}-\frac{b e^3 n x^{3 m+1} (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{8 m^2}+\frac{b^2 d^4 n^2 x^{1-m} \log ^2(x) (f x)^{m-1}}{4 e m}+\frac{2 b^2 d^3 n^2 x (f x)^{m-1}}{m^3}+\frac{3 b^2 d^2 e n^2 x^{m+1} (f x)^{m-1}}{4 m^3}+\frac{2 b^2 d e^2 n^2 x^{2 m+1} (f x)^{m-1}}{9 m^3}+\frac{b^2 e^3 n^2 x^{3 m+1} (f x)^{m-1}}{32 m^3}",1,"((f*x)^m*(72*a^2*m^2*(4*d^3 + 6*d^2*e*x^m + 4*d*e^2*x^(2*m) + e^3*x^(3*m)) - 12*a*b*m*n*(48*d^3 + 36*d^2*e*x^m + 16*d*e^2*x^(2*m) + 3*e^3*x^(3*m)) + b^2*n^2*(576*d^3 + 216*d^2*e*x^m + 64*d*e^2*x^(2*m) + 9*e^3*x^(3*m)) + 12*b*m*(12*a*m*(4*d^3 + 6*d^2*e*x^m + 4*d*e^2*x^(2*m) + e^3*x^(3*m)) - b*n*(48*d^3 + 36*d^2*e*x^m + 16*d*e^2*x^(2*m) + 3*e^3*x^(3*m)))*Log[c*x^n] + 72*b^2*m^2*(4*d^3 + 6*d^2*e*x^m + 4*d*e^2*x^(2*m) + e^3*x^(3*m))*Log[c*x^n]^2))/(288*f*m^3)","A",1
360,1,207,298,0.1997366,"\int (f x)^{-1+m} \left(d+e x^m\right)^2 \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[(f*x)^(-1 + m)*(d + e*x^m)^2*(a + b*Log[c*x^n])^2,x]","\frac{(f x)^m \left(18 a^2 m^2 \left(3 d^2+3 d e x^m+e^2 x^{2 m}\right)+6 b m \log \left(c x^n\right) \left(6 a m \left(3 d^2+3 d e x^m+e^2 x^{2 m}\right)-b n \left(18 d^2+9 d e x^m+2 e^2 x^{2 m}\right)\right)-6 a b m n \left(18 d^2+9 d e x^m+2 e^2 x^{2 m}\right)+18 b^2 m^2 \log ^2\left(c x^n\right) \left(3 d^2+3 d e x^m+e^2 x^{2 m}\right)+b^2 n^2 \left(108 d^2+27 d e x^m+4 e^2 x^{2 m}\right)\right)}{54 f m^3}","-\frac{2 b d^3 n x^{1-m} \log (x) (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{3 e m}-\frac{2 b d^2 n x (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{m^2}-\frac{b d e n x^{m+1} (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{m^2}+\frac{x^{1-m} (f x)^{m-1} \left(d+e x^m\right)^3 \left(a+b \log \left(c x^n\right)\right)^2}{3 e m}-\frac{2 b e^2 n x^{2 m+1} (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{9 m^2}+\frac{b^2 d^3 n^2 x^{1-m} \log ^2(x) (f x)^{m-1}}{3 e m}+\frac{2 b^2 d^2 n^2 x (f x)^{m-1}}{m^3}+\frac{b^2 d e n^2 x^{m+1} (f x)^{m-1}}{2 m^3}+\frac{2 b^2 e^2 n^2 x^{2 m+1} (f x)^{m-1}}{27 m^3}",1,"((f*x)^m*(18*a^2*m^2*(3*d^2 + 3*d*e*x^m + e^2*x^(2*m)) - 6*a*b*m*n*(18*d^2 + 9*d*e*x^m + 2*e^2*x^(2*m)) + b^2*n^2*(108*d^2 + 27*d*e*x^m + 4*e^2*x^(2*m)) + 6*b*m*(6*a*m*(3*d^2 + 3*d*e*x^m + e^2*x^(2*m)) - b*n*(18*d^2 + 9*d*e*x^m + 2*e^2*x^(2*m)))*Log[c*x^n] + 18*b^2*m^2*(3*d^2 + 3*d*e*x^m + e^2*x^(2*m))*Log[c*x^n]^2))/(54*f*m^3)","A",1
361,1,125,226,0.1315683,"\int (f x)^{-1+m} \left(d+e x^m\right) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[(f*x)^(-1 + m)*(d + e*x^m)*(a + b*Log[c*x^n])^2,x]","\frac{(f x)^m \left(2 a^2 m^2 \left(2 d+e x^m\right)-2 b m \log \left(c x^n\right) \left(b n \left(4 d+e x^m\right)-2 a m \left(2 d+e x^m\right)\right)-2 a b m n \left(4 d+e x^m\right)+2 b^2 m^2 \log ^2\left(c x^n\right) \left(2 d+e x^m\right)+b^2 n^2 \left(8 d+e x^m\right)\right)}{4 f m^3}","-\frac{b d^2 n x^{1-m} \log (x) (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{e m}+\frac{x^{1-m} (f x)^{m-1} \left(d+e x^m\right)^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 e m}-\frac{2 b d n x (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{m^2}-\frac{b e n x^{m+1} (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{2 m^2}+\frac{b^2 d^2 n^2 x^{1-m} \log ^2(x) (f x)^{m-1}}{2 e m}+\frac{2 b^2 d n^2 x (f x)^{m-1}}{m^3}+\frac{b^2 e n^2 x^{m+1} (f x)^{m-1}}{4 m^3}",1,"((f*x)^m*(2*a^2*m^2*(2*d + e*x^m) - 2*a*b*m*n*(4*d + e*x^m) + b^2*n^2*(8*d + e*x^m) - 2*b*m*(-2*a*m*(2*d + e*x^m) + b*n*(4*d + e*x^m))*Log[c*x^n] + 2*b^2*m^2*(2*d + e*x^m)*Log[c*x^n]^2))/(4*f*m^3)","A",1
362,1,67,69,0.0231364,"\int (f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[(f*x)^(-1 + m)*(a + b*Log[c*x^n])^2,x]","\frac{(f x)^m \left(a^2 m^2+2 b m (a m-b n) \log \left(c x^n\right)-2 a b m n+b^2 m^2 \log ^2\left(c x^n\right)+2 b^2 n^2\right)}{f m^3}","-\frac{2 b n (f x)^m \left(a+b \log \left(c x^n\right)\right)}{f m^2}+\frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)^2}{f m}+\frac{2 b^2 n^2 (f x)^m}{f m^3}",1,"((f*x)^m*(a^2*m^2 - 2*a*b*m*n + 2*b^2*n^2 + 2*b*m*(a*m - b*n)*Log[c*x^n] + b^2*m^2*Log[c*x^n]^2))/(f*m^3)","A",1
363,1,502,129,0.2650551,"\int \frac{(f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right)^2}{d+e x^m} \, dx","Integrate[((f*x)^(-1 + m)*(a + b*Log[c*x^n])^2)/(d + e*x^m),x]","\frac{x^{-m} (f x)^m \left(3 a^2 m^2 \log \left(d-d x^m\right)+3 a^2 m^3 \log (x)-6 b m n \text{Li}_2\left(\frac{e x^m}{d}+1\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)+6 a b m^2 \log \left(c x^n\right) \log \left(d-d x^m\right)+6 a b m^3 \log (x) \log \left(c x^n\right)+6 a b m^2 n \log (x) \log \left(d+e x^m\right)-6 a b m n \log \left(-\frac{e x^m}{d}\right) \log \left(d+e x^m\right)-6 a b m^2 n \log (x) \log \left(d-d x^m\right)-6 a b m^3 n \log ^2(x)+6 b^2 m^2 n \log (x) \log \left(c x^n\right) \log \left(d+e x^m\right)-6 b^2 m n \log \left(c x^n\right) \log \left(-\frac{e x^m}{d}\right) \log \left(d+e x^m\right)+3 b^2 m^2 \log ^2\left(c x^n\right) \log \left(d-d x^m\right)-6 b^2 m^2 n \log (x) \log \left(c x^n\right) \log \left(d-d x^m\right)+3 b^2 m^3 \log (x) \log ^2\left(c x^n\right)-6 b^2 m^3 n \log ^2(x) \log \left(c x^n\right)+3 b^2 m^2 n^2 \log ^2(x) \log \left(\frac{d x^{-m}}{e}+1\right)-6 b^2 m^2 n^2 \log ^2(x) \log \left(d+e x^m\right)-6 b^2 n^2 \text{Li}_3\left(-\frac{d x^{-m}}{e}\right)-6 b^2 m n^2 \log (x) \text{Li}_2\left(-\frac{d x^{-m}}{e}\right)+6 b^2 m n^2 \log (x) \log \left(-\frac{e x^m}{d}\right) \log \left(d+e x^m\right)+3 b^2 m^2 n^2 \log ^2(x) \log \left(d-d x^m\right)+4 b^2 m^3 n^2 \log ^3(x)\right)}{3 e f m^3}","\frac{2 b n x^{1-m} (f x)^{m-1} \text{Li}_2\left(-\frac{e x^m}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e m^2}+\frac{x^{1-m} (f x)^{m-1} \log \left(\frac{e x^m}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e m}-\frac{2 b^2 n^2 x^{1-m} (f x)^{m-1} \text{Li}_3\left(-\frac{e x^m}{d}\right)}{e m^3}",1,"((f*x)^m*(3*a^2*m^3*Log[x] - 6*a*b*m^3*n*Log[x]^2 + 4*b^2*m^3*n^2*Log[x]^3 + 6*a*b*m^3*Log[x]*Log[c*x^n] - 6*b^2*m^3*n*Log[x]^2*Log[c*x^n] + 3*b^2*m^3*Log[x]*Log[c*x^n]^2 + 3*b^2*m^2*n^2*Log[x]^2*Log[1 + d/(e*x^m)] + 3*a^2*m^2*Log[d - d*x^m] - 6*a*b*m^2*n*Log[x]*Log[d - d*x^m] + 3*b^2*m^2*n^2*Log[x]^2*Log[d - d*x^m] + 6*a*b*m^2*Log[c*x^n]*Log[d - d*x^m] - 6*b^2*m^2*n*Log[x]*Log[c*x^n]*Log[d - d*x^m] + 3*b^2*m^2*Log[c*x^n]^2*Log[d - d*x^m] + 6*a*b*m^2*n*Log[x]*Log[d + e*x^m] - 6*b^2*m^2*n^2*Log[x]^2*Log[d + e*x^m] - 6*a*b*m*n*Log[-((e*x^m)/d)]*Log[d + e*x^m] + 6*b^2*m*n^2*Log[x]*Log[-((e*x^m)/d)]*Log[d + e*x^m] + 6*b^2*m^2*n*Log[x]*Log[c*x^n]*Log[d + e*x^m] - 6*b^2*m*n*Log[-((e*x^m)/d)]*Log[c*x^n]*Log[d + e*x^m] - 6*b^2*m*n^2*Log[x]*PolyLog[2, -(d/(e*x^m))] - 6*b*m*n*(a - b*n*Log[x] + b*Log[c*x^n])*PolyLog[2, 1 + (e*x^m)/d] - 6*b^2*n^2*PolyLog[3, -(d/(e*x^m))]))/(3*e*f*m^3*x^m)","B",0
364,1,157,138,0.452215,"\int \frac{(f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right)^2}{\left(d+e x^m\right)^2} \, dx","Integrate[((f*x)^(-1 + m)*(a + b*Log[c*x^n])^2)/(d + e*x^m)^2,x]","\frac{x^{-m} (f x)^m \left(-\frac{m^2 \left(a+b \log \left(c x^n\right)\right)^2}{d+e x^m}-\frac{2 a b m n \log \left(d-d x^m\right)}{d}+\frac{2 b^2 m n \left(n \log (x)-\log \left(c x^n\right)\right) \log \left(d-d x^m\right)}{d}+\frac{2 b^2 n^2 \left(\text{Li}_2\left(\frac{e x^m}{d}+1\right)+\left(\log \left(-\frac{e x^m}{d}\right)-m \log (x)\right) \log \left(d+e x^m\right)+\frac{1}{2} m^2 \log ^2(x)\right)}{d}\right)}{e f m^3}","-\frac{2 b n x^{1-m} (f x)^{m-1} \log \left(\frac{d x^{-m}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d e m^2}-\frac{x^{1-m} (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)^2}{e m \left(d+e x^m\right)}+\frac{2 b^2 n^2 x^{1-m} (f x)^{m-1} \text{Li}_2\left(-\frac{d x^{-m}}{e}\right)}{d e m^3}",1,"((f*x)^m*(-((m^2*(a + b*Log[c*x^n])^2)/(d + e*x^m)) - (2*a*b*m*n*Log[d - d*x^m])/d + (2*b^2*m*n*(n*Log[x] - Log[c*x^n])*Log[d - d*x^m])/d + (2*b^2*n^2*((m^2*Log[x]^2)/2 + (-(m*Log[x]) + Log[-((e*x^m)/d)])*Log[d + e*x^m] + PolyLog[2, 1 + (e*x^m)/d]))/d))/(e*f*m^3*x^m)","A",0
365,1,207,214,0.3561707,"\int \frac{(f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right)^2}{\left(d+e x^m\right)^3} \, dx","Integrate[((f*x)^(-1 + m)*(a + b*Log[c*x^n])^2)/(d + e*x^m)^3,x]","\frac{x^{-m} (f x)^m \left(-\frac{m^2 \left(a+b \log \left(c x^n\right)\right)^2}{\left(d+e x^m\right)^2}+\frac{2 b m n \left(a+b \log \left(c x^n\right)\right)}{d \left(d+e x^m\right)}-\frac{2 a b m n \log \left(d-d x^m\right)}{d^2}+\frac{2 b^2 m n \left(n \log (x)-\log \left(c x^n\right)\right) \log \left(d-d x^m\right)}{d^2}+\frac{2 b^2 n^2 \left(\text{Li}_2\left(\frac{e x^m}{d}+1\right)+\left(\log \left(-\frac{e x^m}{d}\right)-m \log (x)\right) \log \left(d+e x^m\right)+\frac{1}{2} m^2 \log ^2(x)\right)}{d^2}+\frac{2 b^2 n^2 \log \left(d-d x^m\right)}{d^2}\right)}{2 e f m^3}","-\frac{b n x^{1-m} (f x)^{m-1} \log \left(\frac{d x^{-m}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 e m^2}-\frac{b n x (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{d^2 m^2 \left(d+e x^m\right)}-\frac{x^{1-m} (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)^2}{2 e m \left(d+e x^m\right)^2}+\frac{b^2 n^2 x^{1-m} (f x)^{m-1} \text{Li}_2\left(-\frac{d x^{-m}}{e}\right)}{d^2 e m^3}+\frac{b^2 n^2 x^{1-m} (f x)^{m-1} \log \left(d+e x^m\right)}{d^2 e m^3}",1,"((f*x)^m*((2*b*m*n*(a + b*Log[c*x^n]))/(d*(d + e*x^m)) - (m^2*(a + b*Log[c*x^n])^2)/(d + e*x^m)^2 - (2*a*b*m*n*Log[d - d*x^m])/d^2 + (2*b^2*n^2*Log[d - d*x^m])/d^2 + (2*b^2*m*n*(n*Log[x] - Log[c*x^n])*Log[d - d*x^m])/d^2 + (2*b^2*n^2*((m^2*Log[x]^2)/2 + (-(m*Log[x]) + Log[-((e*x^m)/d)])*Log[d + e*x^m] + PolyLog[2, 1 + (e*x^m)/d]))/d^2))/(2*e*f*m^3*x^m)","A",0
366,1,240,346,0.5321302,"\int \frac{(f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right)^2}{\left(d+e x^m\right)^4} \, dx","Integrate[((f*x)^(-1 + m)*(a + b*Log[c*x^n])^2)/(d + e*x^m)^4,x]","\frac{x^{-m} (f x)^m \left(\frac{b n \left(2 a m+2 b m \log \left(c x^n\right)-b n\right)}{d^2 \left(d+e x^m\right)}-\frac{m^2 \left(a+b \log \left(c x^n\right)\right)^2}{\left(d+e x^m\right)^3}+\frac{b m n \left(a+b \log \left(c x^n\right)\right)}{d \left(d+e x^m\right)^2}-\frac{2 a b m n \log \left(d-d x^m\right)}{d^3}+\frac{2 b^2 m n \left(n \log (x)-\log \left(c x^n\right)\right) \log \left(d-d x^m\right)}{d^3}+\frac{2 b^2 n^2 \left(\text{Li}_2\left(\frac{e x^m}{d}+1\right)+\left(\log \left(-\frac{e x^m}{d}\right)-m \log (x)\right) \log \left(d+e x^m\right)+\frac{1}{2} m^2 \log ^2(x)\right)}{d^3}+\frac{3 b^2 n^2 \log \left(d-d x^m\right)}{d^3}\right)}{3 e f m^3}","-\frac{2 b n x^{1-m} (f x)^{m-1} \log \left(\frac{d x^{-m}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^3 e m^2}-\frac{2 b n x (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{3 d^3 m^2 \left(d+e x^m\right)}+\frac{b n x^{1-m} (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)}{3 d e m^2 \left(d+e x^m\right)^2}-\frac{x^{1-m} (f x)^{m-1} \left(a+b \log \left(c x^n\right)\right)^2}{3 e m \left(d+e x^m\right)^3}+\frac{2 b^2 n^2 x^{1-m} (f x)^{m-1} \text{Li}_2\left(-\frac{d x^{-m}}{e}\right)}{3 d^3 e m^3}+\frac{b^2 n^2 x^{1-m} (f x)^{m-1} \log \left(d+e x^m\right)}{d^3 e m^3}-\frac{b^2 n^2 x^{1-m} \log (x) (f x)^{m-1}}{3 d^3 e m^2}-\frac{b^2 n^2 x^{1-m} (f x)^{m-1}}{3 d^2 e m^3 \left(d+e x^m\right)}",1,"((f*x)^m*((b*m*n*(a + b*Log[c*x^n]))/(d*(d + e*x^m)^2) - (m^2*(a + b*Log[c*x^n])^2)/(d + e*x^m)^3 + (b*n*(2*a*m - b*n + 2*b*m*Log[c*x^n]))/(d^2*(d + e*x^m)) - (2*a*b*m*n*Log[d - d*x^m])/d^3 + (3*b^2*n^2*Log[d - d*x^m])/d^3 + (2*b^2*m*n*(n*Log[x] - Log[c*x^n])*Log[d - d*x^m])/d^3 + (2*b^2*n^2*((m^2*Log[x]^2)/2 + (-(m*Log[x]) + Log[-((e*x^m)/d)])*Log[d + e*x^m] + PolyLog[2, 1 + (e*x^m)/d]))/d^3))/(3*e*f*m^3*x^m)","A",0
367,1,73,59,0.1080386,"\int x^5 \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^5*(d + e*x^r)*(a + b*Log[c*x^n]),x]","\frac{x^6 \left(6 a (r+6) \left(d (r+6)+6 e x^r\right)+6 b (r+6) \log \left(c x^n\right) \left(d (r+6)+6 e x^r\right)-b n \left(d (r+6)^2+36 e x^r\right)\right)}{36 (r+6)^2}","\frac{1}{6} \left(d x^6+\frac{6 e x^{r+6}}{r+6}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{36} b d n x^6-\frac{b e n x^{r+6}}{(r+6)^2}",1,"(x^6*(6*a*(6 + r)*(d*(6 + r) + 6*e*x^r) - b*n*(d*(6 + r)^2 + 36*e*x^r) + 6*b*(6 + r)*(d*(6 + r) + 6*e*x^r)*Log[c*x^n]))/(36*(6 + r)^2)","A",1
