1,1,48,0,0.0516624,"\int x^3 (d+e x) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^3*(d + e*x)*(a + b*Log[c*x^n]),x]","\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","\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,"-(b*d*n*x^4)/16 - (b*e*n*x^5)/25 + ((5*d*x^4 + 4*e*x^5)*(a + b*Log[c*x^n]))/20","A",4,3,19,0.1579,1,"{43, 2334, 12}"
2,1,48,0,0.0501997,"\int x^2 (d+e x) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*(d + e*x)*(a + b*Log[c*x^n]),x]","\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","\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,"-(b*d*n*x^3)/9 - (b*e*n*x^4)/16 + ((4*d*x^3 + 3*e*x^4)*(a + b*Log[c*x^n]))/12","A",4,3,19,0.1579,1,"{43, 2334, 12}"
3,1,48,0,0.0361271,"\int x (d+e x) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*(d + e*x)*(a + b*Log[c*x^n]),x]","\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","\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,"-(b*d*n*x^2)/4 - (b*e*n*x^3)/9 + ((3*d*x^2 + 2*e*x^3)*(a + b*Log[c*x^n]))/6","A",4,3,17,0.1765,1,"{43, 2334, 12}"
4,1,41,0,0.0163162,"\int (d+e x) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(d + e*x)*(a + b*Log[c*x^n]),x]","\frac{1}{2} \left(2 d x+e x^2\right) \left(a+b \log \left(c x^n\right)\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,"-(b*d*n*x) - (b*e*n*x^2)/4 + ((2*d*x + e*x^2)*(a + b*Log[c*x^n]))/2","A",2,1,16,0.06250,1,"{2313}"
5,1,44,0,0.0489701,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[((d + e*x)*(a + b*Log[c*x^n]))/x,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","\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 + b*e*x*Log[c*x^n] + (d*(a + b*Log[c*x^n])^2)/(2*b*n)","A",4,3,19,0.1579,1,"{2346, 2301, 2295}"
6,1,43,0,0.0497989,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[((d + e*x)*(a + b*Log[c*x^n]))/x^2,x]","-\left(\frac{d}{x}-e \log (x)\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b d n}{x}-\frac{1}{2} b e n \log ^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}",1,"-((b*d*n)/x) - (b*e*n*Log[x]^2)/2 - (d/x - e*Log[x])*(a + b*Log[c*x^n])","A",4,4,19,0.2105,1,"{43, 2334, 14, 2301}"
7,1,60,0,0.0492517,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[((d + e*x)*(a + b*Log[c*x^n]))/x^3,x]","-\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}","-\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,"-(b*d*n)/(4*x^2) - (b*e*n)/x + (b*e^2*n*Log[x])/(2*d) - ((d + e*x)^2*(a + b*Log[c*x^n]))/(2*d*x^2)","A",4,4,19,0.2105,1,"{37, 2334, 12, 43}"
8,1,48,0,0.0447902,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Int[((d + e*x)*(a + b*Log[c*x^n]))/x^4,x]","-\frac{1}{6} \left(\frac{2 d}{x^3}+\frac{3 e}{x^2}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b d n}{9 x^3}-\frac{b e n}{4 x^2}","-\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,"-(b*d*n)/(9*x^3) - (b*e*n)/(4*x^2) - (((2*d)/x^3 + (3*e)/x^2)*(a + b*Log[c*x^n]))/6","A",4,3,19,0.1579,1,"{43, 2334, 12}"
9,1,74,0,0.0897376,"\int x^3 (d+e x)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^3*(d + e*x)^2*(a + b*Log[c*x^n]),x]","\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","\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,"-(b*d^2*n*x^4)/16 - (2*b*d*e*n*x^5)/25 - (b*e^2*n*x^6)/36 + ((15*d^2*x^4 + 24*d*e*x^5 + 10*e^2*x^6)*(a + b*Log[c*x^n]))/60","A",4,4,21,0.1905,1,"{43, 2334, 12, 14}"
10,1,74,0,0.079526,"\int x^2 (d+e x)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*(d + e*x)^2*(a + b*Log[c*x^n]),x]","\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","\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,"-(b*d^2*n*x^3)/9 - (b*d*e*n*x^4)/8 - (b*e^2*n*x^5)/25 + ((10*d^2*x^3 + 15*d*e*x^4 + 6*e^2*x^5)*(a + b*Log[c*x^n]))/30","A",4,4,21,0.1905,1,"{43, 2334, 12, 14}"
11,1,74,0,0.0628877,"\int x (d+e x)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*(d + e*x)^2*(a + b*Log[c*x^n]),x]","\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","\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,"-(b*d^2*n*x^2)/4 - (2*b*d*e*n*x^3)/9 - (b*e^2*n*x^4)/16 + ((6*d^2*x^2 + 8*d*e*x^3 + 3*e^2*x^4)*(a + b*Log[c*x^n]))/12","A",4,4,19,0.2105,1,"{43, 2334, 12, 14}"
12,1,70,0,0.037794,"\int (d+e x)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(d + e*x)^2*(a + b*Log[c*x^n]),x]","\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","\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,"-(b*d^2*n*x) - (b*d*e*n*x^2)/2 - (b*e^2*n*x^3)/9 - (b*d^3*n*Log[x])/(3*e) + ((d + e*x)^3*(a + b*Log[c*x^n]))/(3*e)","A",4,4,18,0.2222,1,"{32, 2313, 12, 43}"
13,1,63,0,0.0714581,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[((d + e*x)^2*(a + b*Log[c*x^n]))/x,x]","\frac{1}{2} \left(2 d^2 \log (x)+4 d e x+e^2 x^2\right) \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","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,"-(b*n*(4*d + e*x)^2)/4 - (b*d^2*n*Log[x]^2)/2 + ((4*d*e*x + e^2*x^2 + 2*d^2*Log[x])*(a + b*Log[c*x^n]))/2","A",3,3,21,0.1429,1,"{43, 2334, 2301}"
14,1,61,0,0.0759305,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[((d + e*x)^2*(a + b*Log[c*x^n]))/x^2,x]","-\left(\frac{d^2}{x}-2 d e \log (x)-e^2 x\right) \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","-\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) - b*e^2*n*x - b*d*e*n*Log[x]^2 - (d^2/x - e^2*x - 2*d*e*Log[x])*(a + b*Log[c*x^n])","A",3,3,21,0.1429,1,"{43, 2334, 2301}"
15,1,67,0,0.0788719,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[((d + e*x)^2*(a + b*Log[c*x^n]))/x^3,x]","-\frac{1}{2} \left(\frac{d^2}{x^2}+\frac{4 d e}{x}-2 e^2 \log (x)\right) \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)","-\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,"-(b*n*(d + 4*e*x)^2)/(4*x^2) - (b*e^2*n*Log[x]^2)/2 - ((d^2/x^2 + (4*d*e)/x - 2*e^2*Log[x])*(a + b*Log[c*x^n]))/2","A",4,4,21,0.1905,1,"{43, 2334, 37, 2301}"
16,1,75,0,0.0709689,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Int[((d + e*x)^2*(a + b*Log[c*x^n]))/x^4,x]","-\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}","-\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,"-(b*d^2*n)/(9*x^3) - (b*d*e*n)/(2*x^2) - (b*e^2*n)/x + (b*e^3*n*Log[x])/(3*d) - ((d + e*x)^3*(a + b*Log[c*x^n]))/(3*d*x^3)","A",4,4,21,0.1905,1,"{37, 2334, 12, 43}"
17,1,74,0,0.0762334,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)}{x^5} \, dx","Int[((d + e*x)^2*(a + b*Log[c*x^n]))/x^5,x]","-\frac{1}{12} \left(\frac{3 d^2}{x^4}+\frac{8 d e}{x^3}+\frac{6 e^2}{x^2}\right) \left(a+b \log \left(c x^n\right)\right)-\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}","-\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,"-(b*d^2*n)/(16*x^4) - (2*b*d*e*n)/(9*x^3) - (b*e^2*n)/(4*x^2) - (((3*d^2)/x^4 + (8*d*e)/x^3 + (6*e^2)/x^2)*(a + b*Log[c*x^n]))/12","A",4,4,21,0.1905,1,"{43, 2334, 12, 14}"
18,1,74,0,0.075784,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Int[((d + e*x)^2*(a + b*Log[c*x^n]))/x^6,x]","-\frac{1}{30} \left(\frac{6 d^2}{x^5}+\frac{15 d e}{x^4}+\frac{10 e^2}{x^3}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b d^2 n}{25 x^5}-\frac{b d e n}{8 x^4}-\frac{b e^2 n}{9 x^3}","-\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,"-(b*d^2*n)/(25*x^5) - (b*d*e*n)/(8*x^4) - (b*e^2*n)/(9*x^3) - (((6*d^2)/x^5 + (15*d*e)/x^4 + (10*e^2)/x^3)*(a + b*Log[c*x^n]))/30","A",4,4,21,0.1905,1,"{43, 2334, 12, 14}"
19,1,100,0,0.1055687,"\int x^3 (d+e x)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^3*(d + e*x)^3*(a + b*Log[c*x^n]),x]","\frac{1}{140} \left(84 d^2 e x^5+35 d^3 x^4+70 d e^2 x^6+20 e^3 x^7\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3}{25} b d^2 e n x^5-\frac{1}{16} b d^3 n x^4-\frac{1}{12} b d e^2 n x^6-\frac{1}{49} b e^3 n x^7","\frac{1}{140} \left(84 d^2 e x^5+35 d^3 x^4+70 d e^2 x^6+20 e^3 x^7\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3}{25} b d^2 e n x^5-\frac{1}{16} b d^3 n x^4-\frac{1}{12} b d e^2 n x^6-\frac{1}{49} b e^3 n x^7",1,"-(b*d^3*n*x^4)/16 - (3*b*d^2*e*n*x^5)/25 - (b*d*e^2*n*x^6)/12 - (b*e^3*n*x^7)/49 + ((35*d^3*x^4 + 84*d^2*e*x^5 + 70*d*e^2*x^6 + 20*e^3*x^7)*(a + b*Log[c*x^n]))/140","A",4,4,21,0.1905,1,"{43, 2334, 12, 14}"
20,1,100,0,0.1022745,"\int x^2 (d+e x)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*(d + e*x)^3*(a + b*Log[c*x^n]),x]","\frac{1}{60} \left(45 d^2 e x^4+20 d^3 x^3+36 d e^2 x^5+10 e^3 x^6\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3}{16} b d^2 e n x^4-\frac{1}{9} b d^3 n x^3-\frac{3}{25} b d e^2 n x^5-\frac{1}{36} b e^3 n x^6","\frac{1}{60} \left(45 d^2 e x^4+20 d^3 x^3+36 d e^2 x^5+10 e^3 x^6\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3}{16} b d^2 e n x^4-\frac{1}{9} b d^3 n x^3-\frac{3}{25} b d e^2 n x^5-\frac{1}{36} b e^3 n x^6",1,"-(b*d^3*n*x^3)/9 - (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 + ((20*d^3*x^3 + 45*d^2*e*x^4 + 36*d*e^2*x^5 + 10*e^3*x^6)*(a + b*Log[c*x^n]))/60","A",4,4,21,0.1905,1,"{43, 2334, 12, 14}"
21,1,122,0,0.0911198,"\int x (d+e x)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*(d + e*x)^3*(a + b*Log[c*x^n]),x]","-\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{1}{15} b d^2 e n x^3+\frac{b d^4 n x}{5 e}+\frac{3}{20} b d^3 n x^2+\frac{1}{80} b d e^2 n x^4-\frac{b n (d+e x)^5}{25 e^2}","-\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{1}{15} b d^2 e n x^3+\frac{b d^4 n x}{5 e}+\frac{3}{20} b d^3 n x^2+\frac{1}{80} b d e^2 n x^4-\frac{b n (d+e x)^5}{25 e^2}",1,"(b*d^4*n*x)/(5*e) + (3*b*d^3*n*x^2)/20 + (b*d^2*e*n*x^3)/15 + (b*d*e^2*n*x^4)/80 - (b*n*(d + e*x)^5)/(25*e^2) + (b*d^5*n*Log[x])/(20*e^2) - (((5*d*(d + e*x)^4)/e^2 - (4*(d + e*x)^5)/e^2)*(a + b*Log[c*x^n]))/20","A",5,4,19,0.2105,1,"{43, 2334, 12, 80}"
22,1,85,0,0.0434278,"\int (d+e x)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(d + e*x)^3*(a + b*Log[c*x^n]),x]","\frac{(d+e x)^4 \left(a+b \log \left(c x^n\right)\right)}{4 e}-\frac{3}{4} b d^2 e n x^2-\frac{b d^4 n \log (x)}{4 e}-b d^3 n x-\frac{1}{3} b d e^2 n x^3-\frac{1}{16} b e^3 n x^4","\frac{(d+e x)^4 \left(a+b \log \left(c x^n\right)\right)}{4 e}-\frac{3}{4} b d^2 e n x^2-\frac{b d^4 n \log (x)}{4 e}-b d^3 n x-\frac{1}{3} b d e^2 n x^3-\frac{1}{16} b e^3 n x^4",1,"-(b*d^3*n*x) - (3*b*d^2*e*n*x^2)/4 - (b*d*e^2*n*x^3)/3 - (b*e^3*n*x^4)/16 - (b*d^4*n*Log[x])/(4*e) + ((d + e*x)^4*(a + b*Log[c*x^n]))/(4*e)","A",4,4,18,0.2222,1,"{32, 2313, 12, 43}"
23,1,94,0,0.0882038,"\int \frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[((d + e*x)^3*(a + b*Log[c*x^n]))/x,x]","\frac{1}{6} \left(18 d^2 e x+6 d^3 \log (x)+9 d e^2 x^2+2 e^3 x^3\right) \left(a+b \log \left(c x^n\right)\right)-3 b d^2 e n x-\frac{1}{2} b d^3 n \log ^2(x)-\frac{3}{4} b d e^2 n x^2-\frac{1}{9} b e^3 n x^3","3 d^2 e x \left(a+b \log \left(c x^n\right)\right)+d^3 \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}{3} e^3 x^3 \left(a+b \log \left(c x^n\right)\right)-3 b d^2 e n x-\frac{1}{2} b d^3 n \log ^2(x)-\frac{3}{4} b d e^2 n x^2-\frac{1}{9} b e^3 n x^3",1,"-3*b*d^2*e*n*x - (3*b*d*e^2*n*x^2)/4 - (b*e^3*n*x^3)/9 - (b*d^3*n*Log[x]^2)/2 + ((18*d^2*e*x + 9*d*e^2*x^2 + 2*e^3*x^3 + 6*d^3*Log[x])*(a + b*Log[c*x^n]))/6","A",4,3,21,0.1429,1,"{43, 2334, 2301}"
24,1,92,0,0.0877142,"\int \frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[((d + e*x)^3*(a + b*Log[c*x^n]))/x^2,x]","-\frac{1}{2} \left(-6 d^2 e \log (x)+\frac{2 d^3}{x}-6 d e^2 x-e^3 x^2\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3}{2} b d^2 e n \log ^2(x)-\frac{b d^3 n}{x}-3 b d e^2 n x-\frac{1}{4} b e^3 n x^2","3 d^2 e \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{d^3 \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}{2} e^3 x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{3}{2} b d^2 e n \log ^2(x)-\frac{b d^3 n}{x}-3 b d e^2 n x-\frac{1}{4} b e^3 n x^2",1,"-((b*d^3*n)/x) - 3*b*d*e^2*n*x - (b*e^3*n*x^2)/4 - (3*b*d^2*e*n*Log[x]^2)/2 - (((2*d^3)/x - 6*d*e^2*x - e^3*x^2 - 6*d^2*e*Log[x])*(a + b*Log[c*x^n]))/2","A",3,3,21,0.1429,1,"{43, 2334, 2301}"
25,1,91,0,0.0909902,"\int \frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[((d + e*x)^3*(a + b*Log[c*x^n]))/x^3,x]","-\frac{1}{2} \left(\frac{6 d^2 e}{x}+\frac{d^3}{x^2}-6 d e^2 \log (x)-2 e^3 x\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n}{x}-\frac{b d^3 n}{4 x^2}-\frac{3}{2} b d e^2 n \log ^2(x)-b e^3 n x","-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{d^3 \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)+e^3 x \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n}{x}-\frac{b d^3 n}{4 x^2}-\frac{3}{2} b d e^2 n \log ^2(x)-b e^3 n x",1,"-(b*d^3*n)/(4*x^2) - (3*b*d^2*e*n)/x - b*e^3*n*x - (3*b*d*e^2*n*Log[x]^2)/2 - ((d^3/x^2 + (6*d^2*e)/x - 2*e^3*x - 6*d*e^2*Log[x])*(a + b*Log[c*x^n]))/2","A",3,3,21,0.1429,1,"{43, 2334, 2301}"
26,1,98,0,0.1078176,"\int \frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Int[((d + e*x)^3*(a + b*Log[c*x^n]))/x^4,x]","-\frac{1}{6} \left(\frac{9 d^2 e}{x^2}+\frac{2 d^3}{x^3}+\frac{18 d e^2}{x}-6 e^3 \log (x)\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n}{4 x^2}-\frac{b d^3 n}{9 x^3}-\frac{3 b d e^2 n}{x}-\frac{1}{2} b e^3 n \log ^2(x)","-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\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{3 b d^2 e n}{4 x^2}-\frac{b d^3 n}{9 x^3}-\frac{3 b d e^2 n}{x}-\frac{1}{2} b e^3 n \log ^2(x)",1,"-(b*d^3*n)/(9*x^3) - (3*b*d^2*e*n)/(4*x^2) - (3*b*d*e^2*n)/x - (b*e^3*n*Log[x]^2)/2 - (((2*d^3)/x^3 + (9*d^2*e)/x^2 + (18*d*e^2)/x - 6*e^3*Log[x])*(a + b*Log[c*x^n]))/6","A",5,4,21,0.1905,1,"{43, 2334, 14, 2301}"
27,1,90,0,0.082418,"\int \frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{x^5} \, dx","Int[((d + e*x)^3*(a + b*Log[c*x^n]))/x^5,x]","-\frac{(d+e x)^4 \left(a+b \log \left(c x^n\right)\right)}{4 d x^4}-\frac{b d^2 e n}{3 x^3}-\frac{b d^3 n}{16 x^4}-\frac{3 b d e^2 n}{4 x^2}+\frac{b e^4 n \log (x)}{4 d}-\frac{b e^3 n}{x}","-\frac{(d+e x)^4 \left(a+b \log \left(c x^n\right)\right)}{4 d x^4}-\frac{b d^2 e n}{3 x^3}-\frac{b d^3 n}{16 x^4}-\frac{3 b d e^2 n}{4 x^2}+\frac{b e^4 n \log (x)}{4 d}-\frac{b e^3 n}{x}",1,"-(b*d^3*n)/(16*x^4) - (b*d^2*e*n)/(3*x^3) - (3*b*d*e^2*n)/(4*x^2) - (b*e^3*n)/x + (b*e^4*n*Log[x])/(4*d) - ((d + e*x)^4*(a + b*Log[c*x^n]))/(4*d*x^4)","A",4,4,21,0.1905,1,"{37, 2334, 12, 43}"
28,1,133,0,0.0983751,"\int \frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Int[((d + e*x)^3*(a + b*Log[c*x^n]))/x^6,x]","-\frac{1}{20} \left(\frac{4 (d+e x)^4}{d x^5}-\frac{e (d+e x)^4}{d^2 x^4}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b e^5 n \log (x)}{20 d^2}+\frac{b d^2 e n}{80 x^4}-\frac{b n (d+e x)^5}{25 d^2 x^5}+\frac{b d e^2 n}{15 x^3}+\frac{b e^4 n}{5 d x}+\frac{3 b e^3 n}{20 x^2}","\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 d^2 e n}{80 x^4}-\frac{b n (d+e x)^5}{25 d^2 x^5}+\frac{b d e^2 n}{15 x^3}+\frac{b e^4 n}{5 d x}+\frac{3 b e^3 n}{20 x^2}",1,"(b*d^2*e*n)/(80*x^4) + (b*d*e^2*n)/(15*x^3) + (3*b*e^3*n)/(20*x^2) + (b*e^4*n)/(5*d*x) - (b*n*(d + e*x)^5)/(25*d^2*x^5) - (b*e^5*n*Log[x])/(20*d^2) - (((4*(d + e*x)^4)/(d*x^5) - (e*(d + e*x)^4)/(d^2*x^4))*(a + b*Log[c*x^n]))/20","A",5,6,21,0.2857,1,"{45, 37, 2334, 12, 78, 43}"
29,1,100,0,0.0959554,"\int \frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{x^7} \, dx","Int[((d + e*x)^3*(a + b*Log[c*x^n]))/x^7,x]","-\frac{1}{60} \left(\frac{36 d^2 e}{x^5}+\frac{10 d^3}{x^6}+\frac{45 d e^2}{x^4}+\frac{20 e^3}{x^3}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n}{25 x^5}-\frac{b d^3 n}{36 x^6}-\frac{3 b d e^2 n}{16 x^4}-\frac{b e^3 n}{9 x^3}","-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{6 x^6}-\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{3 b d^2 e n}{25 x^5}-\frac{b d^3 n}{36 x^6}-\frac{3 b d e^2 n}{16 x^4}-\frac{b e^3 n}{9 x^3}",1,"-(b*d^3*n)/(36*x^6) - (3*b*d^2*e*n)/(25*x^5) - (3*b*d*e^2*n)/(16*x^4) - (b*e^3*n)/(9*x^3) - (((10*d^3)/x^6 + (36*d^2*e)/x^5 + (45*d*e^2)/x^4 + (20*e^3)/x^3)*(a + b*Log[c*x^n]))/60","A",4,4,21,0.1905,1,"{43, 2334, 12, 14}"
30,1,100,0,0.1062538,"\int \frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)}{x^8} \, dx","Int[((d + e*x)^3*(a + b*Log[c*x^n]))/x^8,x]","-\frac{1}{140} \left(\frac{70 d^2 e}{x^6}+\frac{20 d^3}{x^7}+\frac{84 d e^2}{x^5}+\frac{35 e^3}{x^4}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b d^2 e n}{12 x^6}-\frac{b d^3 n}{49 x^7}-\frac{3 b d e^2 n}{25 x^5}-\frac{b e^3 n}{16 x^4}","-\frac{d^2 e \left(a+b \log \left(c x^n\right)\right)}{2 x^6}-\frac{d^3 \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)}{4 x^4}-\frac{b d^2 e n}{12 x^6}-\frac{b d^3 n}{49 x^7}-\frac{3 b d e^2 n}{25 x^5}-\frac{b e^3 n}{16 x^4}",1,"-(b*d^3*n)/(49*x^7) - (b*d^2*e*n)/(12*x^6) - (3*b*d*e^2*n)/(25*x^5) - (b*e^3*n)/(16*x^4) - (((20*d^3)/x^7 + (70*d^2*e)/x^6 + (84*d*e^2)/x^5 + (35*e^3)/x^4)*(a + b*Log[c*x^n]))/140","A",4,4,21,0.1905,1,"{43, 2334, 12, 14}"
31,1,148,0,0.1773568,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{d+e x} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/(d + e*x),x]","-\frac{b d^3 n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{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^2 n x}{e^3}+\frac{b d n x^2}{4 e^2}-\frac{b n x^3}{9 e}","-\frac{b d^3 n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{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^2 n x}{e^3}+\frac{b d n x^2}{4 e^2}-\frac{b n x^3}{9 e}",1,"(a*d^2*x)/e^3 - (b*d^2*n*x)/e^3 + (b*d*n*x^2)/(4*e^2) - (b*n*x^3)/(9*e) + (b*d^2*x*Log[c*x^n])/e^3 - (d*x^2*(a + b*Log[c*x^n]))/(2*e^2) + (x^3*(a + b*Log[c*x^n]))/(3*e) - (d^3*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^4 - (b*d^3*n*PolyLog[2, -((e*x)/d)])/e^4","A",8,6,21,0.2857,1,"{43, 2351, 2295, 2304, 2317, 2391}"
32,1,107,0,0.1358076,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{d+e x} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/(d + e*x),x]","\frac{b d^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{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 n x}{e^2}-\frac{b n x^2}{4 e}","\frac{b d^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{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 n x}{e^2}-\frac{b n x^2}{4 e}",1,"-((a*d*x)/e^2) + (b*d*n*x)/e^2 - (b*n*x^2)/(4*e) - (b*d*x*Log[c*x^n])/e^2 + (x^2*(a + b*Log[c*x^n]))/(2*e) + (d^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^3 + (b*d^2*n*PolyLog[2, -((e*x)/d)])/e^3","A",7,6,21,0.2857,1,"{43, 2351, 2295, 2304, 2317, 2391}"
33,1,69,0,0.0939894,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{d+e x} \, dx","Int[(x*(a + b*Log[c*x^n]))/(d + e*x),x]","-\frac{b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{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 n x}{e}","-\frac{b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{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 n x}{e}",1,"(a*x)/e - (b*n*x)/e + (b*x*Log[c*x^n])/e - (d*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^2 - (b*d*n*PolyLog[2, -((e*x)/d)])/e^2","A",6,5,19,0.2632,1,"{43, 2351, 2295, 2317, 2391}"
34,1,39,0,0.0260456,"\int \frac{a+b \log \left(c x^n\right)}{d+e x} \, dx","Int[(a + b*Log[c*x^n])/(d + e*x),x]","\frac{b n \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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}",1,"((a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e + (b*n*PolyLog[2, -((e*x)/d)])/e","A",2,2,18,0.1111,1,"{2317, 2391}"
35,1,66,0,0.0908774,"\int \frac{a+b \log \left(c x^n\right)}{x (d+e x)} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x)),x]","-\frac{b n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d}-\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 b d n}","\frac{b n \text{PolyLog}\left(2,-\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])^2/(2*b*d*n) - ((a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d - (b*n*PolyLog[2, -((e*x)/d)])/d","A",4,4,21,0.1905,1,"{2344, 2301, 2317, 2391}"
36,1,95,0,0.1446599,"\int \frac{a+b \log \left(c x^n\right)}{x^2 (d+e x)} \, dx","Int[(a + b*Log[c*x^n])/(x^2*(d + e*x)),x]","\frac{b e n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^2}-\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{2 b d^2 n}+\frac{e \log \left(\frac{e x}{d}+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 n}{d x}","-\frac{b e n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{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 n}{d x}",1,"-((b*n)/(d*x)) - (a + b*Log[c*x^n])/(d*x) - (e*(a + b*Log[c*x^n])^2)/(2*b*d^2*n) + (e*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^2 + (b*e*n*PolyLog[2, -((e*x)/d)])/d^2","A",6,6,21,0.2857,1,"{44, 2351, 2304, 2301, 2317, 2391}"
37,1,135,0,0.170924,"\int \frac{a+b \log \left(c x^n\right)}{x^3 (d+e x)} \, dx","Int[(a + b*Log[c*x^n])/(x^3*(d + e*x)),x]","-\frac{b e^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^3}+\frac{e^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 b d^3 n}-\frac{e^2 \log \left(\frac{e x}{d}+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 n}{d^2 x}-\frac{b n}{4 d x^2}","\frac{b e^2 n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{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 n}{d^2 x}-\frac{b n}{4 d x^2}",1,"-(b*n)/(4*d*x^2) + (b*e*n)/(d^2*x) - (a + b*Log[c*x^n])/(2*d*x^2) + (e*(a + b*Log[c*x^n]))/(d^2*x) + (e^2*(a + b*Log[c*x^n])^2)/(2*b*d^3*n) - (e^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^3 - (b*e^2*n*PolyLog[2, -((e*x)/d)])/d^3","A",7,6,21,0.2857,1,"{44, 2351, 2304, 2301, 2317, 2391}"
38,1,173,0,0.2120915,"\int \frac{a+b \log \left(c x^n\right)}{x^4 (d+e x)} \, dx","Int[(a + b*Log[c*x^n])/(x^4*(d + e*x)),x]","\frac{b e^3 n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^4}-\frac{e^3 \left(a+b \log \left(c x^n\right)\right)^2}{2 b d^4 n}+\frac{e^3 \log \left(\frac{e x}{d}+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^2 n}{d^3 x}+\frac{b e n}{4 d^2 x^2}-\frac{b n}{9 d x^3}","-\frac{b e^3 n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{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^2 n}{d^3 x}+\frac{b e n}{4 d^2 x^2}-\frac{b n}{9 d x^3}",1,"-(b*n)/(9*d*x^3) + (b*e*n)/(4*d^2*x^2) - (b*e^2*n)/(d^3*x) - (a + b*Log[c*x^n])/(3*d*x^3) + (e*(a + b*Log[c*x^n]))/(2*d^2*x^2) - (e^2*(a + b*Log[c*x^n]))/(d^3*x) - (e^3*(a + b*Log[c*x^n])^2)/(2*b*d^4*n) + (e^3*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^4 + (b*e^3*n*PolyLog[2, -((e*x)/d)])/d^4","A",8,6,21,0.2857,1,"{44, 2351, 2304, 2301, 2317, 2391}"
39,1,151,0,0.1809664,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/(d + e*x)^2,x]","\frac{3 b d^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^4}-\frac{d^2 x \left(a+b \log \left(c x^n\right)\right)}{e^3 (d+e x)}+\frac{3 d^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{2 a d x}{e^3}-\frac{2 b d x \log \left(c x^n\right)}{e^3}+\frac{b d^2 n \log (d+e x)}{e^4}+\frac{2 b d n x}{e^3}-\frac{b n x^2}{4 e^2}","\frac{3 b d^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{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 n x}{e^3}-\frac{3 b n x^2}{4 e^2}",1,"(-2*a*d*x)/e^3 + (2*b*d*n*x)/e^3 - (b*n*x^2)/(4*e^2) - (2*b*d*x*Log[c*x^n])/e^3 + (x^2*(a + b*Log[c*x^n]))/(2*e^2) - (d^2*x*(a + b*Log[c*x^n]))/(e^3*(d + e*x)) + (b*d^2*n*Log[d + e*x])/e^4 + (3*d^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^4 + (3*b*d^2*n*PolyLog[2, -((e*x)/d)])/e^4","A",9,8,21,0.3810,1,"{43, 2351, 2295, 2304, 2314, 31, 2317, 2391}"
40,1,106,0,0.1431223,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/(d + e*x)^2,x]","-\frac{2 b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^3}+\frac{d x \left(a+b \log \left(c x^n\right)\right)}{e^2 (d+e x)}-\frac{2 d \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^3}+\frac{a x}{e^2}+\frac{b x \log \left(c x^n\right)}{e^2}-\frac{b d n \log (d+e x)}{e^3}-\frac{b n x}{e^2}","-\frac{2 b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{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{b n x}{e^2}",1,"(a*x)/e^2 - (b*n*x)/e^2 + (b*x*Log[c*x^n])/e^2 + (d*x*(a + b*Log[c*x^n]))/(e^2*(d + e*x)) - (b*d*n*Log[d + e*x])/e^3 - (2*d*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^3 - (2*b*d*n*PolyLog[2, -((e*x)/d)])/e^3","A",8,7,21,0.3333,1,"{43, 2351, 2295, 2314, 31, 2317, 2391}"
41,1,74,0,0.1076565,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2} \, dx","Int[(x*(a + b*Log[c*x^n]))/(d + e*x)^2,x]","\frac{b n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^2}+\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{x \left(a+b \log \left(c x^n\right)\right)}{e (d+e x)}+\frac{b n \log (d+e x)}{e^2}","\frac{b n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{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)}",1,"-((x*(a + b*Log[c*x^n]))/(e*(d + e*x))) + (b*n*Log[d + e*x])/e^2 + ((a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^2 + (b*n*PolyLog[2, -((e*x)/d)])/e^2","A",6,6,19,0.3158,1,"{43, 2351, 2314, 31, 2317, 2391}"
42,1,39,0,0.0187661,"\int \frac{a+b \log \left(c x^n\right)}{(d+e x)^2} \, dx","Int[(a + b*Log[c*x^n])/(d + e*x)^2,x]","\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}","\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,"(x*(a + b*Log[c*x^n]))/(d*(d + e*x)) - (b*n*Log[d + e*x])/(d*e)","A",2,2,18,0.1111,1,"{2314, 31}"
43,1,102,0,0.1597382,"\int \frac{a+b \log \left(c x^n\right)}{x (d+e x)^2} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x)^2),x]","-\frac{b n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^2}-\frac{\log \left(\frac{e x}{d}+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{\left(a+b \log \left(c x^n\right)\right)^2}{2 b d^2 n}+\frac{b n \log (d+e x)}{d^2}","\frac{b n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{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 \log (d+e x)}{d^2}",1,"-((e*x*(a + b*Log[c*x^n]))/(d^2*(d + e*x))) + (a + b*Log[c*x^n])^2/(2*b*d^2*n) + (b*n*Log[d + e*x])/d^2 - ((a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^2 - (b*n*PolyLog[2, -((e*x)/d)])/d^2","A",7,7,21,0.3333,1,"{2347, 2344, 2301, 2317, 2391, 2314, 31}"
44,1,134,0,0.1791548,"\int \frac{a+b \log \left(c x^n\right)}{x^2 (d+e x)^2} \, dx","Int[(a + b*Log[c*x^n])/(x^2*(d + e*x)^2),x]","\frac{2 b e n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^3}+\frac{e^2 x \left(a+b \log \left(c x^n\right)\right)}{d^3 (d+e x)}-\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{b d^3 n}+\frac{2 e \log \left(\frac{e x}{d}+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{b e n \log (d+e x)}{d^3}-\frac{b n}{d^2 x}","-\frac{2 b e n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{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{b e n \log (d+e x)}{d^3}-\frac{b n}{d^2 x}",1,"-((b*n)/(d^2*x)) - (a + b*Log[c*x^n])/(d^2*x) + (e^2*x*(a + b*Log[c*x^n]))/(d^3*(d + e*x)) - (e*(a + b*Log[c*x^n])^2)/(b*d^3*n) - (b*e*n*Log[d + e*x])/d^3 + (2*e*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^3 + (2*b*e*n*PolyLog[2, -((e*x)/d)])/d^3","A",8,8,21,0.3810,1,"{44, 2351, 2304, 2301, 2314, 31, 2317, 2391}"
45,1,178,0,0.2133451,"\int \frac{a+b \log \left(c x^n\right)}{x^3 (d+e x)^2} \, dx","Int[(a + b*Log[c*x^n])/(x^3*(d + e*x)^2),x]","-\frac{3 b e^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{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 \left(a+b \log \left(c x^n\right)\right)^2}{2 b d^4 n}-\frac{3 e^2 \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)}{d^3 x}-\frac{a+b \log \left(c x^n\right)}{2 d^2 x^2}+\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}","\frac{3 b e^2 n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{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{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,"-(b*n)/(4*d^2*x^2) + (2*b*e*n)/(d^3*x) - (a + b*Log[c*x^n])/(2*d^2*x^2) + (2*e*(a + b*Log[c*x^n]))/(d^3*x) - (e^3*x*(a + b*Log[c*x^n]))/(d^4*(d + e*x)) + (3*e^2*(a + b*Log[c*x^n])^2)/(2*b*d^4*n) + (b*e^2*n*Log[d + e*x])/d^4 - (3*e^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^4 - (3*b*e^2*n*PolyLog[2, -((e*x)/d)])/d^4","A",9,8,21,0.3810,1,"{44, 2351, 2304, 2301, 2314, 31, 2317, 2391}"
46,1,167,0,0.2157344,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^3} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/(d + e*x)^3,x]","-\frac{3 b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^4}+\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{2 e^4 (d+e x)^2}+\frac{3 d x \left(a+b \log \left(c x^n\right)\right)}{e^3 (d+e x)}-\frac{3 d \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}+\frac{a x}{e^3}+\frac{b x \log \left(c x^n\right)}{e^3}-\frac{b d^2 n}{2 e^4 (d+e x)}-\frac{b d n \log (x)}{2 e^4}-\frac{5 b d n \log (d+e x)}{2 e^4}-\frac{b n x}{e^3}","-\frac{3 b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{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{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^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 n x}{e^3}",1,"(a*x)/e^3 - (b*n*x)/e^3 - (b*d^2*n)/(2*e^4*(d + e*x)) - (b*d*n*Log[x])/(2*e^4) + (b*x*Log[c*x^n])/e^3 + (d^3*(a + b*Log[c*x^n]))/(2*e^4*(d + e*x)^2) + (3*d*x*(a + b*Log[c*x^n]))/(e^3*(d + e*x)) - (5*b*d*n*Log[d + e*x])/(2*e^4) - (3*d*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^4 - (3*b*d*n*PolyLog[2, -((e*x)/d)])/e^4","A",11,9,21,0.4286,1,"{43, 2351, 2295, 2319, 44, 2314, 31, 2317, 2391}"
47,1,132,0,0.1827315,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^3} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/(d + e*x)^3,x]","\frac{b n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^3}-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{2 e^3 (d+e x)^2}-\frac{2 x \left(a+b \log \left(c x^n\right)\right)}{e^2 (d+e x)}+\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^3}+\frac{b d n}{2 e^3 (d+e x)}+\frac{3 b n \log (d+e x)}{2 e^3}+\frac{b n \log (x)}{2 e^3}","\frac{b n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{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{\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^2 \left(a+b \log \left(c x^n\right)\right)}{2 e (d+e x)^2}",1,"(b*d*n)/(2*e^3*(d + e*x)) + (b*n*Log[x])/(2*e^3) - (d^2*(a + b*Log[c*x^n]))/(2*e^3*(d + e*x)^2) - (2*x*(a + b*Log[c*x^n]))/(e^2*(d + e*x)) + (3*b*n*Log[d + e*x])/(2*e^3) + ((a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^3 + (b*n*PolyLog[2, -((e*x)/d)])/e^3","A",9,8,21,0.3810,1,"{43, 2351, 2319, 44, 2314, 31, 2317, 2391}"
48,1,62,0,0.0500943,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^3} \, dx","Int[(x*(a + b*Log[c*x^n]))/(d + e*x)^3,x]","\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}","\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)/(2*e^2*(d + e*x)) + (x^2*(a + b*Log[c*x^n]))/(2*d*(d + e*x)^2) - (b*n*Log[d + e*x])/(2*d*e^2)","A",3,2,19,0.1053,1,"{2335, 43}"
49,1,76,0,0.0340487,"\int \frac{a+b \log \left(c x^n\right)}{(d+e x)^3} \, dx","Int[(a + b*Log[c*x^n])/(d + e*x)^3,x]","-\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)}","-\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,"(b*n)/(2*d*e*(d + e*x)) + (b*n*Log[x])/(2*d^2*e) - (a + b*Log[c*x^n])/(2*e*(d + e*x)^2) - (b*n*Log[d + e*x])/(2*d^2*e)","A",3,2,18,0.1111,1,"{2319, 44}"
50,1,156,0,0.2496285,"\int \frac{a+b \log \left(c x^n\right)}{x (d+e x)^3} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x)^3),x]","-\frac{b n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^3}-\frac{\log \left(\frac{e x}{d}+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{\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)}{2 d (d+e x)^2}-\frac{b n}{2 d^2 (d+e x)}+\frac{3 b n \log (d+e x)}{2 d^3}-\frac{b n \log (x)}{2 d^3}","\frac{b n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{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}{2 d^2 (d+e x)}+\frac{3 b n \log (d+e x)}{2 d^3}-\frac{b n \log (x)}{2 d^3}",1,"-(b*n)/(2*d^2*(d + e*x)) - (b*n*Log[x])/(2*d^3) + (a + b*Log[c*x^n])/(2*d*(d + e*x)^2) - (e*x*(a + b*Log[c*x^n]))/(d^3*(d + e*x)) + (a + b*Log[c*x^n])^2/(2*b*d^3*n) + (3*b*n*Log[d + e*x])/(2*d^3) - ((a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^3 - (b*n*PolyLog[2, -((e*x)/d)])/d^3","A",11,9,21,0.4286,1,"{2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
51,1,193,0,0.2477525,"\int \frac{a+b \log \left(c x^n\right)}{x^2 (d+e x)^3} \, dx","Int[(a + b*Log[c*x^n])/(x^2*(d + e*x)^3),x]","\frac{3 b e n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{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 \left(a+b \log \left(c x^n\right)\right)^2}{2 b d^4 n}-\frac{e \left(a+b \log \left(c x^n\right)\right)}{2 d^2 (d+e x)^2}+\frac{3 e \log \left(\frac{e x}{d}+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{b e n}{2 d^3 (d+e x)}+\frac{b e n \log (x)}{2 d^4}-\frac{5 b e n \log (d+e x)}{2 d^4}-\frac{b n}{d^3 x}","-\frac{3 b e n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{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{e \left(a+b \log \left(c x^n\right)\right)}{2 d^2 (d+e x)^2}-\frac{a+b \log \left(c x^n\right)}{d^3 x}+\frac{b e n}{2 d^3 (d+e x)}+\frac{b e n \log (x)}{2 d^4}-\frac{5 b e n \log (d+e x)}{2 d^4}-\frac{b n}{d^3 x}",1,"-((b*n)/(d^3*x)) + (b*e*n)/(2*d^3*(d + e*x)) + (b*e*n*Log[x])/(2*d^4) - (a + b*Log[c*x^n])/(d^3*x) - (e*(a + b*Log[c*x^n]))/(2*d^2*(d + e*x)^2) + (2*e^2*x*(a + b*Log[c*x^n]))/(d^4*(d + e*x)) - (3*e*(a + b*Log[c*x^n])^2)/(2*b*d^4*n) - (5*b*e*n*Log[d + e*x])/(2*d^4) + (3*e*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^4 + (3*b*e*n*PolyLog[2, -((e*x)/d)])/d^4","A",11,9,21,0.4286,1,"{44, 2351, 2304, 2301, 2319, 2314, 31, 2317, 2391}"
52,1,239,0,0.2736242,"\int \frac{a+b \log \left(c x^n\right)}{x^3 (d+e x)^3} \, dx","Int[(a + b*Log[c*x^n])/(x^3*(d + e*x)^3),x]","-\frac{6 b e^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^5}-\frac{3 e^3 x \left(a+b \log \left(c x^n\right)\right)}{d^5 (d+e x)}+\frac{3 e^2 \left(a+b \log \left(c x^n\right)\right)^2}{b d^5 n}+\frac{e^2 \left(a+b \log \left(c x^n\right)\right)}{2 d^3 (d+e x)^2}-\frac{6 e^2 \log \left(\frac{e x}{d}+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{a+b \log \left(c x^n\right)}{2 d^3 x^2}-\frac{b e^2 n}{2 d^4 (d+e x)}-\frac{b e^2 n \log (x)}{2 d^5}+\frac{7 b e^2 n \log (d+e x)}{2 d^5}+\frac{3 b e n}{d^4 x}-\frac{b n}{4 d^3 x^2}","\frac{6 b e^2 n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{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{e^2 \left(a+b \log \left(c x^n\right)\right)}{2 d^3 (d+e x)^2}+\frac{3 e \left(a+b \log \left(c x^n\right)\right)}{d^4 x}-\frac{a+b \log \left(c x^n\right)}{2 d^3 x^2}-\frac{b e^2 n}{2 d^4 (d+e x)}-\frac{b e^2 n \log (x)}{2 d^5}+\frac{7 b e^2 n \log (d+e x)}{2 d^5}+\frac{3 b e n}{d^4 x}-\frac{b n}{4 d^3 x^2}",1,"-(b*n)/(4*d^3*x^2) + (3*b*e*n)/(d^4*x) - (b*e^2*n)/(2*d^4*(d + e*x)) - (b*e^2*n*Log[x])/(2*d^5) - (a + b*Log[c*x^n])/(2*d^3*x^2) + (3*e*(a + b*Log[c*x^n]))/(d^4*x) + (e^2*(a + b*Log[c*x^n]))/(2*d^3*(d + e*x)^2) - (3*e^3*x*(a + b*Log[c*x^n]))/(d^5*(d + e*x)) + (3*e^2*(a + b*Log[c*x^n])^2)/(b*d^5*n) + (7*b*e^2*n*Log[d + e*x])/(2*d^5) - (6*e^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^5 - (6*b*e^2*n*PolyLog[2, -((e*x)/d)])/d^5","A",12,9,21,0.4286,1,"{44, 2351, 2304, 2301, 2319, 2314, 31, 2317, 2391}"
53,1,260,0,0.3195223,"\int \frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^4} \, dx","Int[(x^5*(a + b*Log[c*x^n]))/(d + e*x)^4,x]","\frac{10 b d^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^6}+\frac{d^5 \left(a+b \log \left(c x^n\right)\right)}{3 e^6 (d+e x)^3}-\frac{5 d^4 \left(a+b \log \left(c x^n\right)\right)}{2 e^6 (d+e x)^2}-\frac{10 d^2 x \left(a+b \log \left(c x^n\right)\right)}{e^5 (d+e x)}+\frac{10 d^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^6}+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{2 e^4}-\frac{4 a d x}{e^5}-\frac{4 b d x \log \left(c x^n\right)}{e^5}-\frac{b d^4 n}{6 e^6 (d+e x)^2}+\frac{13 b d^3 n}{6 e^6 (d+e x)}+\frac{13 b d^2 n \log (x)}{6 e^6}+\frac{47 b d^2 n \log (d+e x)}{6 e^6}+\frac{4 b d n x}{e^5}-\frac{b n x^2}{4 e^4}","\frac{10 b d^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{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^4 \left(5 a+5 b \log \left(c x^n\right)+b n\right)}{6 e^2 (d+e x)^2}-\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^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 n x}{e^5}-\frac{5 b n x^2}{2 e^4}",1,"(-4*a*d*x)/e^5 + (4*b*d*n*x)/e^5 - (b*n*x^2)/(4*e^4) - (b*d^4*n)/(6*e^6*(d + e*x)^2) + (13*b*d^3*n)/(6*e^6*(d + e*x)) + (13*b*d^2*n*Log[x])/(6*e^6) - (4*b*d*x*Log[c*x^n])/e^5 + (x^2*(a + b*Log[c*x^n]))/(2*e^4) + (d^5*(a + b*Log[c*x^n]))/(3*e^6*(d + e*x)^3) - (5*d^4*(a + b*Log[c*x^n]))/(2*e^6*(d + e*x)^2) - (10*d^2*x*(a + b*Log[c*x^n]))/(e^5*(d + e*x)) + (47*b*d^2*n*Log[d + e*x])/(6*e^6) + (10*d^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^6 + (10*b*d^2*n*PolyLog[2, -((e*x)/d)])/e^6","A",15,10,21,0.4762,1,"{43, 2351, 2295, 2304, 2319, 44, 2314, 31, 2317, 2391}"
54,1,211,0,0.281067,"\int \frac{x^4 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^4} \, dx","Int[(x^4*(a + b*Log[c*x^n]))/(d + e*x)^4,x]","-\frac{4 b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^5}-\frac{d^4 \left(a+b \log \left(c x^n\right)\right)}{3 e^5 (d+e x)^3}+\frac{2 d^3 \left(a+b \log \left(c x^n\right)\right)}{e^5 (d+e x)^2}+\frac{6 d x \left(a+b \log \left(c x^n\right)\right)}{e^4 (d+e x)}-\frac{4 d \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^5}+\frac{a x}{e^4}+\frac{b x \log \left(c x^n\right)}{e^4}+\frac{b d^3 n}{6 e^5 (d+e x)^2}-\frac{5 b d^2 n}{3 e^5 (d+e x)}-\frac{5 b d n \log (x)}{3 e^5}-\frac{13 b d n \log (d+e x)}{3 e^5}-\frac{b n x}{e^4}","-\frac{4 b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^5}-\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^2 \left(12 a+12 b \log \left(c x^n\right)+7 b n\right)}{6 e^3 (d+e x)}-\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^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 n x}{e^4}",1,"(a*x)/e^4 - (b*n*x)/e^4 + (b*d^3*n)/(6*e^5*(d + e*x)^2) - (5*b*d^2*n)/(3*e^5*(d + e*x)) - (5*b*d*n*Log[x])/(3*e^5) + (b*x*Log[c*x^n])/e^4 - (d^4*(a + b*Log[c*x^n]))/(3*e^5*(d + e*x)^3) + (2*d^3*(a + b*Log[c*x^n]))/(e^5*(d + e*x)^2) + (6*d*x*(a + b*Log[c*x^n]))/(e^4*(d + e*x)) - (13*b*d*n*Log[d + e*x])/(3*e^5) - (4*d*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^5 - (4*b*d*n*PolyLog[2, -((e*x)/d)])/e^5","A",14,9,21,0.4286,1,"{43, 2351, 2295, 2319, 44, 2314, 31, 2317, 2391}"
55,1,178,0,0.2540767,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^4} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/(d + e*x)^4,x]","\frac{b n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^4}+\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{3 e^4 (d+e x)^3}-\frac{3 d^2 \left(a+b \log \left(c x^n\right)\right)}{2 e^4 (d+e x)^2}-\frac{3 x \left(a+b \log \left(c x^n\right)\right)}{e^3 (d+e x)}+\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}-\frac{b d^2 n}{6 e^4 (d+e x)^2}+\frac{7 b d n}{6 e^4 (d+e x)}+\frac{11 b n \log (d+e x)}{6 e^4}+\frac{7 b n \log (x)}{6 e^4}","\frac{b n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^4}-\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 \left(6 a+6 b \log \left(c x^n\right)+5 b n\right)}{6 e^3 (d+e x)}+\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^3 \left(a+b \log \left(c x^n\right)\right)}{3 e (d+e x)^3}",1,"-(b*d^2*n)/(6*e^4*(d + e*x)^2) + (7*b*d*n)/(6*e^4*(d + e*x)) + (7*b*n*Log[x])/(6*e^4) + (d^3*(a + b*Log[c*x^n]))/(3*e^4*(d + e*x)^3) - (3*d^2*(a + b*Log[c*x^n]))/(2*e^4*(d + e*x)^2) - (3*x*(a + b*Log[c*x^n]))/(e^3*(d + e*x)) + (11*b*n*Log[d + e*x])/(6*e^4) + ((a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^4 + (b*n*PolyLog[2, -((e*x)/d)])/e^4","A",12,8,21,0.3810,1,"{43, 2351, 2319, 44, 2314, 31, 2317, 2391}"
56,1,79,0,0.070735,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^4} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/(d + e*x)^4,x]","\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}","\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,"(b*d*n)/(6*e^3*(d + e*x)^2) - (2*b*n)/(3*e^3*(d + e*x)) + (x^3*(a + b*Log[c*x^n]))/(3*d*(d + e*x)^3) - (b*n*Log[d + e*x])/(3*d*e^3)","A",3,2,21,0.09524,1,"{2335, 43}"
57,1,117,0,0.0871504,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^4} \, dx","Int[(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 \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}","-\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,"-(b*n)/(6*e^2*(d + e*x)^2) + (b*n)/(6*d*e^2*(d + e*x)) + (b*n*Log[x])/(6*d^2*e^2) + (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*Log[d + e*x])/(6*d^2*e^2)","A",4,4,19,0.2105,1,"{43, 2350, 12, 77}"
58,1,95,0,0.0411906,"\int \frac{a+b \log \left(c x^n\right)}{(d+e x)^4} \, dx","Int[(a + b*Log[c*x^n])/(d + e*x)^4,x]","-\frac{a+b \log \left(c x^n\right)}{3 e (d+e x)^3}+\frac{b n}{3 d^2 e (d+e x)}+\frac{b n \log (x)}{3 d^3 e}-\frac{b n \log (d+e x)}{3 d^3 e}+\frac{b n}{6 d e (d+e x)^2}","-\frac{a+b \log \left(c x^n\right)}{3 e (d+e x)^3}+\frac{b n}{3 d^2 e (d+e x)}+\frac{b n \log (x)}{3 d^3 e}-\frac{b n \log (d+e x)}{3 d^3 e}+\frac{b n}{6 d e (d+e x)^2}",1,"(b*n)/(6*d*e*(d + e*x)^2) + (b*n)/(3*d^2*e*(d + e*x)) + (b*n*Log[x])/(3*d^3*e) - (a + b*Log[c*x^n])/(3*e*(d + e*x)^3) - (b*n*Log[d + e*x])/(3*d^3*e)","A",3,2,18,0.1111,1,"{2319, 44}"
59,1,196,0,0.3574893,"\int \frac{a+b \log \left(c x^n\right)}{x (d+e x)^4} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x)^4),x]","-\frac{b n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^4}-\frac{\log \left(\frac{e x}{d}+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{\left(a+b \log \left(c x^n\right)\right)^2}{2 b d^4 n}+\frac{a+b \log \left(c x^n\right)}{3 d (d+e x)^3}-\frac{5 b n}{6 d^3 (d+e x)}-\frac{b n}{6 d^2 (d+e x)^2}+\frac{11 b n \log (d+e x)}{6 d^4}-\frac{5 b n \log (x)}{6 d^4}","\frac{b n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{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{5 b n}{6 d^3 (d+e x)}-\frac{b n}{6 d^2 (d+e x)^2}+\frac{11 b n \log (d+e x)}{6 d^4}-\frac{5 b n \log (x)}{6 d^4}",1,"-(b*n)/(6*d^2*(d + e*x)^2) - (5*b*n)/(6*d^3*(d + e*x)) - (5*b*n*Log[x])/(6*d^4) + (a + b*Log[c*x^n])/(3*d*(d + e*x)^3) + (a + b*Log[c*x^n])/(2*d^2*(d + e*x)^2) - (e*x*(a + b*Log[c*x^n]))/(d^4*(d + e*x)) + (a + b*Log[c*x^n])^2/(2*b*d^4*n) + (11*b*n*Log[d + e*x])/(6*d^4) - ((a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^4 - (b*n*PolyLog[2, -((e*x)/d)])/d^4","A",15,9,21,0.4286,1,"{2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
60,1,231,0,0.2997591,"\int \frac{a+b \log \left(c x^n\right)}{x^2 (d+e x)^4} \, dx","Int[(a + b*Log[c*x^n])/(x^2*(d + e*x)^4),x]","\frac{4 b e n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^5}+\frac{3 e^2 x \left(a+b \log \left(c x^n\right)\right)}{d^5 (d+e x)}-\frac{2 e \left(a+b \log \left(c x^n\right)\right)^2}{b d^5 n}-\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 e \log \left(\frac{e x}{d}+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{4 b e n}{3 d^4 (d+e x)}+\frac{b e n}{6 d^3 (d+e x)^2}+\frac{4 b e n \log (x)}{3 d^5}-\frac{13 b e n \log (d+e x)}{3 d^5}-\frac{b n}{d^4 x}","-\frac{4 b e n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{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{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{a+b \log \left(c x^n\right)}{d^4 x}+\frac{4 b e n}{3 d^4 (d+e x)}+\frac{b e n}{6 d^3 (d+e x)^2}+\frac{4 b e n \log (x)}{3 d^5}-\frac{13 b e n \log (d+e x)}{3 d^5}-\frac{b n}{d^4 x}",1,"-((b*n)/(d^4*x)) + (b*e*n)/(6*d^3*(d + e*x)^2) + (4*b*e*n)/(3*d^4*(d + e*x)) + (4*b*e*n*Log[x])/(3*d^5) - (a + b*Log[c*x^n])/(d^4*x) - (e*(a + b*Log[c*x^n]))/(3*d^2*(d + e*x)^3) - (e*(a + b*Log[c*x^n]))/(d^3*(d + e*x)^2) + (3*e^2*x*(a + b*Log[c*x^n]))/(d^5*(d + e*x)) - (2*e*(a + b*Log[c*x^n])^2)/(b*d^5*n) - (13*b*e*n*Log[d + e*x])/(3*d^5) + (4*e*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^5 + (4*b*e*n*PolyLog[2, -((e*x)/d)])/d^5","A",14,9,21,0.4286,1,"{44, 2351, 2304, 2301, 2319, 2314, 31, 2317, 2391}"
61,1,285,0,0.3464967,"\int \frac{a+b \log \left(c x^n\right)}{x^3 (d+e x)^4} \, dx","Int[(a + b*Log[c*x^n])/(x^3*(d + e*x)^4),x]","-\frac{10 b e^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^6}-\frac{6 e^3 x \left(a+b \log \left(c x^n\right)\right)}{d^6 (d+e x)}+\frac{5 e^2 \left(a+b \log \left(c x^n\right)\right)^2}{b d^6 n}+\frac{3 e^2 \left(a+b \log \left(c x^n\right)\right)}{2 d^4 (d+e x)^2}+\frac{e^2 \left(a+b \log \left(c x^n\right)\right)}{3 d^3 (d+e x)^3}-\frac{10 e^2 \log \left(\frac{e x}{d}+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{a+b \log \left(c x^n\right)}{2 d^4 x^2}-\frac{11 b e^2 n}{6 d^5 (d+e x)}-\frac{b e^2 n}{6 d^4 (d+e x)^2}-\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{4 b e n}{d^5 x}-\frac{b n}{4 d^4 x^2}","\frac{10 b e^2 n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{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{3 e^2 \left(a+b \log \left(c x^n\right)\right)}{2 d^4 (d+e x)^2}+\frac{e^2 \left(a+b \log \left(c x^n\right)\right)}{3 d^3 (d+e x)^3}+\frac{4 e \left(a+b \log \left(c x^n\right)\right)}{d^5 x}-\frac{a+b \log \left(c x^n\right)}{2 d^4 x^2}-\frac{11 b e^2 n}{6 d^5 (d+e x)}-\frac{b e^2 n}{6 d^4 (d+e x)^2}-\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{4 b e n}{d^5 x}-\frac{b n}{4 d^4 x^2}",1,"-(b*n)/(4*d^4*x^2) + (4*b*e*n)/(d^5*x) - (b*e^2*n)/(6*d^4*(d + e*x)^2) - (11*b*e^2*n)/(6*d^5*(d + e*x)) - (11*b*e^2*n*Log[x])/(6*d^6) - (a + b*Log[c*x^n])/(2*d^4*x^2) + (4*e*(a + b*Log[c*x^n]))/(d^5*x) + (e^2*(a + b*Log[c*x^n]))/(3*d^3*(d + e*x)^3) + (3*e^2*(a + b*Log[c*x^n]))/(2*d^4*(d + e*x)^2) - (6*e^3*x*(a + b*Log[c*x^n]))/(d^6*(d + e*x)) + (5*e^2*(a + b*Log[c*x^n])^2)/(b*d^6*n) + (47*b*e^2*n*Log[d + e*x])/(6*d^6) - (10*e^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^6 - (10*b*e^2*n*PolyLog[2, -((e*x)/d)])/d^6","A",15,9,21,0.4286,1,"{44, 2351, 2304, 2301, 2319, 2314, 31, 2317, 2391}"
62,1,394,0,0.6391851,"\int \frac{x^8 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^7} \, dx","Int[(x^8*(a + b*Log[c*x^n]))/(d + e*x)^7,x]","\frac{28 b d^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^9}-\frac{d^8 \left(a+b \log \left(c x^n\right)\right)}{6 e^9 (d+e x)^6}+\frac{8 d^7 \left(a+b \log \left(c x^n\right)\right)}{5 e^9 (d+e x)^5}-\frac{7 d^6 \left(a+b \log \left(c x^n\right)\right)}{e^9 (d+e x)^4}+\frac{56 d^5 \left(a+b \log \left(c x^n\right)\right)}{3 e^9 (d+e x)^3}-\frac{35 d^4 \left(a+b \log \left(c x^n\right)\right)}{e^9 (d+e x)^2}-\frac{56 d^2 x \left(a+b \log \left(c x^n\right)\right)}{e^8 (d+e x)}+\frac{28 d^2 \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^9}+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{2 e^7}-\frac{7 a d x}{e^8}-\frac{7 b d x \log \left(c x^n\right)}{e^8}+\frac{b d^7 n}{30 e^9 (d+e x)^5}-\frac{43 b d^6 n}{120 e^9 (d+e x)^4}+\frac{167 b d^5 n}{90 e^9 (d+e x)^3}-\frac{131 b d^4 n}{20 e^9 (d+e x)^2}+\frac{219 b d^3 n}{10 e^9 (d+e x)}+\frac{219 b d^2 n \log (x)}{10 e^9}+\frac{341 b d^2 n \log (d+e x)}{10 e^9}+\frac{7 b d n x}{e^8}-\frac{b n x^2}{4 e^7}","\frac{28 b d^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{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^7 \left(8 a+8 b \log \left(c x^n\right)+b n\right)}{30 e^2 (d+e x)^5}-\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^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^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^3 \left(840 a+840 b \log \left(c x^n\right)+743 b n\right)}{90 e^6 (d+e x)}-\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 n x}{e^8}-\frac{7 b n x^2}{e^7}",1,"(-7*a*d*x)/e^8 + (7*b*d*n*x)/e^8 - (b*n*x^2)/(4*e^7) + (b*d^7*n)/(30*e^9*(d + e*x)^5) - (43*b*d^6*n)/(120*e^9*(d + e*x)^4) + (167*b*d^5*n)/(90*e^9*(d + e*x)^3) - (131*b*d^4*n)/(20*e^9*(d + e*x)^2) + (219*b*d^3*n)/(10*e^9*(d + e*x)) + (219*b*d^2*n*Log[x])/(10*e^9) - (7*b*d*x*Log[c*x^n])/e^8 + (x^2*(a + b*Log[c*x^n]))/(2*e^7) - (d^8*(a + b*Log[c*x^n]))/(6*e^9*(d + e*x)^6) + (8*d^7*(a + b*Log[c*x^n]))/(5*e^9*(d + e*x)^5) - (7*d^6*(a + b*Log[c*x^n]))/(e^9*(d + e*x)^4) + (56*d^5*(a + b*Log[c*x^n]))/(3*e^9*(d + e*x)^3) - (35*d^4*(a + b*Log[c*x^n]))/(e^9*(d + e*x)^2) - (56*d^2*x*(a + b*Log[c*x^n]))/(e^8*(d + e*x)) + (341*b*d^2*n*Log[d + e*x])/(10*e^9) + (28*d^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^9 + (28*b*d^2*n*PolyLog[2, -((e*x)/d)])/e^9","A",24,10,21,0.4762,1,"{43, 2351, 2295, 2304, 2319, 44, 2314, 31, 2317, 2391}"
