1,1,19,19,0.0011785,"\int x^3 \log (c x) \, dx","Integrate[x^3*Log[c*x],x]","\frac{1}{4} x^4 \log (c x)-\frac{x^4}{16}","\frac{1}{4} x^4 \log (c x)-\frac{x^4}{16}",1,"-1/16*x^4 + (x^4*Log[c*x])/4","A",1
2,1,19,19,0.0009935,"\int x^2 \log (c x) \, dx","Integrate[x^2*Log[c*x],x]","\frac{1}{3} x^3 \log (c x)-\frac{x^3}{9}","\frac{1}{3} x^3 \log (c x)-\frac{x^3}{9}",1,"-1/9*x^3 + (x^3*Log[c*x])/3","A",1
3,1,19,19,0.0008322,"\int x \log (c x) \, dx","Integrate[x*Log[c*x],x]","\frac{1}{2} x^2 \log (c x)-\frac{x^2}{4}","\frac{1}{2} x^2 \log (c x)-\frac{x^2}{4}",1,"-1/4*x^2 + (x^2*Log[c*x])/2","A",1
4,1,10,10,0.0007346,"\int \log (c x) \, dx","Integrate[Log[c*x],x]","x \log (c x)-x","x \log (c x)-x",1,"-x + x*Log[c*x]","A",1
5,1,10,10,0.0009013,"\int \frac{\log (c x)}{x} \, dx","Integrate[Log[c*x]/x,x]","\frac{1}{2} \log ^2(c x)","\frac{1}{2} \log ^2(c x)",1,"Log[c*x]^2/2","A",1
6,1,15,15,0.0008871,"\int \frac{\log (c x)}{x^2} \, dx","Integrate[Log[c*x]/x^2,x]","-\frac{\log (c x)}{x}-\frac{1}{x}","-\frac{\log (c x)}{x}-\frac{1}{x}",1,"-x^(-1) - Log[c*x]/x","A",1
7,1,19,19,0.0010032,"\int \frac{\log (c x)}{x^3} \, dx","Integrate[Log[c*x]/x^3,x]","-\frac{\log (c x)}{2 x^2}-\frac{1}{4 x^2}","-\frac{\log (c x)}{2 x^2}-\frac{1}{4 x^2}",1,"-1/4*1/x^2 - Log[c*x]/(2*x^2)","A",1
8,1,32,32,0.0013671,"\int x^3 \log ^2(c x) \, dx","Integrate[x^3*Log[c*x]^2,x]","\frac{1}{4} x^4 \log ^2(c x)-\frac{1}{8} x^4 \log (c x)+\frac{x^4}{32}","\frac{1}{4} x^4 \log ^2(c x)-\frac{1}{8} x^4 \log (c x)+\frac{x^4}{32}",1,"x^4/32 - (x^4*Log[c*x])/8 + (x^4*Log[c*x]^2)/4","A",1
9,1,32,32,0.0015053,"\int x^2 \log ^2(c x) \, dx","Integrate[x^2*Log[c*x]^2,x]","\frac{1}{3} x^3 \log ^2(c x)-\frac{2}{9} x^3 \log (c x)+\frac{2 x^3}{27}","\frac{1}{3} x^3 \log ^2(c x)-\frac{2}{9} x^3 \log (c x)+\frac{2 x^3}{27}",1,"(2*x^3)/27 - (2*x^3*Log[c*x])/9 + (x^3*Log[c*x]^2)/3","A",1
10,1,32,32,0.0010803,"\int x \log ^2(c x) \, dx","Integrate[x*Log[c*x]^2,x]","\frac{1}{2} x^2 \log ^2(c x)-\frac{1}{2} x^2 \log (c x)+\frac{x^2}{4}","\frac{1}{2} x^2 \log ^2(c x)-\frac{1}{2} x^2 \log (c x)+\frac{x^2}{4}",1,"x^2/4 - (x^2*Log[c*x])/2 + (x^2*Log[c*x]^2)/2","A",1
11,1,19,19,0.0009356,"\int \log ^2(c x) \, dx","Integrate[Log[c*x]^2,x]","x \log ^2(c x)-2 x \log (c x)+2 x","x \log ^2(c x)-2 x \log (c x)+2 x",1,"2*x - 2*x*Log[c*x] + x*Log[c*x]^2","A",1
12,1,10,10,0.0010966,"\int \frac{\log ^2(c x)}{x} \, dx","Integrate[Log[c*x]^2/x,x]","\frac{1}{3} \log ^3(c x)","\frac{1}{3} \log ^3(c x)",1,"Log[c*x]^3/3","A",1
13,1,26,26,0.0013047,"\int \frac{\log ^2(c x)}{x^2} \, dx","Integrate[Log[c*x]^2/x^2,x]","-\frac{\log ^2(c x)}{x}-\frac{2 \log (c x)}{x}-\frac{2}{x}","-\frac{\log ^2(c x)}{x}-\frac{2 \log (c x)}{x}-\frac{2}{x}",1,"-2/x - (2*Log[c*x])/x - Log[c*x]^2/x","A",1
14,1,32,32,0.0013867,"\int \frac{\log ^2(c x)}{x^3} \, dx","Integrate[Log[c*x]^2/x^3,x]","-\frac{\log ^2(c x)}{2 x^2}-\frac{\log (c x)}{2 x^2}-\frac{1}{4 x^2}","-\frac{\log ^2(c x)}{2 x^2}-\frac{\log (c x)}{2 x^2}-\frac{1}{4 x^2}",1,"-1/4*1/x^2 - Log[c*x]/(2*x^2) - Log[c*x]^2/(2*x^2)","A",1
15,1,45,45,0.0016505,"\int x^3 \log ^3(c x) \, dx","Integrate[x^3*Log[c*x]^3,x]","\frac{1}{4} x^4 \log ^3(c x)-\frac{3}{16} x^4 \log ^2(c x)+\frac{3}{32} x^4 \log (c x)-\frac{3 x^4}{128}","\frac{1}{4} x^4 \log ^3(c x)-\frac{3}{16} x^4 \log ^2(c x)+\frac{3}{32} x^4 \log (c x)-\frac{3 x^4}{128}",1,"(-3*x^4)/128 + (3*x^4*Log[c*x])/32 - (3*x^4*Log[c*x]^2)/16 + (x^4*Log[c*x]^3)/4","A",1
16,1,45,45,0.0015551,"\int x^2 \log ^3(c x) \, dx","Integrate[x^2*Log[c*x]^3,x]","\frac{1}{3} x^3 \log ^3(c x)-\frac{1}{3} x^3 \log ^2(c x)+\frac{2}{9} x^3 \log (c x)-\frac{2 x^3}{27}","\frac{1}{3} x^3 \log ^3(c x)-\frac{1}{3} x^3 \log ^2(c x)+\frac{2}{9} x^3 \log (c x)-\frac{2 x^3}{27}",1,"(-2*x^3)/27 + (2*x^3*Log[c*x])/9 - (x^3*Log[c*x]^2)/3 + (x^3*Log[c*x]^3)/3","A",1
17,1,45,45,0.001216,"\int x \log ^3(c x) \, dx","Integrate[x*Log[c*x]^3,x]","\frac{1}{2} x^2 \log ^3(c x)-\frac{3}{4} x^2 \log ^2(c x)+\frac{3}{4} x^2 \log (c x)-\frac{3 x^2}{8}","\frac{1}{2} x^2 \log ^3(c x)-\frac{3}{4} x^2 \log ^2(c x)+\frac{3}{4} x^2 \log (c x)-\frac{3 x^2}{8}",1,"(-3*x^2)/8 + (3*x^2*Log[c*x])/4 - (3*x^2*Log[c*x]^2)/4 + (x^2*Log[c*x]^3)/2","A",1
18,1,28,28,0.0010723,"\int \log ^3(c x) \, dx","Integrate[Log[c*x]^3,x]","x \log ^3(c x)-3 x \log ^2(c x)+6 x \log (c x)-6 x","x \log ^3(c x)-3 x \log ^2(c x)+6 x \log (c x)-6 x",1,"-6*x + 6*x*Log[c*x] - 3*x*Log[c*x]^2 + x*Log[c*x]^3","A",1
19,1,10,10,0.0010633,"\int \frac{\log ^3(c x)}{x} \, dx","Integrate[Log[c*x]^3/x,x]","\frac{1}{4} \log ^4(c x)","\frac{1}{4} \log ^4(c x)",1,"Log[c*x]^4/4","A",1
20,1,37,37,0.0016686,"\int \frac{\log ^3(c x)}{x^2} \, dx","Integrate[Log[c*x]^3/x^2,x]","-\frac{\log ^3(c x)}{x}-\frac{3 \log ^2(c x)}{x}-\frac{6 \log (c x)}{x}-\frac{6}{x}","-\frac{\log ^3(c x)}{x}-\frac{3 \log ^2(c x)}{x}-\frac{6 \log (c x)}{x}-\frac{6}{x}",1,"-6/x - (6*Log[c*x])/x - (3*Log[c*x]^2)/x - Log[c*x]^3/x","A",1
21,1,45,45,0.0016681,"\int \frac{\log ^3(c x)}{x^3} \, dx","Integrate[Log[c*x]^3/x^3,x]","-\frac{\log ^3(c x)}{2 x^2}-\frac{3 \log ^2(c x)}{4 x^2}-\frac{3 \log (c x)}{4 x^2}-\frac{3}{8 x^2}","-\frac{\log ^3(c x)}{2 x^2}-\frac{3 \log ^2(c x)}{4 x^2}-\frac{3 \log (c x)}{4 x^2}-\frac{3}{8 x^2}",1,"-3/(8*x^2) - (3*Log[c*x])/(4*x^2) - (3*Log[c*x]^2)/(4*x^2) - Log[c*x]^3/(2*x^2)","A",1
22,1,11,11,0.0150727,"\int \frac{x^3}{\log (c x)} \, dx","Integrate[x^3/Log[c*x],x]","\frac{\text{Ei}(4 \log (c x))}{c^4}","\frac{\text{Ei}(4 \log (c x))}{c^4}",1,"ExpIntegralEi[4*Log[c*x]]/c^4","A",1
23,1,11,11,0.015257,"\int \frac{x^2}{\log (c x)} \, dx","Integrate[x^2/Log[c*x],x]","\frac{\text{Ei}(3 \log (c x))}{c^3}","\frac{\text{Ei}(3 \log (c x))}{c^3}",1,"ExpIntegralEi[3*Log[c*x]]/c^3","A",1
24,1,11,11,0.0132305,"\int \frac{x}{\log (c x)} \, dx","Integrate[x/Log[c*x],x]","\frac{\text{Ei}(2 \log (c x))}{c^2}","\frac{\text{Ei}(2 \log (c x))}{c^2}",1,"ExpIntegralEi[2*Log[c*x]]/c^2","A",1
25,1,8,8,0.0047497,"\int \frac{1}{\log (c x)} \, dx","Integrate[Log[c*x]^(-1),x]","\frac{\text{li}(c x)}{c}","\frac{\text{li}(c x)}{c}",1,"LogIntegral[c*x]/c","A",1
26,1,5,5,0.0046866,"\int \frac{1}{x \log (c x)} \, dx","Integrate[1/(x*Log[c*x]),x]","\log (\log (c x))","\log (\log (c x))",1,"Log[Log[c*x]]","A",1
27,1,9,9,0.014058,"\int \frac{1}{x^2 \log (c x)} \, dx","Integrate[1/(x^2*Log[c*x]),x]","c \text{Ei}(-\log (c x))","c \text{Ei}(-\log (c x))",1,"c*ExpIntegralEi[-Log[c*x]]","A",1
28,1,11,11,0.0150586,"\int \frac{1}{x^3 \log (c x)} \, dx","Integrate[1/(x^3*Log[c*x]),x]","c^2 \text{Ei}(-2 \log (c x))","c^2 \text{Ei}(-2 \log (c x))",1,"c^2*ExpIntegralEi[-2*Log[c*x]]","A",1
29,1,24,24,0.0151412,"\int \frac{x^3}{\log ^2(c x)} \, dx","Integrate[x^3/Log[c*x]^2,x]","\frac{4 \text{Ei}(4 \log (c x))}{c^4}-\frac{x^4}{\log (c x)}","\frac{4 \text{Ei}(4 \log (c x))}{c^4}-\frac{x^4}{\log (c x)}",1,"(4*ExpIntegralEi[4*Log[c*x]])/c^4 - x^4/Log[c*x]","A",1
30,1,24,24,0.0168992,"\int \frac{x^2}{\log ^2(c x)} \, dx","Integrate[x^2/Log[c*x]^2,x]","\frac{3 \text{Ei}(3 \log (c x))}{c^3}-\frac{x^3}{\log (c x)}","\frac{3 \text{Ei}(3 \log (c x))}{c^3}-\frac{x^3}{\log (c x)}",1,"(3*ExpIntegralEi[3*Log[c*x]])/c^3 - x^3/Log[c*x]","A",1
31,1,24,24,0.0139232,"\int \frac{x}{\log ^2(c x)} \, dx","Integrate[x/Log[c*x]^2,x]","\frac{2 \text{Ei}(2 \log (c x))}{c^2}-\frac{x^2}{\log (c x)}","\frac{2 \text{Ei}(2 \log (c x))}{c^2}-\frac{x^2}{\log (c x)}",1,"(2*ExpIntegralEi[2*Log[c*x]])/c^2 - x^2/Log[c*x]","A",1
32,1,18,18,0.004466,"\int \frac{1}{\log ^2(c x)} \, dx","Integrate[Log[c*x]^(-2),x]","\frac{\text{li}(c x)}{c}-\frac{x}{\log (c x)}","\frac{\text{li}(c x)}{c}-\frac{x}{\log (c x)}",1,"-(x/Log[c*x]) + LogIntegral[c*x]/c","A",1
33,1,8,8,0.0011617,"\int \frac{1}{x \log ^2(c x)} \, dx","Integrate[1/(x*Log[c*x]^2),x]","-\frac{1}{\log (c x)}","-\frac{1}{\log (c x)}",1,"-Log[c*x]^(-1)","A",1
34,1,22,22,0.0159285,"\int \frac{1}{x^2 \log ^2(c x)} \, dx","Integrate[1/(x^2*Log[c*x]^2),x]","-c \text{Ei}(-\log (c x))-\frac{1}{x \log (c x)}","-c \text{Ei}(-\log (c x))-\frac{1}{x \log (c x)}",1,"-(c*ExpIntegralEi[-Log[c*x]]) - 1/(x*Log[c*x])","A",1
35,1,24,24,0.0152093,"\int \frac{1}{x^3 \log ^2(c x)} \, dx","Integrate[1/(x^3*Log[c*x]^2),x]","-2 c^2 \text{Ei}(-2 \log (c x))-\frac{1}{x^2 \log (c x)}","-2 c^2 \text{Ei}(-2 \log (c x))-\frac{1}{x^2 \log (c x)}",1,"-2*c^2*ExpIntegralEi[-2*Log[c*x]] - 1/(x^2*Log[c*x])","A",1
36,1,37,37,0.0177329,"\int \frac{x^3}{\log ^3(c x)} \, dx","Integrate[x^3/Log[c*x]^3,x]","\frac{8 \text{Ei}(4 \log (c x))}{c^4}-\frac{x^4}{2 \log ^2(c x)}-\frac{2 x^4}{\log (c x)}","\frac{8 \text{Ei}(4 \log (c x))}{c^4}-\frac{x^4}{2 \log ^2(c x)}-\frac{2 x^4}{\log (c x)}",1,"(8*ExpIntegralEi[4*Log[c*x]])/c^4 - x^4/(2*Log[c*x]^2) - (2*x^4)/Log[c*x]","A",1
37,1,41,41,0.0149774,"\int \frac{x^2}{\log ^3(c x)} \, dx","Integrate[x^2/Log[c*x]^3,x]","\frac{9 \text{Ei}(3 \log (c x))}{2 c^3}-\frac{x^3}{2 \log ^2(c x)}-\frac{3 x^3}{2 \log (c x)}","\frac{9 \text{Ei}(3 \log (c x))}{2 c^3}-\frac{x^3}{2 \log ^2(c x)}-\frac{3 x^3}{2 \log (c x)}",1,"(9*ExpIntegralEi[3*Log[c*x]])/(2*c^3) - x^3/(2*Log[c*x]^2) - (3*x^3)/(2*Log[c*x])","A",1
38,1,37,37,0.0050372,"\int \frac{x}{\log ^3(c x)} \, dx","Integrate[x/Log[c*x]^3,x]","\frac{2 \text{Ei}(2 \log (c x))}{c^2}-\frac{x^2}{2 \log ^2(c x)}-\frac{x^2}{\log (c x)}","\frac{2 \text{Ei}(2 \log (c x))}{c^2}-\frac{x^2}{2 \log ^2(c x)}-\frac{x^2}{\log (c x)}",1,"(2*ExpIntegralEi[2*Log[c*x]])/c^2 - x^2/(2*Log[c*x]^2) - x^2/Log[c*x]","A",1
39,1,34,34,0.0056576,"\int \frac{1}{\log ^3(c x)} \, dx","Integrate[Log[c*x]^(-3),x]","\frac{\text{li}(c x)}{2 c}-\frac{x}{2 \log ^2(c x)}-\frac{x}{2 \log (c x)}","\frac{\text{li}(c x)}{2 c}-\frac{x}{2 \log ^2(c x)}-\frac{x}{2 \log (c x)}",1,"-1/2*x/Log[c*x]^2 - x/(2*Log[c*x]) + LogIntegral[c*x]/(2*c)","A",1
40,1,10,10,0.0012064,"\int \frac{1}{x \log ^3(c x)} \, dx","Integrate[1/(x*Log[c*x]^3),x]","-\frac{1}{2 \log ^2(c x)}","-\frac{1}{2 \log ^2(c x)}",1,"-1/2*1/Log[c*x]^2","A",1
41,1,39,39,0.0147748,"\int \frac{1}{x^2 \log ^3(c x)} \, dx","Integrate[1/(x^2*Log[c*x]^3),x]","\frac{1}{2} c \text{Ei}(-\log (c x))-\frac{1}{2 x \log ^2(c x)}+\frac{1}{2 x \log (c x)}","\frac{1}{2} c \text{Ei}(-\log (c x))-\frac{1}{2 x \log ^2(c x)}+\frac{1}{2 x \log (c x)}",1,"(c*ExpIntegralEi[-Log[c*x]])/2 - 1/(2*x*Log[c*x]^2) + 1/(2*x*Log[c*x])","A",1
42,1,36,36,0.0176149,"\int \frac{1}{x^3 \log ^3(c x)} \, dx","Integrate[1/(x^3*Log[c*x]^3),x]","2 c^2 \text{Ei}(-2 \log (c x))-\frac{1}{2 x^2 \log ^2(c x)}+\frac{1}{x^2 \log (c x)}","2 c^2 \text{Ei}(-2 \log (c x))-\frac{1}{2 x^2 \log ^2(c x)}+\frac{1}{x^2 \log (c x)}",1,"2*c^2*ExpIntegralEi[-2*Log[c*x]] - 1/(2*x^2*Log[c*x]^2) + 1/(x^2*Log[c*x])","A",1
43,1,32,27,0.0022321,"\int x^3 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^3*(a + b*Log[c*x^n]),x]","\frac{a x^4}{4}+\frac{1}{4} b x^4 \log \left(c x^n\right)-\frac{1}{16} b n x^4","\frac{1}{4} x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{16} b n x^4",1,"(a*x^4)/4 - (b*n*x^4)/16 + (b*x^4*Log[c*x^n])/4","A",1
44,1,32,27,0.0012519,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^2*(a + b*Log[c*x^n]),x]","\frac{a x^3}{3}+\frac{1}{3} b x^3 \log \left(c x^n\right)-\frac{1}{9} b n x^3","\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b n x^3",1,"(a*x^3)/3 - (b*n*x^3)/9 + (b*x^3*Log[c*x^n])/3","A",1
45,1,32,27,0.0012996,"\int x \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x*(a + b*Log[c*x^n]),x]","\frac{a x^2}{2}+\frac{1}{2} b x^2 \log \left(c x^n\right)-\frac{1}{4} b n x^2","\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b n x^2",1,"(a*x^2)/2 - (b*n*x^2)/4 + (b*x^2*Log[c*x^n])/2","A",1
46,1,18,18,0.0007074,"\int \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[a + b*Log[c*x^n],x]","a x+b x \log \left(c x^n\right)-b n x","a x+b x \log \left(c x^n\right)-b n x",1,"a*x - b*n*x + b*x*Log[c*x^n]","A",1
47,1,21,22,0.0011907,"\int \frac{a+b \log \left(c x^n\right)}{x} \, dx","Integrate[(a + b*Log[c*x^n])/x,x]","a \log (x)+\frac{b \log ^2\left(c x^n\right)}{2 n}","\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 b n}",1,"a*Log[x] + (b*Log[c*x^n]^2)/(2*n)","A",1