368,1,73,59,0.0962378,"\int x^3 \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^3*(d + e*x^r)*(a + b*Log[c*x^n]),x]","\frac{x^4 \left(4 a (r+4) \left(d (r+4)+4 e x^r\right)+4 b (r+4) \log \left(c x^n\right) \left(d (r+4)+4 e x^r\right)-b n \left(d (r+4)^2+16 e x^r\right)\right)}{16 (r+4)^2}","\frac{1}{4} \left(d x^4+\frac{4 e x^{r+4}}{r+4}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{16} b d n x^4-\frac{b e n x^{r+4}}{(r+4)^2}",1,"(x^4*(4*a*(4 + r)*(d*(4 + r) + 4*e*x^r) - b*n*(d*(4 + r)^2 + 16*e*x^r) + 4*b*(4 + r)*(d*(4 + r) + 4*e*x^r)*Log[c*x^n]))/(16*(4 + r)^2)","A",1
369,1,73,59,0.0942682,"\int x \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x*(d + e*x^r)*(a + b*Log[c*x^n]),x]","\frac{x^2 \left(2 a (r+2) \left(d (r+2)+2 e x^r\right)+2 b (r+2) \log \left(c x^n\right) \left(d (r+2)+2 e x^r\right)-b n \left(d (r+2)^2+4 e x^r\right)\right)}{4 (r+2)^2}","\frac{1}{2} \left(d x^2+\frac{2 e x^{r+2}}{r+2}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b d n x^2-\frac{b e n x^{r+2}}{(r+2)^2}",1,"(x^2*(2*a*(2 + r)*(d*(2 + r) + 2*e*x^r) - b*n*(d*(2 + r)^2 + 4*e*x^r) + 2*b*(2 + r)*(d*(2 + r) + 2*e*x^r)*Log[c*x^n]))/(4*(2 + r)^2)","A",1
370,1,54,53,0.0899517,"\int \frac{\left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[((d + e*x^r)*(a + b*Log[c*x^n]))/x,x]","\frac{e x^r (a r-b n)}{r^2}+a d \log (x)+\frac{b d \log ^2\left(c x^n\right)}{2 n}+\frac{b e x^r \log \left(c x^n\right)}{r}","\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}+\frac{e x^r \left(a+b \log \left(c x^n\right)\right)}{r}-\frac{b e n x^r}{r^2}",1,"(e*(-(b*n) + a*r)*x^r)/r^2 + a*d*Log[x] + (b*e*x^r*Log[c*x^n])/r + (b*d*Log[c*x^n]^2)/(2*n)","A",1
371,1,72,71,0.1134692,"\int \frac{\left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Integrate[((d + e*x^r)*(a + b*Log[c*x^n]))/x^3,x]","-\frac{2 a (r-2) \left(d (r-2)-2 e x^r\right)+2 b (r-2) \log \left(c x^n\right) \left(d (r-2)-2 e x^r\right)+b n \left(d (r-2)^2+4 e x^r\right)}{4 (r-2)^2 x^2}","-\frac{d \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{e x^{r-2} \left(a+b \log \left(c x^n\right)\right)}{2-r}-\frac{b d n}{4 x^2}-\frac{b e n x^{r-2}}{(2-r)^2}",1,"-1/4*(2*a*(-2 + r)*(d*(-2 + r) - 2*e*x^r) + b*n*(d*(-2 + r)^2 + 4*e*x^r) + 2*b*(-2 + r)*(d*(-2 + r) - 2*e*x^r)*Log[c*x^n])/((-2 + r)^2*x^2)","A",1
372,1,72,71,0.1161275,"\int \frac{\left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)}{x^5} \, dx","Integrate[((d + e*x^r)*(a + b*Log[c*x^n]))/x^5,x]","-\frac{4 a (r-4) \left(d (r-4)-4 e x^r\right)+4 b (r-4) \log \left(c x^n\right) \left(d (r-4)-4 e x^r\right)+b n \left(d (r-4)^2+16 e x^r\right)}{16 (r-4)^2 x^4}","-\frac{d \left(a+b \log \left(c x^n\right)\right)}{4 x^4}-\frac{e x^{r-4} \left(a+b \log \left(c x^n\right)\right)}{4-r}-\frac{b d n}{16 x^4}-\frac{b e n x^{r-4}}{(4-r)^2}",1,"-1/16*(4*a*(-4 + r)*(d*(-4 + r) - 4*e*x^r) + b*n*(d*(-4 + r)^2 + 16*e*x^r) + 4*b*(-4 + r)*(d*(-4 + r) - 4*e*x^r)*Log[c*x^n])/((-4 + r)^2*x^4)","A",1
373,1,73,59,0.0926765,"\int x^4 \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^4*(d + e*x^r)*(a + b*Log[c*x^n]),x]","\frac{x^5 \left(5 a (r+5) \left(d (r+5)+5 e x^r\right)+5 b (r+5) \log \left(c x^n\right) \left(d (r+5)+5 e x^r\right)-b n \left(d (r+5)^2+25 e x^r\right)\right)}{25 (r+5)^2}","\frac{1}{5} \left(d x^5+\frac{5 e x^{r+5}}{r+5}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{25} b d n x^5-\frac{b e n x^{r+5}}{(r+5)^2}",1,"(x^5*(5*a*(5 + r)*(d*(5 + r) + 5*e*x^r) - b*n*(d*(5 + r)^2 + 25*e*x^r) + 5*b*(5 + r)*(d*(5 + r) + 5*e*x^r)*Log[c*x^n]))/(25*(5 + r)^2)","A",1
374,1,73,59,0.0950979,"\int x^2 \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^2*(d + e*x^r)*(a + b*Log[c*x^n]),x]","\frac{x^3 \left(3 a (r+3) \left(d (r+3)+3 e x^r\right)+3 b (r+3) \log \left(c x^n\right) \left(d (r+3)+3 e x^r\right)-b n \left(d (r+3)^2+9 e x^r\right)\right)}{9 (r+3)^2}","\frac{1}{3} \left(d x^3+\frac{3 e x^{r+3}}{r+3}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b d n x^3-\frac{b e n x^{r+3}}{(r+3)^2}",1,"(x^3*(3*a*(3 + r)*(d*(3 + r) + 3*e*x^r) - b*n*(d*(3 + r)^2 + 9*e*x^r) + 3*b*(3 + r)*(d*(3 + r) + 3*e*x^r)*Log[c*x^n]))/(9*(3 + r)^2)","A",1
375,1,53,57,0.1281319,"\int \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(d + e*x^r)*(a + b*Log[c*x^n]),x]","x \left(\frac{e x^r \left(a+b \log \left(c x^n\right)\right)}{r+1}+a d+b d \log \left(c x^n\right)-b d n-\frac{b e n x^r}{(r+1)^2}\right)","d x \left(a+b \log \left(c x^n\right)\right)+\frac{e x^{r+1} \left(a+b \log \left(c x^n\right)\right)}{r+1}-b d n x-\frac{b e n x^{r+1}}{(r+1)^2}",1,"x*(a*d - b*d*n - (b*e*n*x^r)/(1 + r)^2 + b*d*Log[c*x^n] + (e*x^r*(a + b*Log[c*x^n]))/(1 + r))","A",1
376,1,67,67,0.1089211,"\int \frac{\left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Integrate[((d + e*x^r)*(a + b*Log[c*x^n]))/x^2,x]","-\frac{a (r-1) \left(d (r-1)-e x^r\right)+b (r-1) \log \left(c x^n\right) \left(d (r-1)-e x^r\right)+b n \left(d (r-1)^2+e x^r\right)}{(r-1)^2 x}","-\frac{d \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{e x^{r-1} \left(a+b \log \left(c x^n\right)\right)}{1-r}-\frac{b d n}{x}-\frac{b e n x^{r-1}}{(1-r)^2}",1,"-((a*(-1 + r)*(d*(-1 + r) - e*x^r) + b*n*(d*(-1 + r)^2 + e*x^r) + b*(-1 + r)*(d*(-1 + r) - e*x^r)*Log[c*x^n])/((-1 + r)^2*x))","A",1
377,1,72,71,0.1171927,"\int \frac{\left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Integrate[((d + e*x^r)*(a + b*Log[c*x^n]))/x^4,x]","-\frac{3 a (r-3) \left(d (r-3)-3 e x^r\right)+3 b (r-3) \log \left(c x^n\right) \left(d (r-3)-3 e x^r\right)+b n \left(d (r-3)^2+9 e x^r\right)}{9 (r-3)^2 x^3}","-\frac{d \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{e x^{r-3} \left(a+b \log \left(c x^n\right)\right)}{3-r}-\frac{b d n}{9 x^3}-\frac{b e n x^{r-3}}{(3-r)^2}",1,"-1/9*(3*a*(-3 + r)*(d*(-3 + r) - 3*e*x^r) + b*n*(d*(-3 + r)^2 + 9*e*x^r) + 3*b*(-3 + r)*(d*(-3 + r) - 3*e*x^r)*Log[c*x^n])/((-3 + r)^2*x^3)","A",1
378,1,72,71,0.0971498,"\int \frac{\left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Integrate[((d + e*x^r)*(a + b*Log[c*x^n]))/x^6,x]","-\frac{5 a (r-5) \left(d (r-5)-5 e x^r\right)+5 b (r-5) \log \left(c x^n\right) \left(d (r-5)-5 e x^r\right)+b n \left(d (r-5)^2+25 e x^r\right)}{25 (r-5)^2 x^5}","-\frac{d \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{e x^{r-5} \left(a+b \log \left(c x^n\right)\right)}{5-r}-\frac{b d n}{25 x^5}-\frac{b e n x^{r-5}}{(5-r)^2}",1,"-1/25*(5*a*(-5 + r)*(d*(-5 + r) - 5*e*x^r) + b*n*(d*(-5 + r)^2 + 25*e*x^r) + 5*b*(-5 + r)*(d*(-5 + r) - 5*e*x^r)*Log[c*x^n])/((-5 + r)^2*x^5)","A",1
379,1,118,103,0.2794493,"\int x^5 \left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^5*(d + e*x^r)^2*(a + b*Log[c*x^n]),x]","\frac{1}{36} x^6 \left(6 a \left(d^2+\frac{12 d e x^r}{r+6}+\frac{3 e^2 x^{2 r}}{r+3}\right)+6 b \log \left(c x^n\right) \left(d^2+\frac{12 d e x^r}{r+6}+\frac{3 e^2 x^{2 r}}{r+3}\right)+b n \left(-d^2-\frac{72 d e x^r}{(r+6)^2}-\frac{9 e^2 x^{2 r}}{(r+3)^2}\right)\right)","\frac{1}{6} \left(d^2 x^6+\frac{12 d e x^{r+6}}{r+6}+\frac{3 e^2 x^{2 (r+3)}}{r+3}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{36} b d^2 n x^6-\frac{2 b d e n x^{r+6}}{(r+6)^2}-\frac{b e^2 n x^{2 (r+3)}}{4 (r+3)^2}",1,"(x^6*(b*n*(-d^2 - (72*d*e*x^r)/(6 + r)^2 - (9*e^2*x^(2*r))/(3 + r)^2) + 6*a*(d^2 + (12*d*e*x^r)/(6 + r) + (3*e^2*x^(2*r))/(3 + r)) + 6*b*(d^2 + (12*d*e*x^r)/(6 + r) + (3*e^2*x^(2*r))/(3 + r))*Log[c*x^n]))/36","A",1
380,1,118,103,0.2595045,"\int x^3 \left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^3*(d + e*x^r)^2*(a + b*Log[c*x^n]),x]","\frac{1}{16} x^4 \left(4 a \left(d^2+\frac{8 d e x^r}{r+4}+\frac{2 e^2 x^{2 r}}{r+2}\right)+4 b \log \left(c x^n\right) \left(d^2+\frac{8 d e x^r}{r+4}+\frac{2 e^2 x^{2 r}}{r+2}\right)+b n \left(-d^2-\frac{32 d e x^r}{(r+4)^2}-\frac{4 e^2 x^{2 r}}{(r+2)^2}\right)\right)","\frac{1}{4} \left(d^2 x^4+\frac{8 d e x^{r+4}}{r+4}+\frac{2 e^2 x^{2 (r+2)}}{r+2}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{16} b d^2 n x^4-\frac{2 b d e n x^{r+4}}{(r+4)^2}-\frac{b e^2 n x^{2 (r+2)}}{4 (r+2)^2}",1,"(x^4*(b*n*(-d^2 - (32*d*e*x^r)/(4 + r)^2 - (4*e^2*x^(2*r))/(2 + r)^2) + 4*a*(d^2 + (8*d*e*x^r)/(4 + r) + (2*e^2*x^(2*r))/(2 + r)) + 4*b*(d^2 + (8*d*e*x^r)/(4 + r) + (2*e^2*x^(2*r))/(2 + r))*Log[c*x^n]))/16","A",1
381,1,116,102,0.2397611,"\int x \left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x*(d + e*x^r)^2*(a + b*Log[c*x^n]),x]","\frac{1}{4} x^2 \left(2 a \left(d^2+\frac{4 d e x^r}{r+2}+\frac{e^2 x^{2 r}}{r+1}\right)+2 b \log \left(c x^n\right) \left(d^2+\frac{4 d e x^r}{r+2}+\frac{e^2 x^{2 r}}{r+1}\right)+b n \left(-d^2-\frac{8 d e x^r}{(r+2)^2}-\frac{e^2 x^{2 r}}{(r+1)^2}\right)\right)","\frac{1}{2} \left(d^2 x^2+\frac{4 d e x^{r+2}}{r+2}+\frac{e^2 x^{2 (r+1)}}{r+1}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b d^2 n x^2-\frac{2 b d e n x^{r+2}}{(r+2)^2}-\frac{b e^2 n x^{2 (r+1)}}{4 (r+1)^2}",1,"(x^2*(b*n*(-d^2 - (8*d*e*x^r)/(2 + r)^2 - (e^2*x^(2*r))/(1 + r)^2) + 2*a*(d^2 + (4*d*e*x^r)/(2 + r) + (e^2*x^(2*r))/(1 + r)) + 2*b*(d^2 + (4*d*e*x^r)/(2 + r) + (e^2*x^(2*r))/(1 + r))*Log[c*x^n]))/4","A",1
382,1,90,104,0.2158934,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[((d + e*x^r)^2*(a + b*Log[c*x^n]))/x,x]","\frac{1}{4} \left(\frac{e x^r \left(2 a r \left(4 d+e x^r\right)-b n \left(8 d+e x^r\right)\right)}{r^2}+4 a d^2 \log (x)+\frac{2 b d^2 \log ^2\left(c x^n\right)}{n}+\frac{2 b e x^r \log \left(c x^n\right) \left(4 d+e x^r\right)}{r}\right)","d^2 \log (x) \left(a+b \log \left(c x^n\right)\right)+\frac{2 d e x^r \left(a+b \log \left(c x^n\right)\right)}{r}+\frac{e^2 x^{2 r} \left(a+b \log \left(c x^n\right)\right)}{2 r}-\frac{1}{2} b d^2 n \log ^2(x)-\frac{2 b d e n x^r}{r^2}-\frac{b e^2 n x^{2 r}}{4 r^2}",1,"((e*x^r*(2*a*r*(4*d + e*x^r) - b*n*(8*d + e*x^r)))/r^2 + 4*a*d^2*Log[x] + (2*b*e*x^r*(4*d + e*x^r)*Log[c*x^n])/r + (2*b*d^2*Log[c*x^n]^2)/n)/4","A",1
383,1,120,135,0.3162297,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Integrate[((d + e*x^r)^2*(a + b*Log[c*x^n]))/x^3,x]","\frac{a \left(-2 d^2+\frac{8 d e x^r}{r-2}+\frac{2 e^2 x^{2 r}}{r-1}\right)+2 b \log \left(c x^n\right) \left(-d^2+\frac{4 d e x^r}{r-2}+\frac{e^2 x^{2 r}}{r-1}\right)+b n \left(-d^2-\frac{8 d e x^r}{(r-2)^2}-\frac{e^2 x^{2 r}}{(r-1)^2}\right)}{4 x^2}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{2 d e x^{r-2} \left(a+b \log \left(c x^n\right)\right)}{2-r}-\frac{e^2 x^{-2 (1-r)} \left(a+b \log \left(c x^n\right)\right)}{2 (1-r)}-\frac{b d^2 n}{4 x^2}-\frac{2 b d e n x^{r-2}}{(2-r)^2}-\frac{b e^2 n x^{-2 (1-r)}}{4 (1-r)^2}",1,"(b*n*(-d^2 - (8*d*e*x^r)/(-2 + r)^2 - (e^2*x^(2*r))/(-1 + r)^2) + a*(-2*d^2 + (8*d*e*x^r)/(-2 + r) + (2*e^2*x^(2*r))/(-1 + r)) + 2*b*(-d^2 + (4*d*e*x^r)/(-2 + r) + (e^2*x^(2*r))/(-1 + r))*Log[c*x^n])/(4*x^2)","A",1
384,1,121,135,0.3155178,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^5} \, dx","Integrate[((d + e*x^r)^2*(a + b*Log[c*x^n]))/x^5,x]","\frac{a \left(-4 d^2+\frac{32 d e x^r}{r-4}+\frac{8 e^2 x^{2 r}}{r-2}\right)+4 b \log \left(c x^n\right) \left(-d^2+\frac{8 d e x^r}{r-4}+\frac{2 e^2 x^{2 r}}{r-2}\right)+b n \left(-d^2-\frac{32 d e x^r}{(r-4)^2}-\frac{4 e^2 x^{2 r}}{(r-2)^2}\right)}{16 x^4}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{4 x^4}-\frac{2 d e x^{r-4} \left(a+b \log \left(c x^n\right)\right)}{4-r}-\frac{e^2 x^{-2 (2-r)} \left(a+b \log \left(c x^n\right)\right)}{2 (2-r)}-\frac{b d^2 n}{16 x^4}-\frac{2 b d e n x^{r-4}}{(4-r)^2}-\frac{b e^2 n x^{-2 (2-r)}}{4 (2-r)^2}",1,"(b*n*(-d^2 - (32*d*e*x^r)/(-4 + r)^2 - (4*e^2*x^(2*r))/(-2 + r)^2) + a*(-4*d^2 + (32*d*e*x^r)/(-4 + r) + (8*e^2*x^(2*r))/(-2 + r)) + 4*b*(-d^2 + (8*d*e*x^r)/(-4 + r) + (2*e^2*x^(2*r))/(-2 + r))*Log[c*x^n])/(16*x^4)","A",1
385,1,124,105,0.2616101,"\int x^4 \left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^4*(d + e*x^r)^2*(a + b*Log[c*x^n]),x]","\frac{1}{25} x^5 \left(5 a \left(d^2+\frac{10 d e x^r}{r+5}+\frac{5 e^2 x^{2 r}}{2 r+5}\right)+5 b \log \left(c x^n\right) \left(d^2+\frac{10 d e x^r}{r+5}+\frac{5 e^2 x^{2 r}}{2 r+5}\right)+b n \left(-d^2-\frac{50 d e x^r}{(r+5)^2}-\frac{25 e^2 x^{2 r}}{(2 r+5)^2}\right)\right)","\frac{1}{5} \left(d^2 x^5+\frac{10 d e x^{r+5}}{r+5}+\frac{5 e^2 x^{2 r+5}}{2 r+5}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{25} b d^2 n x^5-\frac{2 b d e n x^{r+5}}{(r+5)^2}-\frac{b e^2 n x^{2 r+5}}{(2 r+5)^2}",1,"(x^5*(b*n*(-d^2 - (50*d*e*x^r)/(5 + r)^2 - (25*e^2*x^(2*r))/(5 + 2*r)^2) + 5*a*(d^2 + (10*d*e*x^r)/(5 + r) + (5*e^2*x^(2*r))/(5 + 2*r)) + 5*b*(d^2 + (10*d*e*x^r)/(5 + r) + (5*e^2*x^(2*r))/(5 + 2*r))*Log[c*x^n]))/25","A",1