63,1,351,0,0.571391,"\int \frac{x^7 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^7} \, dx","Int[(x^7*(a + b*Log[c*x^n]))/(d + e*x)^7,x]","-\frac{7 b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^8}+\frac{d^7 \left(a+b \log \left(c x^n\right)\right)}{6 e^8 (d+e x)^6}-\frac{7 d^6 \left(a+b \log \left(c x^n\right)\right)}{5 e^8 (d+e x)^5}+\frac{21 d^5 \left(a+b \log \left(c x^n\right)\right)}{4 e^8 (d+e x)^4}-\frac{35 d^4 \left(a+b \log \left(c x^n\right)\right)}{3 e^8 (d+e x)^3}+\frac{35 d^3 \left(a+b \log \left(c x^n\right)\right)}{2 e^8 (d+e x)^2}+\frac{21 d x \left(a+b \log \left(c x^n\right)\right)}{e^7 (d+e x)}-\frac{7 d \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^8}+\frac{a x}{e^7}+\frac{b x \log \left(c x^n\right)}{e^7}-\frac{b d^6 n}{30 e^8 (d+e x)^5}+\frac{37 b d^5 n}{120 e^8 (d+e x)^4}-\frac{241 b d^4 n}{180 e^8 (d+e x)^3}+\frac{153 b d^3 n}{40 e^8 (d+e x)^2}-\frac{197 b d^2 n}{20 e^8 (d+e x)}-\frac{197 b d n \log (x)}{20 e^8}-\frac{223 b d n \log (d+e x)}{20 e^8}-\frac{b n x}{e^7}","-\frac{7 b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^8}-\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^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^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^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^2 \left(140 a+140 b \log \left(c x^n\right)+153 b n\right)}{40 e^6 (d+e x)}-\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^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 n x}{e^7}",1,"(a*x)/e^7 - (b*n*x)/e^7 - (b*d^6*n)/(30*e^8*(d + e*x)^5) + (37*b*d^5*n)/(120*e^8*(d + e*x)^4) - (241*b*d^4*n)/(180*e^8*(d + e*x)^3) + (153*b*d^3*n)/(40*e^8*(d + e*x)^2) - (197*b*d^2*n)/(20*e^8*(d + e*x)) - (197*b*d*n*Log[x])/(20*e^8) + (b*x*Log[c*x^n])/e^7 + (d^7*(a + b*Log[c*x^n]))/(6*e^8*(d + e*x)^6) - (7*d^6*(a + b*Log[c*x^n]))/(5*e^8*(d + e*x)^5) + (21*d^5*(a + b*Log[c*x^n]))/(4*e^8*(d + e*x)^4) - (35*d^4*(a + b*Log[c*x^n]))/(3*e^8*(d + e*x)^3) + (35*d^3*(a + b*Log[c*x^n]))/(2*e^8*(d + e*x)^2) + (21*d*x*(a + b*Log[c*x^n]))/(e^7*(d + e*x)) - (223*b*d*n*Log[d + e*x])/(20*e^8) - (7*d*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^8 - (7*b*d*n*PolyLog[2, -((e*x)/d)])/e^8","A",23,9,21,0.4286,1,"{43, 2351, 2295, 2319, 44, 2314, 31, 2317, 2391}"
64,1,316,0,0.5381364,"\int \frac{x^6 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^7} \, dx","Int[(x^6*(a + b*Log[c*x^n]))/(d + e*x)^7,x]","\frac{b n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^7}-\frac{d^6 \left(a+b \log \left(c x^n\right)\right)}{6 e^7 (d+e x)^6}+\frac{6 d^5 \left(a+b \log \left(c x^n\right)\right)}{5 e^7 (d+e x)^5}-\frac{15 d^4 \left(a+b \log \left(c x^n\right)\right)}{4 e^7 (d+e x)^4}+\frac{20 d^3 \left(a+b \log \left(c x^n\right)\right)}{3 e^7 (d+e x)^3}-\frac{15 d^2 \left(a+b \log \left(c x^n\right)\right)}{2 e^7 (d+e x)^2}-\frac{6 x \left(a+b \log \left(c x^n\right)\right)}{e^6 (d+e x)}+\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e^7}+\frac{b d^5 n}{30 e^7 (d+e x)^5}-\frac{31 b d^4 n}{120 e^7 (d+e x)^4}+\frac{163 b d^3 n}{180 e^7 (d+e x)^3}-\frac{79 b d^2 n}{40 e^7 (d+e x)^2}+\frac{71 b d n}{20 e^7 (d+e x)}+\frac{49 b n \log (d+e x)}{20 e^7}+\frac{71 b n \log (x)}{20 e^7}","\frac{b n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^7}-\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^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^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^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 \left(20 a+20 b \log \left(c x^n\right)+29 b n\right)}{20 e^6 (d+e x)}+\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^6 \left(a+b \log \left(c x^n\right)\right)}{6 e (d+e x)^6}",1,"(b*d^5*n)/(30*e^7*(d + e*x)^5) - (31*b*d^4*n)/(120*e^7*(d + e*x)^4) + (163*b*d^3*n)/(180*e^7*(d + e*x)^3) - (79*b*d^2*n)/(40*e^7*(d + e*x)^2) + (71*b*d*n)/(20*e^7*(d + e*x)) + (71*b*n*Log[x])/(20*e^7) - (d^6*(a + b*Log[c*x^n]))/(6*e^7*(d + e*x)^6) + (6*d^5*(a + b*Log[c*x^n]))/(5*e^7*(d + e*x)^5) - (15*d^4*(a + b*Log[c*x^n]))/(4*e^7*(d + e*x)^4) + (20*d^3*(a + b*Log[c*x^n]))/(3*e^7*(d + e*x)^3) - (15*d^2*(a + b*Log[c*x^n]))/(2*e^7*(d + e*x)^2) - (6*x*(a + b*Log[c*x^n]))/(e^6*(d + e*x)) + (49*b*n*Log[d + e*x])/(20*e^7) + ((a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^7 + (b*n*PolyLog[2, -((e*x)/d)])/e^7","A",21,8,21,0.3810,1,"{43, 2351, 2319, 44, 2314, 31, 2317, 2391}"
65,1,136,0,0.1100531,"\int \frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^7} \, dx","Int[(x^5*(a + b*Log[c*x^n]))/(d + e*x)^7,x]","\frac{x^6 \left(a+b \log \left(c x^n\right)\right)}{6 d (d+e x)^6}-\frac{5 b d^2 n}{9 e^6 (d+e x)^3}+\frac{5 b d^3 n}{24 e^6 (d+e x)^4}-\frac{b d^4 n}{30 e^6 (d+e x)^5}-\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}","\frac{x^6 \left(a+b \log \left(c x^n\right)\right)}{6 d (d+e x)^6}-\frac{5 b d^2 n}{9 e^6 (d+e x)^3}+\frac{5 b d^3 n}{24 e^6 (d+e x)^4}-\frac{b d^4 n}{30 e^6 (d+e x)^5}-\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,"-(b*d^4*n)/(30*e^6*(d + e*x)^5) + (5*b*d^3*n)/(24*e^6*(d + e*x)^4) - (5*b*d^2*n)/(9*e^6*(d + e*x)^3) + (5*b*d*n)/(6*e^6*(d + e*x)^2) - (5*b*n)/(6*e^6*(d + e*x)) + (x^6*(a + b*Log[c*x^n]))/(6*d*(d + e*x)^6) - (b*n*Log[d + e*x])/(6*d*e^6)","A",3,2,21,0.09524,1,"{2335, 43}"
66,1,163,0,0.1291239,"\int \frac{x^4 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^7} \, dx","Int[(x^4*(a + b*Log[c*x^n]))/(d + e*x)^7,x]","\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}","\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,"-(b*n*x^5)/(30*d^2*(d + e*x)^5) + (b*d^2*n)/(120*e^5*(d + e*x)^4) - (2*b*d*n)/(45*e^5*(d + e*x)^3) + (b*n)/(10*e^5*(d + e*x)^2) - (2*b*n)/(15*d*e^5*(d + e*x)) + (x^5*(a + b*Log[c*x^n]))/(6*d*(d + e*x)^6) + (x^5*(a + b*Log[c*x^n]))/(30*d^2*(d + e*x)^5) - (b*n*Log[d + e*x])/(30*d^2*e^5)","A",5,6,21,0.2857,1,"{45, 37, 2350, 12, 78, 43}"
67,1,226,0,0.2036825,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^7} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/(d + e*x)^7,x]","\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 d^2 n}{30 e^4 (d+e x)^5}+\frac{b n}{60 d^2 e^4 (d+e x)}+\frac{b n \log (x)}{60 d^3 e^4}-\frac{b n \log (d+e x)}{60 d^3 e^4}+\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 d^2 n}{30 e^4 (d+e x)^5}+\frac{b n}{60 d^2 e^4 (d+e x)}+\frac{b n \log (x)}{60 d^3 e^4}-\frac{b n \log (d+e x)}{60 d^3 e^4}+\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,"-(b*d^2*n)/(30*e^4*(d + e*x)^5) + (13*b*d*n)/(120*e^4*(d + e*x)^4) - (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) + (d^3*(a + b*Log[c*x^n]))/(6*e^4*(d + e*x)^6) - (3*d^2*(a + b*Log[c*x^n]))/(5*e^4*(d + e*x)^5) + (3*d*(a + b*Log[c*x^n]))/(4*e^4*(d + e*x)^4) - (a + b*Log[c*x^n])/(3*e^4*(d + e*x)^3) - (b*n*Log[d + e*x])/(60*d^3*e^4)","A",4,4,21,0.1905,1,"{43, 2350, 12, 1620}"
68,1,199,0,0.1648034,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^7} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/(d + e*x)^7,x]","-\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}{120 d^2 e^3 (d+e x)^2}+\frac{b n}{60 d^3 e^3 (d+e x)}+\frac{b n \log (x)}{60 d^4 e^3}-\frac{b n \log (d+e x)}{60 d^4 e^3}+\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}","-\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}{120 d^2 e^3 (d+e x)^2}+\frac{b n}{60 d^3 e^3 (d+e x)}+\frac{b n \log (x)}{60 d^4 e^3}-\frac{b n \log (d+e x)}{60 d^4 e^3}+\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,"(b*d*n)/(30*e^3*(d + e*x)^5) - (7*b*n)/(120*e^3*(d + e*x)^4) + (b*n)/(180*d*e^3*(d + e*x)^3) + (b*n)/(120*d^2*e^3*(d + e*x)^2) + (b*n)/(60*d^3*e^3*(d + e*x)) + (b*n*Log[x])/(60*d^4*e^3) - (d^2*(a + b*Log[c*x^n]))/(6*e^3*(d + e*x)^6) + (2*d*(a + b*Log[c*x^n]))/(5*e^3*(d + e*x)^5) - (a + b*Log[c*x^n])/(4*e^3*(d + e*x)^4) - (b*n*Log[d + e*x])/(60*d^4*e^3)","A",4,4,21,0.1905,1,"{43, 2350, 12, 893}"
69,1,174,0,0.117887,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^7} \, dx","Int[(x*(a + b*Log[c*x^n]))/(d + e*x)^7,x]","-\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}{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 \log (x)}{30 d^5 e^2}-\frac{b n \log (d+e x)}{30 d^5 e^2}+\frac{b n}{120 d e^2 (d+e x)^4}-\frac{b n}{30 e^2 (d+e x)^5}","-\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}{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 \log (x)}{30 d^5 e^2}-\frac{b n \log (d+e x)}{30 d^5 e^2}+\frac{b n}{120 d e^2 (d+e x)^4}-\frac{b n}{30 e^2 (d+e x)^5}",1,"-(b*n)/(30*e^2*(d + e*x)^5) + (b*n)/(120*d*e^2*(d + e*x)^4) + (b*n)/(90*d^2*e^2*(d + e*x)^3) + (b*n)/(60*d^3*e^2*(d + e*x)^2) + (b*n)/(30*d^4*e^2*(d + e*x)) + (b*n*Log[x])/(30*d^5*e^2) + (d*(a + b*Log[c*x^n]))/(6*e^2*(d + e*x)^6) - (a + b*Log[c*x^n])/(5*e^2*(d + e*x)^5) - (b*n*Log[d + e*x])/(30*d^5*e^2)","A",4,4,19,0.2105,1,"{43, 2350, 12, 77}"
70,1,152,0,0.0654523,"\int \frac{a+b \log \left(c x^n\right)}{(d+e x)^7} \, dx","Int[(a + b*Log[c*x^n])/(d + e*x)^7,x]","-\frac{a+b \log \left(c x^n\right)}{6 e (d+e x)^6}+\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 \log (x)}{6 d^6 e}-\frac{b n \log (d+e x)}{6 d^6 e}+\frac{b n}{30 d e (d+e x)^5}","-\frac{a+b \log \left(c x^n\right)}{6 e (d+e x)^6}+\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 \log (x)}{6 d^6 e}-\frac{b n \log (d+e x)}{6 d^6 e}+\frac{b n}{30 d e (d+e x)^5}",1,"(b*n)/(30*d*e*(d + e*x)^5) + (b*n)/(24*d^2*e*(d + e*x)^4) + (b*n)/(18*d^3*e*(d + e*x)^3) + (b*n)/(12*d^4*e*(d + e*x)^2) + (b*n)/(6*d^5*e*(d + e*x)) + (b*n*Log[x])/(6*d^6*e) - (a + b*Log[c*x^n])/(6*e*(d + e*x)^6) - (b*n*Log[d + e*x])/(6*d^6*e)","A",3,2,18,0.1111,1,"{2319, 44}"
71,1,316,0,0.7260491,"\int \frac{a+b \log \left(c x^n\right)}{x (d+e x)^7} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x)^7),x]","-\frac{b n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^7}-\frac{\log \left(\frac{e x}{d}+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{\left(a+b \log \left(c x^n\right)\right)^2}{2 b d^7 n}+\frac{a+b \log \left(c x^n\right)}{6 d (d+e x)^6}-\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}+\frac{49 b n \log (d+e x)}{20 d^7}-\frac{29 b n \log (x)}{20 d^7}","\frac{b n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{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{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}+\frac{49 b n \log (d+e x)}{20 d^7}-\frac{29 b n \log (x)}{20 d^7}",1,"-(b*n)/(30*d^2*(d + e*x)^5) - (11*b*n)/(120*d^3*(d + e*x)^4) - (37*b*n)/(180*d^4*(d + e*x)^3) - (19*b*n)/(40*d^5*(d + e*x)^2) - (29*b*n)/(20*d^6*(d + e*x)) - (29*b*n*Log[x])/(20*d^7) + (a + b*Log[c*x^n])/(6*d*(d + e*x)^6) + (a + b*Log[c*x^n])/(5*d^2*(d + e*x)^5) + (a + b*Log[c*x^n])/(4*d^3*(d + e*x)^4) + (a + b*Log[c*x^n])/(3*d^4*(d + e*x)^3) + (a + b*Log[c*x^n])/(2*d^5*(d + e*x)^2) - (e*x*(a + b*Log[c*x^n]))/(d^7*(d + e*x)) + (a + b*Log[c*x^n])^2/(2*b*d^7*n) + (49*b*n*Log[d + e*x])/(20*d^7) - ((a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^7 - (b*n*PolyLog[2, -((e*x)/d)])/d^7","A",27,9,21,0.4286,1,"{2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
72,1,361,0,0.5807016,"\int \frac{a+b \log \left(c x^n\right)}{x^2 (d+e x)^7} \, dx","Int[(a + b*Log[c*x^n])/(x^2*(d + e*x)^7),x]","\frac{7 b e n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{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 \left(a+b \log \left(c x^n\right)\right)^2}{2 b d^8 n}-\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 e \log \left(\frac{e x}{d}+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{103 b e n}{20 d^7 (d+e 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}+\frac{103 b e n \log (x)}{20 d^8}-\frac{223 b e n \log (d+e x)}{20 d^8}-\frac{b n}{d^7 x}","-\frac{7 b e n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{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{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{a+b \log \left(c x^n\right)}{d^7 x}+\frac{103 b e n}{20 d^7 (d+e 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}+\frac{103 b e n \log (x)}{20 d^8}-\frac{223 b e n \log (d+e x)}{20 d^8}-\frac{b n}{d^7 x}",1,"-((b*n)/(d^7*x)) + (b*e*n)/(30*d^3*(d + e*x)^5) + (17*b*e*n)/(120*d^4*(d + e*x)^4) + (79*b*e*n)/(180*d^5*(d + e*x)^3) + (53*b*e*n)/(40*d^6*(d + e*x)^2) + (103*b*e*n)/(20*d^7*(d + e*x)) + (103*b*e*n*Log[x])/(20*d^8) - (a + b*Log[c*x^n])/(d^7*x) - (e*(a + b*Log[c*x^n]))/(6*d^2*(d + e*x)^6) - (2*e*(a + b*Log[c*x^n]))/(5*d^3*(d + e*x)^5) - (3*e*(a + b*Log[c*x^n]))/(4*d^4*(d + e*x)^4) - (4*e*(a + b*Log[c*x^n]))/(3*d^5*(d + e*x)^3) - (5*e*(a + b*Log[c*x^n]))/(2*d^6*(d + e*x)^2) + (6*e^2*x*(a + b*Log[c*x^n]))/(d^8*(d + e*x)) - (7*e*(a + b*Log[c*x^n])^2)/(2*b*d^8*n) - (223*b*e*n*Log[d + e*x])/(20*d^8) + (7*e*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^8 + (7*b*e*n*PolyLog[2, -((e*x)/d)])/d^8","A",23,9,21,0.4286,1,"{44, 2351, 2304, 2301, 2319, 2314, 31, 2317, 2391}"
73,1,423,0,0.6365119,"\int \frac{a+b \log \left(c x^n\right)}{x^3 (d+e x)^7} \, dx","Int[(a + b*Log[c*x^n])/(x^3*(d + e*x)^7),x]","-\frac{28 b e^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^9}-\frac{21 e^3 x \left(a+b \log \left(c x^n\right)\right)}{d^9 (d+e x)}+\frac{14 e^2 \left(a+b \log \left(c x^n\right)\right)^2}{b d^9 n}+\frac{15 e^2 \left(a+b \log \left(c x^n\right)\right)}{2 d^7 (d+e 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 e^2 \log \left(\frac{e x}{d}+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{a+b \log \left(c x^n\right)}{2 d^7 x^2}-\frac{131 b e^2 n}{10 d^8 (d+e x)}-\frac{14 b e^2 n}{5 d^7 (d+e 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}-\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{7 b e n}{d^8 x}-\frac{b n}{4 d^7 x^2}","\frac{28 b e^2 n \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{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{15 e^2 \left(a+b \log \left(c x^n\right)\right)}{2 d^7 (d+e 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{7 e \left(a+b \log \left(c x^n\right)\right)}{d^8 x}-\frac{a+b \log \left(c x^n\right)}{2 d^7 x^2}-\frac{131 b e^2 n}{10 d^8 (d+e x)}-\frac{14 b e^2 n}{5 d^7 (d+e 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}-\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{7 b e n}{d^8 x}-\frac{b n}{4 d^7 x^2}",1,"-(b*n)/(4*d^7*x^2) + (7*b*e*n)/(d^8*x) - (b*e^2*n)/(30*d^4*(d + e*x)^5) - (23*b*e^2*n)/(120*d^5*(d + e*x)^4) - (34*b*e^2*n)/(45*d^6*(d + e*x)^3) - (14*b*e^2*n)/(5*d^7*(d + e*x)^2) - (131*b*e^2*n)/(10*d^8*(d + e*x)) - (131*b*e^2*n*Log[x])/(10*d^9) - (a + b*Log[c*x^n])/(2*d^7*x^2) + (7*e*(a + b*Log[c*x^n]))/(d^8*x) + (e^2*(a + b*Log[c*x^n]))/(6*d^3*(d + e*x)^6) + (3*e^2*(a + b*Log[c*x^n]))/(5*d^4*(d + e*x)^5) + (3*e^2*(a + b*Log[c*x^n]))/(2*d^5*(d + e*x)^4) + (10*e^2*(a + b*Log[c*x^n]))/(3*d^6*(d + e*x)^3) + (15*e^2*(a + b*Log[c*x^n]))/(2*d^7*(d + e*x)^2) - (21*e^3*x*(a + b*Log[c*x^n]))/(d^9*(d + e*x)) + (14*e^2*(a + b*Log[c*x^n])^2)/(b*d^9*n) + (341*b*e^2*n*Log[d + e*x])/(10*d^9) - (28*e^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^9 - (28*b*e^2*n*PolyLog[2, -((e*x)/d)])/d^9","A",24,9,21,0.4286,1,"{44, 2351, 2304, 2301, 2319, 2314, 31, 2317, 2391}"
74,1,12,0,0.0109987,"\int \frac{\log (c x)}{1-c x} \, dx","Int[Log[c*x]/(1 - c*x),x]","\frac{\text{PolyLog}(2,1-c x)}{c}","\frac{\text{PolyLog}(2,1-c x)}{c}",1,"PolyLog[2, 1 - c*x]/c","A",1,1,13,0.07692,1,"{2315}"
75,1,10,0,0.0105183,"\int \frac{\log \left(\frac{x}{c}\right)}{c-x} \, dx","Int[Log[x/c]/(c - x),x]","\text{PolyLog}\left(2,1-\frac{x}{c}\right)","\text{PolyLog}\left(2,1-\frac{x}{c}\right)",1,"PolyLog[2, 1 - x/c]","A",1,1,14,0.07143,1,"{2315}"
76,1,109,0,0.1430419,"\int x^2 (d+e x) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Int[x^2*(d + e*x)*(a + b*Log[c*x^n])^2,x]","\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","\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,"(2*b^2*d*n^2*x^3)/27 + (b^2*e*n^2*x^4)/32 - (2*b*d*n*x^3*(a + b*Log[c*x^n]))/9 - (b*e*n*x^4*(a + b*Log[c*x^n]))/8 + (d*x^3*(a + b*Log[c*x^n])^2)/3 + (e*x^4*(a + b*Log[c*x^n])^2)/4","A",6,3,21,0.1429,1,"{2353, 2305, 2304}"
77,1,109,0,0.1119601,"\int x (d+e x) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Int[x*(d + e*x)*(a + b*Log[c*x^n])^2,x]","\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","\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,"(b^2*d*n^2*x^2)/4 + (2*b^2*e*n^2*x^3)/27 - (b*d*n*x^2*(a + b*Log[c*x^n]))/2 - (2*b*e*n*x^3*(a + b*Log[c*x^n]))/9 + (d*x^2*(a + b*Log[c*x^n])^2)/2 + (e*x^3*(a + b*Log[c*x^n])^2)/3","A",6,3,19,0.1579,1,"{2353, 2305, 2304}"
78,1,101,0,0.0715404,"\int (d+e x) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Int[(d + e*x)*(a + b*Log[c*x^n])^2,x]","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","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,"-2*a*b*d*n*x + 2*b^2*d*n^2*x + (b^2*e*n^2*x^2)/4 - 2*b^2*d*n*x*Log[c*x^n] - (b*e*n*x^2*(a + b*Log[c*x^n]))/2 + d*x*(a + b*Log[c*x^n])^2 + (e*x^2*(a + b*Log[c*x^n])^2)/2","A",7,5,18,0.2778,1,"{2330, 2296, 2295, 2305, 2304}"
79,1,70,0,0.0827744,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)^2}{x} \, dx","Int[((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 a b e n x-2 b^2 e n x \log \left(c x^n\right)+2 b^2 e n^2 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 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,"-2*a*b*e*n*x + 2*b^2*e*n^2*x - 2*b^2*e*n*x*Log[c*x^n] + e*x*(a + b*Log[c*x^n])^2 + (d*(a + b*Log[c*x^n])^3)/(3*b*n)","A",6,5,21,0.2381,1,"{2346, 2302, 30, 2296, 2295}"
80,1,72,0,0.1166784,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)^2}{x^2} \, dx","Int[((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)\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}","-\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,"(-2*b^2*d*n^2)/x - (2*b*d*n*(a + b*Log[c*x^n]))/x - (d*(a + b*Log[c*x^n])^2)/x + (e*(a + b*Log[c*x^n])^3)/(3*b*n)","A",6,5,21,0.2381,1,"{2353, 2305, 2304, 2302, 30}"
81,1,103,0,0.1336648,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)^2}{x^3} \, dx","Int[((d + e*x)*(a + b*Log[c*x^n])^2)/x^3,x]","-\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}","-\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,"-(b^2*d*n^2)/(4*x^2) - (2*b^2*e*n^2)/x - (b*d*n*(a + b*Log[c*x^n]))/(2*x^2) - (2*b*e*n*(a + b*Log[c*x^n]))/x - (d*(a + b*Log[c*x^n])^2)/(2*x^2) - (e*(a + b*Log[c*x^n])^2)/x","A",6,3,21,0.1429,1,"{2353, 2305, 2304}"
82,1,109,0,0.1332123,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)^2}{x^4} \, dx","Int[((d + e*x)*(a + b*Log[c*x^n])^2)/x^4,x]","-\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}","-\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,"(-2*b^2*d*n^2)/(27*x^3) - (b^2*e*n^2)/(4*x^2) - (2*b*d*n*(a + b*Log[c*x^n]))/(9*x^3) - (b*e*n*(a + b*Log[c*x^n]))/(2*x^2) - (d*(a + b*Log[c*x^n])^2)/(3*x^3) - (e*(a + b*Log[c*x^n])^2)/(2*x^2)","A",6,3,21,0.1429,1,"{2353, 2305, 2304}"
83,1,109,0,0.1351517,"\int \frac{(d+e x) \left(a+b \log \left(c x^n\right)\right)^2}{x^5} \, dx","Int[((d + e*x)*(a + b*Log[c*x^n])^2)/x^5,x]","-\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}","-\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,"-(b^2*d*n^2)/(32*x^4) - (2*b^2*e*n^2)/(27*x^3) - (b*d*n*(a + b*Log[c*x^n]))/(8*x^4) - (2*b*e*n*(a + b*Log[c*x^n]))/(9*x^3) - (d*(a + b*Log[c*x^n])^2)/(4*x^4) - (e*(a + b*Log[c*x^n])^2)/(3*x^3)","A",6,3,21,0.1429,1,"{2353, 2305, 2304}"
84,1,178,0,0.2183049,"\int x^2 (d+e x)^2 \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Int[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}{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","\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^2*d^2*n^2*x^3)/27 + (b^2*d*e*n^2*x^4)/16 + (2*b^2*e^2*n^2*x^5)/125 - (2*b*d^2*n*x^3*(a + b*Log[c*x^n]))/9 - (b*d*e*n*x^4*(a + b*Log[c*x^n]))/4 - (2*b*e^2*n*x^5*(a + b*Log[c*x^n]))/25 + (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",8,3,23,0.1304,1,"{2353, 2305, 2304}"
85,1,178,0,0.1806198,"\int x (d+e x)^2 \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Int[x*(d + e*x)^2*(a + b*Log[c*x^n])^2,x]","\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","\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,"(b^2*d^2*n^2*x^2)/4 + (4*b^2*d*e*n^2*x^3)/27 + (b^2*e^2*n^2*x^4)/32 - (b*d^2*n*x^2*(a + b*Log[c*x^n]))/2 - (4*b*d*e*n*x^3*(a + b*Log[c*x^n]))/9 - (b*e^2*n*x^4*(a + b*Log[c*x^n]))/8 + (d^2*x^2*(a + b*Log[c*x^n])^2)/2 + (2*d*e*x^3*(a + b*Log[c*x^n])^2)/3 + (e^2*x^4*(a + b*Log[c*x^n])^2)/4","A",8,3,21,0.1429,1,"{2353, 2305, 2304}"
86,1,141,0,0.1265239,"\int (d+e x)^2 \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Int[(d + e*x)^2*(a + b*Log[c*x^n])^2,x]","-\frac{b n \left(18 d^2 e x+6 d^3 \log (x)+9 d e^2 x^2+2 e^3 x^3\right) \left(a+b \log \left(c x^n\right)\right)}{9 e}+\frac{(d+e x)^3 \left(a+b \log \left(c x^n\right)\right)^2}{3 e}+\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","-\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)-b d e n x^2 \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}-\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^2*d^2*n^2*x + (b^2*d*e*n^2*x^2)/2 + (2*b^2*e^2*n^2*x^3)/27 + (b^2*d^3*n^2*Log[x]^2)/(3*e) - (b*n*(18*d^2*e*x + 9*d*e^2*x^2 + 2*e^3*x^3 + 6*d^3*Log[x])*(a + b*Log[c*x^n]))/(9*e) + ((d + e*x)^3*(a + b*Log[c*x^n])^2)/(3*e)","A",5,4,20,0.2000,1,"{2319, 43, 2334, 2301}"
87,1,137,0,0.2313186,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)^2}{x} \, dx","Int[((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+\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","\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,"-4*a*b*d*e*n*x + 4*b^2*d*e*n^2*x + (b^2*e^2*n^2*x^2)/4 - 4*b^2*d*e*n*x*Log[c*x^n] - (b*e^2*n*x^2*(a + b*Log[c*x^n]))/2 + 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)","A",14,8,23,0.3478,1,"{2346, 2302, 30, 2296, 2295, 2330, 2305, 2304}"
88,1,133,0,0.1721773,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)^2}{x^2} \, dx","Int[((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)\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","-\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,"(-2*b^2*d^2*n^2)/x - 2*a*b*e^2*n*x + 2*b^2*e^2*n^2*x - 2*b^2*e^2*n*x*Log[c*x^n] - (2*b*d^2*n*(a + b*Log[c*x^n]))/x - (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)","A",9,7,23,0.3043,1,"{2353, 2296, 2295, 2305, 2304, 2302, 30}"
89,1,137,0,0.1922859,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)^2}{x^3} \, dx","Int[((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(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}","-\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,"-(b^2*d^2*n^2)/(4*x^2) - (4*b^2*d*e*n^2)/x - (b*d^2*n*(a + b*Log[c*x^n]))/(2*x^2) - (4*b*d*e*n*(a + b*Log[c*x^n]))/x - (d^2*(a + b*Log[c*x^n])^2)/(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)","A",8,5,23,0.2174,1,"{2353, 2305, 2304, 2302, 30}"
90,1,168,0,0.2080398,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)^2}{x^4} \, dx","Int[((d + e*x)^2*(a + b*Log[c*x^n])^2)/x^4,x]","-\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}","-\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,"(-2*b^2*d^2*n^2)/(27*x^3) - (b^2*d*e*n^2)/(2*x^2) - (2*b^2*e^2*n^2)/x - (2*b*d^2*n*(a + b*Log[c*x^n]))/(9*x^3) - (b*d*e*n*(a + b*Log[c*x^n]))/x^2 - (2*b*e^2*n*(a + b*Log[c*x^n]))/x - (d^2*(a + b*Log[c*x^n])^2)/(3*x^3) - (d*e*(a + b*Log[c*x^n])^2)/x^2 - (e^2*(a + b*Log[c*x^n])^2)/x","A",8,3,23,0.1304,1,"{2353, 2305, 2304}"
91,1,178,0,0.2053521,"\int \frac{(d+e x)^2 \left(a+b \log \left(c x^n\right)\right)^2}{x^5} \, dx","Int[((d + e*x)^2*(a + b*Log[c*x^n])^2)/x^5,x]","-\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}","-\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,"-(b^2*d^2*n^2)/(32*x^4) - (4*b^2*d*e*n^2)/(27*x^3) - (b^2*e^2*n^2)/(4*x^2) - (b*d^2*n*(a + b*Log[c*x^n]))/(8*x^4) - (4*b*d*e*n*(a + b*Log[c*x^n]))/(9*x^3) - (b*e^2*n*(a + b*Log[c*x^n]))/(2*x^2) - (d^2*(a + b*Log[c*x^n])^2)/(4*x^4) - (2*d*e*(a + b*Log[c*x^n])^2)/(3*x^3) - (e^2*(a + b*Log[c*x^n])^2)/(2*x^2)","A",8,3,23,0.1304,1,"{2353, 2305, 2304}"
92,1,271,0,0.2764858,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)^2}{d+e x} \, dx","Int[(x^3*(a + b*Log[c*x^n])^2)/(d + e*x),x]","-\frac{2 b d^3 n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}+\frac{2 b^2 d^3 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\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^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}","-\frac{2 b d^3 n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}+\frac{2 b^2 d^3 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\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^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,"(-2*a*b*d^2*n*x)/e^3 + (2*b^2*d^2*n^2*x)/e^3 - (b^2*d*n^2*x^2)/(4*e^2) + (2*b^2*n^2*x^3)/(27*e) - (2*b^2*d^2*n*x*Log[c*x^n])/e^3 + (b*d*n*x^2*(a + b*Log[c*x^n]))/(2*e^2) - (2*b*n*x^3*(a + b*Log[c*x^n]))/(9*e) + (d^2*x*(a + b*Log[c*x^n])^2)/e^3 - (d*x^2*(a + b*Log[c*x^n])^2)/(2*e^2) + (x^3*(a + b*Log[c*x^n])^2)/(3*e) - (d^3*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/e^4 - (2*b*d^3*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/e^4 + (2*b^2*d^3*n^2*PolyLog[3, -((e*x)/d)])/e^4","A",12,8,23,0.3478,1,"{2353, 2296, 2295, 2305, 2304, 2317, 2374, 6589}"
93,1,200,0,0.216537,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{d+e x} \, dx","Int[(x^2*(a + b*Log[c*x^n])^2)/(d + e*x),x]","\frac{2 b d^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^3}-\frac{2 b^2 d^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\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 n^2 x}{e^2}+\frac{b^2 n^2 x^2}{4 e}","\frac{2 b d^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^3}-\frac{2 b^2 d^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\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 n^2 x}{e^2}+\frac{b^2 n^2 x^2}{4 e}",1,"(2*a*b*d*n*x)/e^2 - (2*b^2*d*n^2*x)/e^2 + (b^2*n^2*x^2)/(4*e) + (2*b^2*d*n*x*Log[c*x^n])/e^2 - (b*n*x^2*(a + b*Log[c*x^n]))/(2*e) - (d*x*(a + b*Log[c*x^n])^2)/e^2 + (x^2*(a + b*Log[c*x^n])^2)/(2*e) + (d^2*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/e^3 + (2*b*d^2*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/e^3 - (2*b^2*d^2*n^2*PolyLog[3, -((e*x)/d)])/e^3","A",10,8,23,0.3478,1,"{2353, 2296, 2295, 2305, 2304, 2317, 2374, 6589}"
94,1,130,0,0.1551891,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)^2}{d+e x} \, dx","Int[(x*(a + b*Log[c*x^n])^2)/(d + e*x),x]","-\frac{2 b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{2 b^2 d n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\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 n^2 x}{e}","-\frac{2 b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{2 b^2 d n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\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 n^2 x}{e}",1,"(-2*a*b*n*x)/e + (2*b^2*n^2*x)/e - (2*b^2*n*x*Log[c*x^n])/e + (x*(a + b*Log[c*x^n])^2)/e - (d*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/e^2 - (2*b*d*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/e^2 + (2*b^2*d*n^2*PolyLog[3, -((e*x)/d)])/e^2","A",8,6,21,0.2857,1,"{2353, 2296, 2295, 2317, 2374, 6589}"
95,1,72,0,0.0610311,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{d+e x} \, dx","Int[(a + b*Log[c*x^n])^2/(d + e*x),x]","\frac{2 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\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)^2}{e}","\frac{2 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\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)^2}{e}",1,"((a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/e + (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/e - (2*b^2*n^2*PolyLog[3, -((e*x)/d)])/e","A",3,3,20,0.1500,1,"{2317, 2374, 6589}"
96,1,98,0,0.157385,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x (d+e x)} \, dx","Int[(a + b*Log[c*x^n])^2/(x*(d + e*x)),x]","-\frac{2 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{d}-\frac{\log \left(\frac{e x}{d}+1\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{PolyLog}\left(2,-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\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)^2}{d}",1,"(a + b*Log[c*x^n])^3/(3*b*d*n) - ((a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/d - (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/d + (2*b^2*n^2*PolyLog[3, -((e*x)/d)])/d","A",6,6,23,0.2609,1,"{2344, 2302, 30, 2317, 2374, 6589}"
97,1,155,0,0.2415453,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x^2 (d+e x)} \, dx","Int[(a + b*Log[c*x^n])^2/(x^2*(d + e*x)),x]","\frac{2 b e n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}-\frac{2 b^2 e n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{d^2}-\frac{e \left(a+b \log \left(c x^n\right)\right)^3}{3 b d^2 n}+\frac{e \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{d x}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right)}{d x}-\frac{2 b^2 n^2}{d x}","-\frac{2 b e n \text{PolyLog}\left(2,-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}-\frac{2 b^2 e n^2 \text{PolyLog}\left(3,-\frac{d}{e x}\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 n^2}{d x}",1,"(-2*b^2*n^2)/(d*x) - (2*b*n*(a + b*Log[c*x^n]))/(d*x) - (a + b*Log[c*x^n])^2/(d*x) - (e*(a + b*Log[c*x^n])^3)/(3*b*d^2*n) + (e*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/d^2 + (2*b*e*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/d^2 - (2*b^2*e*n^2*PolyLog[3, -((e*x)/d)])/d^2","A",9,8,23,0.3478,1,"{2353, 2305, 2304, 2302, 30, 2317, 2374, 6589}"
98,1,226,0,0.2917879,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x^3 (d+e x)} \, dx","Int[(a + b*Log[c*x^n])^2/(x^3*(d + e*x)),x]","-\frac{2 b e^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}+\frac{2 b^2 e^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{d^3}+\frac{e^2 \left(a+b \log \left(c x^n\right)\right)^3}{3 b d^3 n}-\frac{e^2 \log \left(\frac{e x}{d}+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 n^2}{d^2 x}-\frac{b^2 n^2}{4 d x^2}","\frac{2 b e^2 n \text{PolyLog}\left(2,-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}+\frac{2 b^2 e^2 n^2 \text{PolyLog}\left(3,-\frac{d}{e x}\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 n^2}{d^2 x}-\frac{b^2 n^2}{4 d x^2}",1,"-(b^2*n^2)/(4*d*x^2) + (2*b^2*e*n^2)/(d^2*x) - (b*n*(a + b*Log[c*x^n]))/(2*d*x^2) + (2*b*e*n*(a + b*Log[c*x^n]))/(d^2*x) - (a + b*Log[c*x^n])^2/(2*d*x^2) + (e*(a + b*Log[c*x^n])^2)/(d^2*x) + (e^2*(a + b*Log[c*x^n])^3)/(3*b*d^3*n) - (e^2*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/d^3 - (2*b*e^2*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/d^3 + (2*b^2*e^2*n^2*PolyLog[3, -((e*x)/d)])/d^3","A",11,8,23,0.3478,1,"{2353, 2305, 2304, 2302, 30, 2317, 2374, 6589}"
99,1,295,0,0.3568264,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x^4 (d+e x)} \, dx","Int[(a + b*Log[c*x^n])^2/(x^4*(d + e*x)),x]","\frac{2 b e^3 n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}-\frac{2 b^2 e^3 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{d^4}-\frac{e^3 \left(a+b \log \left(c x^n\right)\right)^3}{3 b d^4 n}+\frac{e^3 \log \left(\frac{e x}{d}+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^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}","-\frac{2 b e^3 n \text{PolyLog}\left(2,-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}-\frac{2 b^2 e^3 n^2 \text{PolyLog}\left(3,-\frac{d}{e x}\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^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,"(-2*b^2*n^2)/(27*d*x^3) + (b^2*e*n^2)/(4*d^2*x^2) - (2*b^2*e^2*n^2)/(d^3*x) - (2*b*n*(a + b*Log[c*x^n]))/(9*d*x^3) + (b*e*n*(a + b*Log[c*x^n]))/(2*d^2*x^2) - (2*b*e^2*n*(a + b*Log[c*x^n]))/(d^3*x) - (a + b*Log[c*x^n])^2/(3*d*x^3) + (e*(a + b*Log[c*x^n])^2)/(2*d^2*x^2) - (e^2*(a + b*Log[c*x^n])^2)/(d^3*x) - (e^3*(a + b*Log[c*x^n])^3)/(3*b*d^4*n) + (e^3*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/d^4 + (2*b*e^3*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/d^4 - (2*b^2*e^3*n^2*PolyLog[3, -((e*x)/d)])/d^4","A",13,8,23,0.3478,1,"{2353, 2305, 2304, 2302, 30, 2317, 2374, 6589}"
100,1,281,0,0.3097208,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2} \, dx","Int[(x^3*(a + b*Log[c*x^n])^2)/(d + e*x)^2,x]","\frac{6 b d^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}+\frac{2 b^2 d^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^4}-\frac{6 b^2 d^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\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{d^2 x \left(a+b \log \left(c x^n\right)\right)^2}{e^3 (d+e x)}+\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{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{4 b^2 d n^2 x}{e^3}+\frac{b^2 n^2 x^2}{4 e^2}","\frac{6 b d^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}+\frac{2 b^2 d^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^4}-\frac{6 b^2 d^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\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{d^2 x \left(a+b \log \left(c x^n\right)\right)^2}{e^3 (d+e x)}+\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{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{4 b^2 d n^2 x}{e^3}+\frac{b^2 n^2 x^2}{4 e^2}",1,"(4*a*b*d*n*x)/e^3 - (4*b^2*d*n^2*x)/e^3 + (b^2*n^2*x^2)/(4*e^2) + (4*b^2*d*n*x*Log[c*x^n])/e^3 - (b*n*x^2*(a + b*Log[c*x^n]))/(2*e^2) - (2*d*x*(a + b*Log[c*x^n])^2)/e^3 + (x^2*(a + b*Log[c*x^n])^2)/(2*e^2) - (d^2*x*(a + b*Log[c*x^n])^2)/(e^3*(d + e*x)) + (2*b*d^2*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^4 + (3*d^2*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/e^4 + (2*b^2*d^2*n^2*PolyLog[2, -((e*x)/d)])/e^4 + (6*b*d^2*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/e^4 - (6*b^2*d^2*n^2*PolyLog[3, -((e*x)/d)])/e^4","A",13,10,23,0.4348,1,"{2353, 2296, 2295, 2305, 2304, 2318, 2317, 2391, 2374, 6589}"
101,1,203,0,0.2605801,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2} \, dx","Int[(x^2*(a + b*Log[c*x^n])^2)/(d + e*x)^2,x]","-\frac{4 b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^3}-\frac{2 b^2 d n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^3}+\frac{4 b^2 d n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\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{d x \left(a+b \log \left(c x^n\right)\right)^2}{e^2 (d+e x)}-\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{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 n^2 x}{e^2}","-\frac{4 b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^3}-\frac{2 b^2 d n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^3}+\frac{4 b^2 d n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\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{d x \left(a+b \log \left(c x^n\right)\right)^2}{e^2 (d+e x)}-\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{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 n^2 x}{e^2}",1,"(-2*a*b*n*x)/e^2 + (2*b^2*n^2*x)/e^2 - (2*b^2*n*x*Log[c*x^n])/e^2 + (x*(a + b*Log[c*x^n])^2)/e^2 + (d*x*(a + b*Log[c*x^n])^2)/(e^2*(d + e*x)) - (2*b*d*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^3 - (2*d*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/e^3 - (2*b^2*d*n^2*PolyLog[2, -((e*x)/d)])/e^3 - (4*b*d*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/e^3 + (4*b^2*d*n^2*PolyLog[3, -((e*x)/d)])/e^3","A",11,8,23,0.3478,1,"{2353, 2296, 2295, 2318, 2317, 2391, 2374, 6589}"
102,1,143,0,0.2016708,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2} \, dx","Int[(x*(a + b*Log[c*x^n])^2)/(d + e*x)^2,x]","\frac{2 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{2 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^2}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\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 n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{2 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^2}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\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)}",1,"-((x*(a + b*Log[c*x^n])^2)/(e*(d + e*x))) + (2*b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^2 + ((a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/e^2 + (2*b^2*n^2*PolyLog[2, -((e*x)/d)])/e^2 + (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/e^2 - (2*b^2*n^2*PolyLog[3, -((e*x)/d)])/e^2","A",8,6,21,0.2857,1,"{2353, 2318, 2317, 2391, 2374, 6589}"
103,1,77,0,0.0581115,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^2} \, dx","Int[(a + b*Log[c*x^n])^2/(d + e*x)^2,x]","-\frac{2 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d e}-\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{PolyLog}\left(2,-\frac{e x}{d}\right)}{d e}-\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)}",1,"(x*(a + b*Log[c*x^n])^2)/(d*(d + e*x)) - (2*b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/(d*e) - (2*b^2*n^2*PolyLog[2, -((e*x)/d)])/(d*e)","A",3,3,20,0.1500,1,"{2318, 2317, 2391}"
104,1,170,0,0.3076376,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x (d+e x)^2} \, dx","Int[(a + b*Log[c*x^n])^2/(x*(d + e*x)^2),x]","-\frac{2 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}+\frac{2 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^2}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{d^2}-\frac{\log \left(\frac{e x}{d}+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 n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}+\frac{\left(a+b \log \left(c x^n\right)\right)^3}{3 b d^2 n}","\frac{2 b n \text{PolyLog}\left(2,-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}+\frac{2 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^2}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{d}{e x}\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)}",1,"-((e*x*(a + b*Log[c*x^n])^2)/(d^2*(d + e*x))) + (a + b*Log[c*x^n])^3/(3*b*d^2*n) + (2*b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^2 - ((a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/d^2 + (2*b^2*n^2*PolyLog[2, -((e*x)/d)])/d^2 - (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/d^2 + (2*b^2*n^2*PolyLog[3, -((e*x)/d)])/d^2","A",10,9,23,0.3913,1,"{2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391}"
105,1,231,0,0.3148665,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x^2 (d+e x)^2} \, dx","Int[(a + b*Log[c*x^n])^2/(x^2*(d + e*x)^2),x]","\frac{4 b e n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}-\frac{2 b^2 e n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^3}-\frac{4 b^2 e n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{d^3}+\frac{e^2 x \left(a+b \log \left(c x^n\right)\right)^2}{d^3 (d+e x)}-\frac{2 e \left(a+b \log \left(c x^n\right)\right)^3}{3 b d^3 n}+\frac{2 e \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{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{\left(a+b \log \left(c x^n\right)\right)^2}{d^2 x}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right)}{d^2 x}-\frac{2 b^2 n^2}{d^2 x}","-\frac{4 b e n \text{PolyLog}\left(2,-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}-\frac{2 b^2 e n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^3}-\frac{4 b^2 e n^2 \text{PolyLog}\left(3,-\frac{d}{e x}\right)}{d^3}+\frac{e^2 x \left(a+b \log \left(c x^n\right)\right)^2}{d^3 (d+e x)}-\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 n^2}{d^2 x}",1,"(-2*b^2*n^2)/(d^2*x) - (2*b*n*(a + b*Log[c*x^n]))/(d^2*x) - (a + b*Log[c*x^n])^2/(d^2*x) + (e^2*x*(a + b*Log[c*x^n])^2)/(d^3*(d + e*x)) - (2*e*(a + b*Log[c*x^n])^3)/(3*b*d^3*n) - (2*b*e*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^3 + (2*e*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/d^3 - (2*b^2*e*n^2*PolyLog[2, -((e*x)/d)])/d^3 + (4*b*e*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/d^3 - (4*b^2*e*n^2*PolyLog[3, -((e*x)/d)])/d^3","A",12,10,23,0.4348,1,"{2353, 2305, 2304, 2302, 30, 2318, 2317, 2391, 2374, 6589}"
106,1,304,0,0.3774457,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x^3 (d+e x)^2} \, dx","Int[(a + b*Log[c*x^n])^2/(x^3*(d + e*x)^2),x]","-\frac{6 b e^2 n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}+\frac{2 b^2 e^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^4}+\frac{6 b^2 e^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{d^4}-\frac{e^3 x \left(a+b \log \left(c x^n\right)\right)^2}{d^4 (d+e x)}+\frac{e^2 \left(a+b \log \left(c x^n\right)\right)^3}{b d^4 n}-\frac{3 e^2 \log \left(\frac{e x}{d}+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{4 b^2 e n^2}{d^3 x}-\frac{b^2 n^2}{4 d^2 x^2}","\frac{6 b e^2 n \text{PolyLog}\left(2,-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}+\frac{2 b^2 e^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^4}+\frac{6 b^2 e^2 n^2 \text{PolyLog}\left(3,-\frac{d}{e x}\right)}{d^4}-\frac{e^3 x \left(a+b \log \left(c x^n\right)\right)^2}{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)^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{4 b^2 e n^2}{d^3 x}-\frac{b^2 n^2}{4 d^2 x^2}",1,"-(b^2*n^2)/(4*d^2*x^2) + (4*b^2*e*n^2)/(d^3*x) - (b*n*(a + b*Log[c*x^n]))/(2*d^2*x^2) + (4*b*e*n*(a + b*Log[c*x^n]))/(d^3*x) - (a + b*Log[c*x^n])^2/(2*d^2*x^2) + (2*e*(a + b*Log[c*x^n])^2)/(d^3*x) - (e^3*x*(a + b*Log[c*x^n])^2)/(d^4*(d + e*x)) + (e^2*(a + b*Log[c*x^n])^3)/(b*d^4*n) + (2*b*e^2*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^4 - (3*e^2*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/d^4 + (2*b^2*e^2*n^2*PolyLog[2, -((e*x)/d)])/d^4 - (6*b*e^2*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/d^4 + (6*b^2*e^2*n^2*PolyLog[3, -((e*x)/d)])/d^4","A",14,10,23,0.4348,1,"{2353, 2305, 2304, 2302, 30, 2318, 2317, 2391, 2374, 6589}"
107,1,296,0,0.4901363,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^3} \, dx","Int[(x^3*(a + b*Log[c*x^n])^2)/(d + e*x)^3,x]","-\frac{6 b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}-\frac{5 b^2 d n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^4}+\frac{6 b^2 d n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{e^4}+\frac{d^3 \left(a+b \log \left(c x^n\right)\right)^2}{2 e^4 (d+e x)^2}+\frac{3 d x \left(a+b \log \left(c x^n\right)\right)^2}{e^3 (d+e x)}-\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{2 e^4}+\frac{b d n x \left(a+b \log \left(c x^n\right)\right)}{e^3 (d+e x)}-\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{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{b^2 d n^2 \log (d+e x)}{e^4}+\frac{2 b^2 n^2 x}{e^3}","-\frac{6 b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}-\frac{5 b^2 d n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^4}+\frac{6 b^2 d n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{e^4}+\frac{d^3 \left(a+b \log \left(c x^n\right)\right)^2}{2 e^4 (d+e x)^2}+\frac{3 d x \left(a+b \log \left(c x^n\right)\right)^2}{e^3 (d+e x)}-\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{2 e^4}+\frac{b d n x \left(a+b \log \left(c x^n\right)\right)}{e^3 (d+e x)}-\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{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{b^2 d n^2 \log (d+e x)}{e^4}+\frac{2 b^2 n^2 x}{e^3}",1,"(-2*a*b*n*x)/e^3 + (2*b^2*n^2*x)/e^3 - (2*b^2*n*x*Log[c*x^n])/e^3 + (b*d*n*x*(a + b*Log[c*x^n]))/(e^3*(d + e*x)) - (d*(a + b*Log[c*x^n])^2)/(2*e^4) + (x*(a + b*Log[c*x^n])^2)/e^3 + (d^3*(a + b*Log[c*x^n])^2)/(2*e^4*(d + e*x)^2) + (3*d*x*(a + b*Log[c*x^n])^2)/(e^3*(d + e*x)) - (b^2*d*n^2*Log[d + e*x])/e^4 - (5*b*d*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^4 - (3*d*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/e^4 - (5*b^2*d*n^2*PolyLog[2, -((e*x)/d)])/e^4 - (6*b*d*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/e^4 + (6*b^2*d*n^2*PolyLog[3, -((e*x)/d)])/e^4","A",19,14,23,0.6087,1,"{2353, 2296, 2295, 2319, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2318, 2374, 6589}"
108,1,232,0,0.4459668,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^3} \, dx","Int[(x^2*(a + b*Log[c*x^n])^2)/(d + e*x)^3,x]","\frac{2 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^3}+\frac{3 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^3}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{e^3}-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 e^3 (d+e x)^2}-\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{e^2 (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)}{e^3}-\frac{2 x \left(a+b \log \left(c x^n\right)\right)^2}{e^2 (d+e x)}+\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^3}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 e^3}+\frac{b^2 n^2 \log (d+e x)}{e^3}","\frac{2 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^3}+\frac{3 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{e^3}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{e^3}-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 e^3 (d+e x)^2}-\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{e^2 (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)}{e^3}-\frac{2 x \left(a+b \log \left(c x^n\right)\right)^2}{e^2 (d+e x)}+\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^3}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 e^3}+\frac{b^2 n^2 \log (d+e x)}{e^3}",1,"-((b*n*x*(a + b*Log[c*x^n]))/(e^2*(d + e*x))) + (a + b*Log[c*x^n])^2/(2*e^3) - (d^2*(a + b*Log[c*x^n])^2)/(2*e^3*(d + e*x)^2) - (2*x*(a + b*Log[c*x^n])^2)/(e^2*(d + e*x)) + (b^2*n^2*Log[d + e*x])/e^3 + (3*b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/e^3 + ((a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/e^3 + (3*b^2*n^2*PolyLog[2, -((e*x)/d)])/e^3 + (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/e^3 - (2*b^2*n^2*PolyLog[3, -((e*x)/d)])/e^3","A",16,12,23,0.5217,1,"{2353, 2319, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2318, 2374, 6589}"
109,1,176,0,0.356785,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^3} \, dx","Int[(x*(a + b*Log[c*x^n])^2)/(d + e*x)^3,x]","-\frac{b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d e^2}-\frac{b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d e^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 d e^2}+\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{2 e^2 (d+e x)^2}+\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{d e (d+e x)}+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{d e (d+e x)}-\frac{b^2 n^2 \log (d+e x)}{d e^2}","-\frac{b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d 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}",1,"(b*n*x*(a + b*Log[c*x^n]))/(d*e*(d + e*x)) - (a + b*Log[c*x^n])^2/(2*d*e^2) + (d*(a + b*Log[c*x^n])^2)/(2*e^2*(d + e*x)^2) + (x*(a + b*Log[c*x^n])^2)/(d*e*(d + e*x)) - (b^2*n^2*Log[d + e*x])/(d*e^2) - (b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/(d*e^2) - (b^2*n^2*PolyLog[2, -((e*x)/d)])/(d*e^2)","A",13,10,21,0.4762,1,"{2353, 2319, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2318}"