48,1,26,23,0.0013147,"\int \frac{a+b \log \left(c x^n\right)}{x^2} \, dx","Integrate[(a + b*Log[c*x^n])/x^2,x]","-\frac{a}{x}-\frac{b \log \left(c x^n\right)}{x}-\frac{b n}{x}","-\frac{a+b \log \left(c x^n\right)}{x}-\frac{b n}{x}",1,"-(a/x) - (b*n)/x - (b*Log[c*x^n])/x","A",1
49,1,32,27,0.0013998,"\int \frac{a+b \log \left(c x^n\right)}{x^3} \, dx","Integrate[(a + b*Log[c*x^n])/x^3,x]","-\frac{a}{2 x^2}-\frac{b \log \left(c x^n\right)}{2 x^2}-\frac{b n}{4 x^2}","-\frac{a+b \log \left(c x^n\right)}{2 x^2}-\frac{b n}{4 x^2}",1,"-1/2*a/x^2 - (b*n)/(4*x^2) - (b*Log[c*x^n])/(2*x^2)","A",1
50,1,43,52,0.0181711,"\int x^3 \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[x^3*(a + b*Log[c*x^n])^2,x]","\frac{1}{32} x^4 \left(-4 b n \left(a+b \log \left(c x^n\right)\right)+8 \left(a+b \log \left(c x^n\right)\right)^2+b^2 n^2\right)","\frac{1}{4} x^4 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{8} b n x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{32} b^2 n^2 x^4",1,"(x^4*(b^2*n^2 - 4*b*n*(a + b*Log[c*x^n]) + 8*(a + b*Log[c*x^n])^2))/32","A",1
51,1,46,52,0.0208599,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[x^2*(a + b*Log[c*x^n])^2,x]","\frac{1}{3} \left(x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{2}{9} b n x^3 \left(-3 a-3 b \log \left(c x^n\right)+b n\right)\right)","\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{9} b n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{2}{27} b^2 n^2 x^3",1,"((2*b*n*x^3*(-3*a + b*n - 3*b*Log[c*x^n]))/9 + x^3*(a + b*Log[c*x^n])^2)/3","A",1
52,1,41,52,0.0154855,"\int x \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[x*(a + b*Log[c*x^n])^2,x]","\frac{1}{4} x^2 \left(2 \left(a+b \log \left(c x^n\right)\right)^2+b n \left(-2 a-2 b \log \left(c x^n\right)+b n\right)\right)","\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} b n x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{4} b^2 n^2 x^2",1,"(x^2*(b*n*(-2*a + b*n - 2*b*Log[c*x^n]) + 2*(a + b*Log[c*x^n])^2))/4","A",1
53,1,33,43,0.0085347,"\int \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[(a + b*Log[c*x^n])^2,x]","x \left(\left(a+b \log \left(c x^n\right)\right)^2-2 b n \left(a+b \log \left(c x^n\right)-b n\right)\right)","x \left(a+b \log \left(c x^n\right)\right)^2-2 a b n x-2 b^2 n x \log \left(c x^n\right)+2 b^2 n^2 x",1,"x*((a + b*Log[c*x^n])^2 - 2*b*n*(a - b*n + b*Log[c*x^n]))","A",1
54,1,22,22,0.0030966,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x} \, dx","Integrate[(a + b*Log[c*x^n])^2/x,x]","\frac{\left(a+b \log \left(c x^n\right)\right)^3}{3 b n}","\frac{\left(a+b \log \left(c x^n\right)\right)^3}{3 b n}",1,"(a + b*Log[c*x^n])^3/(3*b*n)","A",1
55,1,35,46,0.010963,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Log[c*x^n])^2/x^2,x]","-\frac{\left(a+b \log \left(c x^n\right)\right)^2+2 b n \left(a+b \log \left(c x^n\right)+b n\right)}{x}","-\frac{2 b n \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{2 b^2 n^2}{x}",1,"-(((a + b*Log[c*x^n])^2 + 2*b*n*(a + b*n + b*Log[c*x^n]))/x)","A",1
56,1,41,52,0.0134996,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{x^3} \, dx","Integrate[(a + b*Log[c*x^n])^2/x^3,x]","-\frac{2 \left(a+b \log \left(c x^n\right)\right)^2+b n \left(2 a+2 b \log \left(c x^n\right)+b n\right)}{4 x^2}","-\frac{b n \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{b^2 n^2}{4 x^2}",1,"-1/4*(2*(a + b*Log[c*x^n])^2 + b*n*(2*a + b*n + 2*b*Log[c*x^n]))/x^2","A",1
57,1,66,77,0.032409,"\int x^3 \left(a+b \log \left(c x^n\right)\right)^3 \, dx","Integrate[x^3*(a + b*Log[c*x^n])^3,x]","\frac{1}{4} \left(x^4 \left(a+b \log \left(c x^n\right)\right)^3-\frac{3}{32} b n x^4 \left(-4 b n \left(a+b \log \left(c x^n\right)\right)+8 \left(a+b \log \left(c x^n\right)\right)^2+b^2 n^2\right)\right)","\frac{3}{32} b^2 n^2 x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{4} x^4 \left(a+b \log \left(c x^n\right)\right)^3-\frac{3}{16} b n x^4 \left(a+b \log \left(c x^n\right)\right)^2-\frac{3}{128} b^3 n^3 x^4",1,"(x^4*(a + b*Log[c*x^n])^3 - (3*b*n*x^4*(b^2*n^2 - 4*b*n*(a + b*Log[c*x^n]) + 8*(a + b*Log[c*x^n])^2))/32)/4","A",1
58,1,67,77,0.0129804,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^3 \, dx","Integrate[x^2*(a + b*Log[c*x^n])^3,x]","\frac{1}{3} \left(x^3 \left(a+b \log \left(c x^n\right)\right)^3-b n \left(x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{2}{9} b n x^3 \left(-3 a-3 b \log \left(c x^n\right)+b n\right)\right)\right)","\frac{2}{9} b^2 n^2 x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right)^3-\frac{1}{3} b n x^3 \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{27} b^3 n^3 x^3",1,"(x^3*(a + b*Log[c*x^n])^3 - b*n*((2*b*n*x^3*(-3*a + b*n - 3*b*Log[c*x^n]))/9 + x^3*(a + b*Log[c*x^n])^2))/3","A",1
59,1,60,77,0.0300858,"\int x \left(a+b \log \left(c x^n\right)\right)^3 \, dx","Integrate[x*(a + b*Log[c*x^n])^3,x]","\frac{1}{8} x^2 \left(4 \left(a+b \log \left(c x^n\right)\right)^3-3 b n \left(2 \left(a+b \log \left(c x^n\right)\right)^2+b n \left(-2 a-2 b \log \left(c x^n\right)+b n\right)\right)\right)","\frac{3}{4} b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{3}{4} b n x^2 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^3-\frac{3}{8} b^3 n^3 x^2",1,"(x^2*(4*(a + b*Log[c*x^n])^3 - 3*b*n*(b*n*(-2*a + b*n - 2*b*Log[c*x^n]) + 2*(a + b*Log[c*x^n])^2)))/8","A",1
60,1,50,66,0.0096354,"\int \left(a+b \log \left(c x^n\right)\right)^3 \, dx","Integrate[(a + b*Log[c*x^n])^3,x]","x \left(\left(a+b \log \left(c x^n\right)\right)^3-3 b n \left(\left(a+b \log \left(c x^n\right)\right)^2-2 b n \left(a+b \log \left(c x^n\right)-b n\right)\right)\right)","6 a b^2 n^2 x-3 b n x \left(a+b \log \left(c x^n\right)\right)^2+x \left(a+b \log \left(c x^n\right)\right)^3+6 b^3 n^2 x \log \left(c x^n\right)-6 b^3 n^3 x",1,"x*((a + b*Log[c*x^n])^3 - 3*b*n*((a + b*Log[c*x^n])^2 - 2*b*n*(a - b*n + b*Log[c*x^n])))","A",1
61,1,22,22,0.0036589,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3}{x} \, dx","Integrate[(a + b*Log[c*x^n])^3/x,x]","\frac{\left(a+b \log \left(c x^n\right)\right)^4}{4 b n}","\frac{\left(a+b \log \left(c x^n\right)\right)^4}{4 b n}",1,"(a + b*Log[c*x^n])^4/(4*b*n)","A",1
62,1,52,69,0.0193204,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3}{x^2} \, dx","Integrate[(a + b*Log[c*x^n])^3/x^2,x]","-\frac{\left(a+b \log \left(c x^n\right)\right)^3+3 b n \left(\left(a+b \log \left(c x^n\right)\right)^2+2 b n \left(a+b \log \left(c x^n\right)+b n\right)\right)}{x}","-\frac{6 b^2 n^2 \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{\left(a+b \log \left(c x^n\right)\right)^3}{x}-\frac{6 b^3 n^3}{x}",1,"-(((a + b*Log[c*x^n])^3 + 3*b*n*((a + b*Log[c*x^n])^2 + 2*b*n*(a + b*n + b*Log[c*x^n])))/x)","A",1
63,1,60,77,0.0214976,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3}{x^3} \, dx","Integrate[(a + b*Log[c*x^n])^3/x^3,x]","-\frac{4 \left(a+b \log \left(c x^n\right)\right)^3+3 b n \left(2 \left(a+b \log \left(c x^n\right)\right)^2+b n \left(2 a+2 b \log \left(c x^n\right)+b n\right)\right)}{8 x^2}","-\frac{3 b^2 n^2 \left(a+b \log \left(c x^n\right)\right)}{4 x^2}-\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2}{4 x^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^3}{2 x^2}-\frac{3 b^3 n^3}{8 x^2}",1,"-1/8*(4*(a + b*Log[c*x^n])^3 + 3*b*n*(2*(a + b*Log[c*x^n])^2 + b*n*(2*a + b*n + 2*b*Log[c*x^n])))/x^2","A",1
64,1,60,77,0.0257833,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3}{x^4} \, dx","Integrate[(a + b*Log[c*x^n])^3/x^4,x]","-\frac{9 \left(a+b \log \left(c x^n\right)\right)^3+b n \left(9 \left(a+b \log \left(c x^n\right)\right)^2+2 b n \left(3 a+3 b \log \left(c x^n\right)+b n\right)\right)}{27 x^3}","-\frac{2 b^2 n^2 \left(a+b \log \left(c x^n\right)\right)}{9 x^3}-\frac{b n \left(a+b \log \left(c x^n\right)\right)^2}{3 x^3}-\frac{\left(a+b \log \left(c x^n\right)\right)^3}{3 x^3}-\frac{2 b^3 n^3}{27 x^3}",1,"-1/27*(9*(a + b*Log[c*x^n])^3 + b*n*(9*(a + b*Log[c*x^n])^2 + 2*b*n*(3*a + b*n + 3*b*Log[c*x^n])))/x^3","A",1
65,1,51,51,0.0619441,"\int \frac{x^3}{a+b \log \left(c x^n\right)} \, dx","Integrate[x^3/(a + b*Log[c*x^n]),x]","\frac{x^4 e^{-\frac{4 a}{b n}} \left(c x^n\right)^{-4/n} \text{Ei}\left(\frac{4 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b n}","\frac{x^4 e^{-\frac{4 a}{b n}} \left(c x^n\right)^{-4/n} \text{Ei}\left(\frac{4 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b n}",1,"(x^4*ExpIntegralEi[(4*(a + b*Log[c*x^n]))/(b*n)])/(b*E^((4*a)/(b*n))*n*(c*x^n)^(4/n))","A",1
66,1,51,51,0.059762,"\int \frac{x^2}{a+b \log \left(c x^n\right)} \, dx","Integrate[x^2/(a + b*Log[c*x^n]),x]","\frac{x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b n}","\frac{x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b n}",1,"(x^3*ExpIntegralEi[(3*(a + b*Log[c*x^n]))/(b*n)])/(b*E^((3*a)/(b*n))*n*(c*x^n)^(3/n))","A",1
67,1,51,51,0.0524101,"\int \frac{x}{a+b \log \left(c x^n\right)} \, dx","Integrate[x/(a + b*Log[c*x^n]),x]","\frac{x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b n}","\frac{x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b n}",1,"(x^2*ExpIntegralEi[(2*(a + b*Log[c*x^n]))/(b*n)])/(b*E^((2*a)/(b*n))*n*(c*x^n)^(2/n))","A",1
68,1,48,48,0.0438699,"\int \frac{1}{a+b \log \left(c x^n\right)} \, dx","Integrate[(a + b*Log[c*x^n])^(-1),x]","\frac{x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c x^n\right)}{b n}\right)}{b n}","\frac{x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c x^n\right)}{b n}\right)}{b n}",1,"(x*ExpIntegralEi[(a + b*Log[c*x^n])/(b*n)])/(b*E^(a/(b*n))*n*(c*x^n)^n^(-1))","A",1
69,1,18,18,0.0169585,"\int \frac{1}{x \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x*(a + b*Log[c*x^n])),x]","\frac{\log \left(a+b \log \left(c x^n\right)\right)}{b n}","\frac{\log \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"Log[a + b*Log[c*x^n]]/(b*n)","A",1
70,1,48,48,0.0505766,"\int \frac{1}{x^2 \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x^2*(a + b*Log[c*x^n])),x]","\frac{e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \text{Ei}\left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)}{b n x}","\frac{e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \text{Ei}\left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)}{b n x}",1,"(E^(a/(b*n))*(c*x^n)^n^(-1)*ExpIntegralEi[-((a + b*Log[c*x^n])/(b*n))])/(b*n*x)","A",1
71,1,51,51,0.0531658,"\int \frac{1}{x^3 \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x^3*(a + b*Log[c*x^n])),x]","\frac{e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \text{Ei}\left(-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b n x^2}","\frac{e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \text{Ei}\left(-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b n x^2}",1,"(E^((2*a)/(b*n))*(c*x^n)^(2/n)*ExpIntegralEi[(-2*(a + b*Log[c*x^n]))/(b*n)])/(b*n*x^2)","A",1
72,1,51,51,0.0625851,"\int \frac{1}{x^4 \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x^4*(a + b*Log[c*x^n])),x]","\frac{e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \text{Ei}\left(-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b n x^3}","\frac{e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \text{Ei}\left(-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b n x^3}",1,"(E^((3*a)/(b*n))*(c*x^n)^(3/n)*ExpIntegralEi[(-3*(a + b*Log[c*x^n]))/(b*n)])/(b*n*x^3)","A",1
73,1,70,76,0.1480264,"\int \frac{x^3}{\left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[x^3/(a + b*Log[c*x^n])^2,x]","\frac{x^4 \left(4 e^{-\frac{4 a}{b n}} \left(c x^n\right)^{-4/n} \text{Ei}\left(\frac{4 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)-\frac{b n}{a+b \log \left(c x^n\right)}\right)}{b^2 n^2}","\frac{4 x^4 e^{-\frac{4 a}{b n}} \left(c x^n\right)^{-4/n} \text{Ei}\left(\frac{4 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b^2 n^2}-\frac{x^4}{b n \left(a+b \log \left(c x^n\right)\right)}",1,"(x^4*((4*ExpIntegralEi[(4*(a + b*Log[c*x^n]))/(b*n)])/(E^((4*a)/(b*n))*(c*x^n)^(4/n)) - (b*n)/(a + b*Log[c*x^n])))/(b^2*n^2)","A",1