386,1,124,105,0.2667319,"\int x^2 \left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^2*(d + e*x^r)^2*(a + b*Log[c*x^n]),x]","\frac{1}{9} x^3 \left(3 a \left(d^2+\frac{6 d e x^r}{r+3}+\frac{3 e^2 x^{2 r}}{2 r+3}\right)+3 b \log \left(c x^n\right) \left(d^2+\frac{6 d e x^r}{r+3}+\frac{3 e^2 x^{2 r}}{2 r+3}\right)+b n \left(-d^2-\frac{18 d e x^r}{(r+3)^2}-\frac{9 e^2 x^{2 r}}{(2 r+3)^2}\right)\right)","\frac{1}{3} \left(d^2 x^3+\frac{6 d e x^{r+3}}{r+3}+\frac{3 e^2 x^{2 r+3}}{2 r+3}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b d^2 n x^3-\frac{2 b d e n x^{r+3}}{(r+3)^2}-\frac{b e^2 n x^{2 r+3}}{(2 r+3)^2}",1,"(x^3*(b*n*(-d^2 - (18*d*e*x^r)/(3 + r)^2 - (9*e^2*x^(2*r))/(3 + 2*r)^2) + 3*a*(d^2 + (6*d*e*x^r)/(3 + r) + (3*e^2*x^(2*r))/(3 + 2*r)) + 3*b*(d^2 + (6*d*e*x^r)/(3 + r) + (3*e^2*x^(2*r))/(3 + 2*r))*Log[c*x^n]))/9","A",1
387,1,107,113,0.1673189,"\int \left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(d + e*x^r)^2*(a + b*Log[c*x^n]),x]","x \left(\frac{2 d e x^r \left(a+b \log \left(c x^n\right)\right)}{r+1}+\frac{e^2 x^{2 r} \left(a+b \log \left(c x^n\right)\right)}{2 r+1}+a d^2+b d^2 \log \left(c x^n\right)-b d^2 n-\frac{2 b d e n x^r}{(r+1)^2}-\frac{b e^2 n x^{2 r}}{(2 r+1)^2}\right)","d^2 x \left(a+b \log \left(c x^n\right)\right)+\frac{2 d e x^{r+1} \left(a+b \log \left(c x^n\right)\right)}{r+1}+\frac{e^2 x^{2 r+1} \left(a+b \log \left(c x^n\right)\right)}{2 r+1}-b d^2 n x-\frac{2 b d e n x^{r+1}}{(r+1)^2}-\frac{b e^2 n x^{2 r+1}}{(2 r+1)^2}",1,"x*(a*d^2 - b*d^2*n - (2*b*d*e*n*x^r)/(1 + r)^2 - (b*e^2*n*x^(2*r))/(1 + 2*r)^2 + b*d^2*Log[c*x^n] + (2*d*e*x^r*(a + b*Log[c*x^n]))/(1 + r) + (e^2*x^(2*r)*(a + b*Log[c*x^n]))/(1 + 2*r))","A",1
388,1,121,123,0.2994146,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Integrate[((d + e*x^r)^2*(a + b*Log[c*x^n]))/x^2,x]","\frac{a \left(-d^2+\frac{2 d e x^r}{r-1}+\frac{e^2 x^{2 r}}{2 r-1}\right)+b \log \left(c x^n\right) \left(-d^2+\frac{2 d e x^r}{r-1}+\frac{e^2 x^{2 r}}{2 r-1}\right)+b n \left(-d^2-\frac{2 d e x^r}{(r-1)^2}-\frac{e^2 x^{2 r}}{(1-2 r)^2}\right)}{x}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{2 d e x^{r-1} \left(a+b \log \left(c x^n\right)\right)}{1-r}-\frac{e^2 x^{2 r-1} \left(a+b \log \left(c x^n\right)\right)}{1-2 r}-\frac{b d^2 n}{x}-\frac{2 b d e n x^{r-1}}{(1-r)^2}-\frac{b e^2 n x^{2 r-1}}{(1-2 r)^2}",1,"(b*n*(-d^2 - (2*d*e*x^r)/(-1 + r)^2 - (e^2*x^(2*r))/(1 - 2*r)^2) + a*(-d^2 + (2*d*e*x^r)/(-1 + r) + (e^2*x^(2*r))/(-1 + 2*r)) + b*(-d^2 + (2*d*e*x^r)/(-1 + r) + (e^2*x^(2*r))/(-1 + 2*r))*Log[c*x^n])/x","A",1
389,1,127,127,0.3106295,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Integrate[((d + e*x^r)^2*(a + b*Log[c*x^n]))/x^4,x]","\frac{a \left(-3 d^2+\frac{18 d e x^r}{r-3}+\frac{9 e^2 x^{2 r}}{2 r-3}\right)+3 b \log \left(c x^n\right) \left(-d^2+\frac{6 d e x^r}{r-3}+\frac{3 e^2 x^{2 r}}{2 r-3}\right)+b n \left(-d^2-\frac{18 d e x^r}{(r-3)^2}-\frac{9 e^2 x^{2 r}}{(3-2 r)^2}\right)}{9 x^3}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{2 d e x^{r-3} \left(a+b \log \left(c x^n\right)\right)}{3-r}-\frac{e^2 x^{2 r-3} \left(a+b \log \left(c x^n\right)\right)}{3-2 r}-\frac{b d^2 n}{9 x^3}-\frac{2 b d e n x^{r-3}}{(3-r)^2}-\frac{b e^2 n x^{2 r-3}}{(3-2 r)^2}",1,"(b*n*(-d^2 - (18*d*e*x^r)/(-3 + r)^2 - (9*e^2*x^(2*r))/(3 - 2*r)^2) + a*(-3*d^2 + (18*d*e*x^r)/(-3 + r) + (9*e^2*x^(2*r))/(-3 + 2*r)) + 3*b*(-d^2 + (6*d*e*x^r)/(-3 + r) + (3*e^2*x^(2*r))/(-3 + 2*r))*Log[c*x^n])/(9*x^3)","A",1
390,1,127,127,0.3128144,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Integrate[((d + e*x^r)^2*(a + b*Log[c*x^n]))/x^6,x]","\frac{a \left(-5 d^2+\frac{50 d e x^r}{r-5}+\frac{25 e^2 x^{2 r}}{2 r-5}\right)+5 b \log \left(c x^n\right) \left(-d^2+\frac{10 d e x^r}{r-5}+\frac{5 e^2 x^{2 r}}{2 r-5}\right)+b n \left(-d^2-\frac{50 d e x^r}{(r-5)^2}-\frac{25 e^2 x^{2 r}}{(5-2 r)^2}\right)}{25 x^5}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{2 d e x^{r-5} \left(a+b \log \left(c x^n\right)\right)}{5-r}-\frac{e^2 x^{2 r-5} \left(a+b \log \left(c x^n\right)\right)}{5-2 r}-\frac{b d^2 n}{25 x^5}-\frac{2 b d e n x^{r-5}}{(5-r)^2}-\frac{b e^2 n x^{2 r-5}}{(5-2 r)^2}",1,"(b*n*(-d^2 - (50*d*e*x^r)/(-5 + r)^2 - (25*e^2*x^(2*r))/(5 - 2*r)^2) + a*(-5*d^2 + (50*d*e*x^r)/(-5 + r) + (25*e^2*x^(2*r))/(-5 + 2*r)) + 5*b*(-d^2 + (10*d*e*x^r)/(-5 + r) + (5*e^2*x^(2*r))/(-5 + 2*r))*Log[c*x^n])/(25*x^5)","A",1
391,1,127,127,0.3027633,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^8} \, dx","Integrate[((d + e*x^r)^2*(a + b*Log[c*x^n]))/x^8,x]","\frac{a \left(-7 d^2+\frac{98 d e x^r}{r-7}+\frac{49 e^2 x^{2 r}}{2 r-7}\right)+7 b \log \left(c x^n\right) \left(-d^2+\frac{14 d e x^r}{r-7}+\frac{7 e^2 x^{2 r}}{2 r-7}\right)+b n \left(-d^2-\frac{98 d e x^r}{(r-7)^2}-\frac{49 e^2 x^{2 r}}{(7-2 r)^2}\right)}{49 x^7}","-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{7 x^7}-\frac{2 d e x^{r-7} \left(a+b \log \left(c x^n\right)\right)}{7-r}-\frac{e^2 x^{2 r-7} \left(a+b \log \left(c x^n\right)\right)}{7-2 r}-\frac{b d^2 n}{49 x^7}-\frac{2 b d e n x^{r-7}}{(7-r)^2}-\frac{b e^2 n x^{2 r-7}}{(7-2 r)^2}",1,"(b*n*(-d^2 - (98*d*e*x^r)/(-7 + r)^2 - (49*e^2*x^(2*r))/(7 - 2*r)^2) + a*(-7*d^2 + (98*d*e*x^r)/(-7 + r) + (49*e^2*x^(2*r))/(-7 + 2*r)) + 7*b*(-d^2 + (14*d*e*x^r)/(-7 + r) + (7*e^2*x^(2*r))/(-7 + 2*r))*Log[c*x^n])/(49*x^7)","A",1
392,1,172,147,0.3900019,"\int x^5 \left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^5*(d + e*x^r)^3*(a + b*Log[c*x^n]),x]","\frac{1}{36} x^6 \left(6 a \left(d^3+\frac{18 d^2 e x^r}{r+6}+\frac{9 d e^2 x^{2 r}}{r+3}+\frac{2 e^3 x^{3 r}}{r+2}\right)+6 b \log \left(c x^n\right) \left(d^3+\frac{18 d^2 e x^r}{r+6}+\frac{9 d e^2 x^{2 r}}{r+3}+\frac{2 e^3 x^{3 r}}{r+2}\right)+b n \left(-d^3-\frac{108 d^2 e x^r}{(r+6)^2}-\frac{27 d e^2 x^{2 r}}{(r+3)^2}-\frac{4 e^3 x^{3 r}}{(r+2)^2}\right)\right)","\frac{1}{6} \left(d^3 x^6+\frac{18 d^2 e x^{r+6}}{r+6}+\frac{9 d e^2 x^{2 (r+3)}}{r+3}+\frac{2 e^3 x^{3 (r+2)}}{r+2}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{36} b d^3 n x^6-\frac{3 b d^2 e n x^{r+6}}{(r+6)^2}-\frac{3 b d e^2 n x^{2 (r+3)}}{4 (r+3)^2}-\frac{b e^3 n x^{3 (r+2)}}{9 (r+2)^2}",1,"(x^6*(b*n*(-d^3 - (108*d^2*e*x^r)/(6 + r)^2 - (27*d*e^2*x^(2*r))/(3 + r)^2 - (4*e^3*x^(3*r))/(2 + r)^2) + 6*a*(d^3 + (18*d^2*e*x^r)/(6 + r) + (9*d*e^2*x^(2*r))/(3 + r) + (2*e^3*x^(3*r))/(2 + r)) + 6*b*(d^3 + (18*d^2*e*x^r)/(6 + r) + (9*d*e^2*x^(2*r))/(3 + r) + (2*e^3*x^(3*r))/(2 + r))*Log[c*x^n]))/36","A",1
393,1,178,149,0.3573533,"\int x^3 \left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^3*(d + e*x^r)^3*(a + b*Log[c*x^n]),x]","\frac{1}{16} x^4 \left(4 a \left(d^3+\frac{12 d^2 e x^r}{r+4}+\frac{6 d e^2 x^{2 r}}{r+2}+\frac{4 e^3 x^{3 r}}{3 r+4}\right)+4 b \log \left(c x^n\right) \left(d^3+\frac{12 d^2 e x^r}{r+4}+\frac{6 d e^2 x^{2 r}}{r+2}+\frac{4 e^3 x^{3 r}}{3 r+4}\right)+b n \left(-d^3-\frac{48 d^2 e x^r}{(r+4)^2}-\frac{12 d e^2 x^{2 r}}{(r+2)^2}-\frac{16 e^3 x^{3 r}}{(3 r+4)^2}\right)\right)","\frac{1}{4} \left(d^3 x^4+\frac{12 d^2 e x^{r+4}}{r+4}+\frac{6 d e^2 x^{2 (r+2)}}{r+2}+\frac{4 e^3 x^{3 r+4}}{3 r+4}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{16} b d^3 n x^4-\frac{3 b d^2 e n x^{r+4}}{(r+4)^2}-\frac{3 b d e^2 n x^{2 (r+2)}}{4 (r+2)^2}-\frac{b e^3 n x^{3 r+4}}{(3 r+4)^2}",1,"(x^4*(b*n*(-d^3 - (48*d^2*e*x^r)/(4 + r)^2 - (12*d*e^2*x^(2*r))/(2 + r)^2 - (16*e^3*x^(3*r))/(4 + 3*r)^2) + 4*a*(d^3 + (12*d^2*e*x^r)/(4 + r) + (6*d*e^2*x^(2*r))/(2 + r) + (4*e^3*x^(3*r))/(4 + 3*r)) + 4*b*(d^3 + (12*d^2*e*x^r)/(4 + r) + (6*d*e^2*x^(2*r))/(2 + r) + (4*e^3*x^(3*r))/(4 + 3*r))*Log[c*x^n]))/16","A",1
394,1,178,149,0.36041,"\int x \left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x*(d + e*x^r)^3*(a + b*Log[c*x^n]),x]","\frac{1}{4} x^2 \left(2 a \left(d^3+\frac{6 d^2 e x^r}{r+2}+\frac{3 d e^2 x^{2 r}}{r+1}+\frac{2 e^3 x^{3 r}}{3 r+2}\right)+2 b \log \left(c x^n\right) \left(d^3+\frac{6 d^2 e x^r}{r+2}+\frac{3 d e^2 x^{2 r}}{r+1}+\frac{2 e^3 x^{3 r}}{3 r+2}\right)+b n \left(-d^3-\frac{12 d^2 e x^r}{(r+2)^2}-\frac{3 d e^2 x^{2 r}}{(r+1)^2}-\frac{4 e^3 x^{3 r}}{(3 r+2)^2}\right)\right)","\frac{1}{2} \left(d^3 x^2+\frac{6 d^2 e x^{r+2}}{r+2}+\frac{3 d e^2 x^{2 (r+1)}}{r+1}+\frac{2 e^3 x^{3 r+2}}{3 r+2}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b d^3 n x^2-\frac{3 b d^2 e n x^{r+2}}{(r+2)^2}-\frac{3 b d e^2 n x^{2 (r+1)}}{4 (r+1)^2}-\frac{b e^3 n x^{3 r+2}}{(3 r+2)^2}",1,"(x^2*(b*n*(-d^3 - (12*d^2*e*x^r)/(2 + r)^2 - (3*d*e^2*x^(2*r))/(1 + r)^2 - (4*e^3*x^(3*r))/(2 + 3*r)^2) + 2*a*(d^3 + (6*d^2*e*x^r)/(2 + r) + (3*d*e^2*x^(2*r))/(1 + r) + (2*e^3*x^(3*r))/(2 + 3*r)) + 2*b*(d^3 + (6*d^2*e*x^r)/(2 + r) + (3*d*e^2*x^(2*r))/(1 + r) + (2*e^3*x^(3*r))/(2 + 3*r))*Log[c*x^n]))/4","A",1
395,1,132,152,0.373779,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x,x]","\frac{1}{36} \left(\frac{e x^r \left(6 a r \left(18 d^2+9 d e x^r+2 e^2 x^{2 r}\right)-b n \left(108 d^2+27 d e x^r+4 e^2 x^{2 r}\right)\right)}{r^2}+\frac{18 b d^3 \log ^2\left(c x^n\right)}{n}+\frac{6 b e x^r \log \left(c x^n\right) \left(18 d^2+9 d e x^r+2 e^2 x^{2 r}\right)}{r}\right)+a d^3 \log (x)","d^3 \log (x) \left(a+b \log \left(c x^n\right)\right)+\frac{3 d^2 e x^r \left(a+b \log \left(c x^n\right)\right)}{r}+\frac{3 d e^2 x^{2 r} \left(a+b \log \left(c x^n\right)\right)}{2 r}+\frac{e^3 x^{3 r} \left(a+b \log \left(c x^n\right)\right)}{3 r}-\frac{1}{2} b d^3 n \log ^2(x)-\frac{3 b d^2 e n x^r}{r^2}-\frac{3 b d e^2 n x^{2 r}}{4 r^2}-\frac{b e^3 n x^{3 r}}{9 r^2}",1,"a*d^3*Log[x] + ((e*x^r*(6*a*r*(18*d^2 + 9*d*e*x^r + 2*e^2*x^(2*r)) - b*n*(108*d^2 + 27*d*e*x^r + 4*e^2*x^(2*r))))/r^2 + (6*b*e*x^r*(18*d^2 + 9*d*e*x^r + 2*e^2*x^(2*r))*Log[c*x^n])/r + (18*b*d^3*Log[c*x^n]^2)/n)/36","A",1
396,1,181,191,0.419153,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Integrate[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x^3,x]","\frac{a \left(-2 d^3+\frac{12 d^2 e x^r}{r-2}+\frac{6 d e^2 x^{2 r}}{r-1}+\frac{4 e^3 x^{3 r}}{3 r-2}\right)+2 b \log \left(c x^n\right) \left(-d^3+\frac{6 d^2 e x^r}{r-2}+\frac{3 d e^2 x^{2 r}}{r-1}+\frac{2 e^3 x^{3 r}}{3 r-2}\right)+b n \left(-d^3-\frac{12 d^2 e x^r}{(r-2)^2}-\frac{3 d e^2 x^{2 r}}{(r-1)^2}-\frac{4 e^3 x^{3 r}}{(2-3 r)^2}\right)}{4 x^2}","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{3 d^2 e x^{r-2} \left(a+b \log \left(c x^n\right)\right)}{2-r}-\frac{3 d e^2 x^{-2 (1-r)} \left(a+b \log \left(c x^n\right)\right)}{2 (1-r)}-\frac{e^3 x^{3 r-2} \left(a+b \log \left(c x^n\right)\right)}{2-3 r}-\frac{b d^3 n}{4 x^2}-\frac{3 b d^2 e n x^{r-2}}{(2-r)^2}-\frac{3 b d e^2 n x^{-2 (1-r)}}{4 (1-r)^2}-\frac{b e^3 n x^{3 r-2}}{(2-3 r)^2}",1,"(b*n*(-d^3 - (12*d^2*e*x^r)/(-2 + r)^2 - (3*d*e^2*x^(2*r))/(-1 + r)^2 - (4*e^3*x^(3*r))/(2 - 3*r)^2) + a*(-2*d^3 + (12*d^2*e*x^r)/(-2 + r) + (6*d*e^2*x^(2*r))/(-1 + r) + (4*e^3*x^(3*r))/(-2 + 3*r)) + 2*b*(-d^3 + (6*d^2*e*x^r)/(-2 + r) + (3*d*e^2*x^(2*r))/(-1 + r) + (2*e^3*x^(3*r))/(-2 + 3*r))*Log[c*x^n])/(4*x^2)","A",1
397,1,181,191,0.4127569,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^5} \, dx","Integrate[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x^5,x]","\frac{a \left(-4 d^3+\frac{48 d^2 e x^r}{r-4}+\frac{24 d e^2 x^{2 r}}{r-2}+\frac{16 e^3 x^{3 r}}{3 r-4}\right)+4 b \log \left(c x^n\right) \left(-d^3+\frac{12 d^2 e x^r}{r-4}+\frac{6 d e^2 x^{2 r}}{r-2}+\frac{4 e^3 x^{3 r}}{3 r-4}\right)+b n \left(-d^3-\frac{48 d^2 e x^r}{(r-4)^2}-\frac{12 d e^2 x^{2 r}}{(r-2)^2}-\frac{16 e^3 x^{3 r}}{(4-3 r)^2}\right)}{16 x^4}","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{4 x^4}-\frac{3 d^2 e x^{r-4} \left(a+b \log \left(c x^n\right)\right)}{4-r}-\frac{3 d e^2 x^{-2 (2-r)} \left(a+b \log \left(c x^n\right)\right)}{2 (2-r)}-\frac{e^3 x^{3 r-4} \left(a+b \log \left(c x^n\right)\right)}{4-3 r}-\frac{b d^3 n}{16 x^4}-\frac{3 b d^2 e n x^{r-4}}{(4-r)^2}-\frac{3 b d e^2 n x^{-2 (2-r)}}{4 (2-r)^2}-\frac{b e^3 n x^{3 r-4}}{(4-3 r)^2}",1,"(b*n*(-d^3 - (48*d^2*e*x^r)/(-4 + r)^2 - (12*d*e^2*x^(2*r))/(-2 + r)^2 - (16*e^3*x^(3*r))/(4 - 3*r)^2) + a*(-4*d^3 + (48*d^2*e*x^r)/(-4 + r) + (24*d*e^2*x^(2*r))/(-2 + r) + (16*e^3*x^(3*r))/(-4 + 3*r)) + 4*b*(-d^3 + (12*d^2*e*x^r)/(-4 + r) + (6*d*e^2*x^(2*r))/(-2 + r) + (4*e^3*x^(3*r))/(-4 + 3*r))*Log[c*x^n])/(16*x^4)","A",1
398,1,184,151,0.3668653,"\int x^4 \left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^4*(d + e*x^r)^3*(a + b*Log[c*x^n]),x]","\frac{1}{25} x^5 \left(5 a \left(d^3+\frac{15 d^2 e x^r}{r+5}+\frac{15 d e^2 x^{2 r}}{2 r+5}+\frac{5 e^3 x^{3 r}}{3 r+5}\right)+5 b \log \left(c x^n\right) \left(d^3+\frac{15 d^2 e x^r}{r+5}+\frac{15 d e^2 x^{2 r}}{2 r+5}+\frac{5 e^3 x^{3 r}}{3 r+5}\right)+b n \left(-d^3-\frac{75 d^2 e x^r}{(r+5)^2}-\frac{75 d e^2 x^{2 r}}{(2 r+5)^2}-\frac{25 e^3 x^{3 r}}{(3 r+5)^2}\right)\right)","\frac{1}{5} \left(d^3 x^5+\frac{15 d^2 e x^{r+5}}{r+5}+\frac{15 d e^2 x^{2 r+5}}{2 r+5}+\frac{5 e^3 x^{3 r+5}}{3 r+5}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{25} b d^3 n x^5-\frac{3 b d^2 e n x^{r+5}}{(r+5)^2}-\frac{3 b d e^2 n x^{2 r+5}}{(2 r+5)^2}-\frac{b e^3 n x^{3 r+5}}{(3 r+5)^2}",1,"(x^5*(b*n*(-d^3 - (75*d^2*e*x^r)/(5 + r)^2 - (75*d*e^2*x^(2*r))/(5 + 2*r)^2 - (25*e^3*x^(3*r))/(5 + 3*r)^2) + 5*a*(d^3 + (15*d^2*e*x^r)/(5 + r) + (15*d*e^2*x^(2*r))/(5 + 2*r) + (5*e^3*x^(3*r))/(5 + 3*r)) + 5*b*(d^3 + (15*d^2*e*x^r)/(5 + r) + (15*d*e^2*x^(2*r))/(5 + 2*r) + (5*e^3*x^(3*r))/(5 + 3*r))*Log[c*x^n]))/25","A",1