110,1,145,0,0.2014886,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^3} \, dx","Int[(a + b*Log[c*x^n])^2/(d + e*x)^3,x]","-\frac{b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^2 e}-\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{d^2 (d+e x)}-\frac{b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 e}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 d^2 e}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 e (d+e x)^2}+\frac{b^2 n^2 \log (d+e x)}{d^2 e}","\frac{b^2 n^2 \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{d^2 e}-\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 \log (d+e x)}{d^2 e}",1,"-((b*n*x*(a + b*Log[c*x^n]))/(d^2*(d + e*x))) + (a + b*Log[c*x^n])^2/(2*d^2*e) - (a + b*Log[c*x^n])^2/(2*e*(d + e*x)^2) + (b^2*n^2*Log[d + e*x])/(d^2*e) - (b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/(d^2*e) - (b^2*n^2*PolyLog[2, -((e*x)/d)])/(d^2*e)","A",8,8,20,0.4000,1,"{2319, 2347, 2344, 2301, 2317, 2391, 2314, 31}"
111,1,257,0,0.5938479,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x (d+e x)^3} \, dx","Int[(a + b*Log[c*x^n])^2/(x*(d + e*x)^3),x]","-\frac{2 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}+\frac{3 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^3}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\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{b^2 n^2 \log (d+e x)}{d^3}","-\frac{2 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}+\frac{3 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^3}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\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{b^2 n^2 \log (d+e x)}{d^3}",1,"(b*e*n*x*(a + b*Log[c*x^n]))/(d^3*(d + e*x)) - (a + b*Log[c*x^n])^2/(2*d^3) + (a + b*Log[c*x^n])^2/(2*d*(d + e*x)^2) - (e*x*(a + b*Log[c*x^n])^2)/(d^3*(d + e*x)) + (a + b*Log[c*x^n])^3/(3*b*d^3*n) - (b^2*n^2*Log[d + e*x])/d^3 + (3*b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^3 - ((a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/d^3 + (3*b^2*n^2*PolyLog[2, -((e*x)/d)])/d^3 - (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/d^3 + (2*b^2*n^2*PolyLog[3, -((e*x)/d)])/d^3","A",19,13,23,0.5652,1,"{2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391, 2319, 2301, 2314, 31}"
112,1,322,0,0.5377086,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x^2 (d+e x)^3} \, dx","Int[(a + b*Log[c*x^n])^2/(x^2*(d + e*x)^3),x]","\frac{6 b e n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}-\frac{5 b^2 e n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^4}-\frac{6 b^2 e n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{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{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{e \left(a+b \log \left(c x^n\right)\right)^2}{2 d^2 (d+e x)^2}-\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{b^2 e n^2 \log (d+e x)}{d^4}-\frac{2 b^2 n^2}{d^3 x}","\frac{6 b e n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}-\frac{5 b^2 e n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^4}-\frac{6 b^2 e n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{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{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{e \left(a+b \log \left(c x^n\right)\right)^2}{2 d^2 (d+e x)^2}-\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{b^2 e n^2 \log (d+e x)}{d^4}-\frac{2 b^2 n^2}{d^3 x}",1,"(-2*b^2*n^2)/(d^3*x) - (2*b*n*(a + b*Log[c*x^n]))/(d^3*x) - (b*e^2*n*x*(a + b*Log[c*x^n]))/(d^4*(d + e*x)) + (e*(a + b*Log[c*x^n])^2)/(2*d^4) - (a + b*Log[c*x^n])^2/(d^3*x) - (e*(a + b*Log[c*x^n])^2)/(2*d^2*(d + e*x)^2) + (2*e^2*x*(a + b*Log[c*x^n])^2)/(d^4*(d + e*x)) - (e*(a + b*Log[c*x^n])^3)/(b*d^4*n) + (b^2*e*n^2*Log[d + e*x])/d^4 - (5*b*e*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^4 + (3*e*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/d^4 - (5*b^2*e*n^2*PolyLog[2, -((e*x)/d)])/d^4 + (6*b*e*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/d^4 - (6*b^2*e*n^2*PolyLog[3, -((e*x)/d)])/d^4","A",20,16,23,0.6957,1,"{2353, 2305, 2304, 2302, 30, 2319, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2318, 2374, 6589}"
113,1,398,0,0.8256245,"\int \frac{x^4 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^4} \, dx","Int[(x^4*(a + b*Log[c*x^n])^2)/(d + e*x)^4,x]","-\frac{8 b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^5}-\frac{26 b^2 d n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{3 e^5}+\frac{8 b^2 d n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{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{6 d x \left(a+b \log \left(c x^n\right)\right)^2}{e^4 (d+e x)}-\frac{5 d \left(a+b \log \left(c x^n\right)\right)^2}{3 e^5}+\frac{10 b d n x \left(a+b \log \left(c x^n\right)\right)}{3 e^4 (d+e x)}-\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{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{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}","-\frac{8 b d n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^5}-\frac{26 b^2 d n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{3 e^5}+\frac{8 b^2 d n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{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{6 d x \left(a+b \log \left(c x^n\right)\right)^2}{e^4 (d+e x)}-\frac{5 d \left(a+b \log \left(c x^n\right)\right)^2}{3 e^5}+\frac{10 b d n x \left(a+b \log \left(c x^n\right)\right)}{3 e^4 (d+e x)}-\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{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{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,"(-2*a*b*n*x)/e^4 + (2*b^2*n^2*x)/e^4 - (b^2*d^2*n^2)/(3*e^5*(d + e*x)) - (b^2*d*n^2*Log[x])/(3*e^5) - (2*b^2*n*x*Log[c*x^n])/e^4 + (b*d^3*n*(a + b*Log[c*x^n]))/(3*e^5*(d + e*x)^2) + (10*b*d*n*x*(a + b*Log[c*x^n]))/(3*e^4*(d + e*x)) - (5*d*(a + b*Log[c*x^n])^2)/(3*e^5) + (x*(a + b*Log[c*x^n])^2)/e^4 - (d^4*(a + b*Log[c*x^n])^2)/(3*e^5*(d + e*x)^3) + (2*d^3*(a + b*Log[c*x^n])^2)/(e^5*(d + e*x)^2) + (6*d*x*(a + b*Log[c*x^n])^2)/(e^4*(d + e*x)) - (3*b^2*d*n^2*Log[d + e*x])/e^5 - (26*b*d*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/(3*e^5) - (4*d*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/e^5 - (26*b^2*d*n^2*PolyLog[2, -((e*x)/d)])/(3*e^5) - (8*b*d*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/e^5 + (8*b^2*d*n^2*PolyLog[3, -((e*x)/d)])/e^5","A",31,15,23,0.6522,1,"{2353, 2296, 2295, 2319, 2347, 2344, 2301, 2317, 2391, 2314, 31, 44, 2318, 2374, 6589}"
114,1,333,0,0.7858197,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^4} \, dx","Int[(x^3*(a + b*Log[c*x^n])^2)/(d + e*x)^4,x]","\frac{2 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}+\frac{11 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{3 e^4}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{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{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{\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{7 \left(a+b \log \left(c x^n\right)\right)^2}{6 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}","\frac{2 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}+\frac{11 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{3 e^4}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{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{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{\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{7 \left(a+b \log \left(c x^n\right)\right)^2}{6 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,"(b^2*d*n^2)/(3*e^4*(d + e*x)) + (b^2*n^2*Log[x])/(3*e^4) - (b*d^2*n*(a + b*Log[c*x^n]))/(3*e^4*(d + e*x)^2) - (7*b*n*x*(a + b*Log[c*x^n]))/(3*e^3*(d + e*x)) + (7*(a + b*Log[c*x^n])^2)/(6*e^4) + (d^3*(a + b*Log[c*x^n])^2)/(3*e^4*(d + e*x)^3) - (3*d^2*(a + b*Log[c*x^n])^2)/(2*e^4*(d + e*x)^2) - (3*x*(a + b*Log[c*x^n])^2)/(e^3*(d + e*x)) + (2*b^2*n^2*Log[d + e*x])/e^4 + (11*b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/(3*e^4) + ((a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/e^4 + (11*b^2*n^2*PolyLog[2, -((e*x)/d)])/(3*e^4) + (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/e^4 - (2*b^2*n^2*PolyLog[3, -((e*x)/d)])/e^4","A",28,13,23,0.5652,1,"{2353, 2319, 2347, 2344, 2301, 2317, 2391, 2314, 31, 44, 2318, 2374, 6589}"
115,1,274,0,0.7155409,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^4} \, dx","Int[(x^2*(a + b*Log[c*x^n])^2)/(d + e*x)^4,x]","-\frac{2 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{3 d e^3}-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^2}{3 e^3 (d+e x)^3}+\frac{4 b n x \left(a+b \log \left(c x^n\right)\right)}{3 d e^2 (d+e x)}+\frac{b d n \left(a+b \log \left(c x^n\right)\right)}{3 e^3 (d+e x)^2}-\frac{2 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 d e^3}+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{d e^2 (d+e x)}+\frac{d \left(a+b \log \left(c x^n\right)\right)^2}{e^3 (d+e x)^2}-\frac{2 \left(a+b \log \left(c x^n\right)\right)^2}{3 d e^3}-\frac{b^2 n^2}{3 e^3 (d+e x)}-\frac{b^2 n^2 \log (x)}{3 d e^3}-\frac{b^2 n^2 \log (d+e x)}{d e^3}","-\frac{2 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\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{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{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}",1,"-(b^2*n^2)/(3*e^3*(d + e*x)) - (b^2*n^2*Log[x])/(3*d*e^3) + (b*d*n*(a + b*Log[c*x^n]))/(3*e^3*(d + e*x)^2) + (4*b*n*x*(a + b*Log[c*x^n]))/(3*d*e^2*(d + e*x)) - (2*(a + b*Log[c*x^n])^2)/(3*d*e^3) - (d^2*(a + b*Log[c*x^n])^2)/(3*e^3*(d + e*x)^3) + (d*(a + b*Log[c*x^n])^2)/(e^3*(d + e*x)^2) + (x*(a + b*Log[c*x^n])^2)/(d*e^2*(d + e*x)) - (b^2*n^2*Log[d + e*x])/(d*e^3) - (2*b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/(3*d*e^3) - (2*b^2*n^2*PolyLog[2, -((e*x)/d)])/(3*d*e^3)","A",25,11,23,0.4783,1,"{2353, 2319, 2347, 2344, 2301, 2317, 2391, 2314, 31, 44, 2318}"
116,1,229,0,0.6201662,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^4} \, dx","Int[(x*(a + b*Log[c*x^n])^2)/(d + e*x)^4,x]","-\frac{b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{3 d^2 e^2}-\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 x \left(a+b \log \left(c x^n\right)\right)}{3 d^2 e (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 \log (x)}{3 d^2 e^2}+\frac{b^2 n^2}{3 d e^2 (d+e x)}","-\frac{b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{3 d^2 e^2}-\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}{3 d e^2 (d+e x)}",1,"(b^2*n^2)/(3*d*e^2*(d + e*x)) + (b^2*n^2*Log[x])/(3*d^2*e^2) - (b*n*(a + b*Log[c*x^n]))/(3*e^2*(d + e*x)^2) - (b*n*x*(a + b*Log[c*x^n]))/(3*d^2*e*(d + e*x)) + (a + b*Log[c*x^n])^2/(6*d^2*e^2) + (d*(a + b*Log[c*x^n])^2)/(3*e^2*(d + e*x)^3) - (a + b*Log[c*x^n])^2/(2*e^2*(d + e*x)^2) - (b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/(3*d^2*e^2) - (b^2*n^2*PolyLog[2, -((e*x)/d)])/(3*d^2*e^2)","A",22,10,21,0.4762,1,"{2353, 2319, 2347, 2344, 2301, 2317, 2391, 2314, 31, 44}"
117,1,221,0,0.3122959,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^4} \, dx","Int[(a + b*Log[c*x^n])^2/(d + e*x)^4,x]","-\frac{2 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\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{2 b n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^3 e}+\frac{\left(a+b \log \left(c x^n\right)\right)^2}{3 d^3 e}+\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{b^2 n^2}{3 d^2 e (d+e x)}-\frac{b^2 n^2 \log (x)}{3 d^3 e}+\frac{b^2 n^2 \log (d+e x)}{d^3 e}","\frac{2 b^2 n^2 \text{PolyLog}\left(2,-\frac{d}{e x}\right)}{3 d^3 e}-\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{b^2 n^2}{3 d^2 e (d+e x)}-\frac{b^2 n^2 \log (x)}{3 d^3 e}+\frac{b^2 n^2 \log (d+e x)}{d^3 e}",1,"-(b^2*n^2)/(3*d^2*e*(d + e*x)) - (b^2*n^2*Log[x])/(3*d^3*e) + (b*n*(a + b*Log[c*x^n]))/(3*d*e*(d + e*x)^2) - (2*b*n*x*(a + b*Log[c*x^n]))/(3*d^3*(d + e*x)) + (a + b*Log[c*x^n])^2/(3*d^3*e) - (a + b*Log[c*x^n])^2/(3*e*(d + e*x)^3) + (b^2*n^2*Log[d + e*x])/(d^3*e) - (2*b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/(3*d^3*e) - (2*b^2*n^2*PolyLog[2, -((e*x)/d)])/(3*d^3*e)","A",12,9,20,0.4500,1,"{2319, 2347, 2344, 2301, 2317, 2391, 2314, 31, 44}"
118,1,351,0,1.012459,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x (d+e x)^4} \, dx","Int[(a + b*Log[c*x^n])^2/(x*(d + e*x)^4),x]","-\frac{2 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}+\frac{11 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{3 d^4}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\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{\left(a+b \log \left(c x^n\right)\right)^2}{2 d^2 (d+e x)^2}+\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{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)^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}{3 d (d+e x)^3}+\frac{b^2 n^2}{3 d^3 (d+e x)}-\frac{2 b^2 n^2 \log (d+e x)}{d^4}+\frac{b^2 n^2 \log (x)}{3 d^4}","-\frac{2 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^4}+\frac{11 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{3 d^4}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\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{\left(a+b \log \left(c x^n\right)\right)^2}{2 d^2 (d+e x)^2}+\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{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)^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}{3 d (d+e x)^3}+\frac{b^2 n^2}{3 d^3 (d+e x)}-\frac{2 b^2 n^2 \log (d+e x)}{d^4}+\frac{b^2 n^2 \log (x)}{3 d^4}",1,"(b^2*n^2)/(3*d^3*(d + e*x)) + (b^2*n^2*Log[x])/(3*d^4) - (b*n*(a + b*Log[c*x^n]))/(3*d^2*(d + e*x)^2) + (5*b*e*n*x*(a + b*Log[c*x^n]))/(3*d^4*(d + e*x)) - (5*(a + b*Log[c*x^n])^2)/(6*d^4) + (a + b*Log[c*x^n])^2/(3*d*(d + e*x)^3) + (a + b*Log[c*x^n])^2/(2*d^2*(d + e*x)^2) - (e*x*(a + b*Log[c*x^n])^2)/(d^4*(d + e*x)) + (a + b*Log[c*x^n])^3/(3*b*d^4*n) - (2*b^2*n^2*Log[d + e*x])/d^4 + (11*b*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/(3*d^4) - ((a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/d^4 + (11*b^2*n^2*PolyLog[2, -((e*x)/d)])/(3*d^4) - (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/d^4 + (2*b^2*n^2*PolyLog[3, -((e*x)/d)])/d^4","A",32,14,23,0.6087,1,"{2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391, 2319, 2301, 2314, 31, 44}"
119,1,420,0,0.89301,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x^2 (d+e x)^4} \, dx","Int[(a + b*Log[c*x^n])^2/(x^2*(d + e*x)^4),x]","\frac{8 b e n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^5}-\frac{26 b^2 e n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{3 d^5}-\frac{8 b^2 e n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{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{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{e \left(a+b \log \left(c x^n\right)\right)^2}{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 e n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^5}+\frac{b e n \left(a+b \log \left(c x^n\right)\right)}{3 d^3 (d+e x)^2}-\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{b^2 e n^2}{3 d^4 (d+e x)}-\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{2 b^2 n^2}{d^4 x}","\frac{8 b e n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^5}-\frac{26 b^2 e n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{3 d^5}-\frac{8 b^2 e n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{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{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{e \left(a+b \log \left(c x^n\right)\right)^2}{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 e n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^5}+\frac{b e n \left(a+b \log \left(c x^n\right)\right)}{3 d^3 (d+e x)^2}-\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{b^2 e n^2}{3 d^4 (d+e x)}-\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{2 b^2 n^2}{d^4 x}",1,"(-2*b^2*n^2)/(d^4*x) - (b^2*e*n^2)/(3*d^4*(d + e*x)) - (b^2*e*n^2*Log[x])/(3*d^5) - (2*b*n*(a + b*Log[c*x^n]))/(d^4*x) + (b*e*n*(a + b*Log[c*x^n]))/(3*d^3*(d + e*x)^2) - (8*b*e^2*n*x*(a + b*Log[c*x^n]))/(3*d^5*(d + e*x)) + (4*e*(a + b*Log[c*x^n])^2)/(3*d^5) - (a + b*Log[c*x^n])^2/(d^4*x) - (e*(a + b*Log[c*x^n])^2)/(3*d^2*(d + e*x)^3) - (e*(a + b*Log[c*x^n])^2)/(d^3*(d + e*x)^2) + (3*e^2*x*(a + b*Log[c*x^n])^2)/(d^5*(d + e*x)) - (4*e*(a + b*Log[c*x^n])^3)/(3*b*d^5*n) + (3*b^2*e*n^2*Log[d + e*x])/d^5 - (26*b*e*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/(3*d^5) + (4*e*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/d^5 - (26*b^2*e*n^2*PolyLog[2, -((e*x)/d)])/(3*d^5) + (8*b*e*n*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/d^5 - (8*b^2*e*n^2*PolyLog[3, -((e*x)/d)])/d^5","A",32,17,23,0.7391,1,"{2353, 2305, 2304, 2302, 30, 2319, 2347, 2344, 2301, 2317, 2391, 2314, 31, 44, 2318, 2374, 6589}"
120,1,157,0,0.4066567,"\int \frac{x \log ^2(x)}{(d+e x)^4} \, dx","Int[(x*Log[x]^2)/(d + e*x)^4,x]","-\frac{\text{PolyLog}\left(2,-\frac{e x}{d}\right)}{3 d^2 e^2}+\frac{\log ^2(x)}{6 d^2 e^2}-\frac{\log (x) \log \left(\frac{e x}{d}+1\right)}{3 d^2 e^2}+\frac{\log (x)}{3 d^2 e^2}-\frac{x \log (x)}{3 d^2 e (d+e x)}+\frac{1}{3 d e^2 (d+e x)}-\frac{\log ^2(x)}{2 e^2 (d+e x)^2}+\frac{d \log ^2(x)}{3 e^2 (d+e x)^3}-\frac{\log (x)}{3 e^2 (d+e x)^2}","-\frac{\text{PolyLog}\left(2,-\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,"1/(3*d*e^2*(d + e*x)) + Log[x]/(3*d^2*e^2) - Log[x]/(3*e^2*(d + e*x)^2) - (x*Log[x])/(3*d^2*e*(d + e*x)) + Log[x]^2/(6*d^2*e^2) + (d*Log[x]^2)/(3*e^2*(d + e*x)^3) - Log[x]^2/(2*e^2*(d + e*x)^2) - (Log[x]*Log[1 + (e*x)/d])/(3*d^2*e^2) - PolyLog[2, -((e*x)/d)]/(3*d^2*e^2)","A",22,10,13,0.7692,1,"{2353, 2319, 2347, 2344, 2301, 2317, 2391, 2314, 31, 44}"
121,1,130,0,0.2078559,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3}{x (d+e x)} \, dx","Int[(a + b*Log[c*x^n])^3/(x*(d + e*x)),x]","\frac{6 b^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d}-\frac{3 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)^2}{d}-\frac{6 b^3 n^3 \text{PolyLog}\left(4,-\frac{e x}{d}\right)}{d}-\frac{\log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{d}+\frac{\left(a+b \log \left(c x^n\right)\right)^4}{4 b d n}","\frac{6 b^2 n^2 \text{PolyLog}\left(3,-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d}+\frac{3 b n \text{PolyLog}\left(2,-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)^2}{d}+\frac{6 b^3 n^3 \text{PolyLog}\left(4,-\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)^3}{d}",1,"(a + b*Log[c*x^n])^4/(4*b*d*n) - ((a + b*Log[c*x^n])^3*Log[1 + (e*x)/d])/d - (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((e*x)/d)])/d + (6*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((e*x)/d)])/d - (6*b^3*n^3*PolyLog[4, -((e*x)/d)])/d","A",7,7,23,0.3043,1,"{2344, 2302, 30, 2317, 2374, 2383, 6589}"
122,1,234,0,0.3964863,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3}{x (d+e x)^2} \, dx","Int[(a + b*Log[c*x^n])^3/(x*(d + e*x)^2),x]","\frac{6 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}+\frac{6 b^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}-\frac{3 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2}-\frac{6 b^3 n^3 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{d^2}-\frac{6 b^3 n^3 \text{PolyLog}\left(4,-\frac{e x}{d}\right)}{d^2}-\frac{\log \left(\frac{e x}{d}+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{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{\left(a+b \log \left(c x^n\right)\right)^4}{4 b d^2 n}","\frac{6 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}+\frac{6 b^2 n^2 \text{PolyLog}\left(3,-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2}+\frac{3 b n \text{PolyLog}\left(2,-\frac{d}{e x}\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2}-\frac{6 b^3 n^3 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{d^2}+\frac{6 b^3 n^3 \text{PolyLog}\left(4,-\frac{d}{e x}\right)}{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)}",1,"-((e*x*(a + b*Log[c*x^n])^3)/(d^2*(d + e*x))) + (a + b*Log[c*x^n])^4/(4*b*d^2*n) + (3*b*n*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/d^2 - ((a + b*Log[c*x^n])^3*Log[1 + (e*x)/d])/d^2 + (6*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/d^2 - (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((e*x)/d)])/d^2 - (6*b^3*n^3*PolyLog[3, -((e*x)/d)])/d^2 + (6*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((e*x)/d)])/d^2 - (6*b^3*n^3*PolyLog[4, -((e*x)/d)])/d^2","A",12,9,23,0.3913,1,"{2347, 2344, 2302, 30, 2317, 2374, 2383, 6589, 2318}"
123,1,361,0,0.8521268,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3}{x (d+e x)^3} \, dx","Int[(a + b*Log[c*x^n])^3/(x*(d + e*x)^3),x]","\frac{9 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}+\frac{6 b^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}-\frac{3 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^3}-\frac{3 b^3 n^3 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^3}-\frac{9 b^3 n^3 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{d^3}-\frac{6 b^3 n^3 \text{PolyLog}\left(4,-\frac{e x}{d}\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{\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{9 b^2 n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}+\frac{6 b^2 n^2 \text{PolyLog}\left(3,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3}-\frac{3 b n \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^3}-\frac{3 b^3 n^3 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^3}-\frac{9 b^3 n^3 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{d^3}-\frac{6 b^3 n^3 \text{PolyLog}\left(4,-\frac{e x}{d}\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{\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}",1,"(3*b*e*n*x*(a + b*Log[c*x^n])^2)/(2*d^3*(d + e*x)) - (a + b*Log[c*x^n])^3/(2*d^3) + (a + b*Log[c*x^n])^3/(2*d*(d + e*x)^2) - (e*x*(a + b*Log[c*x^n])^3)/(d^3*(d + e*x)) + (a + b*Log[c*x^n])^4/(4*b*d^3*n) - (3*b^2*n^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/d^3 + (9*b*n*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/(2*d^3) - ((a + b*Log[c*x^n])^3*Log[1 + (e*x)/d])/d^3 - (3*b^3*n^3*PolyLog[2, -((e*x)/d)])/d^3 + (9*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/d^3 - (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((e*x)/d)])/d^3 - (9*b^3*n^3*PolyLog[3, -((e*x)/d)])/d^3 + (6*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((e*x)/d)])/d^3 - (6*b^3*n^3*PolyLog[4, -((e*x)/d)])/d^3","A",24,11,23,0.4783,1,"{2347, 2344, 2302, 30, 2317, 2374, 2383, 6589, 2318, 2319, 2391}"
124,1,189,0,0.265735,"\int (d+e x) \sqrt{a+b \log \left(c x^n\right)} \, dx","Int[(d + e*x)*Sqrt[a + b*Log[c*x^n]],x]","-\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)}","-\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,"-(Sqrt[b]*d*Sqrt[n]*Sqrt[Pi]*x*Erfi[Sqrt[a + b*Log[c*x^n]]/(Sqrt[b]*Sqrt[n])])/(2*E^(a/(b*n))*(c*x^n)^n^(-1)) - (Sqrt[b]*e*Sqrt[n]*Sqrt[Pi/2]*x^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*x^n]])/(Sqrt[b]*Sqrt[n])])/(4*E^((2*a)/(b*n))*(c*x^n)^(2/n)) + d*x*Sqrt[a + b*Log[c*x^n]] + (e*x^2*Sqrt[a + b*Log[c*x^n]])/2","A",10,7,20,0.3500,1,"{2330, 2296, 2300, 2180, 2204, 2305, 2310}"
125,1,298,0,0.4665669,"\int (d+e x)^2 \sqrt{a+b \log \left(c x^n\right)} \, dx","Int[(d + e*x)^2*Sqrt[a + b*Log[c*x^n]],x]","-\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)}","-\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,"-(Sqrt[b]*d^2*Sqrt[n]*Sqrt[Pi]*x*Erfi[Sqrt[a + b*Log[c*x^n]]/(Sqrt[b]*Sqrt[n])])/(2*E^(a/(b*n))*(c*x^n)^n^(-1)) - (Sqrt[b]*d*e*Sqrt[n]*Sqrt[Pi/2]*x^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*x^n]])/(Sqrt[b]*Sqrt[n])])/(2*E^((2*a)/(b*n))*(c*x^n)^(2/n)) - (Sqrt[b]*e^2*Sqrt[n]*Sqrt[Pi/3]*x^3*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)) + d^2*x*Sqrt[a + b*Log[c*x^n]] + d*e*x^2*Sqrt[a + b*Log[c*x^n]] + (e^2*x^3*Sqrt[a + b*Log[c*x^n]])/3","A",14,7,22,0.3182,1,"{2330, 2296, 2300, 2180, 2204, 2305, 2310}"
126,1,402,0,0.6152559,"\int (d+e x)^3 \sqrt{a+b \log \left(c x^n\right)} \, dx","Int[(d + e*x)^3*Sqrt[a + b*Log[c*x^n]],x]","-\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{\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{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)}","-\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{\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{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,"-(Sqrt[b]*d^3*Sqrt[n]*Sqrt[Pi]*x*Erfi[Sqrt[a + b*Log[c*x^n]]/(Sqrt[b]*Sqrt[n])])/(2*E^(a/(b*n))*(c*x^n)^n^(-1)) - (Sqrt[b]*e^3*Sqrt[n]*Sqrt[Pi]*x^4*Erfi[(2*Sqrt[a + b*Log[c*x^n]])/(Sqrt[b]*Sqrt[n])])/(16*E^((4*a)/(b*n))*(c*x^n)^(4/n)) - (3*Sqrt[b]*d^2*e*Sqrt[n]*Sqrt[Pi/2]*x^2*Erfi[(Sqrt[2]*Sqrt[a + b*Log[c*x^n]])/(Sqrt[b]*Sqrt[n])])/(4*E^((2*a)/(b*n))*(c*x^n)^(2/n)) - (Sqrt[b]*d*e^2*Sqrt[n]*Sqrt[Pi/3]*x^3*Erfi[(Sqrt[3]*Sqrt[a + b*Log[c*x^n]])/(Sqrt[b]*Sqrt[n])])/(2*E^((3*a)/(b*n))*(c*x^n)^(3/n)) + d^3*x*Sqrt[a + b*Log[c*x^n]] + (3*d^2*e*x^2*Sqrt[a + b*Log[c*x^n]])/2 + d*e^2*x^3*Sqrt[a + b*Log[c*x^n]] + (e^3*x^4*Sqrt[a + b*Log[c*x^n]])/4","A",18,7,22,0.3182,1,"{2330, 2296, 2300, 2180, 2204, 2305, 2310}"
127,0,0,0,0.0476515,"\int \frac{\sqrt{a+b \log \left(c x^n\right)}}{d+e x} \, dx","Int[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,"Defer[Int][Sqrt[a + b*Log[c*x^n]]/(d + e*x), x]","A",0,0,0,0,-1,"{}"
128,0,0,0,0.1012366,"\int \frac{\sqrt{a+b \log \left(c x^n\right)}}{(d+e x)^2} \, dx","Int[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,"(x*Sqrt[a + b*Log[c*x^n]])/(d*(d + e*x)) - (b*n*Defer[Int][1/((d + e*x)*Sqrt[a + b*Log[c*x^n]]), x])/(2*d)","A",0,0,0,0,-1,"{}"
129,0,0,0,0.1977997,"\int \frac{\sqrt{a+b \log \left(c x^n\right)}}{(d+e x)^3} \, dx","Int[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,"-Sqrt[a + b*Log[c*x^n]]/(2*e*(d + e*x)^2) + (b*n*Defer[Int][1/(x*(d + e*x)^2*Sqrt[a + b*Log[c*x^n]]), x])/(4*e)","A",0,0,0,0,-1,"{}"
130,1,242,0,0.2196378,"\int x^3 \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^3*Sqrt[d + e*x]*(a + b*Log[c*x^n]),x]","-\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^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{64 b d^{9/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{315 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}","-\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^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{64 b d^{9/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{315 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,"(64*b*d^4*n*Sqrt[d + e*x])/(315*e^4) + (64*b*d^3*n*(d + e*x)^(3/2))/(945*e^4) - (356*b*d^2*n*(d + e*x)^(5/2))/(1575*e^4) + (80*b*d*n*(d + e*x)^(7/2))/(441*e^4) - (4*b*n*(d + e*x)^(9/2))/(81*e^4) - (64*b*d^(9/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(315*e^4) - (2*d^3*(d + e*x)^(3/2)*(a + b*Log[c*x^n]))/(3*e^4) + (6*d^2*(d + e*x)^(5/2)*(a + b*Log[c*x^n]))/(5*e^4) - (6*d*(d + e*x)^(7/2)*(a + b*Log[c*x^n]))/(7*e^4) + (2*(d + e*x)^(9/2)*(a + b*Log[c*x^n]))/(9*e^4)","A",8,7,23,0.3043,1,"{43, 2350, 12, 1620, 50, 63, 208}"
131,1,192,0,0.176065,"\int x^2 \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*Sqrt[d + e*x]*(a + b*Log[c*x^n]),x]","\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^3 n \sqrt{d+e x}}{105 e^3}-\frac{32 b d^2 n (d+e x)^{3/2}}{315 e^3}+\frac{32 b d^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{105 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}","\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^3 n \sqrt{d+e x}}{105 e^3}-\frac{32 b d^2 n (d+e x)^{3/2}}{315 e^3}+\frac{32 b d^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{105 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,"(-32*b*d^3*n*Sqrt[d + e*x])/(105*e^3) - (32*b*d^2*n*(d + e*x)^(3/2))/(315*e^3) + (36*b*d*n*(d + e*x)^(5/2))/(175*e^3) - (4*b*n*(d + e*x)^(7/2))/(49*e^3) + (32*b*d^(7/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(105*e^3) + (2*d^2*(d + e*x)^(3/2)*(a + b*Log[c*x^n]))/(3*e^3) - (4*d*(d + e*x)^(5/2)*(a + b*Log[c*x^n]))/(5*e^3) + (2*(d + e*x)^(7/2)*(a + b*Log[c*x^n]))/(7*e^3)","A",6,6,23,0.2609,1,"{43, 2350, 12, 897, 1261, 208}"
132,1,142,0,0.1008474,"\int x \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Sqrt[d + e*x]*(a + b*Log[c*x^n]),x]","-\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^2 n \sqrt{d+e x}}{15 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 n (d+e x)^{3/2}}{45 e^2}-\frac{4 b n (d+e x)^{5/2}}{25 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^2 n \sqrt{d+e x}}{15 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 n (d+e x)^{3/2}}{45 e^2}-\frac{4 b n (d+e x)^{5/2}}{25 e^2}",1,"(8*b*d^2*n*Sqrt[d + e*x])/(15*e^2) + (8*b*d*n*(d + e*x)^(3/2))/(45*e^2) - (4*b*n*(d + e*x)^(5/2))/(25*e^2) - (8*b*d^(5/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(15*e^2) - (2*d*(d + e*x)^(3/2)*(a + b*Log[c*x^n]))/(3*e^2) + (2*(d + e*x)^(5/2)*(a + b*Log[c*x^n]))/(5*e^2)","A",7,7,21,0.3333,1,"{43, 2350, 12, 80, 50, 63, 208}"
133,1,94,0,0.042146,"\int \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sqrt[d + e*x]*(a + b*Log[c*x^n]),x]","\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}","\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,"(-4*b*d*n*Sqrt[d + e*x])/(3*e) - (4*b*n*(d + e*x)^(3/2))/(9*e) + (4*b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(3*e) + (2*(d + e*x)^(3/2)*(a + b*Log[c*x^n]))/(3*e)","A",5,4,20,0.2000,1,"{2319, 50, 63, 208}"
134,1,211,0,0.3305935,"\int \frac{\sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[(Sqrt[d + e*x]*(a + b*Log[c*x^n]))/x,x]","-2 b \sqrt{d} n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\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)-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)","-2 b \sqrt{d} n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\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)-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,"-4*b*n*Sqrt[d + e*x] + 4*b*Sqrt[d]*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + 2*b*Sqrt[d]*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]^2 + 2*Sqrt[d + e*x]*(a + b*Log[c*x^n]) - 2*Sqrt[d]*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*(a + b*Log[c*x^n]) - 4*b*Sqrt[d]*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])] - 2*b*Sqrt[d]*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])]","A",12,11,23,0.4783,1,"{2346, 63, 208, 2348, 12, 5984, 5918, 2402, 2315, 2319, 50}"
135,1,221,0,0.2778432,"\int \frac{\sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[(Sqrt[d + e*x]*(a + b*Log[c*x^n]))/x^2,x]","-\frac{b e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{\sqrt{d}}-\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 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}}","-\frac{b e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{\sqrt{d}}-\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 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,"-((b*n*Sqrt[d + e*x])/x) - (b*e*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/Sqrt[d] + (b*e*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]^2)/Sqrt[d] - (Sqrt[d + e*x]*(a + b*Log[c*x^n]))/x - (e*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*(a + b*Log[c*x^n]))/Sqrt[d] - (2*b*e*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])])/Sqrt[d] - (b*e*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])])/Sqrt[d]","A",11,9,23,0.3913,1,"{47, 63, 208, 2350, 14, 5984, 5918, 2402, 2315}"
136,1,298,0,0.3390089,"\int \frac{\sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[(Sqrt[d + e*x]*(a + b*Log[c*x^n]))/x^3,x]","\frac{b e^2 n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{4 d^{3/2}}+\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 \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}","\frac{b e^2 n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{4 d^{3/2}}+\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 \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,"-(b*n*Sqrt[d + e*x])/(4*x^2) - (3*b*e*n*Sqrt[d + e*x])/(8*d*x) - (b*e^2*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(8*d^(3/2)) - (b*e^2*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]^2)/(4*d^(3/2)) - (Sqrt[d + e*x]*(a + b*Log[c*x^n]))/(2*x^2) - (e*Sqrt[d + e*x]*(a + b*Log[c*x^n]))/(4*d*x) + (e^2*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*(a + b*Log[c*x^n]))/(4*d^(3/2)) + (b*e^2*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])])/(2*d^(3/2)) + (b*e^2*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])])/(4*d^(3/2))","A",16,11,23,0.4783,1,"{47, 51, 63, 208, 2350, 12, 14, 5984, 5918, 2402, 2315}"
137,1,263,0,0.2402735,"\int x^3 (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^3*(d + e*x)^(3/2)*(a + b*Log[c*x^n]),x]","-\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^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{64 b d^{11/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{1155 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}","-\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^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{64 b d^{11/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{1155 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,"(64*b*d^5*n*Sqrt[d + e*x])/(1155*e^4) + (64*b*d^4*n*(d + e*x)^(3/2))/(3465*e^4) + (64*b*d^3*n*(d + e*x)^(5/2))/(5775*e^4) - (172*b*d^2*n*(d + e*x)^(7/2))/(1617*e^4) + (32*b*d*n*(d + e*x)^(9/2))/(297*e^4) - (4*b*n*(d + e*x)^(11/2))/(121*e^4) - (64*b*d^(11/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(1155*e^4) - (2*d^3*(d + e*x)^(5/2)*(a + b*Log[c*x^n]))/(5*e^4) + (6*d^2*(d + e*x)^(7/2)*(a + b*Log[c*x^n]))/(7*e^4) - (2*d*(d + e*x)^(9/2)*(a + b*Log[c*x^n]))/(3*e^4) + (2*(d + e*x)^(11/2)*(a + b*Log[c*x^n]))/(11*e^4)","A",9,7,23,0.3043,1,"{43, 2350, 12, 1620, 50, 63, 208}"
138,1,213,0,0.1973967,"\int x^2 (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*(d + e*x)^(3/2)*(a + b*Log[c*x^n]),x]","\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^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{32 b d^{9/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{315 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}","\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^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{32 b d^{9/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{315 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,"(-32*b*d^4*n*Sqrt[d + e*x])/(315*e^3) - (32*b*d^3*n*(d + e*x)^(3/2))/(945*e^3) - (32*b*d^2*n*(d + e*x)^(5/2))/(1575*e^3) + (44*b*d*n*(d + e*x)^(7/2))/(441*e^3) - (4*b*n*(d + e*x)^(9/2))/(81*e^3) + (32*b*d^(9/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(315*e^3) + (2*d^2*(d + e*x)^(5/2)*(a + b*Log[c*x^n]))/(5*e^3) - (4*d*(d + e*x)^(7/2)*(a + b*Log[c*x^n]))/(7*e^3) + (2*(d + e*x)^(9/2)*(a + b*Log[c*x^n]))/(9*e^3)","A",6,6,23,0.2609,1,"{43, 2350, 12, 897, 1261, 208}"
139,1,163,0,0.1170067,"\int x (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*(d + e*x)^(3/2)*(a + b*Log[c*x^n]),x]","-\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^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^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{35 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}","-\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^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^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{35 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,"(8*b*d^3*n*Sqrt[d + e*x])/(35*e^2) + (8*b*d^2*n*(d + e*x)^(3/2))/(105*e^2) + (8*b*d*n*(d + e*x)^(5/2))/(175*e^2) - (4*b*n*(d + e*x)^(7/2))/(49*e^2) - (8*b*d^(7/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(35*e^2) - (2*d*(d + e*x)^(5/2)*(a + b*Log[c*x^n]))/(5*e^2) + (2*(d + e*x)^(7/2)*(a + b*Log[c*x^n]))/(7*e^2)","A",8,7,21,0.3333,1,"{43, 2350, 12, 80, 50, 63, 208}"
140,1,115,0,0.050536,"\int (d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(d + e*x)^(3/2)*(a + b*Log[c*x^n]),x]","\frac{2 (d+e x)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e}-\frac{4 b d^2 n \sqrt{d+e x}}{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 n (d+e x)^{3/2}}{15 e}-\frac{4 b n (d+e x)^{5/2}}{25 e}","\frac{2 (d+e x)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e}-\frac{4 b d^2 n \sqrt{d+e x}}{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 n (d+e x)^{3/2}}{15 e}-\frac{4 b n (d+e x)^{5/2}}{25 e}",1,"(-4*b*d^2*n*Sqrt[d + e*x])/(5*e) - (4*b*d*n*(d + e*x)^(3/2))/(15*e) - (4*b*n*(d + e*x)^(5/2))/(25*e) + (4*b*d^(5/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(5*e) + (2*(d + e*x)^(5/2)*(a + b*Log[c*x^n]))/(5*e)","A",6,4,20,0.2000,1,"{2319, 50, 63, 208}"
141,1,255,0,0.4562447,"\int \frac{(d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[((d + e*x)^(3/2)*(a + b*Log[c*x^n]))/x,x]","-2 b d^{3/2} n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\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 \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}","-2 b d^{3/2} n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\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 \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,"(-16*b*d*n*Sqrt[d + e*x])/3 - (4*b*n*(d + e*x)^(3/2))/9 + (16*b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/3 + 2*b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]^2 + 2*d*Sqrt[d + e*x]*(a + b*Log[c*x^n]) + (2*(d + e*x)^(3/2)*(a + b*Log[c*x^n]))/3 - 2*d^(3/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*(a + b*Log[c*x^n]) - 4*b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])] - 2*b*d^(3/2)*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])]","A",18,11,23,0.4783,1,"{2346, 63, 208, 2348, 12, 5984, 5918, 2402, 2315, 2319, 50}"
142,1,259,0,0.3242653,"\int \frac{(d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[((d + e*x)^(3/2)*(a + b*Log[c*x^n]))/x^2,x]","-3 b \sqrt{d} e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)-\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)-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)","-3 b \sqrt{d} e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)-\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)-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*b*e*n*Sqrt[d + e*x] - (b*d*n*Sqrt[d + e*x])/x + 3*b*Sqrt[d]*e*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + 3*b*Sqrt[d]*e*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]^2 + 3*e*Sqrt[d + e*x]*(a + b*Log[c*x^n]) - ((d + e*x)^(3/2)*(a + b*Log[c*x^n]))/x - 3*Sqrt[d]*e*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*(a + b*Log[c*x^n]) - 6*b*Sqrt[d]*e*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])] - 3*b*Sqrt[d]*e*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])]","A",14,10,23,0.4348,1,"{47, 50, 63, 208, 2350, 14, 5984, 5918, 2402, 2315}"
143,1,293,0,0.383664,"\int \frac{(d+e x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[((d + e*x)^(3/2)*(a + b*Log[c*x^n]))/x^3,x]","-\frac{3 b e^2 n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{4 \sqrt{d}}-\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 \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}","-\frac{3 b e^2 n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{4 \sqrt{d}}-\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 \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,"-(b*d*n*Sqrt[d + e*x])/(4*x^2) - (11*b*e*n*Sqrt[d + e*x])/(8*x) - (9*b*e^2*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(8*Sqrt[d]) + (3*b*e^2*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]^2)/(4*Sqrt[d]) - (3*e*Sqrt[d + e*x]*(a + b*Log[c*x^n]))/(4*x) - ((d + e*x)^(3/2)*(a + b*Log[c*x^n]))/(2*x^2) - (3*e^2*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*(a + b*Log[c*x^n]))/(4*Sqrt[d]) - (3*b*e^2*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])])/(2*Sqrt[d]) - (3*b*e^2*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])])/(4*Sqrt[d])","A",16,11,23,0.4783,1,"{47, 63, 208, 2350, 12, 14, 51, 5984, 5918, 2402, 2315}"
144,1,217,0,0.203931,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d+e x}} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/Sqrt[d + e*x],x]","-\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^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^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{35 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}","-\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^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^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{35 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,"(64*b*d^3*n*Sqrt[d + e*x])/(35*e^4) - (76*b*d^2*n*(d + e*x)^(3/2))/(105*e^4) + (64*b*d*n*(d + e*x)^(5/2))/(175*e^4) - (4*b*n*(d + e*x)^(7/2))/(49*e^4) - (64*b*d^(7/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(35*e^4) - (2*d^3*Sqrt[d + e*x]*(a + b*Log[c*x^n]))/e^4 + (2*d^2*(d + e*x)^(3/2)*(a + b*Log[c*x^n]))/e^4 - (6*d*(d + e*x)^(5/2)*(a + b*Log[c*x^n]))/(5*e^4) + (2*(d + e*x)^(7/2)*(a + b*Log[c*x^n]))/(7*e^4)","A",7,7,23,0.3043,1,"{43, 2350, 12, 1620, 50, 63, 208}"
145,1,169,0,0.1691237,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d+e x}} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/Sqrt[d + e*x],x]","\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^2 n \sqrt{d+e x}}{15 e^3}+\frac{32 b d^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{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}","\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^2 n \sqrt{d+e x}}{15 e^3}+\frac{32 b d^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{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,"(-32*b*d^2*n*Sqrt[d + e*x])/(15*e^3) + (28*b*d*n*(d + e*x)^(3/2))/(45*e^3) - (4*b*n*(d + e*x)^(5/2))/(25*e^3) + (32*b*d^(5/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(15*e^3) + (2*d^2*Sqrt[d + e*x]*(a + b*Log[c*x^n]))/e^3 - (4*d*(d + e*x)^(3/2)*(a + b*Log[c*x^n]))/(3*e^3) + (2*(d + e*x)^(5/2)*(a + b*Log[c*x^n]))/(5*e^3)","A",6,6,23,0.2609,1,"{43, 2350, 12, 897, 1261, 208}"
146,1,119,0,0.0912596,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d+e x}} \, dx","Int[(x*(a + b*Log[c*x^n]))/Sqrt[d + e*x],x]","-\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}","-\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,"(8*b*d*n*Sqrt[d + e*x])/(3*e^2) - (4*b*n*(d + e*x)^(3/2))/(9*e^2) - (8*b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(3*e^2) - (2*d*Sqrt[d + e*x]*(a + b*Log[c*x^n]))/e^2 + (2*(d + e*x)^(3/2)*(a + b*Log[c*x^n]))/(3*e^2)","A",6,7,21,0.3333,1,"{43, 2350, 12, 80, 50, 63, 208}"
147,1,69,0,0.0337705,"\int \frac{a+b \log \left(c x^n\right)}{\sqrt{d+e x}} \, dx","Int[(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)\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}","\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*n*Sqrt[d + e*x])/e + (4*b*Sqrt[d]*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/e + (2*Sqrt[d + e*x]*(a + b*Log[c*x^n]))/e","A",4,4,20,0.2000,1,"{2319, 50, 63, 208}"
148,1,152,0,0.198971,"\int \frac{a+b \log \left(c x^n\right)}{x \sqrt{d+e x}} \, dx","Int[(a + b*Log[c*x^n])/(x*Sqrt[d + e*x]),x]","-\frac{2 b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{\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 \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}}","-\frac{2 b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{\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 \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*b*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]^2)/Sqrt[d] - (2*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*(a + b*Log[c*x^n]))/Sqrt[d] - (4*b*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])])/Sqrt[d] - (2*b*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])])/Sqrt[d]","A",7,8,23,0.3478,1,"{63, 208, 2348, 12, 5984, 5918, 2402, 2315}"
149,1,226,0,0.2703742,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \sqrt{d+e x}} \, dx","Int[(a + b*Log[c*x^n])/(x^2*Sqrt[d + e*x]),x]","\frac{b e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{d^{3/2}}+\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 \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}","\frac{b e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{d^{3/2}}+\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 \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,"-((b*n*Sqrt[d + e*x])/(d*x)) - (b*e*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/d^(3/2) - (b*e*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]^2)/d^(3/2) - (Sqrt[d + e*x]*(a + b*Log[c*x^n]))/(d*x) + (e*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*(a + b*Log[c*x^n]))/d^(3/2) + (2*b*e*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])])/d^(3/2) + (b*e*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])])/d^(3/2)","A",11,10,23,0.4348,1,"{51, 63, 208, 2350, 14, 47, 5984, 5918, 2402, 2315}"
150,1,304,0,0.3362277,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \sqrt{d+e x}} \, dx","Int[(a + b*Log[c*x^n])/(x^3*Sqrt[d + e*x]),x]","-\frac{3 b e^2 n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{4 d^{5/2}}-\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 \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}","-\frac{3 b e^2 n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{4 d^{5/2}}-\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 \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,"-(b*n*Sqrt[d + e*x])/(4*d*x^2) + (5*b*e*n*Sqrt[d + e*x])/(8*d^2*x) + (7*b*e^2*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(8*d^(5/2)) + (3*b*e^2*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]^2)/(4*d^(5/2)) - (Sqrt[d + e*x]*(a + b*Log[c*x^n]))/(2*d*x^2) + (3*e*Sqrt[d + e*x]*(a + b*Log[c*x^n]))/(4*d^2*x) - (3*e^2*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*(a + b*Log[c*x^n]))/(4*d^(5/2)) - (3*b*e^2*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])])/(2*d^(5/2)) - (3*b*e^2*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])])/(4*d^(5/2))","A",16,11,23,0.4783,1,"{51, 63, 208, 2350, 12, 14, 47, 5984, 5918, 2402, 2315}"
151,1,194,0,0.1952513,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^{3/2}} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/(d + e*x)^(3/2),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{44 b d^2 n \sqrt{d+e x}}{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{16 b d n (d+e x)^{3/2}}{15 e^4}-\frac{4 b n (d+e x)^{5/2}}{25 e^4}","\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{44 b d^2 n \sqrt{d+e x}}{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{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,"(-44*b*d^2*n*Sqrt[d + e*x])/(5*e^4) + (16*b*d*n*(d + e*x)^(3/2))/(15*e^4) - (4*b*n*(d + e*x)^(5/2))/(25*e^4) + (64*b*d^(5/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(5*e^4) + (2*d^3*(a + b*Log[c*x^n]))/(e^4*Sqrt[d + e*x]) + (6*d^2*Sqrt[d + e*x]*(a + b*Log[c*x^n]))/e^4 - (2*d*(d + e*x)^(3/2)*(a + b*Log[c*x^n]))/e^4 + (2*(d + e*x)^(5/2)*(a + b*Log[c*x^n]))/(5*e^4)","A",6,6,23,0.2609,1,"{43, 2350, 12, 1620, 63, 208}"