74,1,70,76,0.1429016,"\int \frac{x^2}{\left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[x^2/(a + b*Log[c*x^n])^2,x]","\frac{x^3 \left(3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)-\frac{b n}{a+b \log \left(c x^n\right)}\right)}{b^2 n^2}","\frac{3 x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b^2 n^2}-\frac{x^3}{b n \left(a+b \log \left(c x^n\right)\right)}",1,"(x^3*((3*ExpIntegralEi[(3*(a + b*Log[c*x^n]))/(b*n)])/(E^((3*a)/(b*n))*(c*x^n)^(3/n)) - (b*n)/(a + b*Log[c*x^n])))/(b^2*n^2)","A",1
75,1,70,76,0.1237646,"\int \frac{x}{\left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[x/(a + b*Log[c*x^n])^2,x]","\frac{x^2 \left(2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)-\frac{b n}{a+b \log \left(c x^n\right)}\right)}{b^2 n^2}","\frac{2 x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b^2 n^2}-\frac{x^2}{b n \left(a+b \log \left(c x^n\right)\right)}",1,"(x^2*((2*ExpIntegralEi[(2*(a + b*Log[c*x^n]))/(b*n)])/(E^((2*a)/(b*n))*(c*x^n)^(2/n)) - (b*n)/(a + b*Log[c*x^n])))/(b^2*n^2)","A",1
76,1,66,70,0.1243332,"\int \frac{1}{\left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])^(-2),x]","\frac{x \left(e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c x^n\right)}{b n}\right)-\frac{b n}{a+b \log \left(c x^n\right)}\right)}{b^2 n^2}","\frac{x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c x^n\right)}{b n}\right)}{b^2 n^2}-\frac{x}{b n \left(a+b \log \left(c x^n\right)\right)}",1,"(x*(ExpIntegralEi[(a + b*Log[c*x^n])/(b*n)]/(E^(a/(b*n))*(c*x^n)^n^(-1)) - (b*n)/(a + b*Log[c*x^n])))/(b^2*n^2)","A",1
77,1,20,20,0.0042969,"\int \frac{1}{x \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[1/(x*(a + b*Log[c*x^n])^2),x]","-\frac{1}{b n \left(a+b \log \left(c x^n\right)\right)}","-\frac{1}{b n \left(a+b \log \left(c x^n\right)\right)}",1,"-(1/(b*n*(a + b*Log[c*x^n])))","A",1
78,1,76,73,0.1200828,"\int \frac{1}{x^2 \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[1/(x^2*(a + b*Log[c*x^n])^2),x]","-\frac{e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)+b n}{b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)}","-\frac{e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \text{Ei}\left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)}{b^2 n^2 x}-\frac{1}{b n x \left(a+b \log \left(c x^n\right)\right)}",1,"-((b*n + E^(a/(b*n))*(c*x^n)^n^(-1)*ExpIntegralEi[-((a + b*Log[c*x^n])/(b*n))]*(a + b*Log[c*x^n]))/(b^2*n^2*x*(a + b*Log[c*x^n])))","A",1
79,1,80,76,0.0923143,"\int \frac{1}{x^3 \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[1/(x^3*(a + b*Log[c*x^n])^2),x]","-\frac{2 e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)+b n}{b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)}","-\frac{2 e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \text{Ei}\left(-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b^2 n^2 x^2}-\frac{1}{b n x^2 \left(a+b \log \left(c x^n\right)\right)}",1,"-((b*n + 2*E^((2*a)/(b*n))*(c*x^n)^(2/n)*ExpIntegralEi[(-2*(a + b*Log[c*x^n]))/(b*n)]*(a + b*Log[c*x^n]))/(b^2*n^2*x^2*(a + b*Log[c*x^n])))","A",1
80,1,80,76,0.0993689,"\int \frac{1}{x^4 \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[1/(x^4*(a + b*Log[c*x^n])^2),x]","-\frac{3 e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)+b n}{b^2 n^2 x^3 \left(a+b \log \left(c x^n\right)\right)}","-\frac{3 e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \text{Ei}\left(-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b^2 n^2 x^3}-\frac{1}{b n x^3 \left(a+b \log \left(c x^n\right)\right)}",1,"-((b*n + 3*E^((3*a)/(b*n))*(c*x^n)^(3/n)*ExpIntegralEi[(-3*(a + b*Log[c*x^n]))/(b*n)]*(a + b*Log[c*x^n]))/(b^2*n^2*x^3*(a + b*Log[c*x^n])))","A",1
81,1,89,101,0.1360315,"\int \frac{x^3}{\left(a+b \log \left(c x^n\right)\right)^3} \, dx","Integrate[x^3/(a + b*Log[c*x^n])^3,x]","\frac{x^4 \left(16 e^{-\frac{4 a}{b n}} \left(c x^n\right)^{-4/n} \text{Ei}\left(\frac{4 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)-\frac{b n \left(4 a+4 b \log \left(c x^n\right)+b n\right)}{\left(a+b \log \left(c x^n\right)\right)^2}\right)}{2 b^3 n^3}","\frac{8 x^4 e^{-\frac{4 a}{b n}} \left(c x^n\right)^{-4/n} \text{Ei}\left(\frac{4 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b^3 n^3}-\frac{2 x^4}{b^2 n^2 \left(a+b \log \left(c x^n\right)\right)}-\frac{x^4}{2 b n \left(a+b \log \left(c x^n\right)\right)^2}",1,"(x^4*((16*ExpIntegralEi[(4*(a + b*Log[c*x^n]))/(b*n)])/(E^((4*a)/(b*n))*(c*x^n)^(4/n)) - (b*n*(4*a + b*n + 4*b*Log[c*x^n]))/(a + b*Log[c*x^n])^2))/(2*b^3*n^3)","A",1
82,1,89,105,0.1311203,"\int \frac{x^2}{\left(a+b \log \left(c x^n\right)\right)^3} \, dx","Integrate[x^2/(a + b*Log[c*x^n])^3,x]","\frac{x^3 \left(9 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)-\frac{b n \left(3 a+3 b \log \left(c x^n\right)+b n\right)}{\left(a+b \log \left(c x^n\right)\right)^2}\right)}{2 b^3 n^3}","\frac{9 x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{2 b^3 n^3}-\frac{3 x^3}{2 b^2 n^2 \left(a+b \log \left(c x^n\right)\right)}-\frac{x^3}{2 b n \left(a+b \log \left(c x^n\right)\right)^2}",1,"(x^3*((9*ExpIntegralEi[(3*(a + b*Log[c*x^n]))/(b*n)])/(E^((3*a)/(b*n))*(c*x^n)^(3/n)) - (b*n*(3*a + b*n + 3*b*Log[c*x^n]))/(a + b*Log[c*x^n])^2))/(2*b^3*n^3)","A",1
83,1,89,101,0.1308396,"\int \frac{x}{\left(a+b \log \left(c x^n\right)\right)^3} \, dx","Integrate[x/(a + b*Log[c*x^n])^3,x]","\frac{x^2 \left(4 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)-\frac{b n \left(2 a+2 b \log \left(c x^n\right)+b n\right)}{\left(a+b \log \left(c x^n\right)\right)^2}\right)}{2 b^3 n^3}","\frac{2 x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \text{Ei}\left(\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b^3 n^3}-\frac{x^2}{b^2 n^2 \left(a+b \log \left(c x^n\right)\right)}-\frac{x^2}{2 b n \left(a+b \log \left(c x^n\right)\right)^2}",1,"(x^2*((4*ExpIntegralEi[(2*(a + b*Log[c*x^n]))/(b*n)])/(E^((2*a)/(b*n))*(c*x^n)^(2/n)) - (b*n*(2*a + b*n + 2*b*Log[c*x^n]))/(a + b*Log[c*x^n])^2))/(2*b^3*n^3)","A",1
84,1,82,98,0.1178366,"\int \frac{1}{\left(a+b \log \left(c x^n\right)\right)^3} \, dx","Integrate[(a + b*Log[c*x^n])^(-3),x]","\frac{x \left(e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c x^n\right)}{b n}\right)-\frac{b n \left(a+b \log \left(c x^n\right)+b n\right)}{\left(a+b \log \left(c x^n\right)\right)^2}\right)}{2 b^3 n^3}","\frac{x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \text{Ei}\left(\frac{a+b \log \left(c x^n\right)}{b n}\right)}{2 b^3 n^3}-\frac{x}{2 b^2 n^2 \left(a+b \log \left(c x^n\right)\right)}-\frac{x}{2 b n \left(a+b \log \left(c x^n\right)\right)^2}",1,"(x*(ExpIntegralEi[(a + b*Log[c*x^n])/(b*n)]/(E^(a/(b*n))*(c*x^n)^n^(-1)) - (b*n*(a + b*n + b*Log[c*x^n]))/(a + b*Log[c*x^n])^2))/(2*b^3*n^3)","A",1
85,1,22,22,0.0037054,"\int \frac{1}{x \left(a+b \log \left(c x^n\right)\right)^3} \, dx","Integrate[1/(x*(a + b*Log[c*x^n])^3),x]","-\frac{1}{2 b n \left(a+b \log \left(c x^n\right)\right)^2}","-\frac{1}{2 b n \left(a+b \log \left(c x^n\right)\right)^2}",1,"-1/2*1/(b*n*(a + b*Log[c*x^n])^2)","A",1
86,1,94,102,0.0964373,"\int \frac{1}{x^2 \left(a+b \log \left(c x^n\right)\right)^3} \, dx","Integrate[1/(x^2*(a + b*Log[c*x^n])^3),x]","\frac{e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(a+b \log \left(c x^n\right)\right)^2 \text{Ei}\left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)+b n \left(a+b \log \left(c x^n\right)-b n\right)}{2 b^3 n^3 x \left(a+b \log \left(c x^n\right)\right)^2}","\frac{e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \text{Ei}\left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)}{2 b^3 n^3 x}+\frac{1}{2 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)}-\frac{1}{2 b n x \left(a+b \log \left(c x^n\right)\right)^2}",1,"(E^(a/(b*n))*(c*x^n)^n^(-1)*ExpIntegralEi[-((a + b*Log[c*x^n])/(b*n))]*(a + b*Log[c*x^n])^2 + b*n*(a - b*n + b*Log[c*x^n]))/(2*b^3*n^3*x*(a + b*Log[c*x^n])^2)","A",1
87,1,89,100,0.1194816,"\int \frac{1}{x^3 \left(a+b \log \left(c x^n\right)\right)^3} \, dx","Integrate[1/(x^3*(a + b*Log[c*x^n])^3),x]","\frac{4 e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \text{Ei}\left(-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)+\frac{b n \left(2 a+2 b \log \left(c x^n\right)-b n\right)}{\left(a+b \log \left(c x^n\right)\right)^2}}{2 b^3 n^3 x^2}","\frac{2 e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \text{Ei}\left(-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b^3 n^3 x^2}+\frac{1}{b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)}-\frac{1}{2 b n x^2 \left(a+b \log \left(c x^n\right)\right)^2}",1,"(4*E^((2*a)/(b*n))*(c*x^n)^(2/n)*ExpIntegralEi[(-2*(a + b*Log[c*x^n]))/(b*n)] + (b*n*(2*a - b*n + 2*b*Log[c*x^n]))/(a + b*Log[c*x^n])^2)/(2*b^3*n^3*x^2)","A",1
88,1,89,105,0.1169618,"\int \frac{1}{x^4 \left(a+b \log \left(c x^n\right)\right)^3} \, dx","Integrate[1/(x^4*(a + b*Log[c*x^n])^3),x]","\frac{9 e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \text{Ei}\left(-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)+\frac{b n \left(3 a+3 b \log \left(c x^n\right)-b n\right)}{\left(a+b \log \left(c x^n\right)\right)^2}}{2 b^3 n^3 x^3}","\frac{9 e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \text{Ei}\left(-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{2 b^3 n^3 x^3}+\frac{3}{2 b^2 n^2 x^3 \left(a+b \log \left(c x^n\right)\right)}-\frac{1}{2 b n x^3 \left(a+b \log \left(c x^n\right)\right)^2}",1,"(9*E^((3*a)/(b*n))*(c*x^n)^(3/n)*ExpIntegralEi[(-3*(a + b*Log[c*x^n]))/(b*n)] + (b*n*(3*a - b*n + 3*b*Log[c*x^n]))/(a + b*Log[c*x^n])^2)/(2*b^3*n^3*x^3)","A",1
89,1,29,41,0.0147772,"\int (d x)^{5/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(d*x)^(5/2)*(a + b*Log[c*x^n]),x]","\frac{2}{49} x (d x)^{5/2} \left(7 a+7 b \log \left(c x^n\right)-2 b n\right)","\frac{2 (d x)^{7/2} \left(a+b \log \left(c x^n\right)\right)}{7 d}-\frac{4 b n (d x)^{7/2}}{49 d}",1,"(2*x*(d*x)^(5/2)*(7*a - 2*b*n + 7*b*Log[c*x^n]))/49","A",1
90,1,29,41,0.0104262,"\int (d x)^{3/2} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(d*x)^(3/2)*(a + b*Log[c*x^n]),x]","\frac{2}{25} x (d x)^{3/2} \left(5 a+5 b \log \left(c x^n\right)-2 b n\right)","\frac{2 (d x)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{5 d}-\frac{4 b n (d x)^{5/2}}{25 d}",1,"(2*x*(d*x)^(3/2)*(5*a - 2*b*n + 5*b*Log[c*x^n]))/25","A",1
91,1,29,41,0.0073932,"\int \sqrt{d x} \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Sqrt[d*x]*(a + b*Log[c*x^n]),x]","\frac{2}{9} x \sqrt{d x} \left(3 a+3 b \log \left(c x^n\right)-2 b n\right)","\frac{2 (d x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{3 d}-\frac{4 b n (d x)^{3/2}}{9 d}",1,"(2*x*Sqrt[d*x]*(3*a - 2*b*n + 3*b*Log[c*x^n]))/9","A",1
92,1,24,37,0.0063328,"\int \frac{a+b \log \left(c x^n\right)}{\sqrt{d x}} \, dx","Integrate[(a + b*Log[c*x^n])/Sqrt[d*x],x]","\frac{2 x \left(a+b \log \left(c x^n\right)-2 b n\right)}{\sqrt{d x}}","\frac{2 \sqrt{d x} \left(a+b \log \left(c x^n\right)\right)}{d}-\frac{4 b n \sqrt{d x}}{d}",1,"(2*x*(a - 2*b*n + b*Log[c*x^n]))/Sqrt[d*x]","A",1
93,1,24,37,0.0074087,"\int \frac{a+b \log \left(c x^n\right)}{(d x)^{3/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(d*x)^(3/2),x]","-\frac{2 x \left(a+b \log \left(c x^n\right)+2 b n\right)}{(d x)^{3/2}}","-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{d \sqrt{d x}}-\frac{4 b n}{d \sqrt{d x}}",1,"(-2*x*(a + 2*b*n + b*Log[c*x^n]))/(d*x)^(3/2)","A",1
94,1,29,41,0.0088092,"\int \frac{a+b \log \left(c x^n\right)}{(d x)^{5/2}} \, dx","Integrate[(a + b*Log[c*x^n])/(d*x)^(5/2),x]","-\frac{2 x \left(3 a+3 b \log \left(c x^n\right)+2 b n\right)}{9 (d x)^{5/2}}","-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{3 d (d x)^{3/2}}-\frac{4 b n}{9 d (d x)^{3/2}}",1,"(-2*x*(3*a + 2*b*n + 3*b*Log[c*x^n]))/(9*(d*x)^(5/2))","A",1
95,1,61,73,0.0213931,"\int (d x)^{5/2} \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[(d*x)^(5/2)*(a + b*Log[c*x^n])^2,x]","\frac{2}{343} x (d x)^{5/2} \left(49 a^2+14 b (7 a-2 b n) \log \left(c x^n\right)-28 a b n+49 b^2 \log ^2\left(c x^n\right)+8 b^2 n^2\right)","\frac{2 (d x)^{7/2} \left(a+b \log \left(c x^n\right)\right)^2}{7 d}-\frac{8 b n (d x)^{7/2} \left(a+b \log \left(c x^n\right)\right)}{49 d}+\frac{16 b^2 n^2 (d x)^{7/2}}{343 d}",1,"(2*x*(d*x)^(5/2)*(49*a^2 - 28*a*b*n + 8*b^2*n^2 + 14*b*(7*a - 2*b*n)*Log[c*x^n] + 49*b^2*Log[c*x^n]^2))/343","A",1