399,1,176,148,0.357401,"\int x^2 \left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^2*(d + e*x^r)^3*(a + b*Log[c*x^n]),x]","\frac{1}{9} x^3 \left(3 a \left(d^3+\frac{9 d^2 e x^r}{r+3}+\frac{9 d e^2 x^{2 r}}{2 r+3}+\frac{e^3 x^{3 r}}{r+1}\right)+3 b \log \left(c x^n\right) \left(d^3+\frac{9 d^2 e x^r}{r+3}+\frac{9 d e^2 x^{2 r}}{2 r+3}+\frac{e^3 x^{3 r}}{r+1}\right)+b n \left(-d^3-\frac{27 d^2 e x^r}{(r+3)^2}-\frac{27 d e^2 x^{2 r}}{(2 r+3)^2}-\frac{e^3 x^{3 r}}{(r+1)^2}\right)\right)","\frac{1}{3} \left(d^3 x^3+\frac{9 d^2 e x^{r+3}}{r+3}+\frac{9 d e^2 x^{2 r+3}}{2 r+3}+\frac{e^3 x^{3 (r+1)}}{r+1}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b d^3 n x^3-\frac{3 b d^2 e n x^{r+3}}{(r+3)^2}-\frac{3 b d e^2 n x^{2 r+3}}{(2 r+3)^2}-\frac{b e^3 n x^{3 (r+1)}}{9 (r+1)^2}",1,"(x^3*(b*n*(-d^3 - (27*d^2*e*x^r)/(3 + r)^2 - (27*d*e^2*x^(2*r))/(3 + 2*r)^2 - (e^3*x^(3*r))/(1 + r)^2) + 3*a*(d^3 + (9*d^2*e*x^r)/(3 + r) + (9*d*e^2*x^(2*r))/(3 + 2*r) + (e^3*x^(3*r))/(1 + r)) + 3*b*(d^3 + (9*d^2*e*x^r)/(3 + r) + (9*d*e^2*x^(2*r))/(3 + 2*r) + (e^3*x^(3*r))/(1 + r))*Log[c*x^n]))/9","A",1
400,1,159,169,0.2364884,"\int \left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(d + e*x^r)^3*(a + b*Log[c*x^n]),x]","x \left(\frac{3 d^2 e x^r \left(a+b \log \left(c x^n\right)\right)}{r+1}+\frac{3 d e^2 x^{2 r} \left(a+b \log \left(c x^n\right)\right)}{2 r+1}+\frac{e^3 x^{3 r} \left(a+b \log \left(c x^n\right)\right)}{3 r+1}+a d^3+b d^3 \log \left(c x^n\right)-b d^3 n-\frac{3 b d^2 e n x^r}{(r+1)^2}-\frac{3 b d e^2 n x^{2 r}}{(2 r+1)^2}-\frac{b e^3 n x^{3 r}}{(3 r+1)^2}\right)","d^3 x \left(a+b \log \left(c x^n\right)\right)+\frac{3 d^2 e x^{r+1} \left(a+b \log \left(c x^n\right)\right)}{r+1}+\frac{3 d e^2 x^{2 r+1} \left(a+b \log \left(c x^n\right)\right)}{2 r+1}+\frac{e^3 x^{3 r+1} \left(a+b \log \left(c x^n\right)\right)}{3 r+1}-b d^3 n x-\frac{3 b d^2 e n x^{r+1}}{(r+1)^2}-\frac{3 b d e^2 n x^{2 r+1}}{(2 r+1)^2}-\frac{b e^3 n x^{3 r+1}}{(3 r+1)^2}",1,"x*(a*d^3 - b*d^3*n - (3*b*d^2*e*n*x^r)/(1 + r)^2 - (3*b*d*e^2*n*x^(2*r))/(1 + 2*r)^2 - (b*e^3*n*x^(3*r))/(1 + 3*r)^2 + b*d^3*Log[c*x^n] + (3*d^2*e*x^r*(a + b*Log[c*x^n]))/(1 + r) + (3*d*e^2*x^(2*r)*(a + b*Log[c*x^n]))/(1 + 2*r) + (e^3*x^(3*r)*(a + b*Log[c*x^n]))/(1 + 3*r))","A",1
401,1,181,179,0.4157141,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Integrate[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x^2,x]","\frac{a \left(-d^3+\frac{3 d^2 e x^r}{r-1}+\frac{3 d e^2 x^{2 r}}{2 r-1}+\frac{e^3 x^{3 r}}{3 r-1}\right)+b \log \left(c x^n\right) \left(-d^3+\frac{3 d^2 e x^r}{r-1}+\frac{3 d e^2 x^{2 r}}{2 r-1}+\frac{e^3 x^{3 r}}{3 r-1}\right)+b n \left(-d^3-\frac{3 d^2 e x^r}{(r-1)^2}-\frac{3 d e^2 x^{2 r}}{(1-2 r)^2}-\frac{e^3 x^{3 r}}{(1-3 r)^2}\right)}{x}","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{3 d^2 e x^{r-1} \left(a+b \log \left(c x^n\right)\right)}{1-r}-\frac{3 d e^2 x^{2 r-1} \left(a+b \log \left(c x^n\right)\right)}{1-2 r}-\frac{e^3 x^{3 r-1} \left(a+b \log \left(c x^n\right)\right)}{1-3 r}-\frac{b d^3 n}{x}-\frac{3 b d^2 e n x^{r-1}}{(1-r)^2}-\frac{3 b d e^2 n x^{2 r-1}}{(1-2 r)^2}-\frac{b e^3 n x^{3 r-1}}{(1-3 r)^2}",1,"(b*n*(-d^3 - (3*d^2*e*x^r)/(-1 + r)^2 - (3*d*e^2*x^(2*r))/(1 - 2*r)^2 - (e^3*x^(3*r))/(1 - 3*r)^2) + a*(-d^3 + (3*d^2*e*x^r)/(-1 + r) + (3*d*e^2*x^(2*r))/(-1 + 2*r) + (e^3*x^(3*r))/(-1 + 3*r)) + b*(-d^3 + (3*d^2*e*x^r)/(-1 + r) + (3*d*e^2*x^(2*r))/(-1 + 2*r) + (e^3*x^(3*r))/(-1 + 3*r))*Log[c*x^n])/x","A",1
402,1,180,191,0.3943649,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Integrate[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x^4,x]","\frac{3 a \left(-d^3+\frac{9 d^2 e x^r}{r-3}+\frac{9 d e^2 x^{2 r}}{2 r-3}+\frac{e^3 x^{3 r}}{r-1}\right)+3 b \log \left(c x^n\right) \left(-d^3+\frac{9 d^2 e x^r}{r-3}+\frac{9 d e^2 x^{2 r}}{2 r-3}+\frac{e^3 x^{3 r}}{r-1}\right)+b n \left(-d^3-\frac{27 d^2 e x^r}{(r-3)^2}-\frac{27 d e^2 x^{2 r}}{(3-2 r)^2}-\frac{e^3 x^{3 r}}{(r-1)^2}\right)}{9 x^3}","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{3 d^2 e x^{r-3} \left(a+b \log \left(c x^n\right)\right)}{3-r}-\frac{3 d e^2 x^{2 r-3} \left(a+b \log \left(c x^n\right)\right)}{3-2 r}-\frac{e^3 x^{-3 (1-r)} \left(a+b \log \left(c x^n\right)\right)}{3 (1-r)}-\frac{b d^3 n}{9 x^3}-\frac{3 b d^2 e n x^{r-3}}{(3-r)^2}-\frac{3 b d e^2 n x^{2 r-3}}{(3-2 r)^2}-\frac{b e^3 n x^{-3 (1-r)}}{9 (1-r)^2}",1,"(b*n*(-d^3 - (27*d^2*e*x^r)/(-3 + r)^2 - (27*d*e^2*x^(2*r))/(3 - 2*r)^2 - (e^3*x^(3*r))/(-1 + r)^2) + 3*a*(-d^3 + (9*d^2*e*x^r)/(-3 + r) + (9*d*e^2*x^(2*r))/(-3 + 2*r) + (e^3*x^(3*r))/(-1 + r)) + 3*b*(-d^3 + (9*d^2*e*x^r)/(-3 + r) + (9*d*e^2*x^(2*r))/(-3 + 2*r) + (e^3*x^(3*r))/(-1 + r))*Log[c*x^n])/(9*x^3)","A",1
403,1,187,183,0.4197137,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Integrate[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x^6,x]","\frac{a \left(-5 d^3+\frac{75 d^2 e x^r}{r-5}+\frac{75 d e^2 x^{2 r}}{2 r-5}+\frac{25 e^3 x^{3 r}}{3 r-5}\right)+5 b \log \left(c x^n\right) \left(-d^3+\frac{15 d^2 e x^r}{r-5}+\frac{15 d e^2 x^{2 r}}{2 r-5}+\frac{5 e^3 x^{3 r}}{3 r-5}\right)+b n \left(-d^3-\frac{75 d^2 e x^r}{(r-5)^2}-\frac{75 d e^2 x^{2 r}}{(5-2 r)^2}-\frac{25 e^3 x^{3 r}}{(5-3 r)^2}\right)}{25 x^5}","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{3 d^2 e x^{r-5} \left(a+b \log \left(c x^n\right)\right)}{5-r}-\frac{3 d e^2 x^{2 r-5} \left(a+b \log \left(c x^n\right)\right)}{5-2 r}-\frac{e^3 x^{3 r-5} \left(a+b \log \left(c x^n\right)\right)}{5-3 r}-\frac{b d^3 n}{25 x^5}-\frac{3 b d^2 e n x^{r-5}}{(5-r)^2}-\frac{3 b d e^2 n x^{2 r-5}}{(5-2 r)^2}-\frac{b e^3 n x^{3 r-5}}{(5-3 r)^2}",1,"(b*n*(-d^3 - (75*d^2*e*x^r)/(-5 + r)^2 - (75*d*e^2*x^(2*r))/(5 - 2*r)^2 - (25*e^3*x^(3*r))/(5 - 3*r)^2) + a*(-5*d^3 + (75*d^2*e*x^r)/(-5 + r) + (75*d*e^2*x^(2*r))/(-5 + 2*r) + (25*e^3*x^(3*r))/(-5 + 3*r)) + 5*b*(-d^3 + (15*d^2*e*x^r)/(-5 + r) + (15*d*e^2*x^(2*r))/(-5 + 2*r) + (5*e^3*x^(3*r))/(-5 + 3*r))*Log[c*x^n])/(25*x^5)","A",1
404,1,188,183,0.4109881,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^8} \, dx","Integrate[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x^8,x]","\frac{7 a \left(-d^3+\frac{21 d^2 e x^r}{r-7}+\frac{21 d e^2 x^{2 r}}{2 r-7}+\frac{7 e^3 x^{3 r}}{3 r-7}\right)+7 b \log \left(c x^n\right) \left(-d^3+\frac{21 d^2 e x^r}{r-7}+\frac{21 d e^2 x^{2 r}}{2 r-7}+\frac{7 e^3 x^{3 r}}{3 r-7}\right)+b n \left(-d^3-\frac{147 d^2 e x^r}{(r-7)^2}-\frac{147 d e^2 x^{2 r}}{(7-2 r)^2}-\frac{49 e^3 x^{3 r}}{(7-3 r)^2}\right)}{49 x^7}","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{7 x^7}-\frac{3 d^2 e x^{r-7} \left(a+b \log \left(c x^n\right)\right)}{7-r}-\frac{3 d e^2 x^{2 r-7} \left(a+b \log \left(c x^n\right)\right)}{7-2 r}-\frac{e^3 x^{3 r-7} \left(a+b \log \left(c x^n\right)\right)}{7-3 r}-\frac{b d^3 n}{49 x^7}-\frac{3 b d^2 e n x^{r-7}}{(7-r)^2}-\frac{3 b d e^2 n x^{2 r-7}}{(7-2 r)^2}-\frac{b e^3 n x^{3 r-7}}{(7-3 r)^2}",1,"(b*n*(-d^3 - (147*d^2*e*x^r)/(-7 + r)^2 - (147*d*e^2*x^(2*r))/(7 - 2*r)^2 - (49*e^3*x^(3*r))/(7 - 3*r)^2) + 7*a*(-d^3 + (21*d^2*e*x^r)/(-7 + r) + (21*d*e^2*x^(2*r))/(-7 + 2*r) + (7*e^3*x^(3*r))/(-7 + 3*r)) + 7*b*(-d^3 + (21*d^2*e*x^r)/(-7 + r) + (21*d*e^2*x^(2*r))/(-7 + 2*r) + (7*e^3*x^(3*r))/(-7 + 3*r))*Log[c*x^n])/(49*x^7)","A",1
405,1,182,191,0.4145408,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^{10}} \, dx","Integrate[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x^10,x]","\frac{9 a \left(-d^3+\frac{27 d^2 e x^r}{r-9}+\frac{27 d e^2 x^{2 r}}{2 r-9}+\frac{3 e^3 x^{3 r}}{r-3}\right)+9 b \log \left(c x^n\right) \left(-d^3+\frac{27 d^2 e x^r}{r-9}+\frac{27 d e^2 x^{2 r}}{2 r-9}+\frac{3 e^3 x^{3 r}}{r-3}\right)+b n \left(-d^3-\frac{243 d^2 e x^r}{(r-9)^2}-\frac{243 d e^2 x^{2 r}}{(9-2 r)^2}-\frac{9 e^3 x^{3 r}}{(r-3)^2}\right)}{81 x^9}","-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{9 x^9}-\frac{3 d^2 e x^{r-9} \left(a+b \log \left(c x^n\right)\right)}{9-r}-\frac{3 d e^2 x^{2 r-9} \left(a+b \log \left(c x^n\right)\right)}{9-2 r}-\frac{e^3 x^{-3 (3-r)} \left(a+b \log \left(c x^n\right)\right)}{3 (3-r)}-\frac{b d^3 n}{81 x^9}-\frac{3 b d^2 e n x^{r-9}}{(9-r)^2}-\frac{3 b d e^2 n x^{2 r-9}}{(9-2 r)^2}-\frac{b e^3 n x^{-3 (3-r)}}{9 (3-r)^2}",1,"(b*n*(-d^3 - (243*d^2*e*x^r)/(-9 + r)^2 - (243*d*e^2*x^(2*r))/(9 - 2*r)^2 - (9*e^3*x^(3*r))/(-3 + r)^2) + 9*a*(-d^3 + (27*d^2*e*x^r)/(-9 + r) + (27*d*e^2*x^(2*r))/(-9 + 2*r) + (3*e^3*x^(3*r))/(-3 + r)) + 9*b*(-d^3 + (27*d^2*e*x^r)/(-9 + r) + (27*d*e^2*x^(2*r))/(-9 + 2*r) + (3*e^3*x^(3*r))/(-3 + r))*Log[c*x^n])/(81*x^9)","A",1
406,1,87,26,0.1242224,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{d+e x^r} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/(d + e*x^r),x]","\frac{x^4 \left(4 \, _2F_1\left(1,\frac{4}{r};\frac{r+4}{r};-\frac{e x^r}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \, _3F_2\left(1,\frac{4}{r},\frac{4}{r};1+\frac{4}{r},1+\frac{4}{r};-\frac{e x^r}{d}\right)\right)}{16 d}","\text{Int}\left(\frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{d+e x^r},x\right)",0,"(x^4*(-(b*n*HypergeometricPFQ[{1, 4/r, 4/r}, {1 + 4/r, 1 + 4/r}, -((e*x^r)/d)]) + 4*Hypergeometric2F1[1, 4/r, (4 + r)/r, -((e*x^r)/d)]*(a + b*Log[c*x^n])))/(16*d)","B",0
407,1,87,24,0.1067022,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{d+e x^r} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/(d + e*x^r),x]","\frac{x^2 \left(2 \, _2F_1\left(1,\frac{2}{r};\frac{r+2}{r};-\frac{e x^r}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \, _3F_2\left(1,\frac{2}{r},\frac{2}{r};1+\frac{2}{r},1+\frac{2}{r};-\frac{e x^r}{d}\right)\right)}{4 d}","\text{Int}\left(\frac{x \left(a+b \log \left(c x^n\right)\right)}{d+e x^r},x\right)",0,"(x^2*(-(b*n*HypergeometricPFQ[{1, 2/r, 2/r}, {1 + 2/r, 1 + 2/r}, -((e*x^r)/d)]) + 2*Hypergeometric2F1[1, 2/r, (2 + r)/r, -((e*x^r)/d)]*(a + b*Log[c*x^n])))/(4*d)","B",0
408,1,108,54,0.1207526,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x^r)),x]","\frac{-2 r \log \left(d-d x^r\right) \left(a+b \log \left(c x^n\right)\right)+2 b n \text{Li}_2\left(\frac{e x^r}{d}+1\right)+2 b n r \log (x) \left(\log \left(d-d x^r\right)-\log \left(d+e x^r\right)\right)+2 b n \log \left(-\frac{e x^r}{d}\right) \log \left(d+e x^r\right)+b n r^2 \log ^2(x)}{2 d r^2}","\frac{b n \text{Li}_2\left(-\frac{d x^{-r}}{e}\right)}{d r^2}-\frac{\log \left(\frac{d x^{-r}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d r}",1,"(b*n*r^2*Log[x]^2 - 2*r*(a + b*Log[c*x^n])*Log[d - d*x^r] + 2*b*n*r*Log[x]*(Log[d - d*x^r] - Log[d + e*x^r]) + 2*b*n*Log[-((e*x^r)/d)]*Log[d + e*x^r] + 2*b*n*PolyLog[2, 1 + (e*x^r)/d])/(2*d*r^2)","A",0
409,1,86,26,0.1171407,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^r\right)} \, dx","Integrate[(a + b*Log[c*x^n])/(x^3*(d + e*x^r)),x]","-\frac{b n \, _3F_2\left(1,-\frac{2}{r},-\frac{2}{r};1-\frac{2}{r},1-\frac{2}{r};-\frac{e x^r}{d}\right)+2 \, _2F_1\left(1,-\frac{2}{r};\frac{r-2}{r};-\frac{e x^r}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{4 d x^2}","\text{Int}\left(\frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^r\right)},x\right)",0,"-1/4*(b*n*HypergeometricPFQ[{1, -2/r, -2/r}, {1 - 2/r, 1 - 2/r}, -((e*x^r)/d)] + 2*Hypergeometric2F1[1, -2/r, (-2 + r)/r, -((e*x^r)/d)]*(a + b*Log[c*x^n]))/(d*x^2)","B",0
410,1,87,26,0.1149664,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{d+e x^r} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e*x^r),x]","\frac{x^3 \left(3 \, _2F_1\left(1,\frac{3}{r};\frac{r+3}{r};-\frac{e x^r}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \, _3F_2\left(1,\frac{3}{r},\frac{3}{r};1+\frac{3}{r},1+\frac{3}{r};-\frac{e x^r}{d}\right)\right)}{9 d}","\text{Int}\left(\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{d+e x^r},x\right)",0,"(x^3*(-(b*n*HypergeometricPFQ[{1, 3/r, 3/r}, {1 + 3/r, 1 + 3/r}, -((e*x^r)/d)]) + 3*Hypergeometric2F1[1, 3/r, (3 + r)/r, -((e*x^r)/d)]*(a + b*Log[c*x^n])))/(9*d)","B",0