152,1,146,0,0.1619735,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^{3/2}} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/(d + e*x)^(3/2),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}","-\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,"(20*b*d*n*Sqrt[d + e*x])/(3*e^3) - (4*b*n*(d + e*x)^(3/2))/(9*e^3) - (32*b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(3*e^3) - (2*d^2*(a + b*Log[c*x^n]))/(e^3*Sqrt[d + e*x]) - (4*d*Sqrt[d + e*x]*(a + b*Log[c*x^n]))/e^3 + (2*(d + e*x)^(3/2)*(a + b*Log[c*x^n]))/(3*e^3)","A",6,6,23,0.2609,1,"{43, 2350, 12, 897, 1153, 208}"
153,1,94,0,0.086686,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^{3/2}} \, dx","Int[(x*(a + b*Log[c*x^n]))/(d + e*x)^(3/2),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}","\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,"(-4*b*n*Sqrt[d + e*x])/e^2 + (8*b*Sqrt[d]*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/e^2 + (2*d*(a + b*Log[c*x^n]))/(e^2*Sqrt[d + e*x]) + (2*Sqrt[d + e*x]*(a + b*Log[c*x^n]))/e^2","A",5,6,21,0.2857,1,"{43, 2350, 12, 80, 63, 208}"
154,1,53,0,0.0321486,"\int \frac{a+b \log \left(c x^n\right)}{(d+e x)^{3/2}} \, dx","Int[(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",3,3,20,0.1500,1,"{2319, 63, 208}"
155,1,201,0,0.3197704,"\int \frac{a+b \log \left(c x^n\right)}{x (d+e x)^{3/2}} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x)^(3/2)),x]","-\frac{2 b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{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 \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}}","-\frac{2 b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{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 \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,"(4*b*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/d^(3/2) + (2*b*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]^2)/d^(3/2) + (2*(a + b*Log[c*x^n]))/(d*Sqrt[d + e*x]) - (2*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*(a + b*Log[c*x^n]))/d^(3/2) - (4*b*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])])/d^(3/2) - (2*b*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])])/d^(3/2)","A",11,10,23,0.4348,1,"{2347, 63, 208, 2348, 12, 5984, 5918, 2402, 2315, 2319}"
156,1,255,0,0.517039,"\int \frac{a+b \log \left(c x^n\right)}{x^2 (d+e x)^{3/2}} \, dx","Int[(a + b*Log[c*x^n])/(x^2*(d + e*x)^(3/2)),x]","\frac{3 b e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{d^{5/2}}-\frac{3 \sqrt{d+e x} \left(a+b \log \left(c x^n\right)\right)}{d^2 x}+\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{2 \left(a+b \log \left(c x^n\right)\right)}{d x \sqrt{d+e x}}-\frac{b n \sqrt{d+e x}}{d^2 x}-\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{3 b e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x}}\right)}{d^{5/2}}-\frac{3 e \left(a+b \log \left(c x^n\right)\right)}{d^2 \sqrt{d+e x}}+\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{a+b \log \left(c x^n\right)}{d x \sqrt{d+e x}}-\frac{b n \sqrt{d+e x}}{d^2 x}-\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}}",1,"-((b*n*Sqrt[d + e*x])/(d^2*x)) - (5*b*e*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/d^(5/2) - (3*b*e*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]^2)/d^(5/2) + (2*(a + b*Log[c*x^n]))/(d*x*Sqrt[d + e*x]) - (3*Sqrt[d + e*x]*(a + b*Log[c*x^n]))/(d^2*x) + (3*e*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*(a + b*Log[c*x^n]))/d^(5/2) + (6*b*e*n*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])])/d^(5/2) + (3*b*e*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x])])/d^(5/2)","A",15,12,23,0.5217,1,"{51, 63, 208, 2350, 12, 14, 47, 50, 5984, 5918, 2402, 2315}"
157,0,0,0,0.086478,"\int \frac{x^2}{(d+e x) \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[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,"Defer[Int][x^2/((d + e*x)*(a + b*Log[c*x^n])), x]","A",0,0,0,0,-1,"{}"
158,0,0,0,0.0605134,"\int \frac{x}{(d+e x) \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[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,"Defer[Int][x/((d + e*x)*(a + b*Log[c*x^n])), x]","A",0,0,0,0,-1,"{}"
159,0,0,0,0.030349,"\int \frac{1}{(d+e x) \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[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,"Defer[Int][1/((d + e*x)*(a + b*Log[c*x^n])), x]","A",0,0,0,0,-1,"{}"
160,0,0,0,0.0822645,"\int \frac{1}{x (d+e x) \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[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,"Defer[Int][1/(x*(d + e*x)*(a + b*Log[c*x^n])), x]","A",0,0,0,0,-1,"{}"
161,0,0,0,0.0890865,"\int \frac{1}{x^2 (d+e x) \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[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,"Defer[Int][1/(x^2*(d + e*x)*(a + b*Log[c*x^n])), x]","A",0,0,0,0,-1,"{}"
162,1,211,0,0.2282656,"\int (f x)^m (d+e x)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(f*x)^m*(d + e*x)^3*(a + b*Log[c*x^n]),x]","\frac{3 d^2 e (f x)^{m+2} \left(a+b \log \left(c x^n\right)\right)}{f^2 (m+2)}+\frac{d^3 (f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+1)}+\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{3 b d^2 e n (f x)^{m+2}}{f^2 (m+2)^2}-\frac{b d^3 n (f x)^{m+1}}{f (m+1)^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}","\frac{3 d^2 e (f x)^{m+2} \left(a+b \log \left(c x^n\right)\right)}{f^2 (m+2)}+\frac{d^3 (f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+1)}+\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{3 b d^2 e n (f x)^{m+2}}{f^2 (m+2)^2}-\frac{b d^3 n (f x)^{m+1}}{f (m+1)^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,"-((b*d^3*n*(f*x)^(1 + m))/(f*(1 + m)^2)) - (3*b*d^2*e*n*(f*x)^(2 + m))/(f^2*(2 + m)^2) - (3*b*d*e^2*n*(f*x)^(3 + m))/(f^3*(3 + m)^2) - (b*e^3*n*(f*x)^(4 + m))/(f^4*(4 + m)^2) + (d^3*(f*x)^(1 + m)*(a + b*Log[c*x^n]))/(f*(1 + m)) + (3*d^2*e*(f*x)^(2 + m)*(a + b*Log[c*x^n]))/(f^2*(2 + m)) + (3*d*e^2*(f*x)^(3 + m)*(a + b*Log[c*x^n]))/(f^3*(3 + m)) + (e^3*(f*x)^(4 + m)*(a + b*Log[c*x^n]))/(f^4*(4 + m))","A",3,3,23,0.1304,1,"{43, 2350, 14}"
163,1,153,0,0.1725595,"\int (f x)^m (d+e x)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(f*x)^m*(d + e*x)^2*(a + b*Log[c*x^n]),x]","\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}","\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,"-((b*d^2*n*(f*x)^(1 + m))/(f*(1 + m)^2)) - (2*b*d*e*n*(f*x)^(2 + m))/(f^2*(2 + m)^2) - (b*e^2*n*(f*x)^(3 + m))/(f^3*(3 + m)^2) + (d^2*(f*x)^(1 + m)*(a + b*Log[c*x^n]))/(f*(1 + m)) + (2*d*e*(f*x)^(2 + m)*(a + b*Log[c*x^n]))/(f^2*(2 + m)) + (e^2*(f*x)^(3 + m)*(a + b*Log[c*x^n]))/(f^3*(3 + m))","A",4,4,23,0.1739,1,"{43, 2350, 12, 14}"
164,1,95,0,0.0812859,"\int (f x)^m (d+e x) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(f*x)^m*(d + e*x)*(a + b*Log[c*x^n]),x]","\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}","\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,"-((b*d*n*(f*x)^(1 + m))/(f*(1 + m)^2)) - (b*e*n*(f*x)^(2 + m))/(f^2*(2 + m)^2) + (d*(f*x)^(1 + m)*(a + b*Log[c*x^n]))/(f*(1 + m)) + (e*(f*x)^(2 + m)*(a + b*Log[c*x^n]))/(f^2*(2 + m))","A",3,2,21,0.09524,1,"{43, 2350}"
165,1,46,0,0.0165148,"\int (f x)^m \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(f*x)^m*(a + b*Log[c*x^n]),x]","\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}","\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,"-((b*n*(f*x)^(1 + m))/(f*(1 + m)^2)) + ((f*x)^(1 + m)*(a + b*Log[c*x^n]))/(f*(1 + m))","A",1,1,16,0.06250,1,"{2304}"
166,0,0,0,0.0550209,"\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{d+e x} \, dx","Int[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x),x]","\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{d+e x} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{d+e x},x\right)",0,"Defer[Int][((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x), x]","A",0,0,0,0,-1,"{}"
167,0,0,0,0.0529172,"\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2} \, dx","Int[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x)^2,x]","\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x)^2, x]","A",0,0,0,0,-1,"{}"
168,0,0,0,0.0189418,"\int x (a+b x)^m \log \left(c x^n\right) \, dx","Int[x*(a + b*x)^m*Log[c*x^n],x]","\int x (a+b x)^m \log \left(c x^n\right) \, dx","\text{Int}\left(x (a+b x)^m \log \left(c x^n\right),x\right)",0,"Defer[Int][x*(a + b*x)^m*Log[c*x^n], x]","A",0,0,0,0,-1,"{}"
169,1,68,0,0.0283179,"\int (a+b x)^m \log \left(c x^n\right) \, dx","Int[(a + b*x)^m*Log[c*x^n],x]","\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)}","\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,"(n*(a + b*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, 1 + (b*x)/a])/(a*b*(2 + 3*m + m^2)) + ((a + b*x)^(1 + m)*Log[c*x^n])/(b*(1 + m))","A",2,2,14,0.1429,1,"{2319, 65}"
170,0,0,0,0.0291745,"\int \frac{(a+b x)^m \log \left(c x^n\right)}{x} \, dx","Int[((a + b*x)^m*Log[c*x^n])/x,x]","\int \frac{(a+b x)^m \log \left(c x^n\right)}{x} \, dx","\text{Int}\left(\frac{(a+b x)^m \log \left(c x^n\right)}{x},x\right)",0,"Defer[Int][((a + b*x)^m*Log[c*x^n])/x, x]","A",0,0,0,0,-1,"{}"
171,1,48,0,0.0430605,"\int x^5 \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^5*(d + e*x^2)*(a + b*Log[c*x^n]),x]","\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","\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,"-(b*d*n*x^6)/36 - (b*e*n*x^8)/64 + ((4*d*x^6 + 3*e*x^8)*(a + b*Log[c*x^n]))/24","A",2,2,21,0.09524,1,"{14, 2334}"
172,1,48,0,0.0415739,"\int x^3 \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^3*(d + e*x^2)*(a + b*Log[c*x^n]),x]","\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","\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,"-(b*d*n*x^4)/16 - (b*e*n*x^6)/36 + ((3*d*x^4 + 2*e*x^6)*(a + b*Log[c*x^n]))/12","A",2,2,21,0.09524,1,"{14, 2334}"
173,1,47,0,0.0366205,"\int x \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*(d + e*x^2)*(a + b*Log[c*x^n]),x]","\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","\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,"-(b*d*n*x^2)/4 - (b*e*n*x^4)/16 + ((2*d*x^2 + e*x^4)*(a + b*Log[c*x^n]))/4","A",4,3,19,0.1579,1,"{14, 2334, 12}"
174,1,52,0,0.064304,"\int \frac{\left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[((d + e*x^2)*(a + b*Log[c*x^n]))/x,x]","\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","\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,"-(b*e*n*x^2)/4 + (e*x^2*(a + b*Log[c*x^n]))/2 + (d*(a + b*Log[c*x^n])^2)/(2*b*n)","A",4,4,21,0.1905,1,"{14, 2351, 2301, 2304}"
175,1,47,0,0.0485854,"\int \frac{\left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[((d + e*x^2)*(a + b*Log[c*x^n]))/x^3,x]","-\frac{1}{2} \left(\frac{d}{x^2}-2 e \log (x)\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b d n}{4 x^2}-\frac{1}{2} b e n \log ^2(x)","-\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,"-(b*d*n)/(4*x^2) - (b*e*n*Log[x]^2)/2 - ((d/x^2 - 2*e*Log[x])*(a + b*Log[c*x^n]))/2","A",3,3,21,0.1429,1,"{14, 2334, 2301}"
176,1,47,0,0.0474705,"\int \frac{\left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right)}{x^5} \, dx","Int[((d + e*x^2)*(a + b*Log[c*x^n]))/x^5,x]","-\frac{1}{4} \left(\frac{d}{x^4}+\frac{2 e}{x^2}\right) \left(a+b \log \left(c x^n\right)\right)-\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,"-(b*d*n)/(16*x^4) - (b*e*n)/(4*x^2) - ((d/x^4 + (2*e)/x^2)*(a + b*Log[c*x^n]))/4","A",4,3,21,0.1429,1,"{14, 2334, 12}"
177,1,48,0,0.0431169,"\int x^4 \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^4*(d + e*x^2)*(a + b*Log[c*x^n]),x]","\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","\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,"-(b*d*n*x^5)/25 - (b*e*n*x^7)/49 + ((7*d*x^5 + 5*e*x^7)*(a + b*Log[c*x^n]))/35","A",2,2,21,0.09524,1,"{14, 2334}"
178,1,48,0,0.0418457,"\int x^2 \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*(d + e*x^2)*(a + b*Log[c*x^n]),x]","\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","\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,"-(b*d*n*x^3)/9 - (b*e*n*x^5)/25 + ((5*d*x^3 + 3*e*x^5)*(a + b*Log[c*x^n]))/15","A",2,2,21,0.09524,1,"{14, 2334}"
179,1,41,0,0.0176313,"\int \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(d + e*x^2)*(a + b*Log[c*x^n]),x]","\frac{1}{3} \left(3 d x+e x^3\right) \left(a+b \log \left(c x^n\right)\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,"-(b*d*n*x) - (b*e*n*x^3)/9 + ((3*d*x + e*x^3)*(a + b*Log[c*x^n]))/3","A",2,1,18,0.05556,1,"{2313}"
180,1,37,0,0.0394148,"\int \frac{\left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[((d + e*x^2)*(a + b*Log[c*x^n]))/x^2,x]","-\left(\frac{d}{x}-e x\right) \left(a+b \log \left(c x^n\right)\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,"-((b*d*n)/x) - b*e*n*x - (d/x - e*x)*(a + b*Log[c*x^n])","A",2,2,21,0.09524,1,"{14, 2334}"
181,1,45,0,0.0466648,"\int \frac{\left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Int[((d + e*x^2)*(a + b*Log[c*x^n]))/x^4,x]","-\frac{1}{3} \left(\frac{d}{x^3}+\frac{3 e}{x}\right) \left(a+b \log \left(c x^n\right)\right)-\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,"-(b*d*n)/(9*x^3) - (b*e*n)/x - ((d/x^3 + (3*e)/x)*(a + b*Log[c*x^n]))/3","A",4,3,21,0.1429,1,"{14, 2334, 12}"
182,1,48,0,0.0457509,"\int \frac{\left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Int[((d + e*x^2)*(a + b*Log[c*x^n]))/x^6,x]","-\frac{1}{15} \left(\frac{3 d}{x^5}+\frac{5 e}{x^3}\right) \left(a+b \log \left(c x^n\right)\right)-\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,"-(b*d*n)/(25*x^5) - (b*e*n)/(9*x^3) - (((3*d)/x^5 + (5*e)/x^3)*(a + b*Log[c*x^n]))/15","A",4,3,21,0.1429,1,"{14, 2334, 12}"
183,1,74,0,0.0865796,"\int x^5 \left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^5*(d + e*x^2)^2*(a + b*Log[c*x^n]),x]","\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}","\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,"-(b*d^2*n*x^6)/36 - (b*d*e*n*x^8)/32 - (b*e^2*n*x^10)/100 + ((10*d^2*x^6 + 15*d*e*x^8 + 6*e^2*x^10)*(a + b*Log[c*x^n]))/60","A",4,5,23,0.2174,1,"{266, 43, 2334, 12, 14}"
184,1,74,0,0.088268,"\int x^3 \left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^3*(d + e*x^2)^2*(a + b*Log[c*x^n]),x]","\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","\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,"-(b*d^2*n*x^4)/16 - (b*d*e*n*x^6)/18 - (b*e^2*n*x^8)/64 + ((6*d^2*x^4 + 8*d*e*x^6 + 3*e^2*x^8)*(a + b*Log[c*x^n]))/24","A",4,5,23,0.2174,1,"{266, 43, 2334, 12, 14}"
185,1,76,0,0.0678022,"\int x \left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*(d + e*x^2)^2*(a + b*Log[c*x^n]),x]","\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","\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,"-(b*d^2*n*x^2)/4 - (b*d*e*n*x^4)/8 - (b*e^2*n*x^6)/36 - (b*d^3*n*Log[x])/(6*e) + ((d + e*x^2)^3*(a + b*Log[c*x^n]))/(6*e)","A",5,5,21,0.2381,1,"{261, 2334, 12, 266, 43}"
186,1,73,0,0.0818464,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[((d + e*x^2)^2*(a + b*Log[c*x^n]))/x,x]","\frac{1}{4} \left(4 d^2 \log (x)+4 d e x^2+e^2 x^4\right) \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","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,"-(b*d*e*n*x^2)/2 - (b*e^2*n*x^4)/16 - (b*d^2*n*Log[x]^2)/2 + ((4*d*e*x^2 + e^2*x^4 + 4*d^2*Log[x])*(a + b*Log[c*x^n]))/4","A",3,4,23,0.1739,1,"{266, 43, 2334, 2301}"
187,1,71,0,0.0986328,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[((d + e*x^2)^2*(a + b*Log[c*x^n]))/x^3,x]","-\frac{1}{2} \left(\frac{d^2}{x^2}-4 d e \log (x)-e^2 x^2\right) \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","-\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)/(4*x^2) - (b*e^2*n*x^2)/4 - b*d*e*n*Log[x]^2 - ((d^2/x^2 - e^2*x^2 - 4*d*e*Log[x])*(a + b*Log[c*x^n]))/2","A",7,6,23,0.2609,1,"{266, 43, 2334, 12, 14, 2301}"
188,1,73,0,0.0892583,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^5} \, dx","Int[((d + e*x^2)^2*(a + b*Log[c*x^n]))/x^5,x]","-\frac{1}{4} \left(\frac{d^2}{x^4}+\frac{4 d e}{x^2}-4 e^2 \log (x)\right) \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)","-\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)/(16*x^4) - (b*d*e*n)/(2*x^2) - (b*e^2*n*Log[x]^2)/2 - ((d^2/x^4 + (4*d*e)/x^2 - 4*e^2*Log[x])*(a + b*Log[c*x^n]))/4","A",5,5,23,0.2174,1,"{266, 43, 2334, 14, 2301}"
189,1,74,0,0.0723918,"\int x^4 \left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^4*(d + e*x^2)^2*(a + b*Log[c*x^n]),x]","\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","\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,"-(b*d^2*n*x^5)/25 - (2*b*d*e*n*x^7)/49 - (b*e^2*n*x^9)/81 + ((63*d^2*x^5 + 90*d*e*x^7 + 35*e^2*x^9)*(a + b*Log[c*x^n]))/315","A",2,2,23,0.08696,1,"{270, 2334}"
190,1,74,0,0.0711839,"\int x^2 \left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*(d + e*x^2)^2*(a + b*Log[c*x^n]),x]","\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","\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,"-(b*d^2*n*x^3)/9 - (2*b*d*e*n*x^5)/25 - (b*e^2*n*x^7)/49 + ((35*d^2*x^3 + 42*d*e*x^5 + 15*e^2*x^7)*(a + b*Log[c*x^n]))/105","A",2,2,23,0.08696,1,"{270, 2334}"
191,1,68,0,0.0351193,"\int \left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(d + e*x^2)^2*(a + b*Log[c*x^n]),x]","\frac{1}{15} \left(15 d^2 x+10 d e x^3+3 e^2 x^5\right) \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","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,"-(b*d^2*n*x) - (2*b*d*e*n*x^3)/9 - (b*e^2*n*x^5)/25 + ((15*d^2*x + 10*d*e*x^3 + 3*e^2*x^5)*(a + b*Log[c*x^n]))/15","A",2,2,20,0.1000,1,"{194, 2313}"
192,1,66,0,0.0706047,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[((d + e*x^2)^2*(a + b*Log[c*x^n]))/x^2,x]","-\frac{1}{3} \left(\frac{3 d^2}{x}-6 d e x-e^2 x^3\right) \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","-\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*b*d*e*n*x - (b*e^2*n*x^3)/9 - (((3*d^2)/x - 6*d*e*x - e^2*x^3)*(a + b*Log[c*x^n]))/3","A",2,2,23,0.08696,1,"{270, 2334}"
193,1,65,0,0.0725627,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Int[((d + e*x^2)^2*(a + b*Log[c*x^n]))/x^4,x]","-\frac{1}{3} \left(\frac{d^2}{x^3}+\frac{6 d e}{x}-3 e^2 x\right) \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","-\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,"-(b*d^2*n)/(9*x^3) - (2*b*d*e*n)/x - b*e^2*n*x - ((d^2/x^3 + (6*d*e)/x - 3*e^2*x)*(a + b*Log[c*x^n]))/3","A",2,2,23,0.08696,1,"{270, 2334}"
194,1,72,0,0.0826226,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Int[((d + e*x^2)^2*(a + b*Log[c*x^n]))/x^6,x]","-\frac{1}{15} \left(\frac{3 d^2}{x^5}+\frac{10 d e}{x^3}+\frac{15 e^2}{x}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b d^2 n}{25 x^5}-\frac{2 b d e n}{9 x^3}-\frac{b e^2 n}{x}","-\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,"-(b*d^2*n)/(25*x^5) - (2*b*d*e*n)/(9*x^3) - (b*e^2*n)/x - (((3*d^2)/x^5 + (10*d*e)/x^3 + (15*e^2)/x)*(a + b*Log[c*x^n]))/15","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
195,1,74,0,0.0826563,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^8} \, dx","Int[((d + e*x^2)^2*(a + b*Log[c*x^n]))/x^8,x]","-\frac{1}{105} \left(\frac{15 d^2}{x^7}+\frac{42 d e}{x^5}+\frac{35 e^2}{x^3}\right) \left(a+b \log \left(c x^n\right)\right)-\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,"-(b*d^2*n)/(49*x^7) - (2*b*d*e*n)/(25*x^5) - (b*e^2*n)/(9*x^3) - (((15*d^2)/x^7 + (42*d*e)/x^5 + (35*e^2)/x^3)*(a + b*Log[c*x^n]))/105","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
196,1,100,0,0.106148,"\int x^5 \left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^5*(d + e*x^2)^3*(a + b*Log[c*x^n]),x]","\frac{1}{120} \left(45 d^2 e x^8+20 d^3 x^6+36 d e^2 x^{10}+10 e^3 x^{12}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3}{64} b d^2 e n x^8-\frac{1}{36} b d^3 n x^6-\frac{3}{100} b d e^2 n x^{10}-\frac{1}{144} b e^3 n x^{12}","\frac{1}{120} \left(45 d^2 e x^8+20 d^3 x^6+36 d e^2 x^{10}+10 e^3 x^{12}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3}{64} b d^2 e n x^8-\frac{1}{36} b d^3 n x^6-\frac{3}{100} b d e^2 n x^{10}-\frac{1}{144} b e^3 n x^{12}",1,"-(b*d^3*n*x^6)/36 - (3*b*d^2*e*n*x^8)/64 - (3*b*d*e^2*n*x^10)/100 - (b*e^3*n*x^12)/144 + ((20*d^3*x^6 + 45*d^2*e*x^8 + 36*d*e^2*x^10 + 10*e^3*x^12)*(a + b*Log[c*x^n]))/120","A",4,5,23,0.2174,1,"{266, 43, 2334, 12, 14}"
197,1,130,0,0.1522596,"\int x^3 \left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^3*(d + e*x^2)^3*(a + b*Log[c*x^n]),x]","-\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{1}{60} b d^2 e n x^6+\frac{b d^4 n x^2}{20 e}+\frac{3}{80} b d^3 n x^4+\frac{1}{320} b d e^2 n x^8-\frac{b n \left(d+e x^2\right)^5}{100 e^2}","-\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{1}{60} b d^2 e n x^6+\frac{b d^4 n x^2}{20 e}+\frac{3}{80} b d^3 n x^4+\frac{1}{320} b d e^2 n x^8-\frac{b n \left(d+e x^2\right)^5}{100 e^2}",1,"(b*d^4*n*x^2)/(20*e) + (3*b*d^3*n*x^4)/80 + (b*d^2*e*n*x^6)/60 + (b*d*e^2*n*x^8)/320 - (b*n*(d + e*x^2)^5)/(100*e^2) + (b*d^5*n*Log[x])/(40*e^2) - (((5*d*(d + e*x^2)^4)/e^2 - (4*(d + e*x^2)^5)/e^2)*(a + b*Log[c*x^n]))/40","A",6,6,23,0.2609,1,"{266, 43, 2334, 12, 446, 80}"
198,1,91,0,0.0746843,"\int x \left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*(d + e*x^2)^3*(a + b*Log[c*x^n]),x]","\frac{\left(d+e x^2\right)^4 \left(a+b \log \left(c x^n\right)\right)}{8 e}-\frac{3}{16} b d^2 e n x^4-\frac{b d^4 n \log (x)}{8 e}-\frac{1}{4} b d^3 n x^2-\frac{1}{12} b d e^2 n x^6-\frac{1}{64} b e^3 n x^8","\frac{\left(d+e x^2\right)^4 \left(a+b \log \left(c x^n\right)\right)}{8 e}-\frac{3}{16} b d^2 e n x^4-\frac{b d^4 n \log (x)}{8 e}-\frac{1}{4} b d^3 n x^2-\frac{1}{12} b d e^2 n x^6-\frac{1}{64} b e^3 n x^8",1,"-(b*d^3*n*x^2)/4 - (3*b*d^2*e*n*x^4)/16 - (b*d*e^2*n*x^6)/12 - (b*e^3*n*x^8)/64 - (b*d^4*n*Log[x])/(8*e) + ((d + e*x^2)^4*(a + b*Log[c*x^n]))/(8*e)","A",5,5,21,0.2381,1,"{261, 2334, 12, 266, 43}"
199,1,100,0,0.1044619,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[((d + e*x^2)^3*(a + b*Log[c*x^n]))/x,x]","\frac{1}{12} \left(18 d^2 e x^2+12 d^3 \log (x)+9 d e^2 x^4+2 e^3 x^6\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3}{4} b d^2 e n x^2-\frac{1}{2} b d^3 n \log ^2(x)-\frac{3}{16} b d e^2 n x^4-\frac{1}{36} b e^3 n x^6","\frac{3}{2} d^2 e x^2 \left(a+b \log \left(c x^n\right)\right)+d^3 \log (x) \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{3}{4} b d^2 e n x^2-\frac{1}{2} b d^3 n \log ^2(x)-\frac{3}{16} b d e^2 n x^4-\frac{1}{36} b e^3 n x^6",1,"(-3*b*d^2*e*n*x^2)/4 - (3*b*d*e^2*n*x^4)/16 - (b*e^3*n*x^6)/36 - (b*d^3*n*Log[x]^2)/2 + ((18*d^2*e*x^2 + 9*d*e^2*x^4 + 2*e^3*x^6 + 12*d^3*Log[x])*(a + b*Log[c*x^n]))/12","A",5,5,23,0.2174,1,"{266, 43, 2334, 14, 2301}"
200,1,100,0,0.1248338,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[((d + e*x^2)^3*(a + b*Log[c*x^n]))/x^3,x]","-\frac{1}{4} \left(-12 d^2 e \log (x)+\frac{2 d^3}{x^2}-6 d e^2 x^2-e^3 x^4\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3}{2} b d^2 e n \log ^2(x)-\frac{b d^3 n}{4 x^2}-\frac{3}{4} b d e^2 n x^2-\frac{1}{16} b e^3 n x^4","3 d^2 e \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{2 x^2}+\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{3}{2} b d^2 e n \log ^2(x)-\frac{b d^3 n}{4 x^2}-\frac{3}{4} b d e^2 n x^2-\frac{1}{16} b e^3 n x^4",1,"-(b*d^3*n)/(4*x^2) - (3*b*d*e^2*n*x^2)/4 - (b*e^3*n*x^4)/16 - (3*b*d^2*e*n*Log[x]^2)/2 - (((2*d^3)/x^2 - 6*d*e^2*x^2 - e^3*x^4 - 12*d^2*e*Log[x])*(a + b*Log[c*x^n]))/4","A",7,6,23,0.2609,1,"{266, 43, 2334, 12, 14, 2301}"
201,1,99,0,0.122787,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^5} \, dx","Int[((d + e*x^2)^3*(a + b*Log[c*x^n]))/x^5,x]","-\frac{1}{4} \left(\frac{6 d^2 e}{x^2}+\frac{d^3}{x^4}-12 d e^2 \log (x)-2 e^3 x^2\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n}{4 x^2}-\frac{b d^3 n}{16 x^4}-\frac{3}{2} b d e^2 n \log ^2(x)-\frac{1}{4} b e^3 n x^2","-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{4 x^4}+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{3 b d^2 e n}{4 x^2}-\frac{b d^3 n}{16 x^4}-\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)/(16*x^4) - (3*b*d^2*e*n)/(4*x^2) - (b*e^3*n*x^2)/4 - (3*b*d*e^2*n*Log[x]^2)/2 - ((d^3/x^4 + (6*d^2*e)/x^2 - 2*e^3*x^2 - 12*d*e^2*Log[x])*(a + b*Log[c*x^n]))/4","A",7,6,23,0.2609,1,"{266, 43, 2334, 12, 14, 2301}"
202,1,100,0,0.0875338,"\int x^4 \left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^4*(d + e*x^2)^3*(a + b*Log[c*x^n]),x]","\frac{\left(495 d^2 e x^7+231 d^3 x^5+385 d e^2 x^9+105 e^3 x^{11}\right) \left(a+b \log \left(c x^n\right)\right)}{1155}-\frac{3}{49} b d^2 e n x^7-\frac{1}{25} b d^3 n x^5-\frac{1}{27} b d e^2 n x^9-\frac{1}{121} b e^3 n x^{11}","\frac{\left(495 d^2 e x^7+231 d^3 x^5+385 d e^2 x^9+105 e^3 x^{11}\right) \left(a+b \log \left(c x^n\right)\right)}{1155}-\frac{3}{49} b d^2 e n x^7-\frac{1}{25} b d^3 n x^5-\frac{1}{27} b d e^2 n x^9-\frac{1}{121} b e^3 n x^{11}",1,"-(b*d^3*n*x^5)/25 - (3*b*d^2*e*n*x^7)/49 - (b*d*e^2*n*x^9)/27 - (b*e^3*n*x^11)/121 + ((231*d^3*x^5 + 495*d^2*e*x^7 + 385*d*e^2*x^9 + 105*e^3*x^11)*(a + b*Log[c*x^n]))/1155","A",2,2,23,0.08696,1,"{270, 2334}"
203,1,100,0,0.0865099,"\int x^2 \left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*(d + e*x^2)^3*(a + b*Log[c*x^n]),x]","\frac{1}{315} \left(189 d^2 e x^5+105 d^3 x^3+135 d e^2 x^7+35 e^3 x^9\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3}{25} b d^2 e n x^5-\frac{1}{9} b d^3 n x^3-\frac{3}{49} b d e^2 n x^7-\frac{1}{81} b e^3 n x^9","\frac{1}{315} \left(189 d^2 e x^5+105 d^3 x^3+135 d e^2 x^7+35 e^3 x^9\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3}{25} b d^2 e n x^5-\frac{1}{9} b d^3 n x^3-\frac{3}{49} b d e^2 n x^7-\frac{1}{81} b e^3 n x^9",1,"-(b*d^3*n*x^3)/9 - (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 + ((105*d^3*x^3 + 189*d^2*e*x^5 + 135*d*e^2*x^7 + 35*e^3*x^9)*(a + b*Log[c*x^n]))/315","A",2,2,23,0.08696,1,"{270, 2334}"
204,1,94,0,0.0479855,"\int \left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(d + e*x^2)^3*(a + b*Log[c*x^n]),x]","\frac{1}{35} \left(35 d^2 e x^3+35 d^3 x+21 d e^2 x^5+5 e^3 x^7\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{3} b d^2 e n x^3-b d^3 n x-\frac{3}{25} b d e^2 n x^5-\frac{1}{49} b e^3 n x^7","d^2 e x^3 \left(a+b \log \left(c x^n\right)\right)+d^3 x \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)-\frac{1}{3} b d^2 e n x^3-b d^3 n x-\frac{3}{25} b d e^2 n x^5-\frac{1}{49} b e^3 n x^7",1,"-(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 + ((35*d^3*x + 35*d^2*e*x^3 + 21*d*e^2*x^5 + 5*e^3*x^7)*(a + b*Log[c*x^n]))/35","A",2,2,20,0.1000,1,"{194, 2313}"
205,1,92,0,0.0823846,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[((d + e*x^2)^3*(a + b*Log[c*x^n]))/x^2,x]","-\frac{1}{5} \left(-15 d^2 e x+\frac{5 d^3}{x}-5 d e^2 x^3-e^3 x^5\right) \left(a+b \log \left(c x^n\right)\right)-3 b d^2 e n x-\frac{b d^3 n}{x}-\frac{1}{3} b d e^2 n x^3-\frac{1}{25} b e^3 n x^5","3 d^2 e x \left(a+b \log \left(c x^n\right)\right)-\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 b d^2 e n x-\frac{b d^3 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*b*d^2*e*n*x - (b*d*e^2*n*x^3)/3 - (b*e^3*n*x^5)/25 - (((5*d^3)/x - 15*d^2*e*x - 5*d*e^2*x^3 - e^3*x^5)*(a + b*Log[c*x^n]))/5","A",2,2,23,0.08696,1,"{270, 2334}"
206,1,91,0,0.0910002,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Int[((d + e*x^2)^3*(a + b*Log[c*x^n]))/x^4,x]","-\frac{1}{3} \left(\frac{9 d^2 e}{x}+\frac{d^3}{x^3}-9 d e^2 x-e^3 x^3\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n}{x}-\frac{b d^3 n}{9 x^3}-3 b d e^2 n x-\frac{1}{9} b e^3 n x^3","-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{3 x^3}+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{3 b d^2 e n}{x}-\frac{b d^3 n}{9 x^3}-3 b d e^2 n x-\frac{1}{9} b e^3 n x^3",1,"-(b*d^3*n)/(9*x^3) - (3*b*d^2*e*n)/x - 3*b*d*e^2*n*x - (b*e^3*n*x^3)/9 - ((d^3/x^3 + (9*d^2*e)/x - 9*d*e^2*x - e^3*x^3)*(a + b*Log[c*x^n]))/3","A",3,3,23,0.1304,1,"{270, 2334, 12}"
207,1,91,0,0.0860084,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Int[((d + e*x^2)^3*(a + b*Log[c*x^n]))/x^6,x]","-\frac{1}{5} \left(\frac{5 d^2 e}{x^3}+\frac{d^3}{x^5}+\frac{15 d e^2}{x}-5 e^3 x\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b d^2 e n}{3 x^3}-\frac{b d^3 n}{25 x^5}-\frac{3 b d e^2 n}{x}-b e^3 n x","-\frac{d^2 e \left(a+b \log \left(c x^n\right)\right)}{x^3}-\frac{d^3 \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)}{x}+e^3 x \left(a+b \log \left(c x^n\right)\right)-\frac{b d^2 e n}{3 x^3}-\frac{b d^3 n}{25 x^5}-\frac{3 b d e^2 n}{x}-b e^3 n x",1,"-(b*d^3*n)/(25*x^5) - (b*d^2*e*n)/(3*x^3) - (3*b*d*e^2*n)/x - b*e^3*n*x - ((d^3/x^5 + (5*d^2*e)/x^3 + (15*d*e^2)/x - 5*e^3*x)*(a + b*Log[c*x^n]))/5","A",2,2,23,0.08696,1,"{270, 2334}"
208,1,98,0,0.1005073,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^8} \, dx","Int[((d + e*x^2)^3*(a + b*Log[c*x^n]))/x^8,x]","-\frac{1}{35} \left(\frac{21 d^2 e}{x^5}+\frac{5 d^3}{x^7}+\frac{35 d e^2}{x^3}+\frac{35 e^3}{x}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n}{25 x^5}-\frac{b d^3 n}{49 x^7}-\frac{b d e^2 n}{3 x^3}-\frac{b e^3 n}{x}","-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{7 x^7}-\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{3 b d^2 e n}{25 x^5}-\frac{b d^3 n}{49 x^7}-\frac{b d e^2 n}{3 x^3}-\frac{b e^3 n}{x}",1,"-(b*d^3*n)/(49*x^7) - (3*b*d^2*e*n)/(25*x^5) - (b*d*e^2*n)/(3*x^3) - (b*e^3*n)/x - (((5*d^3)/x^7 + (21*d^2*e)/x^5 + (35*d*e^2)/x^3 + (35*e^3)/x)*(a + b*Log[c*x^n]))/35","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
209,1,100,0,0.0977795,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^{10}} \, dx","Int[((d + e*x^2)^3*(a + b*Log[c*x^n]))/x^10,x]","-\frac{1}{315} \left(\frac{135 d^2 e}{x^7}+\frac{35 d^3}{x^9}+\frac{189 d e^2}{x^5}+\frac{105 e^3}{x^3}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n}{49 x^7}-\frac{b d^3 n}{81 x^9}-\frac{3 b d e^2 n}{25 x^5}-\frac{b e^3 n}{9 x^3}","-\frac{3 d^2 e \left(a+b \log \left(c x^n\right)\right)}{7 x^7}-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{9 x^9}-\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{3 b d^2 e n}{49 x^7}-\frac{b d^3 n}{81 x^9}-\frac{3 b d e^2 n}{25 x^5}-\frac{b e^3 n}{9 x^3}",1,"-(b*d^3*n)/(81*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) - (((35*d^3)/x^9 + (135*d^2*e)/x^7 + (189*d*e^2)/x^5 + (105*e^3)/x^3)*(a + b*Log[c*x^n]))/315","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
210,1,121,0,0.1733415,"\int \frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{d+e x^2} \, dx","Int[(x^5*(a + b*Log[c*x^n]))/(d + e*x^2),x]","\frac{b d^2 n \text{PolyLog}\left(2,-\frac{e x^2}{d}\right)}{4 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 n x^2}{4 e^2}-\frac{b n x^4}{16 e}","\frac{b d^2 n \text{PolyLog}\left(2,-\frac{e x^2}{d}\right)}{4 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 n x^2}{4 e^2}-\frac{b n x^4}{16 e}",1,"(b*d*n*x^2)/(4*e^2) - (b*n*x^4)/(16*e) - (d*x^2*(a + b*Log[c*x^n]))/(2*e^2) + (x^4*(a + b*Log[c*x^n]))/(4*e) + (d^2*(a + b*Log[c*x^n])*Log[1 + (e*x^2)/d])/(2*e^3) + (b*d^2*n*PolyLog[2, -((e*x^2)/d)])/(4*e^3)","A",6,6,23,0.2609,1,"{266, 43, 2351, 2304, 2337, 2391}"
211,1,83,0,0.1425175,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{d+e x^2} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/(d + e*x^2),x]","-\frac{b d n \text{PolyLog}\left(2,-\frac{e x^2}{d}\right)}{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 n x^2}{4 e}","-\frac{b d n \text{PolyLog}\left(2,-\frac{e x^2}{d}\right)}{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 n x^2}{4 e}",1,"-(b*n*x^2)/(4*e) + (x^2*(a + b*Log[c*x^n]))/(2*e) - (d*(a + b*Log[c*x^n])*Log[1 + (e*x^2)/d])/(2*e^2) - (b*d*n*PolyLog[2, -((e*x^2)/d)])/(4*e^2)","A",5,6,23,0.2609,1,"{266, 43, 2351, 2304, 2337, 2391}"
212,1,49,0,0.0483188,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{d+e x^2} \, dx","Int[(x*(a + b*Log[c*x^n]))/(d + e*x^2),x]","\frac{b n \text{PolyLog}\left(2,-\frac{e x^2}{d}\right)}{4 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{PolyLog}\left(2,-\frac{e x^2}{d}\right)}{4 e}+\frac{\log \left(\frac{e x^2}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 e}",1,"((a + b*Log[c*x^n])*Log[1 + (e*x^2)/d])/(2*e) + (b*n*PolyLog[2, -((e*x^2)/d)])/(4*e)","A",2,2,21,0.09524,1,"{2337, 2391}"
213,1,49,0,0.0645087,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^2\right)} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x^2)),x]","\frac{b n \text{PolyLog}\left(2,-\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}","\frac{b n \text{PolyLog}\left(2,-\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,"-(Log[1 + d/(e*x^2)]*(a + b*Log[c*x^n]))/(2*d) + (b*n*PolyLog[2, -(d/(e*x^2))])/(4*d)","A",2,2,23,0.08696,1,"{2345, 2391}"
214,1,109,0,0.1764005,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^2\right)} \, dx","Int[(a + b*Log[c*x^n])/(x^3*(d + e*x^2)),x]","\frac{b e n \text{PolyLog}\left(2,-\frac{e x^2}{d}\right)}{4 d^2}-\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{2 b d^2 n}+\frac{e \log \left(\frac{e x^2}{d}+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 n}{4 d x^2}","-\frac{b e n \text{PolyLog}\left(2,-\frac{d}{e x^2}\right)}{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 n}{4 d x^2}",1,"-(b*n)/(4*d*x^2) - (a + b*Log[c*x^n])/(2*d*x^2) - (e*(a + b*Log[c*x^n])^2)/(2*b*d^2*n) + (e*(a + b*Log[c*x^n])*Log[1 + (e*x^2)/d])/(2*d^2) + (b*e*n*PolyLog[2, -((e*x^2)/d)])/(4*d^2)","A",6,7,23,0.3043,1,"{266, 44, 2351, 2304, 2301, 2337, 2391}"
215,1,149,0,0.2140492,"\int \frac{a+b \log \left(c x^n\right)}{x^5 \left(d+e x^2\right)} \, dx","Int[(a + b*Log[c*x^n])/(x^5*(d + e*x^2)),x]","-\frac{b e^2 n \text{PolyLog}\left(2,-\frac{e x^2}{d}\right)}{4 d^3}+\frac{e^2 \left(a+b \log \left(c x^n\right)\right)^2}{2 b d^3 n}-\frac{e^2 \log \left(\frac{e x^2}{d}+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 n}{4 d^2 x^2}-\frac{b n}{16 d x^4}","\frac{b e^2 n \text{PolyLog}\left(2,-\frac{d}{e x^2}\right)}{4 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 n}{4 d^2 x^2}-\frac{b n}{16 d x^4}",1,"-(b*n)/(16*d*x^4) + (b*e*n)/(4*d^2*x^2) - (a + b*Log[c*x^n])/(4*d*x^4) + (e*(a + b*Log[c*x^n]))/(2*d^2*x^2) + (e^2*(a + b*Log[c*x^n])^2)/(2*b*d^3*n) - (e^2*(a + b*Log[c*x^n])*Log[1 + (e*x^2)/d])/(2*d^3) - (b*e^2*n*PolyLog[2, -((e*x^2)/d)])/(4*d^3)","A",7,7,23,0.3043,1,"{266, 44, 2351, 2304, 2301, 2337, 2391}"
216,1,167,0,0.2065526,"\int \frac{x^4 \left(a+b \log \left(c x^n\right)\right)}{d+e x^2} \, dx","Int[(x^4*(a + b*Log[c*x^n]))/(d + e*x^2),x]","-\frac{i b d^{3/2} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 e^{5/2}}+\frac{i b d^{3/2} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 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{b d n x}{e^2}-\frac{b n x^3}{9 e}","-\frac{i b d^{3/2} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 e^{5/2}}+\frac{i b d^{3/2} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 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{b d n x}{e^2}-\frac{b n x^3}{9 e}",1,"-((a*d*x)/e^2) + (b*d*n*x)/e^2 - (b*n*x^3)/(9*e) - (b*d*x*Log[c*x^n])/e^2 + (x^3*(a + b*Log[c*x^n]))/(3*e) + (d^(3/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/e^(5/2) - ((I/2)*b*d^(3/2)*n*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]])/e^(5/2) + ((I/2)*b*d^(3/2)*n*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])/e^(5/2)","A",10,9,23,0.3913,1,"{302, 205, 2351, 2295, 2304, 2324, 12, 4848, 2391}"
217,1,132,0,0.164603,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{d+e x^2} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/(d + e*x^2),x]","\frac{i b \sqrt{d} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 e^{3/2}}-\frac{i b \sqrt{d} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{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{b n x}{e}","\frac{i b \sqrt{d} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 e^{3/2}}-\frac{i b \sqrt{d} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{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{b n x}{e}",1,"(a*x)/e - (b*n*x)/e + (b*x*Log[c*x^n])/e - (Sqrt[d]*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/e^(3/2) + ((I/2)*b*Sqrt[d]*n*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]])/e^(3/2) - ((I/2)*b*Sqrt[d]*n*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])/e^(3/2)","A",9,8,23,0.3478,1,"{321, 205, 2351, 2295, 2324, 12, 4848, 2391}"
218,1,105,0,0.0660322,"\int \frac{a+b \log \left(c x^n\right)}{d+e x^2} \, dx","Int[(a + b*Log[c*x^n])/(d + e*x^2),x]","-\frac{i b n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 \sqrt{d} \sqrt{e}}+\frac{i b n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\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{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 \sqrt{d} \sqrt{e}}+\frac{i b n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\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}}",1,"(ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(Sqrt[d]*Sqrt[e]) - ((I/2)*b*n*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*Sqrt[e]) + ((I/2)*b*n*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*Sqrt[e])","A",5,5,20,0.2500,1,"{205, 2324, 12, 4848, 2391}"
219,1,134,0,0.1745696,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^2\right)} \, dx","Int[(a + b*Log[c*x^n])/(x^2*(d + e*x^2)),x]","\frac{i b \sqrt{e} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2}}-\frac{i b \sqrt{e} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2}}-\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{b n}{d x}","\frac{i b \sqrt{e} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2}}-\frac{i b \sqrt{e} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2}}-\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{b n}{d x}",1,"-((b*n)/(d*x)) - (a + b*Log[c*x^n])/(d*x) - (Sqrt[e]*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/d^(3/2) + ((I/2)*b*Sqrt[e]*n*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]])/d^(3/2) - ((I/2)*b*Sqrt[e]*n*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])/d^(3/2)","A",8,8,23,0.3478,1,"{325, 205, 2351, 2304, 2324, 12, 4848, 2391}"
220,1,165,0,0.1974249,"\int \frac{a+b \log \left(c x^n\right)}{x^4 \left(d+e x^2\right)} \, dx","Int[(a + b*Log[c*x^n])/(x^4*(d + e*x^2)),x]","-\frac{i b e^{3/2} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 d^{5/2}}+\frac{i b e^{3/2} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 d^{5/2}}+\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{b e n}{d^2 x}-\frac{b n}{9 d x^3}","-\frac{i b e^{3/2} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 d^{5/2}}+\frac{i b e^{3/2} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{2 d^{5/2}}+\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{b e n}{d^2 x}-\frac{b n}{9 d x^3}",1,"-(b*n)/(9*d*x^3) + (b*e*n)/(d^2*x) - (a + b*Log[c*x^n])/(3*d*x^3) + (e*(a + b*Log[c*x^n]))/(d^2*x) + (e^(3/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/d^(5/2) - ((I/2)*b*e^(3/2)*n*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]])/d^(5/2) + ((I/2)*b*e^(3/2)*n*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])/d^(5/2)","A",9,8,23,0.3478,1,"{325, 205, 2351, 2304, 2324, 12, 4848, 2391}"
221,1,129,0,0.2203627,"\int \frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^5*(a + b*Log[c*x^n]))/(d + e*x^2)^2,x]","-\frac{b d n \text{PolyLog}\left(2,-\frac{e x^2}{d}\right)}{2 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{d \log \left(\frac{e x^2}{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^2}-\frac{b d n \log \left(d+e x^2\right)}{4 e^3}-\frac{b n x^2}{4 e^2}","-\frac{b d n \text{PolyLog}\left(2,-\frac{e x^2}{d}\right)}{2 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{d \log \left(\frac{e x^2}{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^2}-\frac{b d n \log \left(d+e x^2\right)}{4 e^3}-\frac{b n x^2}{4 e^2}",1,"-(b*n*x^2)/(4*e^2) + (x^2*(a + b*Log[c*x^n]))/(2*e^2) + (d*x^2*(a + b*Log[c*x^n]))/(2*e^2*(d + e*x^2)) - (b*d*n*Log[d + e*x^2])/(4*e^3) - (d*(a + b*Log[c*x^n])*Log[1 + (e*x^2)/d])/e^3 - (b*d*n*PolyLog[2, -((e*x^2)/d)])/(2*e^3)","A",7,8,23,0.3478,1,"{266, 43, 2351, 2304, 2335, 260, 2337, 2391}"
222,1,95,0,0.1878153,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/(d + e*x^2)^2,x]","\frac{b n \text{PolyLog}\left(2,-\frac{e x^2}{d}\right)}{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 \log \left(d+e x^2\right)}{4 e^2}","\frac{b n \text{PolyLog}\left(2,-\frac{e x^2}{d}\right)}{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 \log \left(d+e x^2\right)}{4 e^2}",1,"-(x^2*(a + b*Log[c*x^n]))/(2*e*(d + e*x^2)) + (b*n*Log[d + e*x^2])/(4*e^2) + ((a + b*Log[c*x^n])*Log[1 + (e*x^2)/d])/(2*e^2) + (b*n*PolyLog[2, -((e*x^2)/d)])/(4*e^2)","A",6,7,23,0.3043,1,"{266, 43, 2351, 2335, 260, 2337, 2391}"
223,1,50,0,0.041939,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x*(a + b*Log[c*x^n]))/(d + e*x^2)^2,x]","\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}","\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,"(x^2*(a + b*Log[c*x^n]))/(2*d*(d + e*x^2)) - (b*n*Log[d + e*x^2])/(4*d*e)","A",2,2,21,0.09524,1,"{2335, 260}"
224,1,82,0,0.1403746,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^2\right)^2} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x^2)^2),x]","\frac{b n \text{PolyLog}\left(2,-\frac{d}{e x^2}\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{PolyLog}\left(2,-\frac{d}{e x^2}\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)}",1,"(a + b*Log[c*x^n])/(2*d*(d + e*x^2)) - (Log[1 + d/(e*x^2)]*(2*a - b*n + 2*b*Log[c*x^n]))/(4*d^2) + (b*n*PolyLog[2, -(d/(e*x^2))])/(4*d^2)","A",3,3,23,0.1304,1,"{2340, 2345, 2391}"
225,1,159,0,0.2890986,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^2\right)^2} \, dx","Int[(a + b*Log[c*x^n])/(x^3*(d + e*x^2)^2),x]","\frac{b e n \text{PolyLog}\left(2,-\frac{e x^2}{d}\right)}{2 d^3}-\frac{e \left(4 a+4 b \log \left(c x^n\right)-b n\right)^2}{16 b d^3 n}+\frac{e \log \left(\frac{e x^2}{d}+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 n}{2 d^2 x^2}","-\frac{b e n \text{PolyLog}\left(2,-\frac{d}{e x^2}\right)}{2 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 n}{2 d^2 x^2}",1,"-(b*n)/(2*d^2*x^2) + (a + b*Log[c*x^n])/(2*d*x^2*(d + e*x^2)) - (4*a - b*n + 4*b*Log[c*x^n])/(4*d^2*x^2) - (e*(4*a - b*n + 4*b*Log[c*x^n])^2)/(16*b*d^3*n) + (e*(4*a - b*n + 4*b*Log[c*x^n])*Log[1 + (e*x^2)/d])/(4*d^3) + (b*e*n*PolyLog[2, -((e*x^2)/d)])/(2*d^3)","A",7,8,23,0.3478,1,"{2340, 266, 44, 2351, 2304, 2301, 2337, 2391}"
226,1,191,0,0.296781,"\int \frac{x^4 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^4*(a + b*Log[c*x^n]))/(d + e*x^2)^2,x]","\frac{3 i b \sqrt{d} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 e^{5/2}}-\frac{3 i b \sqrt{d} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 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{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{a x}{e^2}+\frac{b x \log \left(c x^n\right)}{e^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}","\frac{3 i b \sqrt{d} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 e^{5/2}}-\frac{3 i b \sqrt{d} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 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{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{a x}{e^2}+\frac{b x \log \left(c x^n\right)}{e^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,"(a*x)/e^2 - (b*n*x)/e^2 - (b*Sqrt[d]*n*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*e^(5/2)) + (b*x*Log[c*x^n])/e^2 + (d*x*(a + b*Log[c*x^n]))/(2*e^2*(d + e*x^2)) - (3*Sqrt[d]*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(2*e^(5/2)) + (((3*I)/4)*b*Sqrt[d]*n*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]])/e^(5/2) - (((3*I)/4)*b*Sqrt[d]*n*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])/e^(5/2)","A",16,10,23,0.4348,1,"{288, 321, 205, 2351, 2295, 2323, 2324, 12, 4848, 2391}"
227,1,164,0,0.2690793,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/(d + e*x^2)^2,x]","-\frac{i b n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 \sqrt{d} e^{3/2}}+\frac{i b n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 \sqrt{d} 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{b n \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 \sqrt{d} e^{3/2}}","-\frac{i b n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 \sqrt{d} e^{3/2}}+\frac{i b n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 \sqrt{d} 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{b n \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 \sqrt{d} e^{3/2}}",1,"(b*n*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*Sqrt[d]*e^(3/2)) - (x*(a + b*Log[c*x^n]))/(2*e*(d + e*x^2)) + (ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(2*Sqrt[d]*e^(3/2)) - ((I/4)*b*n*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*e^(3/2)) + ((I/4)*b*n*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*e^(3/2))","A",14,8,23,0.3478,1,"{288, 205, 2351, 2323, 2324, 12, 4848, 2391}"
228,1,164,0,0.0990367,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+e x^2\right)^2} \, dx","Int[(a + b*Log[c*x^n])/(d + e*x^2)^2,x]","-\frac{i b n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{3/2} \sqrt{e}}+\frac{i b n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{3/2} \sqrt{e}}+\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{b n \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2} \sqrt{e}}","-\frac{i b n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{3/2} \sqrt{e}}+\frac{i b n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{3/2} \sqrt{e}}+\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{b n \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2} \sqrt{e}}",1,"-(b*n*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(3/2)*Sqrt[e]) + (x*(a + b*Log[c*x^n]))/(2*d*(d + e*x^2)) + (ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(2*d^(3/2)*Sqrt[e]) - ((I/4)*b*n*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]])/(d^(3/2)*Sqrt[e]) + ((I/4)*b*n*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])/(d^(3/2)*Sqrt[e])","A",7,6,20,0.3000,1,"{2323, 205, 2324, 12, 4848, 2391}"
229,1,183,0,0.2838441,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^2\right)^2} \, dx","Int[(a + b*Log[c*x^n])/(x^2*(d + e*x^2)^2),x]","\frac{3 i b \sqrt{e} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{5/2}}-\frac{3 i b \sqrt{e} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{5/2}}-\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 b n}{2 d^2 x}","\frac{3 i b \sqrt{e} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{5/2}}-\frac{3 i b \sqrt{e} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{5/2}}-\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 b n}{2 d^2 x}",1,"(-3*b*n)/(2*d^2*x) + (a + b*Log[c*x^n])/(2*d*x*(d + e*x^2)) - (3*a - b*n + 3*b*Log[c*x^n])/(2*d^2*x) - (Sqrt[e]*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(3*a - b*n + 3*b*Log[c*x^n]))/(2*d^(5/2)) + (((3*I)/4)*b*Sqrt[e]*n*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]])/d^(5/2) - (((3*I)/4)*b*Sqrt[e]*n*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])/d^(5/2)","A",9,9,23,0.3913,1,"{2340, 325, 205, 2351, 2304, 2324, 12, 4848, 2391}"