96,1,61,73,0.0182919,"\int (d x)^{3/2} \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[(d*x)^(3/2)*(a + b*Log[c*x^n])^2,x]","\frac{2}{125} x (d x)^{3/2} \left(25 a^2+10 b (5 a-2 b n) \log \left(c x^n\right)-20 a b n+25 b^2 \log ^2\left(c x^n\right)+8 b^2 n^2\right)","\frac{2 (d x)^{5/2} \left(a+b \log \left(c x^n\right)\right)^2}{5 d}-\frac{8 b n (d x)^{5/2} \left(a+b \log \left(c x^n\right)\right)}{25 d}+\frac{16 b^2 n^2 (d x)^{5/2}}{125 d}",1,"(2*x*(d*x)^(3/2)*(25*a^2 - 20*a*b*n + 8*b^2*n^2 + 10*b*(5*a - 2*b*n)*Log[c*x^n] + 25*b^2*Log[c*x^n]^2))/125","A",1
97,1,61,73,0.0167247,"\int \sqrt{d x} \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[Sqrt[d*x]*(a + b*Log[c*x^n])^2,x]","\frac{2}{27} x \sqrt{d x} \left(9 a^2+6 b (3 a-2 b n) \log \left(c x^n\right)-12 a b n+9 b^2 \log ^2\left(c x^n\right)+8 b^2 n^2\right)","-\frac{8 b n (d x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}{9 d}+\frac{2 (d x)^{3/2} \left(a+b \log \left(c x^n\right)\right)^2}{3 d}+\frac{16 b^2 n^2 (d x)^{3/2}}{27 d}",1,"(2*x*Sqrt[d*x]*(9*a^2 - 12*a*b*n + 8*b^2*n^2 + 6*b*(3*a - 2*b*n)*Log[c*x^n] + 9*b^2*Log[c*x^n]^2))/27","A",1
98,1,54,67,0.0141531,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{d x}} \, dx","Integrate[(a + b*Log[c*x^n])^2/Sqrt[d*x],x]","\frac{2 x \left(a^2+2 b (a-2 b n) \log \left(c x^n\right)-4 a b n+b^2 \log ^2\left(c x^n\right)+8 b^2 n^2\right)}{\sqrt{d x}}","-\frac{8 b n \sqrt{d x} \left(a+b \log \left(c x^n\right)\right)}{d}+\frac{2 \sqrt{d x} \left(a+b \log \left(c x^n\right)\right)^2}{d}+\frac{16 b^2 n^2 \sqrt{d x}}{d}",1,"(2*x*(a^2 - 4*a*b*n + 8*b^2*n^2 + 2*b*(a - 2*b*n)*Log[c*x^n] + b^2*Log[c*x^n]^2))/Sqrt[d*x]","A",1
99,1,54,67,0.0133802,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{(d x)^{3/2}} \, dx","Integrate[(a + b*Log[c*x^n])^2/(d*x)^(3/2),x]","-\frac{2 x \left(a^2+2 b (a+2 b n) \log \left(c x^n\right)+4 a b n+b^2 \log ^2\left(c x^n\right)+8 b^2 n^2\right)}{(d x)^{3/2}}","-\frac{8 b n \left(a+b \log \left(c x^n\right)\right)}{d \sqrt{d x}}-\frac{2 \left(a+b \log \left(c x^n\right)\right)^2}{d \sqrt{d x}}-\frac{16 b^2 n^2}{d \sqrt{d x}}",1,"(-2*x*(a^2 + 4*a*b*n + 8*b^2*n^2 + 2*b*(a + 2*b*n)*Log[c*x^n] + b^2*Log[c*x^n]^2))/(d*x)^(3/2)","A",1
100,1,61,73,0.0163233,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2}{(d x)^{5/2}} \, dx","Integrate[(a + b*Log[c*x^n])^2/(d*x)^(5/2),x]","-\frac{2 x \left(9 a^2+6 b (3 a+2 b n) \log \left(c x^n\right)+12 a b n+9 b^2 \log ^2\left(c x^n\right)+8 b^2 n^2\right)}{27 (d x)^{5/2}}","-\frac{8 b n \left(a+b \log \left(c x^n\right)\right)}{9 d (d x)^{3/2}}-\frac{2 \left(a+b \log \left(c x^n\right)\right)^2}{3 d (d x)^{3/2}}-\frac{16 b^2 n^2}{27 d (d x)^{3/2}}",1,"(-2*x*(9*a^2 + 12*a*b*n + 8*b^2*n^2 + 6*b*(3*a + 2*b*n)*Log[c*x^n] + 9*b^2*Log[c*x^n]^2))/(27*(d*x)^(5/2))","A",1
101,1,62,64,0.0843487,"\int \frac{(d x)^{5/2}}{a+b \log \left(c x^n\right)} \, dx","Integrate[(d*x)^(5/2)/(a + b*Log[c*x^n]),x]","\frac{x (d x)^{5/2} e^{-\frac{7 a}{2 b n}} \left(c x^n\right)^{\left.-\frac{7}{2}\right/n} \text{Ei}\left(\frac{7 \left(a+b \log \left(c x^n\right)\right)}{2 b n}\right)}{b n}","\frac{(d x)^{7/2} e^{-\frac{7 a}{2 b n}} \left(c x^n\right)^{\left.-\frac{7}{2}\right/n} \text{Ei}\left(\frac{7 \left(a+b \log \left(c x^n\right)\right)}{2 b n}\right)}{b d n}",1,"(x*(d*x)^(5/2)*ExpIntegralEi[(7*(a + b*Log[c*x^n]))/(2*b*n)])/(b*E^((7*a)/(2*b*n))*n*(c*x^n)^(7/(2*n)))","A",1
102,1,62,64,0.0746022,"\int \frac{(d x)^{3/2}}{a+b \log \left(c x^n\right)} \, dx","Integrate[(d*x)^(3/2)/(a + b*Log[c*x^n]),x]","\frac{x (d x)^{3/2} e^{-\frac{5 a}{2 b n}} \left(c x^n\right)^{\left.-\frac{5}{2}\right/n} \text{Ei}\left(\frac{5 \left(a+b \log \left(c x^n\right)\right)}{2 b n}\right)}{b n}","\frac{(d x)^{5/2} e^{-\frac{5 a}{2 b n}} \left(c x^n\right)^{\left.-\frac{5}{2}\right/n} \text{Ei}\left(\frac{5 \left(a+b \log \left(c x^n\right)\right)}{2 b n}\right)}{b d n}",1,"(x*(d*x)^(3/2)*ExpIntegralEi[(5*(a + b*Log[c*x^n]))/(2*b*n)])/(b*E^((5*a)/(2*b*n))*n*(c*x^n)^(5/(2*n)))","A",1
103,1,62,64,0.0753004,"\int \frac{\sqrt{d x}}{a+b \log \left(c x^n\right)} \, dx","Integrate[Sqrt[d*x]/(a + b*Log[c*x^n]),x]","\frac{x \sqrt{d x} e^{-\frac{3 a}{2 b n}} \left(c x^n\right)^{\left.-\frac{3}{2}\right/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c x^n\right)\right)}{2 b n}\right)}{b n}","\frac{(d x)^{3/2} e^{-\frac{3 a}{2 b n}} \left(c x^n\right)^{\left.-\frac{3}{2}\right/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c x^n\right)\right)}{2 b n}\right)}{b d n}",1,"(x*Sqrt[d*x]*ExpIntegralEi[(3*(a + b*Log[c*x^n]))/(2*b*n)])/(b*E^((3*a)/(2*b*n))*n*(c*x^n)^(3/(2*n)))","A",1
104,1,62,64,0.0659256,"\int \frac{1}{\sqrt{d x} \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(Sqrt[d*x]*(a + b*Log[c*x^n])),x]","\frac{x e^{-\frac{a}{2 b n}} \left(c x^n\right)^{\left.-\frac{1}{2}\right/n} \text{Ei}\left(\frac{a+b \log \left(c x^n\right)}{2 b n}\right)}{b n \sqrt{d x}}","\frac{\sqrt{d x} e^{-\frac{a}{2 b n}} \left(c x^n\right)^{\left.-\frac{1}{2}\right/n} \text{Ei}\left(\frac{a+b \log \left(c x^n\right)}{2 b n}\right)}{b d n}",1,"(x*ExpIntegralEi[(a + b*Log[c*x^n])/(2*b*n)])/(b*E^(a/(2*b*n))*n*Sqrt[d*x]*(c*x^n)^(1/(2*n)))","A",1
105,1,62,67,0.0794504,"\int \frac{1}{(d x)^{3/2} \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/((d*x)^(3/2)*(a + b*Log[c*x^n])),x]","\frac{x e^{\frac{a}{2 b n}} \left(c x^n\right)^{\left.\frac{1}{2}\right/n} \text{Ei}\left(-\frac{a+b \log \left(c x^n\right)}{2 b n}\right)}{b n (d x)^{3/2}}","\frac{e^{\frac{a}{2 b n}} \left(c x^n\right)^{\left.\frac{1}{2}\right/n} \text{Ei}\left(\frac{-a-b \log \left(c x^n\right)}{2 b n}\right)}{b d n \sqrt{d x}}",1,"(E^(a/(2*b*n))*x*(c*x^n)^(1/(2*n))*ExpIntegralEi[-1/2*(a + b*Log[c*x^n])/(b*n)])/(b*n*(d*x)^(3/2))","A",1
106,1,62,64,0.0777458,"\int \frac{1}{(d x)^{5/2} \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/((d*x)^(5/2)*(a + b*Log[c*x^n])),x]","\frac{x e^{\frac{3 a}{2 b n}} \left(c x^n\right)^{\left.\frac{3}{2}\right/n} \text{Ei}\left(-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{2 b n}\right)}{b n (d x)^{5/2}}","\frac{e^{\frac{3 a}{2 b n}} \left(c x^n\right)^{\left.\frac{3}{2}\right/n} \text{Ei}\left(-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{2 b n}\right)}{b d n (d x)^{3/2}}",1,"(E^((3*a)/(2*b*n))*x*(c*x^n)^(3/(2*n))*ExpIntegralEi[(-3*(a + b*Log[c*x^n]))/(2*b*n)])/(b*n*(d*x)^(5/2))","A",1
107,1,84,98,0.1635022,"\int \frac{(d x)^{5/2}}{\left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[(d*x)^(5/2)/(a + b*Log[c*x^n])^2,x]","\frac{x (d x)^{5/2} \left(7 e^{-\frac{7 a}{2 b n}} \left(c x^n\right)^{\left.-\frac{7}{2}\right/n} \text{Ei}\left(\frac{7 \left(a+b \log \left(c x^n\right)\right)}{2 b n}\right)-\frac{2 b n}{a+b \log \left(c x^n\right)}\right)}{2 b^2 n^2}","\frac{7 (d x)^{7/2} e^{-\frac{7 a}{2 b n}} \left(c x^n\right)^{\left.-\frac{7}{2}\right/n} \text{Ei}\left(\frac{7 \left(a+b \log \left(c x^n\right)\right)}{2 b n}\right)}{2 b^2 d n^2}-\frac{(d x)^{7/2}}{b d n \left(a+b \log \left(c x^n\right)\right)}",1,"(x*(d*x)^(5/2)*((7*ExpIntegralEi[(7*(a + b*Log[c*x^n]))/(2*b*n)])/(E^((7*a)/(2*b*n))*(c*x^n)^(7/(2*n))) - (2*b*n)/(a + b*Log[c*x^n])))/(2*b^2*n^2)","A",1
108,1,84,98,0.1753143,"\int \frac{(d x)^{3/2}}{\left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[(d*x)^(3/2)/(a + b*Log[c*x^n])^2,x]","\frac{x (d x)^{3/2} \left(5 e^{-\frac{5 a}{2 b n}} \left(c x^n\right)^{\left.-\frac{5}{2}\right/n} \text{Ei}\left(\frac{5 \left(a+b \log \left(c x^n\right)\right)}{2 b n}\right)-\frac{2 b n}{a+b \log \left(c x^n\right)}\right)}{2 b^2 n^2}","\frac{5 (d x)^{5/2} e^{-\frac{5 a}{2 b n}} \left(c x^n\right)^{\left.-\frac{5}{2}\right/n} \text{Ei}\left(\frac{5 \left(a+b \log \left(c x^n\right)\right)}{2 b n}\right)}{2 b^2 d n^2}-\frac{(d x)^{5/2}}{b d n \left(a+b \log \left(c x^n\right)\right)}",1,"(x*(d*x)^(3/2)*((5*ExpIntegralEi[(5*(a + b*Log[c*x^n]))/(2*b*n)])/(E^((5*a)/(2*b*n))*(c*x^n)^(5/(2*n))) - (2*b*n)/(a + b*Log[c*x^n])))/(2*b^2*n^2)","A",1
109,1,84,98,0.1683971,"\int \frac{\sqrt{d x}}{\left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[Sqrt[d*x]/(a + b*Log[c*x^n])^2,x]","\frac{x \sqrt{d x} \left(3 e^{-\frac{3 a}{2 b n}} \left(c x^n\right)^{\left.-\frac{3}{2}\right/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c x^n\right)\right)}{2 b n}\right)-\frac{2 b n}{a+b \log \left(c x^n\right)}\right)}{2 b^2 n^2}","\frac{3 (d x)^{3/2} e^{-\frac{3 a}{2 b n}} \left(c x^n\right)^{\left.-\frac{3}{2}\right/n} \text{Ei}\left(\frac{3 \left(a+b \log \left(c x^n\right)\right)}{2 b n}\right)}{2 b^2 d n^2}-\frac{(d x)^{3/2}}{b d n \left(a+b \log \left(c x^n\right)\right)}",1,"(x*Sqrt[d*x]*((3*ExpIntegralEi[(3*(a + b*Log[c*x^n]))/(2*b*n)])/(E^((3*a)/(2*b*n))*(c*x^n)^(3/(2*n))) - (2*b*n)/(a + b*Log[c*x^n])))/(2*b^2*n^2)","A",1
110,1,83,98,0.1979539,"\int \frac{1}{\sqrt{d x} \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[1/(Sqrt[d*x]*(a + b*Log[c*x^n])^2),x]","\frac{x \left(e^{-\frac{a}{2 b n}} \left(c x^n\right)^{\left.-\frac{1}{2}\right/n} \text{Ei}\left(\frac{a+b \log \left(c x^n\right)}{2 b n}\right)-\frac{2 b n}{a+b \log \left(c x^n\right)}\right)}{2 b^2 n^2 \sqrt{d x}}","\frac{\sqrt{d x} e^{-\frac{a}{2 b n}} \left(c x^n\right)^{\left.-\frac{1}{2}\right/n} \text{Ei}\left(\frac{a+b \log \left(c x^n\right)}{2 b n}\right)}{2 b^2 d n^2}-\frac{\sqrt{d x}}{b d n \left(a+b \log \left(c x^n\right)\right)}",1,"(x*(ExpIntegralEi[(a + b*Log[c*x^n])/(2*b*n)]/(E^(a/(2*b*n))*(c*x^n)^(1/(2*n))) - (2*b*n)/(a + b*Log[c*x^n])))/(2*b^2*n^2*Sqrt[d*x])","A",1
111,1,93,101,0.1630898,"\int \frac{1}{(d x)^{3/2} \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[1/((d*x)^(3/2)*(a + b*Log[c*x^n])^2),x]","-\frac{x \left(e^{\frac{a}{2 b n}} \left(c x^n\right)^{\left.\frac{1}{2}\right/n} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(-\frac{a+b \log \left(c x^n\right)}{2 b n}\right)+2 b n\right)}{2 b^2 n^2 (d x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}","-\frac{e^{\frac{a}{2 b n}} \left(c x^n\right)^{\left.\frac{1}{2}\right/n} \text{Ei}\left(\frac{-a-b \log \left(c x^n\right)}{2 b n}\right)}{2 b^2 d n^2 \sqrt{d x}}-\frac{1}{b d n \sqrt{d x} \left(a+b \log \left(c x^n\right)\right)}",1,"-1/2*(x*(2*b*n + E^(a/(2*b*n))*(c*x^n)^(1/(2*n))*ExpIntegralEi[-1/2*(a + b*Log[c*x^n])/(b*n)]*(a + b*Log[c*x^n])))/(b^2*n^2*(d*x)^(3/2)*(a + b*Log[c*x^n]))","A",1
112,1,94,98,0.1490149,"\int \frac{1}{(d x)^{5/2} \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[1/((d*x)^(5/2)*(a + b*Log[c*x^n])^2),x]","-\frac{x \left(3 e^{\frac{3 a}{2 b n}} \left(c x^n\right)^{\left.\frac{3}{2}\right/n} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{2 b n}\right)+2 b n\right)}{2 b^2 n^2 (d x)^{5/2} \left(a+b \log \left(c x^n\right)\right)}","-\frac{3 e^{\frac{3 a}{2 b n}} \left(c x^n\right)^{\left.\frac{3}{2}\right/n} \text{Ei}\left(-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{2 b n}\right)}{2 b^2 d n^2 (d x)^{3/2}}-\frac{1}{b d n (d x)^{3/2} \left(a+b \log \left(c x^n\right)\right)}",1,"-1/2*(x*(2*b*n + 3*E^((3*a)/(2*b*n))*(c*x^n)^(3/(2*n))*ExpIntegralEi[(-3*(a + b*Log[c*x^n]))/(2*b*n)]*(a + b*Log[c*x^n])))/(b^2*n^2*(d*x)^(5/2)*(a + b*Log[c*x^n]))","A",1
113,1,85,85,0.0451979,"\int \sqrt{a+b \log \left(c x^n\right)} \, dx","Integrate[Sqrt[a + b*Log[c*x^n]],x]","x \sqrt{a+b \log \left(c x^n\right)}-\frac{1}{2} \sqrt{\pi } \sqrt{b} \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)","x \sqrt{a+b \log \left(c x^n\right)}-\frac{1}{2} \sqrt{\pi } \sqrt{b} \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)",1,"-1/2*(Sqrt[b]*Sqrt[n]*Sqrt[Pi]*x*Erfi[Sqrt[a + b*Log[c*x^n]]/(Sqrt[b]*Sqrt[n])])/(E^(a/(b*n))*(c*x^n)^n^(-1)) + x*Sqrt[a + b*Log[c*x^n]]","A",1
114,1,61,64,0.0233212,"\int x^3 \sqrt{\log \left(a x^n\right)} \, dx","Integrate[x^3*Sqrt[Log[a*x^n]],x]","\frac{1}{16} x^4 \left(4 \sqrt{\log \left(a x^n\right)}-\sqrt{\pi } \sqrt{n} \left(a x^n\right)^{-4/n} \text{erfi}\left(\frac{2 \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)\right)","\frac{1}{4} x^4 \sqrt{\log \left(a x^n\right)}-\frac{1}{16} \sqrt{\pi } \sqrt{n} x^4 \left(a x^n\right)^{-4/n} \text{erfi}\left(\frac{2 \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)",1,"(x^4*(-((Sqrt[n]*Sqrt[Pi]*Erfi[(2*Sqrt[Log[a*x^n]])/Sqrt[n]])/(a*x^n)^(4/n)) + 4*Sqrt[Log[a*x^n]]))/16","A",1