411,1,69,23,0.085968,"\int \frac{a+b \log \left(c x^n\right)}{d+e x^r} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*x^r),x]","\frac{x \left(\, _2F_1\left(1,\frac{1}{r};1+\frac{1}{r};-\frac{e x^r}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \, _3F_2\left(1,\frac{1}{r},\frac{1}{r};1+\frac{1}{r},1+\frac{1}{r};-\frac{e x^r}{d}\right)\right)}{d}","\text{Int}\left(\frac{a+b \log \left(c x^n\right)}{d+e x^r},x\right)",0,"(x*(-(b*n*HypergeometricPFQ[{1, r^(-1), r^(-1)}, {1 + r^(-1), 1 + r^(-1)}, -((e*x^r)/d)]) + Hypergeometric2F1[1, r^(-1), 1 + r^(-1), -((e*x^r)/d)]*(a + b*Log[c*x^n])))/d","B",0
412,1,83,26,0.1032557,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^r\right)} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*(d + e*x^r)),x]","-\frac{b n \, _3F_2\left(1,-\frac{1}{r},-\frac{1}{r};1-\frac{1}{r},1-\frac{1}{r};-\frac{e x^r}{d}\right)+\, _2F_1\left(1,-\frac{1}{r};\frac{r-1}{r};-\frac{e x^r}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d x}","\text{Int}\left(\frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^r\right)},x\right)",0,"-((b*n*HypergeometricPFQ[{1, -r^(-1), -r^(-1)}, {1 - r^(-1), 1 - r^(-1)}, -((e*x^r)/d)] + Hypergeometric2F1[1, -r^(-1), (-1 + r)/r, -((e*x^r)/d)]*(a + b*Log[c*x^n]))/(d*x))","B",0
413,1,140,26,0.261741,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^r\right)^2} \, dx","Integrate[(x^3*(a + b*Log[c*x^n]))/(d + e*x^r)^2,x]","\frac{x^4 \left(-b n (r-4) \left(d+e x^r\right) \, _3F_2\left(1,\frac{4}{r},\frac{4}{r};1+\frac{4}{r},1+\frac{4}{r};-\frac{e x^r}{d}\right)+4 \left(d+e x^r\right) \, _2F_1\left(1,\frac{4}{r};\frac{r+4}{r};-\frac{e x^r}{d}\right) \left(a (r-4)+b (r-4) \log \left(c x^n\right)-b n\right)+16 d \left(a+b \log \left(c x^n\right)\right)\right)}{16 d^2 r \left(d+e x^r\right)}","\text{Int}\left(\frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^r\right)^2},x\right)",0,"(x^4*(-(b*n*(-4 + r)*(d + e*x^r)*HypergeometricPFQ[{1, 4/r, 4/r}, {1 + 4/r, 1 + 4/r}, -((e*x^r)/d)]) + 16*d*(a + b*Log[c*x^n]) + 4*(d + e*x^r)*Hypergeometric2F1[1, 4/r, (4 + r)/r, -((e*x^r)/d)]*(-(b*n) + a*(-4 + r) + b*(-4 + r)*Log[c*x^n])))/(16*d^2*r*(d + e*x^r))","B",0
414,1,140,24,0.2394635,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^r\right)^2} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/(d + e*x^r)^2,x]","\frac{x^2 \left(-b n (r-2) \left(d+e x^r\right) \, _3F_2\left(1,\frac{2}{r},\frac{2}{r};1+\frac{2}{r},1+\frac{2}{r};-\frac{e x^r}{d}\right)+2 \left(d+e x^r\right) \, _2F_1\left(1,\frac{2}{r};\frac{r+2}{r};-\frac{e x^r}{d}\right) \left(a (r-2)+b (r-2) \log \left(c x^n\right)-b n\right)+4 d \left(a+b \log \left(c x^n\right)\right)\right)}{4 d^2 r \left(d+e x^r\right)}","\text{Int}\left(\frac{x \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^r\right)^2},x\right)",0,"(x^2*(-(b*n*(-2 + r)*(d + e*x^r)*HypergeometricPFQ[{1, 2/r, 2/r}, {1 + 2/r, 1 + 2/r}, -((e*x^r)/d)]) + 4*d*(a + b*Log[c*x^n]) + 2*(d + e*x^r)*Hypergeometric2F1[1, 2/r, (2 + r)/r, -((e*x^r)/d)]*(-(b*n) + a*(-2 + r) + b*(-2 + r)*Log[c*x^n])))/(4*d^2*r*(d + e*x^r))","B",0
415,1,132,102,0.3766843,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x^r)^2),x]","\frac{\frac{d r \left(a+b \log \left(c x^n\right)\right)}{d+e x^r}-a r \log \left(d-d x^r\right)+b r \left(n \log (x)-\log \left(c x^n\right)\right) \log \left(d-d x^r\right)+b n \left(\text{Li}_2\left(\frac{e x^r}{d}+1\right)+\left(\log \left(-\frac{e x^r}{d}\right)-r \log (x)\right) \log \left(d+e x^r\right)+\frac{1}{2} r^2 \log ^2(x)\right)+b n \log \left(d-d x^r\right)}{d^2 r^2}","-\frac{\log \left(\frac{d x^{-r}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 r}-\frac{e x^r \left(a+b \log \left(c x^n\right)\right)}{d^2 r \left(d+e x^r\right)}+\frac{b n \text{Li}_2\left(-\frac{d x^{-r}}{e}\right)}{d^2 r^2}+\frac{b n \log \left(d+e x^r\right)}{d^2 r^2}",1,"((d*r*(a + b*Log[c*x^n]))/(d + e*x^r) + b*n*Log[d - d*x^r] - a*r*Log[d - d*x^r] + b*r*(n*Log[x] - Log[c*x^n])*Log[d - d*x^r] + b*n*((r^2*Log[x]^2)/2 + (-(r*Log[x]) + Log[-((e*x^r)/d)])*Log[d + e*x^r] + PolyLog[2, 1 + (e*x^r)/d]))/(d^2*r^2)","A",0
416,1,205,26,3.1600605,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^r\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])/(x^3*(d + e*x^r)^2),x]","\frac{4 b e n (r+2) x^r \left(d+e x^r\right) \, _3F_2\left(1,1-\frac{2}{r},1-\frac{2}{r};2-\frac{2}{r},2-\frac{2}{r};-\frac{e x^r}{d}\right)-(r-2) \left(4 e x^r \left(d+e x^r\right) \, _2F_1\left(1,\frac{r-2}{r};2-\frac{2}{r};-\frac{e x^r}{d}\right) \left(a (r+2)+b (r+2) \log \left(c x^n\right)-b n\right)+d (r-2) \left(2 a \left(d r+e (r+2) x^r\right)+2 b \log \left(c x^n\right) \left(d r+e (r+2) x^r\right)+b n r \left(d+e x^r\right)\right)\right)}{4 d^3 (r-2)^2 r x^2 \left(d+e x^r\right)}","\text{Int}\left(\frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^r\right)^2},x\right)",0,"(4*b*e*n*(2 + r)*x^r*(d + e*x^r)*HypergeometricPFQ[{1, 1 - 2/r, 1 - 2/r}, {2 - 2/r, 2 - 2/r}, -((e*x^r)/d)] - (-2 + r)*(4*e*x^r*(d + e*x^r)*Hypergeometric2F1[1, (-2 + r)/r, 2 - 2/r, -((e*x^r)/d)]*(-(b*n) + a*(2 + r) + b*(2 + r)*Log[c*x^n]) + d*(-2 + r)*(b*n*r*(d + e*x^r) + 2*a*(d*r + e*(2 + r)*x^r) + 2*b*(d*r + e*(2 + r)*x^r)*Log[c*x^n])))/(4*d^3*(-2 + r)^2*r*x^2*(d + e*x^r))","B",0
417,1,140,26,0.2496993,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^r\right)^2} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e*x^r)^2,x]","\frac{x^3 \left(-b n (r-3) \left(d+e x^r\right) \, _3F_2\left(1,\frac{3}{r},\frac{3}{r};1+\frac{3}{r},1+\frac{3}{r};-\frac{e x^r}{d}\right)+3 \left(d+e x^r\right) \, _2F_1\left(1,\frac{3}{r};\frac{r+3}{r};-\frac{e x^r}{d}\right) \left(a (r-3)+b (r-3) \log \left(c x^n\right)-b n\right)+9 d \left(a+b \log \left(c x^n\right)\right)\right)}{9 d^2 r \left(d+e x^r\right)}","\text{Int}\left(\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^r\right)^2},x\right)",0,"(x^3*(-(b*n*(-3 + r)*(d + e*x^r)*HypergeometricPFQ[{1, 3/r, 3/r}, {1 + 3/r, 1 + 3/r}, -((e*x^r)/d)]) + 9*d*(a + b*Log[c*x^n]) + 3*(d + e*x^r)*Hypergeometric2F1[1, 3/r, (3 + r)/r, -((e*x^r)/d)]*(-(b*n) + a*(-3 + r) + b*(-3 + r)*Log[c*x^n])))/(9*d^2*r*(d + e*x^r))","B",0
418,1,161,23,2.6197464,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+e x^r\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*x^r)^2,x]","\frac{x \left(-b n (r-1) \left(d+e x^r\right) \, _3F_2\left(1,\frac{1}{r},\frac{1}{r};1+\frac{1}{r},1+\frac{1}{r};-\frac{e x^r}{d}\right)+a e r x^r \, _2F_1\left(2,\frac{1}{r};1+\frac{1}{r};-\frac{e x^r}{d}\right)+a d r \, _2F_1\left(2,\frac{1}{r};1+\frac{1}{r};-\frac{e x^r}{d}\right)-b \left(d+e x^r\right) \left(n-(r-1) \log \left(c x^n\right)\right) \, _2F_1\left(1,\frac{1}{r};1+\frac{1}{r};-\frac{e x^r}{d}\right)+b d \log \left(c x^n\right)\right)}{d^2 r \left(d+e x^r\right)}","\text{Int}\left(\frac{a+b \log \left(c x^n\right)}{\left(d+e x^r\right)^2},x\right)",0,"(x*(a*d*r*Hypergeometric2F1[2, r^(-1), 1 + r^(-1), -((e*x^r)/d)] + a*e*r*x^r*Hypergeometric2F1[2, r^(-1), 1 + r^(-1), -((e*x^r)/d)] - b*n*(-1 + r)*(d + e*x^r)*HypergeometricPFQ[{1, r^(-1), r^(-1)}, {1 + r^(-1), 1 + r^(-1)}, -((e*x^r)/d)] + b*d*Log[c*x^n] - b*(d + e*x^r)*Hypergeometric2F1[1, r^(-1), 1 + r^(-1), -((e*x^r)/d)]*(n - (-1 + r)*Log[c*x^n])))/(d^2*r*(d + e*x^r))","B",0
419,1,135,26,0.2048816,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^r\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*(d + e*x^r)^2),x]","\frac{-b n (r+1) \left(d+e x^r\right) \, _3F_2\left(1,-\frac{1}{r},-\frac{1}{r};1-\frac{1}{r},1-\frac{1}{r};-\frac{e x^r}{d}\right)-\left(d+e x^r\right) \, _2F_1\left(1,-\frac{1}{r};\frac{r-1}{r};-\frac{e x^r}{d}\right) \left(a r+a+b (r+1) \log \left(c x^n\right)-b n\right)+d \left(a+b \log \left(c x^n\right)\right)}{d^2 r x \left(d+e x^r\right)}","\text{Int}\left(\frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^r\right)^2},x\right)",0,"(-(b*n*(1 + r)*(d + e*x^r)*HypergeometricPFQ[{1, -r^(-1), -r^(-1)}, {1 - r^(-1), 1 - r^(-1)}, -((e*x^r)/d)]) + d*(a + b*Log[c*x^n]) - (d + e*x^r)*Hypergeometric2F1[1, -r^(-1), (-1 + r)/r, -((e*x^r)/d)]*(a - b*n + a*r + b*(1 + r)*Log[c*x^n]))/(d^2*r*x*(d + e*x^r))","B",0
420,1,37,37,0.0186529,"\int \frac{a+b \log \left(c x^n\right)}{x \left(c-x^{-n}\right)} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(c - x^(-n))),x]","\frac{\log \left(1-c x^n\right) \left(a+b \log \left(c x^n\right)\right)+b \text{Li}_2\left(c x^n\right)}{c n}","\frac{a \log \left(1-c x^n\right)}{c n}-\frac{b \text{Li}_2\left(1-c x^n\right)}{c n}",1,"((a + b*Log[c*x^n])*Log[1 - c*x^n] + b*PolyLog[2, c*x^n])/(c*n)","A",1
421,1,132,152,0.33934,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x,x]","\frac{1}{36} \left(\frac{e x^r \left(6 a r \left(18 d^2+9 d e x^r+2 e^2 x^{2 r}\right)-b n \left(108 d^2+27 d e x^r+4 e^2 x^{2 r}\right)\right)}{r^2}+\frac{18 b d^3 \log ^2\left(c x^n\right)}{n}+\frac{6 b e x^r \log \left(c x^n\right) \left(18 d^2+9 d e x^r+2 e^2 x^{2 r}\right)}{r}\right)+a d^3 \log (x)","d^3 \log (x) \left(a+b \log \left(c x^n\right)\right)+\frac{3 d^2 e x^r \left(a+b \log \left(c x^n\right)\right)}{r}+\frac{3 d e^2 x^{2 r} \left(a+b \log \left(c x^n\right)\right)}{2 r}+\frac{e^3 x^{3 r} \left(a+b \log \left(c x^n\right)\right)}{3 r}-\frac{1}{2} b d^3 n \log ^2(x)-\frac{3 b d^2 e n x^r}{r^2}-\frac{3 b d e^2 n x^{2 r}}{4 r^2}-\frac{b e^3 n x^{3 r}}{9 r^2}",1,"a*d^3*Log[x] + ((e*x^r*(6*a*r*(18*d^2 + 9*d*e*x^r + 2*e^2*x^(2*r)) - b*n*(108*d^2 + 27*d*e*x^r + 4*e^2*x^(2*r))))/r^2 + (6*b*e*x^r*(18*d^2 + 9*d*e*x^r + 2*e^2*x^(2*r))*Log[c*x^n])/r + (18*b*d^3*Log[c*x^n]^2)/n)/36","A",1
422,1,90,104,0.2170094,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[((d + e*x^r)^2*(a + b*Log[c*x^n]))/x,x]","\frac{1}{4} \left(\frac{e x^r \left(2 a r \left(4 d+e x^r\right)-b n \left(8 d+e x^r\right)\right)}{r^2}+4 a d^2 \log (x)+\frac{2 b d^2 \log ^2\left(c x^n\right)}{n}+\frac{2 b e x^r \log \left(c x^n\right) \left(4 d+e x^r\right)}{r}\right)","d^2 \log (x) \left(a+b \log \left(c x^n\right)\right)+\frac{2 d e x^r \left(a+b \log \left(c x^n\right)\right)}{r}+\frac{e^2 x^{2 r} \left(a+b \log \left(c x^n\right)\right)}{2 r}-\frac{1}{2} b d^2 n \log ^2(x)-\frac{2 b d e n x^r}{r^2}-\frac{b e^2 n x^{2 r}}{4 r^2}",1,"((e*x^r*(2*a*r*(4*d + e*x^r) - b*n*(8*d + e*x^r)))/r^2 + 4*a*d^2*Log[x] + (2*b*e*x^r*(4*d + e*x^r)*Log[c*x^n])/r + (2*b*d^2*Log[c*x^n]^2)/n)/4","A",1
423,1,54,53,0.0867239,"\int \frac{\left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[((d + e*x^r)*(a + b*Log[c*x^n]))/x,x]","\frac{e x^r (a r-b n)}{r^2}+a d \log (x)+\frac{b d \log ^2\left(c x^n\right)}{2 n}+\frac{b e x^r \log \left(c x^n\right)}{r}","\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}+\frac{e x^r \left(a+b \log \left(c x^n\right)\right)}{r}-\frac{b e n x^r}{r^2}",1,"(e*(-(b*n) + a*r)*x^r)/r^2 + a*d*Log[x] + (b*e*x^r*Log[c*x^n])/r + (b*d*Log[c*x^n]^2)/(2*n)","A",1
424,1,108,54,0.1078522,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x^r)),x]","\frac{-2 r \log \left(d-d x^r\right) \left(a+b \log \left(c x^n\right)\right)+2 b n \text{Li}_2\left(\frac{e x^r}{d}+1\right)+2 b n r \log (x) \left(\log \left(d-d x^r\right)-\log \left(d+e x^r\right)\right)+2 b n \log \left(-\frac{e x^r}{d}\right) \log \left(d+e x^r\right)+b n r^2 \log ^2(x)}{2 d r^2}","\frac{b n \text{Li}_2\left(-\frac{d x^{-r}}{e}\right)}{d r^2}-\frac{\log \left(\frac{d x^{-r}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d r}",1,"(b*n*r^2*Log[x]^2 - 2*r*(a + b*Log[c*x^n])*Log[d - d*x^r] + 2*b*n*r*Log[x]*(Log[d - d*x^r] - Log[d + e*x^r]) + 2*b*n*Log[-((e*x^r)/d)]*Log[d + e*x^r] + 2*b*n*PolyLog[2, 1 + (e*x^r)/d])/(2*d*r^2)","A",0
425,1,132,102,0.2986989,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x^r)^2),x]","\frac{\frac{d r \left(a+b \log \left(c x^n\right)\right)}{d+e x^r}-a r \log \left(d-d x^r\right)+b r \left(n \log (x)-\log \left(c x^n\right)\right) \log \left(d-d x^r\right)+b n \left(\text{Li}_2\left(\frac{e x^r}{d}+1\right)+\left(\log \left(-\frac{e x^r}{d}\right)-r \log (x)\right) \log \left(d+e x^r\right)+\frac{1}{2} r^2 \log ^2(x)\right)+b n \log \left(d-d x^r\right)}{d^2 r^2}","-\frac{\log \left(\frac{d x^{-r}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 r}-\frac{e x^r \left(a+b \log \left(c x^n\right)\right)}{d^2 r \left(d+e x^r\right)}+\frac{b n \text{Li}_2\left(-\frac{d x^{-r}}{e}\right)}{d^2 r^2}+\frac{b n \log \left(d+e x^r\right)}{d^2 r^2}",1,"((d*r*(a + b*Log[c*x^n]))/(d + e*x^r) + b*n*Log[d - d*x^r] - a*r*Log[d - d*x^r] + b*r*(n*Log[x] - Log[c*x^n])*Log[d - d*x^r] + b*n*((r^2*Log[x]^2)/2 + (-(r*Log[x]) + Log[-((e*x^r)/d)])*Log[d + e*x^r] + PolyLog[2, 1 + (e*x^r)/d]))/(d^2*r^2)","A",0