230,1,224,0,0.3089391,"\int \frac{a+b \log \left(c x^n\right)}{x^4 \left(d+e x^2\right)^2} \, dx","Int[(a + b*Log[c*x^n])/(x^4*(d + e*x^2)^2),x]","-\frac{5 i b e^{3/2} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{7/2}}+\frac{5 i b e^{3/2} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{7/2}}+\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 b e n}{2 d^3 x}-\frac{5 b n}{18 d^2 x^3}","-\frac{5 i b e^{3/2} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{7/2}}+\frac{5 i b e^{3/2} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{4 d^{7/2}}+\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 b e n}{2 d^3 x}-\frac{5 b n}{18 d^2 x^3}",1,"(-5*b*n)/(18*d^2*x^3) + (5*b*e*n)/(2*d^3*x) + (a + b*Log[c*x^n])/(2*d*x^3*(d + e*x^2)) - (5*a - b*n + 5*b*Log[c*x^n])/(6*d^2*x^3) + (e*(5*a - b*n + 5*b*Log[c*x^n]))/(2*d^3*x) + (e^(3/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(5*a - b*n + 5*b*Log[c*x^n]))/(2*d^(7/2)) - (((5*I)/4)*b*e^(3/2)*n*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]])/d^(7/2) + (((5*I)/4)*b*e^(3/2)*n*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])/d^(7/2)","A",10,9,23,0.3913,1,"{2340, 325, 205, 2351, 2304, 2324, 12, 4848, 2391}"
231,1,152,0,0.2867877,"\int \frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^5*(a + b*Log[c*x^n]))/(d + e*x^2)^3,x]","\frac{b n \text{PolyLog}\left(2,-\frac{e x^2}{d}\right)}{4 e^3}-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{4 e^3 \left(d+e x^2\right)^2}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{e^2 \left(d+e x^2\right)}+\frac{\log \left(\frac{e x^2}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 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}","\frac{b n \text{PolyLog}\left(2,-\frac{e x^2}{d}\right)}{4 e^3}-\frac{d^2 \left(a+b \log \left(c x^n\right)\right)}{4 e^3 \left(d+e x^2\right)^2}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{e^2 \left(d+e x^2\right)}+\frac{\log \left(\frac{e x^2}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 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,"(b*d*n)/(8*e^3*(d + e*x^2)) + (b*n*Log[x])/(4*e^3) - (d^2*(a + b*Log[c*x^n]))/(4*e^3*(d + e*x^2)^2) - (x^2*(a + b*Log[c*x^n]))/(e^2*(d + e*x^2)) + (3*b*n*Log[d + e*x^2])/(8*e^3) + ((a + b*Log[c*x^n])*Log[1 + (e*x^2)/d])/(2*e^3) + (b*n*PolyLog[2, -((e*x^2)/d)])/(4*e^3)","A",10,9,23,0.3913,1,"{266, 43, 2351, 2338, 44, 2335, 260, 2337, 2391}"
232,1,68,0,0.079546,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/(d + e*x^2)^3,x]","\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}","\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,"-(b*n)/(8*e^2*(d + e*x^2)) + (x^4*(a + b*Log[c*x^n]))/(4*d*(d + e*x^2)^2) - (b*n*Log[d + e*x^2])/(8*d*e^2)","A",4,3,23,0.1304,1,"{2335, 266, 43}"
233,1,82,0,0.0657028,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x*(a + b*Log[c*x^n]))/(d + e*x^2)^3,x]","-\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)}","-\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) - (a + b*Log[c*x^n])/(4*e*(d + e*x^2)^2) - (b*n*Log[d + e*x^2])/(8*d^2*e)","A",4,3,21,0.1429,1,"{2338, 266, 44}"
234,1,115,0,0.2175594,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^2\right)^3} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x^2)^3),x]","\frac{b n \text{PolyLog}\left(2,-\frac{d}{e x^2}\right)}{4 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{PolyLog}\left(2,-\frac{d}{e x^2}\right)}{4 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}",1,"(a + b*Log[c*x^n])/(4*d*(d + e*x^2)^2) - (Log[1 + d/(e*x^2)]*(4*a - 3*b*n + 4*b*Log[c*x^n]))/(8*d^3) + (4*a - b*n + 4*b*Log[c*x^n])/(8*d^2*(d + e*x^2)) + (b*n*PolyLog[2, -(d/(e*x^2))])/(4*d^3)","A",4,3,23,0.1304,1,"{2340, 2345, 2391}"
235,1,195,0,0.3901891,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^2\right)^3} \, dx","Int[(a + b*Log[c*x^n])/(x^3*(d + e*x^2)^3),x]","\frac{3 b e n \text{PolyLog}\left(2,-\frac{e x^2}{d}\right)}{4 d^4}-\frac{e \left(12 a+12 b \log \left(c x^n\right)-5 b n\right)^2}{96 b d^4 n}+\frac{e \log \left(\frac{e x^2}{d}+1\right) \left(12 a+12 b \log \left(c x^n\right)-5 b n\right)}{8 d^4}+\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{12 a+12 b \log \left(c x^n\right)-5 b n}{8 d^3 x^2}+\frac{a+b \log \left(c x^n\right)}{4 d x^2 \left(d+e x^2\right)^2}-\frac{3 b n}{4 d^3 x^2}","-\frac{3 b e n \text{PolyLog}\left(2,-\frac{d}{e x^2}\right)}{4 d^4}+\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{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{a+b \log \left(c x^n\right)}{4 d x^2 \left(d+e x^2\right)^2}-\frac{3 b n}{4 d^3 x^2}",1,"(-3*b*n)/(4*d^3*x^2) + (a + b*Log[c*x^n])/(4*d*x^2*(d + e*x^2)^2) + (6*a - b*n + 6*b*Log[c*x^n])/(8*d^2*x^2*(d + e*x^2)) - (12*a - 5*b*n + 12*b*Log[c*x^n])/(8*d^3*x^2) - (e*(12*a - 5*b*n + 12*b*Log[c*x^n])^2)/(96*b*d^4*n) + (e*(12*a - 5*b*n + 12*b*Log[c*x^n])*Log[1 + (e*x^2)/d])/(8*d^4) + (3*b*e*n*PolyLog[2, -((e*x^2)/d)])/(4*d^4)","A",8,8,23,0.3478,1,"{2340, 266, 44, 2351, 2304, 2301, 2337, 2391}"
236,1,211,0,0.4576638,"\int \frac{x^4 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^4*(a + b*Log[c*x^n]))/(d + e*x^2)^3,x]","-\frac{3 i b n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 \sqrt{d} e^{5/2}}+\frac{3 i b n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 \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 \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{b n x}{8 e^2 \left(d+e x^2\right)}+\frac{b n \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 \sqrt{d} e^{5/2}}","-\frac{3 i b n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 \sqrt{d} e^{5/2}}+\frac{3 i b n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 \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 \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{b n x}{8 e^2 \left(d+e x^2\right)}+\frac{b n \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 \sqrt{d} e^{5/2}}",1,"-(b*n*x)/(8*e^2*(d + e*x^2)) + (b*n*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*Sqrt[d]*e^(5/2)) + (d*x*(a + b*Log[c*x^n]))/(4*e^2*(d + e*x^2)^2) - (5*x*(a + b*Log[c*x^n]))/(8*e^2*(d + e*x^2)) + (3*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(8*Sqrt[d]*e^(5/2)) - (((3*I)/16)*b*n*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*e^(5/2)) + (((3*I)/16)*b*n*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*e^(5/2))","A",24,9,23,0.3913,1,"{288, 205, 2351, 2323, 2324, 12, 4848, 2391, 199}"
237,1,187,0,0.3687458,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/(d + e*x^2)^3,x]","-\frac{i b n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{3/2} e^{3/2}}+\frac{i b n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{3/2} 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{b n x}{8 d e \left(d+e x^2\right)}","-\frac{i b n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{3/2} e^{3/2}}+\frac{i b n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{3/2} 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{b n x}{8 d e \left(d+e x^2\right)}",1,"(b*n*x)/(8*d*e*(d + e*x^2)) - (x*(a + b*Log[c*x^n]))/(4*e*(d + e*x^2)^2) + (x*(a + b*Log[c*x^n]))/(8*d*e*(d + e*x^2)) + (ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(8*d^(3/2)*e^(3/2)) - ((I/16)*b*n*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]])/(d^(3/2)*e^(3/2)) + ((I/16)*b*n*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])/(d^(3/2)*e^(3/2))","A",19,9,23,0.3913,1,"{288, 199, 205, 2351, 2323, 2324, 12, 4848, 2391}"
238,1,210,0,0.1458053,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+e x^2\right)^3} \, dx","Int[(a + b*Log[c*x^n])/(d + e*x^2)^3,x]","-\frac{3 i b n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{5/2} \sqrt{e}}+\frac{3 i b n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 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{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{x \left(a+b \log \left(c x^n\right)\right)}{4 d \left(d+e x^2\right)^2}-\frac{b n x}{8 d^2 \left(d+e x^2\right)}-\frac{b n \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{5/2} \sqrt{e}}","-\frac{3 i b n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{5/2} \sqrt{e}}+\frac{3 i b n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 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{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{x \left(a+b \log \left(c x^n\right)\right)}{4 d \left(d+e x^2\right)^2}-\frac{b n x}{8 d^2 \left(d+e x^2\right)}-\frac{b n \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{5/2} \sqrt{e}}",1,"-(b*n*x)/(8*d^2*(d + e*x^2)) - (b*n*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(5/2)*Sqrt[e]) + (x*(a + b*Log[c*x^n]))/(4*d*(d + e*x^2)^2) + (3*x*(a + b*Log[c*x^n]))/(8*d^2*(d + e*x^2)) + (3*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(8*d^(5/2)*Sqrt[e]) - (((3*I)/16)*b*n*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]])/(d^(5/2)*Sqrt[e]) + (((3*I)/16)*b*n*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])/(d^(5/2)*Sqrt[e])","A",10,7,20,0.3500,1,"{2323, 205, 2324, 12, 4848, 2391, 199}"
239,1,219,0,0.3664394,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^2\right)^3} \, dx","Int[(a + b*Log[c*x^n])/(x^2*(d + e*x^2)^3),x]","\frac{15 i b \sqrt{e} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{7/2}}-\frac{15 i b \sqrt{e} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{7/2}}+\frac{5 a+5 b \log \left(c x^n\right)-b n}{8 d^2 x \left(d+e x^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{a+b \log \left(c x^n\right)}{4 d x \left(d+e x^2\right)^2}-\frac{15 b n}{8 d^3 x}","\frac{15 i b \sqrt{e} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{7/2}}-\frac{15 i b \sqrt{e} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{7/2}}+\frac{5 a+5 b \log \left(c x^n\right)-b n}{8 d^2 x \left(d+e x^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{a+b \log \left(c x^n\right)}{4 d x \left(d+e x^2\right)^2}-\frac{15 b n}{8 d^3 x}",1,"(-15*b*n)/(8*d^3*x) + (a + b*Log[c*x^n])/(4*d*x*(d + e*x^2)^2) + (5*a - b*n + 5*b*Log[c*x^n])/(8*d^2*x*(d + e*x^2)) - (15*a - 8*b*n + 15*b*Log[c*x^n])/(8*d^3*x) - (Sqrt[e]*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(15*a - 8*b*n + 15*b*Log[c*x^n]))/(8*d^(7/2)) + (((15*I)/16)*b*Sqrt[e]*n*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]])/d^(7/2) - (((15*I)/16)*b*Sqrt[e]*n*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])/d^(7/2)","A",10,9,23,0.3913,1,"{2340, 325, 205, 2351, 2304, 2324, 12, 4848, 2391}"
240,1,260,0,0.4209938,"\int \frac{a+b \log \left(c x^n\right)}{x^4 \left(d+e x^2\right)^3} \, dx","Int[(a + b*Log[c*x^n])/(x^4*(d + e*x^2)^3),x]","-\frac{35 i b e^{3/2} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{9/2}}+\frac{35 i b e^{3/2} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{9/2}}+\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{7 a+7 b \log \left(c x^n\right)-b n}{8 d^2 x^3 \left(d+e x^2\right)}-\frac{35 a+35 b \log \left(c x^n\right)-12 b n}{24 d^3 x^3}+\frac{a+b \log \left(c x^n\right)}{4 d x^3 \left(d+e x^2\right)^2}+\frac{35 b e n}{8 d^4 x}-\frac{35 b n}{72 d^3 x^3}","-\frac{35 i b e^{3/2} n \text{PolyLog}\left(2,-\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{9/2}}+\frac{35 i b e^{3/2} n \text{PolyLog}\left(2,\frac{i \sqrt{e} x}{\sqrt{d}}\right)}{16 d^{9/2}}+\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{7 a+7 b \log \left(c x^n\right)-b n}{8 d^2 x^3 \left(d+e x^2\right)}-\frac{35 a+35 b \log \left(c x^n\right)-12 b n}{24 d^3 x^3}+\frac{a+b \log \left(c x^n\right)}{4 d x^3 \left(d+e x^2\right)^2}+\frac{35 b e n}{8 d^4 x}-\frac{35 b n}{72 d^3 x^3}",1,"(-35*b*n)/(72*d^3*x^3) + (35*b*e*n)/(8*d^4*x) + (a + b*Log[c*x^n])/(4*d*x^3*(d + e*x^2)^2) + (7*a - b*n + 7*b*Log[c*x^n])/(8*d^2*x^3*(d + e*x^2)) - (35*a - 12*b*n + 35*b*Log[c*x^n])/(24*d^3*x^3) + (e*(35*a - 12*b*n + 35*b*Log[c*x^n]))/(8*d^4*x) + (e^(3/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(35*a - 12*b*n + 35*b*Log[c*x^n]))/(8*d^(9/2)) - (((35*I)/16)*b*e^(3/2)*n*PolyLog[2, ((-I)*Sqrt[e]*x)/Sqrt[d]])/d^(9/2) + (((35*I)/16)*b*e^(3/2)*n*PolyLog[2, (I*Sqrt[e]*x)/Sqrt[d]])/d^(9/2)","A",11,9,23,0.3913,1,"{2340, 325, 205, 2351, 2304, 2324, 12, 4848, 2391}"
241,1,17,0,0.0434263,"\int \frac{x \log \left(c x^2\right)}{1-c x^2} \, dx","Int[(x*Log[c*x^2])/(1 - c*x^2),x]","\frac{\text{PolyLog}\left(2,1-c x^2\right)}{2 c}","\frac{\text{PolyLog}\left(2,1-c x^2\right)}{2 c}",1,"PolyLog[2, 1 - c*x^2]/(2*c)","A",2,2,18,0.1111,1,"{2336, 2315}"
242,1,16,0,0.0429158,"\int \frac{x \log \left(\frac{x^2}{c}\right)}{c-x^2} \, dx","Int[(x*Log[x^2/c])/(c - x^2),x]","\frac{1}{2} \text{PolyLog}\left(2,1-\frac{x^2}{c}\right)","\frac{1}{2} \text{PolyLog}\left(2,1-\frac{x^2}{c}\right)",1,"PolyLog[2, 1 - x^2/c]/2","A",2,2,19,0.1053,1,"{2336, 2315}"
243,1,22,0,0.0220914,"\int \frac{\log (x)}{1-x^2} \, dx","Int[Log[x]/(1 - x^2),x]","\frac{1}{2} \text{PolyLog}(2,-x)-\frac{1}{2} \text{PolyLog}(2,x)+\log (x) \tanh ^{-1}(x)","\frac{1}{2} \text{PolyLog}(2,-x)-\frac{1}{2} \text{PolyLog}(2,x)+\log (x) \tanh ^{-1}(x)",1,"ArcTanh[x]*Log[x] + PolyLog[2, -x]/2 - PolyLog[2, x]/2","A",2,3,12,0.2500,1,"{206, 2324, 5912}"
244,1,32,0,0.0356959,"\int \frac{\log (x)}{1+x^2} \, dx","Int[Log[x]/(1 + x^2),x]","-\frac{1}{2} i \text{PolyLog}(2,-i x)+\frac{1}{2} i \text{PolyLog}(2,i x)+\log (x) \tan ^{-1}(x)","-\frac{1}{2} i \text{PolyLog}(2,-i x)+\frac{1}{2} i \text{PolyLog}(2,i x)+\log (x) \tan ^{-1}(x)",1,"ArcTan[x]*Log[x] - (I/2)*PolyLog[2, (-I)*x] + (I/2)*PolyLog[2, I*x]","A",4,4,10,0.4000,1,"{203, 2324, 4848, 2391}"
245,1,62,0,0.0387105,"\int \frac{a+b \log (c x)}{1-e x^2} \, dx","Int[(a + b*Log[c*x])/(1 - e*x^2),x]","\frac{b \text{PolyLog}\left(2,-\sqrt{e} x\right)}{2 \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\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{PolyLog}\left(2,-\sqrt{e} x\right)}{2 \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\sqrt{e} x\right)}{2 \sqrt{e}}+\frac{\tanh ^{-1}\left(\sqrt{e} x\right) (a+b \log (c x))}{\sqrt{e}}",1,"(ArcTanh[Sqrt[e]*x]*(a + b*Log[c*x]))/Sqrt[e] + (b*PolyLog[2, -(Sqrt[e]*x)])/(2*Sqrt[e]) - (b*PolyLog[2, Sqrt[e]*x])/(2*Sqrt[e])","A",3,4,19,0.2105,1,"{206, 2324, 12, 5912}"
246,1,66,0,0.0387247,"\int \frac{a+b \log \left(c x^n\right)}{1-e x^2} \, dx","Int[(a + b*Log[c*x^n])/(1 - e*x^2),x]","\frac{b n \text{PolyLog}\left(2,-\sqrt{e} x\right)}{2 \sqrt{e}}-\frac{b n \text{PolyLog}\left(2,\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{PolyLog}\left(2,-\sqrt{e} x\right)}{2 \sqrt{e}}-\frac{b n \text{PolyLog}\left(2,\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}}",1,"(ArcTanh[Sqrt[e]*x]*(a + b*Log[c*x^n]))/Sqrt[e] + (b*n*PolyLog[2, -(Sqrt[e]*x)])/(2*Sqrt[e]) - (b*n*PolyLog[2, Sqrt[e]*x])/(2*Sqrt[e])","A",3,4,21,0.1905,1,"{206, 2324, 12, 5912}"
247,1,509,0,0.6118176,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{\left(d+e x^2\right)^2} \, dx","Int[(a + b*Log[c*x^n])^2/(d + e*x^2)^2,x]","\frac{b n \text{PolyLog}\left(2,-\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{PolyLog}\left(2,\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^2 n^2 \text{PolyLog}\left(2,-\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}+\frac{b^2 n^2 \text{PolyLog}\left(2,\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}-\frac{b^2 n^2 \text{PolyLog}\left(3,-\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}+\frac{b^2 n^2 \text{PolyLog}\left(3,\frac{\sqrt{e} x}{\sqrt{-d}}\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 n \text{PolyLog}\left(2,-\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{PolyLog}\left(2,\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^2 n^2 \text{PolyLog}\left(2,-\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}+\frac{b^2 n^2 \text{PolyLog}\left(2,\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}-\frac{b^2 n^2 \text{PolyLog}\left(3,-\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}+\frac{b^2 n^2 \text{PolyLog}\left(3,\frac{\sqrt{e} x}{\sqrt{-d}}\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}}",1,"(x*(a + b*Log[c*x^n])^2)/(4*(-d)^(3/2)*(Sqrt[-d] - Sqrt[e]*x)) + (x*(a + b*Log[c*x^n])^2)/(4*(-d)^(3/2)*(Sqrt[-d] + Sqrt[e]*x)) + (b*n*(a + b*Log[c*x^n])*Log[1 - (Sqrt[e]*x)/Sqrt[-d]])/(2*(-d)^(3/2)*Sqrt[e]) - ((a + b*Log[c*x^n])^2*Log[1 - (Sqrt[e]*x)/Sqrt[-d]])/(4*(-d)^(3/2)*Sqrt[e]) - (b*n*(a + b*Log[c*x^n])*Log[1 + (Sqrt[e]*x)/Sqrt[-d]])/(2*(-d)^(3/2)*Sqrt[e]) + ((a + b*Log[c*x^n])^2*Log[1 + (Sqrt[e]*x)/Sqrt[-d]])/(4*(-d)^(3/2)*Sqrt[e]) - (b^2*n^2*PolyLog[2, -((Sqrt[e]*x)/Sqrt[-d])])/(2*(-d)^(3/2)*Sqrt[e]) + (b*n*(a + b*Log[c*x^n])*PolyLog[2, -((Sqrt[e]*x)/Sqrt[-d])])/(2*(-d)^(3/2)*Sqrt[e]) + (b^2*n^2*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]])/(2*(-d)^(3/2)*Sqrt[e]) - (b*n*(a + b*Log[c*x^n])*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]])/(2*(-d)^(3/2)*Sqrt[e]) - (b^2*n^2*PolyLog[3, -((Sqrt[e]*x)/Sqrt[-d])])/(2*(-d)^(3/2)*Sqrt[e]) + (b^2*n^2*PolyLog[3, (Sqrt[e]*x)/Sqrt[-d]])/(2*(-d)^(3/2)*Sqrt[e])","A",16,6,22,0.2727,1,"{2330, 2318, 2317, 2391, 2374, 6589}"
248,1,711,0,0.8459755,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3}{\left(d+e x^2\right)^2} \, dx","Int[(a + b*Log[c*x^n])^3/(d + e*x^2)^2,x]","-\frac{3 b^2 n^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(3,-\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{PolyLog}\left(3,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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^3 n^3 \text{PolyLog}\left(3,-\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}-\frac{3 b^3 n^3 \text{PolyLog}\left(3,\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}+\frac{3 b^3 n^3 \text{PolyLog}\left(4,-\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}-\frac{3 b^3 n^3 \text{PolyLog}\left(4,\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-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^2 n^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(3,-\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{PolyLog}\left(3,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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^3 n^3 \text{PolyLog}\left(3,-\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}-\frac{3 b^3 n^3 \text{PolyLog}\left(3,\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}+\frac{3 b^3 n^3 \text{PolyLog}\left(4,-\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-d)^{3/2} \sqrt{e}}-\frac{3 b^3 n^3 \text{PolyLog}\left(4,\frac{\sqrt{e} x}{\sqrt{-d}}\right)}{2 (-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}}",1,"(x*(a + b*Log[c*x^n])^3)/(4*(-d)^(3/2)*(Sqrt[-d] - Sqrt[e]*x)) + (x*(a + b*Log[c*x^n])^3)/(4*(-d)^(3/2)*(Sqrt[-d] + Sqrt[e]*x)) + (3*b*n*(a + b*Log[c*x^n])^2*Log[1 - (Sqrt[e]*x)/Sqrt[-d]])/(4*(-d)^(3/2)*Sqrt[e]) - ((a + b*Log[c*x^n])^3*Log[1 - (Sqrt[e]*x)/Sqrt[-d]])/(4*(-d)^(3/2)*Sqrt[e]) - (3*b*n*(a + b*Log[c*x^n])^2*Log[1 + (Sqrt[e]*x)/Sqrt[-d]])/(4*(-d)^(3/2)*Sqrt[e]) + ((a + b*Log[c*x^n])^3*Log[1 + (Sqrt[e]*x)/Sqrt[-d]])/(4*(-d)^(3/2)*Sqrt[e]) - (3*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((Sqrt[e]*x)/Sqrt[-d])])/(2*(-d)^(3/2)*Sqrt[e]) + (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((Sqrt[e]*x)/Sqrt[-d])])/(4*(-d)^(3/2)*Sqrt[e]) + (3*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]])/(2*(-d)^(3/2)*Sqrt[e]) - (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, (Sqrt[e]*x)/Sqrt[-d]])/(4*(-d)^(3/2)*Sqrt[e]) + (3*b^3*n^3*PolyLog[3, -((Sqrt[e]*x)/Sqrt[-d])])/(2*(-d)^(3/2)*Sqrt[e]) - (3*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((Sqrt[e]*x)/Sqrt[-d])])/(2*(-d)^(3/2)*Sqrt[e]) - (3*b^3*n^3*PolyLog[3, (Sqrt[e]*x)/Sqrt[-d]])/(2*(-d)^(3/2)*Sqrt[e]) + (3*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, (Sqrt[e]*x)/Sqrt[-d]])/(2*(-d)^(3/2)*Sqrt[e]) + (3*b^3*n^3*PolyLog[4, -((Sqrt[e]*x)/Sqrt[-d])])/(2*(-d)^(3/2)*Sqrt[e]) - (3*b^3*n^3*PolyLog[4, (Sqrt[e]*x)/Sqrt[-d]])/(2*(-d)^(3/2)*Sqrt[e])","A",20,6,22,0.2727,1,"{2330, 2318, 2317, 2374, 6589, 2383}"
249,0,0,0,0.0332444,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[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,"Defer[Int][1/((d + e*x^2)^2*(a + b*Log[c*x^n])), x]","A",0,0,0,0,-1,"{}"
250,0,0,0,0.0324521,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Int[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,"Defer[Int][1/((d + e*x^2)^2*(a + b*Log[c*x^n])^2), x]","A",0,0,0,0,-1,"{}"
251,1,208,0,0.249717,"\int x^5 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^5*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]),x]","\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^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{8 b d^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{105 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}","\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^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{8 b d^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{105 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^3*n*Sqrt[d + e*x^2])/(105*e^3) - (8*b*d^2*n*(d + e*x^2)^(3/2))/(315*e^3) + (9*b*d*n*(d + e*x^2)^(5/2))/(175*e^3) - (b*n*(d + e*x^2)^(7/2))/(49*e^3) + (8*b*d^(7/2)*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(105*e^3) + (d^2*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/(3*e^3) - (2*d*(d + e*x^2)^(5/2)*(a + b*Log[c*x^n]))/(5*e^3) + ((d + e*x^2)^(7/2)*(a + b*Log[c*x^n]))/(7*e^3)","A",7,8,25,0.3200,1,"{266, 43, 2350, 12, 1251, 897, 1261, 208}"
252,1,154,0,0.1754447,"\int x^3 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^3*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]),x]","-\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^2 n \sqrt{d+e x^2}}{15 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 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}","-\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^2 n \sqrt{d+e x^2}}{15 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 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^2*n*Sqrt[d + e*x^2])/(15*e^2) + (2*b*d*n*(d + e*x^2)^(3/2))/(45*e^2) - (b*n*(d + e*x^2)^(5/2))/(25*e^2) - (2*b*d^(5/2)*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(15*e^2) - (d*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/(3*e^2) + ((d + e*x^2)^(5/2)*(a + b*Log[c*x^n]))/(5*e^2)","A",8,9,25,0.3600,1,"{266, 43, 2350, 12, 446, 80, 50, 63, 208}"
253,1,102,0,0.0878957,"\int x \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]),x]","\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}","\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,"-(b*d*n*Sqrt[d + e*x^2])/(3*e) - (b*n*(d + e*x^2)^(3/2))/(9*e) + (b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(3*e) + ((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/(3*e)","A",6,5,23,0.2174,1,"{2338, 266, 50, 63, 208}"
254,1,220,0,0.3337008,"\int \frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/x,x]","-\frac{1}{2} b \sqrt{d} n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\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)-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)","-\frac{1}{2} b \sqrt{d} n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\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)-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]) + b*Sqrt[d]*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]] + (b*Sqrt[d]*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]^2)/2 + (Sqrt[d + e*x^2] - Sqrt[d]*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])*(a + b*Log[c*x^n]) - b*Sqrt[d]*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])] - (b*Sqrt[d]*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/2","A",12,9,25,0.3600,1,"{266, 50, 63, 208, 2348, 5984, 5918, 2402, 2315}"
255,1,252,0,0.3759952,"\int \frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/x^3,x]","-\frac{b e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right)}{4 \sqrt{d}}-\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 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}}","-\frac{b e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right)}{4 \sqrt{d}}-\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 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,"-(b*n*Sqrt[d + e*x^2])/(4*x^2) - (b*e*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(4*Sqrt[d]) + (b*e*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]^2)/(4*Sqrt[d]) - (Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/(2*x^2) - (e*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]*(a + b*Log[c*x^n]))/(2*Sqrt[d]) - (b*e*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/(2*Sqrt[d]) - (b*e*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/(4*Sqrt[d])","A",14,11,25,0.4400,1,"{266, 47, 63, 208, 2350, 12, 14, 5984, 5918, 2402, 2315}"
256,1,469,0,0.5977337,"\int x^4 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^4*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]),x]","-\frac{b d^{5/2} n \sqrt{d+e x^2} \text{PolyLog}\left(2,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{d^2 x \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{16 e^2}+\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{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{7 b d^2 n x \sqrt{d+e x^2}}{192 e^2}+\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{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}","-\frac{b d^{5/2} n \sqrt{d+e x^2} \text{PolyLog}\left(2,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{d^2 x \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{16 e^2}+\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{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{7 b d^2 n x \sqrt{d+e x^2}}{192 e^2}+\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{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,"(7*b*d^2*n*x*Sqrt[d + e*x^2])/(192*e^2) - (5*b*d*n*x^3*Sqrt[d + e*x^2])/(288*e) - (b*n*x^5*Sqrt[d + e*x^2])/36 + (5*b*d^(5/2)*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])/(192*e^(5/2)*Sqrt[1 + (e*x^2)/d]) + (b*d^(5/2)*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]^2)/(32*e^(5/2)*Sqrt[1 + (e*x^2)/d]) - (b*d^(5/2)*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[1 - E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(16*e^(5/2)*Sqrt[1 + (e*x^2)/d]) - (d^2*x*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/(16*e^2) + (d*x^3*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/(24*e) + (x^5*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/6 + (d^(5/2)*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(16*e^(5/2)*Sqrt[1 + (e*x^2)/d]) - (b*d^(5/2)*n*Sqrt[d + e*x^2]*PolyLog[2, E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(32*e^(5/2)*Sqrt[1 + (e*x^2)/d])","A",19,13,25,0.5200,1,"{2341, 279, 321, 215, 2350, 12, 14, 195, 5659, 3716, 2190, 2279, 2391}"
257,1,410,0,0.4131098,"\int x^2 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]),x]","\frac{b d^{3/2} n \sqrt{d+e x^2} \text{PolyLog}\left(2,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{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{1}{4} x^3 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)+\frac{d x \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{8 e}-\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{b n x \left(d+e x^2\right)^{3/2}}{16 e}-\frac{b d n x \sqrt{d+e x^2}}{32 e}","\frac{b d^{3/2} n \sqrt{d+e x^2} \text{PolyLog}\left(2,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{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{1}{4} x^3 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)+\frac{d x \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{8 e}-\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{1}{16} b n x^3 \sqrt{d+e x^2}-\frac{3 b d n x \sqrt{d+e x^2}}{32 e}",1,"-(b*d*n*x*Sqrt[d + e*x^2])/(32*e) - (b*n*x*(d + e*x^2)^(3/2))/(16*e) - (b*d^(3/2)*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])/(32*e^(3/2)*Sqrt[1 + (e*x^2)/d]) - (b*d^(3/2)*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]^2)/(16*e^(3/2)*Sqrt[1 + (e*x^2)/d]) + (b*d^(3/2)*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[1 - E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(8*e^(3/2)*Sqrt[1 + (e*x^2)/d]) + (d*x*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/(8*e) + (x^3*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/4 - (d^(3/2)*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(8*e^(3/2)*Sqrt[1 + (e*x^2)/d]) + (b*d^(3/2)*n*Sqrt[d + e*x^2]*PolyLog[2, E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(16*e^(3/2)*Sqrt[1 + (e*x^2)/d])","A",11,12,25,0.4800,1,"{2341, 279, 321, 215, 2350, 388, 195, 5659, 3716, 2190, 2279, 2391}"
258,1,330,0,0.2006766,"\int \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sqrt[d + e*x^2]*(a + b*Log[c*x^n]),x]","-\frac{b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{4 \sqrt{e} \sqrt{d+e x^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 \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} \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}}","-\frac{b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{4 \sqrt{e} \sqrt{d+e x^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 \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} \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,"-(b*n*x*Sqrt[d + e*x^2])/4 + (b*d^(3/2)*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]^2)/(4*Sqrt[e]*Sqrt[d + e*x^2]) - (b*d*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(4*Sqrt[e]) - (b*d^(3/2)*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[1 - E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(2*Sqrt[e]*Sqrt[d + e*x^2]) + (x*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/2 + (d^(3/2)*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(2*Sqrt[e]*Sqrt[d + e*x^2]) - (b*d^(3/2)*n*Sqrt[1 + (e*x^2)/d]*PolyLog[2, E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(4*Sqrt[e]*Sqrt[d + e*x^2])","A",11,11,22,0.5000,1,"{2321, 195, 217, 206, 2327, 2325, 5659, 3716, 2190, 2279, 2391}"
259,1,345,0,0.3941414,"\int \frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/x^2,x]","-\frac{b \sqrt{e} n \sqrt{d+e x^2} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 \sqrt{d} \sqrt{\frac{e x^2}{d}+1}}-\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 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}}","-\frac{b \sqrt{e} n \sqrt{d+e x^2} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 \sqrt{d} \sqrt{\frac{e x^2}{d}+1}}-\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 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])/x) + (b*Sqrt[e]*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*Sqrt[1 + (e*x^2)/d]) + (b*Sqrt[e]*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]^2)/(2*Sqrt[d]*Sqrt[1 + (e*x^2)/d]) - (b*Sqrt[e]*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[1 - E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(Sqrt[d]*Sqrt[1 + (e*x^2)/d]) - (Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/x + (Sqrt[e]*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(Sqrt[d]*Sqrt[1 + (e*x^2)/d]) - (b*Sqrt[e]*n*Sqrt[d + e*x^2]*PolyLog[2, E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(2*Sqrt[d]*Sqrt[1 + (e*x^2)/d])","A",11,10,25,0.4000,1,"{2341, 277, 215, 2350, 14, 5659, 3716, 2190, 2279, 2391}"
260,1,112,0,0.1040046,"\int \frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/x^4,x]","-\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}","-\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,"-(b*e*n*Sqrt[d + e*x^2])/(3*d*x) - (b*n*(d + e*x^2)^(3/2))/(9*d*x^3) + (b*e^(3/2)*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(3*d) - ((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/(3*d*x^3)","A",5,4,25,0.1600,1,"{2335, 277, 217, 206}"
261,1,170,0,0.151702,"\int \frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/x^6,x]","\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^2 n \sqrt{d+e x^2}}{15 d^2 x}-\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 n \left(d+e x^2\right)^{3/2}}{45 d^2 x^3}-\frac{b n \left(d+e x^2\right)^{5/2}}{25 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^2 n \sqrt{d+e x^2}}{15 d^2 x}-\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 n \left(d+e x^2\right)^{3/2}}{45 d^2 x^3}-\frac{b n \left(d+e x^2\right)^{5/2}}{25 d^2 x^5}",1,"(2*b*e^2*n*Sqrt[d + e*x^2])/(15*d^2*x) + (2*b*e*n*(d + e*x^2)^(3/2))/(45*d^2*x^3) - (b*n*(d + e*x^2)^(5/2))/(25*d^2*x^5) - (2*b*e^(5/2)*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(15*d^2) - ((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/(5*d*x^5) + (2*e*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/(15*d^2*x^3)","A",7,8,25,0.3200,1,"{271, 264, 2350, 12, 451, 277, 217, 206}"
262,1,230,0,0.1987626,"\int \frac{\sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{x^8} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/x^8,x]","-\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^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{8 b e^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{105 d^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}","-\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^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{8 b e^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{105 d^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,"(-8*b*e^3*n*Sqrt[d + e*x^2])/(105*d^3*x) - (8*b*e^2*n*(d + e*x^2)^(3/2))/(315*d^3*x^3) - (b*n*(d + e*x^2)^(5/2))/(49*d^2*x^7) + (38*b*e*n*(d + e*x^2)^(5/2))/(1225*d^3*x^5) + (8*b*e^(7/2)*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(105*d^3) - ((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/(7*d*x^7) + (4*e*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/(35*d^2*x^5) - (8*e^2*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/(105*d^3*x^3)","A",8,9,25,0.3600,1,"{271, 264, 2350, 12, 1265, 451, 277, 217, 206}"
263,1,231,0,0.2768489,"\int x^5 \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^5*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]),x]","\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^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{8 b d^{9/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{315 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}","\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^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{8 b d^{9/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{315 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,"(-8*b*d^4*n*Sqrt[d + e*x^2])/(315*e^3) - (8*b*d^3*n*(d + e*x^2)^(3/2))/(945*e^3) - (8*b*d^2*n*(d + e*x^2)^(5/2))/(1575*e^3) + (11*b*d*n*(d + e*x^2)^(7/2))/(441*e^3) - (b*n*(d + e*x^2)^(9/2))/(81*e^3) + (8*b*d^(9/2)*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(315*e^3) + (d^2*(d + e*x^2)^(5/2)*(a + b*Log[c*x^n]))/(5*e^3) - (2*d*(d + e*x^2)^(7/2)*(a + b*Log[c*x^n]))/(7*e^3) + ((d + e*x^2)^(9/2)*(a + b*Log[c*x^n]))/(9*e^3)","A",7,8,25,0.3200,1,"{266, 43, 2350, 12, 1251, 897, 1261, 208}"
264,1,177,0,0.2047168,"\int x^3 \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^3*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]),x]","-\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^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^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{35 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}","-\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^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^{7/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{35 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^3*n*Sqrt[d + e*x^2])/(35*e^2) + (2*b*d^2*n*(d + e*x^2)^(3/2))/(105*e^2) + (2*b*d*n*(d + e*x^2)^(5/2))/(175*e^2) - (b*n*(d + e*x^2)^(7/2))/(49*e^2) - (2*b*d^(7/2)*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(35*e^2) - (d*(d + e*x^2)^(5/2)*(a + b*Log[c*x^n]))/(5*e^2) + ((d + e*x^2)^(7/2)*(a + b*Log[c*x^n]))/(7*e^2)","A",9,9,25,0.3600,1,"{266, 43, 2350, 12, 446, 80, 50, 63, 208}"
265,1,125,0,0.1062745,"\int x \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]),x]","\frac{\left(d+e x^2\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 e}-\frac{b d^2 n \sqrt{d+e x^2}}{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 n \left(d+e x^2\right)^{3/2}}{15 e}-\frac{b n \left(d+e x^2\right)^{5/2}}{25 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^2 n \sqrt{d+e x^2}}{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 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,"-(b*d^2*n*Sqrt[d + e*x^2])/(5*e) - (b*d*n*(d + e*x^2)^(3/2))/(15*e) - (b*n*(d + e*x^2)^(5/2))/(25*e) + (b*d^(5/2)*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(5*e) + ((d + e*x^2)^(5/2)*(a + b*Log[c*x^n]))/(5*e)","A",7,5,23,0.2174,1,"{2338, 266, 50, 63, 208}"
266,1,260,0,0.3920619,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/x,x]","-\frac{1}{2} b d^{3/2} n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\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 \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}","-\frac{1}{2} b d^{3/2} n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\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 \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,"(-4*b*d*n*Sqrt[d + e*x^2])/3 - (b*n*(d + e*x^2)^(3/2))/9 + (4*b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/3 + (b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]^2)/2 + ((3*d*Sqrt[d + e*x^2] + (d + e*x^2)^(3/2) - 3*d^(3/2)*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])*(a + b*Log[c*x^n]))/3 - b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])] - (b*d^(3/2)*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/2","A",17,9,25,0.3600,1,"{266, 50, 63, 208, 2348, 5984, 5918, 2402, 2315}"
267,1,295,0,0.4417302,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/x^3,x]","-\frac{3}{4} b \sqrt{d} e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\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)-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)","-\frac{3}{4} b \sqrt{d} e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\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)-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]) - (b*d*n*Sqrt[d + e*x^2])/(4*x^2) + (3*b*Sqrt[d]*e*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/4 + (3*b*Sqrt[d]*e*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]^2)/4 + (3*e*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/2 - ((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/(2*x^2) - (3*Sqrt[d]*e*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]*(a + b*Log[c*x^n]))/2 - (3*b*Sqrt[d]*e*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/2 - (3*b*Sqrt[d]*e*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/4","A",18,12,25,0.4800,1,"{266, 47, 50, 63, 208, 2350, 12, 14, 5984, 5918, 2402, 2315}"
268,1,464,0,0.5927897,"\int x^2 \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]),x]","\frac{b d^{5/2} n \sqrt{d+e x^2} \text{PolyLog}\left(2,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{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} \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}","\frac{b d^{5/2} n \sqrt{d+e x^2} \text{PolyLog}\left(2,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{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} \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,"(-11*b*d^2*n*x*Sqrt[d + e*x^2])/(192*e) - (23*b*d*n*x^3*Sqrt[d + e*x^2])/288 - (b*e*n*x^5*Sqrt[d + e*x^2])/36 - (b*d^(5/2)*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])/(192*e^(3/2)*Sqrt[1 + (e*x^2)/d]) - (b*d^(5/2)*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]^2)/(32*e^(3/2)*Sqrt[1 + (e*x^2)/d]) + (b*d^(5/2)*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[1 - E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(16*e^(3/2)*Sqrt[1 + (e*x^2)/d]) + (d^2*x*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/(16*e) + (d*x^3*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/8 + (x^3*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/6 - (d^(5/2)*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(16*e^(3/2)*Sqrt[1 + (e*x^2)/d]) + (b*d^(5/2)*n*Sqrt[d + e*x^2]*PolyLog[2, E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(32*e^(3/2)*Sqrt[1 + (e*x^2)/d])","A",19,13,25,0.5200,1,"{2341, 279, 321, 215, 2350, 12, 14, 195, 5659, 3716, 2190, 2279, 2391}"
269,1,378,0,0.2690061,"\int \left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]),x]","-\frac{3 b d^{5/2} n \sqrt{\frac{e x^2}{d}+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{16 \sqrt{e} \sqrt{d+e x^2}}+\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} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{16 \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{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}{32} b d n x \sqrt{d+e x^2}-\frac{1}{16} b n x \left(d+e x^2\right)^{3/2}","-\frac{3 b d^{5/2} n \sqrt{\frac{e x^2}{d}+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{16 \sqrt{e} \sqrt{d+e x^2}}+\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} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{16 \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{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}{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,"(-9*b*d*n*x*Sqrt[d + e*x^2])/32 - (b*n*x*(d + e*x^2)^(3/2))/16 + (3*b*d^(5/2)*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]^2)/(16*Sqrt[e]*Sqrt[d + e*x^2]) - (9*b*d^2*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(32*Sqrt[e]) - (3*b*d^(5/2)*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[1 - E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(8*Sqrt[e]*Sqrt[d + e*x^2]) + (3*d*x*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/8 + (x*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/4 + (3*d^(5/2)*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(8*Sqrt[e]*Sqrt[d + e*x^2]) - (3*b*d^(5/2)*n*Sqrt[1 + (e*x^2)/d]*PolyLog[2, E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(16*Sqrt[e]*Sqrt[d + e*x^2])","A",16,11,22,0.5000,1,"{2321, 195, 217, 206, 2327, 2325, 5659, 3716, 2190, 2279, 2391}"
270,1,400,0,0.4806089,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/x^2,x]","-\frac{3 b \sqrt{d} \sqrt{e} n \sqrt{d+e x^2} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{4 \sqrt{\frac{e x^2}{d}+1}}-\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{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}}","-\frac{3 b \sqrt{d} \sqrt{e} n \sqrt{d+e x^2} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{4 \sqrt{\frac{e x^2}{d}+1}}-\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{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*d*n*Sqrt[d + e*x^2])/x) - (b*e*n*x*Sqrt[d + e*x^2])/4 + (3*b*Sqrt[d]*Sqrt[e]*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])/(4*Sqrt[1 + (e*x^2)/d]) + (3*b*Sqrt[d]*Sqrt[e]*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]^2)/(4*Sqrt[1 + (e*x^2)/d]) - (3*b*Sqrt[d]*Sqrt[e]*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[1 - E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(2*Sqrt[1 + (e*x^2)/d]) + (3*e*x*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/2 - ((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/x + (3*Sqrt[d]*Sqrt[e]*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(2*Sqrt[1 + (e*x^2)/d]) - (3*b*Sqrt[d]*Sqrt[e]*n*Sqrt[d + e*x^2]*PolyLog[2, E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(4*Sqrt[1 + (e*x^2)/d])","A",14,12,25,0.4800,1,"{2341, 277, 195, 215, 2350, 12, 14, 5659, 3716, 2190, 2279, 2391}"
271,1,400,0,0.4444246,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/x^4,x]","-\frac{b e^{3/2} n \sqrt{d+e x^2} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 \sqrt{d} \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{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{e \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{x}+\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{b n \left(d+e x^2\right)^{3/2}}{9 x^3}-\frac{4 b e n \sqrt{d+e x^2}}{3 x}","-\frac{b e^{3/2} n \sqrt{d+e x^2} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 \sqrt{d} \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{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{e \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{x}+\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{b n \left(d+e x^2\right)^{3/2}}{9 x^3}-\frac{4 b e n \sqrt{d+e x^2}}{3 x}",1,"(-4*b*e*n*Sqrt[d + e*x^2])/(3*x) - (b*n*(d + e*x^2)^(3/2))/(9*x^3) + (4*b*e^(3/2)*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])/(3*Sqrt[d]*Sqrt[1 + (e*x^2)/d]) + (b*e^(3/2)*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]^2)/(2*Sqrt[d]*Sqrt[1 + (e*x^2)/d]) - (b*e^(3/2)*n*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[1 - E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(Sqrt[d]*Sqrt[1 + (e*x^2)/d]) - (e*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/x - ((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/(3*x^3) + (e^(3/2)*Sqrt[d + e*x^2]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(Sqrt[d]*Sqrt[1 + (e*x^2)/d]) - (b*e^(3/2)*n*Sqrt[d + e*x^2]*PolyLog[2, E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(2*Sqrt[d]*Sqrt[1 + (e*x^2)/d])","A",11,10,25,0.4000,1,"{2341, 277, 215, 2350, 451, 5659, 3716, 2190, 2279, 2391}"
272,1,138,0,0.1219851,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/x^6,x]","-\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^2 n \sqrt{d+e x^2}}{5 d x}+\frac{b e^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{5 d}-\frac{b e n \left(d+e x^2\right)^{3/2}}{15 d x^3}-\frac{b n \left(d+e x^2\right)^{5/2}}{25 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^2 n \sqrt{d+e x^2}}{5 d x}+\frac{b e^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{5 d}-\frac{b e n \left(d+e x^2\right)^{3/2}}{15 d x^3}-\frac{b n \left(d+e x^2\right)^{5/2}}{25 d x^5}",1,"-(b*e^2*n*Sqrt[d + e*x^2])/(5*d*x) - (b*e*n*(d + e*x^2)^(3/2))/(15*d*x^3) - (b*n*(d + e*x^2)^(5/2))/(25*d*x^5) + (b*e^(5/2)*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(5*d) - ((d + e*x^2)^(5/2)*(a + b*Log[c*x^n]))/(5*d*x^5)","A",6,4,25,0.1600,1,"{2335, 277, 217, 206}"
273,1,196,0,0.1718825,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x^8} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/x^8,x]","\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^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{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 n \left(d+e x^2\right)^{5/2}}{175 d^2 x^5}-\frac{b n \left(d+e x^2\right)^{7/2}}{49 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^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{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 n \left(d+e x^2\right)^{5/2}}{175 d^2 x^5}-\frac{b n \left(d+e x^2\right)^{7/2}}{49 d^2 x^7}",1,"(2*b*e^3*n*Sqrt[d + e*x^2])/(35*d^2*x) + (2*b*e^2*n*(d + e*x^2)^(3/2))/(105*d^2*x^3) + (2*b*e*n*(d + e*x^2)^(5/2))/(175*d^2*x^5) - (b*n*(d + e*x^2)^(7/2))/(49*d^2*x^7) - (2*b*e^(7/2)*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(35*d^2) - ((d + e*x^2)^(5/2)*(a + b*Log[c*x^n]))/(7*d*x^7) + (2*e*(d + e*x^2)^(5/2)*(a + b*Log[c*x^n]))/(35*d^2*x^5)","A",8,8,25,0.3200,1,"{271, 264, 2350, 12, 451, 277, 217, 206}"