115,1,67,72,0.0353915,"\int x^2 \sqrt{\log \left(a x^n\right)} \, dx","Integrate[x^2*Sqrt[Log[a*x^n]],x]","\frac{1}{18} x^3 \left(6 \sqrt{\log \left(a x^n\right)}-\sqrt{3 \pi } \sqrt{n} \left(a x^n\right)^{-3/n} \text{erfi}\left(\frac{\sqrt{3} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)\right)","\frac{1}{3} x^3 \sqrt{\log \left(a x^n\right)}-\frac{1}{6} \sqrt{\frac{\pi }{3}} \sqrt{n} x^3 \left(a x^n\right)^{-3/n} \text{erfi}\left(\frac{\sqrt{3} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)",1,"(x^3*(-((Sqrt[n]*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[Log[a*x^n]])/Sqrt[n]])/(a*x^n)^(3/n)) + 6*Sqrt[Log[a*x^n]]))/18","A",1
116,1,67,72,0.0344321,"\int x \sqrt{\log \left(a x^n\right)} \, dx","Integrate[x*Sqrt[Log[a*x^n]],x]","\frac{1}{8} x^2 \left(4 \sqrt{\log \left(a x^n\right)}-\sqrt{2 \pi } \sqrt{n} \left(a x^n\right)^{-2/n} \text{erfi}\left(\frac{\sqrt{2} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)\right)","\frac{1}{2} x^2 \sqrt{\log \left(a x^n\right)}-\frac{1}{4} \sqrt{\frac{\pi }{2}} \sqrt{n} x^2 \left(a x^n\right)^{-2/n} \text{erfi}\left(\frac{\sqrt{2} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)",1,"(x^2*(-((Sqrt[n]*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[Log[a*x^n]])/Sqrt[n]])/(a*x^n)^(2/n)) + 4*Sqrt[Log[a*x^n]]))/8","A",1
117,1,56,56,0.0184976,"\int \sqrt{\log \left(a x^n\right)} \, dx","Integrate[Sqrt[Log[a*x^n]],x]","x \sqrt{\log \left(a x^n\right)}-\frac{1}{2} \sqrt{\pi } \sqrt{n} x \left(a x^n\right)^{-1/n} \text{erfi}\left(\frac{\sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)","x \sqrt{\log \left(a x^n\right)}-\frac{1}{2} \sqrt{\pi } \sqrt{n} x \left(a x^n\right)^{-1/n} \text{erfi}\left(\frac{\sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)",1,"-1/2*(Sqrt[n]*Sqrt[Pi]*x*Erfi[Sqrt[Log[a*x^n]]/Sqrt[n]])/(a*x^n)^n^(-1) + x*Sqrt[Log[a*x^n]]","A",1
118,1,17,17,0.0017214,"\int \frac{\sqrt{\log \left(a x^n\right)}}{x} \, dx","Integrate[Sqrt[Log[a*x^n]]/x,x]","\frac{2 \log ^{\frac{3}{2}}\left(a x^n\right)}{3 n}","\frac{2 \log ^{\frac{3}{2}}\left(a x^n\right)}{3 n}",1,"(2*Log[a*x^n]^(3/2))/(3*n)","A",1
119,1,65,59,0.0511584,"\int \frac{\sqrt{\log \left(a x^n\right)}}{x^2} \, dx","Integrate[Sqrt[Log[a*x^n]]/x^2,x]","-\frac{2 \log \left(a x^n\right)+n \left(a x^n\right)^{\frac{1}{n}} \sqrt{\frac{\log \left(a x^n\right)}{n}} \Gamma \left(\frac{1}{2},\frac{\log \left(a x^n\right)}{n}\right)}{2 x \sqrt{\log \left(a x^n\right)}}","\frac{\sqrt{\pi } \sqrt{n} \left(a x^n\right)^{\frac{1}{n}} \text{erf}\left(\frac{\sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{2 x}-\frac{\sqrt{\log \left(a x^n\right)}}{x}",1,"-1/2*(2*Log[a*x^n] + n*(a*x^n)^n^(-1)*Gamma[1/2, Log[a*x^n]/n]*Sqrt[Log[a*x^n]/n])/(x*Sqrt[Log[a*x^n]])","A",1
120,1,73,72,0.0478448,"\int \frac{\sqrt{\log \left(a x^n\right)}}{x^3} \, dx","Integrate[Sqrt[Log[a*x^n]]/x^3,x]","-\frac{4 \log \left(a x^n\right)+\sqrt{2} n \left(a x^n\right)^{2/n} \sqrt{\frac{\log \left(a x^n\right)}{n}} \Gamma \left(\frac{1}{2},\frac{2 \log \left(a x^n\right)}{n}\right)}{8 x^2 \sqrt{\log \left(a x^n\right)}}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{n} \left(a x^n\right)^{2/n} \text{erf}\left(\frac{\sqrt{2} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{4 x^2}-\frac{\sqrt{\log \left(a x^n\right)}}{2 x^2}",1,"-1/8*(4*Log[a*x^n] + Sqrt[2]*n*(a*x^n)^(2/n)*Gamma[1/2, (2*Log[a*x^n])/n]*Sqrt[Log[a*x^n]/n])/(x^2*Sqrt[Log[a*x^n]])","A",1
121,1,73,82,0.0442221,"\int x^3 \log ^{\frac{3}{2}}\left(a x^n\right) \, dx","Integrate[x^3*Log[a*x^n]^(3/2),x]","\frac{1}{128} x^4 \left(3 \sqrt{\pi } n^{3/2} \left(a x^n\right)^{-4/n} \text{erfi}\left(\frac{2 \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)+4 \sqrt{\log \left(a x^n\right)} \left(8 \log \left(a x^n\right)-3 n\right)\right)","\frac{3}{128} \sqrt{\pi } n^{3/2} x^4 \left(a x^n\right)^{-4/n} \text{erfi}\left(\frac{2 \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)+\frac{1}{4} x^4 \log ^{\frac{3}{2}}\left(a x^n\right)-\frac{3}{32} n x^4 \sqrt{\log \left(a x^n\right)}",1,"(x^4*((3*n^(3/2)*Sqrt[Pi]*Erfi[(2*Sqrt[Log[a*x^n]])/Sqrt[n]])/(a*x^n)^(4/n) + 4*Sqrt[Log[a*x^n]]*(-3*n + 8*Log[a*x^n])))/128","A",1
122,1,76,90,0.0535281,"\int x^2 \log ^{\frac{3}{2}}\left(a x^n\right) \, dx","Integrate[x^2*Log[a*x^n]^(3/2),x]","\frac{1}{36} x^3 \left(\sqrt{3 \pi } n^{3/2} \left(a x^n\right)^{-3/n} \text{erfi}\left(\frac{\sqrt{3} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)-6 \left(n-2 \log \left(a x^n\right)\right) \sqrt{\log \left(a x^n\right)}\right)","\frac{1}{12} \sqrt{\frac{\pi }{3}} n^{3/2} x^3 \left(a x^n\right)^{-3/n} \text{erfi}\left(\frac{\sqrt{3} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)+\frac{1}{3} x^3 \log ^{\frac{3}{2}}\left(a x^n\right)-\frac{1}{6} n x^3 \sqrt{\log \left(a x^n\right)}",1,"(x^3*((n^(3/2)*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[Log[a*x^n]])/Sqrt[n]])/(a*x^n)^(3/n) - 6*(n - 2*Log[a*x^n])*Sqrt[Log[a*x^n]]))/36","A",1
123,1,79,90,0.0582387,"\int x \log ^{\frac{3}{2}}\left(a x^n\right) \, dx","Integrate[x*Log[a*x^n]^(3/2),x]","\frac{1}{32} x^2 \left(3 \sqrt{2 \pi } n^{3/2} \left(a x^n\right)^{-2/n} \text{erfi}\left(\frac{\sqrt{2} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)+4 \sqrt{\log \left(a x^n\right)} \left(4 \log \left(a x^n\right)-3 n\right)\right)","\frac{3}{16} \sqrt{\frac{\pi }{2}} n^{3/2} x^2 \left(a x^n\right)^{-2/n} \text{erfi}\left(\frac{\sqrt{2} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)+\frac{1}{2} x^2 \log ^{\frac{3}{2}}\left(a x^n\right)-\frac{3}{8} n x^2 \sqrt{\log \left(a x^n\right)}",1,"(x^2*((3*n^(3/2)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[Log[a*x^n]])/Sqrt[n]])/(a*x^n)^(2/n) + 4*Sqrt[Log[a*x^n]]*(-3*n + 4*Log[a*x^n])))/32","A",1
124,1,72,72,0.0396778,"\int \log ^{\frac{3}{2}}\left(a x^n\right) \, dx","Integrate[Log[a*x^n]^(3/2),x]","\frac{3}{4} \sqrt{\pi } n^{3/2} x \left(a x^n\right)^{-1/n} \text{erfi}\left(\frac{\sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)+x \log ^{\frac{3}{2}}\left(a x^n\right)-\frac{3}{2} n x \sqrt{\log \left(a x^n\right)}","\frac{3}{4} \sqrt{\pi } n^{3/2} x \left(a x^n\right)^{-1/n} \text{erfi}\left(\frac{\sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)+x \log ^{\frac{3}{2}}\left(a x^n\right)-\frac{3}{2} n x \sqrt{\log \left(a x^n\right)}",1,"(3*n^(3/2)*Sqrt[Pi]*x*Erfi[Sqrt[Log[a*x^n]]/Sqrt[n]])/(4*(a*x^n)^n^(-1)) - (3*n*x*Sqrt[Log[a*x^n]])/2 + x*Log[a*x^n]^(3/2)","A",1
125,1,17,17,0.0017841,"\int \frac{\log ^{\frac{3}{2}}\left(a x^n\right)}{x} \, dx","Integrate[Log[a*x^n]^(3/2)/x,x]","\frac{2 \log ^{\frac{5}{2}}\left(a x^n\right)}{5 n}","\frac{2 \log ^{\frac{5}{2}}\left(a x^n\right)}{5 n}",1,"(2*Log[a*x^n]^(5/2))/(5*n)","A",1
126,1,79,77,0.0577433,"\int \frac{\log ^{\frac{3}{2}}\left(a x^n\right)}{x^2} \, dx","Integrate[Log[a*x^n]^(3/2)/x^2,x]","-\frac{3 n^2 \left(a x^n\right)^{\frac{1}{n}} \sqrt{\frac{\log \left(a x^n\right)}{n}} \Gamma \left(\frac{1}{2},\frac{\log \left(a x^n\right)}{n}\right)+4 \log ^2\left(a x^n\right)+6 n \log \left(a x^n\right)}{4 x \sqrt{\log \left(a x^n\right)}}","\frac{3 \sqrt{\pi } n^{3/2} \left(a x^n\right)^{\frac{1}{n}} \text{erf}\left(\frac{\sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{4 x}-\frac{\log ^{\frac{3}{2}}\left(a x^n\right)}{x}-\frac{3 n \sqrt{\log \left(a x^n\right)}}{2 x}",1,"-1/4*(6*n*Log[a*x^n] + 4*Log[a*x^n]^2 + 3*n^2*(a*x^n)^n^(-1)*Gamma[1/2, Log[a*x^n]/n]*Sqrt[Log[a*x^n]/n])/(x*Sqrt[Log[a*x^n]])","A",1
127,1,88,90,0.0658998,"\int \frac{\log ^{\frac{3}{2}}\left(a x^n\right)}{x^3} \, dx","Integrate[Log[a*x^n]^(3/2)/x^3,x]","-\frac{3 \sqrt{2} n^2 \left(a x^n\right)^{2/n} \sqrt{\frac{\log \left(a x^n\right)}{n}} \Gamma \left(\frac{1}{2},\frac{2 \log \left(a x^n\right)}{n}\right)+4 \log \left(a x^n\right) \left(4 \log \left(a x^n\right)+3 n\right)}{32 x^2 \sqrt{\log \left(a x^n\right)}}","\frac{3 \sqrt{\frac{\pi }{2}} n^{3/2} \left(a x^n\right)^{2/n} \text{erf}\left(\frac{\sqrt{2} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{16 x^2}-\frac{\log ^{\frac{3}{2}}\left(a x^n\right)}{2 x^2}-\frac{3 n \sqrt{\log \left(a x^n\right)}}{8 x^2}",1,"-1/32*(3*Sqrt[2]*n^2*(a*x^n)^(2/n)*Gamma[1/2, (2*Log[a*x^n])/n]*Sqrt[Log[a*x^n]/n] + 4*Log[a*x^n]*(3*n + 4*Log[a*x^n]))/(x^2*Sqrt[Log[a*x^n]])","A",1
128,1,46,46,0.0061601,"\int \frac{x^3}{\sqrt{\log \left(a x^n\right)}} \, dx","Integrate[x^3/Sqrt[Log[a*x^n]],x]","\frac{\sqrt{\pi } x^4 \left(a x^n\right)^{-4/n} \text{erfi}\left(\frac{2 \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{2 \sqrt{n}}","\frac{\sqrt{\pi } x^4 \left(a x^n\right)^{-4/n} \text{erfi}\left(\frac{2 \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{2 \sqrt{n}}",1,"(Sqrt[Pi]*x^4*Erfi[(2*Sqrt[Log[a*x^n]])/Sqrt[n]])/(2*Sqrt[n]*(a*x^n)^(4/n))","A",1
129,1,51,51,0.0094283,"\int \frac{x^2}{\sqrt{\log \left(a x^n\right)}} \, dx","Integrate[x^2/Sqrt[Log[a*x^n]],x]","\frac{\sqrt{\frac{\pi }{3}} x^3 \left(a x^n\right)^{-3/n} \text{erfi}\left(\frac{\sqrt{3} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{\sqrt{n}}","\frac{\sqrt{\frac{\pi }{3}} x^3 \left(a x^n\right)^{-3/n} \text{erfi}\left(\frac{\sqrt{3} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{\sqrt{n}}",1,"(Sqrt[Pi/3]*x^3*Erfi[(Sqrt[3]*Sqrt[Log[a*x^n]])/Sqrt[n]])/(Sqrt[n]*(a*x^n)^(3/n))","A",1
130,1,51,51,0.008879,"\int \frac{x}{\sqrt{\log \left(a x^n\right)}} \, dx","Integrate[x/Sqrt[Log[a*x^n]],x]","\frac{\sqrt{\frac{\pi }{2}} x^2 \left(a x^n\right)^{-2/n} \text{erfi}\left(\frac{\sqrt{2} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{\sqrt{n}}","\frac{\sqrt{\frac{\pi }{2}} x^2 \left(a x^n\right)^{-2/n} \text{erfi}\left(\frac{\sqrt{2} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{\sqrt{n}}",1,"(Sqrt[Pi/2]*x^2*Erfi[(Sqrt[2]*Sqrt[Log[a*x^n]])/Sqrt[n]])/(Sqrt[n]*(a*x^n)^(2/n))","A",1
131,1,40,40,0.003963,"\int \frac{1}{\sqrt{\log \left(a x^n\right)}} \, dx","Integrate[1/Sqrt[Log[a*x^n]],x]","\frac{\sqrt{\pi } x \left(a x^n\right)^{-1/n} \text{erfi}\left(\frac{\sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{\sqrt{n}}","\frac{\sqrt{\pi } x \left(a x^n\right)^{-1/n} \text{erfi}\left(\frac{\sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{\sqrt{n}}",1,"(Sqrt[Pi]*x*Erfi[Sqrt[Log[a*x^n]]/Sqrt[n]])/(Sqrt[n]*(a*x^n)^n^(-1))","A",1
132,1,15,15,0.0015101,"\int \frac{1}{x \sqrt{\log \left(a x^n\right)}} \, dx","Integrate[1/(x*Sqrt[Log[a*x^n]]),x]","\frac{2 \sqrt{\log \left(a x^n\right)}}{n}","\frac{2 \sqrt{\log \left(a x^n\right)}}{n}",1,"(2*Sqrt[Log[a*x^n]])/n","A",1
133,1,52,40,0.0356594,"\int \frac{1}{x^2 \sqrt{\log \left(a x^n\right)}} \, dx","Integrate[1/(x^2*Sqrt[Log[a*x^n]]),x]","-\frac{\left(a x^n\right)^{\frac{1}{n}} \sqrt{\frac{\log \left(a x^n\right)}{n}} \Gamma \left(\frac{1}{2},\frac{\log \left(a x^n\right)}{n}\right)}{x \sqrt{\log \left(a x^n\right)}}","\frac{\sqrt{\pi } \left(a x^n\right)^{\frac{1}{n}} \text{erf}\left(\frac{\sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{\sqrt{n} x}",1,"-(((a*x^n)^n^(-1)*Gamma[1/2, Log[a*x^n]/n]*Sqrt[Log[a*x^n]/n])/(x*Sqrt[Log[a*x^n]]))","A",1
134,1,60,51,0.0356923,"\int \frac{1}{x^3 \sqrt{\log \left(a x^n\right)}} \, dx","Integrate[1/(x^3*Sqrt[Log[a*x^n]]),x]","-\frac{\left(a x^n\right)^{2/n} \sqrt{\frac{\log \left(a x^n\right)}{n}} \Gamma \left(\frac{1}{2},\frac{2 \log \left(a x^n\right)}{n}\right)}{\sqrt{2} x^2 \sqrt{\log \left(a x^n\right)}}","\frac{\sqrt{\frac{\pi }{2}} \left(a x^n\right)^{2/n} \text{erf}\left(\frac{\sqrt{2} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{\sqrt{n} x^2}",1,"-(((a*x^n)^(2/n)*Gamma[1/2, (2*Log[a*x^n])/n]*Sqrt[Log[a*x^n]/n])/(Sqrt[2]*x^2*Sqrt[Log[a*x^n]]))","A",1