426,1,170,169,0.2375905,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)^3} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x^r)^3),x]","\frac{\frac{d^2 r \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^r\right)^2}+\frac{d \left(2 a r+2 b r \log \left(c x^n\right)-b n\right)}{d+e x^r}-2 a r \log \left(d-d x^r\right)+2 b r \left(n \log (x)-\log \left(c x^n\right)\right) \log \left(d-d x^r\right)+2 b n \left(\text{Li}_2\left(\frac{e x^r}{d}+1\right)+\left(\log \left(-\frac{e x^r}{d}\right)-r \log (x)\right) \log \left(d+e x^r\right)+\frac{1}{2} r^2 \log ^2(x)\right)+3 b n \log \left(d-d x^r\right)}{2 d^3 r^2}","-\frac{\log \left(\frac{d x^{-r}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^3 r}-\frac{e x^r \left(a+b \log \left(c x^n\right)\right)}{d^3 r \left(d+e x^r\right)}+\frac{a+b \log \left(c x^n\right)}{2 d r \left(d+e x^r\right)^2}+\frac{b n \text{Li}_2\left(-\frac{d x^{-r}}{e}\right)}{d^3 r^2}+\frac{3 b n \log \left(d+e x^r\right)}{2 d^3 r^2}-\frac{b n \log (x)}{2 d^3 r}-\frac{b n}{2 d^2 r^2 \left(d+e x^r\right)}",1,"((d^2*r*(a + b*Log[c*x^n]))/(d + e*x^r)^2 + (d*(-(b*n) + 2*a*r + 2*b*r*Log[c*x^n]))/(d + e*x^r) + 3*b*n*Log[d - d*x^r] - 2*a*r*Log[d - d*x^r] + 2*b*r*(n*Log[x] - Log[c*x^n])*Log[d - d*x^r] + 2*b*n*((r^2*Log[x]^2)/2 + (-(r*Log[x]) + Log[-((e*x^r)/d)])*Log[d + e*x^r] + PolyLog[2, 1 + (e*x^r)/d]))/(2*d^3*r^2)","A",0
427,1,262,245,0.4486498,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)^2}{x} \, dx","Integrate[((d + e*x^r)^3*(a + b*Log[c*x^n])^2)/x,x]","\frac{e n x^r \left(18 a^2 r^2 \left(18 d^2+9 d e x^r+2 e^2 x^{2 r}\right)-6 a b n r \left(108 d^2+27 d e x^r+4 e^2 x^{2 r}\right)+b^2 n^2 \left(648 d^2+81 d e x^r+8 e^2 x^{2 r}\right)\right)+108 a^2 d^3 n r^3 \log (x)-6 b e n r x^r \log \left(c x^n\right) \left(b n \left(108 d^2+27 d e x^r+4 e^2 x^{2 r}\right)-6 a r \left(18 d^2+9 d e x^r+2 e^2 x^{2 r}\right)\right)+18 b r^2 \log ^2\left(c x^n\right) \left(6 a d^3 r+b e n x^r \left(18 d^2+9 d e x^r+2 e^2 x^{2 r}\right)\right)+36 b^2 d^3 r^3 \log ^3\left(c x^n\right)}{108 n r^3}","\frac{d^3 \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}-\frac{6 b d^2 e n x^r \left(a+b \log \left(c x^n\right)\right)}{r^2}+\frac{3 d^2 e x^r \left(a+b \log \left(c x^n\right)\right)^2}{r}-\frac{3 b d e^2 n x^{2 r} \left(a+b \log \left(c x^n\right)\right)}{2 r^2}+\frac{3 d e^2 x^{2 r} \left(a+b \log \left(c x^n\right)\right)^2}{2 r}-\frac{2 b e^3 n x^{3 r} \left(a+b \log \left(c x^n\right)\right)}{9 r^2}+\frac{e^3 x^{3 r} \left(a+b \log \left(c x^n\right)\right)^2}{3 r}+\frac{6 b^2 d^2 e n^2 x^r}{r^3}+\frac{3 b^2 d e^2 n^2 x^{2 r}}{4 r^3}+\frac{2 b^2 e^3 n^2 x^{3 r}}{27 r^3}",1,"(e*n*x^r*(18*a^2*r^2*(18*d^2 + 9*d*e*x^r + 2*e^2*x^(2*r)) - 6*a*b*n*r*(108*d^2 + 27*d*e*x^r + 4*e^2*x^(2*r)) + b^2*n^2*(648*d^2 + 81*d*e*x^r + 8*e^2*x^(2*r))) + 108*a^2*d^3*n*r^3*Log[x] - 6*b*e*n*r*x^r*(-6*a*r*(18*d^2 + 9*d*e*x^r + 2*e^2*x^(2*r)) + b*n*(108*d^2 + 27*d*e*x^r + 4*e^2*x^(2*r)))*Log[c*x^n] + 18*b*r^2*(6*a*d^3*r + b*e*n*x^r*(18*d^2 + 9*d*e*x^r + 2*e^2*x^(2*r)))*Log[c*x^n]^2 + 36*b^2*d^3*r^3*Log[c*x^n]^3)/(108*n*r^3)","A",1
428,1,179,161,0.272879,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)^2}{x} \, dx","Integrate[((d + e*x^r)^2*(a + b*Log[c*x^n])^2)/x,x]","\frac{3 e n x^r \left(2 a^2 r^2 \left(4 d+e x^r\right)-2 a b n r \left(8 d+e x^r\right)+b^2 n^2 \left(16 d+e x^r\right)\right)+12 a^2 d^2 n r^3 \log (x)+6 b r^2 \log ^2\left(c x^n\right) \left(2 a d^2 r+b e n x^r \left(4 d+e x^r\right)\right)-6 b e n r x^r \log \left(c x^n\right) \left(b n \left(8 d+e x^r\right)-2 a r \left(4 d+e x^r\right)\right)+4 b^2 d^2 r^3 \log ^3\left(c x^n\right)}{12 n r^3}","\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}-\frac{4 b d e n x^r \left(a+b \log \left(c x^n\right)\right)}{r^2}+\frac{2 d e x^r \left(a+b \log \left(c x^n\right)\right)^2}{r}-\frac{b e^2 n x^{2 r} \left(a+b \log \left(c x^n\right)\right)}{2 r^2}+\frac{e^2 x^{2 r} \left(a+b \log \left(c x^n\right)\right)^2}{2 r}+\frac{4 b^2 d e n^2 x^r}{r^3}+\frac{b^2 e^2 n^2 x^{2 r}}{4 r^3}",1,"(3*e*n*x^r*(2*a^2*r^2*(4*d + e*x^r) - 2*a*b*n*r*(8*d + e*x^r) + b^2*n^2*(16*d + e*x^r)) + 12*a^2*d^2*n*r^3*Log[x] - 6*b*e*n*r*x^r*(-2*a*r*(4*d + e*x^r) + b*n*(8*d + e*x^r))*Log[c*x^n] + 6*b*r^2*(2*a*d^2*r + b*e*n*x^r*(4*d + e*x^r))*Log[c*x^n]^2 + 4*b^2*d^2*r^3*Log[c*x^n]^3)/(12*n*r^3)","A",1
429,1,109,80,0.147914,"\int \frac{\left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)^2}{x} \, dx","Integrate[((d + e*x^r)*(a + b*Log[c*x^n])^2)/x,x]","\frac{e x^r \left(a^2 r^2-2 a b n r+2 b^2 n^2\right)}{r^3}+a^2 d \log (x)+\frac{b \log ^2\left(c x^n\right) \left(a d r+b e n x^r\right)}{n r}-\frac{2 b e x^r (b n-a r) \log \left(c x^n\right)}{r^2}+\frac{b^2 d \log ^3\left(c x^n\right)}{3 n}","\frac{d \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}-\frac{2 b e n x^r \left(a+b \log \left(c x^n\right)\right)}{r^2}+\frac{e x^r \left(a+b \log \left(c x^n\right)\right)^2}{r}+\frac{2 b^2 e n^2 x^r}{r^3}",1,"(e*(2*b^2*n^2 - 2*a*b*n*r + a^2*r^2)*x^r)/r^3 + a^2*d*Log[x] - (2*b*e*(b*n - a*r)*x^r*Log[c*x^n])/r^2 + (b*(a*d*r + b*e*n*x^r)*Log[c*x^n]^2)/(n*r) + (b^2*d*Log[c*x^n]^3)/(3*n)","A",1
430,1,270,94,0.3081842,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x \left(d+e x^r\right)} \, dx","Integrate[(a + b*Log[c*x^n])^2/(x*(d + e*x^r)),x]","-\frac{a^2 r^2 \log \left(d-d x^r\right)-2 a b r^2 \left(n \log (x)-\log \left(c x^n\right)\right) \log \left(d-d x^r\right)-2 a b n r \left(\text{Li}_2\left(\frac{e x^r}{d}+1\right)+\left(\log \left(-\frac{e x^r}{d}\right)-r \log (x)\right) \log \left(d+e x^r\right)+\frac{1}{2} r^2 \log ^2(x)\right)+2 b^2 n r \left(n \log (x)-\log \left(c x^n\right)\right) \left(\text{Li}_2\left(\frac{e x^r}{d}+1\right)+\left(\log \left(-\frac{e x^r}{d}\right)-r \log (x)\right) \log \left(d+e x^r\right)+\frac{1}{2} r^2 \log ^2(x)\right)+b^2 r^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 \log \left(d-d x^r\right)+b^2 n^2 \left(-2 \text{Li}_3\left(-\frac{d x^{-r}}{e}\right)-2 r \log (x) \text{Li}_2\left(-\frac{d x^{-r}}{e}\right)+r^2 \log ^2(x) \log \left(\frac{d x^{-r}}{e}+1\right)\right)}{d r^3}","\frac{2 b n \text{Li}_2\left(-\frac{d x^{-r}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{d r^2}-\frac{\log \left(\frac{d x^{-r}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d r}+\frac{2 b^2 n^2 \text{Li}_3\left(-\frac{d x^{-r}}{e}\right)}{d r^3}",1,"-((a^2*r^2*Log[d - d*x^r] - 2*a*b*r^2*(n*Log[x] - Log[c*x^n])*Log[d - d*x^r] + b^2*r^2*(-(n*Log[x]) + Log[c*x^n])^2*Log[d - d*x^r] - 2*a*b*n*r*((r^2*Log[x]^2)/2 + (-(r*Log[x]) + Log[-((e*x^r)/d)])*Log[d + e*x^r] + PolyLog[2, 1 + (e*x^r)/d]) + 2*b^2*n*r*(n*Log[x] - Log[c*x^n])*((r^2*Log[x]^2)/2 + (-(r*Log[x]) + Log[-((e*x^r)/d)])*Log[d + e*x^r] + PolyLog[2, 1 + (e*x^r)/d]) + b^2*n^2*(r^2*Log[x]^2*Log[1 + d/(e*x^r)] - 2*r*Log[x]*PolyLog[2, -(d/(e*x^r))] - 2*PolyLog[3, -(d/(e*x^r))]))/(d*r^3))","B",0
431,1,397,182,0.3965089,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x \left(d+e x^r\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])^2/(x*(d + e*x^r)^2),x]","\frac{-a^2 r^2 \log \left(d-d x^r\right)+\frac{d r^2 \left(a+b \log \left(c x^n\right)\right)^2}{d+e x^r}+2 a b r^2 \left(n \log (x)-\log \left(c x^n\right)\right) \log \left(d-d x^r\right)+2 a b n r \left(\text{Li}_2\left(\frac{e x^r}{d}+1\right)+\left(\log \left(-\frac{e x^r}{d}\right)-r \log (x)\right) \log \left(d+e x^r\right)+\frac{1}{2} r^2 \log ^2(x)\right)+2 a b n r \log \left(d-d x^r\right)+2 b^2 n r \left(\log \left(c x^n\right)-n \log (x)\right) \left(\text{Li}_2\left(\frac{e x^r}{d}+1\right)+\left(\log \left(-\frac{e x^r}{d}\right)-r \log (x)\right) \log \left(d+e x^r\right)+\frac{1}{2} r^2 \log ^2(x)\right)+b^2 \left(-r^2\right) \left(\log \left(c x^n\right)-n \log (x)\right)^2 \log \left(d-d x^r\right)+2 b^2 n r \left(\log \left(c x^n\right)-n \log (x)\right) \log \left(d-d x^r\right)-b^2 n^2 \left(-2 \text{Li}_3\left(-\frac{d x^{-r}}{e}\right)-2 r \log (x) \text{Li}_2\left(-\frac{d x^{-r}}{e}\right)+r^2 \log ^2(x) \log \left(\frac{d x^{-r}}{e}+1\right)\right)-2 b^2 n^2 \left(\text{Li}_2\left(\frac{e x^r}{d}+1\right)+\left(\log \left(-\frac{e x^r}{d}\right)-r \log (x)\right) \log \left(d+e x^r\right)+\frac{1}{2} r^2 \log ^2(x)\right)}{d^2 r^3}","\frac{2 b n \text{Li}_2\left(-\frac{d x^{-r}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 r^2}+\frac{2 b n \log \left(\frac{d x^{-r}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 r^2}-\frac{\log \left(\frac{d x^{-r}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2 r}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{d r \left(d+e x^r\right)}-\frac{2 b^2 n^2 \text{Li}_2\left(-\frac{d x^{-r}}{e}\right)}{d^2 r^3}+\frac{2 b^2 n^2 \text{Li}_3\left(-\frac{d x^{-r}}{e}\right)}{d^2 r^3}",1,"((d*r^2*(a + b*Log[c*x^n])^2)/(d + e*x^r) + 2*a*b*n*r*Log[d - d*x^r] - a^2*r^2*Log[d - d*x^r] + 2*a*b*r^2*(n*Log[x] - Log[c*x^n])*Log[d - d*x^r] + 2*b^2*n*r*(-(n*Log[x]) + Log[c*x^n])*Log[d - d*x^r] - b^2*r^2*(-(n*Log[x]) + Log[c*x^n])^2*Log[d - d*x^r] - 2*b^2*n^2*((r^2*Log[x]^2)/2 + (-(r*Log[x]) + Log[-((e*x^r)/d)])*Log[d + e*x^r] + PolyLog[2, 1 + (e*x^r)/d]) + 2*a*b*n*r*((r^2*Log[x]^2)/2 + (-(r*Log[x]) + Log[-((e*x^r)/d)])*Log[d + e*x^r] + PolyLog[2, 1 + (e*x^r)/d]) + 2*b^2*n*r*(-(n*Log[x]) + Log[c*x^n])*((r^2*Log[x]^2)/2 + (-(r*Log[x]) + Log[-((e*x^r)/d)])*Log[d + e*x^r] + PolyLog[2, 1 + (e*x^r)/d]) - b^2*n^2*(r^2*Log[x]^2*Log[1 + d/(e*x^r)] - 2*r*Log[x]*PolyLog[2, -(d/(e*x^r))] - 2*PolyLog[3, -(d/(e*x^r))]))/(d^2*r^3)","B",0
432,1,459,267,0.6065138,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x \left(d+e x^r\right)^3} \, dx","Integrate[(a + b*Log[c*x^n])^2/(x*(d + e*x^r)^3),x]","\frac{-2 a^2 r^2 \log \left(d-d x^r\right)+\frac{d^2 r^2 \left(a+b \log \left(c x^n\right)\right)^2}{\left(d+e x^r\right)^2}+\frac{2 d r \left(a+b \log \left(c x^n\right)\right) \left(a r+b r \log \left(c x^n\right)-b n\right)}{d+e x^r}+4 a b r^2 \left(n \log (x)-\log \left(c x^n\right)\right) \log \left(d-d x^r\right)+4 a b n r \left(\text{Li}_2\left(\frac{e x^r}{d}+1\right)+\left(\log \left(-\frac{e x^r}{d}\right)-r \log (x)\right) \log \left(d+e x^r\right)+\frac{1}{2} r^2 \log ^2(x)\right)+6 a b n r \log \left(d-d x^r\right)+4 b^2 n r \left(\log \left(c x^n\right)-n \log (x)\right) \left(\text{Li}_2\left(\frac{e x^r}{d}+1\right)+\left(\log \left(-\frac{e x^r}{d}\right)-r \log (x)\right) \log \left(d+e x^r\right)+\frac{1}{2} r^2 \log ^2(x)\right)-2 b^2 r^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 \log \left(d-d x^r\right)+6 b^2 n r \left(\log \left(c x^n\right)-n \log (x)\right) \log \left(d-d x^r\right)-2 b^2 n^2 \left(-2 \text{Li}_3\left(-\frac{d x^{-r}}{e}\right)-2 r \log (x) \text{Li}_2\left(-\frac{d x^{-r}}{e}\right)+r^2 \log ^2(x) \log \left(\frac{d x^{-r}}{e}+1\right)\right)-6 b^2 n^2 \left(\text{Li}_2\left(\frac{e x^r}{d}+1\right)+\left(\log \left(-\frac{e x^r}{d}\right)-r \log (x)\right) \log \left(d+e x^r\right)+\frac{1}{2} r^2 \log ^2(x)\right)-2 b^2 n^2 \log \left(d-d x^r\right)}{2 d^3 r^3}","\frac{2 b n \text{Li}_2\left(-\frac{d x^{-r}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3 r^2}+\frac{3 b n \log \left(\frac{d x^{-r}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^3 r^2}+\frac{b e n x^r \left(a+b \log \left(c x^n\right)\right)}{d^3 r^2 \left(d+e x^r\right)}-\frac{\log \left(\frac{d x^{-r}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^3 r}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{d^2 r \left(d+e x^r\right)}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 d r \left(d+e x^r\right)^2}-\frac{3 b^2 n^2 \text{Li}_2\left(-\frac{d x^{-r}}{e}\right)}{d^3 r^3}+\frac{2 b^2 n^2 \text{Li}_3\left(-\frac{d x^{-r}}{e}\right)}{d^3 r^3}-\frac{b^2 n^2 \log \left(d+e x^r\right)}{d^3 r^3}",1,"((d^2*r^2*(a + b*Log[c*x^n])^2)/(d + e*x^r)^2 + (2*d*r*(a + b*Log[c*x^n])*(-(b*n) + a*r + b*r*Log[c*x^n]))/(d + e*x^r) - 2*b^2*n^2*Log[d - d*x^r] + 6*a*b*n*r*Log[d - d*x^r] - 2*a^2*r^2*Log[d - d*x^r] + 4*a*b*r^2*(n*Log[x] - Log[c*x^n])*Log[d - d*x^r] + 6*b^2*n*r*(-(n*Log[x]) + Log[c*x^n])*Log[d - d*x^r] - 2*b^2*r^2*(-(n*Log[x]) + Log[c*x^n])^2*Log[d - d*x^r] - 6*b^2*n^2*((r^2*Log[x]^2)/2 + (-(r*Log[x]) + Log[-((e*x^r)/d)])*Log[d + e*x^r] + PolyLog[2, 1 + (e*x^r)/d]) + 4*a*b*n*r*((r^2*Log[x]^2)/2 + (-(r*Log[x]) + Log[-((e*x^r)/d)])*Log[d + e*x^r] + PolyLog[2, 1 + (e*x^r)/d]) + 4*b^2*n*r*(-(n*Log[x]) + Log[c*x^n])*((r^2*Log[x]^2)/2 + (-(r*Log[x]) + Log[-((e*x^r)/d)])*Log[d + e*x^r] + PolyLog[2, 1 + (e*x^r)/d]) - 2*b^2*n^2*(r^2*Log[x]^2*Log[1 + d/(e*x^r)] - 2*r*Log[x]*PolyLog[2, -(d/(e*x^r))] - 2*PolyLog[3, -(d/(e*x^r))]))/(2*d^3*r^3)","A",0