274,1,256,0,0.2205683,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x^{10}} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/x^10,x]","-\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^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{8 b e^{9/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{315 d^3}+\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}","-\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^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{8 b e^{9/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{315 d^3}+\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,"(-8*b*e^4*n*Sqrt[d + e*x^2])/(315*d^3*x) - (8*b*e^3*n*(d + e*x^2)^(3/2))/(945*d^3*x^3) - (8*b*e^2*n*(d + e*x^2)^(5/2))/(1575*d^3*x^5) - (b*n*(d + e*x^2)^(7/2))/(81*d^2*x^9) + (50*b*e*n*(d + e*x^2)^(7/2))/(3969*d^3*x^7) + (8*b*e^(9/2)*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(315*d^3) - ((d + e*x^2)^(5/2)*(a + b*Log[c*x^n]))/(9*d*x^9) + (4*e*(d + e*x^2)^(5/2)*(a + b*Log[c*x^n]))/(63*d^2*x^7) - (8*e^2*(d + e*x^2)^(5/2)*(a + b*Log[c*x^n]))/(315*d^3*x^5)","A",9,9,25,0.3600,1,"{271, 264, 2350, 12, 1265, 451, 277, 217, 206}"
275,1,60,0,0.0454512,"\int x \sqrt{4+x^2} \log (x) \, dx","Int[x*Sqrt[4 + x^2]*Log[x],x]","-\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)","-\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,"(-4*Sqrt[4 + x^2])/3 - (4 + x^2)^(3/2)/9 + (8*ArcTanh[Sqrt[4 + x^2]/2])/3 + ((4 + x^2)^(3/2)*Log[x])/3","A",6,5,13,0.3846,1,"{2338, 266, 50, 63, 207}"
276,1,182,0,0.2283031,"\int \frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x^5*(a + b*Log[c*x^n]))/Sqrt[d + e*x^2],x]","\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^2 n \sqrt{d+e x^2}}{15 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{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}","\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^2 n \sqrt{d+e x^2}}{15 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{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,"(-8*b*d^2*n*Sqrt[d + e*x^2])/(15*e^3) + (7*b*d*n*(d + e*x^2)^(3/2))/(45*e^3) - (b*n*(d + e*x^2)^(5/2))/(25*e^3) + (8*b*d^(5/2)*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(15*e^3) + (d^2*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/e^3 - (2*d*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/(3*e^3) + ((d + e*x^2)^(5/2)*(a + b*Log[c*x^n]))/(5*e^3)","A",7,8,25,0.3200,1,"{266, 43, 2350, 12, 1251, 897, 1261, 208}"
277,1,129,0,0.1643367,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/Sqrt[d + e*x^2],x]","-\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}","-\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,"(2*b*d*n*Sqrt[d + e*x^2])/(3*e^2) - (b*n*(d + e*x^2)^(3/2))/(9*e^2) - (2*b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(3*e^2) - (d*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/e^2 + ((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/(3*e^2)","A",7,9,25,0.3600,1,"{266, 43, 2350, 12, 446, 80, 50, 63, 208}"
278,1,73,0,0.0778711,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x*(a + b*Log[c*x^n]))/Sqrt[d + e*x^2],x]","\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}","\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,"-((b*n*Sqrt[d + e*x^2])/e) + (b*Sqrt[d]*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/e + (Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/e","A",5,5,23,0.2174,1,"{2338, 266, 50, 63, 208}"
279,1,166,0,0.2624488,"\int \frac{a+b \log \left(c x^n\right)}{x \sqrt{d+e x^2}} \, dx","Int[(a + b*Log[c*x^n])/(x*Sqrt[d + e*x^2]),x]","-\frac{b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right)}{2 \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 \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}}","-\frac{b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right)}{2 \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 \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*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]^2)/(2*Sqrt[d]) - (ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]*(a + b*Log[c*x^n]))/Sqrt[d] - (b*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/Sqrt[d] - (b*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/(2*Sqrt[d])","A",8,9,25,0.3600,1,"{266, 63, 208, 2348, 12, 5984, 5918, 2402, 2315}"
280,1,258,0,0.3727155,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \sqrt{d+e x^2}} \, dx","Int[(a + b*Log[c*x^n])/(x^3*Sqrt[d + e*x^2]),x]","\frac{b e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right)}{4 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 \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}","\frac{b e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right)}{4 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 \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[d + e*x^2])/(4*d*x^2) - (b*e*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(4*d^(3/2)) - (b*e*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]^2)/(4*d^(3/2)) - (Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/(2*d*x^2) + (e*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]*(a + b*Log[c*x^n]))/(2*d^(3/2)) + (b*e*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/(2*d^(3/2)) + (b*e*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/(4*d^(3/2))","A",14,12,25,0.4800,1,"{266, 51, 63, 208, 2350, 12, 14, 47, 5984, 5918, 2402, 2315}"
281,1,359,0,0.410335,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/Sqrt[d + e*x^2],x]","\frac{b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{4 e^{3/2} \sqrt{d+e x^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} \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}","\frac{b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{4 e^{3/2} \sqrt{d+e x^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} \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*x*Sqrt[d + e*x^2])/(4*e) - (b*d^(3/2)*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])/(4*e^(3/2)*Sqrt[d + e*x^2]) - (b*d^(3/2)*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]^2)/(4*e^(3/2)*Sqrt[d + e*x^2]) + (b*d^(3/2)*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[1 - E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(2*e^(3/2)*Sqrt[d + e*x^2]) + (x*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/(2*e) - (d^(3/2)*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(2*e^(3/2)*Sqrt[d + e*x^2]) + (b*d^(3/2)*n*Sqrt[1 + (e*x^2)/d]*PolyLog[2, E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(4*e^(3/2)*Sqrt[d + e*x^2])","A",12,12,25,0.4800,1,"{2341, 321, 215, 2350, 12, 14, 195, 5659, 3716, 2190, 2279, 2391}"
282,1,250,0,0.1390326,"\int \frac{a+b \log \left(c x^n\right)}{\sqrt{d+e x^2}} \, dx","Int[(a + b*Log[c*x^n])/Sqrt[d + e*x^2],x]","-\frac{b \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 \sqrt{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)}{\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}}","-\frac{b \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 \sqrt{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)}{\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,"(b*Sqrt[d]*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]^2)/(2*Sqrt[e]*Sqrt[d + e*x^2]) - (b*Sqrt[d]*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[1 - E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(Sqrt[e]*Sqrt[d + e*x^2]) + (Sqrt[d]*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(Sqrt[e]*Sqrt[d + e*x^2]) - (b*Sqrt[d]*n*Sqrt[1 + (e*x^2)/d]*PolyLog[2, E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(2*Sqrt[e]*Sqrt[d + e*x^2])","A",7,7,22,0.3182,1,"{2327, 2325, 5659, 3716, 2190, 2279, 2391}"
283,1,81,0,0.0910108,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \sqrt{d+e x^2}} \, dx","Int[(a + b*Log[c*x^n])/(x^2*Sqrt[d + e*x^2]),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}","-\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,"-((b*n*Sqrt[d + e*x^2])/(d*x)) + (b*Sqrt[e]*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/d - (Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/(d*x)","A",4,4,25,0.1600,1,"{2335, 277, 217, 206}"
284,1,144,0,0.1329699,"\int \frac{a+b \log \left(c x^n\right)}{x^4 \sqrt{d+e x^2}} \, dx","Int[(a + b*Log[c*x^n])/(x^4*Sqrt[d + e*x^2]),x]","\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}","\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,"(2*b*e*n*Sqrt[d + e*x^2])/(3*d^2*x) - (b*n*(d + e*x^2)^(3/2))/(9*d^2*x^3) - (2*b*e^(3/2)*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(3*d^2) - (Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/(3*d*x^3) + (2*e*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/(3*d^2*x)","A",6,8,25,0.3200,1,"{271, 264, 2350, 12, 451, 277, 217, 206}"
285,1,204,0,0.1773434,"\int \frac{a+b \log \left(c x^n\right)}{x^6 \sqrt{d+e x^2}} \, dx","Int[(a + b*Log[c*x^n])/(x^6*Sqrt[d + e*x^2]),x]","-\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^2 n \sqrt{d+e x^2}}{15 d^3 x}+\frac{8 b e^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{15 d^3}+\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}","-\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^2 n \sqrt{d+e x^2}}{15 d^3 x}+\frac{8 b e^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{15 d^3}+\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,"(-8*b*e^2*n*Sqrt[d + e*x^2])/(15*d^3*x) - (b*n*(d + e*x^2)^(3/2))/(25*d^2*x^5) + (26*b*e*n*(d + e*x^2)^(3/2))/(225*d^3*x^3) + (8*b*e^(5/2)*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(15*d^3) - (Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/(5*d*x^5) + (4*e*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/(15*d^2*x^3) - (8*e^2*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/(15*d^3*x)","A",7,9,25,0.3600,1,"{271, 264, 2350, 12, 1265, 451, 277, 217, 206}"
286,1,209,0,0.2958934,"\int \frac{x^7 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^7*(a + b*Log[c*x^n]))/(d + e*x^2)^(3/2),x]","\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{11 b d^2 n \sqrt{d+e x^2}}{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{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}","\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{11 b d^2 n \sqrt{d+e x^2}}{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{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,"(-11*b*d^2*n*Sqrt[d + e*x^2])/(5*e^4) + (4*b*d*n*(d + e*x^2)^(3/2))/(15*e^4) - (b*n*(d + e*x^2)^(5/2))/(25*e^4) + (16*b*d^(5/2)*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(5*e^4) + (d^3*(a + b*Log[c*x^n]))/(e^4*Sqrt[d + e*x^2]) + (3*d^2*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/e^4 - (d*(d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/e^4 + ((d + e*x^2)^(5/2)*(a + b*Log[c*x^n]))/(5*e^4)","A",7,8,25,0.3200,1,"{266, 43, 2350, 12, 1799, 1620, 63, 208}"
287,1,158,0,0.2180351,"\int \frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^5*(a + b*Log[c*x^n]))/(d + e*x^2)^(3/2),x]","-\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}","-\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,"(5*b*d*n*Sqrt[d + e*x^2])/(3*e^3) - (b*n*(d + e*x^2)^(3/2))/(9*e^3) - (8*b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(3*e^3) - (d^2*(a + b*Log[c*x^n]))/(e^3*Sqrt[d + e*x^2]) - (2*d*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/e^3 + ((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/(3*e^3)","A",7,8,25,0.3200,1,"{266, 43, 2350, 12, 1251, 897, 1153, 208}"
288,1,100,0,0.1600544,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/(d + e*x^2)^(3/2),x]","\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}","\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,"-((b*n*Sqrt[d + e*x^2])/e^2) + (2*b*Sqrt[d]*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/e^2 + (d*(a + b*Log[c*x^n]))/(e^2*Sqrt[d + e*x^2]) + (Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/e^2","A",6,8,25,0.3200,1,"{266, 43, 2350, 12, 446, 80, 63, 208}"
289,1,57,0,0.0778206,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x*(a + b*Log[c*x^n]))/(d + e*x^2)^(3/2),x]","-\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}","-\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,"-((b*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(Sqrt[d]*e)) - (a + b*Log[c*x^n])/(e*Sqrt[d + e*x^2])","A",4,4,23,0.1739,1,"{2338, 266, 63, 208}"
290,1,209,0,0.3339535,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x^2)^(3/2)),x]","-\frac{b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right)}{2 d^{3/2}}+\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 \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}}","-\frac{b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right)}{2 d^{3/2}}+\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 \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*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/d^(3/2) + (b*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]^2)/(2*d^(3/2)) + (1/(d*Sqrt[d + e*x^2]) - ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]/d^(3/2))*(a + b*Log[c*x^n]) - (b*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/d^(3/2) - (b*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/(2*d^(3/2))","A",11,9,25,0.3600,1,"{266, 51, 63, 208, 2348, 5984, 5918, 2402, 2315}"
291,1,286,0,0.3863552,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*Log[c*x^n])/(x^3*(d + e*x^2)^(3/2)),x]","\frac{3 b e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right)}{4 d^{5/2}}-\frac{3 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{2 d^2 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{a+b \log \left(c x^n\right)}{d x^2 \sqrt{d+e x^2}}-\frac{b n \sqrt{d+e x^2}}{4 d^2 x^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{3 b e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right)}{4 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{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{a+b \log \left(c x^n\right)}{2 d x^2 \sqrt{d+e x^2}}-\frac{b n \sqrt{d+e x^2}}{4 d^2 x^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}}",1,"-(b*n*Sqrt[d + e*x^2])/(4*d^2*x^2) - (5*b*e*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(4*d^(5/2)) - (3*b*e*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]^2)/(4*d^(5/2)) + (a + b*Log[c*x^n])/(d*x^2*Sqrt[d + e*x^2]) - (3*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/(2*d^2*x^2) + (3*e*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]*(a + b*Log[c*x^n]))/(2*d^(5/2)) + (3*b*e*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/(2*d^(5/2)) + (3*b*e*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/(4*d^(5/2))","A",12,11,25,0.4400,1,"{266, 51, 63, 208, 2350, 446, 78, 5984, 5918, 2402, 2315}"
292,1,328,0,0.4741715,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/(d + e*x^2)^(3/2),x]","-\frac{b \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 e^{3/2} \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} \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}}","-\frac{b \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 e^{3/2} \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} \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,"(b*Sqrt[d]*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])/(e^(3/2)*Sqrt[d + e*x^2]) + (b*Sqrt[d]*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]^2)/(2*e^(3/2)*Sqrt[d + e*x^2]) - (b*Sqrt[d]*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[1 - E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(e^(3/2)*Sqrt[d + e*x^2]) - (x*(a + b*Log[c*x^n]))/(e*Sqrt[d + e*x^2]) + (Sqrt[d]*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(e^(3/2)*Sqrt[d + e*x^2]) - (b*Sqrt[d]*n*Sqrt[1 + (e*x^2)/d]*PolyLog[2, E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(2*e^(3/2)*Sqrt[d + e*x^2])","A",11,11,25,0.4400,1,"{2341, 288, 215, 2350, 14, 21, 5659, 3716, 2190, 2279, 2391}"
293,1,58,0,0.0340499,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*Log[c*x^n])/(d + e*x^2)^(3/2),x]","\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}}","\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,"-((b*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(d*Sqrt[e])) + (x*(a + b*Log[c*x^n]))/(d*Sqrt[d + e*x^2])","A",3,3,22,0.1364,1,"{2314, 217, 206}"
294,1,110,0,0.1297014,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*Log[c*x^n])/(x^2*(d + e*x^2)^(3/2)),x]","-\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}","-\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,"-((b*n*Sqrt[d + e*x^2])/(d^2*x)) + (2*b*Sqrt[e]*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/d^2 - (a + b*Log[c*x^n])/(d*x*Sqrt[d + e*x^2]) - (2*e*x*(a + b*Log[c*x^n]))/(d^2*Sqrt[d + e*x^2])","A",5,7,25,0.2800,1,"{271, 191, 2350, 12, 451, 217, 206}"
295,1,176,0,0.1661273,"\int \frac{a+b \log \left(c x^n\right)}{x^4 \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*Log[c*x^n])/(x^4*(d + e*x^2)^(3/2)),x]","\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}","\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,"-(b*n*Sqrt[d + e*x^2])/(9*d^2*x^3) + (14*b*e*n*Sqrt[d + e*x^2])/(9*d^3*x) - (8*b*e^(3/2)*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(3*d^3) - (a + b*Log[c*x^n])/(3*d*x^3*Sqrt[d + e*x^2]) + (4*e*(a + b*Log[c*x^n]))/(3*d^2*x*Sqrt[d + e*x^2]) + (8*e^2*x*(a + b*Log[c*x^n]))/(3*d^3*Sqrt[d + e*x^2])","A",6,8,25,0.3200,1,"{271, 191, 2350, 12, 1265, 451, 217, 206}"
296,1,236,0,0.2703365,"\int \frac{a+b \log \left(c x^n\right)}{x^6 \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*Log[c*x^n])/(x^6*(d + e*x^2)^(3/2)),x]","-\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{148 b e^2 n \sqrt{d+e x^2}}{75 d^4 x}+\frac{16 b e^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{5 d^4}+\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}","-\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{148 b e^2 n \sqrt{d+e x^2}}{75 d^4 x}+\frac{16 b e^{5/2} n \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{5 d^4}+\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,"-(b*n*Sqrt[d + e*x^2])/(25*d^2*x^5) + (14*b*e*n*Sqrt[d + e*x^2])/(75*d^3*x^3) - (148*b*e^2*n*Sqrt[d + e*x^2])/(75*d^4*x) + (16*b*e^(5/2)*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(5*d^4) - (a + b*Log[c*x^n])/(5*d*x^5*Sqrt[d + e*x^2]) + (2*e*(a + b*Log[c*x^n]))/(5*d^2*x^3*Sqrt[d + e*x^2]) - (8*e^2*(a + b*Log[c*x^n]))/(5*d^3*x*Sqrt[d + e*x^2]) - (16*e^3*x*(a + b*Log[c*x^n]))/(5*d^4*Sqrt[d + e*x^2])","A",8,10,25,0.4000,1,"{271, 191, 2350, 12, 1807, 1585, 1265, 451, 217, 206}"
297,1,212,0,0.3237873,"\int \frac{x^7 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^7*(a + b*Log[c*x^n]))/(d + e*x^2)^(5/2),x]","\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{b d^2 n}{3 e^4 \sqrt{d+e x^2}}-\frac{16 b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{3 e^4}+\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}","\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{b d^2 n}{3 e^4 \sqrt{d+e x^2}}-\frac{16 b d^{3/2} n \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{3 e^4}+\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,"-(b*d^2*n)/(3*e^4*Sqrt[d + e*x^2]) + (8*b*d*n*Sqrt[d + e*x^2])/(3*e^4) - (b*n*(d + e*x^2)^(3/2))/(9*e^4) - (16*b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(3*e^4) + (d^3*(a + b*Log[c*x^n]))/(3*e^4*(d + e*x^2)^(3/2)) - (3*d^2*(a + b*Log[c*x^n]))/(e^4*Sqrt[d + e*x^2]) - (3*d*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/e^4 + ((d + e*x^2)^(3/2)*(a + b*Log[c*x^n]))/(3*e^4)","A",9,8,25,0.3200,1,"{266, 43, 2350, 12, 1799, 1619, 63, 208}"
298,1,155,0,0.2346363,"\int \frac{x^5 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^5*(a + b*Log[c*x^n]))/(d + e*x^2)^(5/2),x]","-\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}","-\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,"(b*d*n)/(3*e^3*Sqrt[d + e*x^2]) - (b*n*Sqrt[d + e*x^2])/e^3 + (8*b*Sqrt[d]*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(3*e^3) - (d^2*(a + b*Log[c*x^n]))/(3*e^3*(d + e*x^2)^(3/2)) + (2*d*(a + b*Log[c*x^n]))/(e^3*Sqrt[d + e*x^2]) + (Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/e^3","A",7,8,25,0.3200,1,"{266, 43, 2350, 12, 1251, 897, 1261, 206}"
299,1,108,0,0.1608312,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/(d + e*x^2)^(5/2),x]","-\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}","-\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,"-(b*n)/(3*e^2*Sqrt[d + e*x^2]) - (2*b*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(3*Sqrt[d]*e^2) + (d*(a + b*Log[c*x^n]))/(3*e^2*(d + e*x^2)^(3/2)) - (a + b*Log[c*x^n])/(e^2*Sqrt[d + e*x^2])","A",6,8,25,0.3200,1,"{266, 43, 2350, 12, 446, 78, 63, 208}"
300,1,84,0,0.0879107,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x*(a + b*Log[c*x^n]))/(d + e*x^2)^(5/2),x]","-\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}}","-\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,"(b*n)/(3*d*e*Sqrt[d + e*x^2]) - (b*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(3*d^(3/2)*e) - (a + b*Log[c*x^n])/(3*e*(d + e*x^2)^(3/2))","A",5,5,23,0.2174,1,"{2338, 266, 51, 63, 208}"
301,1,251,0,0.4038805,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x^2)^(5/2)),x]","-\frac{b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right)}{2 d^{5/2}}+\frac{1}{3} \left(\frac{3}{d^2 \sqrt{d+e x^2}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{d^{5/2}}+\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}{3 d^2 \sqrt{d+e x^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 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right)}{2 d^{5/2}}+\frac{1}{3} \left(\frac{3}{d^2 \sqrt{d+e x^2}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{d^{5/2}}+\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}{3 d^2 \sqrt{d+e x^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}}",1,"-(b*n)/(3*d^2*Sqrt[d + e*x^2]) + (4*b*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(3*d^(5/2)) + (b*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]^2)/(2*d^(5/2)) + ((1/(d*(d + e*x^2)^(3/2)) + 3/(d^2*Sqrt[d + e*x^2]) - (3*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/d^(5/2))*(a + b*Log[c*x^n]))/3 - (b*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/d^(5/2) - (b*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/(2*d^(5/2))","A",15,9,25,0.3600,1,"{266, 51, 63, 208, 2348, 5984, 5918, 2402, 2315}"
302,1,341,0,0.4877473,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*Log[c*x^n])/(x^3*(d + e*x^2)^(5/2)),x]","\frac{5 b e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right)}{4 d^{7/2}}-\frac{5 \sqrt{d+e x^2} \left(a+b \log \left(c x^n\right)\right)}{2 d^3 x^2}+\frac{5 \left(a+b \log \left(c x^n\right)\right)}{3 d^2 x^2 \sqrt{d+e x^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{a+b \log \left(c x^n\right)}{3 d x^2 \left(d+e x^2\right)^{3/2}}-\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}}-\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{5 b e n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^2}}\right)}{4 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{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{a+b \log \left(c x^n\right)}{2 d x^2 \left(d+e x^2\right)^{3/2}}-\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}}-\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}}",1,"(b*e*n)/(3*d^3*Sqrt[d + e*x^2]) - (b*n*Sqrt[d + e*x^2])/(4*d^3*x^2) - (31*b*e*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(12*d^(7/2)) - (5*b*e*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]^2)/(4*d^(7/2)) + (a + b*Log[c*x^n])/(3*d*x^2*(d + e*x^2)^(3/2)) + (5*(a + b*Log[c*x^n]))/(3*d^2*x^2*Sqrt[d + e*x^2]) - (5*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/(2*d^3*x^2) + (5*e*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]*(a + b*Log[c*x^n]))/(2*d^(7/2)) + (5*b*e*n*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/(2*d^(7/2)) + (5*b*e*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^2])])/(4*d^(7/2))","A",13,13,25,0.5200,1,"{266, 51, 63, 208, 2350, 1251, 897, 1259, 453, 5984, 5918, 2402, 2315}"
303,1,443,0,0.5393441,"\int \frac{x^6 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^6*(a + b*Log[c*x^n]))/(d + e*x^2)^(5/2),x]","\frac{5 b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{4 e^{7/2} \sqrt{d+e x^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^3 \left(a+b \log \left(c x^n\right)\right)}{3 e^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{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} \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}}","\frac{5 b d^{3/2} n \sqrt{\frac{e x^2}{d}+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{4 e^{7/2} \sqrt{d+e x^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^3 \left(a+b \log \left(c x^n\right)\right)}{3 e^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{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} \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*d*n*x)/(3*e^3*Sqrt[d + e*x^2]) - (b*n*x*Sqrt[d + e*x^2])/(4*e^3) - (31*b*d^(3/2)*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])/(12*e^(7/2)*Sqrt[d + e*x^2]) - (5*b*d^(3/2)*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]^2)/(4*e^(7/2)*Sqrt[d + e*x^2]) + (5*b*d^(3/2)*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[1 - E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(2*e^(7/2)*Sqrt[d + e*x^2]) - (x^5*(a + b*Log[c*x^n]))/(3*e*(d + e*x^2)^(3/2)) - (5*x^3*(a + b*Log[c*x^n]))/(3*e^2*Sqrt[d + e*x^2]) + (5*x*Sqrt[d + e*x^2]*(a + b*Log[c*x^n]))/(2*e^3) - (5*d^(3/2)*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(2*e^(7/2)*Sqrt[d + e*x^2]) + (5*b*d^(3/2)*n*Sqrt[1 + (e*x^2)/d]*PolyLog[2, E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(4*e^(7/2)*Sqrt[d + e*x^2])","A",12,13,25,0.5200,1,"{2341, 288, 321, 215, 2350, 21, 1157, 388, 5659, 3716, 2190, 2279, 2391}"
304,1,383,0,0.5567505,"\int \frac{x^4 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^4*(a + b*Log[c*x^n]))/(d + e*x^2)^(5/2),x]","-\frac{b \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 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{\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^3 \left(a+b \log \left(c x^n\right)\right)}{3 e \left(d+e x^2\right)^{3/2}}-\frac{b n x}{3 e^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 \sqrt{d} n \sqrt{\frac{e x^2}{d}+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 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{\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^3 \left(a+b \log \left(c x^n\right)\right)}{3 e \left(d+e x^2\right)^{3/2}}-\frac{b n x}{3 e^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}}",1,"-(b*n*x)/(3*e^2*Sqrt[d + e*x^2]) + (4*b*Sqrt[d]*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])/(3*e^(5/2)*Sqrt[d + e*x^2]) + (b*Sqrt[d]*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]^2)/(2*e^(5/2)*Sqrt[d + e*x^2]) - (b*Sqrt[d]*n*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[1 - E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(e^(5/2)*Sqrt[d + e*x^2]) - (x^3*(a + b*Log[c*x^n]))/(3*e*(d + e*x^2)^(3/2)) - (x*(a + b*Log[c*x^n]))/(e^2*Sqrt[d + e*x^2]) + (Sqrt[d]*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*(a + b*Log[c*x^n]))/(e^(5/2)*Sqrt[d + e*x^2]) - (b*Sqrt[d]*n*Sqrt[1 + (e*x^2)/d]*PolyLog[2, E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(2*e^(5/2)*Sqrt[d + e*x^2])","A",11,11,25,0.4400,1,"{2341, 288, 215, 2350, 21, 385, 5659, 3716, 2190, 2279, 2391}"
305,1,89,0,0.1088277,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/(d + e*x^2)^(5/2),x]","\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}}","\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,"(b*n*x)/(3*d*e*Sqrt[d + e*x^2]) - (b*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(3*d*e^(3/2)) + (x^3*(a + b*Log[c*x^n]))/(3*d*(d + e*x^2)^(3/2))","A",4,4,25,0.1600,1,"{2335, 288, 217, 206}"
306,1,113,0,0.0694104,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*Log[c*x^n])/(d + e*x^2)^(5/2),x]","\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}}","\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,"-(b*n*x)/(3*d^2*Sqrt[d + e*x^2]) - (2*b*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(3*d^2*Sqrt[e]) + (x*(a + b*Log[c*x^n]))/(3*d*(d + e*x^2)^(3/2)) + (2*x*(a + b*Log[c*x^n]))/(3*d^2*Sqrt[d + e*x^2])","A",5,5,22,0.2273,1,"{2323, 2314, 217, 206, 191}"
307,1,166,0,0.1686635,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*Log[c*x^n])/(x^2*(d + e*x^2)^(5/2)),x]","-\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{b n}{d^2 x \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{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{b n}{d^2 x \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}",1,"-((b*n)/(d^2*x*Sqrt[d + e*x^2])) - (2*b*e*n*x)/(3*d^3*Sqrt[d + e*x^2]) + (8*b*Sqrt[e]*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(3*d^3) - (a + b*Log[c*x^n])/(d*x*(d + e*x^2)^(3/2)) - (4*e*x*(a + b*Log[c*x^n]))/(3*d^2*(d + e*x^2)^(3/2)) - (8*e*x*(a + b*Log[c*x^n]))/(3*d^3*Sqrt[d + e*x^2])","A",6,9,25,0.3600,1,"{271, 192, 191, 2350, 12, 1265, 385, 217, 206}"
308,1,230,0,0.2588898,"\int \frac{a+b \log \left(c x^n\right)}{x^4 \left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*Log[c*x^n])/(x^4*(d + e*x^2)^(5/2)),x]","\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{b e^2 n x}{3 d^4 \sqrt{d+e x^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{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}","\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{b e^2 n x}{3 d^4 \sqrt{d+e x^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{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,"-(b*e^2*n*x)/(3*d^4*Sqrt[d + e*x^2]) - (b*n*Sqrt[d + e*x^2])/(9*d^3*x^3) + (23*b*e*n*Sqrt[d + e*x^2])/(9*d^4*x) - (16*b*e^(3/2)*n*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(3*d^4) - (a + b*Log[c*x^n])/(3*d*x^3*(d + e*x^2)^(3/2)) + (2*e*(a + b*Log[c*x^n]))/(d^2*x*(d + e*x^2)^(3/2)) + (8*e^2*x*(a + b*Log[c*x^n]))/(3*d^3*(d + e*x^2)^(3/2)) + (16*e^2*x*(a + b*Log[c*x^n]))/(3*d^4*Sqrt[d + e*x^2])","A",7,10,25,0.4000,1,"{271, 192, 191, 2350, 12, 1805, 1265, 451, 217, 206}"
309,1,251,0,0.5197581,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/(Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\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}}","-\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,"(2*b*d^2*n*(d^2 - e^2*x^2))/(3*e^4*Sqrt[d - e*x]*Sqrt[d + e*x]) - (b*n*(d^2 - e^2*x^2)^2)/(9*e^4*Sqrt[d - e*x]*Sqrt[d + e*x]) - (2*b*d^4*n*Sqrt[1 - (e^2*x^2)/d^2]*ArcTanh[Sqrt[1 - (e^2*x^2)/d^2]])/(3*e^4*Sqrt[d - e*x]*Sqrt[d + e*x]) - (d^2*(d^2 - e^2*x^2)*(a + b*Log[c*x^n]))/(e^4*Sqrt[d - e*x]*Sqrt[d + e*x]) + ((d^2 - e^2*x^2)^2*(a + b*Log[c*x^n]))/(3*e^4*Sqrt[d - e*x]*Sqrt[d + e*x])","A",8,10,33,0.3030,1,"{2342, 266, 43, 2350, 12, 446, 80, 50, 63, 208}"
310,1,148,0,0.2959291,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(x*(a + b*Log[c*x^n]))/(Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\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}}","-\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*n*(d^2 - e^2*x^2))/(e^2*Sqrt[d - e*x]*Sqrt[d + e*x]) - (b*d^2*n*Sqrt[1 - (e^2*x^2)/d^2]*ArcTanh[Sqrt[1 - (e^2*x^2)/d^2]])/(e^2*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((d^2 - e^2*x^2)*(a + b*Log[c*x^n]))/(e^2*Sqrt[d - e*x]*Sqrt[d + e*x])","A",6,6,31,0.1935,1,"{2342, 2338, 266, 50, 63, 208}"
311,1,301,0,0.6048638,"\int \frac{a+b \log \left(c x^n\right)}{x \sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(a + b*Log[c*x^n])/(x*Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{b n \sqrt{1-\frac{e^2 x^2}{d^2}} \text{PolyLog}\left(2,-\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{\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}} \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}}","-\frac{b n \sqrt{1-\frac{e^2 x^2}{d^2}} \text{PolyLog}\left(2,-\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{\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}} \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,"(b*n*Sqrt[1 - (e^2*x^2)/d^2]*ArcTanh[Sqrt[1 - (e^2*x^2)/d^2]]^2)/(2*Sqrt[d - e*x]*Sqrt[d + e*x]) - (Sqrt[1 - (e^2*x^2)/d^2]*ArcTanh[Sqrt[1 - (e^2*x^2)/d^2]]*(a + b*Log[c*x^n]))/(Sqrt[d - e*x]*Sqrt[d + e*x]) - (b*n*Sqrt[1 - (e^2*x^2)/d^2]*ArcTanh[Sqrt[1 - (e^2*x^2)/d^2]]*Log[2/(1 - Sqrt[1 - (e^2*x^2)/d^2])])/(Sqrt[d - e*x]*Sqrt[d + e*x]) - (b*n*Sqrt[1 - (e^2*x^2)/d^2]*PolyLog[2, -((1 + Sqrt[1 - (e^2*x^2)/d^2])/(1 - Sqrt[1 - (e^2*x^2)/d^2]))])/(2*Sqrt[d - e*x]*Sqrt[d + e*x])","A",8,9,33,0.2727,1,"{2342, 266, 63, 208, 2348, 5984, 5918, 2402, 2315}"
312,1,489,0,0.7243495,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(a + b*Log[c*x^n])/(x^3*Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{b e^2 n \sqrt{1-\frac{e^2 x^2}{d^2}} \text{PolyLog}\left(2,-\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{\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 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}}","-\frac{b e^2 n \sqrt{1-\frac{e^2 x^2}{d^2}} \text{PolyLog}\left(2,-\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{\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 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))/(4*d^2*x^2*Sqrt[d - e*x]*Sqrt[d + e*x]) + (b*e^2*n*Sqrt[1 - (e^2*x^2)/d^2]*ArcTanh[Sqrt[1 - (e^2*x^2)/d^2]])/(4*d^2*Sqrt[d - e*x]*Sqrt[d + e*x]) + (b*e^2*n*Sqrt[1 - (e^2*x^2)/d^2]*ArcTanh[Sqrt[1 - (e^2*x^2)/d^2]]^2)/(4*d^2*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((d^2 - e^2*x^2)*(a + b*Log[c*x^n]))/(2*d^2*x^2*Sqrt[d - e*x]*Sqrt[d + e*x]) - (e^2*Sqrt[1 - (e^2*x^2)/d^2]*ArcTanh[Sqrt[1 - (e^2*x^2)/d^2]]*(a + b*Log[c*x^n]))/(2*d^2*Sqrt[d - e*x]*Sqrt[d + e*x]) - (b*e^2*n*Sqrt[1 - (e^2*x^2)/d^2]*ArcTanh[Sqrt[1 - (e^2*x^2)/d^2]]*Log[2/(1 - Sqrt[1 - (e^2*x^2)/d^2])])/(2*d^2*Sqrt[d - e*x]*Sqrt[d + e*x]) - (b*e^2*n*Sqrt[1 - (e^2*x^2)/d^2]*PolyLog[2, -((1 + Sqrt[1 - (e^2*x^2)/d^2])/(1 - Sqrt[1 - (e^2*x^2)/d^2]))])/(4*d^2*Sqrt[d - e*x]*Sqrt[d + e*x])","A",13,11,33,0.3333,1,"{2342, 266, 51, 63, 208, 2350, 47, 5984, 5918, 2402, 2315}"
313,1,406,0,0.6121821,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/(Sqrt[d - e*x]*Sqrt[d + e*x]),x]","\frac{i b d^3 n \sqrt{1-\frac{e^2 x^2}{d^2}} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(\frac{e x}{d}\right)}\right)}{4 e^3 \sqrt{d-e x} \sqrt{d+e x}}-\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}} \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}}","\frac{i b d^3 n \sqrt{1-\frac{e^2 x^2}{d^2}} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(\frac{e x}{d}\right)}\right)}{4 e^3 \sqrt{d-e x} \sqrt{d+e x}}-\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}} \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,"(b*n*x*(d^2 - e^2*x^2))/(4*e^2*Sqrt[d - e*x]*Sqrt[d + e*x]) + (b*d^3*n*Sqrt[1 - (e^2*x^2)/d^2]*ArcSin[(e*x)/d])/(4*e^3*Sqrt[d - e*x]*Sqrt[d + e*x]) + ((I/4)*b*d^3*n*Sqrt[1 - (e^2*x^2)/d^2]*ArcSin[(e*x)/d]^2)/(e^3*Sqrt[d - e*x]*Sqrt[d + e*x]) - (b*d^3*n*Sqrt[1 - (e^2*x^2)/d^2]*ArcSin[(e*x)/d]*Log[1 - E^((2*I)*ArcSin[(e*x)/d])])/(2*e^3*Sqrt[d - e*x]*Sqrt[d + e*x]) - (x*(d^2 - e^2*x^2)*(a + b*Log[c*x^n]))/(2*e^2*Sqrt[d - e*x]*Sqrt[d + e*x]) + (d^3*Sqrt[1 - (e^2*x^2)/d^2]*ArcSin[(e*x)/d]*(a + b*Log[c*x^n]))/(2*e^3*Sqrt[d - e*x]*Sqrt[d + e*x]) + ((I/4)*b*d^3*n*Sqrt[1 - (e^2*x^2)/d^2]*PolyLog[2, E^((2*I)*ArcSin[(e*x)/d])])/(e^3*Sqrt[d - e*x]*Sqrt[d + e*x])","A",12,12,33,0.3636,1,"{2342, 321, 216, 2350, 12, 14, 195, 4625, 3717, 2190, 2279, 2391}"
314,1,248,0,0.216421,"\int \frac{a+b \log \left(c x^n\right)}{\sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(a + b*Log[c*x^n])/(Sqrt[d - e*x]*Sqrt[d + e*x]),x]","\frac{i b d n \sqrt{1-\frac{e^2 x^2}{d^2}} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(\frac{e x}{d}\right)}\right)}{2 e \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}} \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}}","\frac{i b d n \sqrt{1-\frac{e^2 x^2}{d^2}} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(\frac{e x}{d}\right)}\right)}{2 e \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}} \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,"((I/2)*b*d*n*Sqrt[1 - (e^2*x^2)/d^2]*ArcSin[(e*x)/d]^2)/(e*Sqrt[d - e*x]*Sqrt[d + e*x]) - (b*d*n*Sqrt[1 - (e^2*x^2)/d^2]*ArcSin[(e*x)/d]*Log[1 - E^((2*I)*ArcSin[(e*x)/d])])/(e*Sqrt[d - e*x]*Sqrt[d + e*x]) + (d*Sqrt[1 - (e^2*x^2)/d^2]*ArcSin[(e*x)/d]*(a + b*Log[c*x^n]))/(e*Sqrt[d - e*x]*Sqrt[d + e*x]) + ((I/2)*b*d*n*Sqrt[1 - (e^2*x^2)/d^2]*PolyLog[2, E^((2*I)*ArcSin[(e*x)/d])])/(e*Sqrt[d - e*x]*Sqrt[d + e*x])","A",7,7,30,0.2333,1,"{2328, 2326, 4625, 3717, 2190, 2279, 2391}"
315,1,142,0,0.399996,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(a + b*Log[c*x^n])/(x^2*Sqrt[d - e*x]*Sqrt[d + e*x]),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}}","-\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*n*(d^2 - e^2*x^2))/(d^2*x*Sqrt[d - e*x]*Sqrt[d + e*x])) - (b*e*n*Sqrt[1 - (e^2*x^2)/d^2]*ArcSin[(e*x)/d])/(d*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((d^2 - e^2*x^2)*(a + b*Log[c*x^n]))/(d^2*x*Sqrt[d - e*x]*Sqrt[d + e*x])","A",4,4,33,0.1212,1,"{2342, 2335, 277, 216}"
316,1,252,0,0.475077,"\int \frac{a+b \log \left(c x^n\right)}{x^4 \sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(a + b*Log[c*x^n])/(x^4*Sqrt[d - e*x]*Sqrt[d + e*x]),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{\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 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}}","-\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{\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 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,"(-2*b*e^2*n*(d^2 - e^2*x^2))/(3*d^4*x*Sqrt[d - e*x]*Sqrt[d + e*x]) - (b*n*(d^2 - e^2*x^2)^2)/(9*d^4*x^3*Sqrt[d - e*x]*Sqrt[d + e*x]) - (2*b*e^3*n*Sqrt[1 - (e^2*x^2)/d^2]*ArcSin[(e*x)/d])/(3*d^3*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((d^2 - e^2*x^2)*(a + b*Log[c*x^n]))/(3*d^2*x^3*Sqrt[d - e*x]*Sqrt[d + e*x]) - (2*e^2*(d^2 - e^2*x^2)*(a + b*Log[c*x^n]))/(3*d^4*x*Sqrt[d - e*x]*Sqrt[d + e*x])","A",6,8,33,0.2424,1,"{2342, 271, 264, 2350, 12, 451, 277, 216}"
317,1,34,0,0.0397769,"\int \frac{x \log (x)}{\sqrt{-1+x^2}} \, dx","Int[(x*Log[x])/Sqrt[-1 + x^2],x]","-\sqrt{x^2-1}+\sqrt{x^2-1} \log (x)+\tan ^{-1}\left(\sqrt{x^2-1}\right)","-\sqrt{x^2-1}+\sqrt{x^2-1} \log (x)+\tan ^{-1}\left(\sqrt{x^2-1}\right)",1,"-Sqrt[-1 + x^2] + ArcTan[Sqrt[-1 + x^2]] + Sqrt[-1 + x^2]*Log[x]","A",5,5,13,0.3846,1,"{2338, 266, 50, 63, 203}"
318,1,211,0,1.6840972,"\int (f x)^m \left(d+e x^2\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^3*(a + b*Log[c*x^n]),x]","\frac{3 d^2 e (f x)^{m+3} \left(a+b \log \left(c x^n\right)\right)}{f^3 (m+3)}+\frac{d^3 (f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+1)}+\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{3 b d^2 e n (f x)^{m+3}}{f^3 (m+3)^2}-\frac{b d^3 n (f x)^{m+1}}{f (m+1)^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}","\frac{3 d^2 e (f x)^{m+3} \left(a+b \log \left(c x^n\right)\right)}{f^3 (m+3)}+\frac{d^3 (f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+1)}+\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{3 b d^2 e n (f x)^{m+3}}{f^3 (m+3)^2}-\frac{b d^3 n (f x)^{m+1}}{f (m+1)^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,"-((b*d^3*n*(f*x)^(1 + m))/(f*(1 + m)^2)) - (3*b*d^2*e*n*(f*x)^(3 + m))/(f^3*(3 + m)^2) - (3*b*d*e^2*n*(f*x)^(5 + m))/(f^5*(5 + m)^2) - (b*e^3*n*(f*x)^(7 + m))/(f^7*(7 + m)^2) + (d^3*(f*x)^(1 + m)*(a + b*Log[c*x^n]))/(f*(1 + m)) + (3*d^2*e*(f*x)^(3 + m)*(a + b*Log[c*x^n]))/(f^3*(3 + m)) + (3*d*e^2*(f*x)^(5 + m)*(a + b*Log[c*x^n]))/(f^5*(5 + m)) + (e^3*(f*x)^(7 + m)*(a + b*Log[c*x^n]))/(f^7*(7 + m))","A",3,3,25,0.1200,1,"{270, 2350, 14}"
319,1,153,0,0.1799935,"\int (f x)^m \left(d+e x^2\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^2*(a + b*Log[c*x^n]),x]","\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}","\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,"-((b*d^2*n*(f*x)^(1 + m))/(f*(1 + m)^2)) - (2*b*d*e*n*(f*x)^(3 + m))/(f^3*(3 + m)^2) - (b*e^2*n*(f*x)^(5 + m))/(f^5*(5 + m)^2) + (d^2*(f*x)^(1 + m)*(a + b*Log[c*x^n]))/(f*(1 + m)) + (2*d*e*(f*x)^(3 + m)*(a + b*Log[c*x^n]))/(f^3*(3 + m)) + (e^2*(f*x)^(5 + m)*(a + b*Log[c*x^n]))/(f^5*(5 + m))","A",4,4,25,0.1600,1,"{270, 2350, 12, 14}"
320,1,95,0,0.085458,"\int (f x)^m \left(d+e x^2\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(f*x)^m*(d + e*x^2)*(a + b*Log[c*x^n]),x]","\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}","\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,"-((b*d*n*(f*x)^(1 + m))/(f*(1 + m)^2)) - (b*e*n*(f*x)^(3 + m))/(f^3*(3 + m)^2) + (d*(f*x)^(1 + m)*(a + b*Log[c*x^n]))/(f*(1 + m)) + (e*(f*x)^(3 + m)*(a + b*Log[c*x^n]))/(f^3*(3 + m))","A",3,2,23,0.08696,1,"{14, 2350}"
321,1,46,0,0.0165448,"\int (f x)^m \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(f*x)^m*(a + b*Log[c*x^n]),x]","\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}","\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,"-((b*n*(f*x)^(1 + m))/(f*(1 + m)^2)) + ((f*x)^(1 + m)*(a + b*Log[c*x^n]))/(f*(1 + m))","A",1,1,16,0.06250,1,"{2304}"
322,0,0,0,0.067045,"\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{d+e x^2} \, dx","Int[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x^2),x]","\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{d+e x^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{d+e x^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x^2), x]","A",0,0,0,0,-1,"{}"
323,0,0,0,0.0643994,"\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^2} \, dx","Int[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x^2)^2,x]","\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^2\right)^2} \, dx","\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,"Defer[Int][((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x^2)^2, x]","A",0,0,0,0,-1,"{}"
324,1,1198,0,1.4349754,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3}{\left(d+e x^3\right)^2} \, dx","Int[(a + b*Log[c*x^n])^3/(d + e*x^3)^2,x]","\frac{2 b^3 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,\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{PolyLog}\left(4,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,\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{PolyLog}\left(3,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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}}","\frac{2 b^3 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,\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{PolyLog}\left(4,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,\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{PolyLog}\left(3,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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*Log[c*x^n])^3)/(9*d^(5/3)*(d^(1/3) + e^(1/3)*x)) - ((-1)^(1/3)*x*(a + b*Log[c*x^n])^3)/((1 + (-1)^(1/3))^4*d^(5/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x)) + (x*(a + b*Log[c*x^n])^3)/(9*d^(5/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)) - (b*n*(a + b*Log[c*x^n])^2*Log[1 + (e^(1/3)*x)/d^(1/3)])/(3*d^(5/3)*e^(1/3)) + (2*(a + b*Log[c*x^n])^3*Log[1 + (e^(1/3)*x)/d^(1/3)])/(9*d^(5/3)*e^(1/3)) + (3*(-1)^(1/3)*b*n*(a + b*Log[c*x^n])^2*Log[1 - ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^4*d^(5/3)*e^(1/3)) - ((2*I)*Sqrt[3]*(a + b*Log[c*x^n])^3*Log[1 - ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^5*d^(5/3)*e^(1/3)) + ((-1)^(1/3)*b*n*(a + b*Log[c*x^n])^2*Log[1 + ((-1)^(2/3)*e^(1/3)*x)/d^(1/3)])/(3*d^(5/3)*e^(1/3)) + (2*(a + b*Log[c*x^n])^3*Log[1 + ((-1)^(2/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^4*d^(5/3)*e^(1/3)) - (2*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((e^(1/3)*x)/d^(1/3))])/(3*d^(5/3)*e^(1/3)) + (2*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((e^(1/3)*x)/d^(1/3))])/(3*d^(5/3)*e^(1/3)) + (6*(-1)^(1/3)*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^4*d^(5/3)*e^(1/3)) - ((6*I)*Sqrt[3]*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^5*d^(5/3)*e^(1/3)) + (2*(-1)^(1/3)*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))])/(3*d^(5/3)*e^(1/3)) + (6*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))])/((1 + (-1)^(1/3))^4*d^(5/3)*e^(1/3)) + (2*b^3*n^3*PolyLog[3, -((e^(1/3)*x)/d^(1/3))])/(3*d^(5/3)*e^(1/3)) - (4*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((e^(1/3)*x)/d^(1/3))])/(3*d^(5/3)*e^(1/3)) - (6*(-1)^(1/3)*b^3*n^3*PolyLog[3, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^4*d^(5/3)*e^(1/3)) + ((12*I)*Sqrt[3]*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^5*d^(5/3)*e^(1/3)) - (2*(-1)^(1/3)*b^3*n^3*PolyLog[3, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))])/(3*d^(5/3)*e^(1/3)) - (12*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))])/((1 + (-1)^(1/3))^4*d^(5/3)*e^(1/3)) + (4*b^3*n^3*PolyLog[4, -((e^(1/3)*x)/d^(1/3))])/(3*d^(5/3)*e^(1/3)) - ((12*I)*Sqrt[3]*b^3*n^3*PolyLog[4, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^5*d^(5/3)*e^(1/3)) + (12*b^3*n^3*PolyLog[4, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))])/((1 + (-1)^(1/3))^4*d^(5/3)*e^(1/3))","A",26,6,22,0.2727,1,"{2330, 2318, 2317, 2374, 6589, 2383}"
325,1,860,0,0.7710238,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{\left(d+e x^3\right)^2} \, dx","Int[(a + b*Log[c*x^n])^2/(d + e*x^3)^2,x]","-\frac{2 b^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,\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{PolyLog}\left(3,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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}}","-\frac{2 b^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,\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{PolyLog}\left(3,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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*Log[c*x^n])^2)/(9*d^(5/3)*(d^(1/3) + e^(1/3)*x)) - ((-1)^(1/3)*x*(a + b*Log[c*x^n])^2)/((1 + (-1)^(1/3))^4*d^(5/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x)) + (x*(a + b*Log[c*x^n])^2)/(9*d^(5/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)) - (2*b*n*(a + b*Log[c*x^n])*Log[1 + (e^(1/3)*x)/d^(1/3)])/(9*d^(5/3)*e^(1/3)) + (2*(a + b*Log[c*x^n])^2*Log[1 + (e^(1/3)*x)/d^(1/3)])/(9*d^(5/3)*e^(1/3)) + (2*(-1)^(1/3)*b*n*(a + b*Log[c*x^n])*Log[1 - ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^4*d^(5/3)*e^(1/3)) - ((2*I)*Sqrt[3]*(a + b*Log[c*x^n])^2*Log[1 - ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^5*d^(5/3)*e^(1/3)) + (2*(-1)^(1/3)*b*n*(a + b*Log[c*x^n])*Log[1 + ((-1)^(2/3)*e^(1/3)*x)/d^(1/3)])/(9*d^(5/3)*e^(1/3)) + (2*(a + b*Log[c*x^n])^2*Log[1 + ((-1)^(2/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^4*d^(5/3)*e^(1/3)) - (2*b^2*n^2*PolyLog[2, -((e^(1/3)*x)/d^(1/3))])/(9*d^(5/3)*e^(1/3)) + (4*b*n*(a + b*Log[c*x^n])*PolyLog[2, -((e^(1/3)*x)/d^(1/3))])/(9*d^(5/3)*e^(1/3)) + (2*(-1)^(1/3)*b^2*n^2*PolyLog[2, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^4*d^(5/3)*e^(1/3)) - ((4*I)*Sqrt[3]*b*n*(a + b*Log[c*x^n])*PolyLog[2, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^5*d^(5/3)*e^(1/3)) + (2*(-1)^(1/3)*b^2*n^2*PolyLog[2, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))])/(9*d^(5/3)*e^(1/3)) + (4*b*n*(a + b*Log[c*x^n])*PolyLog[2, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))])/((1 + (-1)^(1/3))^4*d^(5/3)*e^(1/3)) - (4*b^2*n^2*PolyLog[3, -((e^(1/3)*x)/d^(1/3))])/(9*d^(5/3)*e^(1/3)) + ((4*I)*Sqrt[3]*b^2*n^2*PolyLog[3, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^5*d^(5/3)*e^(1/3)) - (4*b^2*n^2*PolyLog[3, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))])/((1 + (-1)^(1/3))^4*d^(5/3)*e^(1/3))","A",20,6,22,0.2727,1,"{2330, 2318, 2317, 2391, 2374, 6589}"