135,1,73,63,0.0470734,"\int \frac{x^3}{\log ^{\frac{3}{2}}\left(a x^n\right)} \, dx","Integrate[x^3/Log[a*x^n]^(3/2),x]","-\frac{2 x^4 \left(a x^n\right)^{-4/n} \left(\left(a x^n\right)^{4/n}-2 \sqrt{-\frac{\log \left(a x^n\right)}{n}} \Gamma \left(\frac{1}{2},-\frac{4 \log \left(a x^n\right)}{n}\right)\right)}{n \sqrt{\log \left(a x^n\right)}}","\frac{4 \sqrt{\pi } x^4 \left(a x^n\right)^{-4/n} \text{erfi}\left(\frac{2 \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{n^{3/2}}-\frac{2 x^4}{n \sqrt{\log \left(a x^n\right)}}",1,"(-2*x^4*((a*x^n)^(4/n) - 2*Gamma[1/2, (-4*Log[a*x^n])/n]*Sqrt[-(Log[a*x^n]/n)]))/(n*(a*x^n)^(4/n)*Sqrt[Log[a*x^n]])","A",1
136,1,78,69,0.0532457,"\int \frac{x^2}{\log ^{\frac{3}{2}}\left(a x^n\right)} \, dx","Integrate[x^2/Log[a*x^n]^(3/2),x]","-\frac{2 x^3 \left(a x^n\right)^{-3/n} \left(\left(a x^n\right)^{3/n}-\sqrt{3} \sqrt{-\frac{\log \left(a x^n\right)}{n}} \Gamma \left(\frac{1}{2},-\frac{3 \log \left(a x^n\right)}{n}\right)\right)}{n \sqrt{\log \left(a x^n\right)}}","\frac{2 \sqrt{3 \pi } x^3 \left(a x^n\right)^{-3/n} \text{erfi}\left(\frac{\sqrt{3} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{n^{3/2}}-\frac{2 x^3}{n \sqrt{\log \left(a x^n\right)}}",1,"(-2*x^3*((a*x^n)^(3/n) - Sqrt[3]*Gamma[1/2, (-3*Log[a*x^n])/n]*Sqrt[-(Log[a*x^n]/n)]))/(n*(a*x^n)^(3/n)*Sqrt[Log[a*x^n]])","A",1
137,1,78,69,0.0502803,"\int \frac{x}{\log ^{\frac{3}{2}}\left(a x^n\right)} \, dx","Integrate[x/Log[a*x^n]^(3/2),x]","-\frac{2 x^2 \left(a x^n\right)^{-2/n} \left(\left(a x^n\right)^{2/n}-\sqrt{2} \sqrt{-\frac{\log \left(a x^n\right)}{n}} \Gamma \left(\frac{1}{2},-\frac{2 \log \left(a x^n\right)}{n}\right)\right)}{n \sqrt{\log \left(a x^n\right)}}","\frac{2 \sqrt{2 \pi } x^2 \left(a x^n\right)^{-2/n} \text{erfi}\left(\frac{\sqrt{2} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{n^{3/2}}-\frac{2 x^2}{n \sqrt{\log \left(a x^n\right)}}",1,"(-2*x^2*((a*x^n)^(2/n) - Sqrt[2]*Gamma[1/2, (-2*Log[a*x^n])/n]*Sqrt[-(Log[a*x^n]/n)]))/(n*(a*x^n)^(2/n)*Sqrt[Log[a*x^n]])","A",1
138,1,69,58,0.0356029,"\int \frac{1}{\log ^{\frac{3}{2}}\left(a x^n\right)} \, dx","Integrate[Log[a*x^n]^(-3/2),x]","-\frac{2 x \left(a x^n\right)^{-1/n} \left(\left(a x^n\right)^{\frac{1}{n}}-\sqrt{-\frac{\log \left(a x^n\right)}{n}} \Gamma \left(\frac{1}{2},-\frac{\log \left(a x^n\right)}{n}\right)\right)}{n \sqrt{\log \left(a x^n\right)}}","\frac{2 \sqrt{\pi } x \left(a x^n\right)^{-1/n} \text{erfi}\left(\frac{\sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{n^{3/2}}-\frac{2 x}{n \sqrt{\log \left(a x^n\right)}}",1,"(-2*x*((a*x^n)^n^(-1) - Gamma[1/2, -(Log[a*x^n]/n)]*Sqrt[-(Log[a*x^n]/n)]))/(n*(a*x^n)^n^(-1)*Sqrt[Log[a*x^n]])","A",1
139,1,15,15,0.0019128,"\int \frac{1}{x \log ^{\frac{3}{2}}\left(a x^n\right)} \, dx","Integrate[1/(x*Log[a*x^n]^(3/2)),x]","-\frac{2}{n \sqrt{\log \left(a x^n\right)}}","-\frac{2}{n \sqrt{\log \left(a x^n\right)}}",1,"-2/(n*Sqrt[Log[a*x^n]])","A",1
140,1,58,60,0.0499572,"\int \frac{1}{x^2 \log ^{\frac{3}{2}}\left(a x^n\right)} \, dx","Integrate[1/(x^2*Log[a*x^n]^(3/2)),x]","\frac{2 \left(\left(a x^n\right)^{\frac{1}{n}} \sqrt{\frac{\log \left(a x^n\right)}{n}} \Gamma \left(\frac{1}{2},\frac{\log \left(a x^n\right)}{n}\right)-1\right)}{n x \sqrt{\log \left(a x^n\right)}}","-\frac{2 \sqrt{\pi } \left(a x^n\right)^{\frac{1}{n}} \text{erf}\left(\frac{\sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{n^{3/2} x}-\frac{2}{n x \sqrt{\log \left(a x^n\right)}}",1,"(2*(-1 + (a*x^n)^n^(-1)*Gamma[1/2, Log[a*x^n]/n]*Sqrt[Log[a*x^n]/n]))/(n*x*Sqrt[Log[a*x^n]])","A",1
141,1,66,69,0.0492573,"\int \frac{1}{x^3 \log ^{\frac{3}{2}}\left(a x^n\right)} \, dx","Integrate[1/(x^3*Log[a*x^n]^(3/2)),x]","\frac{2 \left(\sqrt{2} \left(a x^n\right)^{2/n} \sqrt{\frac{\log \left(a x^n\right)}{n}} \Gamma \left(\frac{1}{2},\frac{2 \log \left(a x^n\right)}{n}\right)-1\right)}{n x^2 \sqrt{\log \left(a x^n\right)}}","-\frac{2 \sqrt{2 \pi } \left(a x^n\right)^{2/n} \text{erf}\left(\frac{\sqrt{2} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{n^{3/2} x^2}-\frac{2}{n x^2 \sqrt{\log \left(a x^n\right)}}",1,"(2*(-1 + Sqrt[2]*(a*x^n)^(2/n)*Gamma[1/2, (2*Log[a*x^n])/n]*Sqrt[Log[a*x^n]/n]))/(n*x^2*Sqrt[Log[a*x^n]])","A",1
142,1,87,87,0.0655332,"\int \frac{x^3}{\log ^{\frac{5}{2}}\left(a x^n\right)} \, dx","Integrate[x^3/Log[a*x^n]^(5/2),x]","-\frac{2 x^4 \left(a x^n\right)^{-4/n} \left(\left(a x^n\right)^{4/n} \left(8 \log \left(a x^n\right)+n\right)+16 n \left(-\frac{\log \left(a x^n\right)}{n}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{4 \log \left(a x^n\right)}{n}\right)\right)}{3 n^2 \log ^{\frac{3}{2}}\left(a x^n\right)}","\frac{32 \sqrt{\pi } x^4 \left(a x^n\right)^{-4/n} \text{erfi}\left(\frac{2 \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{3 n^{5/2}}-\frac{16 x^4}{3 n^2 \sqrt{\log \left(a x^n\right)}}-\frac{2 x^4}{3 n \log ^{\frac{3}{2}}\left(a x^n\right)}",1,"(-2*x^4*(16*n*Gamma[1/2, (-4*Log[a*x^n])/n]*(-(Log[a*x^n]/n))^(3/2) + (a*x^n)^(4/n)*(n + 8*Log[a*x^n])))/(3*n^2*(a*x^n)^(4/n)*Log[a*x^n]^(3/2))","A",1
143,1,92,89,0.0687188,"\int \frac{x^2}{\log ^{\frac{5}{2}}\left(a x^n\right)} \, dx","Integrate[x^2/Log[a*x^n]^(5/2),x]","-\frac{2 x^3 \left(a x^n\right)^{-3/n} \left(\left(a x^n\right)^{3/n} \left(6 \log \left(a x^n\right)+n\right)+6 \sqrt{3} n \left(-\frac{\log \left(a x^n\right)}{n}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{3 \log \left(a x^n\right)}{n}\right)\right)}{3 n^2 \log ^{\frac{3}{2}}\left(a x^n\right)}","\frac{4 \sqrt{3 \pi } x^3 \left(a x^n\right)^{-3/n} \text{erfi}\left(\frac{\sqrt{3} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{n^{5/2}}-\frac{4 x^3}{n^2 \sqrt{\log \left(a x^n\right)}}-\frac{2 x^3}{3 n \log ^{\frac{3}{2}}\left(a x^n\right)}",1,"(-2*x^3*(6*Sqrt[3]*n*Gamma[1/2, (-3*Log[a*x^n])/n]*(-(Log[a*x^n]/n))^(3/2) + (a*x^n)^(3/n)*(n + 6*Log[a*x^n])))/(3*n^2*(a*x^n)^(3/n)*Log[a*x^n]^(3/2))","A",1
144,1,92,93,0.0661688,"\int \frac{x}{\log ^{\frac{5}{2}}\left(a x^n\right)} \, dx","Integrate[x/Log[a*x^n]^(5/2),x]","-\frac{2 x^2 \left(a x^n\right)^{-2/n} \left(\left(a x^n\right)^{2/n} \left(4 \log \left(a x^n\right)+n\right)+4 \sqrt{2} n \left(-\frac{\log \left(a x^n\right)}{n}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{2 \log \left(a x^n\right)}{n}\right)\right)}{3 n^2 \log ^{\frac{3}{2}}\left(a x^n\right)}","\frac{8 \sqrt{2 \pi } x^2 \left(a x^n\right)^{-2/n} \text{erfi}\left(\frac{\sqrt{2} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{3 n^{5/2}}-\frac{8 x^2}{3 n^2 \sqrt{\log \left(a x^n\right)}}-\frac{2 x^2}{3 n \log ^{\frac{3}{2}}\left(a x^n\right)}",1,"(-2*x^2*(4*Sqrt[2]*n*Gamma[1/2, (-2*Log[a*x^n])/n]*(-(Log[a*x^n]/n))^(3/2) + (a*x^n)^(2/n)*(n + 4*Log[a*x^n])))/(3*n^2*(a*x^n)^(2/n)*Log[a*x^n]^(3/2))","A",1
145,1,83,80,0.059615,"\int \frac{1}{\log ^{\frac{5}{2}}\left(a x^n\right)} \, dx","Integrate[Log[a*x^n]^(-5/2),x]","-\frac{2 x \left(a x^n\right)^{-1/n} \left(\left(a x^n\right)^{\frac{1}{n}} \left(2 \log \left(a x^n\right)+n\right)+2 n \left(-\frac{\log \left(a x^n\right)}{n}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{\log \left(a x^n\right)}{n}\right)\right)}{3 n^2 \log ^{\frac{3}{2}}\left(a x^n\right)}","\frac{4 \sqrt{\pi } x \left(a x^n\right)^{-1/n} \text{erfi}\left(\frac{\sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{3 n^{5/2}}-\frac{4 x}{3 n^2 \sqrt{\log \left(a x^n\right)}}-\frac{2 x}{3 n \log ^{\frac{3}{2}}\left(a x^n\right)}",1,"(-2*x*(2*n*Gamma[1/2, -(Log[a*x^n]/n)]*(-(Log[a*x^n]/n))^(3/2) + (a*x^n)^n^(-1)*(n + 2*Log[a*x^n])))/(3*n^2*(a*x^n)^n^(-1)*Log[a*x^n]^(3/2))","A",1
146,1,17,17,0.0023281,"\int \frac{1}{x \log ^{\frac{5}{2}}\left(a x^n\right)} \, dx","Integrate[1/(x*Log[a*x^n]^(5/2)),x]","-\frac{2}{3 n \log ^{\frac{3}{2}}\left(a x^n\right)}","-\frac{2}{3 n \log ^{\frac{3}{2}}\left(a x^n\right)}",1,"-2/(3*n*Log[a*x^n]^(3/2))","A",1
147,1,70,84,0.0720806,"\int \frac{1}{x^2 \log ^{\frac{5}{2}}\left(a x^n\right)} \, dx","Integrate[1/(x^2*Log[a*x^n]^(5/2)),x]","-\frac{2 \left(-2 \log \left(a x^n\right)+2 n \left(a x^n\right)^{\frac{1}{n}} \left(\frac{\log \left(a x^n\right)}{n}\right)^{3/2} \Gamma \left(\frac{1}{2},\frac{\log \left(a x^n\right)}{n}\right)+n\right)}{3 n^2 x \log ^{\frac{3}{2}}\left(a x^n\right)}","\frac{4 \sqrt{\pi } \left(a x^n\right)^{\frac{1}{n}} \text{erf}\left(\frac{\sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{3 n^{5/2} x}+\frac{4}{3 n^2 x \sqrt{\log \left(a x^n\right)}}-\frac{2}{3 n x \log ^{\frac{3}{2}}\left(a x^n\right)}",1,"(-2*(n - 2*Log[a*x^n] + 2*n*(a*x^n)^n^(-1)*Gamma[1/2, Log[a*x^n]/n]*(Log[a*x^n]/n)^(3/2)))/(3*n^2*x*Log[a*x^n]^(3/2))","A",1
148,1,78,93,0.0640999,"\int \frac{1}{x^3 \log ^{\frac{5}{2}}\left(a x^n\right)} \, dx","Integrate[1/(x^3*Log[a*x^n]^(5/2)),x]","-\frac{2 \left(-4 \log \left(a x^n\right)+4 \sqrt{2} n \left(a x^n\right)^{2/n} \left(\frac{\log \left(a x^n\right)}{n}\right)^{3/2} \Gamma \left(\frac{1}{2},\frac{2 \log \left(a x^n\right)}{n}\right)+n\right)}{3 n^2 x^2 \log ^{\frac{3}{2}}\left(a x^n\right)}","\frac{8 \sqrt{2 \pi } \left(a x^n\right)^{2/n} \text{erf}\left(\frac{\sqrt{2} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{3 n^{5/2} x^2}+\frac{8}{3 n^2 x^2 \sqrt{\log \left(a x^n\right)}}-\frac{2}{3 n x^2 \log ^{\frac{3}{2}}\left(a x^n\right)}",1,"(-2*(n - 4*Log[a*x^n] + 4*Sqrt[2]*n*(a*x^n)^(2/n)*Gamma[1/2, (2*Log[a*x^n])/n]*(Log[a*x^n]/n)^(3/2)))/(3*n^2*x^2*Log[a*x^n]^(3/2))","A",1
149,1,17,21,0.0123826,"\int (d x)^m \left(a+\frac{a (1+m) \log \left(c x^n\right)}{n}\right) \, dx","Integrate[(d*x)^m*(a + (a*(1 + m)*Log[c*x^n])/n),x]","\frac{a x (d x)^m \log \left(c x^n\right)}{n}","\frac{a (d x)^{m+1} \log \left(c x^n\right)}{d n}",1,"(a*x*(d*x)^m*Log[c*x^n])/n","A",1
150,1,76,116,0.0478182,"\int (d x)^m \left(a+b \log \left(c x^n\right)\right)^3 \, dx","Integrate[(d*x)^m*(a + b*Log[c*x^n])^3,x]","\frac{x (d x)^m \left(\left(a+b \log \left(c x^n\right)\right)^3-\frac{3 b n \left((m+1)^2 \left(a+b \log \left(c x^n\right)\right)^2+2 b n \left(b n-(m+1) \left(a+b \log \left(c x^n\right)\right)\right)\right)}{(m+1)^3}\right)}{m+1}","\frac{6 b^2 n^2 (d x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{d (m+1)^3}+\frac{(d x)^{m+1} \left(a+b \log \left(c x^n\right)\right)^3}{d (m+1)}-\frac{3 b n (d x)^{m+1} \left(a+b \log \left(c x^n\right)\right)^2}{d (m+1)^2}-\frac{6 b^3 n^3 (d x)^{m+1}}{d (m+1)^4}",1,"(x*(d*x)^m*((a + b*Log[c*x^n])^3 - (3*b*n*((1 + m)^2*(a + b*Log[c*x^n])^2 + 2*b*n*(b*n - (1 + m)*(a + b*Log[c*x^n]))))/(1 + m)^3))/(1 + m)","A",1
151,1,76,81,0.0365748,"\int (d x)^m \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[(d*x)^m*(a + b*Log[c*x^n])^2,x]","\frac{x (d x)^m \left(a^2 (m+1)^2+2 b (m+1) (a m+a-b n) \log \left(c x^n\right)-2 a b (m+1) n+b^2 (m+1)^2 \log ^2\left(c x^n\right)+2 b^2 n^2\right)}{(m+1)^3}","\frac{(d x)^{m+1} \left(a+b \log \left(c x^n\right)\right)^2}{d (m+1)}-\frac{2 b n (d x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{d (m+1)^2}+\frac{2 b^2 n^2 (d x)^{m+1}}{d (m+1)^3}",1,"(x*(d*x)^m*(a^2*(1 + m)^2 - 2*a*b*(1 + m)*n + 2*b^2*n^2 + 2*b*(1 + m)*(a + a*m - b*n)*Log[c*x^n] + b^2*(1 + m)^2*Log[c*x^n]^2))/(1 + m)^3","A",1
152,1,32,46,0.0130826,"\int (d x)^m \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[(d*x)^m*(a + b*Log[c*x^n]),x]","\frac{x (d x)^m \left(a m+a+b (m+1) \log \left(c x^n\right)-b n\right)}{(m+1)^2}","\frac{(d x)^{m+1} \left(a+b \log \left(c x^n\right)\right)}{d (m+1)}-\frac{b n (d x)^{m+1}}{d (m+1)^2}",1,"(x*(d*x)^m*(a + a*m - b*n + b*(1 + m)*Log[c*x^n]))/(1 + m)^2","A",1
153,1,67,66,0.119886,"\int \frac{(d x)^m}{a+b \log \left(c x^n\right)} \, dx","Integrate[(d*x)^m/(a + b*Log[c*x^n]),x]","\frac{x^{-m} (d x)^m \exp \left(-\frac{(m+1) \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)}{b n}\right) \text{Ei}\left(\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b n}","\frac{(d x)^{m+1} e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \text{Ei}\left(\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b d n}",1,"((d*x)^m*ExpIntegralEi[((1 + m)*(a + b*Log[c*x^n]))/(b*n)])/(b*E^(((1 + m)*(a + b*(-(n*Log[x]) + Log[c*x^n])))/(b*n))*n*x^m)","A",1