433,0,0,327,0.5510451,"\int \frac{\left(d+e x^r\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[((d + e*x^r)^(5/2)*(a + b*Log[c*x^n]))/x,x]","\int \frac{\left(d+e x^r\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","\frac{2}{15} \left(-\frac{15 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{r}+\frac{15 d^2 \sqrt{d+e x^r}}{r}+\frac{5 d \left(d+e x^r\right)^{3/2}}{r}+\frac{3 \left(d+e x^r\right)^{5/2}}{r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 b d^{5/2} n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^r+d}}\right)}{r^2}+\frac{2 b d^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)^2}{r^2}+\frac{92 b d^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{15 r^2}-\frac{4 b d^{5/2} n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{r^2}-\frac{92 b d^2 n \sqrt{d+e x^r}}{15 r^2}-\frac{32 b d n \left(d+e x^r\right)^{3/2}}{45 r^2}-\frac{4 b n \left(d+e x^r\right)^{5/2}}{25 r^2}",1,"Integrate[((d + e*x^r)^(5/2)*(a + b*Log[c*x^n]))/x, x]","F",-1
434,0,0,284,0.4434291,"\int \frac{\left(d+e x^r\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[((d + e*x^r)^(3/2)*(a + b*Log[c*x^n]))/x,x]","\int \frac{\left(d+e x^r\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","\frac{2}{3} \left(-\frac{3 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{r}+\frac{3 d \sqrt{d+e x^r}}{r}+\frac{\left(d+e x^r\right)^{3/2}}{r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 b d^{3/2} n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^r+d}}\right)}{r^2}+\frac{2 b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)^2}{r^2}+\frac{16 b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{3 r^2}-\frac{4 b d^{3/2} n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{r^2}-\frac{4 b n \left(d+e x^r\right)^{3/2}}{9 r^2}-\frac{16 b d n \sqrt{d+e x^r}}{3 r^2}",1,"Integrate[((d + e*x^r)^(3/2)*(a + b*Log[c*x^n]))/x, x]","F",-1
435,0,0,240,0.3500697,"\int \frac{\sqrt{d+e x^r} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[(Sqrt[d + e*x^r]*(a + b*Log[c*x^n]))/x,x]","\int \frac{\sqrt{d+e x^r} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","2 \left(\frac{\sqrt{d+e x^r}}{r}-\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 b \sqrt{d} n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^r+d}}\right)}{r^2}-\frac{4 b n \sqrt{d+e x^r}}{r^2}+\frac{2 b \sqrt{d} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)^2}{r^2}+\frac{4 b \sqrt{d} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{r^2}-\frac{4 b \sqrt{d} n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{r^2}",1,"Integrate[(Sqrt[d + e*x^r]*(a + b*Log[c*x^n]))/x, x]","F",-1
436,0,0,174,0.1179202,"\int \frac{a+b \log \left(c x^n\right)}{x \sqrt{d+e x^r}} \, dx","Integrate[(a + b*Log[c*x^n])/(x*Sqrt[d + e*x^r]),x]","\int \frac{a+b \log \left(c x^n\right)}{x \sqrt{d+e x^r}} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d} r}-\frac{2 b n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^r+d}}\right)}{\sqrt{d} r^2}+\frac{2 b n \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)^2}{\sqrt{d} r^2}-\frac{4 b n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{\sqrt{d} r^2}",1,"Integrate[(a + b*Log[c*x^n])/(x*Sqrt[d + e*x^r]), x]","F",-1
437,0,0,225,0.3004007,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)^{3/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x^r)^(3/2)),x]","\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)^{3/2}} \, dx","2 \left(\frac{1}{d r \sqrt{d+e x^r}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{d^{3/2} r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 b n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^r+d}}\right)}{d^{3/2} r^2}+\frac{2 b n \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)^2}{d^{3/2} r^2}+\frac{4 b n \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{d^{3/2} r^2}-\frac{4 b n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{d^{3/2} r^2}",1,"Integrate[(a + b*Log[c*x^n])/(x*(d + e*x^r)^(3/2)), x]","F",-1
438,0,0,271,0.3648757,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)^{5/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x^r)^(5/2)),x]","\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)^{5/2}} \, dx","\frac{2}{3} \left(-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{d^{5/2} r}+\frac{3}{d^2 r \sqrt{d+e x^r}}+\frac{1}{d r \left(d+e x^r\right)^{3/2}}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 b n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^r+d}}\right)}{d^{5/2} r^2}+\frac{2 b n \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)^2}{d^{5/2} r^2}+\frac{16 b n \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{3 d^{5/2} r^2}-\frac{4 b n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{d^{5/2} r^2}-\frac{4 b n}{3 d^2 r^2 \sqrt{d+e x^r}}",1,"Integrate[(a + b*Log[c*x^n])/(x*(d + e*x^r)^(5/2)), x]","F",-1
439,0,0,314,0.4239248,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)^{7/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*x^r)^(7/2)),x]","\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)^{7/2}} \, dx","\frac{2}{15} \left(-\frac{15 \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{d^{7/2} r}+\frac{15}{d^3 r \sqrt{d+e x^r}}+\frac{5}{d^2 r \left(d+e x^r\right)^{3/2}}+\frac{3}{d r \left(d+e x^r\right)^{5/2}}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 b n \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{e x^r+d}}\right)}{d^{7/2} r^2}+\frac{2 b n \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)^2}{d^{7/2} r^2}+\frac{92 b n \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{15 d^{7/2} r^2}-\frac{4 b n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{d^{7/2} r^2}-\frac{32 b n}{15 d^3 r^2 \sqrt{d+e x^r}}-\frac{4 b n}{15 d^2 r^2 \left(d+e x^r\right)^{3/2}}",1,"Integrate[(a + b*Log[c*x^n])/(x*(d + e*x^r)^(7/2)), x]","F",-1
440,1,178,233,0.4811791,"\int (f x)^m \left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^m*(d + e*x^r)^3*(a + b*Log[c*x^n]),x]","x (f x)^m \left(\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{m+1}+\frac{3 d^2 e x^r \left(a+b \log \left(c x^n\right)\right)}{m+r+1}+\frac{3 d e^2 x^{2 r} \left(a+b \log \left(c x^n\right)\right)}{m+2 r+1}+\frac{e^3 x^{3 r} \left(a+b \log \left(c x^n\right)\right)}{m+3 r+1}-\frac{b d^3 n}{(m+1)^2}-\frac{3 b d^2 e n x^r}{(m+r+1)^2}-\frac{3 b d e^2 n x^{2 r}}{(m+2 r+1)^2}-\frac{b e^3 n x^{3 r}}{(m+3 r+1)^2}\right)","\frac{d^3 (f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+1)}+\frac{3 d^2 e x^{r+1} (f x)^m \left(a+b \log \left(c x^n\right)\right)}{m+r+1}+\frac{3 d e^2 x^{2 r+1} (f x)^m \left(a+b \log \left(c x^n\right)\right)}{m+2 r+1}+\frac{e^3 x^{3 r+1} (f x)^m \left(a+b \log \left(c x^n\right)\right)}{m+3 r+1}-\frac{b d^3 n (f x)^{m+1}}{f (m+1)^2}-\frac{3 b d^2 e n x^{r+1} (f x)^m}{(m+r+1)^2}-\frac{3 b d e^2 n x^{2 r+1} (f x)^m}{(m+2 r+1)^2}-\frac{b e^3 n x^{3 r+1} (f x)^m}{(m+3 r+1)^2}",1,"x*(f*x)^m*(-((b*d^3*n)/(1 + m)^2) - (3*b*d^2*e*n*x^r)/(1 + m + r)^2 - (3*b*d*e^2*n*x^(2*r))/(1 + m + 2*r)^2 - (b*e^3*n*x^(3*r))/(1 + m + 3*r)^2 + (d^3*(a + b*Log[c*x^n]))/(1 + m) + (3*d^2*e*x^r*(a + b*Log[c*x^n]))/(1 + m + r) + (3*d*e^2*x^(2*r)*(a + b*Log[c*x^n]))/(1 + m + 2*r) + (e^3*x^(3*r)*(a + b*Log[c*x^n]))/(1 + m + 3*r))","A",1
441,1,124,165,0.2602663,"\int (f x)^m \left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^m*(d + e*x^r)^2*(a + b*Log[c*x^n]),x]","x (f x)^m \left(\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{m+1}+\frac{2 d e x^r \left(a+b \log \left(c x^n\right)\right)}{m+r+1}+\frac{e^2 x^{2 r} \left(a+b \log \left(c x^n\right)\right)}{m+2 r+1}-\frac{b d^2 n}{(m+1)^2}-\frac{2 b d e n x^r}{(m+r+1)^2}-\frac{b e^2 n x^{2 r}}{(m+2 r+1)^2}\right)","\frac{d^2 (f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+1)}+\frac{2 d e x^{r+1} (f x)^m \left(a+b \log \left(c x^n\right)\right)}{m+r+1}+\frac{e^2 x^{2 r+1} (f x)^m \left(a+b \log \left(c x^n\right)\right)}{m+2 r+1}-\frac{b d^2 n (f x)^{m+1}}{f (m+1)^2}-\frac{2 b d e n x^{r+1} (f x)^m}{(m+r+1)^2}-\frac{b e^2 n x^{2 r+1} (f x)^m}{(m+2 r+1)^2}",1,"x*(f*x)^m*(-((b*d^2*n)/(1 + m)^2) - (2*b*d*e*n*x^r)/(1 + m + r)^2 - (b*e^2*n*x^(2*r))/(1 + m + 2*r)^2 + (d^2*(a + b*Log[c*x^n]))/(1 + m) + (2*d*e*x^r*(a + b*Log[c*x^n]))/(1 + m + r) + (e^2*x^(2*r)*(a + b*Log[c*x^n]))/(1 + m + 2*r))","A",1
442,1,70,97,0.1247005,"\int (f x)^m \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^m*(d + e*x^r)*(a + b*Log[c*x^n]),x]","x (f x)^m \left(\frac{d \left(a+b \log \left(c x^n\right)\right)}{m+1}+\frac{e x^r \left(a+b \log \left(c x^n\right)\right)}{m+r+1}-\frac{b d n}{(m+1)^2}-\frac{b e n x^r}{(m+r+1)^2}\right)","\frac{d (f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+1)}+\frac{e x^{r+1} (f x)^m \left(a+b \log \left(c x^n\right)\right)}{m+r+1}-\frac{b d n (f x)^{m+1}}{f (m+1)^2}-\frac{b e n x^{r+1} (f x)^m}{(m+r+1)^2}",1,"x*(f*x)^m*(-((b*d*n)/(1 + m)^2) - (b*e*n*x^r)/(1 + m + r)^2 + (d*(a + b*Log[c*x^n]))/(1 + m) + (e*x^r*(a + b*Log[c*x^n]))/(1 + m + r))","A",1
443,1,32,46,0.0139307,"\int (f x)^m \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^m*(a + b*Log[c*x^n]),x]","\frac{x (f x)^m \left(a m+a+b (m+1) \log \left(c x^n\right)-b n\right)}{(m+1)^2}","\frac{(f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+1)}-\frac{b n (f x)^{m+1}}{f (m+1)^2}",1,"(x*(f*x)^m*(a + a*m - b*n + b*(1 + m)*Log[c*x^n]))/(1 + m)^2","A",1
444,1,111,28,0.1563466,"\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{d+e x^r} \, dx","Integrate[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x^r),x]","\frac{x (f x)^m \left((m+1) \left(a+b \log \left(c x^n\right)\right) \, _2F_1\left(1,\frac{m+1}{r};\frac{m+r+1}{r};-\frac{e x^r}{d}\right)-b n \, _3F_2\left(1,\frac{m}{r}+\frac{1}{r},\frac{m}{r}+\frac{1}{r};\frac{m}{r}+\frac{1}{r}+1,\frac{m}{r}+\frac{1}{r}+1;-\frac{e x^r}{d}\right)\right)}{d (m+1)^2}","\text{Int}\left(\frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{d+e x^r},x\right)",0,"(x*(f*x)^m*(-(b*n*HypergeometricPFQ[{1, r^(-1) + m/r, r^(-1) + m/r}, {1 + r^(-1) + m/r, 1 + r^(-1) + m/r}, -((e*x^r)/d)]) + (1 + m)*Hypergeometric2F1[1, (1 + m)/r, (1 + m + r)/r, -((e*x^r)/d)]*(a + b*Log[c*x^n])))/(d*(1 + m)^2)","B",0
445,1,177,28,0.3860007,"\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^r\right)^2} \, dx","Integrate[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x^r)^2,x]","\frac{x (f x)^m \left(b n (m-r+1) \left(d+e x^r\right) \, _3F_2\left(1,\frac{m}{r}+\frac{1}{r},\frac{m}{r}+\frac{1}{r};\frac{m}{r}+\frac{1}{r}+1,\frac{m}{r}+\frac{1}{r}+1;-\frac{e x^r}{d}\right)-(m+1) \left(\left(d+e x^r\right) \, _2F_1\left(1,\frac{m+1}{r};\frac{m+r+1}{r};-\frac{e x^r}{d}\right) \left(a (m-r+1)+b (m-r+1) \log \left(c x^n\right)+b n\right)-d (m+1) \left(a+b \log \left(c x^n\right)\right)\right)\right)}{d^2 (m+1)^2 r \left(d+e x^r\right)}","\text{Int}\left(\frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^r\right)^2},x\right)",0,"(x*(f*x)^m*(b*n*(1 + m - r)*(d + e*x^r)*HypergeometricPFQ[{1, r^(-1) + m/r, r^(-1) + m/r}, {1 + r^(-1) + m/r, 1 + r^(-1) + m/r}, -((e*x^r)/d)] - (1 + m)*(-(d*(1 + m)*(a + b*Log[c*x^n])) + (d + e*x^r)*Hypergeometric2F1[1, (1 + m)/r, (1 + m + r)/r, -((e*x^r)/d)]*(b*n + a*(1 + m - r) + b*(1 + m - r)*Log[c*x^n]))))/(d^2*(1 + m)^2*r*(d + e*x^r))","B",0
446,1,143,102,0.5896314,"\int \left(d+e x^{-\frac{1}{1+q}}\right)^q \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(d + e/x^(1 + q)^(-1))^q*(a + b*Log[c*x^n]),x]","\frac{x^{-\frac{1}{q+1}} \left(d+e x^{-\frac{1}{q+1}}\right)^q \left(\frac{d x^{\frac{1}{q+1}}}{e}+1\right)^{-q} \left(-b d n (q+1)^2 x^{\frac{q+2}{q+1}} \, _3F_2\left(1,1,-q;2,2;-\frac{d x^{\frac{1}{q+1}}}{e}\right)+\left(d x^{\frac{q+2}{q+1}}+e x\right) \left(\frac{d x^{\frac{1}{q+1}}}{e}+1\right)^q \left(a+b \log \left(c x^n\right)\right)-b e n x \log (x)\right)}{d}","\frac{x \left(d+e x^{-\frac{1}{q+1}}\right)^{q+1} \left(a+b \log \left(c x^n\right)\right)}{d}-b n x \left(d+e x^{-\frac{1}{q+1}}\right)^q \left(\frac{e x^{-\frac{1}{q+1}}}{d}+1\right)^{-q} \, _2F_1\left(-q-1,-q-1;-q;-\frac{e x^{-\frac{1}{q+1}}}{d}\right)",1,"((d + e/x^(1 + q)^(-1))^q*(-(b*d*n*(1 + q)^2*x^((2 + q)/(1 + q))*HypergeometricPFQ[{1, 1, -q}, {2, 2}, -((d*x^(1 + q)^(-1))/e)]) - b*e*n*x*Log[x] + (1 + (d*x^(1 + q)^(-1))/e)^q*(e*x + d*x^((2 + q)/(1 + q)))*(a + b*Log[c*x^n])))/(d*x^(1 + q)^(-1)*(1 + (d*x^(1 + q)^(-1))/e)^q)","A",1