326,1,520,0,0.4571301,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+e x^3\right)^2} \, dx","Int[(a + b*Log[c*x^n])/(d + e*x^3)^2,x]","\frac{2 b n \text{PolyLog}\left(2,-\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}\right)}{9 d^{5/3} \sqrt[3]{e}}-\frac{2 i \sqrt{3} b n \text{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{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{\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}}","\frac{2 b n \text{PolyLog}\left(2,-\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}\right)}{9 d^{5/3} \sqrt[3]{e}}-\frac{2 i \sqrt{3} b n \text{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{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{\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,"(x*(a + b*Log[c*x^n]))/(9*d^(5/3)*(d^(1/3) + e^(1/3)*x)) - ((-1)^(1/3)*x*(a + b*Log[c*x^n]))/((1 + (-1)^(1/3))^4*d^(5/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x)) + (x*(a + b*Log[c*x^n]))/(9*d^(5/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)) + ((-1)^(1/3)*b*n*Log[-((-1)^(2/3)*d^(1/3)) - e^(1/3)*x])/((1 + (-1)^(1/3))^4*d^(5/3)*e^(1/3)) - (b*n*Log[d^(1/3) + e^(1/3)*x])/(9*d^(5/3)*e^(1/3)) + ((-1)^(1/3)*b*n*Log[d^(1/3) + (-1)^(2/3)*e^(1/3)*x])/(9*d^(5/3)*e^(1/3)) + (2*(a + b*Log[c*x^n])*Log[1 + (e^(1/3)*x)/d^(1/3)])/(9*d^(5/3)*e^(1/3)) - ((2*I)*Sqrt[3]*(a + b*Log[c*x^n])*Log[1 - ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^5*d^(5/3)*e^(1/3)) + (2*(a + b*Log[c*x^n])*Log[1 + ((-1)^(2/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^4*d^(5/3)*e^(1/3)) + (2*b*n*PolyLog[2, -((e^(1/3)*x)/d^(1/3))])/(9*d^(5/3)*e^(1/3)) - ((2*I)*Sqrt[3]*b*n*PolyLog[2, ((-1)^(1/3)*e^(1/3)*x)/d^(1/3)])/((1 + (-1)^(1/3))^5*d^(5/3)*e^(1/3)) + (2*b*n*PolyLog[2, -(((-1)^(2/3)*e^(1/3)*x)/d^(1/3))])/((1 + (-1)^(1/3))^4*d^(5/3)*e^(1/3))","A",14,11,20,0.5500,1,"{199, 200, 31, 634, 617, 204, 628, 2330, 2314, 2317, 2391}"
327,0,0,0,0.0324842,"\int \frac{1}{\left(d+e x^3\right)^2 \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[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,"Defer[Int][1/((d + e*x^3)^2*(a + b*Log[c*x^n])), x]","A",0,0,0,0,-1,"{}"
328,0,0,0,0.0301049,"\int \frac{1}{\left(d+e x^3\right)^2 \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Int[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,"Defer[Int][1/((d + e*x^3)^2*(a + b*Log[c*x^n])^2), x]","A",0,0,0,0,-1,"{}"
329,1,185,0,0.1999149,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{d+\frac{e}{x}} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/(d + e/x),x]","\frac{b e^4 n \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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^2 n x^2}{4 d^3}+\frac{b e^3 n x}{d^4}+\frac{b e n x^3}{9 d^2}-\frac{b n x^4}{16 d}","\frac{b e^4 n \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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^2 n x^2}{4 d^3}+\frac{b e^3 n x}{d^4}+\frac{b e n x^3}{9 d^2}-\frac{b n x^4}{16 d}",1,"-((a*e^3*x)/d^4) + (b*e^3*n*x)/d^4 - (b*e^2*n*x^2)/(4*d^3) + (b*e*n*x^3)/(9*d^2) - (b*n*x^4)/(16*d) - (b*e^3*x*Log[c*x^n])/d^4 + (e^2*x^2*(a + b*Log[c*x^n]))/(2*d^3) - (e*x^3*(a + b*Log[c*x^n]))/(3*d^2) + (x^4*(a + b*Log[c*x^n]))/(4*d) + (e^4*(a + b*Log[c*x^n])*Log[1 + (d*x)/e])/d^5 + (b*e^4*n*PolyLog[2, -((d*x)/e)])/d^5","A",9,7,23,0.3043,1,"{263, 43, 2351, 2295, 2304, 2317, 2391}"
330,1,148,0,0.1682422,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{d+\frac{e}{x}} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/(d + e/x),x]","-\frac{b e^3 n \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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^2 n x}{d^3}+\frac{b e n x^2}{4 d^2}-\frac{b n x^3}{9 d}","-\frac{b e^3 n \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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^2 n x}{d^3}+\frac{b e n x^2}{4 d^2}-\frac{b n x^3}{9 d}",1,"(a*e^2*x)/d^3 - (b*e^2*n*x)/d^3 + (b*e*n*x^2)/(4*d^2) - (b*n*x^3)/(9*d) + (b*e^2*x*Log[c*x^n])/d^3 - (e*x^2*(a + b*Log[c*x^n]))/(2*d^2) + (x^3*(a + b*Log[c*x^n]))/(3*d) - (e^3*(a + b*Log[c*x^n])*Log[1 + (d*x)/e])/d^4 - (b*e^3*n*PolyLog[2, -((d*x)/e)])/d^4","A",8,7,23,0.3043,1,"{263, 43, 2351, 2295, 2304, 2317, 2391}"
331,1,107,0,0.1200857,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{d+\frac{e}{x}} \, dx","Int[(x*(a + b*Log[c*x^n]))/(d + e/x),x]","\frac{b e^2 n \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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 n x}{d^2}-\frac{b n x^2}{4 d}","\frac{b e^2 n \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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 n x}{d^2}-\frac{b n x^2}{4 d}",1,"-((a*e*x)/d^2) + (b*e*n*x)/d^2 - (b*n*x^2)/(4*d) - (b*e*x*Log[c*x^n])/d^2 + (x^2*(a + b*Log[c*x^n]))/(2*d) + (e^2*(a + b*Log[c*x^n])*Log[1 + (d*x)/e])/d^3 + (b*e^2*n*PolyLog[2, -((d*x)/e)])/d^3","A",7,7,21,0.3333,1,"{263, 43, 2351, 2295, 2304, 2317, 2391}"
332,1,69,0,0.0780385,"\int \frac{a+b \log \left(c x^n\right)}{d+\frac{e}{x}} \, dx","Int[(a + b*Log[c*x^n])/(d + e/x),x]","-\frac{b e n \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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 n x}{d}","-\frac{b e n \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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 n x}{d}",1,"(a*x)/d - (b*n*x)/d + (b*x*Log[c*x^n])/d - (e*(a + b*Log[c*x^n])*Log[1 + (d*x)/e])/d^2 - (b*e*n*PolyLog[2, -((d*x)/e)])/d^2","A",6,6,20,0.3000,1,"{193, 43, 2330, 2295, 2317, 2391}"
333,1,39,0,0.0750483,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+\frac{e}{x}\right) x} \, dx","Int[(a + b*Log[c*x^n])/((d + e/x)*x),x]","\frac{b n \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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}",1,"((a + b*Log[c*x^n])*Log[1 + (d*x)/e])/d + (b*n*PolyLog[2, -((d*x)/e)])/d","A",3,3,23,0.1304,1,"{2333, 2317, 2391}"
334,1,44,0,0.0660136,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+\frac{e}{x}\right) x^2} \, dx","Int[(a + b*Log[c*x^n])/((d + e/x)*x^2),x]","\frac{b n \text{PolyLog}\left(2,-\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}","\frac{b n \text{PolyLog}\left(2,-\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,"-((Log[1 + e/(d*x)]*(a + b*Log[c*x^n]))/e) + (b*n*PolyLog[2, -(e/(d*x))])/e","A",2,2,23,0.08696,1,"{2337, 2391}"
335,1,95,0,0.1473364,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+\frac{e}{x}\right) x^3} \, dx","Int[(a + b*Log[c*x^n])/((d + e/x)*x^3),x]","\frac{b d n \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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 n}{e x}","\frac{b d n \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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 n}{e x}",1,"-((b*n)/(e*x)) - (a + b*Log[c*x^n])/(e*x) - (d*(a + b*Log[c*x^n])^2)/(2*b*e^2*n) + (d*(a + b*Log[c*x^n])*Log[1 + (d*x)/e])/e^2 + (b*d*n*PolyLog[2, -((d*x)/e)])/e^2","A",6,7,23,0.3043,1,"{263, 44, 2351, 2304, 2301, 2317, 2391}"
336,1,135,0,0.1765222,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+\frac{e}{x}\right) x^4} \, dx","Int[(a + b*Log[c*x^n])/((d + e/x)*x^4),x]","-\frac{b d^2 n \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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 n}{e^2 x}-\frac{b n}{4 e x^2}","-\frac{b d^2 n \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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 n}{e^2 x}-\frac{b n}{4 e x^2}",1,"-(b*n)/(4*e*x^2) + (b*d*n)/(e^2*x) - (a + b*Log[c*x^n])/(2*e*x^2) + (d*(a + b*Log[c*x^n]))/(e^2*x) + (d^2*(a + b*Log[c*x^n])^2)/(2*b*e^3*n) - (d^2*(a + b*Log[c*x^n])*Log[1 + (d*x)/e])/e^3 - (b*d^2*n*PolyLog[2, -((d*x)/e)])/e^3","A",7,7,23,0.3043,1,"{263, 44, 2351, 2304, 2301, 2317, 2391}"
337,1,170,0,0.1809927,"\int \frac{x^3 (a+b \log (c x))}{d+\frac{e}{x}} \, dx","Int[(x^3*(a + b*Log[c*x]))/(d + e/x),x]","\frac{b e^4 \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{d^5}+\frac{e^2 x^2 (a+b \log (c x))}{2 d^3}+\frac{e^4 \log \left(\frac{d x}{e}+1\right) (a+b \log (c x))}{d^5}-\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^2 x^2}{4 d^3}+\frac{b e^3 x}{d^4}+\frac{b e x^3}{9 d^2}-\frac{b x^4}{16 d}","\frac{b e^4 \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{d^5}+\frac{e^2 x^2 (a+b \log (c x))}{2 d^3}+\frac{e^4 \log \left(\frac{d x}{e}+1\right) (a+b \log (c x))}{d^5}-\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^2 x^2}{4 d^3}+\frac{b e^3 x}{d^4}+\frac{b e x^3}{9 d^2}-\frac{b x^4}{16 d}",1,"-((a*e^3*x)/d^4) + (b*e^3*x)/d^4 - (b*e^2*x^2)/(4*d^3) + (b*e*x^3)/(9*d^2) - (b*x^4)/(16*d) - (b*e^3*x*Log[c*x])/d^4 + (e^2*x^2*(a + b*Log[c*x]))/(2*d^3) - (e*x^3*(a + b*Log[c*x]))/(3*d^2) + (x^4*(a + b*Log[c*x]))/(4*d) + (e^4*(a + b*Log[c*x])*Log[1 + (d*x)/e])/d^5 + (b*e^4*PolyLog[2, -((d*x)/e)])/d^5","A",9,7,21,0.3333,1,"{263, 43, 2351, 2295, 2304, 2317, 2391}"
338,1,136,0,0.1516265,"\int \frac{x^2 (a+b \log (c x))}{d+\frac{e}{x}} \, dx","Int[(x^2*(a + b*Log[c*x]))/(d + e/x),x]","-\frac{b e^3 \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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^2 x}{d^3}+\frac{b e x^2}{4 d^2}-\frac{b x^3}{9 d}","-\frac{b e^3 \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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^2 x}{d^3}+\frac{b e x^2}{4 d^2}-\frac{b x^3}{9 d}",1,"(a*e^2*x)/d^3 - (b*e^2*x)/d^3 + (b*e*x^2)/(4*d^2) - (b*x^3)/(9*d) + (b*e^2*x*Log[c*x])/d^3 - (e*x^2*(a + b*Log[c*x]))/(2*d^2) + (x^3*(a + b*Log[c*x]))/(3*d) - (e^3*(a + b*Log[c*x])*Log[1 + (d*x)/e])/d^4 - (b*e^3*PolyLog[2, -((d*x)/e)])/d^4","A",8,7,21,0.3333,1,"{263, 43, 2351, 2295, 2304, 2317, 2391}"
339,1,98,0,0.1104425,"\int \frac{x (a+b \log (c x))}{d+\frac{e}{x}} \, dx","Int[(x*(a + b*Log[c*x]))/(d + e/x),x]","\frac{b e^2 \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{d^3}+\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 x}{d^2}-\frac{b x^2}{4 d}","\frac{b e^2 \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{d^3}+\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 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[1 + (d*x)/e])/d^3 + (b*e^2*PolyLog[2, -((d*x)/e)])/d^3","A",7,7,19,0.3684,1,"{263, 43, 2351, 2295, 2304, 2317, 2391}"
340,1,63,0,0.0700568,"\int \frac{a+b \log (c x)}{d+\frac{e}{x}} \, dx","Int[(a + b*Log[c*x])/(d + e/x),x]","-\frac{b e \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{d^2}-\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 x}{d}","-\frac{b e \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{d^2}-\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 x}{d}",1,"(a*x)/d - (b*x)/d + (b*x*Log[c*x])/d - (e*(a + b*Log[c*x])*Log[1 + (d*x)/e])/d^2 - (b*e*PolyLog[2, -((d*x)/e)])/d^2","A",6,6,18,0.3333,1,"{193, 43, 2330, 2295, 2317, 2391}"
341,1,36,0,0.0707699,"\int \frac{a+b \log (c x)}{\left(d+\frac{e}{x}\right) x} \, dx","Int[(a + b*Log[c*x])/((d + e/x)*x),x]","\frac{b \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{d}+\frac{\log \left(\frac{d x}{e}+1\right) (a+b \log (c x))}{d}","\frac{b \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{d}+\frac{\log \left(\frac{d x}{e}+1\right) (a+b \log (c x))}{d}",1,"((a + b*Log[c*x])*Log[1 + (d*x)/e])/d + (b*PolyLog[2, -((d*x)/e)])/d","A",3,3,21,0.1429,1,"{2333, 2317, 2391}"
342,1,41,0,0.0617503,"\int \frac{a+b \log (c x)}{\left(d+\frac{e}{x}\right) x^2} \, dx","Int[(a + b*Log[c*x])/((d + e/x)*x^2),x]","\frac{b \text{PolyLog}\left(2,-\frac{e}{d x}\right)}{e}-\frac{\log \left(\frac{e}{d x}+1\right) (a+b \log (c x))}{e}","\frac{b \text{PolyLog}\left(2,-\frac{e}{d x}\right)}{e}-\frac{\log \left(\frac{e}{d x}+1\right) (a+b \log (c x))}{e}",1,"-((Log[1 + e/(d*x)]*(a + b*Log[c*x]))/e) + (b*PolyLog[2, -(e/(d*x))])/e","A",2,2,21,0.09524,1,"{2337, 2391}"
343,1,84,0,0.1312923,"\int \frac{a+b \log (c x)}{\left(d+\frac{e}{x}\right) x^3} \, dx","Int[(a + b*Log[c*x])/((d + e/x)*x^3),x]","\frac{b d \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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}{e x}","\frac{b d \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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}{e x}",1,"-(b/(e*x)) - (a + b*Log[c*x])/(e*x) - (d*(a + b*Log[c*x])^2)/(2*b*e^2) + (d*(a + b*Log[c*x])*Log[1 + (d*x)/e])/e^2 + (b*d*PolyLog[2, -((d*x)/e)])/e^2","A",6,7,21,0.3333,1,"{263, 44, 2351, 2304, 2301, 2317, 2391}"
344,1,121,0,0.1559153,"\int \frac{a+b \log (c x)}{\left(d+\frac{e}{x}\right) x^4} \, dx","Int[(a + b*Log[c*x])/((d + e/x)*x^4),x]","-\frac{b d^2 \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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}{e^2 x}-\frac{b}{4 e x^2}","-\frac{b d^2 \text{PolyLog}\left(2,-\frac{d x}{e}\right)}{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}{e^2 x}-\frac{b}{4 e x^2}",1,"-b/(4*e*x^2) + (b*d)/(e^2*x) - (a + b*Log[c*x])/(2*e*x^2) + (d*(a + b*Log[c*x]))/(e^2*x) + (d^2*(a + b*Log[c*x])^2)/(2*b*e^3) - (d^2*(a + b*Log[c*x])*Log[1 + (d*x)/e])/e^3 - (b*d^2*PolyLog[2, -((d*x)/e)])/e^3","A",7,7,21,0.3333,1,"{263, 44, 2351, 2304, 2301, 2317, 2391}"
345,1,17,0,0.0651177,"\int \frac{x^{-1+n} \log \left(e x^n\right)}{1-e x^n} \, dx","Int[(x^(-1 + n)*Log[e*x^n])/(1 - e*x^n),x]","\frac{\text{PolyLog}\left(2,1-e x^n\right)}{e n}","\frac{\text{PolyLog}\left(2,1-e x^n\right)}{e n}",1,"PolyLog[2, 1 - e*x^n]/(e*n)","A",2,2,22,0.09091,1,"{2336, 2315}"
346,1,16,0,0.0631588,"\int \frac{x^{-1+n} \log \left(\frac{x^n}{d}\right)}{d-x^n} \, dx","Int[(x^(-1 + n)*Log[x^n/d])/(d - x^n),x]","\frac{\text{PolyLog}\left(2,1-\frac{x^n}{d}\right)}{n}","\frac{\text{PolyLog}\left(2,1-\frac{x^n}{d}\right)}{n}",1,"PolyLog[2, 1 - x^n/d]/n","A",2,2,23,0.08696,1,"{2336, 2315}"
347,1,20,0,0.0685046,"\int \frac{x^{-1+n} \log \left(-\frac{e x^n}{d}\right)}{d+e x^n} \, dx","Int[(x^(-1 + n)*Log[-((e*x^n)/d)])/(d + e*x^n),x]","-\frac{\text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{e n}","-\frac{\text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{e n}",1,"-(PolyLog[2, 1 + (e*x^n)/d]/(e*n))","A",2,2,25,0.08000,1,"{2336, 2315}"
348,1,14,0,0.0767902,"\int \frac{\log \left(\frac{a}{x}\right)}{a x-x^2} \, dx","Int[Log[a/x]/(a*x - x^2),x]","\frac{\text{PolyLog}\left(2,1-\frac{a}{x}\right)}{a}","\frac{\text{PolyLog}\left(2,1-\frac{a}{x}\right)}{a}",1,"PolyLog[2, 1 - a/x]/a","A",4,4,18,0.2222,1,"{1593, 2343, 2333, 2315}"
349,1,17,0,0.0868039,"\int \frac{\log \left(\frac{a}{x^2}\right)}{a x-x^3} \, dx","Int[Log[a/x^2]/(a*x - x^3),x]","\frac{\text{PolyLog}\left(2,1-\frac{a}{x^2}\right)}{2 a}","\frac{\text{PolyLog}\left(2,1-\frac{a}{x^2}\right)}{2 a}",1,"PolyLog[2, 1 - a/x^2]/(2*a)","A",4,4,18,0.2222,1,"{1593, 2343, 2333, 2315}"
350,1,26,0,0.0903546,"\int \frac{\log \left(a x^{1-n}\right)}{a x-x^n} \, dx","Int[Log[a*x^(1 - n)]/(a*x - x^n),x]","-\frac{\text{PolyLog}\left(2,1-a x^{1-n}\right)}{a (1-n)}","-\frac{\text{PolyLog}\left(2,1-a x^{1-n}\right)}{a (1-n)}",1,"-(PolyLog[2, 1 - a*x^(1 - n)]/(a*(1 - n)))","A",3,3,22,0.1364,1,"{1593, 2336, 2315}"
351,1,171,0,0.2147698,"\int (f x)^{-1+m} \left(d+e x^m\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(f*x)^(-1 + m)*(d + e*x^m)^3*(a + b*Log[c*x^n]),x]","\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{3 b d^2 e n x^{m+1} (f x)^{m-1}}{4 m^2}-\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{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}","\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{3 b d^2 e n x^{m+1} (f x)^{m-1}}{4 m^2}-\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{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,"-((b*d^3*n*x*(f*x)^(-1 + m))/m^2) - (3*b*d^2*e*n*x^(1 + m)*(f*x)^(-1 + m))/(4*m^2) - (b*d*e^2*n*x^(1 + 2*m)*(f*x)^(-1 + m))/(3*m^2) - (b*e^3*n*x^(1 + 3*m)*(f*x)^(-1 + m))/(16*m^2) - (b*d^4*n*x^(1 - m)*(f*x)^(-1 + m)*Log[x])/(4*e*m) + (x^(1 - m)*(f*x)^(-1 + m)*(d + e*x^m)^4*(a + b*Log[c*x^n]))/(4*e*m)","A",5,4,27,0.1481,1,"{2339, 2338, 266, 43}"
352,1,142,0,0.1950206,"\int (f x)^{-1+m} \left(d+e x^m\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(f*x)^(-1 + m)*(d + e*x^m)^2*(a + b*Log[c*x^n]),x]","\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}","\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,"-((b*d^2*n*x*(f*x)^(-1 + m))/m^2) - (b*d*e*n*x^(1 + m)*(f*x)^(-1 + m))/(2*m^2) - (b*e^2*n*x^(1 + 2*m)*(f*x)^(-1 + m))/(9*m^2) - (b*d^3*n*x^(1 - m)*(f*x)^(-1 + m)*Log[x])/(3*e*m) + (x^(1 - m)*(f*x)^(-1 + m)*(d + e*x^m)^3*(a + b*Log[c*x^n]))/(3*e*m)","A",5,4,27,0.1481,1,"{2339, 2338, 266, 43}"
353,1,113,0,0.1169687,"\int (f x)^{-1+m} \left(d+e x^m\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(f*x)^(-1 + m)*(d + e*x^m)*(a + b*Log[c*x^n]),x]","\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 e m}-\frac{b d^2 n x^{1-m} \log (x) (f x)^{m-1}}{2 e m}-\frac{b d n x (f x)^{m-1}}{m^2}-\frac{b e n x^{m+1} (f x)^{m-1}}{4 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,"-((b*d*n*x*(f*x)^(-1 + m))/m^2) - (b*e*n*x^(1 + m)*(f*x)^(-1 + m))/(4*m^2) - (b*d^2*n*x^(1 - m)*(f*x)^(-1 + m)*Log[x])/(2*e*m) + (x^(1 - m)*(f*x)^(-1 + m)*(d + e*x^m)^2*(a + b*Log[c*x^n]))/(2*e*m)","A",5,4,25,0.1600,1,"{2339, 2338, 266, 43}"
354,1,38,0,0.0173125,"\int (f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(f*x)^(-1 + m)*(a + b*Log[c*x^n]),x]","\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}","\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,"-((b*n*(f*x)^m)/(f*m^2)) + ((f*x)^m*(a + b*Log[c*x^n]))/(f*m)","A",1,1,18,0.05556,1,"{2304}"
355,1,77,0,0.1914447,"\int \frac{(f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right)}{d+e x^m} \, dx","Int[((f*x)^(-1 + m)*(a + b*Log[c*x^n]))/(d + e*x^m),x]","\frac{b n x^{1-m} (f x)^{m-1} \text{PolyLog}\left(2,-\frac{e x^m}{d}\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)}{e m}","\frac{b n x^{1-m} (f x)^{m-1} \text{PolyLog}\left(2,-\frac{e x^m}{d}\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)}{e m}",1,"(x^(1 - m)*(f*x)^(-1 + m)*(a + b*Log[c*x^n])*Log[1 + (e*x^m)/d])/(e*m) + (b*n*x^(1 - m)*(f*x)^(-1 + m)*PolyLog[2, -((e*x^m)/d)])/(e*m^2)","A",3,3,27,0.1111,1,"{2339, 2337, 2391}"
356,1,69,0,0.1071186,"\int \frac{(f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^m\right)^2} \, dx","Int[((f*x)^(-1 + m)*(a + b*Log[c*x^n]))/(d + e*x^m)^2,x]","\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}","\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 + b*Log[c*x^n]))/(d*f*m*(d + e*x^m)) - (b*n*(f*x)^m*Log[d + e*x^m])/(d*e*f*m^2*x^m)","A",3,3,27,0.1111,1,"{2335, 268, 260}"
357,1,150,0,0.2152509,"\int \frac{(f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^m\right)^3} \, dx","Int[((f*x)^(-1 + m)*(a + b*Log[c*x^n]))/(d + e*x^m)^3,x]","-\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)}","-\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,"(b*n*x^(1 - m)*(f*x)^(-1 + m))/(2*d*e*m^2*(d + e*x^m)) + (b*n*x^(1 - m)*(f*x)^(-1 + m)*Log[x])/(2*d^2*e*m) - (x^(1 - m)*(f*x)^(-1 + m)*(a + b*Log[c*x^n]))/(2*e*m*(d + e*x^m)^2) - (b*n*x^(1 - m)*(f*x)^(-1 + m)*Log[d + e*x^m])/(2*d^2*e*m^2)","A",5,4,27,0.1481,1,"{2339, 2338, 266, 44}"
358,1,188,0,0.2340497,"\int \frac{(f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^m\right)^4} \, dx","Int[((f*x)^(-1 + m)*(a + b*Log[c*x^n]))/(d + e*x^m)^4,x]","-\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}}{3 d^2 e m^2 \left(d+e x^m\right)}-\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}}{6 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)}{3 e m \left(d+e x^m\right)^3}+\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} \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}}{6 d e m^2 \left(d+e x^m\right)^2}",1,"(b*n*x^(1 - m)*(f*x)^(-1 + m))/(6*d*e*m^2*(d + e*x^m)^2) + (b*n*x^(1 - m)*(f*x)^(-1 + m))/(3*d^2*e*m^2*(d + e*x^m)) + (b*n*x^(1 - m)*(f*x)^(-1 + m)*Log[x])/(3*d^3*e*m) - (x^(1 - m)*(f*x)^(-1 + m)*(a + b*Log[c*x^n]))/(3*e*m*(d + e*x^m)^3) - (b*n*x^(1 - m)*(f*x)^(-1 + m)*Log[d + e*x^m])/(3*d^3*e*m^2)","A",5,4,27,0.1481,1,"{2339, 2338, 266, 44}"
359,1,294,0,0.4805048,"\int (f x)^{-1+m} \left(d+e x^m\right)^3 \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Int[(f*x)^(-1 + m)*(d + e*x^m)^3*(a + b*Log[c*x^n])^2,x]","-\frac{b n x^{1-m} (f x)^{m-1} \left(\frac{36 d^2 e^2 x^{2 m}}{m}+\frac{48 d^3 e x^m}{m}+12 d^4 \log (x)+\frac{16 d e^3 x^{3 m}}{m}+\frac{3 e^4 x^{4 m}}{m}\right) \left(a+b \log \left(c x^n\right)\right)}{24 e m}+\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{3 b^2 d^2 e n^2 x^{m+1} (f x)^{m-1}}{4 m^3}+\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{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}","-\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{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{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{3 b^2 d^2 e n^2 x^{m+1} (f x)^{m-1}}{4 m^3}+\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{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,"(2*b^2*d^3*n^2*x*(f*x)^(-1 + m))/m^3 + (3*b^2*d^2*e*n^2*x^(1 + m)*(f*x)^(-1 + m))/(4*m^3) + (2*b^2*d*e^2*n^2*x^(1 + 2*m)*(f*x)^(-1 + m))/(9*m^3) + (b^2*e^3*n^2*x^(1 + 3*m)*(f*x)^(-1 + m))/(32*m^3) + (b^2*d^4*n^2*x^(1 - m)*(f*x)^(-1 + m)*Log[x]^2)/(4*e*m) - (b*n*x^(1 - m)*(f*x)^(-1 + m)*((48*d^3*e*x^m)/m + (36*d^2*e^2*x^(2*m))/m + (16*d*e^3*x^(3*m))/m + (3*e^4*x^(4*m))/m + 12*d^4*Log[x])*(a + b*Log[c*x^n]))/(24*e*m) + (x^(1 - m)*(f*x)^(-1 + m)*(d + e*x^m)^4*(a + b*Log[c*x^n])^2)/(4*e*m)","A",7,7,29,0.2414,1,"{2339, 2338, 266, 43, 2334, 14, 2301}"
360,1,245,0,0.4398307,"\int (f x)^{-1+m} \left(d+e x^m\right)^2 \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Int[(f*x)^(-1 + m)*(d + e*x^m)^2*(a + b*Log[c*x^n])^2,x]","-\frac{b n x^{1-m} (f x)^{m-1} \left(\frac{18 d^2 e x^m}{m}+6 d^3 \log (x)+\frac{9 d e^2 x^{2 m}}{m}+\frac{2 e^3 x^{3 m}}{m}\right) \left(a+b \log \left(c x^n\right)\right)}{9 e m}+\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{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}","-\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,"(2*b^2*d^2*n^2*x*(f*x)^(-1 + m))/m^3 + (b^2*d*e*n^2*x^(1 + m)*(f*x)^(-1 + m))/(2*m^3) + (2*b^2*e^2*n^2*x^(1 + 2*m)*(f*x)^(-1 + m))/(27*m^3) + (b^2*d^3*n^2*x^(1 - m)*(f*x)^(-1 + m)*Log[x]^2)/(3*e*m) - (b*n*x^(1 - m)*(f*x)^(-1 + m)*((18*d^2*e*x^m)/m + (9*d*e^2*x^(2*m))/m + (2*e^3*x^(3*m))/m + 6*d^3*Log[x])*(a + b*Log[c*x^n]))/(9*e*m) + (x^(1 - m)*(f*x)^(-1 + m)*(d + e*x^m)^3*(a + b*Log[c*x^n])^2)/(3*e*m)","A",7,8,29,0.2759,1,"{2339, 2338, 266, 43, 2334, 12, 14, 2301}"
361,1,195,0,0.3027617,"\int (f x)^{-1+m} \left(d+e x^m\right) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Int[(f*x)^(-1 + m)*(d + e*x^m)*(a + b*Log[c*x^n])^2,x]","-\frac{b n x^{1-m} (f x)^{m-1} \left(2 d^2 \log (x)+\frac{4 d e x^m}{m}+\frac{e^2 x^{2 m}}{m}\right) \left(a+b \log \left(c x^n\right)\right)}{2 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{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}","-\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,"(2*b^2*d*n^2*x*(f*x)^(-1 + m))/m^3 + (b^2*e*n^2*x^(1 + m)*(f*x)^(-1 + m))/(4*m^3) + (b^2*d^2*n^2*x^(1 - m)*(f*x)^(-1 + m)*Log[x]^2)/(2*e*m) - (b*n*x^(1 - m)*(f*x)^(-1 + m)*((4*d*e*x^m)/m + (e^2*x^(2*m))/m + 2*d^2*Log[x])*(a + b*Log[c*x^n]))/(2*e*m) + (x^(1 - m)*(f*x)^(-1 + m)*(d + e*x^m)^2*(a + b*Log[c*x^n])^2)/(2*e*m)","A",7,8,27,0.2963,1,"{2339, 2338, 266, 43, 2334, 12, 14, 2301}"
362,1,69,0,0.0495456,"\int (f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Int[(f*x)^(-1 + m)*(a + b*Log[c*x^n])^2,x]","-\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}","-\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,"(2*b^2*n^2*(f*x)^m)/(f*m^3) - (2*b*n*(f*x)^m*(a + b*Log[c*x^n]))/(f*m^2) + ((f*x)^m*(a + b*Log[c*x^n])^2)/(f*m)","A",2,2,20,0.1000,1,"{2305, 2304}"
363,1,129,0,0.3011307,"\int \frac{(f x)^{-1+m} \left(a+b \log \left(c x^n\right)\right)^2}{d+e x^m} \, dx","Int[((f*x)^(-1 + m)*(a + b*Log[c*x^n])^2)/(d + e*x^m),x]","\frac{2 b n x^{1-m} (f x)^{m-1} \text{PolyLog}\left(2,-\frac{e x^m}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e m^2}-\frac{2 b^2 n^2 x^{1-m} (f x)^{m-1} \text{PolyLog}\left(3,-\frac{e x^m}{d}\right)}{e m^3}+\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 n x^{1-m} (f x)^{m-1} \text{PolyLog}\left(2,-\frac{e x^m}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{e m^2}-\frac{2 b^2 n^2 x^{1-m} (f x)^{m-1} \text{PolyLog}\left(3,-\frac{e x^m}{d}\right)}{e m^3}+\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}",1,"(x^(1 - m)*(f*x)^(-1 + m)*(a + b*Log[c*x^n])^2*Log[1 + (e*x^m)/d])/(e*m) + (2*b*n*x^(1 - m)*(f*x)^(-1 + m)*(a + b*Log[c*x^n])*PolyLog[2, -((e*x^m)/d)])/(e*m^2) - (2*b^2*n^2*x^(1 - m)*(f*x)^(-1 + m)*PolyLog[3, -((e*x^m)/d)])/(e*m^3)","A",4,4,29,0.1379,1,"{2339, 2337, 2374, 6589}"
364,1,138,0,0.3401032,"\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","Int[((f*x)^(-1 + m)*(a + b*Log[c*x^n])^2)/(d + e*x^m)^2,x]","\frac{2 b^2 n^2 x^{1-m} (f x)^{m-1} \text{PolyLog}\left(2,-\frac{d x^{-m}}{e}\right)}{d e 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{PolyLog}\left(2,-\frac{d x^{-m}}{e}\right)}{d e 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)}",1,"-((x^(1 - m)*(f*x)^(-1 + m)*(a + b*Log[c*x^n])^2)/(e*m*(d + e*x^m))) - (2*b*n*x^(1 - m)*(f*x)^(-1 + m)*(a + b*Log[c*x^n])*Log[1 + d/(e*x^m)])/(d*e*m^2) + (2*b^2*n^2*x^(1 - m)*(f*x)^(-1 + m)*PolyLog[2, -(d/(e*x^m))])/(d*e*m^3)","A",4,4,29,0.1379,1,"{2339, 2338, 2345, 2391}"
365,1,214,0,0.512463,"\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","Int[((f*x)^(-1 + m)*(a + b*Log[c*x^n])^2)/(d + e*x^m)^3,x]","\frac{b^2 n^2 x^{1-m} (f x)^{m-1} \text{PolyLog}\left(2,-\frac{d x^{-m}}{e}\right)}{d^2 e 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} \log \left(d+e x^m\right)}{d^2 e m^3}","\frac{b^2 n^2 x^{1-m} (f x)^{m-1} \text{PolyLog}\left(2,-\frac{d x^{-m}}{e}\right)}{d^2 e 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} \log \left(d+e x^m\right)}{d^2 e m^3}",1,"-((b*n*x*(f*x)^(-1 + m)*(a + b*Log[c*x^n]))/(d^2*m^2*(d + e*x^m))) - (x^(1 - m)*(f*x)^(-1 + m)*(a + b*Log[c*x^n])^2)/(2*e*m*(d + e*x^m)^2) - (b*n*x^(1 - m)*(f*x)^(-1 + m)*(a + b*Log[c*x^n])*Log[1 + d/(e*x^m)])/(d^2*e*m^2) + (b^2*n^2*x^(1 - m)*(f*x)^(-1 + m)*Log[d + e*x^m])/(d^2*e*m^3) + (b^2*n^2*x^(1 - m)*(f*x)^(-1 + m)*PolyLog[2, -(d/(e*x^m))])/(d^2*e*m^3)","A",7,7,29,0.2414,1,"{2339, 2338, 2349, 2345, 2391, 2335, 260}"
366,1,346,0,0.7142421,"\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","Int[((f*x)^(-1 + m)*(a + b*Log[c*x^n])^2)/(d + e*x^m)^4,x]","\frac{2 b^2 n^2 x^{1-m} (f x)^{m-1} \text{PolyLog}\left(2,-\frac{d x^{-m}}{e}\right)}{3 d^3 e 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{b^2 n^2 x^{1-m} (f x)^{m-1}}{3 d^2 e m^3 \left(d+e x^m\right)}-\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} \log \left(d+e x^m\right)}{d^3 e m^3}","\frac{2 b^2 n^2 x^{1-m} (f x)^{m-1} \text{PolyLog}\left(2,-\frac{d x^{-m}}{e}\right)}{3 d^3 e 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{b^2 n^2 x^{1-m} (f x)^{m-1}}{3 d^2 e m^3 \left(d+e x^m\right)}-\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} \log \left(d+e x^m\right)}{d^3 e m^3}",1,"-(b^2*n^2*x^(1 - m)*(f*x)^(-1 + m))/(3*d^2*e*m^3*(d + e*x^m)) - (b^2*n^2*x^(1 - m)*(f*x)^(-1 + m)*Log[x])/(3*d^3*e*m^2) + (b*n*x^(1 - m)*(f*x)^(-1 + m)*(a + b*Log[c*x^n]))/(3*d*e*m^2*(d + e*x^m)^2) - (2*b*n*x*(f*x)^(-1 + m)*(a + b*Log[c*x^n]))/(3*d^3*m^2*(d + e*x^m)) - (x^(1 - m)*(f*x)^(-1 + m)*(a + b*Log[c*x^n])^2)/(3*e*m*(d + e*x^m)^3) - (2*b*n*x^(1 - m)*(f*x)^(-1 + m)*(a + b*Log[c*x^n])*Log[1 + d/(e*x^m)])/(3*d^3*e*m^2) + (b^2*n^2*x^(1 - m)*(f*x)^(-1 + m)*Log[d + e*x^m])/(d^3*e*m^3) + (2*b^2*n^2*x^(1 - m)*(f*x)^(-1 + m)*PolyLog[2, -(d/(e*x^m))])/(3*d^3*e*m^3)","A",12,9,29,0.3103,1,"{2339, 2338, 2349, 2345, 2391, 2335, 260, 266, 44}"
367,1,59,0,0.0790428,"\int x^5 \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^5*(d + e*x^r)*(a + b*Log[c*x^n]),x]","\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}","\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,"-(b*d*n*x^6)/36 - (b*e*n*x^(6 + r))/(6 + r)^2 + ((d*x^6 + (6*e*x^(6 + r))/(6 + r))*(a + b*Log[c*x^n]))/6","A",4,3,21,0.1429,1,"{14, 2334, 12}"
368,1,59,0,0.0796116,"\int x^3 \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^3*(d + e*x^r)*(a + b*Log[c*x^n]),x]","\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}","\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,"-(b*d*n*x^4)/16 - (b*e*n*x^(4 + r))/(4 + r)^2 + ((d*x^4 + (4*e*x^(4 + r))/(4 + r))*(a + b*Log[c*x^n]))/4","A",4,3,21,0.1429,1,"{14, 2334, 12}"
369,1,59,0,0.0634667,"\int x \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*(d + e*x^r)*(a + b*Log[c*x^n]),x]","\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}","\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,"-(b*d*n*x^2)/4 - (b*e*n*x^(2 + r))/(2 + r)^2 + ((d*x^2 + (2*e*x^(2 + r))/(2 + r))*(a + b*Log[c*x^n]))/2","A",4,3,19,0.1579,1,"{14, 2334, 12}"
370,1,53,0,0.0880529,"\int \frac{\left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[((d + e*x^r)*(a + b*Log[c*x^n]))/x,x]","\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}","\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,"-((b*e*n*x^r)/r^2) + (e*x^r*(a + b*Log[c*x^n]))/r + (d*(a + b*Log[c*x^n])^2)/(2*b*n)","A",4,4,21,0.1905,1,"{14, 2351, 2301, 2304}"
371,1,63,0,0.0743005,"\int \frac{\left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[((d + e*x^r)*(a + b*Log[c*x^n]))/x^3,x]","-\frac{1}{2} \left(\frac{d}{x^2}+\frac{2 e x^{r-2}}{2-r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b d n}{4 x^2}-\frac{b e n x^{r-2}}{(2-r)^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,"-(b*d*n)/(4*x^2) - (b*e*n*x^(-2 + r))/(2 - r)^2 - ((d/x^2 + (2*e*x^(-2 + r))/(2 - r))*(a + b*Log[c*x^n]))/2","A",2,2,21,0.09524,1,"{14, 2334}"
372,1,63,0,0.0741268,"\int \frac{\left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)}{x^5} \, dx","Int[((d + e*x^r)*(a + b*Log[c*x^n]))/x^5,x]","-\frac{1}{4} \left(\frac{d}{x^4}+\frac{4 e x^{r-4}}{4-r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b d n}{16 x^4}-\frac{b e n x^{r-4}}{(4-r)^2}","-\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,"-(b*d*n)/(16*x^4) - (b*e*n*x^(-4 + r))/(4 - r)^2 - ((d/x^4 + (4*e*x^(-4 + r))/(4 - r))*(a + b*Log[c*x^n]))/4","A",2,2,21,0.09524,1,"{14, 2334}"
373,1,59,0,0.0802939,"\int x^4 \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^4*(d + e*x^r)*(a + b*Log[c*x^n]),x]","\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}","\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,"-(b*d*n*x^5)/25 - (b*e*n*x^(5 + r))/(5 + r)^2 + ((d*x^5 + (5*e*x^(5 + r))/(5 + r))*(a + b*Log[c*x^n]))/5","A",4,3,21,0.1429,1,"{14, 2334, 12}"
374,1,59,0,0.0804727,"\int x^2 \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*(d + e*x^r)*(a + b*Log[c*x^n]),x]","\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}","\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,"-(b*d*n*x^3)/9 - (b*e*n*x^(3 + r))/(3 + r)^2 + ((d*x^3 + (3*e*x^(3 + r))/(3 + r))*(a + b*Log[c*x^n]))/3","A",4,3,21,0.1429,1,"{14, 2334, 12}"
375,1,49,0,0.0339829,"\int \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(d + e*x^r)*(a + b*Log[c*x^n]),x]","\left(d x+\frac{e x^{r+1}}{r+1}\right) \left(a+b \log \left(c x^n\right)\right)-b d n x-\frac{b e n x^{r+1}}{(r+1)^2}","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,"-(b*d*n*x) - (b*e*n*x^(1 + r))/(1 + r)^2 + (d*x + (e*x^(1 + r))/(1 + r))*(a + b*Log[c*x^n])","A",3,2,18,0.1111,1,"{2313, 12}"
376,1,58,0,0.0766622,"\int \frac{\left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[((d + e*x^r)*(a + b*Log[c*x^n]))/x^2,x]","-\left(\frac{d}{x}+\frac{e x^{r-1}}{1-r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b d n}{x}-\frac{b e n x^{r-1}}{(1-r)^2}","-\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,"-((b*d*n)/x) - (b*e*n*x^(-1 + r))/(1 - r)^2 - (d/x + (e*x^(-1 + r))/(1 - r))*(a + b*Log[c*x^n])","A",4,3,21,0.1429,1,"{14, 2334, 12}"
377,1,63,0,0.0732404,"\int \frac{\left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Int[((d + e*x^r)*(a + b*Log[c*x^n]))/x^4,x]","-\frac{1}{3} \left(\frac{d}{x^3}+\frac{3 e x^{r-3}}{3-r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b d n}{9 x^3}-\frac{b e n x^{r-3}}{(3-r)^2}","-\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,"-(b*d*n)/(9*x^3) - (b*e*n*x^(-3 + r))/(3 - r)^2 - ((d/x^3 + (3*e*x^(-3 + r))/(3 - r))*(a + b*Log[c*x^n]))/3","A",2,2,21,0.09524,1,"{14, 2334}"
378,1,63,0,0.0721168,"\int \frac{\left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Int[((d + e*x^r)*(a + b*Log[c*x^n]))/x^6,x]","-\frac{1}{5} \left(\frac{d}{x^5}+\frac{5 e x^{r-5}}{5-r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b d n}{25 x^5}-\frac{b e n x^{r-5}}{(5-r)^2}","-\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,"-(b*d*n)/(25*x^5) - (b*e*n*x^(-5 + r))/(5 - r)^2 - ((d/x^5 + (5*e*x^(-5 + r))/(5 - r))*(a + b*Log[c*x^n]))/5","A",2,2,21,0.09524,1,"{14, 2334}"
379,1,103,0,0.1561005,"\int x^5 \left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^5*(d + e*x^r)^2*(a + b*Log[c*x^n]),x]","\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}","\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,"-(b*d^2*n*x^6)/36 - (b*e^2*n*x^(2*(3 + r)))/(4*(3 + r)^2) - (2*b*d*e*n*x^(6 + r))/(6 + r)^2 + ((d^2*x^6 + (3*e^2*x^(2*(3 + r)))/(3 + r) + (12*d*e*x^(6 + r))/(6 + r))*(a + b*Log[c*x^n]))/6","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
380,1,103,0,0.1543361,"\int x^3 \left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^3*(d + e*x^r)^2*(a + b*Log[c*x^n]),x]","\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}","\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,"-(b*d^2*n*x^4)/16 - (b*e^2*n*x^(2*(2 + r)))/(4*(2 + r)^2) - (2*b*d*e*n*x^(4 + r))/(4 + r)^2 + ((d^2*x^4 + (2*e^2*x^(2*(2 + r)))/(2 + r) + (8*d*e*x^(4 + r))/(4 + r))*(a + b*Log[c*x^n]))/4","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
381,1,102,0,0.1316011,"\int x \left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*(d + e*x^r)^2*(a + b*Log[c*x^n]),x]","\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}","\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,"-(b*d^2*n*x^2)/4 - (b*e^2*n*x^(2*(1 + r)))/(4*(1 + r)^2) - (2*b*d*e*n*x^(2 + r))/(2 + r)^2 + ((d^2*x^2 + (e^2*x^(2*(1 + r)))/(1 + r) + (4*d*e*x^(2 + r))/(2 + r))*(a + b*Log[c*x^n]))/2","A",4,4,21,0.1905,1,"{270, 2334, 12, 14}"
382,1,87,0,0.1338589,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[((d + e*x^r)^2*(a + b*Log[c*x^n]))/x,x]","\frac{1}{2} \left(2 d^2 \log (x)+\frac{4 d e x^r}{r}+\frac{e^2 x^{2 r}}{r}\right) \left(a+b \log \left(c x^n\right)\right)-\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}","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,"(-2*b*d*e*n*x^r)/r^2 - (b*e^2*n*x^(2*r))/(4*r^2) - (b*d^2*n*Log[x]^2)/2 + (((4*d*e*x^r)/r + (e^2*x^(2*r))/r + 2*d^2*Log[x])*(a + b*Log[c*x^n]))/2","A",5,6,23,0.2609,1,"{266, 43, 2334, 12, 14, 2301}"
383,1,114,0,0.1628124,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[((d + e*x^r)^2*(a + b*Log[c*x^n]))/x^3,x]","-\frac{1}{2} \left(\frac{d^2}{x^2}+\frac{4 d e x^{r-2}}{2-r}+\frac{e^2 x^{-2 (1-r)}}{1-r}\right) \left(a+b \log \left(c x^n\right)\right)-\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}","-\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*d^2*n)/(4*x^2) - (b*e^2*n)/(4*(1 - r)^2*x^(2*(1 - r))) - (2*b*d*e*n*x^(-2 + r))/(2 - r)^2 - ((d^2/x^2 + e^2/((1 - r)*x^(2*(1 - r))) + (4*d*e*x^(-2 + r))/(2 - r))*(a + b*Log[c*x^n]))/2","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
384,1,115,0,0.163582,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^5} \, dx","Int[((d + e*x^r)^2*(a + b*Log[c*x^n]))/x^5,x]","-\frac{1}{4} \left(\frac{d^2}{x^4}+\frac{8 d e x^{r-4}}{4-r}+\frac{2 e^2 x^{-2 (2-r)}}{2-r}\right) \left(a+b \log \left(c x^n\right)\right)-\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}","-\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*d^2*n)/(16*x^4) - (b*e^2*n)/(4*(2 - r)^2*x^(2*(2 - r))) - (2*b*d*e*n*x^(-4 + r))/(4 - r)^2 - ((d^2/x^4 + (2*e^2)/((2 - r)*x^(2*(2 - r))) + (8*d*e*x^(-4 + r))/(4 - r))*(a + b*Log[c*x^n]))/4","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
385,1,105,0,0.1602607,"\int x^4 \left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^4*(d + e*x^r)^2*(a + b*Log[c*x^n]),x]","\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}","\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,"-(b*d^2*n*x^5)/25 - (2*b*d*e*n*x^(5 + r))/(5 + r)^2 - (b*e^2*n*x^(5 + 2*r))/(5 + 2*r)^2 + ((d^2*x^5 + (10*d*e*x^(5 + r))/(5 + r) + (5*e^2*x^(5 + 2*r))/(5 + 2*r))*(a + b*Log[c*x^n]))/5","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
386,1,105,0,0.1599395,"\int x^2 \left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*(d + e*x^r)^2*(a + b*Log[c*x^n]),x]","\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}","\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,"-(b*d^2*n*x^3)/9 - (2*b*d*e*n*x^(3 + r))/(3 + r)^2 - (b*e^2*n*x^(3 + 2*r))/(3 + 2*r)^2 + ((d^2*x^3 + (6*d*e*x^(3 + r))/(3 + r) + (3*e^2*x^(3 + 2*r))/(3 + 2*r))*(a + b*Log[c*x^n]))/3","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
387,1,95,0,0.0762582,"\int \left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(d + e*x^r)^2*(a + b*Log[c*x^n]),x]","\left(d^2 x+\frac{2 d e x^{r+1}}{r+1}+\frac{e^2 x^{2 r+1}}{2 r+1}\right) \left(a+b \log \left(c x^n\right)\right)-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}","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,"-(b*d^2*n*x) - (2*b*d*e*n*x^(1 + r))/(1 + r)^2 - (b*e^2*n*x^(1 + 2*r))/(1 + 2*r)^2 + (d^2*x + (2*d*e*x^(1 + r))/(1 + r) + (e^2*x^(1 + 2*r))/(1 + 2*r))*(a + b*Log[c*x^n])","A",2,2,20,0.1000,1,"{244, 2313}"
388,1,104,0,0.1669153,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[((d + e*x^r)^2*(a + b*Log[c*x^n]))/x^2,x]","-\left(\frac{d^2}{x}+\frac{2 d e x^{r-1}}{1-r}+\frac{e^2 x^{2 r-1}}{1-2 r}\right) \left(a+b \log \left(c x^n\right)\right)-\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}","-\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*d^2*n)/x) - (2*b*d*e*n*x^(-1 + r))/(1 - r)^2 - (b*e^2*n*x^(-1 + 2*r))/(1 - 2*r)^2 - (d^2/x + (2*d*e*x^(-1 + r))/(1 - r) + (e^2*x^(-1 + 2*r))/(1 - 2*r))*(a + b*Log[c*x^n])","A",3,3,23,0.1304,1,"{270, 2334, 14}"
389,1,109,0,0.1729237,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Int[((d + e*x^r)^2*(a + b*Log[c*x^n]))/x^4,x]","-\frac{1}{3} \left(\frac{d^2}{x^3}+\frac{6 d e x^{r-3}}{3-r}+\frac{3 e^2 x^{2 r-3}}{3-2 r}\right) \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^{r-3}}{(3-r)^2}-\frac{b e^2 n x^{2 r-3}}{(3-2 r)^2}","-\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*d^2*n)/(9*x^3) - (2*b*d*e*n*x^(-3 + r))/(3 - r)^2 - (b*e^2*n*x^(-3 + 2*r))/(3 - 2*r)^2 - ((d^2/x^3 + (6*d*e*x^(-3 + r))/(3 - r) + (3*e^2*x^(-3 + 2*r))/(3 - 2*r))*(a + b*Log[c*x^n]))/3","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
390,1,109,0,0.1730235,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Int[((d + e*x^r)^2*(a + b*Log[c*x^n]))/x^6,x]","-\frac{1}{5} \left(\frac{d^2}{x^5}+\frac{10 d e x^{r-5}}{5-r}+\frac{5 e^2 x^{2 r-5}}{5-2 r}\right) \left(a+b \log \left(c x^n\right)\right)-\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}","-\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*d^2*n)/(25*x^5) - (2*b*d*e*n*x^(-5 + r))/(5 - r)^2 - (b*e^2*n*x^(-5 + 2*r))/(5 - 2*r)^2 - ((d^2/x^5 + (10*d*e*x^(-5 + r))/(5 - r) + (5*e^2*x^(-5 + 2*r))/(5 - 2*r))*(a + b*Log[c*x^n]))/5","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
391,1,109,0,0.1772959,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x^8} \, dx","Int[((d + e*x^r)^2*(a + b*Log[c*x^n]))/x^8,x]","-\frac{1}{7} \left(\frac{d^2}{x^7}+\frac{14 d e x^{r-7}}{7-r}+\frac{7 e^2 x^{2 r-7}}{7-2 r}\right) \left(a+b \log \left(c x^n\right)\right)-\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}","-\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*d^2*n)/(49*x^7) - (2*b*d*e*n*x^(-7 + r))/(7 - r)^2 - (b*e^2*n*x^(-7 + 2*r))/(7 - 2*r)^2 - ((d^2/x^7 + (14*d*e*x^(-7 + r))/(7 - r) + (7*e^2*x^(-7 + 2*r))/(7 - 2*r))*(a + b*Log[c*x^n]))/7","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
392,1,147,0,0.3810702,"\int x^5 \left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^5*(d + e*x^r)^3*(a + b*Log[c*x^n]),x]","\frac{1}{6} \left(\frac{18 d^2 e x^{r+6}}{r+6}+d^3 x^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{3 b d^2 e n x^{r+6}}{(r+6)^2}-\frac{1}{36} b d^3 n x^6-\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}","\frac{1}{6} \left(\frac{18 d^2 e x^{r+6}}{r+6}+d^3 x^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{3 b d^2 e n x^{r+6}}{(r+6)^2}-\frac{1}{36} b d^3 n x^6-\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,"-(b*d^3*n*x^6)/36 - (b*e^3*n*x^(3*(2 + r)))/(9*(2 + r)^2) - (3*b*d*e^2*n*x^(2*(3 + r)))/(4*(3 + r)^2) - (3*b*d^2*e*n*x^(6 + r))/(6 + r)^2 + ((d^3*x^6 + (2*e^3*x^(3*(2 + r)))/(2 + r) + (9*d*e^2*x^(2*(3 + r)))/(3 + r) + (18*d^2*e*x^(6 + r))/(6 + r))*(a + b*Log[c*x^n]))/6","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
393,1,149,0,0.3852348,"\int x^3 \left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^3*(d + e*x^r)^3*(a + b*Log[c*x^n]),x]","\frac{1}{4} \left(\frac{12 d^2 e x^{r+4}}{r+4}+d^3 x^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{3 b d^2 e n x^{r+4}}{(r+4)^2}-\frac{1}{16} b d^3 n x^4-\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}","\frac{1}{4} \left(\frac{12 d^2 e x^{r+4}}{r+4}+d^3 x^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{3 b d^2 e n x^{r+4}}{(r+4)^2}-\frac{1}{16} b d^3 n x^4-\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,"-(b*d^3*n*x^4)/16 - (3*b*d*e^2*n*x^(2*(2 + r)))/(4*(2 + r)^2) - (3*b*d^2*e*n*x^(4 + r))/(4 + r)^2 - (b*e^3*n*x^(4 + 3*r))/(4 + 3*r)^2 + ((d^3*x^4 + (6*d*e^2*x^(2*(2 + r)))/(2 + r) + (12*d^2*e*x^(4 + r))/(4 + r) + (4*e^3*x^(4 + 3*r))/(4 + 3*r))*(a + b*Log[c*x^n]))/4","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
394,1,149,0,0.3483063,"\int x \left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*(d + e*x^r)^3*(a + b*Log[c*x^n]),x]","\frac{1}{2} \left(\frac{6 d^2 e x^{r+2}}{r+2}+d^3 x^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{3 b d^2 e n x^{r+2}}{(r+2)^2}-\frac{1}{4} b d^3 n x^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}","\frac{1}{2} \left(\frac{6 d^2 e x^{r+2}}{r+2}+d^3 x^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{3 b d^2 e n x^{r+2}}{(r+2)^2}-\frac{1}{4} b d^3 n x^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,"-(b*d^3*n*x^2)/4 - (3*b*d*e^2*n*x^(2*(1 + r)))/(4*(1 + r)^2) - (3*b*d^2*e*n*x^(2 + r))/(2 + r)^2 - (b*e^3*n*x^(2 + 3*r))/(2 + 3*r)^2 + ((d^3*x^2 + (3*d*e^2*x^(2*(1 + r)))/(1 + r) + (6*d^2*e*x^(2 + r))/(2 + r) + (2*e^3*x^(2 + 3*r))/(2 + 3*r))*(a + b*Log[c*x^n]))/2","A",4,4,21,0.1905,1,"{270, 2334, 12, 14}"
395,1,124,0,0.1709915,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x,x]","\frac{1}{6} \left(\frac{18 d^2 e x^r}{r}+6 d^3 \log (x)+\frac{9 d e^2 x^{2 r}}{r}+\frac{2 e^3 x^{3 r}}{r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n x^r}{r^2}-\frac{1}{2} b d^3 n \log ^2(x)-\frac{3 b d e^2 n x^{2 r}}{4 r^2}-\frac{b e^3 n x^{3 r}}{9 r^2}","\frac{3 d^2 e x^r \left(a+b \log \left(c x^n\right)\right)}{r}+d^3 \log (x) \left(a+b \log \left(c x^n\right)\right)+\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{3 b d^2 e n x^r}{r^2}-\frac{1}{2} b d^3 n \log ^2(x)-\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,"(-3*b*d^2*e*n*x^r)/r^2 - (3*b*d*e^2*n*x^(2*r))/(4*r^2) - (b*e^3*n*x^(3*r))/(9*r^2) - (b*d^3*n*Log[x]^2)/2 + (((18*d^2*e*x^r)/r + (9*d*e^2*x^(2*r))/r + (2*e^3*x^(3*r))/r + 6*d^3*Log[x])*(a + b*Log[c*x^n]))/6","A",5,6,23,0.2609,1,"{266, 43, 2334, 12, 14, 2301}"
396,1,161,0,0.4076962,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x^3,x]","-\frac{1}{2} \left(\frac{6 d^2 e x^{r-2}}{2-r}+\frac{d^3}{x^2}+\frac{3 d e^2 x^{-2 (1-r)}}{1-r}+\frac{2 e^3 x^{3 r-2}}{2-3 r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n x^{r-2}}{(2-r)^2}-\frac{b d^3 n}{4 x^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}","-\frac{3 d^2 e x^{r-2} \left(a+b \log \left(c x^n\right)\right)}{2-r}-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\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{3 b d^2 e n x^{r-2}}{(2-r)^2}-\frac{b d^3 n}{4 x^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*d^3*n)/(4*x^2) - (3*b*d*e^2*n)/(4*(1 - r)^2*x^(2*(1 - r))) - (3*b*d^2*e*n*x^(-2 + r))/(2 - r)^2 - (b*e^3*n*x^(-2 + 3*r))/(2 - 3*r)^2 - ((d^3/x^2 + (3*d*e^2)/((1 - r)*x^(2*(1 - r))) + (6*d^2*e*x^(-2 + r))/(2 - r) + (2*e^3*x^(-2 + 3*r))/(2 - 3*r))*(a + b*Log[c*x^n]))/2","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
397,1,161,0,0.3965304,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^5} \, dx","Int[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x^5,x]","-\frac{1}{4} \left(\frac{12 d^2 e x^{r-4}}{4-r}+\frac{d^3}{x^4}+\frac{6 d e^2 x^{-2 (2-r)}}{2-r}+\frac{4 e^3 x^{3 r-4}}{4-3 r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n x^{r-4}}{(4-r)^2}-\frac{b d^3 n}{16 x^4}-\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}","-\frac{3 d^2 e x^{r-4} \left(a+b \log \left(c x^n\right)\right)}{4-r}-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{4 x^4}-\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{3 b d^2 e n x^{r-4}}{(4-r)^2}-\frac{b d^3 n}{16 x^4}-\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*d^3*n)/(16*x^4) - (3*b*d*e^2*n)/(4*(2 - r)^2*x^(2*(2 - r))) - (3*b*d^2*e*n*x^(-4 + r))/(4 - r)^2 - (b*e^3*n*x^(-4 + 3*r))/(4 - 3*r)^2 - ((d^3/x^4 + (6*d*e^2)/((2 - r)*x^(2*(2 - r))) + (12*d^2*e*x^(-4 + r))/(4 - r) + (4*e^3*x^(-4 + 3*r))/(4 - 3*r))*(a + b*Log[c*x^n]))/4","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
398,1,151,0,0.380962,"\int x^4 \left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^4*(d + e*x^r)^3*(a + b*Log[c*x^n]),x]","\frac{1}{5} \left(\frac{15 d^2 e x^{r+5}}{r+5}+d^3 x^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{3 b d^2 e n x^{r+5}}{(r+5)^2}-\frac{1}{25} b d^3 n x^5-\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}","\frac{1}{5} \left(\frac{15 d^2 e x^{r+5}}{r+5}+d^3 x^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{3 b d^2 e n x^{r+5}}{(r+5)^2}-\frac{1}{25} b d^3 n x^5-\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,"-(b*d^3*n*x^5)/25 - (3*b*d^2*e*n*x^(5 + r))/(5 + r)^2 - (3*b*d*e^2*n*x^(5 + 2*r))/(5 + 2*r)^2 - (b*e^3*n*x^(5 + 3*r))/(5 + 3*r)^2 + ((d^3*x^5 + (15*d^2*e*x^(5 + r))/(5 + r) + (15*d*e^2*x^(5 + 2*r))/(5 + 2*r) + (5*e^3*x^(5 + 3*r))/(5 + 3*r))*(a + b*Log[c*x^n]))/5","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