154,1,89,100,0.242381,"\int \frac{(d x)^m}{\left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[(d*x)^m/(a + b*Log[c*x^n])^2,x]","\frac{(d x)^m \left((m+1) x^{-m} \exp \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \text{Ei}\left(\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)-\frac{b n x}{a+b \log \left(c x^n\right)}\right)}{b^2 n^2}","\frac{(m+1) (d x)^{m+1} e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \text{Ei}\left(\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{b^2 d n^2}-\frac{(d x)^{m+1}}{b d n \left(a+b \log \left(c x^n\right)\right)}",1,"((d*x)^m*(((1 + m)*ExpIntegralEi[((1 + m)*(a + b*Log[c*x^n]))/(b*n)])/(E^(((1 + m)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*x^m) - (b*n*x)/(a + b*Log[c*x^n])))/(b^2*n^2)","A",1
155,1,113,142,0.3693881,"\int \frac{(d x)^m}{\left(a+b \log \left(c x^n\right)\right)^3} \, dx","Integrate[(d*x)^m/(a + b*Log[c*x^n])^3,x]","\frac{(d x)^m \left((m+1)^2 x^{-m} \exp \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \text{Ei}\left(\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)-\frac{b n x \left(a m+a+b (m+1) \log \left(c x^n\right)+b n\right)}{\left(a+b \log \left(c x^n\right)\right)^2}\right)}{2 b^3 n^3}","\frac{(m+1)^2 (d x)^{m+1} e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \text{Ei}\left(\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{2 b^3 d n^3}-\frac{(m+1) (d x)^{m+1}}{2 b^2 d n^2 \left(a+b \log \left(c x^n\right)\right)}-\frac{(d x)^{m+1}}{2 b d n \left(a+b \log \left(c x^n\right)\right)^2}",1,"((d*x)^m*(((1 + m)^2*ExpIntegralEi[((1 + m)*(a + b*Log[c*x^n]))/(b*n)])/(E^(((1 + m)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*x^m) - (b*n*x*(a + a*m + b*n + b*(1 + m)*Log[c*x^n]))/(a + b*Log[c*x^n])^2))/(2*b^3*n^3)","A",1
156,1,40,74,0.007958,"\int (d x)^{-1+n} \log ^3\left(c x^n\right) \, dx","Integrate[(d*x)^(-1 + n)*Log[c*x^n]^3,x]","\frac{(d x)^n \left(\log ^3\left(c x^n\right)-3 \log ^2\left(c x^n\right)+6 \log \left(c x^n\right)-6\right)}{d n}","\frac{(d x)^n \log ^3\left(c x^n\right)}{d n}-\frac{3 (d x)^n \log ^2\left(c x^n\right)}{d n}+\frac{6 (d x)^n \log \left(c x^n\right)}{d n}-\frac{6 (d x)^n}{d n}",1,"((d*x)^n*(-6 + 6*Log[c*x^n] - 3*Log[c*x^n]^2 + Log[c*x^n]^3))/(d*n)","A",1
157,1,30,53,0.0063993,"\int (d x)^{-1+n} \log ^2\left(c x^n\right) \, dx","Integrate[(d*x)^(-1 + n)*Log[c*x^n]^2,x]","\frac{(d x)^n \left(\log ^2\left(c x^n\right)-2 \log \left(c x^n\right)+2\right)}{d n}","\frac{(d x)^n \log ^2\left(c x^n\right)}{d n}-\frac{2 (d x)^n \log \left(c x^n\right)}{d n}+\frac{2 (d x)^n}{d n}",1,"((d*x)^n*(2 - 2*Log[c*x^n] + Log[c*x^n]^2))/(d*n)","A",1
158,1,20,32,0.0043467,"\int (d x)^{-1+n} \log \left(c x^n\right) \, dx","Integrate[(d*x)^(-1 + n)*Log[c*x^n],x]","\frac{(d x)^n \left(\log \left(c x^n\right)-1\right)}{d n}","\frac{(d x)^n \log \left(c x^n\right)}{d n}-\frac{(d x)^n}{d n}",1,"((d*x)^n*(-1 + Log[c*x^n]))/(d*n)","A",1
159,1,27,27,0.0082792,"\int \frac{(d x)^{-1+n}}{\log \left(c x^n\right)} \, dx","Integrate[(d*x)^(-1 + n)/Log[c*x^n],x]","\frac{x^{1-n} (d x)^{n-1} \text{li}\left(c x^n\right)}{c n}","\frac{x^{1-n} (d x)^{n-1} \text{li}\left(c x^n\right)}{c n}",1,"(x^(1 - n)*(d*x)^(-1 + n)*LogIntegral[c*x^n])/(c*n)","A",1
160,1,49,49,0.0174804,"\int \frac{(d x)^{-1+n}}{\log ^2\left(c x^n\right)} \, dx","Integrate[(d*x)^(-1 + n)/Log[c*x^n]^2,x]","\frac{x^{1-n} (d x)^{n-1} \text{li}\left(c x^n\right)}{c n}-\frac{x (d x)^{n-1}}{n \log \left(c x^n\right)}","\frac{x^{1-n} (d x)^{n-1} \text{li}\left(c x^n\right)}{c n}-\frac{(d x)^n}{d n \log \left(c x^n\right)}",1,"-((x*(d*x)^(-1 + n))/(n*Log[c*x^n])) + (x^(1 - n)*(d*x)^(-1 + n)*LogIntegral[c*x^n])/(c*n)","A",1
161,1,61,77,0.0243321,"\int \frac{(d x)^{-1+n}}{\log ^3\left(c x^n\right)} \, dx","Integrate[(d*x)^(-1 + n)/Log[c*x^n]^3,x]","\frac{x^{-n} (d x)^n \left(\text{li}\left(c x^n\right) \log ^2\left(c x^n\right)-c x^n \left(\log \left(c x^n\right)+1\right)\right)}{2 c d n \log ^2\left(c x^n\right)}","\frac{x^{1-n} (d x)^{n-1} \text{li}\left(c x^n\right)}{2 c n}-\frac{(d x)^n}{2 d n \log ^2\left(c x^n\right)}-\frac{(d x)^n}{2 d n \log \left(c x^n\right)}",1,"((d*x)^n*(-(c*x^n*(1 + Log[c*x^n])) + Log[c*x^n]^2*LogIntegral[c*x^n]))/(2*c*d*n*x^n*Log[c*x^n]^2)","A",1
162,1,101,111,0.1887533,"\int x^m \log ^{\frac{3}{2}}\left(a x^n\right) \, dx","Integrate[x^m*Log[a*x^n]^(3/2),x]","\frac{x^{m+1} \left(3 \sqrt{\pi } n^{3/2} \left(a x^n\right)^{-\frac{m+1}{n}} \text{erfi}\left(\frac{\sqrt{m+1} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)+2 \sqrt{m+1} \sqrt{\log \left(a x^n\right)} \left(2 (m+1) \log \left(a x^n\right)-3 n\right)\right)}{4 (m+1)^{5/2}}","\frac{3 \sqrt{\pi } n^{3/2} x^{m+1} \left(a x^n\right)^{-\frac{m+1}{n}} \text{erfi}\left(\frac{\sqrt{m+1} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{4 (m+1)^{5/2}}+\frac{x^{m+1} \log ^{\frac{3}{2}}\left(a x^n\right)}{m+1}-\frac{3 n x^{m+1} \sqrt{\log \left(a x^n\right)}}{2 (m+1)^2}",1,"(x^(1 + m)*((3*n^(3/2)*Sqrt[Pi]*Erfi[(Sqrt[1 + m]*Sqrt[Log[a*x^n]])/Sqrt[n]])/(a*x^n)^((1 + m)/n) + 2*Sqrt[1 + m]*Sqrt[Log[a*x^n]]*(-3*n + 2*(1 + m)*Log[a*x^n])))/(4*(1 + m)^(5/2))","A",1
163,1,86,86,0.0521127,"\int x^m \sqrt{\log \left(a x^n\right)} \, dx","Integrate[x^m*Sqrt[Log[a*x^n]],x]","\frac{x^{m+1} \sqrt{\log \left(a x^n\right)}}{m+1}-\frac{\sqrt{\pi } \sqrt{n} x^{m+1} \left(a x^n\right)^{-\frac{m+1}{n}} \text{erfi}\left(\frac{\sqrt{m+1} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{2 (m+1)^{3/2}}","\frac{x^{m+1} \sqrt{\log \left(a x^n\right)}}{m+1}-\frac{\sqrt{\pi } \sqrt{n} x^{m+1} \left(a x^n\right)^{-\frac{m+1}{n}} \text{erfi}\left(\frac{\sqrt{m+1} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{2 (m+1)^{3/2}}",1,"-1/2*(Sqrt[n]*Sqrt[Pi]*x^(1 + m)*Erfi[(Sqrt[1 + m]*Sqrt[Log[a*x^n]])/Sqrt[n]])/((1 + m)^(3/2)*(a*x^n)^((1 + m)/n)) + (x^(1 + m)*Sqrt[Log[a*x^n]])/(1 + m)","A",1
164,1,61,61,0.0109717,"\int \frac{x^m}{\sqrt{\log \left(a x^n\right)}} \, dx","Integrate[x^m/Sqrt[Log[a*x^n]],x]","\frac{\sqrt{\pi } x^{m+1} \left(a x^n\right)^{-\frac{m+1}{n}} \text{erfi}\left(\frac{\sqrt{m+1} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{\sqrt{m+1} \sqrt{n}}","\frac{\sqrt{\pi } x^{m+1} \left(a x^n\right)^{-\frac{m+1}{n}} \text{erfi}\left(\frac{\sqrt{m+1} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{\sqrt{m+1} \sqrt{n}}",1,"(Sqrt[Pi]*x^(1 + m)*Erfi[(Sqrt[1 + m]*Sqrt[Log[a*x^n]])/Sqrt[n]])/(Sqrt[1 + m]*Sqrt[n]*(a*x^n)^((1 + m)/n))","A",1
165,1,86,83,0.1984459,"\int \frac{x^m}{\log ^{\frac{3}{2}}\left(a x^n\right)} \, dx","Integrate[x^m/Log[a*x^n]^(3/2),x]","\frac{2 \sqrt{\pi } \sqrt{m+1} e^{-\frac{(m+1) \left(\log \left(a x^n\right)-n \log (x)\right)}{n}} \text{erfi}\left(\frac{\sqrt{m+1} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{n^{3/2}}-\frac{2 x^{m+1}}{n \sqrt{\log \left(a x^n\right)}}","\frac{2 \sqrt{\pi } \sqrt{m+1} x^{m+1} \left(a x^n\right)^{-\frac{m+1}{n}} \text{erfi}\left(\frac{\sqrt{m+1} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{n^{3/2}}-\frac{2 x^{m+1}}{n \sqrt{\log \left(a x^n\right)}}",1,"(2*Sqrt[1 + m]*Sqrt[Pi]*Erfi[(Sqrt[1 + m]*Sqrt[Log[a*x^n]])/Sqrt[n]])/(E^(((1 + m)*(-(n*Log[x]) + Log[a*x^n]))/n)*n^(3/2)) - (2*x^(1 + m))/(n*Sqrt[Log[a*x^n]])","A",1
166,1,103,112,0.4217704,"\int \frac{x^m}{\log ^{\frac{5}{2}}\left(a x^n\right)} \, dx","Integrate[x^m/Log[a*x^n]^(5/2),x]","\frac{2 \left(\frac{2 \sqrt{\pi } (m+1)^{3/2} e^{\frac{(m+1) \left(n \log (x)-\log \left(a x^n\right)\right)}{n}} \text{erfi}\left(\frac{\sqrt{m+1} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{\sqrt{n}}-\frac{x^{m+1} \left(2 (m+1) \log \left(a x^n\right)+n\right)}{\log ^{\frac{3}{2}}\left(a x^n\right)}\right)}{3 n^2}","\frac{4 \sqrt{\pi } (m+1)^{3/2} x^{m+1} \left(a x^n\right)^{-\frac{m+1}{n}} \text{erfi}\left(\frac{\sqrt{m+1} \sqrt{\log \left(a x^n\right)}}{\sqrt{n}}\right)}{3 n^{5/2}}-\frac{4 (m+1) x^{m+1}}{3 n^2 \sqrt{\log \left(a x^n\right)}}-\frac{2 x^{m+1}}{3 n \log ^{\frac{3}{2}}\left(a x^n\right)}",1,"(2*((2*E^(((1 + m)*(n*Log[x] - Log[a*x^n]))/n)*(1 + m)^(3/2)*Sqrt[Pi]*Erfi[(Sqrt[1 + m]*Sqrt[Log[a*x^n]])/Sqrt[n]])/Sqrt[n] - (x^(1 + m)*(n + 2*(1 + m)*Log[a*x^n]))/Log[a*x^n]^(3/2)))/(3*n^2)","A",1
167,1,107,106,0.1417034,"\int (d x)^m \left(a+b \log \left(c x^n\right)\right)^p \, dx","Integrate[(d*x)^m*(a + b*Log[c*x^n])^p,x]","\frac{x^{-m} (d x)^m \left(a+b \log \left(c x^n\right)\right)^p \exp \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m+1}","\frac{(d x)^{m+1} e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{d (m+1)}",1,"((d*x)^m*Gamma[1 + p, -(((1 + m)*(a + b*Log[c*x^n]))/(b*n))]*(a + b*Log[c*x^n])^p)/(E^(((1 + m)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*(1 + m)*x^m*(-(((1 + m)*(a + b*Log[c*x^n]))/(b*n)))^p)","A",1
168,1,89,89,0.0971062,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^p \, dx","Integrate[x^2*(a + b*Log[c*x^n])^p,x]","3^{-p-1} x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)","3^{-p-1} x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)",1,"(3^(-1 - p)*x^3*Gamma[1 + p, (-3*(a + b*Log[c*x^n]))/(b*n)]*(a + b*Log[c*x^n])^p)/(E^((3*a)/(b*n))*(c*x^n)^(3/n)*(-((a + b*Log[c*x^n])/(b*n)))^p)","A",1
169,1,89,89,0.0844891,"\int x \left(a+b \log \left(c x^n\right)\right)^p \, dx","Integrate[x*(a + b*Log[c*x^n])^p,x]","2^{-p-1} x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)","2^{-p-1} x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)",1,"(2^(-1 - p)*x^2*Gamma[1 + p, (-2*(a + b*Log[c*x^n]))/(b*n)]*(a + b*Log[c*x^n])^p)/(E^((2*a)/(b*n))*(c*x^n)^(2/n)*(-((a + b*Log[c*x^n])/(b*n)))^p)","A",1
170,1,80,80,0.0729051,"\int \left(a+b \log \left(c x^n\right)\right)^p \, dx","Integrate[(a + b*Log[c*x^n])^p,x]","x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c x^n\right)}{b n}\right)","x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c x^n\right)}{b n}\right)",1,"(x*Gamma[1 + p, -((a + b*Log[c*x^n])/(b*n))]*(a + b*Log[c*x^n])^p)/(E^(a/(b*n))*(c*x^n)^n^(-1)*(-((a + b*Log[c*x^n])/(b*n)))^p)","A",1
171,1,26,26,0.0076785,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^p}{x} \, dx","Integrate[(a + b*Log[c*x^n])^p/x,x]","\frac{\left(a+b \log \left(c x^n\right)\right)^{p+1}}{b n (p+1)}","\frac{\left(a+b \log \left(c x^n\right)\right)^{p+1}}{b n (p+1)}",1,"(a + b*Log[c*x^n])^(1 + p)/(b*n*(1 + p))","A",1
172,1,78,78,0.0831221,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^p}{x^2} \, dx","Integrate[(a + b*Log[c*x^n])^p/x^2,x]","-\frac{e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,\frac{a+b \log \left(c x^n\right)}{b n}\right)}{x}","-\frac{e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,\frac{a+b \log \left(c x^n\right)}{b n}\right)}{x}",1,"-((E^(a/(b*n))*(c*x^n)^n^(-1)*Gamma[1 + p, (a + b*Log[c*x^n])/(b*n)]*(a + b*Log[c*x^n])^p)/(x*((a + b*Log[c*x^n])/(b*n))^p))","A",1
173,1,89,89,0.08605,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^p}{x^3} \, dx","Integrate[(a + b*Log[c*x^n])^p/x^3,x]","-\frac{2^{-p-1} e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{x^2}","-\frac{2^{-p-1} e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{x^2}",1,"-((2^(-1 - p)*E^((2*a)/(b*n))*(c*x^n)^(2/n)*Gamma[1 + p, (2*(a + b*Log[c*x^n]))/(b*n)]*(a + b*Log[c*x^n])^p)/(x^2*((a + b*Log[c*x^n])/(b*n))^p))","A",1
174,1,89,89,0.0889826,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^p}{x^4} \, dx","Integrate[(a + b*Log[c*x^n])^p/x^4,x]","-\frac{3^{-p-1} e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{x^3}","-\frac{3^{-p-1} e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{x^3}",1,"-((3^(-1 - p)*E^((3*a)/(b*n))*(c*x^n)^(3/n)*Gamma[1 + p, (3*(a + b*Log[c*x^n]))/(b*n)]*(a + b*Log[c*x^n])^p)/(x^3*((a + b*Log[c*x^n])/(b*n))^p))","A",1
175,1,82,86,0.1154283,"\int (d x)^m (a+b \log (c x))^p \, dx","Integrate[(d*x)^m*(a + b*Log[c*x])^p,x]","\frac{e^{-\frac{a (m+1)}{b}} (c x)^{-m} (d x)^m (a+b \log (c x))^p \left(-\frac{(m+1) (a+b \log (c x))}{b}\right)^{-p} \Gamma \left(p+1,-\frac{(m+1) (a+b \log (c x))}{b}\right)}{c (m+1)}","\frac{e^{-\frac{a (m+1)}{b}} (c x)^{-m-1} (d x)^{m+1} (a+b \log (c x))^p \left(-\frac{(m+1) (a+b \log (c x))}{b}\right)^{-p} \Gamma \left(p+1,-\frac{(m+1) (a+b \log (c x))}{b}\right)}{d (m+1)}",1,"((d*x)^m*Gamma[1 + p, -(((1 + m)*(a + b*Log[c*x]))/b)]*(a + b*Log[c*x])^p)/(c*E^((a*(1 + m))/b)*(1 + m)*(c*x)^m*(-(((1 + m)*(a + b*Log[c*x]))/b))^p)","A",1