447,1,98,119,0.345054,"\int (f x)^{-1-(1+q) r} \left(d+e x^r\right)^q \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(f*x)^(-1 - (1 + q)*r)*(d + e*x^r)^q*(a + b*Log[c*x^n]),x]","-\frac{(f x)^{-((q+1) r)} \left(d+e x^r\right)^q \left(\frac{(q+1) r \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)}{d}+b n \left(\frac{e x^r}{d}+1\right)^{-q} \, _2F_1\left(-q-1,-q-1;-q;-\frac{e x^r}{d}\right)\right)}{f (q+1)^2 r^2}","-\frac{(f x)^{-((q+1) r)} \left(d+e x^r\right)^{q+1} \left(a+b \log \left(c x^n\right)\right)}{d f (q+1) r}-\frac{b n (f x)^{-((q+1) r)} \left(d+e x^r\right)^q \left(\frac{e x^r}{d}+1\right)^{-q} \, _2F_1\left(-q-1,-q-1;-q;-\frac{e x^r}{d}\right)}{f (q+1)^2 r^2}",1,"-(((d + e*x^r)^q*((b*n*Hypergeometric2F1[-1 - q, -1 - q, -q, -((e*x^r)/d)])/(1 + (e*x^r)/d)^q + ((1 + q)*r*(d + e*x^r)*(a + b*Log[c*x^n]))/d))/(f*(1 + q)^2*r^2*(f*x)^((1 + q)*r)))","A",1
448,1,408,480,1.8980379,"\int (f x)^m \left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)^p \, dx","Integrate[(f*x)^m*(d + e*x^r)^3*(a + b*Log[c*x^n])^p,x]","x^{-m} (f x)^m \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{d^3 \exp \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+1}+e \left(\frac{3 d^2 \exp \left(-\frac{(m+r+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \left(-\frac{(m+r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+r+1}+e \left(\frac{3 d \exp \left(-\frac{(m+2 r+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \left(-\frac{(m+2 r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+2 r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+2 r+1}+\frac{e \exp \left(-\frac{(m+3 r+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \left(-\frac{(m+3 r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+3 r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+3 r+1}\right)\right)\right)","\frac{d^3 (f x)^{m+1} e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{f (m+1)}+\frac{3 d^2 e x^{r+1} (f x)^m e^{-\frac{a (m+r+1)}{b n}} \left(c x^n\right)^{-\frac{m+r+1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+r+1}+\frac{3 d e^2 x^{2 r+1} (f x)^m e^{-\frac{a (m+2 r+1)}{b n}} \left(c x^n\right)^{-\frac{m+2 r+1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+2 r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+2 r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+2 r+1}+\frac{e^3 x^{3 r+1} (f x)^m e^{-\frac{a (m+3 r+1)}{b n}} \left(c x^n\right)^{-\frac{m+3 r+1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+3 r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+3 r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+3 r+1}",1,"((f*x)^m*(a + b*Log[c*x^n])^p*((d^3*Gamma[1 + p, -(((1 + m)*(a + b*Log[c*x^n]))/(b*n))])/(E^(((1 + m)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*(1 + m)*(-(((1 + m)*(a + b*Log[c*x^n]))/(b*n)))^p) + e*((3*d^2*Gamma[1 + p, -(((1 + m + r)*(a + b*Log[c*x^n]))/(b*n))])/(E^(((1 + m + r)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*(1 + m + r)*(-(((1 + m + r)*(a + b*Log[c*x^n]))/(b*n)))^p) + e*((3*d*Gamma[1 + p, -(((1 + m + 2*r)*(a + b*Log[c*x^n]))/(b*n))])/(E^(((1 + m + 2*r)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*(1 + m + 2*r)*(-(((1 + m + 2*r)*(a + b*Log[c*x^n]))/(b*n)))^p) + (e*Gamma[1 + p, -(((1 + m + 3*r)*(a + b*Log[c*x^n]))/(b*n))])/(E^(((1 + m + 3*r)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*(1 + m + 3*r)*(-(((1 + m + 3*r)*(a + b*Log[c*x^n]))/(b*n)))^p)))))/x^m","A",1
449,1,304,350,0.9702862,"\int (f x)^m \left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)^p \, dx","Integrate[(f*x)^m*(d + e*x^r)^2*(a + b*Log[c*x^n])^p,x]","x^{-m} (f x)^m \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{d^2 \exp \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+1}+e \left(\frac{2 d \exp \left(-\frac{(m+r+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \left(-\frac{(m+r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+r+1}+\frac{e \exp \left(-\frac{(m+2 r+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \left(-\frac{(m+2 r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+2 r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+2 r+1}\right)\right)","\frac{d^2 (f x)^{m+1} e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{f (m+1)}+\frac{2 d e x^{r+1} (f x)^m e^{-\frac{a (m+r+1)}{b n}} \left(c x^n\right)^{-\frac{m+r+1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+r+1}+\frac{e^2 x^{2 r+1} (f x)^m e^{-\frac{a (m+2 r+1)}{b n}} \left(c x^n\right)^{-\frac{m+2 r+1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+2 r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+2 r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+2 r+1}",1,"((f*x)^m*(a + b*Log[c*x^n])^p*((d^2*Gamma[1 + p, -(((1 + m)*(a + b*Log[c*x^n]))/(b*n))])/(E^(((1 + m)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*(1 + m)*(-(((1 + m)*(a + b*Log[c*x^n]))/(b*n)))^p) + e*((2*d*Gamma[1 + p, -(((1 + m + r)*(a + b*Log[c*x^n]))/(b*n))])/(E^(((1 + m + r)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*(1 + m + r)*(-(((1 + m + r)*(a + b*Log[c*x^n]))/(b*n)))^p) + (e*Gamma[1 + p, -(((1 + m + 2*r)*(a + b*Log[c*x^n]))/(b*n))])/(E^(((1 + m + 2*r)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*(1 + m + 2*r)*(-(((1 + m + 2*r)*(a + b*Log[c*x^n]))/(b*n)))^p))))/x^m","A",1
450,1,200,220,0.4623259,"\int (f x)^m \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)^p \, dx","Integrate[(f*x)^m*(d + e*x^r)*(a + b*Log[c*x^n])^p,x]","x^{-m} (f x)^m \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{d \exp \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+1}+\frac{e \exp \left(-\frac{(m+r+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \left(-\frac{(m+r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+r+1}\right)","\frac{d (f x)^{m+1} e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{f (m+1)}+\frac{e x^{r+1} (f x)^m e^{-\frac{a (m+r+1)}{b n}} \left(c x^n\right)^{-\frac{m+r+1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+r+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+r+1}",1,"((f*x)^m*(a + b*Log[c*x^n])^p*((d*Gamma[1 + p, -(((1 + m)*(a + b*Log[c*x^n]))/(b*n))])/(E^(((1 + m)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*(1 + m)*(-(((1 + m)*(a + b*Log[c*x^n]))/(b*n)))^p) + (e*Gamma[1 + p, -(((1 + m + r)*(a + b*Log[c*x^n]))/(b*n))])/(E^(((1 + m + r)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*(1 + m + r)*(-(((1 + m + r)*(a + b*Log[c*x^n]))/(b*n)))^p)))/x^m","A",1
451,1,107,106,0.0670714,"\int (f x)^m \left(a+b \log \left(c x^n\right)\right)^p \, dx","Integrate[(f*x)^m*(a + b*Log[c*x^n])^p,x]","\frac{x^{-m} (f x)^m \left(a+b \log \left(c x^n\right)\right)^p \exp \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+1}","\frac{(f x)^{m+1} e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{f (m+1)}",1,"((f*x)^m*Gamma[1 + p, -(((1 + m)*(a + b*Log[c*x^n]))/(b*n))]*(a + b*Log[c*x^n])^p)/(E^(((1 + m)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*(1 + m)*x^m*(-(((1 + m)*(a + b*Log[c*x^n]))/(b*n)))^p)","A",1
452,0,0,30,3.0675682,"\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)^p}{d+e x^r} \, dx","Integrate[((f*x)^m*(a + b*Log[c*x^n])^p)/(d + e*x^r),x]","\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)^p}{d+e x^r} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)^p}{d+e x^r},x\right)",0,"Integrate[((f*x)^m*(a + b*Log[c*x^n])^p)/(d + e*x^r), x]","A",-1
453,0,0,30,3.251512,"\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)^p}{\left(d+e x^r\right)^2} \, dx","Integrate[((f*x)^m*(a + b*Log[c*x^n])^p)/(d + e*x^r)^2,x]","\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)^p}{\left(d+e x^r\right)^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)^p}{\left(d+e x^r\right)^2},x\right)",0,"Integrate[((f*x)^m*(a + b*Log[c*x^n])^p)/(d + e*x^r)^2, x]","A",-1
454,1,108,115,0.1787375,"\int \frac{(f+g x) \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^3} \, dx","Integrate[((f + g*x)*(a + b*Log[c*x^n]))/(d + e*x)^3,x]","\frac{-\frac{(e f-d g) \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2}-\frac{2 g \left(a+b \log \left(c x^n\right)\right)}{d+e x}+\frac{b n (e f-d g) \left(\frac{d}{d+e x}-\log (d+e x)+\log (x)\right)}{d^2}+\frac{2 b g n (\log (x)-\log (d+e x))}{d}}{2 e^2}","-\frac{(f+g x)^2 \left(a+b \log \left(c x^n\right)\right)}{2 (d+e x)^2 (e f-d g)}-\frac{b n (d g+e f) \log (d+e x)}{2 d^2 e^2}+\frac{b f^2 n \log (x)}{2 d^2 (e f-d g)}+\frac{b n (e f-d g)}{2 d e^2 (d+e x)}",1,"(-(((e*f - d*g)*(a + b*Log[c*x^n]))/(d + e*x)^2) - (2*g*(a + b*Log[c*x^n]))/(d + e*x) + (2*b*g*n*(Log[x] - Log[d + e*x]))/d + (b*(e*f - d*g)*n*(d/(d + e*x) + Log[x] - Log[d + e*x]))/d^2)/(2*e^2)","A",1
455,1,244,202,0.2510749,"\int \frac{(f+g x) \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^3} \, dx","Integrate[((f + g*x)*(a + b*Log[c*x^n])^2)/(d + e*x)^3,x]","\frac{\frac{(e f-d g) \left(-2 b n (d+e x) \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)+(d+e x) \left(a+b \log \left(c x^n\right)\right)^2+2 b d n \left(a+b \log \left(c x^n\right)\right)-2 b^2 n^2 (d+e x) \text{Li}_2\left(-\frac{e x}{d}\right)-2 b^2 n^2 (d+e x) (\log (x)-\log (d+e x))\right)}{d^2 (d+e x)}+\frac{2 g \left(\left(a+b \log \left(c x^n\right)\right) \left(a+b \log \left(c x^n\right)-2 b n \log \left(\frac{e x}{d}+1\right)\right)-2 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)\right)}{d}-\frac{(e f-d g) \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2}-\frac{2 g \left(a+b \log \left(c x^n\right)\right)^2}{d+e x}}{2 e^2}","-\frac{b n (d g+e f) \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 e^2}+\frac{f^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 d^2 (e f-d g)}-\frac{b n x (e f-d g) \left(a+b \log \left(c x^n\right)\right)}{d^2 e (d+e x)}-\frac{(f+g x)^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 (d+e x)^2 (e f-d g)}-\frac{b^2 n^2 (d g+e f) \text{Li}_2\left(-\frac{e x}{d}\right)}{d^2 e^2}+\frac{b^2 n^2 (e f-d g) \log (d+e x)}{d^2 e^2}",1,"(-(((e*f - d*g)*(a + b*Log[c*x^n])^2)/(d + e*x)^2) - (2*g*(a + b*Log[c*x^n])^2)/(d + e*x) + (2*g*((a + b*Log[c*x^n])*(a + b*Log[c*x^n] - 2*b*n*Log[1 + (e*x)/d]) - 2*b^2*n^2*PolyLog[2, -((e*x)/d)]))/d + ((e*f - d*g)*(2*b*d*n*(a + b*Log[c*x^n]) + (d + e*x)*(a + b*Log[c*x^n])^2 - 2*b^2*n^2*(d + e*x)*(Log[x] - Log[d + e*x]) - 2*b*n*(d + e*x)*(a + b*Log[c*x^n])*Log[1 + (e*x)/d] - 2*b^2*n^2*(d + e*x)*PolyLog[2, -((e*x)/d)]))/(d^2*(d + e*x)))/(2*e^2)","A",1
456,1,339,295,0.3881777,"\int \frac{(f+g x) \left(a+b \log \left(c x^n\right)\right)^3}{(d+e x)^3} \, dx","Integrate[((f + g*x)*(a + b*Log[c*x^n])^3)/(d + e*x)^3,x]","\frac{\frac{(e f-d g) \left(-3 b n (d+e x) \left(\left(a+b \log \left(c x^n\right)\right) \left(a+b \log \left(c x^n\right)-2 b n \log \left(\frac{e x}{d}+1\right)\right)-2 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right)\right)-6 b^2 n^2 (d+e x) \left(\text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)-b n \text{Li}_3\left(-\frac{e x}{d}\right)\right)+(d+e x) \left(a+b \log \left(c x^n\right)\right)^3-3 b n (d+e x) \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+3 b d n \left(a+b \log \left(c x^n\right)\right)^2\right)}{d^2 (d+e x)}+\frac{2 g \left(-6 b^2 n^2 \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)+\left(a+b \log \left(c x^n\right)\right)^2 \left(a+b \log \left(c x^n\right)-3 b n \log \left(\frac{e x}{d}+1\right)\right)+6 b^3 n^3 \text{Li}_3\left(-\frac{e x}{d}\right)\right)}{d}-\frac{(e f-d g) \left(a+b \log \left(c x^n\right)\right)^3}{(d+e x)^2}-\frac{2 g \left(a+b \log \left(c x^n\right)\right)^3}{d+e x}}{2 e^2}","-\frac{3 b^2 n^2 (d g+e f) \text{Li}_2\left(-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 e^2}+\frac{3 b^2 n^2 (e f-d g) \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 e^2}-\frac{3 b n (d g+e f) \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 d^2 e^2}+\frac{f^2 \left(a+b \log \left(c x^n\right)\right)^3}{2 d^2 (e f-d g)}-\frac{3 b n x (e f-d g) \left(a+b \log \left(c x^n\right)\right)^2}{2 d^2 e (d+e x)}-\frac{(f+g x)^2 \left(a+b \log \left(c x^n\right)\right)^3}{2 (d+e x)^2 (e f-d g)}+\frac{3 b^3 n^3 (e f-d g) \text{Li}_2\left(-\frac{e x}{d}\right)}{d^2 e^2}+\frac{3 b^3 n^3 (d g+e f) \text{Li}_3\left(-\frac{e x}{d}\right)}{d^2 e^2}",1,"(-(((e*f - d*g)*(a + b*Log[c*x^n])^3)/(d + e*x)^2) - (2*g*(a + b*Log[c*x^n])^3)/(d + e*x) + (2*g*((a + b*Log[c*x^n])^2*(a + b*Log[c*x^n] - 3*b*n*Log[1 + (e*x)/d]) - 6*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] + 6*b^3*n^3*PolyLog[3, -((e*x)/d)]))/d + ((e*f - d*g)*(3*b*d*n*(a + b*Log[c*x^n])^2 + (d + e*x)*(a + b*Log[c*x^n])^3 - 3*b*n*(d + e*x)*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d] - 3*b*n*(d + e*x)*((a + b*Log[c*x^n])*(a + b*Log[c*x^n] - 2*b*n*Log[1 + (e*x)/d]) - 2*b^2*n^2*PolyLog[2, -((e*x)/d)]) - 6*b^2*n^2*(d + e*x)*((a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)] - b*n*PolyLog[3, -((e*x)/d)])))/(d^2*(d + e*x)))/(2*e^2)","A",1