399,1,148,0,0.3806948,"\int x^2 \left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*(d + e*x^r)^3*(a + b*Log[c*x^n]),x]","\frac{1}{3} \left(\frac{9 d^2 e x^{r+3}}{r+3}+d^3 x^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{3 b d^2 e n x^{r+3}}{(r+3)^2}-\frac{1}{9} b d^3 n x^3-\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}","\frac{1}{3} \left(\frac{9 d^2 e x^{r+3}}{r+3}+d^3 x^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{3 b d^2 e n x^{r+3}}{(r+3)^2}-\frac{1}{9} b d^3 n x^3-\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,"-(b*d^3*n*x^3)/9 - (b*e^3*n*x^(3*(1 + r)))/(9*(1 + r)^2) - (3*b*d^2*e*n*x^(3 + r))/(3 + r)^2 - (3*b*d*e^2*n*x^(3 + 2*r))/(3 + 2*r)^2 + ((d^3*x^3 + (e^3*x^(3*(1 + r)))/(1 + r) + (9*d^2*e*x^(3 + r))/(3 + r) + (9*d*e^2*x^(3 + 2*r))/(3 + 2*r))*(a + b*Log[c*x^n]))/3","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
400,1,141,0,0.10286,"\int \left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(d + e*x^r)^3*(a + b*Log[c*x^n]),x]","\left(\frac{3 d^2 e x^{r+1}}{r+1}+d^3 x+\frac{3 d e^2 x^{2 r+1}}{2 r+1}+\frac{e^3 x^{3 r+1}}{3 r+1}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n x^{r+1}}{(r+1)^2}-b d^3 n x-\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}","\frac{3 d^2 e x^{r+1} \left(a+b \log \left(c x^n\right)\right)}{r+1}+d^3 x \left(a+b \log \left(c x^n\right)\right)+\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}-\frac{3 b d^2 e n x^{r+1}}{(r+1)^2}-b d^3 n x-\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,"-(b*d^3*n*x) - (3*b*d^2*e*n*x^(1 + r))/(1 + r)^2 - (3*b*d*e^2*n*x^(1 + 2*r))/(1 + 2*r)^2 - (b*e^3*n*x^(1 + 3*r))/(1 + 3*r)^2 + (d^3*x + (3*d^2*e*x^(1 + r))/(1 + r) + (3*d*e^2*x^(1 + 2*r))/(1 + 2*r) + (e^3*x^(1 + 3*r))/(1 + 3*r))*(a + b*Log[c*x^n])","A",2,2,20,0.1000,1,"{244, 2313}"
401,1,150,0,0.3973232,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x^2,x]","-\left(\frac{3 d^2 e x^{r-1}}{1-r}+\frac{d^3}{x}+\frac{3 d e^2 x^{2 r-1}}{1-2 r}+\frac{e^3 x^{3 r-1}}{1-3 r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n x^{r-1}}{(1-r)^2}-\frac{b d^3 n}{x}-\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}","-\frac{3 d^2 e x^{r-1} \left(a+b \log \left(c x^n\right)\right)}{1-r}-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{x}-\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{3 b d^2 e n x^{r-1}}{(1-r)^2}-\frac{b d^3 n}{x}-\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*d^3*n)/x) - (3*b*d^2*e*n*x^(-1 + r))/(1 - r)^2 - (3*b*d*e^2*n*x^(-1 + 2*r))/(1 - 2*r)^2 - (b*e^3*n*x^(-1 + 3*r))/(1 - 3*r)^2 - (d^3/x + (3*d^2*e*x^(-1 + r))/(1 - r) + (3*d*e^2*x^(-1 + 2*r))/(1 - 2*r) + (e^3*x^(-1 + 3*r))/(1 - 3*r))*(a + b*Log[c*x^n])","A",3,3,23,0.1304,1,"{270, 2334, 14}"
402,1,160,0,0.3932301,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Int[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x^4,x]","-\frac{1}{3} \left(\frac{9 d^2 e x^{r-3}}{3-r}+\frac{d^3}{x^3}+\frac{9 d e^2 x^{2 r-3}}{3-2 r}+\frac{e^3 x^{-3 (1-r)}}{1-r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n x^{r-3}}{(3-r)^2}-\frac{b d^3 n}{9 x^3}-\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}","-\frac{3 d^2 e x^{r-3} \left(a+b \log \left(c x^n\right)\right)}{3-r}-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\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{3 b d^2 e n x^{r-3}}{(3-r)^2}-\frac{b d^3 n}{9 x^3}-\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*d^3*n)/(9*x^3) - (b*e^3*n)/(9*(1 - r)^2*x^(3*(1 - r))) - (3*b*d^2*e*n*x^(-3 + r))/(3 - r)^2 - (3*b*d*e^2*n*x^(-3 + 2*r))/(3 - 2*r)^2 - ((d^3/x^3 + e^3/((1 - r)*x^(3*(1 - r))) + (9*d^2*e*x^(-3 + r))/(3 - r) + (9*d*e^2*x^(-3 + 2*r))/(3 - 2*r))*(a + b*Log[c*x^n]))/3","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
403,1,155,0,0.4115215,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^6} \, dx","Int[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x^6,x]","-\frac{1}{5} \left(\frac{15 d^2 e x^{r-5}}{5-r}+\frac{d^3}{x^5}+\frac{15 d e^2 x^{2 r-5}}{5-2 r}+\frac{5 e^3 x^{3 r-5}}{5-3 r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n x^{r-5}}{(5-r)^2}-\frac{b d^3 n}{25 x^5}-\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}","-\frac{3 d^2 e x^{r-5} \left(a+b \log \left(c x^n\right)\right)}{5-r}-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{5 x^5}-\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{3 b d^2 e n x^{r-5}}{(5-r)^2}-\frac{b d^3 n}{25 x^5}-\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*d^3*n)/(25*x^5) - (3*b*d^2*e*n*x^(-5 + r))/(5 - r)^2 - (3*b*d*e^2*n*x^(-5 + 2*r))/(5 - 2*r)^2 - (b*e^3*n*x^(-5 + 3*r))/(5 - 3*r)^2 - ((d^3/x^5 + (15*d^2*e*x^(-5 + r))/(5 - r) + (15*d*e^2*x^(-5 + 2*r))/(5 - 2*r) + (5*e^3*x^(-5 + 3*r))/(5 - 3*r))*(a + b*Log[c*x^n]))/5","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
404,1,155,0,0.4126313,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^8} \, dx","Int[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x^8,x]","-\frac{1}{7} \left(\frac{21 d^2 e x^{r-7}}{7-r}+\frac{d^3}{x^7}+\frac{21 d e^2 x^{2 r-7}}{7-2 r}+\frac{7 e^3 x^{3 r-7}}{7-3 r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n x^{r-7}}{(7-r)^2}-\frac{b d^3 n}{49 x^7}-\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}","-\frac{3 d^2 e x^{r-7} \left(a+b \log \left(c x^n\right)\right)}{7-r}-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{7 x^7}-\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{3 b d^2 e n x^{r-7}}{(7-r)^2}-\frac{b d^3 n}{49 x^7}-\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*d^3*n)/(49*x^7) - (3*b*d^2*e*n*x^(-7 + r))/(7 - r)^2 - (3*b*d*e^2*n*x^(-7 + 2*r))/(7 - 2*r)^2 - (b*e^3*n*x^(-7 + 3*r))/(7 - 3*r)^2 - ((d^3/x^7 + (21*d^2*e*x^(-7 + r))/(7 - r) + (21*d*e^2*x^(-7 + 2*r))/(7 - 2*r) + (7*e^3*x^(-7 + 3*r))/(7 - 3*r))*(a + b*Log[c*x^n]))/7","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
405,1,161,0,0.4189936,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x^{10}} \, dx","Int[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x^10,x]","-\frac{1}{9} \left(\frac{27 d^2 e x^{r-9}}{9-r}+\frac{d^3}{x^9}+\frac{27 d e^2 x^{2 r-9}}{9-2 r}+\frac{3 e^3 x^{-3 (3-r)}}{3-r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n x^{r-9}}{(9-r)^2}-\frac{b d^3 n}{81 x^9}-\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}","-\frac{3 d^2 e x^{r-9} \left(a+b \log \left(c x^n\right)\right)}{9-r}-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)}{9 x^9}-\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{3 b d^2 e n x^{r-9}}{(9-r)^2}-\frac{b d^3 n}{81 x^9}-\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*d^3*n)/(81*x^9) - (b*e^3*n)/(9*(3 - r)^2*x^(3*(3 - r))) - (3*b*d^2*e*n*x^(-9 + r))/(9 - r)^2 - (3*b*d*e^2*n*x^(-9 + 2*r))/(9 - 2*r)^2 - ((d^3/x^9 + (3*e^3)/((3 - r)*x^(3*(3 - r))) + (27*d^2*e*x^(-9 + r))/(9 - r) + (27*d*e^2*x^(-9 + 2*r))/(9 - 2*r))*(a + b*Log[c*x^n]))/9","A",4,4,23,0.1739,1,"{270, 2334, 12, 14}"
406,0,0,0,0.0642847,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{d+e x^r} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/(d + e*x^r),x]","\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{d+e x^r} \, dx","\text{Int}\left(\frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{d+e x^r},x\right)",0,"Defer[Int][(x^3*(a + b*Log[c*x^n]))/(d + e*x^r), x]","A",0,0,0,0,-1,"{}"
407,0,0,0,0.0411681,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{d+e x^r} \, dx","Int[(x*(a + b*Log[c*x^n]))/(d + e*x^r),x]","\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{d+e x^r} \, dx","\text{Int}\left(\frac{x \left(a+b \log \left(c x^n\right)\right)}{d+e x^r},x\right)",0,"Defer[Int][(x*(a + b*Log[c*x^n]))/(d + e*x^r), x]","A",0,0,0,0,-1,"{}"
408,1,54,0,0.0777626,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x^r)),x]","\frac{b n \text{PolyLog}\left(2,-\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}","\frac{b n \text{PolyLog}\left(2,-\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,"-(((a + b*Log[c*x^n])*Log[1 + d/(e*x^r)])/(d*r)) + (b*n*PolyLog[2, -(d/(e*x^r))])/(d*r^2)","A",2,2,23,0.08696,1,"{2345, 2391}"
409,0,0,0,0.0640177,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^r\right)} \, dx","Int[(a + b*Log[c*x^n])/(x^3*(d + e*x^r)),x]","\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^r\right)} \, dx","\text{Int}\left(\frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^r\right)},x\right)",0,"Defer[Int][(a + b*Log[c*x^n])/(x^3*(d + e*x^r)), x]","A",0,0,0,0,-1,"{}"
410,0,0,0,0.0648725,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{d+e x^r} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/(d + e*x^r),x]","\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{d+e x^r} \, dx","\text{Int}\left(\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{d+e x^r},x\right)",0,"Defer[Int][(x^2*(a + b*Log[c*x^n]))/(d + e*x^r), x]","A",0,0,0,0,-1,"{}"
411,0,0,0,0.0180241,"\int \frac{a+b \log \left(c x^n\right)}{d+e x^r} \, dx","Int[(a + b*Log[c*x^n])/(d + e*x^r),x]","\int \frac{a+b \log \left(c x^n\right)}{d+e x^r} \, dx","\text{Int}\left(\frac{a+b \log \left(c x^n\right)}{d+e x^r},x\right)",0,"Defer[Int][(a + b*Log[c*x^n])/(d + e*x^r), x]","A",0,0,0,0,-1,"{}"
412,0,0,0,0.0655535,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^r\right)} \, dx","Int[(a + b*Log[c*x^n])/(x^2*(d + e*x^r)),x]","\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^r\right)} \, dx","\text{Int}\left(\frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^r\right)},x\right)",0,"Defer[Int][(a + b*Log[c*x^n])/(x^2*(d + e*x^r)), x]","A",0,0,0,0,-1,"{}"
413,0,0,0,0.0639346,"\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^r\right)^2} \, dx","Int[(x^3*(a + b*Log[c*x^n]))/(d + e*x^r)^2,x]","\int \frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^r\right)^2} \, dx","\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,"Defer[Int][(x^3*(a + b*Log[c*x^n]))/(d + e*x^r)^2, x]","A",0,0,0,0,-1,"{}"
414,0,0,0,0.0397893,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^r\right)^2} \, dx","Int[(x*(a + b*Log[c*x^n]))/(d + e*x^r)^2,x]","\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^r\right)^2} \, dx","\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,"Defer[Int][(x*(a + b*Log[c*x^n]))/(d + e*x^r)^2, x]","A",0,0,0,0,-1,"{}"
415,1,102,0,0.2328984,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)^2} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x^r)^2),x]","\frac{b n \text{PolyLog}\left(2,-\frac{d x^{-r}}{e}\right)}{d^2 r^2}-\frac{e x^r \left(a+b \log \left(c x^n\right)\right)}{d^2 r \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)}{d^2 r}+\frac{b n \log \left(d+e x^r\right)}{d^2 r^2}","\frac{b n \text{PolyLog}\left(2,-\frac{d x^{-r}}{e}\right)}{d^2 r^2}-\frac{e x^r \left(a+b \log \left(c x^n\right)\right)}{d^2 r \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)}{d^2 r}+\frac{b n \log \left(d+e x^r\right)}{d^2 r^2}",1,"-((e*x^r*(a + b*Log[c*x^n]))/(d^2*r*(d + e*x^r))) - ((a + b*Log[c*x^n])*Log[1 + d/(e*x^r)])/(d^2*r) + (b*n*Log[d + e*x^r])/(d^2*r^2) + (b*n*PolyLog[2, -(d/(e*x^r))])/(d^2*r^2)","A",5,5,23,0.2174,1,"{2349, 2345, 2391, 2335, 260}"
416,0,0,0,0.0629914,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^r\right)^2} \, dx","Int[(a + b*Log[c*x^n])/(x^3*(d + e*x^r)^2),x]","\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^r\right)^2} \, dx","\text{Int}\left(\frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e x^r\right)^2},x\right)",0,"Defer[Int][(a + b*Log[c*x^n])/(x^3*(d + e*x^r)^2), x]","A",0,0,0,0,-1,"{}"
417,0,0,0,0.0628515,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^r\right)^2} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/(d + e*x^r)^2,x]","\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^r\right)^2} \, dx","\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,"Defer[Int][(x^2*(a + b*Log[c*x^n]))/(d + e*x^r)^2, x]","A",0,0,0,0,-1,"{}"
418,0,0,0,0.0168403,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+e x^r\right)^2} \, dx","Int[(a + b*Log[c*x^n])/(d + e*x^r)^2,x]","\int \frac{a+b \log \left(c x^n\right)}{\left(d+e x^r\right)^2} \, dx","\text{Int}\left(\frac{a+b \log \left(c x^n\right)}{\left(d+e x^r\right)^2},x\right)",0,"Defer[Int][(a + b*Log[c*x^n])/(d + e*x^r)^2, x]","A",0,0,0,0,-1,"{}"
419,0,0,0,0.0622788,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^r\right)^2} \, dx","Int[(a + b*Log[c*x^n])/(x^2*(d + e*x^r)^2),x]","\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^r\right)^2} \, dx","\text{Int}\left(\frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e x^r\right)^2},x\right)",0,"Defer[Int][(a + b*Log[c*x^n])/(x^2*(d + e*x^r)^2), x]","A",0,0,0,0,-1,"{}"
420,1,37,0,0.1440236,"\int \frac{a+b \log \left(c x^n\right)}{x \left(c-x^{-n}\right)} \, dx","Int[(a + b*Log[c*x^n])/(x*(c - x^(-n))),x]","\frac{a \log \left(1-c x^n\right)}{c n}-\frac{b \text{PolyLog}\left(2,1-c x^n\right)}{c n}","\frac{a \log \left(1-c x^n\right)}{c n}-\frac{b \text{PolyLog}\left(2,1-c x^n\right)}{c n}",1,"(a*Log[1 - c*x^n])/(c*n) - (b*PolyLog[2, 1 - c*x^n])/(c*n)","A",4,4,25,0.1600,1,"{2343, 2333, 2316, 2315}"
421,1,124,0,0.1539878,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[((d + e*x^r)^3*(a + b*Log[c*x^n]))/x,x]","\frac{1}{6} \left(\frac{18 d^2 e x^r}{r}+6 d^3 \log (x)+\frac{9 d e^2 x^{2 r}}{r}+\frac{2 e^3 x^{3 r}}{r}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b d^2 e n x^r}{r^2}-\frac{1}{2} b d^3 n \log ^2(x)-\frac{3 b d e^2 n x^{2 r}}{4 r^2}-\frac{b e^3 n x^{3 r}}{9 r^2}","\frac{3 d^2 e x^r \left(a+b \log \left(c x^n\right)\right)}{r}+d^3 \log (x) \left(a+b \log \left(c x^n\right)\right)+\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{3 b d^2 e n x^r}{r^2}-\frac{1}{2} b d^3 n \log ^2(x)-\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,"(-3*b*d^2*e*n*x^r)/r^2 - (3*b*d*e^2*n*x^(2*r))/(4*r^2) - (b*e^3*n*x^(3*r))/(9*r^2) - (b*d^3*n*Log[x]^2)/2 + (((18*d^2*e*x^r)/r + (9*d*e^2*x^(2*r))/r + (2*e^3*x^(3*r))/r + 6*d^3*Log[x])*(a + b*Log[c*x^n]))/6","A",5,6,23,0.2609,1,"{266, 43, 2334, 12, 14, 2301}"
422,1,87,0,0.1272371,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[((d + e*x^r)^2*(a + b*Log[c*x^n]))/x,x]","\frac{1}{2} \left(2 d^2 \log (x)+\frac{4 d e x^r}{r}+\frac{e^2 x^{2 r}}{r}\right) \left(a+b \log \left(c x^n\right)\right)-\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}","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,"(-2*b*d*e*n*x^r)/r^2 - (b*e^2*n*x^(2*r))/(4*r^2) - (b*d^2*n*Log[x]^2)/2 + (((4*d*e*x^r)/r + (e^2*x^(2*r))/r + 2*d^2*Log[x])*(a + b*Log[c*x^n]))/2","A",5,6,23,0.2609,1,"{266, 43, 2334, 12, 14, 2301}"
423,1,53,0,0.0847481,"\int \frac{\left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[((d + e*x^r)*(a + b*Log[c*x^n]))/x,x]","\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}","\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,"-((b*e*n*x^r)/r^2) + (e*x^r*(a + b*Log[c*x^n]))/r + (d*(a + b*Log[c*x^n])^2)/(2*b*n)","A",4,4,21,0.1905,1,"{14, 2351, 2301, 2304}"
424,1,54,0,0.0753664,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x^r)),x]","\frac{b n \text{PolyLog}\left(2,-\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}","\frac{b n \text{PolyLog}\left(2,-\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,"-(((a + b*Log[c*x^n])*Log[1 + d/(e*x^r)])/(d*r)) + (b*n*PolyLog[2, -(d/(e*x^r))])/(d*r^2)","A",2,2,23,0.08696,1,"{2345, 2391}"
425,1,102,0,0.2292729,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)^2} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x^r)^2),x]","\frac{b n \text{PolyLog}\left(2,-\frac{d x^{-r}}{e}\right)}{d^2 r^2}-\frac{e x^r \left(a+b \log \left(c x^n\right)\right)}{d^2 r \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)}{d^2 r}+\frac{b n \log \left(d+e x^r\right)}{d^2 r^2}","\frac{b n \text{PolyLog}\left(2,-\frac{d x^{-r}}{e}\right)}{d^2 r^2}-\frac{e x^r \left(a+b \log \left(c x^n\right)\right)}{d^2 r \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)}{d^2 r}+\frac{b n \log \left(d+e x^r\right)}{d^2 r^2}",1,"-((e*x^r*(a + b*Log[c*x^n]))/(d^2*r*(d + e*x^r))) - ((a + b*Log[c*x^n])*Log[1 + d/(e*x^r)])/(d^2*r) + (b*n*Log[d + e*x^r])/(d^2*r^2) + (b*n*PolyLog[2, -(d/(e*x^r))])/(d^2*r^2)","A",5,5,23,0.2174,1,"{2349, 2345, 2391, 2335, 260}"
426,1,169,0,0.4092807,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)^3} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x^r)^3),x]","\frac{b n \text{PolyLog}\left(2,-\frac{d x^{-r}}{e}\right)}{d^3 r^2}-\frac{e x^r \left(a+b \log \left(c x^n\right)\right)}{d^3 r \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)}{d^3 r}+\frac{a+b \log \left(c x^n\right)}{2 d r \left(d+e x^r\right)^2}-\frac{b n}{2 d^2 r^2 \left(d+e x^r\right)}+\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 \text{PolyLog}\left(2,-\frac{d x^{-r}}{e}\right)}{d^3 r^2}-\frac{e x^r \left(a+b \log \left(c x^n\right)\right)}{d^3 r \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)}{d^3 r}+\frac{a+b \log \left(c x^n\right)}{2 d r \left(d+e x^r\right)^2}-\frac{b n}{2 d^2 r^2 \left(d+e x^r\right)}+\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}",1,"-(b*n)/(2*d^2*r^2*(d + e*x^r)) - (b*n*Log[x])/(2*d^3*r) + (a + b*Log[c*x^n])/(2*d*r*(d + e*x^r)^2) - (e*x^r*(a + b*Log[c*x^n]))/(d^3*r*(d + e*x^r)) - ((a + b*Log[c*x^n])*Log[1 + d/(e*x^r)])/(d^3*r) + (3*b*n*Log[d + e*x^r])/(2*d^3*r^2) + (b*n*PolyLog[2, -(d/(e*x^r))])/(d^3*r^2)","A",10,8,23,0.3478,1,"{2349, 2345, 2391, 2335, 260, 2338, 266, 44}"
427,1,245,0,0.3034028,"\int \frac{\left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)^2}{x} \, dx","Int[((d + e*x^r)^3*(a + b*Log[c*x^n])^2)/x,x]","-\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{d^3 \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}-\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}","-\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{d^3 \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}-\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,"(6*b^2*d^2*e*n^2*x^r)/r^3 + (3*b^2*d*e^2*n^2*x^(2*r))/(4*r^3) + (2*b^2*e^3*n^2*x^(3*r))/(27*r^3) - (6*b*d^2*e*n*x^r*(a + b*Log[c*x^n]))/r^2 - (3*b*d*e^2*n*x^(2*r)*(a + b*Log[c*x^n]))/(2*r^2) - (2*b*e^3*n*x^(3*r)*(a + b*Log[c*x^n]))/(9*r^2) + (3*d^2*e*x^r*(a + b*Log[c*x^n])^2)/r + (3*d*e^2*x^(2*r)*(a + b*Log[c*x^n])^2)/(2*r) + (e^3*x^(3*r)*(a + b*Log[c*x^n])^2)/(3*r) + (d^3*(a + b*Log[c*x^n])^3)/(3*b*n)","A",10,5,25,0.2000,1,"{2353, 2302, 30, 2305, 2304}"
428,1,161,0,0.2367193,"\int \frac{\left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)^2}{x} \, dx","Int[((d + e*x^r)^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}-\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}","\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,"(4*b^2*d*e*n^2*x^r)/r^3 + (b^2*e^2*n^2*x^(2*r))/(4*r^3) - (4*b*d*e*n*x^r*(a + b*Log[c*x^n]))/r^2 - (b*e^2*n*x^(2*r)*(a + b*Log[c*x^n]))/(2*r^2) + (2*d*e*x^r*(a + b*Log[c*x^n])^2)/r + (e^2*x^(2*r)*(a + b*Log[c*x^n])^2)/(2*r) + (d^2*(a + b*Log[c*x^n])^3)/(3*b*n)","A",8,5,25,0.2000,1,"{2353, 2302, 30, 2305, 2304}"
429,1,80,0,0.1390851,"\int \frac{\left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)^2}{x} \, dx","Int[((d + e*x^r)*(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}-\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}","\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,"(2*b^2*e*n^2*x^r)/r^3 - (2*b*e*n*x^r*(a + b*Log[c*x^n]))/r^2 + (e*x^r*(a + b*Log[c*x^n])^2)/r + (d*(a + b*Log[c*x^n])^3)/(3*b*n)","A",6,5,23,0.2174,1,"{2353, 2302, 30, 2305, 2304}"
430,1,94,0,0.1351878,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x \left(d+e x^r\right)} \, dx","Int[(a + b*Log[c*x^n])^2/(x*(d + e*x^r)),x]","\frac{2 b n \text{PolyLog}\left(2,-\frac{d x^{-r}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{d r^2}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{d x^{-r}}{e}\right)}{d r^3}-\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 n \text{PolyLog}\left(2,-\frac{d x^{-r}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{d r^2}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{d x^{-r}}{e}\right)}{d r^3}-\frac{\log \left(\frac{d x^{-r}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d r}",1,"-(((a + b*Log[c*x^n])^2*Log[1 + d/(e*x^r)])/(d*r)) + (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -(d/(e*x^r))])/(d*r^2) + (2*b^2*n^2*PolyLog[3, -(d/(e*x^r))])/(d*r^3)","A",3,3,25,0.1200,1,"{2345, 2374, 6589}"
431,1,182,0,0.4265351,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x \left(d+e x^r\right)^2} \, dx","Int[(a + b*Log[c*x^n])^2/(x*(d + e*x^r)^2),x]","\frac{2 b n \text{PolyLog}\left(2,-\frac{d x^{-r}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 r^2}-\frac{2 b^2 n^2 \text{PolyLog}\left(2,-\frac{d x^{-r}}{e}\right)}{d^2 r^3}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{d x^{-r}}{e}\right)}{d^2 r^3}+\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 n \text{PolyLog}\left(2,-\frac{d x^{-r}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 r^2}-\frac{2 b^2 n^2 \text{PolyLog}\left(2,-\frac{d x^{-r}}{e}\right)}{d^2 r^3}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{d x^{-r}}{e}\right)}{d^2 r^3}+\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)}",1,"(a + b*Log[c*x^n])^2/(d*r*(d + e*x^r)) + (2*b*n*(a + b*Log[c*x^n])*Log[1 + d/(e*x^r)])/(d^2*r^2) - ((a + b*Log[c*x^n])^2*Log[1 + d/(e*x^r)])/(d^2*r) - (2*b^2*n^2*PolyLog[2, -(d/(e*x^r))])/(d^2*r^3) + (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -(d/(e*x^r))])/(d^2*r^2) + (2*b^2*n^2*PolyLog[3, -(d/(e*x^r))])/(d^2*r^3)","A",7,6,25,0.2400,1,"{2349, 2345, 2374, 6589, 2338, 2391}"
432,1,267,0,0.891979,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x \left(d+e x^r\right)^3} \, dx","Int[(a + b*Log[c*x^n])^2/(x*(d + e*x^r)^3),x]","\frac{2 b n \text{PolyLog}\left(2,-\frac{d x^{-r}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3 r^2}-\frac{3 b^2 n^2 \text{PolyLog}\left(2,-\frac{d x^{-r}}{e}\right)}{d^3 r^3}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{d x^{-r}}{e}\right)}{d^3 r^3}+\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{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{\left(a+b \log \left(c x^n\right)\right)^2}{d^2 r \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}{2 d r \left(d+e x^r\right)^2}-\frac{b^2 n^2 \log \left(d+e x^r\right)}{d^3 r^3}","\frac{2 b n \text{PolyLog}\left(2,-\frac{d x^{-r}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{d^3 r^2}-\frac{3 b^2 n^2 \text{PolyLog}\left(2,-\frac{d x^{-r}}{e}\right)}{d^3 r^3}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\frac{d x^{-r}}{e}\right)}{d^3 r^3}+\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{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{\left(a+b \log \left(c x^n\right)\right)^2}{d^2 r \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}{2 d r \left(d+e x^r\right)^2}-\frac{b^2 n^2 \log \left(d+e x^r\right)}{d^3 r^3}",1,"(b*e*n*x^r*(a + b*Log[c*x^n]))/(d^3*r^2*(d + e*x^r)) + (a + b*Log[c*x^n])^2/(2*d*r*(d + e*x^r)^2) + (a + b*Log[c*x^n])^2/(d^2*r*(d + e*x^r)) + (3*b*n*(a + b*Log[c*x^n])*Log[1 + d/(e*x^r)])/(d^3*r^2) - ((a + b*Log[c*x^n])^2*Log[1 + d/(e*x^r)])/(d^3*r) - (b^2*n^2*Log[d + e*x^r])/(d^3*r^3) - (3*b^2*n^2*PolyLog[2, -(d/(e*x^r))])/(d^3*r^3) + (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -(d/(e*x^r))])/(d^3*r^2) + (2*b^2*n^2*PolyLog[3, -(d/(e*x^r))])/(d^3*r^3)","A",14,8,25,0.3200,1,"{2349, 2345, 2374, 6589, 2338, 2391, 2335, 260}"
433,1,327,0,0.4802871,"\int \frac{\left(d+e x^r\right)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[((d + e*x^r)^(5/2)*(a + b*Log[c*x^n]))/x,x]","-\frac{2 b d^{5/2} n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right)}{r^2}+\frac{2}{15} \left(\frac{15 d^2 \sqrt{d+e x^r}}{r}-\frac{15 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{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{92 b d^2 n \sqrt{d+e x^r}}{15 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{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}","-\frac{2 b d^{5/2} n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right)}{r^2}+\frac{2}{15} \left(\frac{15 d^2 \sqrt{d+e x^r}}{r}-\frac{15 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{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{92 b d^2 n \sqrt{d+e x^r}}{15 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{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,"(-92*b*d^2*n*Sqrt[d + e*x^r])/(15*r^2) - (32*b*d*n*(d + e*x^r)^(3/2))/(45*r^2) - (4*b*n*(d + e*x^r)^(5/2))/(25*r^2) + (92*b*d^(5/2)*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]])/(15*r^2) + (2*b*d^(5/2)*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]]^2)/r^2 + (2*((15*d^2*Sqrt[d + e*x^r])/r + (5*d*(d + e*x^r)^(3/2))/r + (3*(d + e*x^r)^(5/2))/r - (15*d^(5/2)*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]])/r)*(a + b*Log[c*x^n]))/15 - (4*b*d^(5/2)*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^r])])/r^2 - (2*b*d^(5/2)*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^r])])/r^2","A",23,9,25,0.3600,1,"{266, 50, 63, 208, 2348, 5984, 5918, 2402, 2315}"
434,1,284,0,0.3914272,"\int \frac{\left(d+e x^r\right)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[((d + e*x^r)^(3/2)*(a + b*Log[c*x^n]))/x,x]","-\frac{2 b d^{3/2} n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right)}{r^2}+\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 \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}","-\frac{2 b d^{3/2} n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right)}{r^2}+\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 \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,"(-16*b*d*n*Sqrt[d + e*x^r])/(3*r^2) - (4*b*n*(d + e*x^r)^(3/2))/(9*r^2) + (16*b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]])/(3*r^2) + (2*b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]]^2)/r^2 + (2*((3*d*Sqrt[d + e*x^r])/r + (d + e*x^r)^(3/2)/r - (3*d^(3/2)*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]])/r)*(a + b*Log[c*x^n]))/3 - (4*b*d^(3/2)*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^r])])/r^2 - (2*b*d^(3/2)*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^r])])/r^2","A",17,9,25,0.3600,1,"{266, 50, 63, 208, 2348, 5984, 5918, 2402, 2315}"
435,1,240,0,0.3170361,"\int \frac{\sqrt{d+e x^r} \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[(Sqrt[d + e*x^r]*(a + b*Log[c*x^n]))/x,x]","-\frac{2 b \sqrt{d} n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right)}{r^2}+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{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}","-\frac{2 b \sqrt{d} n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right)}{r^2}+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{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,"(-4*b*n*Sqrt[d + e*x^r])/r^2 + (4*b*Sqrt[d]*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]])/r^2 + (2*b*Sqrt[d]*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]]^2)/r^2 + 2*(Sqrt[d + e*x^r]/r - (Sqrt[d]*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]])/r)*(a + b*Log[c*x^n]) - (4*b*Sqrt[d]*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^r])])/r^2 - (2*b*Sqrt[d]*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^r])])/r^2","A",12,9,25,0.3600,1,"{266, 50, 63, 208, 2348, 5984, 5918, 2402, 2315}"
436,1,174,0,0.2693327,"\int \frac{a+b \log \left(c x^n\right)}{x \sqrt{d+e x^r}} \, dx","Int[(a + b*Log[c*x^n])/(x*Sqrt[d + e*x^r]),x]","-\frac{2 b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right)}{\sqrt{d} r^2}-\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 \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}","-\frac{2 b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right)}{\sqrt{d} r^2}-\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 \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,"(2*b*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]]^2)/(Sqrt[d]*r^2) - (2*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]]*(a + b*Log[c*x^n]))/(Sqrt[d]*r) - (4*b*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^r])])/(Sqrt[d]*r^2) - (2*b*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^r])])/(Sqrt[d]*r^2)","A",8,9,25,0.3600,1,"{266, 63, 208, 2348, 12, 5984, 5918, 2402, 2315}"
437,1,225,0,0.342926,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)^{3/2}} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x^r)^(3/2)),x]","-\frac{2 b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right)}{d^{3/2} r^2}+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 \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}","-\frac{2 b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right)}{d^{3/2} r^2}+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 \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,"(4*b*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]])/(d^(3/2)*r^2) + (2*b*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]]^2)/(d^(3/2)*r^2) + 2*(1/(d*r*Sqrt[d + e*x^r]) - ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]]/(d^(3/2)*r))*(a + b*Log[c*x^n]) - (4*b*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^r])])/(d^(3/2)*r^2) - (2*b*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^r])])/(d^(3/2)*r^2)","A",11,9,25,0.3600,1,"{266, 51, 63, 208, 2348, 5984, 5918, 2402, 2315}"
438,1,271,0,0.4158625,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)^{5/2}} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x^r)^(5/2)),x]","-\frac{2 b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right)}{d^{5/2} r^2}+\frac{2}{3} \left(\frac{3}{d^2 r \sqrt{d+e x^r}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{d^{5/2} 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{4 b n}{3 d^2 r^2 \sqrt{d+e x^r}}+\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{2 b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right)}{d^{5/2} r^2}+\frac{2}{3} \left(\frac{3}{d^2 r \sqrt{d+e x^r}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{d^{5/2} 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{4 b n}{3 d^2 r^2 \sqrt{d+e x^r}}+\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}",1,"(-4*b*n)/(3*d^2*r^2*Sqrt[d + e*x^r]) + (16*b*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]])/(3*d^(5/2)*r^2) + (2*b*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]]^2)/(d^(5/2)*r^2) + (2*(1/(d*r*(d + e*x^r)^(3/2)) + 3/(d^2*r*Sqrt[d + e*x^r]) - (3*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]])/(d^(5/2)*r))*(a + b*Log[c*x^n]))/3 - (4*b*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^r])])/(d^(5/2)*r^2) - (2*b*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^r])])/(d^(5/2)*r^2)","A",15,9,25,0.3600,1,"{266, 51, 63, 208, 2348, 5984, 5918, 2402, 2315}"
439,1,314,0,0.4708362,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e x^r\right)^{7/2}} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*x^r)^(7/2)),x]","-\frac{2 b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right)}{d^{7/2} r^2}+\frac{2}{15} \left(\frac{15}{d^3 r \sqrt{d+e x^r}}+\frac{5}{d^2 r \left(d+e x^r\right)^{3/2}}-\frac{15 \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{d^{7/2} r}+\frac{3}{d r \left(d+e x^r\right)^{5/2}}\right) \left(a+b \log \left(c x^n\right)\right)-\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}}+\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{2 b n \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}-\sqrt{d+e x^r}}\right)}{d^{7/2} r^2}+\frac{2}{15} \left(\frac{15}{d^3 r \sqrt{d+e x^r}}+\frac{5}{d^2 r \left(d+e x^r\right)^{3/2}}-\frac{15 \tanh ^{-1}\left(\frac{\sqrt{d+e x^r}}{\sqrt{d}}\right)}{d^{7/2} r}+\frac{3}{d r \left(d+e x^r\right)^{5/2}}\right) \left(a+b \log \left(c x^n\right)\right)-\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}}+\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}",1,"(-4*b*n)/(15*d^2*r^2*(d + e*x^r)^(3/2)) - (32*b*n)/(15*d^3*r^2*Sqrt[d + e*x^r]) + (92*b*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]])/(15*d^(7/2)*r^2) + (2*b*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]]^2)/(d^(7/2)*r^2) + (2*(3/(d*r*(d + e*x^r)^(5/2)) + 5/(d^2*r*(d + e*x^r)^(3/2)) + 15/(d^3*r*Sqrt[d + e*x^r]) - (15*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]])/(d^(7/2)*r))*(a + b*Log[c*x^n]))/15 - (4*b*n*ArcTanh[Sqrt[d + e*x^r]/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^r])])/(d^(7/2)*r^2) - (2*b*n*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] - Sqrt[d + e*x^r])])/(d^(7/2)*r^2)","A",20,9,25,0.3600,1,"{266, 51, 63, 208, 2348, 5984, 5918, 2402, 2315}"
440,1,233,0,1.9872469,"\int (f x)^m \left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(f*x)^m*(d + e*x^r)^3*(a + b*Log[c*x^n]),x]","\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{d^3 (f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+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{3 b d^2 e n x^{r+1} (f x)^m}{(m+r+1)^2}-\frac{b d^3 n (f x)^{m+1}}{f (m+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}","\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{d^3 (f x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{f (m+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{3 b d^2 e n x^{r+1} (f x)^m}{(m+r+1)^2}-\frac{b d^3 n (f x)^{m+1}}{f (m+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,"(-3*b*d^2*e*n*x^(1 + r)*(f*x)^m)/(1 + m + r)^2 - (3*b*d*e^2*n*x^(1 + 2*r)*(f*x)^m)/(1 + m + 2*r)^2 - (b*e^3*n*x^(1 + 3*r)*(f*x)^m)/(1 + m + 3*r)^2 - (b*d^3*n*(f*x)^(1 + m))/(f*(1 + m)^2) + (3*d^2*e*x^(1 + r)*(f*x)^m*(a + b*Log[c*x^n]))/(1 + m + r) + (3*d*e^2*x^(1 + 2*r)*(f*x)^m*(a + b*Log[c*x^n]))/(1 + m + 2*r) + (e^3*x^(1 + 3*r)*(f*x)^m*(a + b*Log[c*x^n]))/(1 + m + 3*r) + (d^3*(f*x)^(1 + m)*(a + b*Log[c*x^n]))/(f*(1 + m))","A",9,5,25,0.2000,1,"{270, 20, 30, 2350, 14}"
441,1,165,0,0.1853991,"\int (f x)^m \left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(f*x)^m*(d + e*x^r)^2*(a + b*Log[c*x^n]),x]","\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}","\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,"(-2*b*d*e*n*x^(1 + r)*(f*x)^m)/(1 + m + r)^2 - (b*e^2*n*x^(1 + 2*r)*(f*x)^m)/(1 + m + 2*r)^2 - (b*d^2*n*(f*x)^(1 + m))/(f*(1 + m)^2) + (2*d*e*x^(1 + r)*(f*x)^m*(a + b*Log[c*x^n]))/(1 + m + r) + (e^2*x^(1 + 2*r)*(f*x)^m*(a + b*Log[c*x^n]))/(1 + m + 2*r) + (d^2*(f*x)^(1 + m)*(a + b*Log[c*x^n]))/(f*(1 + m))","A",7,5,25,0.2000,1,"{270, 20, 30, 2350, 14}"
442,1,97,0,0.1027069,"\int (f x)^m \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(f*x)^m*(d + e*x^r)*(a + b*Log[c*x^n]),x]","\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}","\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,"-((b*e*n*x^(1 + r)*(f*x)^m)/(1 + m + r)^2) - (b*d*n*(f*x)^(1 + m))/(f*(1 + m)^2) + (e*x^(1 + r)*(f*x)^m*(a + b*Log[c*x^n]))/(1 + m + r) + (d*(f*x)^(1 + m)*(a + b*Log[c*x^n]))/(f*(1 + m))","A",5,4,23,0.1739,1,"{14, 20, 30, 2350}"
443,1,46,0,0.0171639,"\int (f x)^m \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(f*x)^m*(a + b*Log[c*x^n]),x]","\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}","\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,"-((b*n*(f*x)^(1 + m))/(f*(1 + m)^2)) + ((f*x)^(1 + m)*(a + b*Log[c*x^n]))/(f*(1 + m))","A",1,1,16,0.06250,1,"{2304}"
444,0,0,0,0.0701191,"\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{d+e x^r} \, dx","Int[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x^r),x]","\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{d+e x^r} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{d+e x^r},x\right)",0,"Defer[Int][((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x^r), x]","A",0,0,0,0,-1,"{}"
445,0,0,0,0.0688923,"\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{\left(d+e x^r\right)^2} \, dx","Int[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x^r)^2,x]","\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)}{\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)}{\left(d+e x^r\right)^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x^r)^2, x]","A",0,0,0,0,-1,"{}"
446,1,102,0,0.0440655,"\int \left(d+e x^{-\frac{1}{1+q}}\right)^q \left(a+b \log \left(c x^n\right)\right) \, dx","Int[(d + e/x^(1 + q)^(-1))^q*(a + b*Log[c*x^n]),x]","\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)","\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,"-((b*n*x*(d + e/x^(1 + q)^(-1))^q*Hypergeometric2F1[-1 - q, -1 - q, -q, -(e/(d*x^(1 + q)^(-1)))])/(1 + e/(d*x^(1 + q)^(-1)))^q) + (x*(d + e/x^(1 + q)^(-1))^(1 + q)*(a + b*Log[c*x^n]))/d","A",3,3,26,0.1154,1,"{2314, 246, 245}"
447,1,119,0,0.1326198,"\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","Int[(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+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}","-\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,"-((b*n*(d + e*x^r)^q*Hypergeometric2F1[-1 - q, -1 - q, -q, -((e*x^r)/d)])/(f*(1 + q)^2*r^2*(f*x)^((1 + q)*r)*(1 + (e*x^r)/d)^q)) - ((d + e*x^r)^(1 + q)*(a + b*Log[c*x^n]))/(d*f*(1 + q)*r*(f*x)^((1 + q)*r))","A",3,3,32,0.09375,1,"{2335, 365, 364}"
448,1,480,0,0.6602582,"\int (f x)^m \left(d+e x^r\right)^3 \left(a+b \log \left(c x^n\right)\right)^p \, dx","Int[(f*x)^m*(d + e*x^r)^3*(a + b*Log[c*x^n])^p,x]","\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} \text{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{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} \text{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 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} \text{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} \text{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}","\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} \text{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{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} \text{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 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} \text{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} \text{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,"(d^3*(f*x)^(1 + m)*Gamma[1 + p, -(((1 + m)*(a + b*Log[c*x^n]))/(b*n))]*(a + b*Log[c*x^n])^p)/(E^((a*(1 + m))/(b*n))*f*(1 + m)*(c*x^n)^((1 + m)/n)*(-(((1 + m)*(a + b*Log[c*x^n]))/(b*n)))^p) + (3*d^2*e*x^(1 + r)*(f*x)^m*Gamma[1 + p, -(((1 + m + r)*(a + b*Log[c*x^n]))/(b*n))]*(a + b*Log[c*x^n])^p)/(E^((a*(1 + m + r))/(b*n))*(1 + m + r)*(c*x^n)^((1 + m + r)/n)*(-(((1 + m + r)*(a + b*Log[c*x^n]))/(b*n)))^p) + (3*d*e^2*x^(1 + 2*r)*(f*x)^m*Gamma[1 + p, -(((1 + m + 2*r)*(a + b*Log[c*x^n]))/(b*n))]*(a + b*Log[c*x^n])^p)/(E^((a*(1 + m + 2*r))/(b*n))*(1 + m + 2*r)*(c*x^n)^((1 + m + 2*r)/n)*(-(((1 + m + 2*r)*(a + b*Log[c*x^n]))/(b*n)))^p) + (e^3*x^(1 + 3*r)*(f*x)^m*Gamma[1 + p, -(((1 + m + 3*r)*(a + b*Log[c*x^n]))/(b*n))]*(a + b*Log[c*x^n])^p)/(E^((a*(1 + m + 3*r))/(b*n))*(1 + m + 3*r)*(c*x^n)^((1 + m + 3*r)/n)*(-(((1 + m + 3*r)*(a + b*Log[c*x^n]))/(b*n)))^p)","A",13,4,27,0.1481,1,"{2353, 2310, 2181, 20}"
449,1,350,0,0.4127137,"\int (f x)^m \left(d+e x^r\right)^2 \left(a+b \log \left(c x^n\right)\right)^p \, dx","Int[(f*x)^m*(d + e*x^r)^2*(a + b*Log[c*x^n])^p,x]","\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} \text{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} \text{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} \text{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{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} \text{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} \text{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} \text{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,"(d^2*(f*x)^(1 + m)*Gamma[1 + p, -(((1 + m)*(a + b*Log[c*x^n]))/(b*n))]*(a + b*Log[c*x^n])^p)/(E^((a*(1 + m))/(b*n))*f*(1 + m)*(c*x^n)^((1 + m)/n)*(-(((1 + m)*(a + b*Log[c*x^n]))/(b*n)))^p) + (2*d*e*x^(1 + r)*(f*x)^m*Gamma[1 + p, -(((1 + m + r)*(a + b*Log[c*x^n]))/(b*n))]*(a + b*Log[c*x^n])^p)/(E^((a*(1 + m + r))/(b*n))*(1 + m + r)*(c*x^n)^((1 + m + r)/n)*(-(((1 + m + r)*(a + b*Log[c*x^n]))/(b*n)))^p) + (e^2*x^(1 + 2*r)*(f*x)^m*Gamma[1 + p, -(((1 + m + 2*r)*(a + b*Log[c*x^n]))/(b*n))]*(a + b*Log[c*x^n])^p)/(E^((a*(1 + m + 2*r))/(b*n))*(1 + m + 2*r)*(c*x^n)^((1 + m + 2*r)/n)*(-(((1 + m + 2*r)*(a + b*Log[c*x^n]))/(b*n)))^p)","A",10,4,27,0.1481,1,"{2353, 2310, 2181, 20}"
450,1,220,0,0.2562115,"\int (f x)^m \left(d+e x^r\right) \left(a+b \log \left(c x^n\right)\right)^p \, dx","Int[(f*x)^m*(d + e*x^r)*(a + b*Log[c*x^n])^p,x]","\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} \text{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} \text{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{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} \text{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} \text{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,"(d*(f*x)^(1 + m)*Gamma[1 + p, -(((1 + m)*(a + b*Log[c*x^n]))/(b*n))]*(a + b*Log[c*x^n])^p)/(E^((a*(1 + m))/(b*n))*f*(1 + m)*(c*x^n)^((1 + m)/n)*(-(((1 + m)*(a + b*Log[c*x^n]))/(b*n)))^p) + (e*x^(1 + r)*(f*x)^m*Gamma[1 + p, -(((1 + m + r)*(a + b*Log[c*x^n]))/(b*n))]*(a + b*Log[c*x^n])^p)/(E^((a*(1 + m + r))/(b*n))*(1 + m + r)*(c*x^n)^((1 + m + r)/n)*(-(((1 + m + r)*(a + b*Log[c*x^n]))/(b*n)))^p)","A",7,4,25,0.1600,1,"{2353, 2310, 2181, 20}"
451,1,106,0,0.0671816,"\int (f x)^m \left(a+b \log \left(c x^n\right)\right)^p \, dx","Int[(f*x)^m*(a + b*Log[c*x^n])^p,x]","\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} \text{Gamma}\left(p+1,-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{f (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} \text{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)^(1 + m)*Gamma[1 + p, -(((1 + m)*(a + b*Log[c*x^n]))/(b*n))]*(a + b*Log[c*x^n])^p)/(E^((a*(1 + m))/(b*n))*f*(1 + m)*(c*x^n)^((1 + m)/n)*(-(((1 + m)*(a + b*Log[c*x^n]))/(b*n)))^p)","A",2,2,18,0.1111,1,"{2310, 2181}"
452,0,0,0,0.0995713,"\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)^p}{d+e x^r} \, dx","Int[((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,"Defer[Int][((f*x)^m*(a + b*Log[c*x^n])^p)/(d + e*x^r), x]","A",0,0,0,0,-1,"{}"
453,0,0,0,0.1019422,"\int \frac{(f x)^m \left(a+b \log \left(c x^n\right)\right)^p}{\left(d+e x^r\right)^2} \, dx","Int[((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,"Defer[Int][((f*x)^m*(a + b*Log[c*x^n])^p)/(d + e*x^r)^2, x]","A",0,0,0,0,-1,"{}"
454,1,151,0,0.1455139,"\int \frac{(f+g x) \left(a+b \log \left(c x^n\right)\right)}{(d+e x)^3} \, dx","Int[((f + g*x)*(a + b*Log[c*x^n]))/(d + e*x)^3,x]","-\frac{(e f-d g) \left(a+b \log \left(c x^n\right)\right)}{2 e^2 (d+e x)^2}+\frac{g x \left(a+b \log \left(c x^n\right)\right)}{d e (d+e x)}+\frac{b n \log (x) (e f-d g)}{2 d^2 e^2}-\frac{b n (e f-d g) \log (d+e x)}{2 d^2 e^2}+\frac{b n (e f-d g)}{2 d e^2 (d+e x)}-\frac{b g n \log (d+e x)}{d 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,"(b*(e*f - d*g)*n)/(2*d*e^2*(d + e*x)) + (b*(e*f - d*g)*n*Log[x])/(2*d^2*e^2) - ((e*f - d*g)*(a + b*Log[c*x^n]))/(2*e^2*(d + e*x)^2) + (g*x*(a + b*Log[c*x^n]))/(d*e*(d + e*x)) - (b*g*n*Log[d + e*x])/(d*e^2) - (b*(e*f - d*g)*n*Log[d + e*x])/(2*d^2*e^2)","A",7,5,23,0.2174,1,"{2357, 2319, 44, 2314, 31}"
455,1,278,0,0.4052619,"\int \frac{(f+g x) \left(a+b \log \left(c x^n\right)\right)^2}{(d+e x)^3} \, dx","Int[((f + g*x)*(a + b*Log[c*x^n])^2)/(d + e*x)^3,x]","-\frac{b^2 n^2 (e f-d g) \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^2 e^2}-\frac{2 b^2 g n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d e^2}-\frac{b n (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{(e f-d g) \left(a+b \log \left(c x^n\right)\right)^2}{2 d^2 e^2}-\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{(e f-d g) \left(a+b \log \left(c x^n\right)\right)^2}{2 e^2 (d+e x)^2}-\frac{2 b g n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d e^2}+\frac{g x \left(a+b \log \left(c x^n\right)\right)^2}{d e (d+e x)}+\frac{b^2 n^2 (e f-d g) \log (d+e x)}{d^2 e^2}","-\frac{b^2 n^2 (d g+e f) \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^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 (e f-d g) \log (d+e x)}{d^2 e^2}",1,"-((b*(e*f - d*g)*n*x*(a + b*Log[c*x^n]))/(d^2*e*(d + e*x))) + ((e*f - d*g)*(a + b*Log[c*x^n])^2)/(2*d^2*e^2) - ((e*f - d*g)*(a + b*Log[c*x^n])^2)/(2*e^2*(d + e*x)^2) + (g*x*(a + b*Log[c*x^n])^2)/(d*e*(d + e*x)) + (b^2*(e*f - d*g)*n^2*Log[d + e*x])/(d^2*e^2) - (2*b*g*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/(d*e^2) - (b*(e*f - d*g)*n*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/(d^2*e^2) - (2*b^2*g*n^2*PolyLog[2, -((e*x)/d)])/(d*e^2) - (b^2*(e*f - d*g)*n^2*PolyLog[2, -((e*x)/d)])/(d^2*e^2)","A",13,10,25,0.4000,1,"{2357, 2319, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2318}"
456,1,408,0,0.6242142,"\int \frac{(f+g x) \left(a+b \log \left(c x^n\right)\right)^3}{(d+e x)^3} \, dx","Int[((f + g*x)*(a + b*Log[c*x^n])^3)/(d + e*x)^3,x]","-\frac{3 b^2 n^2 (e f-d g) \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 e^2}-\frac{6 b^2 g n^2 \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d e^2}+\frac{3 b^3 n^3 (e f-d g) \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^2 e^2}+\frac{3 b^3 n^3 (e f-d g) \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{d^2 e^2}+\frac{6 b^3 g n^3 \text{PolyLog}\left(3,-\frac{e x}{d}\right)}{d 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 (e f-d g) \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{(e f-d g) \left(a+b \log \left(c x^n\right)\right)^3}{2 d^2 e^2}-\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{(e f-d g) \left(a+b \log \left(c x^n\right)\right)^3}{2 e^2 (d+e x)^2}-\frac{3 b g n \log \left(\frac{e x}{d}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d e^2}+\frac{g x \left(a+b \log \left(c x^n\right)\right)^3}{d e (d+e x)}","-\frac{3 b^2 n^2 (d g+e f) \text{PolyLog}\left(2,-\frac{e x}{d}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 e^2}+\frac{3 b^3 n^3 (e f-d g) \text{PolyLog}\left(2,-\frac{e x}{d}\right)}{d^2 e^2}+\frac{3 b^3 n^3 (d g+e f) \text{PolyLog}\left(3,-\frac{e x}{d}\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)}",1,"(-3*b*(e*f - d*g)*n*x*(a + b*Log[c*x^n])^2)/(2*d^2*e*(d + e*x)) + ((e*f - d*g)*(a + b*Log[c*x^n])^3)/(2*d^2*e^2) - ((e*f - d*g)*(a + b*Log[c*x^n])^3)/(2*e^2*(d + e*x)^2) + (g*x*(a + b*Log[c*x^n])^3)/(d*e*(d + e*x)) + (3*b^2*(e*f - d*g)*n^2*(a + b*Log[c*x^n])*Log[1 + (e*x)/d])/(d^2*e^2) - (3*b*g*n*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/(d*e^2) - (3*b*(e*f - d*g)*n*(a + b*Log[c*x^n])^2*Log[1 + (e*x)/d])/(2*d^2*e^2) + (3*b^3*(e*f - d*g)*n^3*PolyLog[2, -((e*x)/d)])/(d^2*e^2) - (6*b^2*g*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/(d*e^2) - (3*b^2*(e*f - d*g)*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((e*x)/d)])/(d^2*e^2) + (6*b^3*g*n^3*PolyLog[3, -((e*x)/d)])/(d*e^2) + (3*b^3*(e*f - d*g)*n^3*PolyLog[3, -((e*x)/d)])/(d^2*e^2)","A",17,11,25,0.4400,1,"{2357, 2319, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391}"