176,1,63,63,0.0659905,"\int x^2 (a+b \log (c x))^p \, dx","Integrate[x^2*(a + b*Log[c*x])^p,x]","\frac{3^{-p-1} e^{-\frac{3 a}{b}} (a+b \log (c x))^p \left(-\frac{a+b \log (c x)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 (a+b \log (c x))}{b}\right)}{c^3}","\frac{3^{-p-1} e^{-\frac{3 a}{b}} (a+b \log (c x))^p \left(-\frac{a+b \log (c x)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 (a+b \log (c x))}{b}\right)}{c^3}",1,"(3^(-1 - p)*Gamma[1 + p, (-3*(a + b*Log[c*x]))/b]*(a + b*Log[c*x])^p)/(c^3*E^((3*a)/b)*(-((a + b*Log[c*x])/b))^p)","A",1
177,1,63,63,0.0325256,"\int x (a+b \log (c x))^p \, dx","Integrate[x*(a + b*Log[c*x])^p,x]","\frac{2^{-p-1} e^{-\frac{2 a}{b}} (a+b \log (c x))^p \left(-\frac{a+b \log (c x)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 (a+b \log (c x))}{b}\right)}{c^2}","\frac{2^{-p-1} e^{-\frac{2 a}{b}} (a+b \log (c x))^p \left(-\frac{a+b \log (c x)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 (a+b \log (c x))}{b}\right)}{c^2}",1,"(2^(-1 - p)*Gamma[1 + p, (-2*(a + b*Log[c*x]))/b]*(a + b*Log[c*x])^p)/(c^2*E^((2*a)/b)*(-((a + b*Log[c*x])/b))^p)","A",1
178,1,56,56,0.0281016,"\int (a+b \log (c x))^p \, dx","Integrate[(a + b*Log[c*x])^p,x]","\frac{e^{-\frac{a}{b}} (a+b \log (c x))^p \left(-\frac{a+b \log (c x)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log (c x)}{b}\right)}{c}","\frac{e^{-\frac{a}{b}} (a+b \log (c x))^p \left(-\frac{a+b \log (c x)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log (c x)}{b}\right)}{c}",1,"(Gamma[1 + p, -((a + b*Log[c*x])/b)]*(a + b*Log[c*x])^p)/(c*E^(a/b)*(-((a + b*Log[c*x])/b))^p)","A",1
179,1,21,21,0.0063219,"\int \frac{(a+b \log (c x))^p}{x} \, dx","Integrate[(a + b*Log[c*x])^p/x,x]","\frac{(a+b \log (c x))^{p+1}}{b (p+1)}","\frac{(a+b \log (c x))^{p+1}}{b (p+1)}",1,"(a + b*Log[c*x])^(1 + p)/(b*(1 + p))","A",1
180,1,48,52,0.0350173,"\int \frac{(a+b \log (c x))^p}{x^2} \, dx","Integrate[(a + b*Log[c*x])^p/x^2,x]","-c e^{a/b} \left(\frac{a}{b}+\log (c x)\right)^{-p} (a+b \log (c x))^p \Gamma \left(p+1,\frac{a}{b}+\log (c x)\right)","-c e^{a/b} (a+b \log (c x))^p \left(\frac{a+b \log (c x)}{b}\right)^{-p} \Gamma \left(p+1,\frac{a+b \log (c x)}{b}\right)",1,"-((c*E^(a/b)*Gamma[1 + p, a/b + Log[c*x]]*(a + b*Log[c*x])^p)/(a/b + Log[c*x])^p)","A",1
181,1,63,63,0.0370988,"\int \frac{(a+b \log (c x))^p}{x^3} \, dx","Integrate[(a + b*Log[c*x])^p/x^3,x]","c^2 \left(-2^{-p-1}\right) e^{\frac{2 a}{b}} (a+b \log (c x))^p \left(\frac{a+b \log (c x)}{b}\right)^{-p} \Gamma \left(p+1,\frac{2 (a+b \log (c x))}{b}\right)","c^2 \left(-2^{-p-1}\right) e^{\frac{2 a}{b}} (a+b \log (c x))^p \left(\frac{a+b \log (c x)}{b}\right)^{-p} \Gamma \left(p+1,\frac{2 (a+b \log (c x))}{b}\right)",1,"-((2^(-1 - p)*c^2*E^((2*a)/b)*Gamma[1 + p, (2*(a + b*Log[c*x]))/b]*(a + b*Log[c*x])^p)/((a + b*Log[c*x])/b)^p)","A",1
182,1,63,63,0.0362052,"\int \frac{(a+b \log (c x))^p}{x^4} \, dx","Integrate[(a + b*Log[c*x])^p/x^4,x]","c^3 \left(-3^{-p-1}\right) e^{\frac{3 a}{b}} (a+b \log (c x))^p \left(\frac{a+b \log (c x)}{b}\right)^{-p} \Gamma \left(p+1,\frac{3 (a+b \log (c x))}{b}\right)","c^3 \left(-3^{-p-1}\right) e^{\frac{3 a}{b}} (a+b \log (c x))^p \left(\frac{a+b \log (c x)}{b}\right)^{-p} \Gamma \left(p+1,\frac{3 (a+b \log (c x))}{b}\right)",1,"-((3^(-1 - p)*c^3*E^((3*a)/b)*Gamma[1 + p, (3*(a + b*Log[c*x]))/b]*(a + b*Log[c*x])^p)/((a + b*Log[c*x])/b)^p)","A",1
183,1,103,107,0.1947888,"\int (d x)^m \left(a+b \log \left(c \sqrt{x}\right)\right)^p \, dx","Integrate[(d*x)^m*(a + b*Log[c*Sqrt[x]])^p,x]","\frac{2^{-p} e^{-\frac{2 a (m+1)}{b}} \left(c \sqrt{x}\right)^{-2 m} (d x)^m \left(a+b \log \left(c \sqrt{x}\right)\right)^p \left(-\frac{(m+1) \left(a+b \log \left(c \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 (m+1) \left(a+b \log \left(c \sqrt{x}\right)\right)}{b}\right)}{c^2 (m+1)}","\frac{2^{-p} e^{-\frac{2 a (m+1)}{b}} \left(c \sqrt{x}\right)^{-2 (m+1)} (d x)^{m+1} \left(a+b \log \left(c \sqrt{x}\right)\right)^p \left(-\frac{(m+1) \left(a+b \log \left(c \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 (m+1) \left(a+b \log \left(c \sqrt{x}\right)\right)}{b}\right)}{d (m+1)}",1,"((d*x)^m*Gamma[1 + p, (-2*(1 + m)*(a + b*Log[c*Sqrt[x]]))/b]*(a + b*Log[c*Sqrt[x]])^p)/(2^p*c^2*E^((2*a*(1 + m))/b)*(1 + m)*(c*Sqrt[x])^(2*m)*(-(((1 + m)*(a + b*Log[c*Sqrt[x]]))/b))^p)","A",1
184,1,80,80,0.1063319,"\int x^2 \left(a+b \log \left(c \sqrt{x}\right)\right)^p \, dx","Integrate[x^2*(a + b*Log[c*Sqrt[x]])^p,x]","\frac{2^{-p} 3^{-p-1} e^{-\frac{6 a}{b}} \left(a+b \log \left(c \sqrt{x}\right)\right)^p \left(-\frac{a+b \log \left(c \sqrt{x}\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \sqrt{x}\right)\right)}{b}\right)}{c^6}","\frac{2^{-p} 3^{-p-1} e^{-\frac{6 a}{b}} \left(a+b \log \left(c \sqrt{x}\right)\right)^p \left(-\frac{a+b \log \left(c \sqrt{x}\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \sqrt{x}\right)\right)}{b}\right)}{c^6}",1,"(3^(-1 - p)*Gamma[1 + p, (-6*(a + b*Log[c*Sqrt[x]]))/b]*(a + b*Log[c*Sqrt[x]])^p)/(2^p*c^6*E^((6*a)/b)*(-((a + b*Log[c*Sqrt[x]])/b))^p)","A",1
185,1,75,75,0.0655709,"\int x \left(a+b \log \left(c \sqrt{x}\right)\right)^p \, dx","Integrate[x*(a + b*Log[c*Sqrt[x]])^p,x]","\frac{2^{-2 p-1} e^{-\frac{4 a}{b}} \left(a+b \log \left(c \sqrt{x}\right)\right)^p \left(-\frac{a+b \log \left(c \sqrt{x}\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \sqrt{x}\right)\right)}{b}\right)}{c^4}","\frac{2^{-2 p-1} e^{-\frac{4 a}{b}} \left(a+b \log \left(c \sqrt{x}\right)\right)^p \left(-\frac{a+b \log \left(c \sqrt{x}\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \sqrt{x}\right)\right)}{b}\right)}{c^4}",1,"(2^(-1 - 2*p)*Gamma[1 + p, (-4*(a + b*Log[c*Sqrt[x]]))/b]*(a + b*Log[c*Sqrt[x]])^p)/(c^4*E^((4*a)/b)*(-((a + b*Log[c*Sqrt[x]])/b))^p)","A",1
186,1,73,73,0.0314703,"\int \left(a+b \log \left(c \sqrt{x}\right)\right)^p \, dx","Integrate[(a + b*Log[c*Sqrt[x]])^p,x]","\frac{2^{-p} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \sqrt{x}\right)\right)^p \left(-\frac{a+b \log \left(c \sqrt{x}\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \sqrt{x}\right)\right)}{b}\right)}{c^2}","\frac{2^{-p} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \sqrt{x}\right)\right)^p \left(-\frac{a+b \log \left(c \sqrt{x}\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \sqrt{x}\right)\right)}{b}\right)}{c^2}",1,"(Gamma[1 + p, (-2*(a + b*Log[c*Sqrt[x]]))/b]*(a + b*Log[c*Sqrt[x]])^p)/(2^p*c^2*E^((2*a)/b)*(-((a + b*Log[c*Sqrt[x]])/b))^p)","A",1
187,1,26,26,0.0099866,"\int \frac{\left(a+b \log \left(c \sqrt{x}\right)\right)^p}{x} \, dx","Integrate[(a + b*Log[c*Sqrt[x]])^p/x,x]","\frac{2 \left(a+b \log \left(c \sqrt{x}\right)\right)^{p+1}}{b (p+1)}","\frac{2 \left(a+b \log \left(c \sqrt{x}\right)\right)^{p+1}}{b (p+1)}",1,"(2*(a + b*Log[c*Sqrt[x]])^(1 + p))/(b*(1 + p))","A",1
188,1,73,73,0.0558903,"\int \frac{\left(a+b \log \left(c \sqrt{x}\right)\right)^p}{x^2} \, dx","Integrate[(a + b*Log[c*Sqrt[x]])^p/x^2,x]","c^2 \left(-2^{-p}\right) e^{\frac{2 a}{b}} \left(a+b \log \left(c \sqrt{x}\right)\right)^p \left(\frac{a+b \log \left(c \sqrt{x}\right)}{b}\right)^{-p} \Gamma \left(p+1,\frac{2 \left(a+b \log \left(c \sqrt{x}\right)\right)}{b}\right)","c^2 \left(-2^{-p}\right) e^{\frac{2 a}{b}} \left(a+b \log \left(c \sqrt{x}\right)\right)^p \left(\frac{a+b \log \left(c \sqrt{x}\right)}{b}\right)^{-p} \Gamma \left(p+1,\frac{2 \left(a+b \log \left(c \sqrt{x}\right)\right)}{b}\right)",1,"-((c^2*E^((2*a)/b)*Gamma[1 + p, (2*(a + b*Log[c*Sqrt[x]]))/b]*(a + b*Log[c*Sqrt[x]])^p)/(2^p*((a + b*Log[c*Sqrt[x]])/b)^p))","A",1
189,1,75,75,0.0512259,"\int \frac{\left(a+b \log \left(c \sqrt{x}\right)\right)^p}{x^3} \, dx","Integrate[(a + b*Log[c*Sqrt[x]])^p/x^3,x]","c^4 \left(-2^{-2 p-1}\right) e^{\frac{4 a}{b}} \left(a+b \log \left(c \sqrt{x}\right)\right)^p \left(\frac{a+b \log \left(c \sqrt{x}\right)}{b}\right)^{-p} \Gamma \left(p+1,\frac{4 \left(a+b \log \left(c \sqrt{x}\right)\right)}{b}\right)","c^4 \left(-2^{-2 p-1}\right) e^{\frac{4 a}{b}} \left(a+b \log \left(c \sqrt{x}\right)\right)^p \left(\frac{a+b \log \left(c \sqrt{x}\right)}{b}\right)^{-p} \Gamma \left(p+1,\frac{4 \left(a+b \log \left(c \sqrt{x}\right)\right)}{b}\right)",1,"-((2^(-1 - 2*p)*c^4*E^((4*a)/b)*Gamma[1 + p, (4*(a + b*Log[c*Sqrt[x]]))/b]*(a + b*Log[c*Sqrt[x]])^p)/((a + b*Log[c*Sqrt[x]])/b)^p)","A",1
190,1,80,80,0.0497727,"\int \frac{\left(a+b \log \left(c \sqrt{x}\right)\right)^p}{x^4} \, dx","Integrate[(a + b*Log[c*Sqrt[x]])^p/x^4,x]","c^6 \left(-2^{-p}\right) 3^{-p-1} e^{\frac{6 a}{b}} \left(a+b \log \left(c \sqrt{x}\right)\right)^p \left(\frac{a+b \log \left(c \sqrt{x}\right)}{b}\right)^{-p} \Gamma \left(p+1,\frac{6 \left(a+b \log \left(c \sqrt{x}\right)\right)}{b}\right)","c^6 \left(-2^{-p}\right) 3^{-p-1} e^{\frac{6 a}{b}} \left(a+b \log \left(c \sqrt{x}\right)\right)^p \left(\frac{a+b \log \left(c \sqrt{x}\right)}{b}\right)^{-p} \Gamma \left(p+1,\frac{6 \left(a+b \log \left(c \sqrt{x}\right)\right)}{b}\right)",1,"-((3^(-1 - p)*c^6*E^((6*a)/b)*Gamma[1 + p, (6*(a + b*Log[c*Sqrt[x]]))/b]*(a + b*Log[c*Sqrt[x]])^p)/(2^p*((a + b*Log[c*Sqrt[x]])/b)^p))","A",1
191,1,65,65,0.0516066,"\int x^{-1+n} \left(a+b \log \left(c x^n\right)\right)^p \, dx","Integrate[x^(-1 + n)*(a + b*Log[c*x^n])^p,x]","\frac{e^{-\frac{a}{b}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c x^n\right)}{b}\right)}{c n}","\frac{e^{-\frac{a}{b}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c x^n\right)}{b}\right)}{c n}",1,"(Gamma[1 + p, -((a + b*Log[c*x^n])/b)]*(a + b*Log[c*x^n])^p)/(c*E^(a/b)*n*(-((a + b*Log[c*x^n])/b))^p)","A",1
192,1,118,114,0.2339113,"\int \left(d x^q\right)^m \left(a+b \log \left(c x^n\right)\right)^p \, dx","Integrate[(d*x^q)^m*(a + b*Log[c*x^n])^p,x]","\frac{x^{-m q} \left(d x^q\right)^m \left(a+b \log \left(c x^n\right)\right)^p \exp \left(-\frac{(m q+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \left(-\frac{(m q+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m q+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m q+1}","\frac{x \left(d x^q\right)^m e^{-\frac{a m q+a}{b n}} \left(c x^n\right)^{-\frac{m q+1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m q+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m q+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{m q+1}",1,"((d*x^q)^m*Gamma[1 + p, -(((1 + m*q)*(a + b*Log[c*x^n]))/(b*n))]*(a + b*Log[c*x^n])^p)/(E^(((1 + m*q)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*(1 + m*q)*x^(m*q)*(-(((1 + m*q)*(a + b*Log[c*x^n]))/(b*n)))^p)","A",1
193,1,142,136,0.2437583,"\int \left(\text{d1} x^{\text{q1}}\right)^{\text{m1}} \left(\text{d2} x^{\text{q2}}\right)^{\text{m2}} \left(a+b \log \left(c x^n\right)\right)^p \, dx","Integrate[(d1*x^q1)^m1*(d2*x^q2)^m2*(a + b*Log[c*x^n])^p,x]","\frac{\left(\text{d1} x^{\text{q1}}\right)^{\text{m1}} \left(\text{d2} x^{\text{q2}}\right)^{\text{m2}} x^{-\text{m1} \text{q1}-\text{m2} \text{q2}} \left(a+b \log \left(c x^n\right)\right)^p \exp \left(-\frac{(\text{m1} \text{q1}+\text{m2} \text{q2}+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \left(-\frac{(\text{m1} \text{q1}+\text{m2} \text{q2}+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(\text{m1} \text{q1}+\text{m2} \text{q2}+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{\text{m1} \text{q1}+\text{m2} \text{q2}+1}","\frac{x \left(\text{d1} x^{\text{q1}}\right)^{\text{m1}} \left(\text{d2} x^{\text{q2}}\right)^{\text{m2}} \left(a+b \log \left(c x^n\right)\right)^p e^{-\frac{a (\text{m1} \text{q1}+\text{m2} \text{q2}+1)}{b n}} \left(c x^n\right)^{-\frac{\text{m1} \text{q1}+\text{m2} \text{q2}+1}{n}} \left(-\frac{(\text{m1} \text{q1}+\text{m2} \text{q2}+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(\text{m1} \text{q1}+\text{m2} \text{q2}+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{\text{m1} \text{q1}+\text{m2} \text{q2}+1}",1,"(x^(-(m1*q1) - m2*q2)*(d1*x^q1)^m1*(d2*x^q2)^m2*Gamma[1 + p, -(((1 + m1*q1 + m2*q2)*(a + b*Log[c*x^n]))/(b*n))]*(a + b*Log[c*x^n])^p)/(E^(((1 + m1*q1 + m2*q2)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*(1 + m1*q1 + m2*q2)*(-(((1 + m1*q1 + m2*q2)*(a + b*Log[c*x^n]))/(b*n)))^p)","A",1